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nguyentu1602/statsmodels | statsmodels/graphics/factorplots.py | 28 | 7596 | # -*- coding: utf-8 -*-
"""
Authors: Josef Perktold, Skipper Seabold, Denis A. Engemann
"""
from statsmodels.compat.python import get_function_name, iterkeys, lrange, zip, iteritems
import numpy as np
from statsmodels.graphics.plottools import rainbow
import statsmodels.graphics.utils as utils
def interaction_plot(x, trace, response, func=np.mean, ax=None, plottype='b',
xlabel=None, ylabel=None, colors=[], markers=[],
linestyles=[], legendloc='best', legendtitle=None,
**kwargs):
"""
Interaction plot for factor level statistics.
Note. If categorial factors are supplied levels will be internally
recoded to integers. This ensures matplotlib compatiblity.
uses pandas.DataFrame to calculate an `aggregate` statistic for each
level of the factor or group given by `trace`.
Parameters
----------
x : array-like
The `x` factor levels constitute the x-axis. If a `pandas.Series` is
given its name will be used in `xlabel` if `xlabel` is None.
trace : array-like
The `trace` factor levels will be drawn as lines in the plot.
If `trace` is a `pandas.Series` its name will be used as the
`legendtitle` if `legendtitle` is None.
response : array-like
The reponse or dependent variable. If a `pandas.Series` is given
its name will be used in `ylabel` if `ylabel` is None.
func : function
Anything accepted by `pandas.DataFrame.aggregate`. This is applied to
the response variable grouped by the trace levels.
plottype : str {'line', 'scatter', 'both'}, optional
The type of plot to return. Can be 'l', 's', or 'b'
ax : axes, optional
Matplotlib axes instance
xlabel : str, optional
Label to use for `x`. Default is 'X'. If `x` is a `pandas.Series` it
will use the series names.
ylabel : str, optional
Label to use for `response`. Default is 'func of response'. If
`response` is a `pandas.Series` it will use the series names.
colors : list, optional
If given, must have length == number of levels in trace.
linestyles : list, optional
If given, must have length == number of levels in trace.
markers : list, optional
If given, must have length == number of lovels in trace
kwargs
These will be passed to the plot command used either plot or scatter.
If you want to control the overall plotting options, use kwargs.
Returns
-------
fig : Figure
The figure given by `ax.figure` or a new instance.
Examples
--------
>>> import numpy as np
>>> np.random.seed(12345)
>>> weight = np.random.randint(1,4,size=60)
>>> duration = np.random.randint(1,3,size=60)
>>> days = np.log(np.random.randint(1,30, size=60))
>>> fig = interaction_plot(weight, duration, days,
... colors=['red','blue'], markers=['D','^'], ms=10)
>>> import matplotlib.pyplot as plt
>>> plt.show()
.. plot::
import numpy as np
from statsmodels.graphics.factorplots import interaction_plot
np.random.seed(12345)
weight = np.random.randint(1,4,size=60)
duration = np.random.randint(1,3,size=60)
days = np.log(np.random.randint(1,30, size=60))
fig = interaction_plot(weight, duration, days,
colors=['red','blue'], markers=['D','^'], ms=10)
import matplotlib.pyplot as plt
#plt.show()
"""
from pandas import DataFrame
fig, ax = utils.create_mpl_ax(ax)
response_name = ylabel or getattr(response, 'name', 'response')
ylabel = '%s of %s' % (get_function_name(func), response_name)
xlabel = xlabel or getattr(x, 'name', 'X')
legendtitle = legendtitle or getattr(trace, 'name', 'Trace')
ax.set_ylabel(ylabel)
ax.set_xlabel(xlabel)
x_values = x_levels = None
if isinstance(x[0], str):
x_levels = [l for l in np.unique(x)]
x_values = lrange(len(x_levels))
x = _recode(x, dict(zip(x_levels, x_values)))
data = DataFrame(dict(x=x, trace=trace, response=response))
plot_data = data.groupby(['trace', 'x']).aggregate(func).reset_index()
# return data
# check plot args
n_trace = len(plot_data['trace'].unique())
if linestyles:
try:
assert len(linestyles) == n_trace
except AssertionError as err:
raise ValueError("Must be a linestyle for each trace level")
else: # set a default
linestyles = ['-'] * n_trace
if markers:
try:
assert len(markers) == n_trace
except AssertionError as err:
raise ValueError("Must be a linestyle for each trace level")
else: # set a default
markers = ['.'] * n_trace
if colors:
try:
assert len(colors) == n_trace
except AssertionError as err:
raise ValueError("Must be a linestyle for each trace level")
else: # set a default
#TODO: how to get n_trace different colors?
colors = rainbow(n_trace)
if plottype == 'both' or plottype == 'b':
for i, (values, group) in enumerate(plot_data.groupby(['trace'])):
# trace label
label = str(group['trace'].values[0])
ax.plot(group['x'], group['response'], color=colors[i],
marker=markers[i], label=label,
linestyle=linestyles[i], **kwargs)
elif plottype == 'line' or plottype == 'l':
for i, (values, group) in enumerate(plot_data.groupby(['trace'])):
# trace label
label = str(group['trace'].values[0])
ax.plot(group['x'], group['response'], color=colors[i],
label=label, linestyle=linestyles[i], **kwargs)
elif plottype == 'scatter' or plottype == 's':
for i, (values, group) in enumerate(plot_data.groupby(['trace'])):
# trace label
label = str(group['trace'].values[0])
ax.scatter(group['x'], group['response'], color=colors[i],
label=label, marker=markers[i], **kwargs)
else:
raise ValueError("Plot type %s not understood" % plottype)
ax.legend(loc=legendloc, title=legendtitle)
ax.margins(.1)
if all([x_levels, x_values]):
ax.set_xticks(x_values)
ax.set_xticklabels(x_levels)
return fig
def _recode(x, levels):
""" Recode categorial data to int factor.
Parameters
----------
x : array-like
array like object supporting with numpy array methods of categorially
coded data.
levels : dict
mapping of labels to integer-codings
Returns
-------
out : instance numpy.ndarray
"""
from pandas import Series
name = None
if isinstance(x, Series):
name = x.name
x = x.values
if x.dtype.type not in [np.str_, np.object_]:
raise ValueError('This is not a categorial factor.'
' Array of str type required.')
elif not isinstance(levels, dict):
raise ValueError('This is not a valid value for levels.'
' Dict required.')
elif not (np.unique(x) == np.unique(list(iterkeys(levels)))).all():
raise ValueError('The levels do not match the array values.')
else:
out = np.empty(x.shape[0], dtype=np.int)
for level, coding in iteritems(levels):
out[x == level] = coding
if name:
out = Series(out)
out.name = name
return out
| bsd-3-clause |
jm-begon/scikit-learn | sklearn/__init__.py | 154 | 3014 | """
Machine learning module for Python
==================================
sklearn is a Python module integrating classical machine
learning algorithms in the tightly-knit world of scientific Python
packages (numpy, scipy, matplotlib).
It aims to provide simple and efficient solutions to learning problems
that are accessible to everybody and reusable in various contexts:
machine-learning as a versatile tool for science and engineering.
See http://scikit-learn.org for complete documentation.
"""
import sys
import re
import warnings
# Make sure that DeprecationWarning within this package always gets printed
warnings.filterwarnings('always', category=DeprecationWarning,
module='^{0}\.'.format(re.escape(__name__)))
# PEP0440 compatible formatted version, see:
# https://www.python.org/dev/peps/pep-0440/
#
# Generic release markers:
# X.Y
# X.Y.Z # For bugfix releases
#
# Admissible pre-release markers:
# X.YaN # Alpha release
# X.YbN # Beta release
# X.YrcN # Release Candidate
# X.Y # Final release
#
# Dev branch marker is: 'X.Y.dev' or 'X.Y.devN' where N is an integer.
# 'X.Y.dev0' is the canonical version of 'X.Y.dev'
#
__version__ = '0.17.dev0'
try:
# This variable is injected in the __builtins__ by the build
# process. It used to enable importing subpackages of sklearn when
# the binaries are not built
__SKLEARN_SETUP__
except NameError:
__SKLEARN_SETUP__ = False
if __SKLEARN_SETUP__:
sys.stderr.write('Partial import of sklearn during the build process.\n')
# We are not importing the rest of the scikit during the build
# process, as it may not be compiled yet
else:
from . import __check_build
from .base import clone
__check_build # avoid flakes unused variable error
__all__ = ['calibration', 'cluster', 'covariance', 'cross_decomposition',
'cross_validation', 'datasets', 'decomposition', 'dummy',
'ensemble', 'externals', 'feature_extraction',
'feature_selection', 'gaussian_process', 'grid_search',
'isotonic', 'kernel_approximation', 'kernel_ridge',
'lda', 'learning_curve',
'linear_model', 'manifold', 'metrics', 'mixture', 'multiclass',
'naive_bayes', 'neighbors', 'neural_network', 'pipeline',
'preprocessing', 'qda', 'random_projection', 'semi_supervised',
'svm', 'tree',
# Non-modules:
'clone']
def setup_module(module):
"""Fixture for the tests to assure globally controllable seeding of RNGs"""
import os
import numpy as np
import random
# It could have been provided in the environment
_random_seed = os.environ.get('SKLEARN_SEED', None)
if _random_seed is None:
_random_seed = np.random.uniform() * (2 ** 31 - 1)
_random_seed = int(_random_seed)
print("I: Seeding RNGs with %r" % _random_seed)
np.random.seed(_random_seed)
random.seed(_random_seed)
| bsd-3-clause |
reuk/wayverb | scripts/python/dispersion.py | 2 | 6340 | from math import e, pi
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import colors, ticker, cm
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import operator
def get_base_vectors(flip):
ret = [
np.array([0.0, 2.0 * np.sqrt(2.0) / 3.0, 1.0 / 3.0]),
np.array([ np.sqrt(2.0 / 3.0), -np.sqrt(2.0) / 3.0, 1.0 / 3.0]),
np.array([0.0, 0.0, -1.0]),
np.array([-np.sqrt(2.0 / 3.0), -np.sqrt(2.0) / 3.0, 1.0 / 3.0]),
]
if flip:
ret = [np.array([1, -1, -1]) * i for i in ret]
return ret
def get_vectors():
ret = [i + j for i in get_base_vectors(False) for j in get_base_vectors(True)]
ret = filter(lambda x: np.any(x != np.array([0, 0, 0])), ret)
return ret
# DUYNE METHOD
def get_speed(arr):
"""
The diagrams in the paper appear to be continuous outside of the range
-1.5, 1.5.
However, this function has a strange discontinuity at a radius of 1.4
"""
def get_b(arr):
summed = sum([pow(e, 1j * np.dot(arr, i)) for i in get_vectors()])
return 1.0 - 0.25 * summed.real
def get_ang_g(arr):
b = get_b(arr)
return 0.5 * np.arctan(np.sqrt(4 - b * b) / abs(b))
c = np.sqrt(1.0 / 3.0)
norm = np.linalg.norm(arr)
# this analysis is only valid for frequencies below pi / 2
# (spectrum is mirrored above this limit)
# simulated frequency is equal to magnitude of wave vector (arr)
if norm < pi / 2:
return get_ang_g(arr) / (norm * c)
else:
return None
# CAMPOS METHOD
def get_speed_campos(arr):
def get_b(arr):
x, y, z = arr
a = np.cos(2.0 * x / np.sqrt(3.0)) * np.cos(2.0 * y / np.sqrt(3.0))
b = np.cos(2.0 * x / np.sqrt(3.0)) * np.cos(2.0 * z / np.sqrt(3.0))
c = np.cos(2.0 * y / np.sqrt(3.0)) * np.cos(2.0 * z / np.sqrt(3.0))
return a + b + c - 1
def get_kd(arr):
return np.sqrt(3.0) * np.arccos(get_b(arr) / 2.0) / (2.0 * np.linalg.norm(arr))
return get_kd(arr)
# direction error analysis from @hacihabiboglu
# p(x) = pressure field in spatial(?) domain
# P(w) = pressure field in frequency domain
def get_U():
v = get_base_vectors(True)
U = np.vstack(v)
return U
def eq_21(u, w):
return pow(e, -1j * np.dot(u, w)) - 1
def eq_22(w):
return np.array([eq_21(i, w) for i in get_base_vectors(True)])
def eq_23(w):
return np.dot(np.linalg.pinv(get_U()), eq_22(w))
def hermitian_angle(a, b):
prod = np.dot(a, np.conj(b)).real
mag_a = np.sqrt(np.dot(a, np.conj(a)))
mag_b = np.sqrt(np.dot(b, np.conj(b)))
return (prod / (mag_a * mag_b)).real
def direction_difference(arr):
def get_term_1():
return eq_23(arr)
def get_term_2():
return 1j * arr
return hermitian_angle(get_term_1(), get_term_2())
# monte carlo bandwidth estimation
def random_three_vector():
phi = np.random.uniform(0, pi * 2)
costheta = np.random.uniform(-1, 1)
theta = np.arccos(costheta)
x = np.sin(theta) * np.cos(phi)
y = np.sin(theta) * np.sin(phi)
z = np.cos(theta)
return np.array([x, y, z])
def get_max_valid_frequency(func, accuracy, starting_freq, increments, samples):
last = starting_freq + increments
ret = starting_freq
while True:
sample_points = [random_three_vector() * last for i in range(samples)]
sampled = [func(i) for i in sample_points]
if not all(map(lambda x: x > accuracy, sampled)):
return ret
else:
ret = last
last += increments
def main():
"""
This program duplicates the tetrahedral dispersion diagrams from the paper
'The Tetrahedral Digital Waveguide Mesh' buy Duyne and Smith.
I wrote it to try to understand how to do dispersion analysis - the
analysis here is of the difference of the actual wavefront speed to the
ideal speed.
"""
w = np.array([0, 1, 0])
w /= np.linalg.norm(w)
print "w", w
for i in get_base_vectors(True):
print "u", i
print "21", eq_21(i, w)
print "22", eq_22(w)
print "23", eq_23(w)
print
print direction_difference(w)
func = direction_difference
vfunc = np.vectorize(lambda x, y, z: func(np.array([x, y, z])))
max_val = np.pi / 4
phi, theta = np.mgrid[0:pi:50j, 0:2*pi:50j]
XX = max_val * np.sin(phi) * np.cos(theta)
YY = max_val * np.sin(phi) * np.sin(theta)
ZZ = max_val * np.cos(phi)
zz = vfunc(XX, YY, ZZ)
zzmin, zzmax = zz.min(), zz.max()
print "dispersion error range:", zzmin, "to", zzmax
zz = (zz - zzmin) / (zzmax - zzmin)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(
XX, YY, ZZ, rstride=1, cstride=1, facecolors=cm.jet(zz))
plt.show()
# func = get_speed_campos
# vfunc = np.vectorize(lambda x, y, z: func(np.array([x, y, z])))
#
# min_accuracy = 0.99
# max_val = get_max_valid_frequency(func, min_accuracy, 0.1, 0.001, 20)
# print "maximum radius (frequency): ", max_val / (pi / 2)
# phi, theta = np.mgrid[0:pi:50j, 0:2*pi:50j]
# XX = max_val * np.sin(phi) * np.cos(theta)
# YY = max_val * np.sin(phi) * np.sin(theta)
# ZZ = max_val * np.cos(phi)
# zz = vfunc(XX, YY, ZZ)
# zzmin, zzmax = zz.min(), zz.max()
# print "dispersion error range:", zzmin, "to", zzmax
# zz = (zz - zzmin) / (zzmax - zzmin)
#
# fig = plt.figure()
#
# bounds = pi / 2
# N = 100
# x = np.linspace(-bounds, bounds, N)
# y = np.linspace(-bounds, bounds, N)
# X, Y = np.meshgrid(x, y)
# Z = np.zeros(X.shape)
# depth = np.linspace(0.9, 1, 11)
#
# ### plot 1
# ax = fig.add_subplot(221 + 0)
# z = vfunc(Z, X, Y)
# plt.contourf(X, Y, z, depth)
# cbar = plt.colorbar()
#
# ### plot 2
# ax = fig.add_subplot(221 + 1)
# z = vfunc(X, Z, Y)
# plt.contourf(X, Y, z, depth)
# cbar = plt.colorbar()
#
# ### plot 3
# ax = fig.add_subplot(221 + 2)
# z = vfunc(X, Y, Z)
# plt.contourf(X, Y, z, depth)
# cbar = plt.colorbar()
#
# ax = fig.add_subplot(224, projection='3d')
# ax.plot_surface(
# XX, YY, ZZ, rstride=1, cstride=1, facecolors=cm.jet(zz))
#
# plt.show()
if __name__ == "__main__":
main()
| gpl-2.0 |
mompiou/misorientation | misorientation.py | 1 | 48149 | #!/usr/bin/python
from __future__ import division
import numpy as np
from Tkinter import *
from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg, NavigationToolbar2TkAgg
from matplotlib.figure import Figure
from matplotlib import pyplot as plt
from PIL import Image
from PIL import PngImagePlugin
import ttk
import sys
from fractions import Fraction
from tkFileDialog import *
import os
import matplotlib as mpl
mpl.rcParams['font.size'] = 12
###################################################################"
##### Fonction projection sur l'abaque
####################################################################
def proj(x,y,z):
if z==1:
X=0
Y=0
elif z<-0.000001:
X=250
Y=250
else:
X=x/(1+z)
Y=y/(1+z)
return np.array([X,Y],float)
###################################################################"
##### Fonction rotation
####################################################################
def rotation(phi1,phi,phi2):
phi1=phi1*np.pi/180;
phi=phi*np.pi/180;
phi2=phi2*np.pi/180;
R=np.array([[np.cos(phi1)*np.cos(phi2)-np.cos(phi)*np.sin(phi1)*np.sin(phi2),
-np.cos(phi)*np.cos(phi2)*np.sin(phi1)-np.cos(phi1)*
np.sin(phi2),np.sin(phi)*np.sin(phi1)],[np.cos(phi2)*np.sin(phi1)
+np.cos(phi)*np.cos(phi1)*np.sin(phi2),np.cos(phi)*np.cos(phi1)
*np.cos(phi2)-np.sin(phi1)*np.sin(phi2), -np.cos(phi1)*np.sin(phi)],
[np.sin(phi)*np.sin(phi2), np.cos(phi2)*np.sin(phi), np.cos(phi)]],float)
return R
####################################################################
##### Fonction rotation autour d'un axe
####################################################################
def Rot(th,a,b,c):
th=th*np.pi/180;
aa=a/np.linalg.norm([a,b,c]);
bb=b/np.linalg.norm([a,b,c]);
cc=c/np.linalg.norm([a,b,c]);
c1=np.array([[1,0,0],[0,1,0],[0,0,1]],float)
c2=np.array([[aa**2,aa*bb,aa*cc],[bb*aa,bb**2,bb*cc],[cc*aa,
cc*bb,cc**2]],float)
c3=np.array([[0,-cc,bb],[cc,0,-aa],[-bb,aa,0]],float)
R=np.cos(th)*c1+(1-np.cos(th))*c2+np.sin(th)*c3
return R
####################################################################
##### Fonction cristal
####################################################################
def crist():
global axesA,axeshA,axesB,axeshB,D,Dstar,V
a=eval(a_entry.get())
b=eval(b_entry.get())
c=eval(c_entry.get())
alp=eval(alp_entry.get())
bet=eval(bet_entry.get())
gam=eval(gam_entry.get())
e=eval(e_entry.get())
d2=eval(d_label_var.get())
alp=alp*np.pi/180;
bet=bet*np.pi/180;
gam=gam*np.pi/180;
V=a*b*c*np.sqrt(1-(np.cos(alp)**2)-(np.cos(bet))**2-(np.cos(gam))**2+2*b*c*np.cos(alp)*np.cos(bet)*np.cos(gam))
D=np.array([[a,b*np.cos(gam),c*np.cos(bet)],[0,b*np.sin(gam), c*(np.cos(alp)-np.cos(bet)*np.cos(gam))/np.sin(gam)],[0,0,V/(a*b*np.sin(gam))]])
Dstar=np.transpose(np.linalg.inv(D))
G=np.array([[a**2,a*b*np.cos(gam),a*c*np.cos(bet)],[a*b*np.cos(gam),b**2,b*c*np.cos(alp)],[a*c*np.cos(bet),b*c*np.cos(alp),c**2]])
axes=np.zeros(((2*e+1)**3-1,3))
axesh=np.zeros(((2*e+1)**3-1,3))
id=0
for i in range(-e,e+1):
for j in range(-e,e+1):
for k in range(-e,e+1):
if (i,j,k)!=(0,0,0):
d=1/(np.sqrt(np.dot(np.array([i,j,k]),np.dot(np.linalg.inv(G),np.array([i,j,k])))))
if d>d2*0.1*np.amax([a,b,c]):
if var_uvw.get()==0:
axesh[id,:]=np.dot(Dstar,np.array([i,j,k],float))
axes[id,:]=np.array([i,j,k],float)
else:
axesh[id,:]=np.dot(D,np.array([i,j,k],float))
axes[id,:]=np.array([i,j,k],float)
id=id+1
axesA=axes
axesB=axes
axeshA=axesh
axeshB=axesh
return axesA,axeshA,axesB,axeshB,D,Dstar,V
def dm():
global dmip
a=f.add_subplot(111)
a.figure.clear()
a=f.add_subplot(111)
dmip=dmip-eval(d_entry.get())
d_label_var.set(dmip)
crist()
trace()
return dmip
def dp():
global dmip
a=f.add_subplot(111)
a.figure.clear()
a=f.add_subplot(111)
dmip=dmip+eval(d_entry.get())
d_label_var.set(dmip)
crist()
trace()
return dmip
####################################################################
##### Fonction ajouter un pole
####################################################################
def poleA(pole1,pole2,pole3):
global MA,axesA,axeshA,Ta,V,D,Dstar
fp=f.add_subplot(111)
Gs=np.array([pole1,pole2,pole3],float)
Pp=np.zeros((1,2),float)
if var_uvw.get()==0:
Gsh=np.dot(Dstar,Gs)/np.linalg.norm(np.dot(Dstar,Gs))
else:
Gsh=np.dot(D,Gs)/np.linalg.norm(np.dot(D,Gs))
S=np.dot(MA,Gsh)
if S[2]<0:
S=-S
Gsh=-Gsh
pole1=-pole1
pole2=-pole2
pole3=-pole3
Pp=proj(S[0],S[1],S[2])*600/2
l=str(int(pole1))+str(int(pole2))+str(int(pole3))
fp.plot(Pp[0]+600/2,Pp[1]+600/2,'ro')
fp.annotate(l,(Pp[0]+600/2,Pp[1]+600/2))
fp.axis([0,600,0,600])
fp.axis('off')
fp.figure.canvas.draw()
axesA=np.vstack((axesA,np.array([pole1,pole2,pole3])))
axesA=np.vstack((axesA,np.array([-pole1,-pole2,-pole3])))
Ta=np.vstack((Ta,np.array([S[0],S[1],S[2]])))
Ta=np.vstack((Ta,np.array([-S[0],-S[1],-S[2]])))
axeshA=np.vstack((axeshA,np.array([Gsh[0],Gsh[1],Gsh[2]])))
axeshA=np.vstack((axeshA,np.array([-Gsh[0],-Gsh[1],-Gsh[2]])))
return axesA,axeshA,Ta
def poleB(pole1,pole2,pole3):
global MB,axesB,axeshB,Tb,V,D,Dstar
fp=f.add_subplot(111)
Gs=np.array([pole1,pole2,pole3],float)
Pp=np.zeros((1,2),float)
if var_uvw.get()==0:
Gsh=np.dot(Dstar,Gs)/np.linalg.norm(np.dot(Dstar,Gs))
else:
Gsh=np.dot(D,Gs)/np.linalg.norm(np.dot(D,Gs))
S=np.dot(MB,Gsh)
if S[2]<0:
S=-S
Gsh=-Gsh
pole1=-pole1
pole2=-pole2
pole3=-pole3
Pp=proj(S[0],S[1],S[2])*600/2
l=str(int(pole1))+str(int(pole2))+str(int(pole3))
fp.plot(Pp[0]+600/2,Pp[1]+600/2,'ro')
fp.annotate(l,(Pp[0]+600/2,Pp[1]+600/2))
fp.axis([0,600,0,600])
fp.axis('off')
fp.figure.canvas.draw()
axesB=np.vstack((axesB,np.array([pole1,pole2,pole3])))
axesB=np.vstack((axesB,np.array([-pole1,-pole2,-pole3])))
Tb=np.vstack((Tb,np.array([S[0],S[1],S[2]])))
Tb=np.vstack((Tb,np.array([-S[0],-S[1],-S[2]])))
axeshB=np.vstack((axeshB,np.array([Gsh[0],Gsh[1],Gsh[2]])))
axeshB=np.vstack((axeshB,np.array([-Gsh[0],-Gsh[1],-Gsh[2]])))
return axesB,axeshB,Tb
def addpoleA_sym():
pole1A=eval(pole1A_entry.get())
pole2A=eval(pole2A_entry.get())
pole3A=eval(pole3A_entry.get())
poleA(pole1A,pole2A,pole3A)
poleA(pole1A,pole2A,-pole3A)
poleA(pole1A,-pole2A,pole3A)
poleA(-pole1A,pole2A,pole3A)
poleA(pole2A,pole1A,pole3A)
poleA(pole2A,pole1A,-pole3A)
poleA(pole2A,-pole1A,pole3A)
poleA(-pole2A,pole1A,pole3A)
poleA(pole2A,pole3A,pole1A)
poleA(pole2A,pole3A,-pole1A)
poleA(pole2A,-pole3A,pole1A)
poleA(-pole2A,pole3A,pole1A)
poleA(pole1A,pole3A,pole2A)
poleA(pole1A,pole3A,-pole2A)
poleA(pole1A,-pole3A,pole2A)
poleA(-pole1A,pole3A,pole2A)
poleA(pole3A,pole1A,pole2A)
poleA(pole3A,pole1A,-pole2A)
poleA(pole3A,-pole1A,pole2A)
poleA(-pole3A,pole1A,pole2A)
poleA(pole3A,pole2A,pole1A)
poleA(pole3A,pole2A,-pole1A)
poleA(pole3A,-pole2A,pole1A)
poleA(-pole3A,pole2A,pole1A)
trace()
def addpoleB_sym():
pole1B=eval(pole1B_entry.get())
pole2B=eval(pole2B_entry.get())
pole3B=eval(pole3B_entry.get())
poleB(pole1B,pole2B,pole3B)
poleB(pole1B,pole2B,-pole3B)
poleB(pole1B,-pole2B,pole3B)
poleB(-pole1B,pole2B,pole3B)
poleB(pole2B,pole1B,pole3B)
poleB(pole2B,pole1B,-pole3B)
poleB(pole2B,-pole1B,pole3B)
poleB(-pole2B,pole1B,pole3B)
poleB(pole2B,pole3B,pole1B)
poleB(pole2B,pole3B,-pole1B)
poleB(pole2B,-pole3B,pole1B)
poleB(-pole2B,pole3B,pole1B)
poleB(pole1B,pole3B,pole2B)
poleB(pole1B,pole3B,-pole2B)
poleB(pole1B,-pole3B,pole2B)
poleB(-pole1B,pole3B,pole2B)
poleB(pole3B,pole1B,pole2B)
poleB(pole3B,pole1B,-pole2B)
poleB(pole3B,-pole1B,pole2B)
poleB(-pole3B,pole1B,pole2B)
poleB(pole3B,pole2B,pole1B)
poleB(pole3B,pole2B,-pole1B)
poleB(pole3B,-pole2B,pole1B)
poleB(-pole3B,pole2B,pole1B)
trace()
def addpoleA():
pole1A=eval(pole1A_entry.get())
pole2A=eval(pole2A_entry.get())
pole3A=eval(pole3A_entry.get())
poleA(pole1A,pole2A,pole3A)
trace()
def addpoleB():
pole1B=eval(pole1B_entry.get())
pole2B=eval(pole2B_entry.get())
pole3B=eval(pole3B_entry.get())
poleB(pole1B,pole2B,pole3B)
trace()
####################################################################
##### Fonction tracer plan
####################################################################
def trace_planA():
global MA,axes,axesh,Ta,V,D,Dstar
f2=f.add_subplot(111)
pole1A=eval(pole1A_entry.get())
pole2A=eval(pole2A_entry.get())
pole3A=eval(pole3A_entry.get())
Gs=np.array([pole1A,pole2A,pole3A],float)
if var_uvw.get()==0:
Gsh=np.dot(Dstar,Gs)/np.linalg.norm(np.dot(Dstar,Gs))
else:
Gsh=np.dot(D,Gs)/np.linalg.norm(np.dot(D,Gs))
S=np.dot(MA,Gsh)
if S[2]<0:
S=-S
Gsh=-Gsh
pole1A=-pole1A
pole2A=-pole2A
pole3A=-pole3A
r=np.sqrt(S[0]**2+S[1]**2+S[2]**2)
A=np.zeros((2,100))
Q=np.zeros((1,2))
if S[2]==0:
t=90
w=0
else:
t=np.arctan2(S[1],S[0])*180/np.pi
w=0
ph=np.arccos(S[2]/r)*180/np.pi
for g in np.linspace(-np.pi,np.pi-0.00001,100):
Aa=np.dot(Rot(t,0,0,1),np.dot(Rot(ph,0,1,0),np.array([np.sin(g),np.cos(g),0])))
A[:,w]=proj(Aa[0],Aa[1],Aa[2])*600/2
if A[0,w]<>75000:
Q=np.vstack((Q,A[:,w]))
w=w+1
Q=np.delete(Q,0,0)
f2.plot(Q[:,0]+600/2,Q[:,1]+600/2,'r')
f2.axis([0,600,0,600])
f2.axis('off')
f2.figure.canvas.draw()
trace()
def trace_planB():
global MB,axes,axesh,Tb,V,D,Dstar
f2=f.add_subplot(111)
pole1B=eval(pole1B_entry.get())
pole2B=eval(pole2B_entry.get())
pole3B=eval(pole3B_entry.get())
Gs=np.array([pole1B,pole2B,pole3B],float)
if var_uvw.get()==0:
Gsh=np.dot(Dstar,Gs)/np.linalg.norm(np.dot(Dstar,Gs))
else:
Gsh=np.dot(D,Gs)/np.linalg.norm(np.dot(D,Gs))
S=np.dot(MB,Gsh)
if S[2]<0:
S=-S
Gsh=-Gsh
pole1B=-pole1B
pole2B=-pole2B
pole3B=-pole3B
r=np.sqrt(S[0]**2+S[1]**2+S[2]**2)
A=np.zeros((2,100))
Q=np.zeros((1,2))
if S[2]==0:
t=90
w=0
else:
t=np.arctan2(S[1],S[0])*180/np.pi
w=0
ph=np.arccos(S[2]/r)*180/np.pi
for g in np.linspace(-np.pi,np.pi-0.00001,100):
Aa=np.dot(Rot(t,0,0,1),np.dot(Rot(ph,0,1,0),np.array([np.sin(g),np.cos(g),0])))
A[:,w]=proj(Aa[0],Aa[1],Aa[2])*600/2
if A[0,w]<>75000:
Q=np.vstack((Q,A[:,w]))
w=w+1
Q=np.delete(Q,0,0)
f2.plot(Q[:,0]+600/2,Q[:,1]+600/2,'r')
f2.axis([0,600,0,600])
f2.axis('off')
f2.figure.canvas.draw()
trace()
####################################################################
##### Click a pole
####################################################################
def click_a_pole(event):
global MB,Dstar,D
x=event.x
y=event.y
x=(x-411)*2/620
y=-(y-400)*2/620
X=2*x/(1+x**2+y**2)
Y=2*y/(1+x**2+y**2)
Z=(-1+x**2+y**2)/(1+x**2+y**2)
if Z<0:
X=-X
Y=-Y
A=np.dot(np.linalg.inv(MB),np.array([X,Y,Z]))
n=0
L=np.zeros((3,16**3))
for i in range(-8,9,1):
for j in range(-8,9,1):
for k in range(-8,9,1):
if np.linalg.norm([i,j,k])<>0:
if var_uvw.get()==0:
Q=np.dot(Dstar,np.array([i,j,k],float))/np.linalg.norm(np.dot(Dstar,np.array([i,j,k],float)))
if np.abs(Q[0]-A[0])<0.05 and np.abs(Q[1]-A[1])<0.05 and np.abs(Q[2]-A[2])<0.05:
L[:,n]=np.array([i,j,k],float)
n=n+1
else:
Q=np.dot(D,np.array([i,j,k],float))/np.linalg.norm(np.dot(D,np.array([i,j,k],float)))
if np.abs(Q[0]-A[0])<0.05 and np.abs(Q[1]-A[1])<0.05 and np.abs(Q[2]-A[2])<0.05:
L[:,n]=np.array([i,j,k],float)
n=n+1
if np.linalg.norm(L[:,0])<>0:
poleB(L[0,0],L[1,0],L[2,0])
trace()
####################################################################
##### Inclinaison-beta
####################################################################
####################################################################
##### Fonction desorientation
####################################################################
def Rota(t,u,v,w,g):
Ae=np.dot(g,np.array([u,v,w]))
Re=Rot(t,Ae[0],Ae[1],Ae[2])
return Re
def cryststruct():
global cs
a=eval(a_entry.get())
b=eval(b_entry.get())
c=eval(c_entry.get())
alp=eval(alp_entry.get())
bet=eval(bet_entry.get())
gam=eval(gam_entry.get())
if gam==90 and alp==90 and bet==90 and a==b and b==c:
cs=1
if gam==120 and alp==90 and bet==90:
cs=2
if gam==90 and alp==90 and bet==90 and a==b and b<>c:
cs=3
if alp<>90 and a==b and b==c:
cs=4
if gam==90 and alp==90 and bet==90 and a<>b and b<>c:
cs=5
if gam<>90 and alp==90 and bet==90 and a<>b and b<>c:
cs=6
if gam<>90 and alp<>90 and bet<>90 and a<>b and b<>c:
cs=7
return cs
def Sy(g):
global cs
if cs==1:
S1=Rota(90,1,0,0,g);
S2=Rota(180,1,0,0,g);
S3=Rota(270,1,0,0,g);
S4=Rota(90,0,1,0,g);
S5=Rota(180,0,1,0,g);
S6=Rota(270,0,1,0,g);
S7=Rota(90,0,0,1,g);
S8=Rota(180,0,0,1,g);
S9=Rota(270,0,0,1,g);
S10=Rota(180,1,1,0,g);
S11=Rota(180,1,0,1,g);
S12=Rota(180,0,1,1,g);
S13=Rota(180,-1,1,0,g);
S14=Rota(180,-1,0,1,g);
S15=Rota(180,0,-1,1,g);
S16=Rota(120,1,1,1,g);
S17=Rota(240,1,1,1,g);
S18=Rota(120,-1,1,1,g);
S19=Rota(240,-1,1,1,g);
S20=Rota(120,1,-1,1,g);
S21=Rota(240,1,-1,1,g);
S22=Rota(120,1,1,-1,g);
S23=Rota(240,1,1,-1,g);
S24=np.eye(3,3);
S=np.vstack((S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,S13,S14,S15,S16,S17,S18,S19,S20,S21,S22,S23,S24))
if cs==2:
S1=Rota(60,0,0,1,g);
S2=Rota(120,0,0,1,g);
S3=Rota(180,0,0,1,g);
S4=Rota(240,0,0,1,g);
S5=Rota(300,0,0,1,g);
S6=np.eye(3,3);
S7=Rota(180,0,0,1,g);
S8=Rota(180,0,1,0,g);
S9=Rota(180,1/2,np.sqrt(3)/2,0,g);
S10=Rota(180,-1/2,np.sqrt(3)/2,0,g);
S11=Rota(180,np.sqrt(3)/2,1/2,0,g);
S12=Rota(180,-np.sqrt(3)/2,1/2,0,g);
S=np.vstack((S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12))
if cs==3:
S1=Rota(90,0,0,1,g);
S2=Rota(180,0,0,1,g);
S3=Rota(270,0,0,1,g);
S4=Rota(180,0,1,0,g);
S5=Rota(180,1,0,0,g);
S6=Rota(180,1,1,0,g);
S7=Rota(180,1,-1,0,g);
S8=np.eye(3,3)
S=np.vstack((S1,S2,S3,S4,S5,S6,S7,S8))
if cs==4:
S1=Rota(60,0,0,1,g);
S2=Rota(120,0,0,1,g);
S3=Rota(180,0,0,1,g);
S4=Rota(240,0,0,1,g);
S5=Rota(300,0,0,1,g);
S6=np.eye(3,3);
S7=Rota(180,0,0,1,g);
S8=Rota(180,0,1,0,g);
S9=Rota(180,1/2,np.sqrt(3)/2,0,g);
S10=Rota(180,-1/2,np.sqrt(3)/2,0,g);
S11=Rota(180,np.sqrt(3)/2,1/2,0,g);
S12=Rota(180,-np.sqrt(3)/2,1/2,0,g);
S=np.vstack((S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12))
if cs==5:
S1=Rota(180,0,0,1,g);
S2=Rota(180,1,0,0,g);
S3=Rota(180,0,1,0,g);
S4=np.eye(3,3);
S=np.vstack((S1,S2,S3,S4))
if cs==6:
S1=Rota(180,0,1,0,g);
S2=np.eye(3,3);
S=np.vstack((S1,S2))
if cs==7:
S=np.eye(3,3);
return S
def null(A, rcond=None):
u, s, vh = np.linalg.svd(A, full_matrices=True)
M, N = u.shape[0], vh.shape[1]
if rcond is None:
rcond = np.finfo(s.dtype).eps * max(M, N)
tol = np.amax(s) * rcond
num = np.sum(s > tol, dtype=int)
Q = vh[num:,:].T.conj()
return Q
def desorientation():
global D0,S,D1,cs,V,Qp
a = f.add_subplot(111)
a.figure.clear()
a = f.add_subplot(111)
fn = os.path.join(os.path.dirname(__file__), 'stereo.png')
img=np.array(Image.open(fn))
cryststruct()
phi1a=eval(phi1A_entry.get())
phia=eval(phiA_entry.get())
phi2a=eval(phi2A_entry.get())
phi1b=eval(phi1B_entry.get())
phib=eval(phiB_entry.get())
phi2b=eval(phi2B_entry.get())
gA=rotation(phi1a,phia,phi2a)
gB=rotation(phi1b,phib,phi2b)
k=0
S=Sy(gA)
D0=np.zeros((int(np.shape(S)[0]/3),5))
D1=np.zeros((int(np.shape(S)[0]/3),3))
Qp=np.zeros((int(np.shape(S)[0]/3),2))
for i in range(0,np.shape(S)[0],3):
In=np.dot(np.array([[S[i,0],S[i+1,0],S[i+2,0]],[S[i,1],S[i+1,1],S[i+2,1]],[S[i,2],S[i+1,2],S[i+2,2]]]),gA)
Ing=np.dot(In,np.array([0,0,1]))
In2=np.dot(Rot(-phi2b,Ing[0],Ing[1],Ing[2]),In)
Ing2=np.dot(In2,np.array([1,0,0]))
In3=np.dot(Rot(-phib,Ing2[0],Ing2[1],Ing2[2]),In2)
Ing3=np.dot(In3,np.array([0,0,1]))
A=np.dot(Rot(-phi1b,Ing3[0],Ing3[1],Ing3[2]),In3)-np.eye(3)
V=null(A,0.001).T
if 0.5*(np.trace(A+np.eye(3))-1)>1:
D0[k,3]=0
elif 0.5*(np.trace(A+np.eye(3))-1)<-1:
D0[k,3]=180
else:
D0[k,3]=np.arccos(0.5*(np.trace(A+np.eye(3))-1))*180/np.pi
if np.abs(D0[k,3])<1e-5:
D0[k,0]=0
D0[k,1]=0
D0[k,2]=0
else:
D0[k,0]=V[0,0]/np.linalg.norm(V)
D0[k,1]=V[0,1]/np.linalg.norm(V)
D0[k,2]=V[0,2]/np.linalg.norm(V)
Ds1=np.dot(np.linalg.inv(gB),np.array([D0[k,0],D0[k,1],D0[k,2]]))
F0=Fraction(Ds1[0]).limit_denominator(10)
F1=Fraction(Ds1[1]).limit_denominator(10)
F2=Fraction(Ds1[2]).limit_denominator(10)
D1[k,0]=F0.numerator*F1.denominator*F2.denominator
D1[k,1]=F1.numerator*F0.denominator*F2.denominator
D1[k,2]=F2.numerator*F0.denominator*F1.denominator
if D0[k,2]<0:
D0[k,0]=-D0[k,0]
D0[k,1]=-D0[k,1]
D0[k,2]=-D0[k,2]
D1[k,0]=-D1[k,0]
D1[k,1]=-D1[k,1]
D1[k,2]=-D1[k,2]
D0[k,4]=k
Qp[k,:]=proj(D0[k,0],D0[k,1],D0[k,2])*600/2
k=k+1
a.plot(Qp[:,0]+600/2,Qp[:,1]+600/2,'ro')
a.axis([0,600,0,600])
a.imshow(img,interpolation="bicubic")
a.axis('off')
a.figure.canvas.draw()
trace()
return Qp,S,D1
####################################################################
##### Fonction principale
####################################################################
def trace():
global Ta,Tb,axesA,axeshA,MA,axesB,axeshB,MB,Qp,S,D1,show_ind,D0
a = f.add_subplot(111)
fn = os.path.join(os.path.dirname(__file__), 'stereo.png')
img=np.array(Image.open(fn))
Pa=np.zeros((np.shape(axesA)[0],2))
Pb=np.zeros((np.shape(axesB)[0],2))
for i in range(0,np.shape(axesA)[0]):
axeshA[i,:]=axeshA[i,:]/np.linalg.norm(axeshA[i,:])
Ta[i,:]=np.dot(MA,axeshA[i,:])
Pa[i,:]=proj(Ta[i,0],Ta[i,1],Ta[i,2])*600/2
if show_ind.get()==1:
m=np.amax([np.abs(axesA[i,0]),np.abs(axesA[i,1]),np.abs(axesA[i,2])])
if (np.around(axesA[i,0]/m)==axesA[i,0]/m) & (np.around(axesA[i,1]/m)==axesA[i,1]/m) & (np.around(axesA[i,2]/m)==axesA[i,2]/m):
sA=str(int(axesA[i,0]/m))+str(int(axesA[i,1]/m))+str(int(axesA[i,2]/m))
else:
sA=str(int(axesA[i,0]))+str(int(axesA[i,1]))+str(int(axesA[i,2]))
a.annotate(sA,(Pa[i,0]+600/2,Pa[i,1]+600/2))
for i in range(0,np.shape(axesB)[0]):
axeshB[i,:]=axeshB[i,:]/np.linalg.norm(axeshB[i,:])
Tb[i,:]=np.dot(MB,axeshB[i,:])
Pb[i,:]=proj(Tb[i,0],Tb[i,1],Tb[i,2])*600/2
if show_ind.get()==1:
m=np.amax([np.abs(axesB[i,0]),np.abs(axesB[i,1]),np.abs(axesB[i,2])])
if (np.around(axesB[i,0]/m)==axesB[i,0]/m) & (np.around(axesB[i,1]/m)==axesB[i,1]/m) & (np.around(axesB[i,2]/m)==axesB[i,2]/m):
sB=str(int(axesB[i,0]/m))+str(int(axesB[i,1]/m))+str(int(axesB[i,2]/m))
else:
sB=str(int(axesB[i,0]))+str(int(axesB[i,1]))+str(int(axesB[i,2]))
a.annotate(sB,(Pb[i,0]+600/2,Pb[i,1]+600/2))
for l in range(0,int(np.shape(S)[0]/3)):
if show_angle.get()==1:
sangle=str(np.round(D0[l,3],decimals=1))
a.annotate(sangle,(Qp[l,0]+600/2,Qp[l,1]+600/2),size=8)
if show_axe.get()==1:
saxe=str(int(D1[l,0]))+','+str(int(D1[l,1]))+','+str(int(D1[l,2]))
a.annotate(saxe,(Qp[l,0]+600/2,Qp[l,1]+600/2),size=8)
if show_num.get()==1:
snum=str(int(D0[l,4]))
a.annotate(snum,(Qp[l,0]+600/2,Qp[l,1]+600/2),size=10)
a.plot(Pa[:,0]+600/2,Pa[:,1]+600/2,'bo')
a.plot(Pb[:,0]+600/2,Pb[:,1]+600/2,'go')
a.plot(Qp[:,0]+600/2,Qp[:,1]+600/2,'ro')
a.axis([0,600,0,600])
a.imshow(img,interpolation="bicubic")
a.axis('off')
a.figure.canvas.draw()
def princ():
global Ta,Tb,MA,MB
a = f.add_subplot(111)
a.figure.clear()
a = f.add_subplot(111)
phi1a=eval(phi1A_entry.get())
phia=eval(phiA_entry.get())
phi2a=eval(phi2A_entry.get())
phi1b=eval(phi1B_entry.get())
phib=eval(phiB_entry.get())
phi2b=eval(phi2B_entry.get())
fn = os.path.join(os.path.dirname(__file__), 'stereo.png')
img=np.array(Image.open(fn))
crist()
Pa=np.zeros((np.shape(axesA)[0],2))
Ta=np.zeros((np.shape(axesA)))
Pb=np.zeros((np.shape(axesB)[0],2))
Tb=np.zeros((np.shape(axesB)))
for i in range(0,np.shape(axesA)[0]):
axeshA[i,:]=axeshA[i,:]/np.linalg.norm(axeshA[i,:])
Ta[i,:]=np.dot(rotation(phi1a,phia,phi2a),axeshA[i,:])
Pa[i,:]=proj(Ta[i,0],Ta[i,1],Ta[i,2])*600/2
m=np.amax([np.abs(axesA[i,0]),np.abs(axesA[i,1]),np.abs(axesA[i,2])])
if (np.around(axesA[i,0]/m)==axesA[i,0]/m) & (np.around(axesA[i,1]/m)==axesA[i,1]/m) & (np.around(axesA[i,2]/m)==axesA[i,2]/m):
sA=str(int(axesA[i,0]/m))+str(int(axesA[i,1]/m))+str(int(axesA[i,2]/m))
else:
sA=str(int(axesA[i,0]))+str(int(axesA[i,1]))+str(int(axesA[i,2]))
a.annotate(sA,(Pa[i,0]+600/2,Pa[i,1]+600/2))
for i in range(0,np.shape(axesB)[0]):
axeshB[i,:]=axeshB[i,:]/np.linalg.norm(axeshB[i,:])
Tb[i,:]=np.dot(rotation(phi1b,phib,phi2b),axeshB[i,:])
Pb[i,:]=proj(Tb[i,0],Tb[i,1],Tb[i,2])*600/2
m=np.amax([np.abs(axesB[i,0]),np.abs(axesB[i,1]),np.abs(axesB[i,2])])
if (np.around(axesB[i,0]/m)==axesB[i,0]/m) & (np.around(axesB[i,1]/m)==axesB[i,1]/m) & (np.around(axesB[i,2]/m)==axesB[i,2]/m):
sB=str(int(axesA[i,0]/m))+str(int(axesA[i,1]/m))+str(int(axesA[i,2]/m))
else:
sB=str(int(axesB[i,0]))+str(int(axesB[i,1]))+str(int(axesB[i,2]))
a.annotate(sB,(Pb[i,0]+600/2,Pb[i,1]+600/2))
a.plot(Pa[:,0]+600/2,Pa[:,1]+600/2,'bo')
a.plot(Pb[:,0]+600/2,Pb[:,1]+600/2,'go')
a.axis([0,600,0,600])
a.imshow(img,interpolation="bicubic")
a.axis('off')
a.figure.canvas.draw()
MA=rotation(phi1a,phia,phi2a)
MB=rotation(phi1b,phib,phi2b)
return Ta,MA,MB,Tb
######################################################################
# GUI
######################################################################
def file_save():
global D1,D0,D
fout = asksaveasfile(mode='w', defaultextension=".txt")
for i in range(np.shape(D1)[0]):
text2save = str(int(D0[i,4]))+'\t'+'['+str(int(D1[i,0]))+','+str(int(D1[i,1]))+','+str(int(D1[i,2]))+']'+'\t '+str(np.around(D0[i,3],decimals=2))
fout.write("%s\n" % text2save)
fout.close()
def image_save():
s = asksaveasfile(mode='w', defaultextension=".jpg")
if s:
f.savefig(s.name)
#s.close()
####################################################
#fonction d'initialisation
##################################################
def init():
global var_uvw,D1,S,Qp,show_ind,show_angle,show_axe,show_num,dmip,d_label_var
fn = os.path.join(os.path.dirname(__file__), 'stereo.png')
img=np.array(Image.open(fn))
a = f.add_subplot(111)
a.axis('off')
a.imshow(img,interpolation="bicubic")
a.figure.canvas.draw()
S=np.zeros((1,5))
Qp=np.zeros((1,2))
D1=np.zeros((1,5))
var_uvw=IntVar()
show_ind=IntVar()
show_angle=IntVar()
show_axe=IntVar()
show_num=IntVar()
d_label_var=StringVar()
d_label_var.set(0)
dmip=0
return var_uvw,show_ind,show_angle,show_axe,show_num
##############################################################
# fonction pour quitter
#######################################################
def _quit():
root.quit() # stops mainloop
root.destroy() # this is necessary on Windows to prevent
# Fatal Python Error: PyEval_RestoreThread: NULL tstate
#############################################################
root = Tk()
root.wm_title("Misorientation")
root.geometry('1220x798+10+40')
root.configure(bg = '#BDBDBD')
#root.resizable(0,0)
#s=ttk.Style()
#s.theme_use('clam')
style = ttk.Style()
theme = style.theme_use()
default = style.lookup(theme, 'background')
################################################
# Creation d'une zone pour tracer des graphiques
################################################
f = Figure(facecolor='white',figsize=[2,2],dpi=100)
canvas = FigureCanvasTkAgg(f, master=root)
canvas.get_tk_widget().place(x=0,y=0,height=800,width=800)
canvas._tkcanvas.bind('<Button-3>', click_a_pole)
canvas.show()
toolbar = NavigationToolbar2TkAgg( canvas, root )
toolbar.zoom('off')
toolbar.update()
###################################################
init()
#import _imaging
#print _imaging.__file__
##############################################
# Boutons
##############################################
phi1A_entry = Entry (master=root)
phi1A_entry.place(relx=0.72,rely=0.5,relheight=0.03,relwidth=0.07)
phi1A_entry.configure(background="white")
phi1A_entry.configure(foreground="black")
phi1A_entry.configure(highlightbackground="#e0e0dfdfe3e3")
phi1A_entry.configure(highlightcolor="#000000")
phi1A_entry.configure(insertbackground="#000000")
phi1A_entry.configure(selectbackground="#c4c4c4")
phi1A_entry.configure(selectforeground="black")
phiA_entry = Entry (master=root)
phiA_entry.place(relx=0.72,rely=0.55,relheight=0.03,relwidth=0.07)
phiA_entry.configure(background="white")
phiA_entry.configure(foreground="black")
phiA_entry.configure(highlightcolor="black")
phiA_entry.configure(insertbackground="black")
phiA_entry.configure(selectbackground="#c4c4c4")
phiA_entry.configure(selectforeground="black")
label_euler = Label (master=root)
label_euler.place(relx=0.77,rely=0.42,height=46,width=163)
label_euler.configure(activebackground="#cccccc")
label_euler.configure(activeforeground="black")
label_euler.configure(cursor="fleur")
label_euler.configure(foreground="black")
label_euler.configure(highlightcolor="black")
label_euler.configure(text='''Euler angles \n A blue , B green''')
phi2A_entry = Entry (master=root)
phi2A_entry.place(relx=0.72,rely=0.6,relheight=0.03,relwidth=0.07)
phi2A_entry.configure(background="white")
phi2A_entry.configure(foreground="black")
phi2A_entry.configure(highlightcolor="black")
phi2A_entry.configure(insertbackground="black")
phi2A_entry.configure(selectbackground="#c4c4c4")
phi2A_entry.configure(selectforeground="black")
button_trace = Button (master=root)
button_trace.place(relx=0.7,rely=0.66,height=21,width=49)
button_trace.configure(activebackground="#f9f9f9")
button_trace.configure(activeforeground="black")
button_trace.configure(background="#ff0000")
button_trace.configure(command=princ)
button_trace.configure(foreground="black")
button_trace.configure(highlightcolor="black")
button_trace.configure(pady="0")
button_trace.configure(text='''PLOT''')
Phi1A_label = Label (master=root)
Phi1A_label.place(relx=0.67,rely=0.5,height=19,width=50)
Phi1A_label.configure(activebackground="#cccccc")
Phi1A_label.configure(activeforeground="black")
Phi1A_label.configure(foreground="black")
Phi1A_label.configure(highlightcolor="black")
Phi1A_label.configure(text='''Phi1A''')
PhiA_label = Label (master=root)
PhiA_label.place(relx=0.67,rely=0.55,height=19,width=50)
PhiA_label.configure(activebackground="#cccccc")
PhiA_label.configure(activeforeground="black")
PhiA_label.configure(foreground="black")
PhiA_label.configure(highlightcolor="black")
PhiA_label.configure(text='''PhiA''')
Phi2A_label = Label (master=root)
Phi2A_label.place(relx=0.67,rely=0.6,height=19,width=50)
Phi2A_label.configure(activebackground="#cccccc")
Phi2A_label.configure(activeforeground="black")
Phi2A_label.configure(foreground="black")
Phi2A_label.configure(highlightcolor="black")
Phi2A_label.configure(text='''Phi2A''')
phi1B_entry = Entry (master=root)
phi1B_entry.place(relx=0.86,rely=0.5,relheight=0.03,relwidth=0.07)
phi1B_entry.configure(background="white")
phi1B_entry.configure(foreground="black")
phi1B_entry.configure(highlightbackground="#e0e0dfdfe3e3")
phi1B_entry.configure(highlightcolor="#000000")
phi1B_entry.configure(insertbackground="#000000")
phi1B_entry.configure(selectbackground="#c4c4c4")
phi1B_entry.configure(selectforeground="black")
Phi1B = Label (master=root)
Phi1B.place(relx=0.81,rely=0.5,height=19,width=50)
Phi1B.configure(activebackground="#cccccc")
Phi1B.configure(activeforeground="black")
Phi1B.configure(foreground="black")
Phi1B.configure(highlightcolor="black")
Phi1B.configure(text='''Phi1B''')
PhiB_label1 = Label (master=root)
PhiB_label1.place(relx=0.81,rely=0.55,height=19,width=50)
PhiB_label1.configure(activebackground="#cccccc")
PhiB_label1.configure(activeforeground="black")
PhiB_label1.configure(foreground="black")
PhiB_label1.configure(highlightcolor="black")
PhiB_label1.configure(text='''PhiB''')
Phi2B_label2 = Label (master=root)
Phi2B_label2.place(relx=0.81,rely=0.6,height=19,width=50)
Phi2B_label2.configure(activebackground="#cccccc")
Phi2B_label2.configure(activeforeground="black")
Phi2B_label2.configure(foreground="black")
Phi2B_label2.configure(highlightcolor="black")
Phi2B_label2.configure(text='''Phi2B''')
phiB_entry = Entry (master=root)
phiB_entry.place(relx=0.86,rely=0.55,relheight=0.03,relwidth=0.07)
phiB_entry.configure(background="white")
phiB_entry.configure(foreground="black")
phiB_entry.configure(highlightbackground="#e0e0dfdfe3e3")
phiB_entry.configure(highlightcolor="#000000")
phiB_entry.configure(insertbackground="#000000")
phiB_entry.configure(selectbackground="#c4c4c4")
phiB_entry.configure(selectforeground="black")
phi2B_entry = Entry (master=root)
phi2B_entry.place(relx=0.86,rely=0.6,relheight=0.03,relwidth=0.07)
phi2B_entry.configure(background="white")
phi2B_entry.configure(foreground="black")
phi2B_entry.configure(highlightbackground="#e0e0dfdfe3e3")
phi2B_entry.configure(highlightcolor="#000000")
phi2B_entry.configure(insertbackground="#000000")
phi2B_entry.configure(selectbackground="#c4c4c4")
phi2B_entry.configure(selectforeground="black")
button_desorientation = Button (master=root)
button_desorientation.place(relx=0.81,rely=0.66,height=21,width=124)
button_desorientation.configure(activebackground="#f9f9f9")
button_desorientation.configure(activeforeground="black")
button_desorientation.configure(background="#00ff00")
button_desorientation.configure(command=desorientation)
button_desorientation.configure(foreground="black")
button_desorientation.configure(highlightcolor="black")
button_desorientation.configure(pady="0")
button_desorientation.configure(text='''MISORIENTATION''')
Cristal_label = Label (master=root)
Cristal_label.place(relx=0.66,rely=0.03,height=19,width=142)
Cristal_label.configure(text='''Crystal Parameters''')
a_cristal_label = Label (master=root)
a_cristal_label.place(relx=0.68,rely=0.06,height=19,width=12)
a_cristal_label.configure(text='''a''')
b_cristal_label = Label (master=root)
b_cristal_label.place(relx=0.68,rely=0.1,height=19,width=12)
b_cristal_label.configure(activebackground="#f9f9f9")
b_cristal_label.configure(activeforeground="black")
b_cristal_label.configure(foreground="black")
b_cristal_label.configure(highlightcolor="black")
b_cristal_label.configure(text='''b''')
c_cristal_label = Label (master=root)
c_cristal_label.place(relx=0.68,rely=0.14,height=19,width=11)
c_cristal_label.configure(activebackground="#f9f9f9")
c_cristal_label.configure(activeforeground="black")
c_cristal_label.configure(foreground="black")
c_cristal_label.configure(highlightcolor="black")
c_cristal_label.configure(text='''c''')
alp_cristal_label = Label (master=root)
alp_cristal_label.place(relx=0.67,rely=0.18,height=19,width=42)
alp_cristal_label.configure(activebackground="#f9f9f9")
alp_cristal_label.configure(activeforeground="black")
alp_cristal_label.configure(foreground="black")
alp_cristal_label.configure(highlightcolor="black")
alp_cristal_label.configure(text='''alpha''')
bet_cristal_label = Label (master=root)
bet_cristal_label.place(relx=0.67,rely=0.22,height=19,width=42)
bet_cristal_label.configure(activebackground="#f9f9f9")
bet_cristal_label.configure(activeforeground="black")
bet_cristal_label.configure(foreground="black")
bet_cristal_label.configure(highlightcolor="black")
bet_cristal_label.configure(text='''beta''')
gam_cristal_label = Label (master=root)
gam_cristal_label.place(relx=0.66,rely=0.26,height=19,width=52)
gam_cristal_label.configure(activebackground="#f9f9f9")
gam_cristal_label.configure(activeforeground="black")
gam_cristal_label.configure(foreground="black")
gam_cristal_label.configure(highlightcolor="black")
gam_cristal_label.configure(text='''gamma''')
a_entry = Entry (master=root)
a_entry.place(relx=0.7,rely=0.06,relheight=0.03,relwidth=0.06)
a_entry.configure(background="white")
a_entry.configure(insertbackground="black")
b_entry = Entry (master=root)
b_entry.place(relx=0.7,rely=0.1,relheight=0.03,relwidth=0.06)
b_entry.configure(background="white")
b_entry.configure(foreground="black")
b_entry.configure(highlightcolor="black")
b_entry.configure(insertbackground="black")
b_entry.configure(selectbackground="#c4c4c4")
b_entry.configure(selectforeground="black")
c_entry = Entry (master=root)
c_entry.place(relx=0.7,rely=0.14,relheight=0.03,relwidth=0.06)
c_entry.configure(background="white")
c_entry.configure(foreground="black")
c_entry.configure(highlightcolor="black")
c_entry.configure(insertbackground="black")
c_entry.configure(selectbackground="#c4c4c4")
c_entry.configure(selectforeground="black")
alp_entry = Entry (master=root)
alp_entry.place(relx=0.71,rely=0.18,relheight=0.03,relwidth=0.06)
alp_entry.configure(background="white")
alp_entry.configure(foreground="black")
alp_entry.configure(highlightcolor="black")
alp_entry.configure(insertbackground="black")
alp_entry.configure(selectbackground="#c4c4c4")
alp_entry.configure(selectforeground="black")
bet_entry = Entry (master=root)
bet_entry.place(relx=0.71,rely=0.22,relheight=0.03,relwidth=0.06)
bet_entry.configure(background="white")
bet_entry.configure(foreground="black")
bet_entry.configure(highlightcolor="black")
bet_entry.configure(insertbackground="black")
bet_entry.configure(selectbackground="#c4c4c4")
bet_entry.configure(selectforeground="black")
gam_entry = Entry (master=root)
gam_entry.place(relx=0.71,rely=0.26,relheight=0.03,relwidth=0.06)
gam_entry.configure(background="white")
gam_entry.configure(foreground="black")
gam_entry.configure(highlightcolor="black")
gam_entry.configure(insertbackground="black")
gam_entry.configure(selectbackground="#c4c4c4")
gam_entry.configure(selectforeground="black")
uvw_button = Checkbutton (master=root)
uvw_button.place(relx=0.75,rely=0.66,relheight=0.03,relwidth=0.04)
uvw_button.configure(text='''uvw''')
uvw_button.configure(variable=var_uvw)
e_label = Label (master=root)
e_label.place(relx=0.66,rely=0.31,height=19,width=86)
e_label.configure(text='''Max indices''')
e_entry = Entry (master=root)
e_entry.place(relx=0.74,rely=0.31,relheight=0.03,relwidth=0.05)
e_entry.configure(background="white")
e_entry.configure(insertbackground="black")
e2_label = Label (master=root)
e2_label.place(relx=0.68,rely=0.36,height=19,width=12)
e2_label.configure(text='''d''')
dm_button = Button (master=root)
dm_button.place(relx=0.7,rely=0.36,height=21,width=13)
dm_button.configure(activebackground="#f9f9f9")
dm_button.configure(activeforeground="black")
dm_button.configure(command=dm)
dm_button.configure(foreground="black")
dm_button.configure(highlightcolor="black")
dm_button.configure(pady="0")
dm_button.configure(text='''-''')
d_entry = Entry (master=root)
d_entry.place(relx=0.72,rely=0.36,relheight=0.02,relwidth=0.04)
d_entry.configure(background="white")
d_entry.configure(foreground="black")
d_entry.configure(highlightcolor="black")
d_entry.configure(insertbackground="black")
d_entry.configure(selectbackground="#c4c4c4")
d_entry.configure(selectforeground="black")
dp_button = Button (master=root)
dp_button.place(relx=0.76,rely=0.36,height=21,width=17)
dp_button.configure(activebackground="#f9f9f9")
dp_button.configure(activeforeground="black")
dp_button.configure(command=dp)
dp_button.configure(foreground="black")
dp_button.configure(highlightcolor="black")
dp_button.configure(pady="0")
dp_button.configure(text='''+''')
d_label = Label (master=root)
d_label.place(relx=0.73,rely=0.39,height=19,width=16)
d_label.configure(textvariable=d_label_var)
label_addpoleA = Label (master=root)
label_addpoleA.place(relx=0.81,rely=0.03,height=19,width=90)
label_addpoleA.configure(activebackground="#cccccc")
label_addpoleA.configure(activeforeground="black")
label_addpoleA.configure(foreground="black")
label_addpoleA.configure(highlightcolor="black")
label_addpoleA.configure(text='''Add pole A''')
pole1A_entry = Entry (master=root)
pole1A_entry.place(relx=0.81,rely=0.06,relheight=0.02
,relwidth=0.04)
pole1A_entry.configure(background="white")
pole1A_entry.configure(foreground="black")
pole1A_entry.configure(highlightcolor="black")
pole1A_entry.configure(insertbackground="black")
pole1A_entry.configure(selectbackground="#c4c4c4")
pole1A_entry.configure(selectforeground="black")
pole2A_entry = Entry (master=root)
pole2A_entry.place(relx=0.87,rely=0.06,relheight=0.02
,relwidth=0.04)
pole2A_entry.configure(background="white")
pole2A_entry.configure(foreground="black")
pole2A_entry.configure(highlightcolor="black")
pole2A_entry.configure(insertbackground="black")
pole2A_entry.configure(selectbackground="#c4c4c4")
pole2A_entry.configure(selectforeground="black")
pole3A_entry = Entry (master=root)
pole3A_entry.place(relx=0.93,rely=0.06,relheight=0.02
,relwidth=0.04)
pole3A_entry.configure(background="white")
pole3A_entry.configure(foreground="black")
pole3A_entry.configure(highlightcolor="black")
pole3A_entry.configure(insertbackground="black")
pole3A_entry.configure(selectbackground="#c4c4c4")
pole3A_entry.configure(selectforeground="black")
addpoleA_button = Button (master=root)
addpoleA_button.place(relx=0.81,rely=0.11,height=31,width=57)
addpoleA_button.configure(activebackground="#f9f9f9")
addpoleA_button.configure(activeforeground="black")
addpoleA_button.configure(command=addpoleA)
addpoleA_button.configure(foreground="black")
addpoleA_button.configure(highlightcolor="black")
addpoleA_button.configure(pady="0")
addpoleA_button.configure(text='''Add''')
symA_button = Button (master=root)
symA_button.place(relx=0.87,rely=0.11,height=31,width=71)
symA_button.configure(command=addpoleA_sym)
symA_button.configure(pady="0")
symA_button.configure(text='''Symetry''')
trace_planA_button = Button (master=root)
trace_planA_button.place(relx=0.93,rely=0.11,height=31,width=81)
trace_planA_button.configure(command=trace_planA)
trace_planA_button.configure(pady="0")
trace_planA_button.configure(text='''Draw plane''')
label_addpoleB = Label (master=root)
label_addpoleB.place(relx=0.81,rely=0.2,height=19,width=90)
label_addpoleB.configure(activebackground="#cccccc")
label_addpoleB.configure(activeforeground="black")
label_addpoleB.configure(foreground="black")
label_addpoleB.configure(highlightcolor="black")
label_addpoleB.configure(text='''Add pole B''')
pole1B_entry = Entry (master=root)
pole1B_entry.place(relx=0.81,rely=0.24,relheight=0.02
,relwidth=0.04)
pole1B_entry.configure(background="white")
pole1B_entry.configure(foreground="black")
pole1B_entry.configure(highlightcolor="black")
pole1B_entry.configure(insertbackground="black")
pole1B_entry.configure(selectbackground="#c4c4c4")
pole1B_entry.configure(selectforeground="black")
pole2B_entry = Entry (master=root)
pole2B_entry.place(relx=0.87,rely=0.24,relheight=0.02
,relwidth=0.04)
pole2B_entry.configure(background="white")
pole2B_entry.configure(foreground="black")
pole2B_entry.configure(highlightcolor="black")
pole2B_entry.configure(insertbackground="black")
pole2B_entry.configure(selectbackground="#c4c4c4")
pole2B_entry.configure(selectforeground="black")
pole3B_entry = Entry (master=root)
pole3B_entry.place(relx=0.93,rely=0.24,relheight=0.02
,relwidth=0.04)
pole3B_entry.configure(background="white")
pole3B_entry.configure(foreground="black")
pole3B_entry.configure(highlightcolor="black")
pole3B_entry.configure(insertbackground="black")
pole3B_entry.configure(selectbackground="#c4c4c4")
pole3B_entry.configure(selectforeground="black")
addpoleB_button = Button (master=root)
addpoleB_button.place(relx=0.81,rely=0.28,height=31,width=55)
addpoleB_button.configure(activebackground="#f9f9f9")
addpoleB_button.configure(activeforeground="black")
addpoleB_button.configure(command=addpoleB)
addpoleB_button.configure(foreground="black")
addpoleB_button.configure(highlightcolor="black")
addpoleB_button.configure(pady="0")
addpoleB_button.configure(text='''Add''')
symB_button = Button (master=root)
symB_button.place(relx=0.87,rely=0.28,height=31,width=71)
symB_button.configure(command=addpoleB_sym)
symB_button.configure(pady="0")
symB_button.configure(text='''Symetry''')
trace_planB_button = Button (master=root)
trace_planB_button.place(relx=0.93,rely=0.28,height=31,width=81)
trace_planB_button.configure(command=trace_planB)
trace_planB_button.configure(pady="0")
trace_planB_button.configure(text='''Draw plane''')
show_ind_button = Checkbutton (master=root)
show_ind_button.place(relx=0.81,rely=0.7,relheight=0.03
,relwidth=0.11)
show_ind_button.configure(text='''Show indices''')
show_ind_button.configure(variable=show_ind)
show_angle_button = Checkbutton (master=root)
show_angle_button.place(relx=0.81,rely=0.74,relheight=0.03
,relwidth=0.11)
show_angle_button.configure(text='''Show angle''')
show_angle_button.configure(variable=show_angle)
show_axe_button = Checkbutton (master=root)
show_axe_button.place(relx=0.81,rely=0.78,relheight=0.03
,relwidth=0.11)
show_axe_button.configure(text='''Show axes''')
show_axe_button.configure(variable=show_axe)
show_num_button = Checkbutton (master=root)
show_num_button.place(relx=0.81,rely=0.82,relheight=0.03
,relwidth=0.11)
show_num_button.configure(text='''Show numbers''')
show_num_button.configure(variable=show_num)
menu = Menu(master=root)
filemenu = Menu(menu, tearoff=0)
menu.add_cascade(label="Save", menu=filemenu)
root.config(menu=menu)
filemenu.add_command(label="Save data", command=file_save)
filemenu.add_command(label="Save figure", command=image_save)
######################################################################################################
######## importer des structures cristallines depuis un fichier Nom,a,b,c,alpha,beta,gamma,space group
######################################################################################################
def structure(i0):
global x0
a_entry.delete(0,END)
a_entry.insert(1,eval(x0[i0][1]))
b_entry.delete(0,END)
b_entry.insert(1,eval(x0[i0][2]))
c_entry.delete(0,END)
c_entry.insert(1,eval(x0[i0][3]))
alp_entry.delete(0,END)
alp_entry.insert(1,eval(x0[i0][4]))
bet_entry.delete(0,END)
bet_entry.insert(1,eval(x0[i0][5]))
gam_entry.delete(0,END)
gam_entry.insert(1,eval(x0[i0][6]))
def createstructure(i):
return lambda:structure(i)
cristalmenu=Menu(menu,tearoff=0)
menu.add_cascade(label="Structures", menu=cristalmenu)
file_struct=open(os.path.join(os.path.dirname(__file__), 'structure.txt') ,"r")
x0=[]
i=0
for line in file_struct:
x0.append(map(str, line.split()))
cristalmenu.add_command(label=x0[i][0], command=createstructure(i))
i=i+1
file_struct.close()
#######################################################################################################
phi1A_entry.insert(0,0)
phiA_entry.insert(0,0)
phi2A_entry.insert(0,0)
phi1B_entry.insert(0,0)
phiB_entry.insert(0,0)
phi2B_entry.insert(0,0)
e_entry.insert(1,1)
d_entry.insert(1,1)
mainloop()
| gpl-2.0 |
swharden/SWHLab | doc/uses/EPSCs-and-IPSCs/smooth histogram method/05.py | 1 | 1812 | """
MOST OF THIS CODE IS NOT USED
ITS COPY/PASTED AND LEFT HERE FOR CONVENIENCE
"""
import os
import sys
# in case our module isn't installed (running from this folder)
if not os.path.abspath('../../../') in sys.path:
sys.path.append('../../../') # helps spyder get docs
import swhlab
import swhlab.common as cm
import matplotlib.pyplot as plt
import numpy as np
import warnings # suppress VisibleDeprecationWarning warning
warnings.filterwarnings("ignore", category=np.VisibleDeprecationWarning)
def analyzeSweep(abf,plotToo=True,color=None,label=None):
Y=abf.sweepYsmartbase()[abf.pointsPerSec*.5:]
AV,SD=np.average(Y),np.std(Y)
dev=5 # number of stdevs from the avg to set the range
R1,R2=[(AV-SD)*dev,(AV+SD)*dev]
nBins=1000
hist,bins=np.histogram(Y,bins=nBins,range=[R1,R2],density=True)
histSmooth=abf.convolve(hist,cm.kernel_gaussian(nBins/5))
if plotToo:
plt.plot(bins[1:],hist,'.',color=color,alpha=.2,ms=10)
plt.plot(bins[1:],histSmooth,'-',color=color,lw=5,alpha=.5,label=label)
return
if __name__=="__main__":
#abfFile=R"C:\Users\scott\Documents\important\demodata\abfs\16d07022.abf"
abfFile=R"X:\Data\2P01\2016\2016-09-01 PIR TGOT\16d07022.abf"
abf=swhlab.ABF(abfFile)
# prepare figure
plt.figure(figsize=(10,10))
plt.grid()
plt.title("smart baseline value distribution")
plt.xlabel(abf.units2)
plt.ylabel("normalized density")
# do the analysis
abf.kernel=abf.kernel_gaussian(sizeMS=500)
abf.setsweep(175)
analyzeSweep(abf,color='b',label="baseline")
abf.setsweep(200)
analyzeSweep(abf,color='g',label="TGOT")
abf.setsweep(375)
analyzeSweep(abf,color='y',label="washout")
# show figure
plt.legend()
plt.margins(0,.1)
plt.show()
print("DONE")
| mit |
chrisburr/scikit-learn | examples/covariance/plot_sparse_cov.py | 300 | 5078 | """
======================================
Sparse inverse covariance estimation
======================================
Using the GraphLasso estimator to learn a covariance and sparse precision
from a small number of samples.
To estimate a probabilistic model (e.g. a Gaussian model), estimating the
precision matrix, that is the inverse covariance matrix, is as important
as estimating the covariance matrix. Indeed a Gaussian model is
parametrized by the precision matrix.
To be in favorable recovery conditions, we sample the data from a model
with a sparse inverse covariance matrix. In addition, we ensure that the
data is not too much correlated (limiting the largest coefficient of the
precision matrix) and that there a no small coefficients in the
precision matrix that cannot be recovered. In addition, with a small
number of observations, it is easier to recover a correlation matrix
rather than a covariance, thus we scale the time series.
Here, the number of samples is slightly larger than the number of
dimensions, thus the empirical covariance is still invertible. However,
as the observations are strongly correlated, the empirical covariance
matrix is ill-conditioned and as a result its inverse --the empirical
precision matrix-- is very far from the ground truth.
If we use l2 shrinkage, as with the Ledoit-Wolf estimator, as the number
of samples is small, we need to shrink a lot. As a result, the
Ledoit-Wolf precision is fairly close to the ground truth precision, that
is not far from being diagonal, but the off-diagonal structure is lost.
The l1-penalized estimator can recover part of this off-diagonal
structure. It learns a sparse precision. It is not able to
recover the exact sparsity pattern: it detects too many non-zero
coefficients. However, the highest non-zero coefficients of the l1
estimated correspond to the non-zero coefficients in the ground truth.
Finally, the coefficients of the l1 precision estimate are biased toward
zero: because of the penalty, they are all smaller than the corresponding
ground truth value, as can be seen on the figure.
Note that, the color range of the precision matrices is tweaked to
improve readability of the figure. The full range of values of the
empirical precision is not displayed.
The alpha parameter of the GraphLasso setting the sparsity of the model is
set by internal cross-validation in the GraphLassoCV. As can be
seen on figure 2, the grid to compute the cross-validation score is
iteratively refined in the neighborhood of the maximum.
"""
print(__doc__)
# author: Gael Varoquaux <gael.varoquaux@inria.fr>
# License: BSD 3 clause
# Copyright: INRIA
import numpy as np
from scipy import linalg
from sklearn.datasets import make_sparse_spd_matrix
from sklearn.covariance import GraphLassoCV, ledoit_wolf
import matplotlib.pyplot as plt
##############################################################################
# Generate the data
n_samples = 60
n_features = 20
prng = np.random.RandomState(1)
prec = make_sparse_spd_matrix(n_features, alpha=.98,
smallest_coef=.4,
largest_coef=.7,
random_state=prng)
cov = linalg.inv(prec)
d = np.sqrt(np.diag(cov))
cov /= d
cov /= d[:, np.newaxis]
prec *= d
prec *= d[:, np.newaxis]
X = prng.multivariate_normal(np.zeros(n_features), cov, size=n_samples)
X -= X.mean(axis=0)
X /= X.std(axis=0)
##############################################################################
# Estimate the covariance
emp_cov = np.dot(X.T, X) / n_samples
model = GraphLassoCV()
model.fit(X)
cov_ = model.covariance_
prec_ = model.precision_
lw_cov_, _ = ledoit_wolf(X)
lw_prec_ = linalg.inv(lw_cov_)
##############################################################################
# Plot the results
plt.figure(figsize=(10, 6))
plt.subplots_adjust(left=0.02, right=0.98)
# plot the covariances
covs = [('Empirical', emp_cov), ('Ledoit-Wolf', lw_cov_),
('GraphLasso', cov_), ('True', cov)]
vmax = cov_.max()
for i, (name, this_cov) in enumerate(covs):
plt.subplot(2, 4, i + 1)
plt.imshow(this_cov, interpolation='nearest', vmin=-vmax, vmax=vmax,
cmap=plt.cm.RdBu_r)
plt.xticks(())
plt.yticks(())
plt.title('%s covariance' % name)
# plot the precisions
precs = [('Empirical', linalg.inv(emp_cov)), ('Ledoit-Wolf', lw_prec_),
('GraphLasso', prec_), ('True', prec)]
vmax = .9 * prec_.max()
for i, (name, this_prec) in enumerate(precs):
ax = plt.subplot(2, 4, i + 5)
plt.imshow(np.ma.masked_equal(this_prec, 0),
interpolation='nearest', vmin=-vmax, vmax=vmax,
cmap=plt.cm.RdBu_r)
plt.xticks(())
plt.yticks(())
plt.title('%s precision' % name)
ax.set_axis_bgcolor('.7')
# plot the model selection metric
plt.figure(figsize=(4, 3))
plt.axes([.2, .15, .75, .7])
plt.plot(model.cv_alphas_, np.mean(model.grid_scores, axis=1), 'o-')
plt.axvline(model.alpha_, color='.5')
plt.title('Model selection')
plt.ylabel('Cross-validation score')
plt.xlabel('alpha')
plt.show()
| bsd-3-clause |
NelisVerhoef/scikit-learn | examples/manifold/plot_mds.py | 261 | 2616 | """
=========================
Multi-dimensional scaling
=========================
An illustration of the metric and non-metric MDS on generated noisy data.
The reconstructed points using the metric MDS and non metric MDS are slightly
shifted to avoid overlapping.
"""
# Author: Nelle Varoquaux <nelle.varoquaux@gmail.com>
# Licence: BSD
print(__doc__)
import numpy as np
from matplotlib import pyplot as plt
from matplotlib.collections import LineCollection
from sklearn import manifold
from sklearn.metrics import euclidean_distances
from sklearn.decomposition import PCA
n_samples = 20
seed = np.random.RandomState(seed=3)
X_true = seed.randint(0, 20, 2 * n_samples).astype(np.float)
X_true = X_true.reshape((n_samples, 2))
# Center the data
X_true -= X_true.mean()
similarities = euclidean_distances(X_true)
# Add noise to the similarities
noise = np.random.rand(n_samples, n_samples)
noise = noise + noise.T
noise[np.arange(noise.shape[0]), np.arange(noise.shape[0])] = 0
similarities += noise
mds = manifold.MDS(n_components=2, max_iter=3000, eps=1e-9, random_state=seed,
dissimilarity="precomputed", n_jobs=1)
pos = mds.fit(similarities).embedding_
nmds = manifold.MDS(n_components=2, metric=False, max_iter=3000, eps=1e-12,
dissimilarity="precomputed", random_state=seed, n_jobs=1,
n_init=1)
npos = nmds.fit_transform(similarities, init=pos)
# Rescale the data
pos *= np.sqrt((X_true ** 2).sum()) / np.sqrt((pos ** 2).sum())
npos *= np.sqrt((X_true ** 2).sum()) / np.sqrt((npos ** 2).sum())
# Rotate the data
clf = PCA(n_components=2)
X_true = clf.fit_transform(X_true)
pos = clf.fit_transform(pos)
npos = clf.fit_transform(npos)
fig = plt.figure(1)
ax = plt.axes([0., 0., 1., 1.])
plt.scatter(X_true[:, 0], X_true[:, 1], c='r', s=20)
plt.scatter(pos[:, 0], pos[:, 1], s=20, c='g')
plt.scatter(npos[:, 0], npos[:, 1], s=20, c='b')
plt.legend(('True position', 'MDS', 'NMDS'), loc='best')
similarities = similarities.max() / similarities * 100
similarities[np.isinf(similarities)] = 0
# Plot the edges
start_idx, end_idx = np.where(pos)
#a sequence of (*line0*, *line1*, *line2*), where::
# linen = (x0, y0), (x1, y1), ... (xm, ym)
segments = [[X_true[i, :], X_true[j, :]]
for i in range(len(pos)) for j in range(len(pos))]
values = np.abs(similarities)
lc = LineCollection(segments,
zorder=0, cmap=plt.cm.hot_r,
norm=plt.Normalize(0, values.max()))
lc.set_array(similarities.flatten())
lc.set_linewidths(0.5 * np.ones(len(segments)))
ax.add_collection(lc)
plt.show()
| bsd-3-clause |
pauliacomi/pyGAPS | tests/characterisation/test_t_plot.py | 1 | 2958 | """
This test module has tests relating to t-plots
All functions in /calculations/tplot.py are tested here.
The purposes are:
- testing the user-facing API function (tplot)
- testing individual low level functions against known results.
Functions are tested against pre-calculated values on real isotherms.
All pre-calculated data for characterisation can be found in the
/.conftest file together with the other isotherm parameters.
"""
import pytest
from matplotlib.testing.decorators import cleanup
from numpy import isclose
import pygaps
import pygaps.utilities.exceptions as pgEx
from .conftest import DATA
from .conftest import DATA_N77_PATH
@pytest.mark.characterisation
class TestTPlot():
"""Tests t-plot calculations."""
def test_alphas_checks(self, basic_pointisotherm):
"""Checks for built-in safeguards."""
# Will raise a "no suitable model exception"
with pytest.raises(pgEx.ParameterError):
pygaps.t_plot(basic_pointisotherm, thickness_model='random')
@pytest.mark.parametrize('sample', [sample for sample in DATA])
def test_tplot(self, sample):
"""Test calculation with several model isotherms."""
sample = DATA[sample]
# exclude datasets where it is not applicable
if sample.get('t_area', None):
filepath = DATA_N77_PATH / sample['file']
isotherm = pygaps.isotherm_from_json(filepath)
res = pygaps.t_plot(isotherm)
results = res.get('results')
err_relative = 0.1 # 10 percent
err_absolute_area = 0.1 # units
err_absolute_volume = 0.01 # units
assert isclose(
results[-1].get('adsorbed_volume'), sample['t_pore_volume'],
err_relative, err_absolute_area
)
assert isclose(
results[0].get('area'), sample['t_area'], err_relative,
err_absolute_volume
)
def test_tplot_choice(self):
"""Test choice of points."""
sample = DATA['MCM-41']
filepath = DATA_N77_PATH / sample['file']
isotherm = pygaps.isotherm_from_json(filepath)
res = pygaps.t_plot(isotherm, limits=[0.7, 1.0])
results = res.get('results')
err_relative = 0.1 # 10 percent
err_absolute_area = 0.1 # units
err_absolute_volume = 0.01 # units
assert isclose(
results[-1].get('adsorbed_volume'), sample['t_pore_volume'],
err_relative, err_absolute_area
)
assert isclose(
results[-1].get('area'), sample['s_t_area'], err_relative,
err_absolute_volume
)
@cleanup
def test_tplot_output(self):
"""Test verbosity."""
sample = DATA['MCM-41']
filepath = DATA_N77_PATH / sample['file']
isotherm = pygaps.isotherm_from_json(filepath)
pygaps.t_plot(isotherm, 'Halsey', verbose=True)
| mit |
christianurich/VIBe2UrbanSim | 3rdparty/opus/src/vibe_min/indicators/make_indicators.py | 4 | 4825 | # Opus/UrbanSim urban simulation software.
# Copyright (C) 2005-2009 University of Washington
# See opus_core/LICENSE
# script to produce a number of PSRC indicators --
# this illustrates using traits-based configurations programatically
from opus_core.configurations.dataset_pool_configuration import DatasetPoolConfiguration
from opus_core.indicator_framework.core.source_data import SourceData
from opus_core.indicator_framework.image_types.matplotlib_map import Map
from opus_core.indicator_framework.image_types.matplotlib_chart import Chart
from opus_core.indicator_framework.image_types.table import Table
from opus_core.indicator_framework.image_types.geotiff_map import GeotiffMap
from opus_core.indicator_framework.image_types.dataset_table import DatasetTable
from opus_core.indicator_framework.image_types.matplotlib_lorenzcurve import LorenzCurve
#some cache_directories and run descriptions
#cache_directory = r'Y:/urbansim_cache/run_1090.2006_11_14_12_12'
#run_description = '(run 1090 - double highway capacity 11/28/2006)'
#cache_directory = r'Y:/urbansim_cache/run_1091.2006_11_14_12_12'
#run_description = '(run 1091 - baseline 11/28/2006)'
#cache_directory = r'D:\urbansim_cache\run_1454.2006_12_12_16_28'
#run_description = '(run 1454 - travel data from quick travel model)'
cache_directory = r'D:\urbansim_cache\run_1090.2006_11_14_12_12'
run_description = '(run 1453 - travel data from full travel model)'
#cache_directory = r'Y:\urbansim_cache\run_1431.2006_12_08_09_45'
#run_description = '(run 1431 - baseyear travel data from travel model run)'
#cache_directory = r'D:\urbansim_cache\run_1154.2006_11_17_20_06'
#run_description = '(run 1154 - no ugb + double highway capacity 11/28/2006)'
#cache_directory = r'D:\urbansim_cache\run_1155.2006_11_17_20_07'
#run_description = '(run 1155 - no ugb 11/28/2006)'
source_data = SourceData(
cache_directory = cache_directory,
run_description = run_description,
years = [1980, 1981, 1982],
dataset_pool_configuration = DatasetPoolConfiguration(
package_order=['eugene','urbansim','opus_core'],
),
)
single_year_requests = [
Table(
attribute = 'urbansim.zone.population',
dataset_name = 'zone',
source_data = source_data,
),
Table(
attribute = 'urbansim.zone.number_of_jobs',
dataset_name = 'zone',
source_data = source_data,
),
Map(
attribute = 'urbansim.zone.population',
scale = [1, 60000],
dataset_name = 'zone',
source_data = source_data,
),
Map(
attribute = 'urbansim.zone.number_of_jobs',
scale = [1, 60000],
dataset_name = 'zone',
source_data = source_data,
),
Map(
scale = [-8000, 40000],
attribute = 'urbansim_population_change',
source_data = source_data,
expression = {'operation': 'change',
'operands': ['urbansim.zone.population']},
dataset_name = 'zone',
),
Map(
scale = [-2000, 40000],
attribute = 'urbansim_employment_change',
source_data = source_data,
expression = {'operation': 'change',
'operands': ['urbansim.zone.number_of_jobs']},
dataset_name = 'zone',
),
]
source_data = SourceData(
cache_directory = cache_directory,
run_description = run_description,
years = [1980, 1981, 1982],
dataset_pool_configuration = DatasetPoolConfiguration(
package_order=['eugene','urbansim','opus_core'],
),
)
multi_year_requests = [
Table(
attribute = 'alldata.aggregate_all(urbansim.gridcell.residential_units, function=sum)',
dataset_name = 'alldata',
source_data = source_data,
name = 'residential_units'
),
Chart(
attribute = 'alldata.aggregate_all(urbansim.gridcell.residential_units, function=sum)',
dataset_name = 'alldata',
source_data = source_data,
name = 'residential_units'
),
Table(
attribute = 'alldata.aggregate_all(urbansim.gridcell.number_of_jobs, function=sum)',
dataset_name = 'alldata',
source_data = source_data,
name = 'number_of_jobs'
),
]
if __name__ == '__main__':
from opus_core.indicator_framework.core.indicator_factory import IndicatorFactory
IndicatorFactory().create_indicators(
indicators = single_year_requests,
display_error_box = False,
show_results = True)
IndicatorFactory().create_indicators(
indicators = multi_year_requests,
display_error_box = False,
show_results = True) | gpl-2.0 |
boland1992/seissuite_iran | build/lib.linux-x86_64-2.7/seissuite/ant/psdepthmodel.py | 6 | 9233 | """
Module taking care of the forward modelling: theoretical dispersion
curve given a 1D crustal model of velocities and densities.
Uses the binaries of the Computer Programs in Seismology, with
must be installed in *COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR*
"""
import numpy as np
import matplotlib.pyplot as plt
import os
import shutil
import itertools as it
from easyprocess import EasyProcess
import tempfile
import pickle
# getting the dir of the binaries of the Computer Programs in Seismology
# import CONFIG class initalised in ./configs/tmp_config.pickle
config_pickle = 'configs/tmp_config.pickle'
f = open(name=config_pickle, mode='rb')
CONFIG = pickle.load(f)
f.close()
# import variables from initialised CONFIG class.
COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR=CONFIG.COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR
# default header of the model file:
# isotropic, 1D, flat Earth with layers of constant velocity
MODEL_HEADER = """MODEL.01
TEST
ISOTROPIC
KGS
FLAT EARTH
1-D
CONSTANT VELOCITY
LINE08
LINE09
LINE10
LINE11
H VP VS RHO QP QS ETAP ETAS FREFP FREFS"""
class VsModel:
"""
Class holding a layered model of Vs function of depth,
with Vp/Vs and rho/Vs ratio fixed.
"""
def __init__(self, vs, dz, ratio_vp_vs, ratio_rho_vs, name='',
store_vg_at_periods=None):
"""
Initializes model with layers' Vs (vs), layers' thickness (dz),
and layers' ratio Vp/Vs and rho/Vs (ratio_vp_vs, ratio_rho_vs).
"""
# checking shapes
nlayers = np.size(vs)
if np.size(dz) != nlayers - 1:
raise Exception("Size of dz should be nb of layers minus 1")
if not np.size(ratio_vp_vs) in [1, nlayers]:
raise Exception("Size of ratio_vp_vs should be nb of layers or 1")
if not np.size(ratio_rho_vs) in [1, nlayers]:
raise Exception("Size of ratio_rho_vs should be nb of layers or 1")
self.name = name
self.vs = np.array(vs)
self.dz = np.array(dz)
self.ratio_vp_vs = np.array(ratio_vp_vs)
self.ratio_rho_vs = np.array(ratio_rho_vs)
# storing vg model at selected periods if required
self.stored_vgperiods = store_vg_at_periods
if not store_vg_at_periods is None:
self.stored_vg = self.vg_model(store_vg_at_periods)
else:
self.stored_vg = None
def misfit_to_vg(self, periods, vg, sigmavg, squared=True,
use_storedvg=True, storevg=False):
"""
Misfit of modelled vg to observed vg
[vg_model - vg]**2
= Sum ------------------ over periods
2 x sigmavg**2
"""
# using stored vg model if required and available, else re-calculating it
if use_storedvg and np.all(periods == self.stored_vgperiods):
vg_model = self.stored_vg
else:
vg_model = self.vg_model(periods, store=storevg)
misfit = np.sum(((vg_model - vg) / sigmavg)**2) / 2.0
if squared:
misfit = np.sqrt(misfit)
return misfit
def vg_model(self, periods, store=False):
"""
Modelled group velocities, vg, function of period
"""
vs = self.vs
vp = self.ratio_vp_vs * self.vs
rho = self.ratio_rho_vs * self.vs
dz = np.r_[self.dz, 0] # we append a fake thickness
vg = Rayleigh_group_velocities(periods, dz=dz, vp=vp, vs=vs, rho=rho)
if store:
# storing group velocities if required
self.stored_vgperiods = periods
self.stored_vg = vg
return vg
def get_vs_at(self, z):
"""
Returns Vs ad depth(s) *z*
"""
indices = np.searchsorted(np.r_[0, self.dz.cumsum()], z, side='right') - 1
if np.any(indices) < 0:
raise Exception("Depth out of range")
return self.vs[indices]
def plot(self, periods, obsvgarrays=None, fig=None, color='r'):
"""
Plots modelled and observed group velocity function of period (top)
and the model itself, i.e. Vs vs depth (bottom)
"""
if not fig:
fig = plt.figure(figsize=(6.5, 10), tight_layout=True)
axlist = [fig.add_subplot(211), fig.add_subplot(212)]
legend = True
else:
axlist = fig.get_axes()
legend = False # no need to add legend to existing fig
# 1st subplot: group velocity vs period
ax = axlist[0]
self.plot_vg(periods, obsvgarrays=obsvgarrays, ax=ax, legend=legend, color=color)
ax.set_title(self.name)
# 2nd subplot: Vs vs depth
ax = axlist[1]
self.plot_model(ax=ax, color=color)
fig.canvas.draw()
fig.show()
return fig
def plot_vg(self, periods, obsvgarrays=None, ax=None, legend=True, color='r'):
"""
Plots modelled and observed group velocity function of period
"""
# creating figure if not given as input
fig = None
if not ax:
fig = plt.figure()
ax = fig.add_subplot(111)
vg_model = self.vg_model(periods)
ax.plot(periods, vg_model, lw=1.5, color=color, label=self.name)
if obsvgarrays:
for i, vgarray in enumerate(obsvgarrays):
label = 'Observed dispersion curves' if not i else None
ax.plot(periods, vgarray, lw=0.5, color='k', label=label)
ax.set_xlabel('Period (sec)')
ax.set_ylabel('Group velocity (km/s)')
if legend:
ax.legend(loc='best', fontsize=11, framealpha=0.8)
ax.grid(True)
if fig:
fig.show()
def plot_model(self, ax=None, color='r', format_axes=True):
"""
Plots the model, i.e. Vs vs depth
"""
# creating figure if not given as input
fig = None
if not ax:
fig = plt.figure()
ax = fig.add_subplot(111)
x = list(it.chain.from_iterable([[v, v] for v in self.vs]))
y = [0.0] + list(it.chain.from_iterable([[z, z] for z in np.cumsum(self.dz)])) + \
[self.dz.sum() + 15]
ax.plot(x, y, lw=1.5, color=color)
if format_axes:
ax.set_ylim(sorted(ax.get_ylim(), reverse=True))
ax.set_xlabel('Vs (km/s)')
ax.set_ylabel('Depth (km)')
ax.grid(True)
if fig:
fig.show()
def Rayleigh_group_velocities(periods, dz, vp, vs, rho, verbose=False):
"""
Returns the array of Rayleigh wave group velocities at
selected periods, from the 1-D layered Earth model
contained in *dz* (thicknesses), *vp* (P wave velocities),
*vs* (S wave velocities) and *rho* (densities).
The Computer Programs in Seismology, located in dir
*COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR*,
are used for the computation.
"""
if not COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR:
raise Exception("Please provide the dir of the Computer Programs in Seismology")
# making and moving to temporary dir
current_dir = os.getcwd()
tmp_dir = tempfile.mkdtemp()
os.chdir(tmp_dir)
# preparing input files
if verbose:
print 'Preparing model and periods files'
create_model_file('model', dz, vp, vs, rho)
f = open('periods', 'w')
f.write('\n'.join([str(p) for p in periods]))
f.close()
# preparing model
if verbose:
print "Calling sprep96"
cmd = os.path.join(COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR, 'sprep96')
# Rayleigh wave, fundamental mode
p = EasyProcess('"{}" -M model -PARR periods -NMOD 1 -R'.format(cmd)).call()
if verbose:
print p.stdout
# phase dispersion curve
if verbose:
print "Calling sdisp96"
cmd = os.path.join(COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR, 'sdisp96')
p = EasyProcess('"{}" -v'.format(cmd)).call()
if verbose:
print p.stdout
# group dispersion curve
if verbose:
print "Calling sregn96"
cmd = os.path.join(COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR, 'sregn96')
p = EasyProcess('"{}"'.format(cmd)).call()
if verbose:
print p.stdout
# exporting group velocities (-U) of Rayleigh waves (-R) in ascii file
if verbose:
print "Calling sdpegn96"
cmd = os.path.join(COMPUTER_PROGRAMS_IN_SEISMOLOGY_DIR, 'sdpegn96')
p = EasyProcess('"{}" -R -S -U -XLOG -PER -ASC'.format(cmd)).call()
if verbose:
print p.stdout
# loading group velocities from 6th column of ascii file
vg = np.loadtxt('SREGN.ASC', skiprows=1, usecols=(5,))
# removing temp dir
os.chdir(current_dir)
shutil.rmtree(tmp_dir)
return vg
def create_model_file(path, dz, vp, vs, rho):
"""
Writing the 1D model to ascci file, to be used as input
by the Computer Programs in Seismology
"""
qp = np.zeros_like(dz)
qs = np.zeros_like(dz)
etap = np.zeros_like(dz)
etas = np.zeros_like(dz)
frefp = np.ones_like(dz)
frefs = np.ones_like(dz)
f = open(path, mode='w')
f.write(MODEL_HEADER)
a = np.vstack((dz, vp, vs, rho, qp, qs, etap, etas, frefp, frefs))
for col in a.T:
f.write('\n')
col.tofile(f, sep=' ')
f.close() | gpl-3.0 |
aringh/odl | examples/tomo/backends/astra_performance_cuda_parallel_2d_cg.py | 1 | 2880 | """Performance example of running native ASTRA vs using ODL for reconstruction.
In this example, a 512x512 image is reconstructed using the Conjugate Gradient
Least Squares method on the GPU.
In general, ASTRA is faster than ODL since it does not need to perform any
copies and all arithmetic is performed on the GPU. Despite this, ODL is not
much slower. In this example, the overhead is about 60 %, depending on the
hardware used.
"""
import astra
import numpy as np
import matplotlib.pyplot as plt
import scipy
import odl
# Common geometry parameters
domain_size = np.array([512, 512])
n_angles = 180
det_size = 362
niter = 50
phantom = np.rot90(scipy.misc.ascent().astype('float'), -1)
# --- ASTRA ---
# Define ASTRA geometry
vol_geom = astra.create_vol_geom(domain_size[0], domain_size[1])
proj_geom = astra.create_proj_geom('parallel',
np.linalg.norm(domain_size) / det_size,
det_size,
np.linspace(0, np.pi, n_angles))
# Create ASTRA projector
proj_id = astra.create_projector('cuda', proj_geom, vol_geom)
# Create sinogram
sinogram_id, sinogram = astra.create_sino(phantom, proj_id)
# Create a data object for the reconstruction
rec_id = astra.data2d.create('-vol', vol_geom)
# Set up the parameters for a reconstruction algorithm using the CUDA backend
cfg = astra.astra_dict('CGLS_CUDA')
cfg['ReconstructionDataId'] = rec_id
cfg['ProjectionDataId'] = sinogram_id
cfg['ProjectorId'] = proj_id
# Create the algorithm object from the configuration structure
alg_id = astra.algorithm.create(cfg)
with odl.util.Timer('ASTRA run'):
# Run the algorithm
astra.algorithm.run(alg_id, niter)
# Get the result
rec = astra.data2d.get(rec_id)
# Clean up.
astra.algorithm.delete(alg_id)
astra.data2d.delete(rec_id)
astra.data2d.delete(sinogram_id)
astra.projector.delete(proj_id)
# --- ODL ---
# Create reconstruction space
reco_space = odl.uniform_discr(-domain_size / 2, domain_size / 2, domain_size)
# Create geometry
geometry = odl.tomo.parallel_beam_geometry(reco_space, n_angles, det_size)
# Create ray transform
ray_trafo = odl.tomo.RayTransform(reco_space, geometry, impl='astra_cuda')
# Create sinogram
data = ray_trafo(phantom)
# Solve with CGLS (aka CGN)
x = reco_space.zero()
with odl.util.Timer('ODL run'):
odl.solvers.conjugate_gradient_normal(ray_trafo, x, data, niter=niter)
# Display results for comparison
plt.figure('Phantom')
plt.imshow(phantom.T, origin='lower', cmap='bone')
plt.figure('ASTRA sinogram')
plt.imshow(sinogram.T, origin='lower', cmap='bone')
plt.figure('ASTRA reconstruction')
plt.imshow(rec.T, origin='lower', cmap='bone')
plt.figure('ODL sinogram')
plt.imshow(data.asarray().T, origin='lower', cmap='bone')
plt.figure('ODL reconstruction')
plt.imshow(x.asarray().T, origin='lower', cmap='bone')
plt.show()
| mpl-2.0 |
mne-tools/mne-python | examples/connectivity/mne_inverse_connectivity_spectrum.py | 6 | 3460 | """
==============================================================
Compute full spectrum source space connectivity between labels
==============================================================
The connectivity is computed between 4 labels across the spectrum
between 7.5 Hz and 40 Hz.
"""
# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#
# License: BSD (3-clause)
import matplotlib.pyplot as plt
import mne
from mne.datasets import sample
from mne.minimum_norm import apply_inverse_epochs, read_inverse_operator
from mne.connectivity import spectral_connectivity
print(__doc__)
data_path = sample.data_path()
subjects_dir = data_path + '/subjects'
fname_inv = data_path + '/MEG/sample/sample_audvis-meg-oct-6-meg-inv.fif'
fname_raw = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'
fname_event = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif'
# Load data
inverse_operator = read_inverse_operator(fname_inv)
raw = mne.io.read_raw_fif(fname_raw)
events = mne.read_events(fname_event)
# Add a bad channel
raw.info['bads'] += ['MEG 2443']
# Pick MEG channels
picks = mne.pick_types(raw.info, meg=True, eeg=False, stim=False, eog=True,
exclude='bads')
# Define epochs for left-auditory condition
event_id, tmin, tmax = 1, -0.2, 0.5
epochs = mne.Epochs(raw, events, event_id, tmin, tmax, picks=picks,
baseline=(None, 0), reject=dict(mag=4e-12, grad=4000e-13,
eog=150e-6))
# Compute inverse solution and for each epoch. By using "return_generator=True"
# stcs will be a generator object instead of a list.
snr = 1.0 # use lower SNR for single epochs
lambda2 = 1.0 / snr ** 2
method = "dSPM" # use dSPM method (could also be MNE or sLORETA)
stcs = apply_inverse_epochs(epochs, inverse_operator, lambda2, method,
pick_ori="normal", return_generator=True)
# Read some labels
names = ['Aud-lh', 'Aud-rh', 'Vis-lh', 'Vis-rh']
labels = [mne.read_label(data_path + '/MEG/sample/labels/%s.label' % name)
for name in names]
# Average the source estimates within each label using sign-flips to reduce
# signal cancellations, also here we return a generator
src = inverse_operator['src']
label_ts = mne.extract_label_time_course(stcs, labels, src, mode='mean_flip',
return_generator=True)
fmin, fmax = 7.5, 40.
sfreq = raw.info['sfreq'] # the sampling frequency
con, freqs, times, n_epochs, n_tapers = spectral_connectivity(
label_ts, method='wpli2_debiased', mode='multitaper', sfreq=sfreq,
fmin=fmin, fmax=fmax, mt_adaptive=True, n_jobs=1)
n_rows, n_cols = con.shape[:2]
fig, axes = plt.subplots(n_rows, n_cols, sharex=True, sharey=True)
for i in range(n_rows):
for j in range(i + 1):
if i == j:
axes[i, j].set_axis_off()
continue
axes[i, j].plot(freqs, con[i, j, :])
axes[j, i].plot(freqs, con[i, j, :])
if j == 0:
axes[i, j].set_ylabel(names[i])
axes[0, i].set_title(names[i])
if i == (n_rows - 1):
axes[i, j].set_xlabel(names[j])
axes[i, j].set(xlim=[fmin, fmax], ylim=[-0.2, 1])
axes[j, i].set(xlim=[fmin, fmax], ylim=[-0.2, 1])
# Show band limits
for f in [8, 12, 18, 35]:
axes[i, j].axvline(f, color='k')
axes[j, i].axvline(f, color='k')
plt.tight_layout()
plt.show()
| bsd-3-clause |
buqing2009/MissionPlanner | Lib/site-packages/scipy/optimize/nonlin.py | 53 | 46004 | r"""
Nonlinear solvers
=================
.. currentmodule:: scipy.optimize
This is a collection of general-purpose nonlinear multidimensional
solvers. These solvers find *x* for which *F(x) = 0*. Both *x*
and *F* can be multidimensional.
Routines
--------
Large-scale nonlinear solvers:
.. autosummary::
newton_krylov
anderson
General nonlinear solvers:
.. autosummary::
broyden1
broyden2
Simple iterations:
.. autosummary::
excitingmixing
linearmixing
diagbroyden
Examples
========
Small problem
-------------
>>> def F(x):
... return np.cos(x) + x[::-1] - [1, 2, 3, 4]
>>> import scipy.optimize
>>> x = scipy.optimize.broyden1(F, [1,1,1,1], f_tol=1e-14)
>>> x
array([ 4.04674914, 3.91158389, 2.71791677, 1.61756251])
>>> np.cos(x) + x[::-1]
array([ 1., 2., 3., 4.])
Large problem
-------------
Suppose that we needed to solve the following integrodifferential
equation on the square :math:`[0,1]\times[0,1]`:
.. math::
\nabla^2 P = 10 \left(\int_0^1\int_0^1\cosh(P)\,dx\,dy\right)^2
with :math:`P(x,1) = 1` and :math:`P=0` elsewhere on the boundary of
the square.
The solution can be found using the `newton_krylov` solver:
.. plot::
import numpy as np
from scipy.optimize import newton_krylov
from numpy import cosh, zeros_like, mgrid, zeros
# parameters
nx, ny = 75, 75
hx, hy = 1./(nx-1), 1./(ny-1)
P_left, P_right = 0, 0
P_top, P_bottom = 1, 0
def residual(P):
d2x = zeros_like(P)
d2y = zeros_like(P)
d2x[1:-1] = (P[2:] - 2*P[1:-1] + P[:-2]) / hx/hx
d2x[0] = (P[1] - 2*P[0] + P_left)/hx/hx
d2x[-1] = (P_right - 2*P[-1] + P[-2])/hx/hx
d2y[:,1:-1] = (P[:,2:] - 2*P[:,1:-1] + P[:,:-2])/hy/hy
d2y[:,0] = (P[:,1] - 2*P[:,0] + P_bottom)/hy/hy
d2y[:,-1] = (P_top - 2*P[:,-1] + P[:,-2])/hy/hy
return d2x + d2y - 10*cosh(P).mean()**2
# solve
guess = zeros((nx, ny), float)
sol = newton_krylov(residual, guess, method='lgmres', verbose=1)
print 'Residual', abs(residual(sol)).max()
# visualize
import matplotlib.pyplot as plt
x, y = mgrid[0:1:(nx*1j), 0:1:(ny*1j)]
plt.pcolor(x, y, sol)
plt.colorbar()
plt.show()
"""
# Copyright (C) 2009, Pauli Virtanen <pav@iki.fi>
# Distributed under the same license as Scipy.
import sys
import numpy as np
from scipy.linalg import norm, solve, inv, qr, svd, lstsq, LinAlgError
from numpy import asarray, dot, vdot
if sys.platform != 'cli':
import scipy.sparse.linalg
import scipy.sparse
import scipy.lib.blas as blas
import inspect
else:
print "Warning: scipy.optimize.nonlin package is not supported under IronPython yet."
from linesearch import scalar_search_wolfe1, scalar_search_armijo
__all__ = [
'broyden1', 'broyden2', 'anderson', 'linearmixing',
'diagbroyden', 'excitingmixing', 'newton_krylov',
# Deprecated functions:
'broyden_generalized', 'anderson2', 'broyden3']
#------------------------------------------------------------------------------
# Utility functions
#------------------------------------------------------------------------------
class NoConvergence(Exception):
pass
def maxnorm(x):
return np.absolute(x).max()
def _as_inexact(x):
"""Return `x` as an array, of either floats or complex floats"""
x = asarray(x)
if not np.issubdtype(x.dtype, np.inexact):
return asarray(x, dtype=np.float_)
return x
def _array_like(x, x0):
"""Return ndarray `x` as same array subclass and shape as `x0`"""
x = np.reshape(x, np.shape(x0))
wrap = getattr(x0, '__array_wrap__', x.__array_wrap__)
return wrap(x)
def _safe_norm(v):
if not np.isfinite(v).all():
return np.array(np.inf)
return norm(v)
#------------------------------------------------------------------------------
# Generic nonlinear solver machinery
#------------------------------------------------------------------------------
_doc_parts = dict(
params_basic="""
F : function(x) -> f
Function whose root to find; should take and return an array-like
object.
x0 : array-like
Initial guess for the solution
""".strip(),
params_extra="""
iter : int, optional
Number of iterations to make. If omitted (default), make as many
as required to meet tolerances.
verbose : bool, optional
Print status to stdout on every iteration.
maxiter : int, optional
Maximum number of iterations to make. If more are needed to
meet convergence, `NoConvergence` is raised.
f_tol : float, optional
Absolute tolerance (in max-norm) for the residual.
If omitted, default is 6e-6.
f_rtol : float, optional
Relative tolerance for the residual. If omitted, not used.
x_tol : float, optional
Absolute minimum step size, as determined from the Jacobian
approximation. If the step size is smaller than this, optimization
is terminated as successful. If omitted, not used.
x_rtol : float, optional
Relative minimum step size. If omitted, not used.
tol_norm : function(vector) -> scalar, optional
Norm to use in convergence check. Default is the maximum norm.
line_search : {None, 'armijo' (default), 'wolfe'}, optional
Which type of a line search to use to determine the step size in the
direction given by the Jacobian approximation. Defaults to 'armijo'.
callback : function, optional
Optional callback function. It is called on every iteration as
``callback(x, f)`` where `x` is the current solution and `f`
the corresponding residual.
Returns
-------
sol : array-like
An array (of similar array type as `x0`) containing the final solution.
Raises
------
NoConvergence
When a solution was not found.
""".strip()
)
def _set_doc(obj):
if obj.__doc__:
obj.__doc__ = obj.__doc__ % _doc_parts
def nonlin_solve(F, x0, jacobian='krylov', iter=None, verbose=False,
maxiter=None, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None,
tol_norm=None, line_search='armijo', callback=None):
"""
Find a root of a function, in a way suitable for large-scale problems.
Parameters
----------
%(params_basic)s
jacobian : Jacobian
A Jacobian approximation: `Jacobian` object or something that
`asjacobian` can transform to one. Alternatively, a string specifying
which of the builtin Jacobian approximations to use:
krylov, broyden1, broyden2, anderson
diagbroyden, linearmixing, excitingmixing
%(params_extra)s
See Also
--------
asjacobian, Jacobian
Notes
-----
This algorithm implements the inexact Newton method, with
backtracking or full line searches. Several Jacobian
approximations are available, including Krylov and Quasi-Newton
methods.
References
----------
.. [KIM] C. T. Kelley, \"Iterative Methods for Linear and Nonlinear
Equations\". Society for Industrial and Applied Mathematics. (1995)
http://www.siam.org/books/kelley/
"""
condition = TerminationCondition(f_tol=f_tol, f_rtol=f_rtol,
x_tol=x_tol, x_rtol=x_rtol,
iter=iter, norm=tol_norm)
x0 = _as_inexact(x0)
func = lambda z: _as_inexact(F(_array_like(z, x0))).flatten()
x = x0.flatten()
dx = np.inf
Fx = func(x)
Fx_norm = norm(Fx)
jacobian = asjacobian(jacobian)
jacobian.setup(x.copy(), Fx, func)
if maxiter is None:
if iter is not None:
maxiter = iter + 1
else:
maxiter = 100*(x.size+1)
if line_search is True:
line_search = 'armijo'
elif line_search is False:
line_search = None
if line_search not in (None, 'armijo', 'wolfe'):
raise ValueError("Invalid line search")
# Solver tolerance selection
gamma = 0.9
eta_max = 0.9999
eta_treshold = 0.1
eta = 1e-3
for n in xrange(maxiter):
if condition.check(Fx, x, dx):
break
# The tolerance, as computed for scipy.sparse.linalg.* routines
tol = min(eta, eta*Fx_norm)
dx = -jacobian.solve(Fx, tol=tol)
if norm(dx) == 0:
raise ValueError("Jacobian inversion yielded zero vector. "
"This indicates a bug in the Jacobian "
"approximation.")
# Line search, or Newton step
if line_search:
s, x, Fx, Fx_norm_new = _nonlin_line_search(func, x, Fx, dx,
line_search)
else:
s = 1.0
x += dx
Fx = func(x)
Fx_norm_new = norm(Fx)
jacobian.update(x.copy(), Fx)
if callback:
callback(x, Fx)
# Adjust forcing parameters for inexact methods
eta_A = gamma * Fx_norm_new**2 / Fx_norm**2
if gamma * eta**2 < eta_treshold:
eta = min(eta_max, eta_A)
else:
eta = min(eta_max, max(eta_A, gamma*eta**2))
Fx_norm = Fx_norm_new
# Print status
if verbose:
sys.stdout.write("%d: |F(x)| = %g; step %g; tol %g\n" % (
n, norm(Fx), s, eta))
sys.stdout.flush()
else:
raise NoConvergence(_array_like(x, x0))
return _array_like(x, x0)
_set_doc(nonlin_solve)
def _nonlin_line_search(func, x, Fx, dx, search_type='armijo', rdiff=1e-8,
smin=1e-2):
tmp_s = [0]
tmp_Fx = [Fx]
tmp_phi = [norm(Fx)**2]
s_norm = norm(x) / norm(dx)
def phi(s, store=True):
if s == tmp_s[0]:
return tmp_phi[0]
xt = x + s*dx
v = func(xt)
p = _safe_norm(v)**2
if store:
tmp_s[0] = s
tmp_phi[0] = p
tmp_Fx[0] = v
return p
def derphi(s):
ds = (abs(s) + s_norm + 1) * rdiff
return (phi(s+ds, store=False) - phi(s)) / ds
if search_type == 'wolfe':
s, phi1, phi0 = scalar_search_wolfe1(phi, derphi, tmp_phi[0],
xtol=1e-2, amin=smin)
elif search_type == 'armijo':
s, phi1 = scalar_search_armijo(phi, tmp_phi[0], -tmp_phi[0],
amin=smin)
if s is None:
# XXX: No suitable step length found. Take the full Newton step,
# and hope for the best.
s = 1.0
x = x + s*dx
if s == tmp_s[0]:
Fx = tmp_Fx[0]
else:
Fx = func(x)
Fx_norm = norm(Fx)
return s, x, Fx, Fx_norm
class TerminationCondition(object):
"""
Termination condition for an iteration. It is terminated if
- |F| < f_rtol*|F_0|, AND
- |F| < f_tol
AND
- |dx| < x_rtol*|x|, AND
- |dx| < x_tol
"""
def __init__(self, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None,
iter=None, norm=maxnorm):
if f_tol is None:
f_tol = np.finfo(np.float_).eps ** (1./3)
if f_rtol is None:
f_rtol = np.inf
if x_tol is None:
x_tol = np.inf
if x_rtol is None:
x_rtol = np.inf
self.x_tol = x_tol
self.x_rtol = x_rtol
self.f_tol = f_tol
self.f_rtol = f_rtol
self.norm = maxnorm
self.iter = iter
self.f0_norm = None
self.iteration = 0
def check(self, f, x, dx):
self.iteration += 1
f_norm = self.norm(f)
x_norm = self.norm(x)
dx_norm = self.norm(dx)
if self.f0_norm is None:
self.f0_norm = f_norm
if f_norm == 0:
return True
if self.iter is not None:
# backwards compatibility with Scipy 0.6.0
return self.iteration > self.iter
# NB: condition must succeed for rtol=inf even if norm == 0
return ((f_norm <= self.f_tol and f_norm/self.f_rtol <= self.f0_norm)
and (dx_norm <= self.x_tol and dx_norm/self.x_rtol <= x_norm))
#------------------------------------------------------------------------------
# Generic Jacobian approximation
#------------------------------------------------------------------------------
class Jacobian(object):
"""
Common interface for Jacobians or Jacobian approximations.
The optional methods come useful when implementing trust region
etc. algorithms that often require evaluating transposes of the
Jacobian.
Methods
-------
solve
Returns J^-1 * v
update
Updates Jacobian to point `x` (where the function has residual `Fx`)
matvec : optional
Returns J * v
rmatvec : optional
Returns A^H * v
rsolve : optional
Returns A^-H * v
matmat : optional
Returns A * V, where V is a dense matrix with dimensions (N,K).
todense : optional
Form the dense Jacobian matrix. Necessary for dense trust region
algorithms, and useful for testing.
Attributes
----------
shape
Matrix dimensions (M, N)
dtype
Data type of the matrix.
func : callable, optional
Function the Jacobian corresponds to
"""
def __init__(self, **kw):
names = ["solve", "update", "matvec", "rmatvec", "rsolve",
"matmat", "todense", "shape", "dtype"]
for name, value in kw.items():
if name not in names:
raise ValueError("Unknown keyword argument %s" % name)
if value is not None:
setattr(self, name, kw[name])
if hasattr(self, 'todense'):
self.__array__ = lambda: self.todense()
def aspreconditioner(self):
return InverseJacobian(self)
def solve(self, v, tol=0):
raise NotImplementedError
def update(self, x, F):
pass
def setup(self, x, F, func):
self.func = func
self.shape = (F.size, x.size)
self.dtype = F.dtype
if self.__class__.setup is Jacobian.setup:
# Call on the first point unless overridden
self.update(self, x, F)
class InverseJacobian(object):
def __init__(self, jacobian):
self.jacobian = jacobian
self.matvec = jacobian.solve
self.update = jacobian.update
if hasattr(jacobian, 'setup'):
self.setup = jacobian.setup
if hasattr(jacobian, 'rsolve'):
self.rmatvec = jacobian.rsolve
@property
def shape(self):
return self.jacobian.shape
@property
def dtype(self):
return self.jacobian.dtype
def asjacobian(J):
"""
Convert given object to one suitable for use as a Jacobian.
"""
spsolve = scipy.sparse.linalg.spsolve
if isinstance(J, Jacobian):
return J
elif inspect.isclass(J) and issubclass(J, Jacobian):
return J()
elif isinstance(J, np.ndarray):
if J.ndim > 2:
raise ValueError('array must have rank <= 2')
J = np.atleast_2d(np.asarray(J))
if J.shape[0] != J.shape[1]:
raise ValueError('array must be square')
return Jacobian(matvec=lambda v: dot(J, v),
rmatvec=lambda v: dot(J.conj().T, v),
solve=lambda v: solve(J, v),
rsolve=lambda v: solve(J.conj().T, v),
dtype=J.dtype, shape=J.shape)
elif scipy.sparse.isspmatrix(J):
if J.shape[0] != J.shape[1]:
raise ValueError('matrix must be square')
return Jacobian(matvec=lambda v: J*v,
rmatvec=lambda v: J.conj().T * v,
solve=lambda v: spsolve(J, v),
rsolve=lambda v: spsolve(J.conj().T, v),
dtype=J.dtype, shape=J.shape)
elif hasattr(J, 'shape') and hasattr(J, 'dtype') and hasattr(J, 'solve'):
return Jacobian(matvec=getattr(J, 'matvec'),
rmatvec=getattr(J, 'rmatvec'),
solve=J.solve,
rsolve=getattr(J, 'rsolve'),
update=getattr(J, 'update'),
setup=getattr(J, 'setup'),
dtype=J.dtype,
shape=J.shape)
elif callable(J):
# Assume it's a function J(x) that returns the Jacobian
class Jac(Jacobian):
def update(self, x, F):
self.x = x
def solve(self, v, tol=0):
m = J(self.x)
if isinstance(m, np.ndarray):
return solve(m, v)
elif scipy.sparse.isspmatrix(m):
return spsolve(m, v)
else:
raise ValueError("Unknown matrix type")
def matvec(self, v):
m = J(self.x)
if isinstance(m, np.ndarray):
return dot(m, v)
elif scipy.sparse.isspmatrix(m):
return m*v
else:
raise ValueError("Unknown matrix type")
def rsolve(self, v, tol=0):
m = J(self.x)
if isinstance(m, np.ndarray):
return solve(m.conj().T, v)
elif scipy.sparse.isspmatrix(m):
return spsolve(m.conj().T, v)
else:
raise ValueError("Unknown matrix type")
def rmatvec(self, v):
m = J(self.x)
if isinstance(m, np.ndarray):
return dot(m.conj().T, v)
elif scipy.sparse.isspmatrix(m):
return m.conj().T * v
else:
raise ValueError("Unknown matrix type")
return Jac()
elif isinstance(J, str):
return dict(broyden1=BroydenFirst,
broyden2=BroydenSecond,
anderson=Anderson,
diagbroyden=DiagBroyden,
linearmixing=LinearMixing,
excitingmixing=ExcitingMixing,
krylov=KrylovJacobian)[J]()
else:
raise TypeError('Cannot convert object to a Jacobian')
#------------------------------------------------------------------------------
# Broyden
#------------------------------------------------------------------------------
class GenericBroyden(Jacobian):
def setup(self, x0, f0, func):
Jacobian.setup(self, x0, f0, func)
self.last_f = f0
self.last_x = x0
if hasattr(self, 'alpha') and self.alpha is None:
# autoscale the initial Jacobian parameter
self.alpha = 0.5*max(norm(x0), 1) / norm(f0)
def _update(self, x, f, dx, df, dx_norm, df_norm):
raise NotImplementedError
def update(self, x, f):
df = f - self.last_f
dx = x - self.last_x
self._update(x, f, dx, df, norm(dx), norm(df))
self.last_f = f
self.last_x = x
class LowRankMatrix(object):
r"""
A matrix represented as
.. math:: \alpha I + \sum_{n=0}^{n=M} c_n d_n^\dagger
However, if the rank of the matrix reaches the dimension of the vectors,
full matrix representation will be used thereon.
"""
def __init__(self, alpha, n, dtype):
self.alpha = alpha
self.cs = []
self.ds = []
self.n = n
self.dtype = dtype
self.collapsed = None
@staticmethod
def _matvec(v, alpha, cs, ds):
axpy, scal, dotc = blas.get_blas_funcs(['axpy', 'scal', 'dotc'],
cs[:1] + [v])
w = alpha * v
for c, d in zip(cs, ds):
a = dotc(d, v)
w = axpy(c, w, w.size, a)
return w
@staticmethod
def _solve(v, alpha, cs, ds):
"""Evaluate w = M^-1 v"""
if len(cs) == 0:
return v/alpha
# (B + C D^H)^-1 = B^-1 - B^-1 C (I + D^H B^-1 C)^-1 D^H B^-1
axpy, dotc = blas.get_blas_funcs(['axpy', 'dotc'], cs[:1] + [v])
c0 = cs[0]
A = alpha * np.identity(len(cs), dtype=c0.dtype)
for i, d in enumerate(ds):
for j, c in enumerate(cs):
A[i,j] += dotc(d, c)
q = np.zeros(len(cs), dtype=c0.dtype)
for j, d in enumerate(ds):
q[j] = dotc(d, v)
q /= alpha
q = solve(A, q)
w = v/alpha
for c, qc in zip(cs, q):
w = axpy(c, w, w.size, -qc)
return w
def matvec(self, v):
"""Evaluate w = M v"""
if self.collapsed is not None:
return np.dot(self.collapsed, v)
return LowRankMatrix._matvec(v, self.alpha, self.cs, self.ds)
def rmatvec(self, v):
"""Evaluate w = M^H v"""
if self.collapsed is not None:
return np.dot(self.collapsed.T.conj(), v)
return LowRankMatrix._matvec(v, np.conj(self.alpha), self.ds, self.cs)
def solve(self, v, tol=0):
"""Evaluate w = M^-1 v"""
if self.collapsed is not None:
return solve(self.collapsed, v)
return LowRankMatrix._solve(v, self.alpha, self.cs, self.ds)
def rsolve(self, v, tol=0):
"""Evaluate w = M^-H v"""
if self.collapsed is not None:
return solve(self.collapsed.T.conj(), v)
return LowRankMatrix._solve(v, np.conj(self.alpha), self.ds, self.cs)
def append(self, c, d):
if self.collapsed is not None:
self.collapsed += c[:,None] * d[None,:].conj()
return
self.cs.append(c)
self.ds.append(d)
if len(self.cs) > c.size:
self.collapse()
def __array__(self):
if self.collapsed is not None:
return self.collapsed
Gm = self.alpha*np.identity(self.n, dtype=self.dtype)
for c, d in zip(self.cs, self.ds):
Gm += c[:,None]*d[None,:].conj()
return Gm
def collapse(self):
"""Collapse the low-rank matrix to a full-rank one."""
self.collapsed = np.array(self)
self.cs = None
self.ds = None
self.alpha = None
def restart_reduce(self, rank):
"""
Reduce the rank of the matrix by dropping all vectors.
"""
if self.collapsed is not None:
return
assert rank > 0
if len(self.cs) > rank:
del self.cs[:]
del self.ds[:]
def simple_reduce(self, rank):
"""
Reduce the rank of the matrix by dropping oldest vectors.
"""
if self.collapsed is not None:
return
assert rank > 0
while len(self.cs) > rank:
del self.cs[0]
del self.ds[0]
def svd_reduce(self, max_rank, to_retain=None):
"""
Reduce the rank of the matrix by retaining some SVD components.
This corresponds to the \"Broyden Rank Reduction Inverse\"
algorithm described in [vR]_.
Note that the SVD decomposition can be done by solving only a
problem whose size is the effective rank of this matrix, which
is viable even for large problems.
Parameters
----------
max_rank : int
Maximum rank of this matrix after reduction.
to_retain : int, optional
Number of SVD components to retain when reduction is done
(ie. rank > max_rank). Default is ``max_rank - 2``.
References
----------
.. [vR] B.A. van der Rotten, PhD thesis,
\"A limited memory Broyden method to solve high-dimensional
systems of nonlinear equations\". Mathematisch Instituut,
Universiteit Leiden, The Netherlands (2003).
http://www.math.leidenuniv.nl/scripties/Rotten.pdf
"""
if self.collapsed is not None:
return
p = max_rank
if to_retain is not None:
q = to_retain
else:
q = p - 2
if self.cs:
p = min(p, len(self.cs[0]))
q = max(0, min(q, p-1))
m = len(self.cs)
if m < p:
# nothing to do
return
C = np.array(self.cs).T
D = np.array(self.ds).T
D, R = qr(D, mode='qr', econ=True)
C = dot(C, R.T.conj())
U, S, WH = svd(C, full_matrices=False, compute_uv=True)
C = dot(C, inv(WH))
D = dot(D, WH.T.conj())
for k in xrange(q):
self.cs[k] = C[:,k].copy()
self.ds[k] = D[:,k].copy()
del self.cs[q:]
del self.ds[q:]
_doc_parts['broyden_params'] = """
alpha : float, optional
Initial guess for the Jacobian is (-1/alpha).
reduction_method : str or tuple, optional
Method used in ensuring that the rank of the Broyden matrix
stays low. Can either be a string giving the name of the method,
or a tuple of the form ``(method, param1, param2, ...)``
that gives the name of the method and values for additional parameters.
Methods available:
- ``restart``: drop all matrix columns. Has no extra parameters.
- ``simple``: drop oldest matrix column. Has no extra parameters.
- ``svd``: keep only the most significant SVD components.
Extra parameters:
- ``to_retain`: number of SVD components to retain when
rank reduction is done. Default is ``max_rank - 2``.
max_rank : int, optional
Maximum rank for the Broyden matrix.
Default is infinity (ie., no rank reduction).
""".strip()
class BroydenFirst(GenericBroyden):
r"""
Find a root of a function, using Broyden's first Jacobian approximation.
This method is also known as \"Broyden's good method\".
Parameters
----------
%(params_basic)s
%(broyden_params)s
%(params_extra)s
Notes
-----
This algorithm implements the inverse Jacobian Quasi-Newton update
.. math:: H_+ = H + (dx - H df) dx^\dagger H / ( dx^\dagger H df)
which corresponds to Broyden's first Jacobian update
.. math:: J_+ = J + (df - J dx) dx^\dagger / dx^\dagger dx
References
----------
.. [vR] B.A. van der Rotten, PhD thesis,
\"A limited memory Broyden method to solve high-dimensional
systems of nonlinear equations\". Mathematisch Instituut,
Universiteit Leiden, The Netherlands (2003).
http://www.math.leidenuniv.nl/scripties/Rotten.pdf
"""
def __init__(self, alpha=None, reduction_method='restart', max_rank=None):
GenericBroyden.__init__(self)
self.alpha = alpha
self.Gm = None
if max_rank is None:
max_rank = np.inf
self.max_rank = max_rank
if isinstance(reduction_method, str):
reduce_params = ()
else:
reduce_params = reduction_method[1:]
reduction_method = reduction_method[0]
reduce_params = (max_rank - 1,) + reduce_params
if reduction_method == 'svd':
self._reduce = lambda: self.Gm.svd_reduce(*reduce_params)
elif reduction_method == 'simple':
self._reduce = lambda: self.Gm.simple_reduce(*reduce_params)
elif reduction_method == 'restart':
self._reduce = lambda: self.Gm.restart_reduce(*reduce_params)
else:
raise ValueError("Unknown rank reduction method '%s'" %
reduction_method)
def setup(self, x, F, func):
GenericBroyden.setup(self, x, F, func)
self.Gm = LowRankMatrix(-self.alpha, self.shape[0], self.dtype)
def todense(self):
return inv(self.Gm)
def solve(self, f, tol=0):
r = self.Gm.matvec(f)
if not np.isfinite(r).all():
# singular; reset the Jacobian approximation
self.setup(self.last_x, self.last_f, self.func)
return self.Gm.matvec(f)
def matvec(self, f):
return self.Gm.solve(f)
def rsolve(self, f, tol=0):
return self.Gm.rmatvec(f)
def rmatvec(self, f):
return self.Gm.rsolve(f)
def _update(self, x, f, dx, df, dx_norm, df_norm):
self._reduce() # reduce first to preserve secant condition
v = self.Gm.rmatvec(dx)
c = dx - self.Gm.matvec(df)
d = v / vdot(df, v)
self.Gm.append(c, d)
class BroydenSecond(BroydenFirst):
"""
Find a root of a function, using Broyden\'s second Jacobian approximation.
This method is also known as \"Broyden's bad method\".
Parameters
----------
%(params_basic)s
%(broyden_params)s
%(params_extra)s
Notes
-----
This algorithm implements the inverse Jacobian Quasi-Newton update
.. math:: H_+ = H + (dx - H df) df^\dagger / ( df^\dagger df)
corresponding to Broyden's second method.
References
----------
.. [vR] B.A. van der Rotten, PhD thesis,
\"A limited memory Broyden method to solve high-dimensional
systems of nonlinear equations\". Mathematisch Instituut,
Universiteit Leiden, The Netherlands (2003).
http://www.math.leidenuniv.nl/scripties/Rotten.pdf
"""
def _update(self, x, f, dx, df, dx_norm, df_norm):
self._reduce() # reduce first to preserve secant condition
v = df
c = dx - self.Gm.matvec(df)
d = v / df_norm**2
self.Gm.append(c, d)
#------------------------------------------------------------------------------
# Broyden-like (restricted memory)
#------------------------------------------------------------------------------
class Anderson(GenericBroyden):
"""
Find a root of a function, using (extended) Anderson mixing.
The Jacobian is formed by for a 'best' solution in the space
spanned by last `M` vectors. As a result, only a MxM matrix
inversions and MxN multiplications are required. [Ey]_
Parameters
----------
%(params_basic)s
alpha : float, optional
Initial guess for the Jacobian is (-1/alpha).
M : float, optional
Number of previous vectors to retain. Defaults to 5.
w0 : float, optional
Regularization parameter for numerical stability.
Compared to unity, good values of the order of 0.01.
%(params_extra)s
References
----------
.. [Ey] V. Eyert, J. Comp. Phys., 124, 271 (1996).
"""
# Note:
#
# Anderson method maintains a rank M approximation of the inverse Jacobian,
#
# J^-1 v ~ -v*alpha + (dX + alpha dF) A^-1 dF^H v
# A = W + dF^H dF
# W = w0^2 diag(dF^H dF)
#
# so that for w0 = 0 the secant condition applies for last M iterates, ie.,
#
# J^-1 df_j = dx_j
#
# for all j = 0 ... M-1.
#
# Moreover, (from Sherman-Morrison-Woodbury formula)
#
# J v ~ [ b I - b^2 C (I + b dF^H A^-1 C)^-1 dF^H ] v
# C = (dX + alpha dF) A^-1
# b = -1/alpha
#
# and after simplification
#
# J v ~ -v/alpha + (dX/alpha + dF) (dF^H dX - alpha W)^-1 dF^H v
#
def __init__(self, alpha=None, w0=0.01, M=5):
GenericBroyden.__init__(self)
self.alpha = alpha
self.M = M
self.dx = []
self.df = []
self.gamma = None
self.w0 = w0
def solve(self, f, tol=0):
dx = -self.alpha*f
n = len(self.dx)
if n == 0:
return dx
df_f = np.empty(n, dtype=f.dtype)
for k in xrange(n):
df_f[k] = vdot(self.df[k], f)
try:
gamma = solve(self.a, df_f)
except LinAlgError:
# singular; reset the Jacobian approximation
del self.dx[:]
del self.df[:]
return dx
for m in xrange(n):
dx += gamma[m]*(self.dx[m] + self.alpha*self.df[m])
return dx
def matvec(self, f):
dx = -f/self.alpha
n = len(self.dx)
if n == 0:
return dx
df_f = np.empty(n, dtype=f.dtype)
for k in xrange(n):
df_f[k] = vdot(self.df[k], f)
b = np.empty((n, n), dtype=f.dtype)
for i in xrange(n):
for j in xrange(n):
b[i,j] = vdot(self.df[i], self.dx[j])
if i == j and self.w0 != 0:
b[i,j] -= vdot(self.df[i], self.df[i])*self.w0**2*self.alpha
gamma = solve(b, df_f)
for m in xrange(n):
dx += gamma[m]*(self.df[m] + self.dx[m]/self.alpha)
return dx
def _update(self, x, f, dx, df, dx_norm, df_norm):
if self.M == 0:
return
self.dx.append(dx)
self.df.append(df)
while len(self.dx) > self.M:
self.dx.pop(0)
self.df.pop(0)
n = len(self.dx)
a = np.zeros((n, n), dtype=f.dtype)
for i in xrange(n):
for j in xrange(i, n):
if i == j:
wd = self.w0**2
else:
wd = 0
a[i,j] = (1+wd)*vdot(self.df[i], self.df[j])
a += np.triu(a, 1).T.conj()
self.a = a
#------------------------------------------------------------------------------
# Simple iterations
#------------------------------------------------------------------------------
class DiagBroyden(GenericBroyden):
"""
Find a root of a function, using diagonal Broyden Jacobian approximation.
The Jacobian approximation is derived from previous iterations, by
retaining only the diagonal of Broyden matrices.
.. warning::
This algorithm may be useful for specific problems, but whether
it will work may depend strongly on the problem.
Parameters
----------
%(params_basic)s
alpha : float, optional
Initial guess for the Jacobian is (-1/alpha).
%(params_extra)s
"""
def __init__(self, alpha=None):
GenericBroyden.__init__(self)
self.alpha = alpha
def setup(self, x, F, func):
GenericBroyden.setup(self, x, F, func)
self.d = np.ones((self.shape[0],), dtype=self.dtype) / self.alpha
def solve(self, f, tol=0):
return -f / self.d
def matvec(self, f):
return -f * self.d
def rsolve(self, f, tol=0):
return -f / self.d.conj()
def rmatvec(self, f):
return -f * self.d.conj()
def todense(self):
return np.diag(-self.d)
def _update(self, x, f, dx, df, dx_norm, df_norm):
self.d -= (df + self.d*dx)*dx/dx_norm**2
class LinearMixing(GenericBroyden):
"""
Find a root of a function, using a scalar Jacobian approximation.
.. warning::
This algorithm may be useful for specific problems, but whether
it will work may depend strongly on the problem.
Parameters
----------
%(params_basic)s
alpha : float, optional
The Jacobian approximation is (-1/alpha).
%(params_extra)s
"""
def __init__(self, alpha=None):
GenericBroyden.__init__(self)
self.alpha = alpha
def solve(self, f, tol=0):
return -f*self.alpha
def matvec(self, f):
return -f/self.alpha
def rsolve(self, f, tol=0):
return -f*np.conj(self.alpha)
def rmatvec(self, f):
return -f/np.conj(self.alpha)
def todense(self):
return np.diag(-np.ones(self.shape[0])/self.alpha)
def _update(self, x, f, dx, df, dx_norm, df_norm):
pass
class ExcitingMixing(GenericBroyden):
"""
Find a root of a function, using a tuned diagonal Jacobian approximation.
The Jacobian matrix is diagonal and is tuned on each iteration.
.. warning::
This algorithm may be useful for specific problems, but whether
it will work may depend strongly on the problem.
Parameters
----------
%(params_basic)s
alpha : float, optional
Initial Jacobian approximation is (-1/alpha).
alphamax : float, optional
The entries of the diagonal Jacobian are kept in the range
``[alpha, alphamax]``.
%(params_extra)s
"""
def __init__(self, alpha=None, alphamax=1.0):
GenericBroyden.__init__(self)
self.alpha = alpha
self.alphamax = alphamax
self.beta = None
def setup(self, x, F, func):
GenericBroyden.setup(self, x, F, func)
self.beta = self.alpha * np.ones((self.shape[0],), dtype=self.dtype)
def solve(self, f, tol=0):
return -f*self.beta
def matvec(self, f):
return -f/self.beta
def rsolve(self, f, tol=0):
return -f*self.beta.conj()
def rmatvec(self, f):
return -f/self.beta.conj()
def todense(self):
return np.diag(-1/self.beta)
def _update(self, x, f, dx, df, dx_norm, df_norm):
incr = f*self.last_f > 0
self.beta[incr] += self.alpha
self.beta[~incr] = self.alpha
np.clip(self.beta, 0, self.alphamax, out=self.beta)
#------------------------------------------------------------------------------
# Iterative/Krylov approximated Jacobians
#------------------------------------------------------------------------------
class KrylovJacobian(Jacobian):
r"""
Find a root of a function, using Krylov approximation for inverse Jacobian.
This method is suitable for solving large-scale problems.
Parameters
----------
%(params_basic)s
rdiff : float, optional
Relative step size to use in numerical differentiation.
method : {'lgmres', 'gmres', 'bicgstab', 'cgs', 'minres'} or function
Krylov method to use to approximate the Jacobian.
Can be a string, or a function implementing the same interface as
the iterative solvers in `scipy.sparse.linalg`.
The default is `scipy.sparse.linalg.lgmres`.
inner_M : LinearOperator or InverseJacobian
Preconditioner for the inner Krylov iteration.
Note that you can use also inverse Jacobians as (adaptive)
preconditioners. For example,
>>> jac = BroydenFirst()
>>> kjac = KrylovJacobian(inner_M=jac.inverse).
If the preconditioner has a method named 'update', it will be called
as ``update(x, f)`` after each nonlinear step, with ``x`` giving
the current point, and ``f`` the current function value.
inner_tol, inner_maxiter, ...
Parameters to pass on to the \"inner\" Krylov solver.
See `scipy.sparse.linalg.gmres` for details.
outer_k : int, optional
Size of the subspace kept across LGMRES nonlinear iterations.
See `scipy.sparse.linalg.lgmres` for details.
%(params_extra)s
See Also
--------
scipy.sparse.linalg.gmres
scipy.sparse.linalg.lgmres
Notes
-----
This function implements a Newton-Krylov solver. The basic idea is
to compute the inverse of the Jacobian with an iterative Krylov
method. These methods require only evaluating the Jacobian-vector
products, which are conveniently approximated by numerical
differentiation:
.. math:: J v \approx (f(x + \omega*v/|v|) - f(x)) / \omega
Due to the use of iterative matrix inverses, these methods can
deal with large nonlinear problems.
Scipy's `scipy.sparse.linalg` module offers a selection of Krylov
solvers to choose from. The default here is `lgmres`, which is a
variant of restarted GMRES iteration that reuses some of the
information obtained in the previous Newton steps to invert
Jacobians in subsequent steps.
For a review on Newton-Krylov methods, see for example [KK]_,
and for the LGMRES sparse inverse method, see [BJM]_.
References
----------
.. [KK] D.A. Knoll and D.E. Keyes, J. Comp. Phys. 193, 357 (2003).
.. [BJM] A.H. Baker and E.R. Jessup and T. Manteuffel,
SIAM J. Matrix Anal. Appl. 26, 962 (2005).
"""
def __init__(self, rdiff=None, method='lgmres', inner_maxiter=20,
inner_M=None, outer_k=10, **kw):
self.preconditioner = inner_M
self.rdiff = rdiff
self.method = dict(
bicgstab=scipy.sparse.linalg.bicgstab,
gmres=scipy.sparse.linalg.gmres,
lgmres=scipy.sparse.linalg.lgmres,
cgs=scipy.sparse.linalg.cgs,
minres=scipy.sparse.linalg.minres,
).get(method, method)
self.method_kw = dict(maxiter=inner_maxiter, M=self.preconditioner)
if self.method is scipy.sparse.linalg.gmres:
# Replace GMRES's outer iteration with Newton steps
self.method_kw['restrt'] = inner_maxiter
self.method_kw['maxiter'] = 1
elif self.method is scipy.sparse.linalg.lgmres:
self.method_kw['outer_k'] = outer_k
# Replace LGMRES's outer iteration with Newton steps
self.method_kw['maxiter'] = 1
# Carry LGMRES's `outer_v` vectors across nonlinear iterations
self.method_kw.setdefault('outer_v', [])
# But don't carry the corresponding Jacobian*v products, in case
# the Jacobian changes a lot in the nonlinear step
#
# XXX: some trust-region inspired ideas might be more efficient...
# See eg. Brown & Saad. But needs to be implemented separately
# since it's not an inexact Newton method.
self.method_kw.setdefault('store_outer_Av', False)
for key, value in kw.items():
if not key.startswith('inner_'):
raise ValueError("Unknown parameter %s" % key)
self.method_kw[key[6:]] = value
def _update_diff_step(self):
mx = abs(self.x0).max()
mf = abs(self.f0).max()
self.omega = self.rdiff * max(1, mx) / max(1, mf)
def matvec(self, v):
nv = norm(v)
if nv == 0:
return 0*v
sc = self.omega / nv
r = (self.func(self.x0 + sc*v) - self.f0) / sc
if not np.all(np.isfinite(r)) and np.all(np.isfinite(v)):
raise ValueError('Function returned non-finite results')
return r
def solve(self, rhs, tol=0):
sol, info = self.method(self.op, rhs, tol=tol, **self.method_kw)
return sol
def update(self, x, f):
self.x0 = x
self.f0 = f
self._update_diff_step()
# Update also the preconditioner, if possible
if self.preconditioner is not None:
if hasattr(self.preconditioner, 'update'):
self.preconditioner.update(x, f)
def setup(self, x, f, func):
Jacobian.setup(self, x, f, func)
self.x0 = x
self.f0 = f
self.op = scipy.sparse.linalg.aslinearoperator(self)
if self.rdiff is None:
self.rdiff = np.finfo(x.dtype).eps ** (1./2)
self._update_diff_step()
# Setup also the preconditioner, if possible
if self.preconditioner is not None:
if hasattr(self.preconditioner, 'setup'):
self.preconditioner.setup(x, f, func)
#------------------------------------------------------------------------------
# Wrapper functions
#------------------------------------------------------------------------------
def _nonlin_wrapper(name, jac):
"""
Construct a solver wrapper with given name and jacobian approx.
It inspects the keyword arguments of ``jac.__init__``, and allows to
use the same arguments in the wrapper function, in addition to the
keyword arguments of `nonlin_solve`
"""
import inspect
args, varargs, varkw, defaults = inspect.getargspec(jac.__init__)
kwargs = zip(args[-len(defaults):], defaults)
kw_str = ", ".join(["%s=%r" % (k, v) for k, v in kwargs])
if kw_str:
kw_str = ", " + kw_str
kwkw_str = ", ".join(["%s=%s" % (k, k) for k, v in kwargs])
if kwkw_str:
kwkw_str = kwkw_str + ", "
# Construct the wrapper function so that it's keyword arguments
# are visible in pydoc.help etc.
wrapper = """
def %(name)s(F, xin, iter=None %(kw)s, verbose=False, maxiter=None,
f_tol=None, f_rtol=None, x_tol=None, x_rtol=None,
tol_norm=None, line_search='armijo', callback=None, **kw):
jac = %(jac)s(%(kwkw)s **kw)
return nonlin_solve(F, xin, jac, iter, verbose, maxiter,
f_tol, f_rtol, x_tol, x_rtol, tol_norm, line_search,
callback)
"""
wrapper = wrapper % dict(name=name, kw=kw_str, jac=jac.__name__,
kwkw=kwkw_str)
ns = {}
ns.update(globals())
exec wrapper in ns
func = ns[name]
func.__doc__ = jac.__doc__
_set_doc(func)
return func
broyden1 = _nonlin_wrapper('broyden1', BroydenFirst)
broyden2 = _nonlin_wrapper('broyden2', BroydenSecond)
anderson = _nonlin_wrapper('anderson', Anderson)
linearmixing = _nonlin_wrapper('linearmixing', LinearMixing)
diagbroyden = _nonlin_wrapper('diagbroyden', DiagBroyden)
excitingmixing = _nonlin_wrapper('excitingmixing', ExcitingMixing)
newton_krylov = _nonlin_wrapper('newton_krylov', KrylovJacobian)
# Deprecated functions
@np.deprecate
def broyden_generalized(*a, **kw):
"""Use *anderson(..., w0=0)* instead"""
kw.setdefault('w0', 0)
return anderson(*a, **kw)
@np.deprecate
def broyden1_modified(*a, **kw):
"""Use `broyden1` instead"""
return broyden1(*a, **kw)
@np.deprecate
def broyden_modified(*a, **kw):
"""Use `anderson` instead"""
return anderson(*a, **kw)
@np.deprecate
def anderson2(*a, **kw):
"""Use `anderson` instead"""
return anderson(*a, **kw)
@np.deprecate
def broyden3(*a, **kw):
"""Use `broyden2` instead"""
return broyden2(*a, **kw)
@np.deprecate
def vackar(*a, **kw):
"""Use `diagbroyden` instead"""
return diagbroyden(*a, **kw)
| gpl-3.0 |
mariocannistra/radio-astronomy | findsessionrange.py | 1 | 1973 | #!/usr/bin/python
# this source is part of my Hackster.io project: https://www.hackster.io/mariocannistra/radio-astronomy-with-rtl-sdr-raspberrypi-and-amazon-aws-iot-45b617
# this program will determine the overall range of signal strengths received during the whole session.
# this program can be run standalone but is usually run at end of session by doscan.py
# Its output will be stored in 2 files:
# dbminmax.txt and session-overview.png . The first contains two rows of text with just the maximum
# and minimum of the whole session. The second contains a chart of all the min and max values for each of
# the scan files
from glob import glob
import numpy as np
import radioConfig
import subprocess
import os
import datetime
import matplotlib
# Force matplotlib to not use any Xwindows backend.
matplotlib.use('Agg')
import matplotlib.pyplot as plt
globmax = -9000
globmin = 9000
sessmin = np.empty(shape=[0, 1])
sessmax = np.empty(shape=[0, 1])
scantimeline = np.empty(shape=[0, 1])
files_in_dir = sorted(glob("*.csv"))
for fname in files_in_dir:
dbs = np.genfromtxt(fname,dtype='float',delimiter = ',', skip_header=0, skip_footer=0, usecols=(6,),usemask=True)
thismin=dbs.min()
thismax=dbs.max()
scantime=str(fname)[11:17]
print scantime,thismin,thismax
if thismin < globmin:
globmin = thismin
if thismax > globmax:
globmax = thismax
sessmin = np.append(sessmin, thismin)
sessmax = np.append(sessmax, thismax)
scantimeline = np.append(scantimeline, scantime)
mytitle = 'Signal strength range: min %f .. max %f' % (globmin,globmax)
print mytitle
xs = range(len(scantimeline))
plt.plot(xs,sessmin )
plt.plot(xs,sessmax )
plt.xticks(xs,scantimeline,rotation=70)
plt.grid()
plt.title(mytitle)
#plt.show()
plt.savefig('session-overview.png')
sessfile = open("dbminmax.txt", "w")
sessfile.write(str(globmax))
sessfile.write("\n")
sessfile.write(str(globmin))
sessfile.write("\n")
sessfile.close()
| mit |
TAMU-CPT/galaxy-tools | tools/genome_viz/brigaid.py | 1 | 36126 | #!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
AUTHOR
Pedro Cerqueira
github: @pedrorvc
DESCRIPTION
This script serves to create xml files contaning the information necessary
for the execution of BRIG (Blast Ring Image Generator), reducing the time
performing the tedious task of setting up all the information on the GUI
and provides a quick way to produce an image.
The arguments for this script provide some (but not all)
of the available options in BRIG, which were the ones I used to change the most.
USAGE:
brigaid.py -q reference_sequence.fna -rfd path/to/reference/dir -od path/to/output/dir -of path/to/output/dir/output_file
-oi path/to/output/BRIG/output_image -t Image_title -a annotation_file.gbk --genes genes_of_interest.txt
--contig-order contig_order.tsv
"""
import argparse
import csv
import os
import xml.etree.ElementTree as ET
from collections import OrderedDict
from xml.dom import minidom
from Bio import SeqIO
from matplotlib import cm
def listdir_fullpath(path):
""" Gets the full path of the files from a directory
Args:
path (str): full path to a directory
Returns:
list containing the full path of every file contained in the input directory
"""
return [os.path.join(path, f) for f in os.listdir(path)]
def ring_attributes(colour, name, position):
""" Creates ring attributes.
Args:
colour (str): color of the ring.
name (str): name of the ring.
position (str): position of the ring.
Returns:
ring_attrs (dict): attributes of any regular ring of the BRIG xml.
"""
ring_attrs = {"colour" : colour,
"name": name,
"position" : position,
"upperInt" : "90",
"lowerInt" : "70",
"legend" : "yes",
"size" : "30",
"labels" : "no",
"blastType" : "blastn"}
return ring_attrs
def annotation_ring_attributes(position):
""" Creates annotation ring attributes.
Args:
position (str): position of the ring.
Returns:
annotation_ring_attrs (dict): attributes of the annotation ring of the BRIG xml.
"""
annotation_ring_attrs = {"colour" : '172,14,225',
"name": 'null',
"position" : position,
"upperInt" : "70",
"lowerInt" : "50",
"legend" : "yes",
"size" : "30",
"labels" : "no",
"blastType" : "blastn"}
return annotation_ring_attrs
def create_feature_attrs(label, colour, decoration, start, stop):
""" Create attributes for the Feature SubElements of the annotation ring.
Args:
label (str): name of the gene/CDS to annotate
colour (str): colour of the decoration for the annotation
decoration (str): shape of the gene/CDS to annotate, for example, 'clockwise-arrow'
start (str): start of the gene/CDS to annotate
stop (str): stop of the gene/CDS to annotate
Results:
feature_element_attrs (dict): attributes of the feature element.
feature_range_element_attrs (dict): attributes of the feature range element
"""
feature_element_attrs = {'label' : label,
'colour' : colour,
'decoration' : decoration}
feature_range_element_attrs = {'start' : start,
'stop' : stop}
return feature_element_attrs, feature_range_element_attrs
def create_annotation_ring_tsv(annotation_ring, annotation_file):
""" Uses a tsv file to annotate the reference genome.
Args:
annotation_ring: ElementTree SubElement object containing the 'ring' tag and its attributes.
annotation_file (str): Full path to the file containing annotations for the reference genome.
"""
with open(annotation_file) as tsvfile:
reader = csv.DictReader(tsvfile, dialect='excel-tab')
# Obtain the annotations from the file contents
for row in reader:
start = row['#START']
stop = row['STOP']
label = row['Label']
colour = row['Colour']
decoration = row['Decoration']
# Create xml attributes
feature_element_attrs, feature_range_element_attrs = create_feature_attrs(label, colour, decoration, start, stop)
# Create xml elements
feature_element = ET.SubElement(annotation_ring, 'feature', attrib=feature_element_attrs)
feature_range_element = ET.SubElement(feature_element, 'featureRange', attrib=feature_range_element_attrs)
def annotation_ring_feature_elements_gbk_concat(annotation_ring, record, genome_size=False):
""" Creates the annotation ring feature elements, using a concatenated Genbank annotation file.
Args:
annotation_ring: ElementTree SubElement object containing the 'ring' tag and its attributes.
record (SeqRecord): Object of BioPython containing the information of the input Genbank.
genome_size (bool): Size of genome. Integer when a Genbank divided by contigs is provided.
Boolean (False) when a concatenated Genbank is provided.
"""
#if type(genome_size) == int:
# Obtain the features of the Genbank file records
for fea in record.features:
# Get the start and end position of the genome
# Also get the strand
if fea.type == 'CDS':
start = str(fea.location.start.position)
end = str(fea.location.end.position)
strand = fea.location.strand
# Get the label of the gene or product
if 'gene' in fea.qualifiers:
label = str(fea.qualifiers['gene'][0])
elif 'product' in fea.qualifiers:
product = fea.qualifiers['product'][0]
label = str(product)
else:
continue
# Define the decoration of the annotation based on the strand
if strand == -1:
decoration = 'counterclockwise-arrow'
elif strand == 1:
decoration = 'clockwise-arrow'
# Create xml attributes
feature_element_attrs, feature_range_element_attrs = create_feature_attrs(label, "black", decoration, start, end)
# Create xml elements
feature_element = ET.SubElement(annotation_ring, 'feature', attrib=feature_element_attrs)
feature_range_element = ET.SubElement(feature_element, 'featureRange', attrib=feature_range_element_attrs)
# If a genome size is provided, get the size of the records
if type(genome_size) == int:
if fea.type == 'source':
size = fea.location.end.position
try:
size
genome_size += size
return genome_size
except NameError:
pass
def annotation_ring_feature_elements_genes_of_interest_gbk_concat(annotation_ring, record, genes, genome_size=False):
""" Creates the annotation ring feature elements, using a concatenated Genbank annotation file
and specific gene annotations.
Args:
annotation_ring: ElementTree SubElement object containing the 'ring' tag and its attributes.
record (SeqRecord): Object of BioPython containing the information of the input Genbank.
genome_size (bool): Size of genome. Integer when a Genbank divided by contigs is provided.
Boolean (False) when a concatenated Genbank is provided.
"""
for f in record.features:
if f.type == 'CDS':
# Find the 'gene' tag and determine if the gene belongs to the specified genes to be annotated
if 'gene' in f.qualifiers and f.qualifiers['gene'][0] in genes:
label = f.qualifiers['gene'][0]
elif 'product' in f.qualifiers and f.qualifiers['product'][0] in genes:
product = f.qualifiers['product'][0]
label = product
else:
continue
# Determine the start, stop and strand of the gene
start = str(f.location.start.position + genome_size)
end = str(f.location.end.position + genome_size)
strand = f.location.strand
# Define the decoration of the annotation based on the strand
if strand == -1:
decoration = 'counterclockwise-arrow'
elif strand == 1:
decoration = 'clockwise-arrow'
# Create xml attributes
feature_element_attrs, feature_range_element_attrs = create_feature_attrs(label, "black", decoration, start, end)
# Create xml elements
feature_element = ET.SubElement(annotation_ring, 'feature', attrib=feature_element_attrs)
feature_range_element = ET.SubElement(feature_element, 'featureRange', attrib=feature_range_element_attrs)
# If a genome size is provided, get the size of the records
if type(genome_size) == int:
if f.type == "source":
size = f.location.end.position
try:
size
genome_size += size
return genome_size
except NameError:
pass
def create_annotation_ring_gbk_concat(annotation_ring, annotation_file, genes_of_interest, records):
""" Create annotation ring using a concatenated Genbank annotation file.
Args:
annotation_ring: ElementTree SubElement object containing the 'ring' tag and its attributes.
annotation_file (str): Full path to the file containing annotations for the reference genome.
genes_of_interest (str): Full path to the file containing the genes to search for in the Genbank file.
records (SeqRecord): Object of BioPython containing the information of the input Genbank.
"""
if genes_of_interest != []:
# Get the genes to serach in the Genbank file
with open(genes_of_interest, "r") as f:
genes = f.readlines()
genes = [gene.rstrip() for gene in genes]
# Create feature elements of the annotation ring
for seq_record in records:
annotation_ring_feature_elements_genes_of_interest_gbk_concat(annotation_ring, seq_record, genes)
else:
for seq_record in records:
annotation_ring_feature_elements_gbk_concat(annotation_ring, seq_record)
def create_annotation_ring_gbk_contigs(annotation_ring, annotation_file, records, genes_of_interest, contig_order):
""" Create annotation ring using a Genbank annotation file divided by contigs.
Args:
annotation_ring: ElementTree SubElement object containing the 'ring' tag and its attributes.
annotation_file (str): Full path to the file containing annotations for the reference genome.
genes_of_interest (str): Full path to the file containing the genes to search for in the Genbank file.
records (SeqRecord): Object of BioPython containing the information of the input Genbank.
contig_order (str): Full path to the file containing the order of the contigs.
"""
if contig_order != []:
with open(contig_order) as tsvfile:
reader = csv.DictReader(tsvfile, dialect='excel-tab')
# Create an OrderedDict with the contents of the file
# The keys are the order are a number representing the order of the contig
# The values are the names of the contigs
content_dict = OrderedDict()
for r in reader:
content_dict[r["order"]] = r["contig"]
# Create an OrderedDict with the content of each contig
# The keys are the names of the contigs
# The values are SeqRecord objects from BipPython
seq_records_dict = OrderedDict()
for record in records:
seq_records_dict[record.id] = record
if genes_of_interest != []:
with open(genes_of_interest, "r") as f:
genes = f.readlines()
genes = [gene.rstrip() for gene in genes]
genome_size = 0
for i in range(1, len(records)+1):
ord_record = seq_records_dict[content_dict[str(i)]]
gsize = annotation_ring_feature_elements_genes_of_interest_gbk_concat(annotation_ring, ord_record, genes, genome_size)
genome_size = gsize
else:
genome_size = 0
for i in range(1, len(records)+1):
ord_record = seq_records_dict[content_dict[str(i)]]
gsize = annotation_ring_feature_elements_gbk_concat(annotation_ring, ord_record, genome_size)
genome_size = gsize
else:
if genes_of_interest != []:
with open(genes_of_interest, "r") as f:
genes = f.readlines()
genes = [gene.rstrip() for gene in genes]
for seq_record in records:
annotation_ring_feature_elements_genes_of_interest_gbk_concat(annotation_ring, seq_record, genes)
else:
for seq_record in records:
annotation_ring_feature_elements_gbk_concat(annotation_ring, seq_record)
def write_xml(root_elem, output_file):
""" Writes a xml file.
Args:
root_elem is a ElementTree Element object containing all the information
required for the output file.
output_file (str): full path to the output file
"""
xml_file = ET.tostring(root_elem, encoding='utf8').decode('utf8')
pretty_xml_file = minidom.parseString(xml_file).toprettyxml(indent=' ')
output_file = output_file + ".xml"
with open(output_file, "w") as f:
f.write(pretty_xml_file)
####### Create xml elemnts
# Create root element
def create_root_element(blast_options, legend_position, query_file,
output_folder, image_output_file, title, image_format):
"""
Creates the root element of the xml file and its attributes.
Args:
blast_options (str): additional options for blast, for example, -evalue or num_threads
legend_position (str): position of the legend on the image
query_file (str): full path to the query file
output_folder (str): full path to the output folder
image_output_file (str): full path to the image output file
title (str): title of the output image
image_format (str): format of the image output file
Returns:
root: ElementTree Element object containing the BRIG tag and its attributes
"""
root_attrs = {"blastOptions" : blast_options,
"legendPosition" : legend_position,
"queryFile" : query_file,
"outputFolder" : output_folder,
"blastPlus" : "yes",
"outputFile" : os.path.join(output_folder, image_output_file),
"title" : title,
"imageFormat" : image_format,
"queryFastaFile" : query_file,
"cgXML" : os.path.join(output_folder + "/scratch", os.path.basename(query_file) + ".xml")}
root = ET.Element('BRIG', attrib=root_attrs)
return root
#### Create root children
# Create cgview_settings element
def create_cgview_settings_element(root, height, width):
""" Creates the cgview_settings element of the xml file and its attributes.
Args:
root: ElementTree Element object containing the BRIG tag and its attributes.
height (str): height of the output image in pixels
width (str): width of the output image in pixels
Returns:
cgview_settings: ElementTree SubElement object containing the cgview settings tag and its attributes
"""
cgview_settings_attrs = {"arrowheadLength" : "medium",
"backboneColor" : "black",
"backboneRadius" : "600",
"backboneThickness" : "medium",
"backgroundColor" : "white",
"borderColor" : "black",
"featureSlotSpacing" : "medium",
"featureThickness" : "30",
"giveFeaturePositions" : "false",
"globalLabel" : "true",
"height" : height,
"isLinear" : "false",
"labelFont" : "SansSerif,plain,25",
"labelLineLength" : "medium",
"labelLineThickness" : "medium",
"labelPlacementQuality" : "best",
"labelsToKeep" : "1000",
"longTickColor" : "black",
"minimumFeatureLength" : "medium",
"moveInnerLabelsToOuter" :"true",
"origin" : "12",
"rulerFont" : "SansSerif,plain,35",
"rulerFontColor" : "black",
"rulerPadding" : "40",
"rulerUnits" : "bases",
"shortTickColor" : "black",
"shortTickThickness" : "medium",
"showBorder" : "false",
"showShading" : "true",
"showWarning" : "false",
"tickDensity" : "0.2333",
"tickThickness" : "medium",
"titleFont" : "SansSerif,plain,45",
"titleFontColor" : "black",
"useColoredLabelBackgrounds" : "false",
"useInnerLabels" : "true",
"warningFont" : "Default,plain,35",
"warningFontColor" : "black",
"width" : width,
"zeroTickColor" : "black",
"tickLength" : "medium"}
cgview_settings = ET.SubElement(root, 'cgview_settings', attrib=cgview_settings_attrs)
return cgview_settings
# Create brig_settings element
def create_brig_settings_element(root, java_memory):
""" Creates the brig_settings element of the xml file and its attributes.
Args:
root: ElementTree Element object containing the BRIG tag and its attributes.
java_memory (str): amount of memory (in bytes) java is allowed to use for BRIG
Returns:
brig_settings: ElementTree SubElement object containing the brig settings tag and its attributes
"""
brig_settings_attrs = {"Ring1" : "172,14,225",
"Ring2" : "222,149,220",
"Ring3" : "161,221,231",
"Ring4" : "49,34,221",
"Ring5" : "116,152,226",
"Ring6" : "224,206,38",
"Ring7" : "40,191,140",
"Ring8" : "158,223,139",
"Ring9" : "226,38,122",
"Ring10" :"211,41,77",
"defaultUpper" : "70",
"defaultLower" : "50",
"defaultMinimum" : "50",
"genbankFiles" : "gbk,gb,genbank",
"fastaFiles" : "fna,faa,fas,fasta,fa",
"emblFiles" : "embl",
"blastLocation" : "",
"divider" : "3",
"multiplier" : "3",
"memory" : java_memory,
"defaultSpacer" : "0"}
brig_settings = ET.SubElement(root,
"brig_settings",
attrib=brig_settings_attrs)
return brig_settings
## Create special element
def create_special_element(root):
"""Creates the 'special' element of the xml file and its attributes
Args:
root: ElementTree Element object containing the BRIG tag and its attributes.
Returns:
gc_content_special: ElementTree SubElement object containing the 'special' tag and its attributes
gc_skew_special: ElementTree SubElement object containing the 'special' tag and its attributes
"""
gc_content_special = ET.SubElement(root, 'special', attrib={'value' : 'GC Content'})
gc_skew_special = ET.SubElement(root, 'special', attrib={'value' : 'GC Skew'})
return gc_content_special, gc_skew_special
# Create reference dir element
def create_reference_directory_element(root, reference_directory):
""" Creates the 'reference directory' element of the xml file and its attributes.
Args:
root: ElementTree Element object containing the 'BRIG' tag and its attributes.
reference_directory (str): full path to the reference directory that contains
the fasta files used to build the rings.
Returns:
ref_file: ElementTree SubElement object containing the 'refFile' tag and its attributes
"""
ref_dir = ET.SubElement(root,
"refDir",
attrib={"location" : reference_directory})
# Obtain the full path for all the files in the directory
ref_dir_list = listdir_fullpath(reference_directory)
for f in ref_dir_list:
ref_file = ET.SubElement(ref_dir,
"refFile",
attrib={"location" : f})
return ref_file
# Create the ring where the annotations are defined
def create_annotation_ring(root, reference_directory, annotation_file, genes_of_interest, contig_order):
""" Creates the ring that will contain the annotations for the reference genome.
Args:
root: ElementTree Element object containing the 'BRIG' tag and its attributes.
reference_directory (str): full path to the reference directory that contains
the fasta files used to build the rings.
annotation_file (str): Full path to the file containing annotations for the reference genome.
genes_of_interest (str): Full path to the file containing a list of specific genes.
contig_order (str): Full path to the tab-delimited file containing the order of the contigs.
"""
# Determine the position of the annotation ring, which will be the position after the last reference genome
ring_position = len(os.listdir(reference_directory)) + 2
# Create the annotation ring element
annotation_ring = ET.SubElement(root, 'ring', attrib=annotation_ring_attributes(str(ring_position)))
# Check for tab-delimited annotation file input
if list(SeqIO.parse(annotation_file, "genbank")) == []:
create_annotation_ring_tsv(annotation_ring, annotation_file)
else:
# Get the records of the Genbank file
records = [r for r in SeqIO.parse(annotation_file, "genbank")]
### Check if a contig order file has been provided
if len(records) > 1: # If more than 1 record exists, then the Genbank file is divided by contigs
create_annotation_ring_gbk_contigs(annotation_ring, annotation_file, records, genes_of_interest, contig_order)
else:
create_annotation_ring_gbk_concat(annotation_ring, annotation_file, genes_of_interest, records)
## Create remaining rings
def create_ring_element(root, reference_directory, colormap):
""" Creates the ring elements of the xml file, containing the position and color of the rings.
Args:
root: ElementTree Element object containing the 'BRIG' tag and its attributes.
reference_directory (str): full path to the reference directory that contains
the fasta files used to build the rings.
colormap (str): name of the colormap (available in matplotlib) to use for the color of the rings
Returns:
ring_number_element: ElementTree SubElement object containing the 'ring' tag and its attributes
ring_sequence_element: ElementTree SubElement object containing the 'sequence' tag and its attributes
"""
ref_dir_list = listdir_fullpath(reference_directory)
# Gets the colormap from matplotlib with as many colors as the number of files
cmap = cm.get_cmap(colormap, len(ref_dir_list))
list_colormap = cmap.colors.tolist()
# Remove the fourth element (transparency) because it is not necessary
colors_to_use = []
for l in list_colormap:
convert = [round(x * 255) for x in l]
convert.pop()
colors_to_use.append(convert)
#reversed_colors_to_use = colors_to_use[::-1]
# Check if the user provided an order for the rings
has_digit = [os.path.basename(x).split("_")[0].isdigit() for x in ref_dir_list]
if True in has_digit:
# Obtain the ring positions
ring_positions = [os.path.basename(x).split("_")[0] for x in ref_dir_list]
# Reverse sort the positions of the rings, because they will be created
# in a descending order of their positions
ring_positions.sort(reverse=True)
ref_dir_list.sort(reverse=True)
for ring in range(len(ref_dir_list)):
# The ring positions start at 2 due to the special rings (GC Content and GC Skew)
ring_position = int(ring_positions[ring]) + 1
# Select a color for the ring
ring_color = ",".join([str(e) for e in colors_to_use[ring]])
# Define the name of the ring
ring_name = os.path.basename(ref_dir_list[ring]).split("_")[1]
# Create the xml elements
ring_number_element = ET.SubElement(root,
'ring',
ring_attributes(ring_color, ring_name, str(ring_position)))
ring_sequence_element = ET.SubElement(ring_number_element,
"sequence",
attrib={"location" : ref_dir_list[ring]})
else:
# Sort files by lowercase
ref_dir_list.sort(key=lambda y: y.lower())
# The number of rings starts at 2 due to the GC Content and GC Skew
ring_number = len(ref_dir_list) + 1
for ring in range(len(ref_dir_list)):
# Select a color for the ring
ring_color = ",".join([str(e) for e in colors_to_use[ring]])
# Define the name of the ring
ring_name = os.path.basename(ref_dir_list[ring]).split("_")[0]
# Create the xml elements
ring_number_element = ET.SubElement(root,
'ring',
ring_attributes(ring_color, ring_name, str(ring_number)))
ring_sequence_element = ET.SubElement(ring_number_element,
"sequence",
attrib={"location" : ref_dir_list[ring]})
ring_number -= 1
return ring_number_element, ring_sequence_element
## Create special rings
def create_special_ring_element(root):
""" Create the 'special' ring element and its attributes.
Args:
root: ElementTree Element object containing the 'BRIG' tag and its attributes.
Returns:
gc_content_location: ElementTree SubElement object containing the 'sequence' tag and its attributes
gc_skew_location: ElementTree SubElement object containing the 'sequence' tag and its attributes
"""
# Create ring attributes
gc_content_ring_attrs = ring_attributes('225,0,0', "GC Content", "0")
gc_skew_ring_attrs = ring_attributes('225,0,0', "GC Skew", "1")
# Add ring element to root
gc_skew_ring = ET.SubElement(root, 'ring', attrib=gc_skew_ring_attrs)
gc_content_ring = ET.SubElement(root, 'ring', attrib=gc_content_ring_attrs)
# Add sequence element to ring
gc_content_location = ET.SubElement(gc_content_ring, 'sequence', attrib={'location' : 'GC Content'})
gc_skew_location = ET.SubElement(gc_skew_ring, 'sequence', attrib={'location' : 'GC Skew'})
return gc_content_location, gc_skew_location
def main(query_file, reference_directory, output_folder, output_xml, image_output_file, title, annotation_file,
genes_of_interest, contig_order, blast_options, legend_position, image_format, height, width, java_memory, colormap):
root = create_root_element(blast_options, legend_position, query_file,
output_folder, image_output_file, title, image_format)
cgview_settings = create_cgview_settings_element(root, height, width)
brig_settings = create_brig_settings_element(root, java_memory)
special = create_special_element(root)
refdir = create_reference_directory_element(root, reference_directory)
if annotation_file:
create_annotation_ring(root, reference_directory, annotation_file, genes_of_interest, contig_order)
rings = create_ring_element(root, reference_directory, colormap)
special_ring = create_special_ring_element(root)
write_xml(root, output_xml)
print("\n File written to {}".format(output_xml))
def parse_arguments():
parser = argparse.ArgumentParser(description=__doc__,
formatter_class=argparse.RawDescriptionHelpFormatter)
parser.add_argument('-q', '--query', type=str, required=True, dest='query_file',
help='Path to the query/reference FASTA file.')
parser.add_argument('-rfd', '--ref_dir', type=str, required=True, dest='reference_directory',
help='Path to the directory where the FASTA files to compare against the reference are located.')
parser.add_argument('-od', '--out_dir', type=str, required=True, dest='output_folder',
help='Path to the output directory for the results of BRIG.')
parser.add_argument('-of', '--out_xml', type=str, required=True, dest='output_file',
help='Path to the output of this script.')
parser.add_argument('-oi', '--out_img', type=str, required=True, dest='image_output_file',
help='Path to the output file of the resulting image of BRIG.')
parser.add_argument('-t', '--title', type=str, required=True, dest='title',
help='Title of the resulting image from BRIG.')
parser.add_argument('-a', '--annotation', type=str, required=False, dest='annotation_file', default=False,
help='File containing annotations for the reference genome. '
'The annoation file can be a tab-delimited file (.tsv) or a Genbank format file (.gbk, .gb)')
parser.add_argument('--genes', type=str, required=False, dest='genes_of_interest', default=[],
help='File containing a list of specific genes (one gene per line) to search when a Genbank annotation file is provided. ')
parser.add_argument('--contig_order', type=str, required=False, dest='contig_order', default=[],
help='Tab-delimited file containing the order of the contigs when a Genbank (divided by contigs) annotation file is provided. '
'Example: order contig '
'1 Contig8')
parser.add_argument('-b', '--blast_options', type=str, required=False, dest="blast_options", default="-evalue 0.001 -num_threads 6",
help='Options for running BLAST.')
parser.add_argument('-l', '--legend_pos', type=str, required=False, dest="legend_position", default="middle-right",
help='Positon of the legend on the resulting image.'
'The options available are upper, center or lower, '
'paired with left, center or right')
parser.add_argument('-if', '--image_format', type=str, required=False, dest="image_format", default="jpg",
help='Format of the resulting image file.'
'The available options are: jpg, png, svg or svgz.')
parser.add_argument('-ht', '--height', type=str, required=False, dest="height", default="3000",
help='Height (in pixels) of the resulting image.')
parser.add_argument('-wd', '--width', type=str, required=False, dest="width", default="3000",
help='Width (in pixels) of the resulting image.')
parser.add_argument('-jm', '--java_memory', type=str, required=False, dest="java_memory", default="1500",
help='Amount of memory (in bytes) that Java is allowed to use for BRIG.')
parser.add_argument('-cm', '--colormap', type=str, required=False, dest="colormap", default="viridis",
help='Colormap from matplotlib to use for the color of the rings. '
'The available options are: viridis, plasma, inferno, magma and cividis.'
'More options for colormaps at: '
'https://matplotlib.org/users/colormaps.html')
args = parser.parse_args()
return [args.query_file, args.reference_directory, args.output_folder, args.output_file,
args.image_output_file, args.title, args.annotation_file, args.genes_of_interest, args.contig_order,
args.blast_options, args.legend_position, args.image_format, args.height, args.width, args.java_memory, args.colormap]
if __name__ == '__main__':
args = parse_arguments()
main(args[0], args[1], args[2], args[3], args[4], args[5], args[6],
args[7], args[8], args[9], args[10], args[11], args[12], args[13],
args[14], args[15])
| gpl-3.0 |
yuanagain/seniorthesis | venv/lib/python2.7/site-packages/matplotlib/tests/test_basic.py | 7 | 1290 | from __future__ import (absolute_import, division, print_function,
unicode_literals)
from matplotlib.externals import six
from nose.tools import assert_equal
from matplotlib.testing.decorators import knownfailureif
from pylab import *
def test_simple():
assert_equal(1 + 1, 2)
@knownfailureif(True)
def test_simple_knownfail():
# Test the known fail mechanism.
assert_equal(1 + 1, 3)
def test_override_builtins():
ok_to_override = set([
'__name__',
'__doc__',
'__package__',
'__loader__',
'__spec__',
'any',
'all',
'sum'
])
# We could use six.moves.builtins here, but that seems
# to do a little more than just this.
if six.PY3:
builtins = sys.modules['builtins']
else:
builtins = sys.modules['__builtin__']
overridden = False
for key in globals().keys():
if key in dir(builtins):
if (globals()[key] != getattr(builtins, key) and
key not in ok_to_override):
print("'%s' was overridden in globals()." % key)
overridden = True
assert not overridden
if __name__ == '__main__':
import nose
nose.runmodule(argv=['-s', '--with-doctest'], exit=False)
| mit |
crichardson17/starburst_atlas | Low_resolution_sims/DustFree_LowRes/Geneva_noRot_cont/Geneva_noRot_cont_age5/UV2.py | 33 | 7365 | import csv
import matplotlib.pyplot as plt
from numpy import *
import scipy.interpolate
import math
from pylab import *
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
import matplotlib.patches as patches
from matplotlib.path import Path
import os
# ------------------------------------------------------------------------------------------------------
#inputs
for file in os.listdir('.'):
if file.endswith(".grd"):
inputfile = file
for file in os.listdir('.'):
if file.endswith(".txt"):
inputfile2 = file
# ------------------------------------------------------------------------------------------------------
#Patches data
#for the Kewley and Levesque data
verts = [
(1., 7.97712125471966000000), # left, bottom
(1., 9.57712125471966000000), # left, top
(2., 10.57712125471970000000), # right, top
(2., 8.97712125471966000000), # right, bottom
(0., 0.), # ignored
]
codes = [Path.MOVETO,
Path.LINETO,
Path.LINETO,
Path.LINETO,
Path.CLOSEPOLY,
]
path = Path(verts, codes)
# ------------------------
#for the Kewley 01 data
verts2 = [
(2.4, 9.243038049), # left, bottom
(2.4, 11.0211893), # left, top
(2.6, 11.0211893), # right, top
(2.6, 9.243038049), # right, bottom
(0, 0.), # ignored
]
path = Path(verts, codes)
path2 = Path(verts2, codes)
# -------------------------
#for the Moy et al data
verts3 = [
(1., 6.86712125471966000000), # left, bottom
(1., 10.18712125471970000000), # left, top
(3., 12.18712125471970000000), # right, top
(3., 8.86712125471966000000), # right, bottom
(0., 0.), # ignored
]
path = Path(verts, codes)
path3 = Path(verts3, codes)
# ------------------------------------------------------------------------------------------------------
#the routine to add patches for others peoples' data onto our plots.
def add_patches(ax):
patch3 = patches.PathPatch(path3, facecolor='yellow', lw=0)
patch2 = patches.PathPatch(path2, facecolor='green', lw=0)
patch = patches.PathPatch(path, facecolor='red', lw=0)
ax1.add_patch(patch3)
ax1.add_patch(patch2)
ax1.add_patch(patch)
# ------------------------------------------------------------------------------------------------------
#the subplot routine
def add_sub_plot(sub_num):
numplots = 16
plt.subplot(numplots/4.,4,sub_num)
rbf = scipy.interpolate.Rbf(x, y, z[:,sub_num-1], function='linear')
zi = rbf(xi, yi)
contour = plt.contour(xi,yi,zi, levels, colors='c', linestyles = 'dashed')
contour2 = plt.contour(xi,yi,zi, levels2, colors='k', linewidths=1.5)
plt.scatter(max_values[line[sub_num-1],2], max_values[line[sub_num-1],3], c ='k',marker = '*')
plt.annotate(headers[line[sub_num-1]], xy=(8,11), xytext=(6,8.5), fontsize = 10)
plt.annotate(max_values[line[sub_num-1],0], xy= (max_values[line[sub_num-1],2], max_values[line[sub_num-1],3]), xytext = (0, -10), textcoords = 'offset points', ha = 'right', va = 'bottom', fontsize=10)
if sub_num == numplots / 2.:
print "half the plots are complete"
#axis limits
yt_min = 8
yt_max = 23
xt_min = 0
xt_max = 12
plt.ylim(yt_min,yt_max)
plt.xlim(xt_min,xt_max)
plt.yticks(arange(yt_min+1,yt_max,1),fontsize=10)
plt.xticks(arange(xt_min+1,xt_max,1), fontsize = 10)
if sub_num in [2,3,4,6,7,8,10,11,12,14,15,16]:
plt.tick_params(labelleft = 'off')
else:
plt.tick_params(labelleft = 'on')
plt.ylabel('Log ($ \phi _{\mathrm{H}} $)')
if sub_num in [1,2,3,4,5,6,7,8,9,10,11,12]:
plt.tick_params(labelbottom = 'off')
else:
plt.tick_params(labelbottom = 'on')
plt.xlabel('Log($n _{\mathrm{H}} $)')
if sub_num == 1:
plt.yticks(arange(yt_min+1,yt_max+1,1),fontsize=10)
if sub_num == 13:
plt.yticks(arange(yt_min,yt_max,1),fontsize=10)
plt.xticks(arange(xt_min,xt_max,1), fontsize = 10)
if sub_num == 16 :
plt.xticks(arange(xt_min+1,xt_max+1,1), fontsize = 10)
# ---------------------------------------------------
#this is where the grid information (phi and hdens) is read in and saved to grid.
grid = [];
with open(inputfile, 'rb') as f:
csvReader = csv.reader(f,delimiter='\t')
for row in csvReader:
grid.append(row);
grid = asarray(grid)
#here is where the data for each line is read in and saved to dataEmissionlines
dataEmissionlines = [];
with open(inputfile2, 'rb') as f:
csvReader = csv.reader(f,delimiter='\t')
headers = csvReader.next()
for row in csvReader:
dataEmissionlines.append(row);
dataEmissionlines = asarray(dataEmissionlines)
print "import files complete"
# ---------------------------------------------------
#for grid
phi_values = grid[1:len(dataEmissionlines)+1,6]
hdens_values = grid[1:len(dataEmissionlines)+1,7]
#for lines
headers = headers[1:]
Emissionlines = dataEmissionlines[:, 1:]
concatenated_data = zeros((len(Emissionlines),len(Emissionlines[0])))
max_values = zeros((len(Emissionlines[0]),4))
#select the scaling factor
#for 1215
#incident = Emissionlines[1:,4]
#for 4860
incident = Emissionlines[:,57]
#take the ratio of incident and all the lines and put it all in an array concatenated_data
for i in range(len(Emissionlines)):
for j in range(len(Emissionlines[0])):
if math.log(4860.*(float(Emissionlines[i,j])/float(Emissionlines[i,57])), 10) > 0:
concatenated_data[i,j] = math.log(4860.*(float(Emissionlines[i,j])/float(Emissionlines[i,57])), 10)
else:
concatenated_data[i,j] == 0
# for 1215
#for i in range(len(Emissionlines)):
# for j in range(len(Emissionlines[0])):
# if math.log(1215.*(float(Emissionlines[i,j])/float(Emissionlines[i,4])), 10) > 0:
# concatenated_data[i,j] = math.log(1215.*(float(Emissionlines[i,j])/float(Emissionlines[i,4])), 10)
# else:
# concatenated_data[i,j] == 0
#find the maxima to plot onto the contour plots
for j in range(len(concatenated_data[0])):
max_values[j,0] = max(concatenated_data[:,j])
max_values[j,1] = argmax(concatenated_data[:,j], axis = 0)
max_values[j,2] = hdens_values[max_values[j,1]]
max_values[j,3] = phi_values[max_values[j,1]]
#to round off the maxima
max_values[:,0] = [ '%.1f' % elem for elem in max_values[:,0] ]
print "data arranged"
# ---------------------------------------------------
#Creating the grid to interpolate with for contours.
gridarray = zeros((len(Emissionlines),2))
gridarray[:,0] = hdens_values
gridarray[:,1] = phi_values
x = gridarray[:,0]
y = gridarray[:,1]
#change desired lines here!
line = [18, #1549
19, #1640
20, #1665
21, #1671
23, #1750
24, #1860
25, #1888
26, #1907
27, #2297
28, #2321
29, #2471
30, #2326
31, #2335
32, #2665
33, #2798
34] #2803
#create z array for this plot
z = concatenated_data[:,line[:]]
# ---------------------------------------------------
# Interpolate
print "starting interpolation"
xi, yi = linspace(x.min(), x.max(), 10), linspace(y.min(), y.max(), 10)
xi, yi = meshgrid(xi, yi)
# ---------------------------------------------------
print "interpolatation complete; now plotting"
#plot
plt.subplots_adjust(wspace=0, hspace=0) #remove space between plots
levels = arange(10**-1,10, .2)
levels2 = arange(10**-2,10**2, 1)
plt.suptitle("UV Lines Continued", fontsize=14)
# ---------------------------------------------------
for i in range(16):
add_sub_plot(i)
ax1 = plt.subplot(4,4,1)
add_patches(ax1)
print "complete"
plt.savefig('UV_Lines_cntd.pdf')
plt.clf()
| gpl-2.0 |
mlperf/training_results_v0.7 | NVIDIA/benchmarks/minigo/implementations/tensorflow/minigo/oneoffs/training_curve.py | 8 | 5964 | # Copyright 2018 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Used to plot the accuracy of the policy and value networks in
predicting professional game moves and results over the course
of training. Check FLAGS for default values for what models to
load and what sgf files to parse.
Usage:
python training_curve.py
Sample 3 positions from each game
python training_curve.py --num_positions=3
Only grab games after 2005 (default is 2000)
python training_curve.py --min_year=2005
"""
import sys
sys.path.insert(0, '.')
import os.path
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from absl import app, flags
from tqdm import tqdm
import coords
from rl_loop import fsdb
import oneoff_utils
flags.DEFINE_string("sgf_dir", None, "sgf database")
flags.DEFINE_string("plot_dir", "data", "Where to save the plots.")
flags.DEFINE_integer("min_year", "2000",
"Only take sgf games with date >= min_year")
flags.DEFINE_string("komi", "7.5", "Only take sgf games with given komi")
flags.DEFINE_integer("idx_start", 150, "Only take models after given idx")
flags.DEFINE_integer("num_positions", 1,
"How many positions from each game to sample from.")
flags.DEFINE_integer("eval_every", 5,
"Eval every k models to generate the curve")
flags.mark_flag_as_required('sgf_dir')
FLAGS = flags.FLAGS
def batch_run_many(player, positions, batch_size=100):
"""Used to avoid a memory oveflow issue when running the network
on too many positions. TODO: This should be a member function of
player.network?"""
prob_list = []
value_list = []
for idx in range(0, len(positions), batch_size):
probs, values = player.network.run_many(positions[idx:idx + batch_size])
prob_list.append(probs)
value_list.append(values)
return np.concatenate(prob_list, axis=0), np.concatenate(value_list, axis=0)
def eval_player(player, positions, moves, results):
probs, values = batch_run_many(player, positions)
policy_moves = [coords.from_flat(c) for c in np.argmax(probs, axis=1)]
top_move_agree = [moves[idx] == policy_moves[idx]
for idx in range(len(moves))]
square_err = (values - results) ** 2 / 4
return top_move_agree, square_err
def sample_positions_from_games(sgf_files, num_positions=1):
pos_data = []
move_data = []
result_data = []
move_idxs = []
fail_count = 0
for path in tqdm(sgf_files, desc="loading sgfs", unit="games"):
try:
positions, moves, results = oneoff_utils.parse_sgf_to_examples(path)
except KeyboardInterrupt:
raise
except Exception as e:
print("Parse exception:", e)
fail_count += 1
continue
# add entire game
if num_positions == -1:
pos_data.extend(positions)
move_data.extend(moves)
move_idxs.extend(range(len(positions)))
result_data.extend(results)
else:
for idx in np.random.choice(len(positions), num_positions):
pos_data.append(positions[idx])
move_data.append(moves[idx])
result_data.append(results[idx])
move_idxs.append(idx)
print("Sampled {} positions, failed to parse {} files".format(
len(pos_data), fail_count))
return pos_data, move_data, result_data, move_idxs
def get_training_curve_data(
model_dir, pos_data, move_data, result_data, idx_start, eval_every):
model_paths = oneoff_utils.get_model_paths(model_dir)
df = pd.DataFrame()
player = None
print("Evaluating models {}-{}, eval_every={}".format(
idx_start, len(model_paths), eval_every))
for idx in tqdm(range(idx_start, len(model_paths), eval_every)):
if player:
oneoff_utils.restore_params(model_paths[idx], player)
else:
player = oneoff_utils.load_player(model_paths[idx])
correct, squared_errors = eval_player(
player=player, positions=pos_data,
moves=move_data, results=result_data)
avg_acc = np.mean(correct)
avg_mse = np.mean(squared_errors)
print("Model: {}, acc: {:.4f}, mse: {:.4f}".format(
model_paths[idx], avg_acc, avg_mse))
df = df.append({"num": idx, "acc": avg_acc,
"mse": avg_mse}, ignore_index=True)
return df
def save_plots(data_dir, df):
plt.plot(df["num"], df["acc"])
plt.xlabel("Model idx")
plt.ylabel("Accuracy")
plt.title("Accuracy in Predicting Professional Moves")
plot_path = os.path.join(data_dir, "move_acc.pdf")
plt.savefig(plot_path)
plt.figure()
plt.plot(df["num"], df["mse"])
plt.xlabel("Model idx")
plt.ylabel("MSE/4")
plt.title("MSE in predicting outcome")
plot_path = os.path.join(data_dir, "value_mse.pdf")
plt.savefig(plot_path)
def main(unusedargv):
sgf_files = oneoff_utils.find_and_filter_sgf_files(
FLAGS.sgf_dir, FLAGS.min_year, FLAGS.komi)
pos_data, move_data, result_data, move_idxs = sample_positions_from_games(
sgf_files=sgf_files, num_positions=FLAGS.num_positions)
df = get_training_curve_data(fsdb.models_dir(), pos_data, move_data,
result_data, FLAGS.idx_start, FLAGS.eval_every)
save_plots(FLAGS.plot_dir, df)
if __name__ == "__main__":
app.run(main)
| apache-2.0 |
RachitKansal/scikit-learn | examples/model_selection/plot_confusion_matrix.py | 244 | 2496 | """
================
Confusion matrix
================
Example of confusion matrix usage to evaluate the quality
of the output of a classifier on the iris data set. The
diagonal elements represent the number of points for which
the predicted label is equal to the true label, while
off-diagonal elements are those that are mislabeled by the
classifier. The higher the diagonal values of the confusion
matrix the better, indicating many correct predictions.
The figures show the confusion matrix with and without
normalization by class support size (number of elements
in each class). This kind of normalization can be
interesting in case of class imbalance to have a more
visual interpretation of which class is being misclassified.
Here the results are not as good as they could be as our
choice for the regularization parameter C was not the best.
In real life applications this parameter is usually chosen
using :ref:`grid_search`.
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
from sklearn.cross_validation import train_test_split
from sklearn.metrics import confusion_matrix
# import some data to play with
iris = datasets.load_iris()
X = iris.data
y = iris.target
# Split the data into a training set and a test set
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
# Run classifier, using a model that is too regularized (C too low) to see
# the impact on the results
classifier = svm.SVC(kernel='linear', C=0.01)
y_pred = classifier.fit(X_train, y_train).predict(X_test)
def plot_confusion_matrix(cm, title='Confusion matrix', cmap=plt.cm.Blues):
plt.imshow(cm, interpolation='nearest', cmap=cmap)
plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(iris.target_names))
plt.xticks(tick_marks, iris.target_names, rotation=45)
plt.yticks(tick_marks, iris.target_names)
plt.tight_layout()
plt.ylabel('True label')
plt.xlabel('Predicted label')
# Compute confusion matrix
cm = confusion_matrix(y_test, y_pred)
np.set_printoptions(precision=2)
print('Confusion matrix, without normalization')
print(cm)
plt.figure()
plot_confusion_matrix(cm)
# Normalize the confusion matrix by row (i.e by the number of samples
# in each class)
cm_normalized = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]
print('Normalized confusion matrix')
print(cm_normalized)
plt.figure()
plot_confusion_matrix(cm_normalized, title='Normalized confusion matrix')
plt.show()
| bsd-3-clause |
lthurlow/Network-Grapher | proj/external/matplotlib-1.2.1/build/lib.linux-i686-2.7/matplotlib/transforms.py | 2 | 88425 | """
matplotlib includes a framework for arbitrary geometric
transformations that is used determine the final position of all
elements drawn on the canvas.
Transforms are composed into trees of :class:`TransformNode` objects
whose actual value depends on their children. When the contents of
children change, their parents are automatically invalidated. The
next time an invalidated transform is accessed, it is recomputed to
reflect those changes. This invalidation/caching approach prevents
unnecessary recomputations of transforms, and contributes to better
interactive performance.
For example, here is a graph of the transform tree used to plot data
to the graph:
.. image:: ../_static/transforms.png
The framework can be used for both affine and non-affine
transformations. However, for speed, we want use the backend
renderers to perform affine transformations whenever possible.
Therefore, it is possible to perform just the affine or non-affine
part of a transformation on a set of data. The affine is always
assumed to occur after the non-affine. For any transform::
full transform == non-affine part + affine part
The backends are not expected to handle non-affine transformations
themselves.
"""
from __future__ import print_function, division
import numpy as np
from numpy import ma
from matplotlib._path import (affine_transform, count_bboxes_overlapping_bbox,
update_path_extents)
from numpy.linalg import inv
from weakref import WeakValueDictionary
import warnings
try:
set
except NameError:
from sets import Set as set
from path import Path
DEBUG = False
MaskedArray = ma.MaskedArray
class TransformNode(object):
"""
:class:`TransformNode` is the base class for anything that
participates in the transform tree and needs to invalidate its
parents or be invalidated. This includes classes that are not
really transforms, such as bounding boxes, since some transforms
depend on bounding boxes to compute their values.
"""
_gid = 0
# Invalidation may affect only the affine part. If the
# invalidation was "affine-only", the _invalid member is set to
# INVALID_AFFINE_ONLY
INVALID_NON_AFFINE = 1
INVALID_AFFINE = 2
INVALID = INVALID_NON_AFFINE | INVALID_AFFINE
# Some metadata about the transform, used to determine whether an
# invalidation is affine-only
is_affine = False
is_bbox = False
pass_through = False
"""
If pass_through is True, all ancestors will always be
invalidated, even if 'self' is already invalid.
"""
def __init__(self, shorthand_name=None):
"""
Creates a new :class:`TransformNode`.
**shorthand_name** - a string representing the "name" of this
transform. The name carries no significance
other than to improve the readability of
``str(transform)`` when DEBUG=True.
"""
# Parents are stored in a WeakValueDictionary, so that if the
# parents are deleted, references from the children won't keep
# them alive.
self._parents = WeakValueDictionary()
# TransformNodes start out as invalid until their values are
# computed for the first time.
self._invalid = 1
self._shorthand_name = shorthand_name or ''
if DEBUG:
def __str__(self):
# either just return the name of this TransformNode, or it's repr
return self._shorthand_name or repr(self)
def __getstate__(self):
d = self.__dict__.copy()
# turn the weakkey dictionary into a normal dictionary
d['_parents'] = dict(self._parents.iteritems())
return d
def __setstate__(self, data_dict):
self.__dict__ = data_dict
# turn the normal dictionary back into a WeakValueDictionary
self._parents = WeakValueDictionary(self._parents)
def __copy__(self, *args):
raise NotImplementedError(
"TransformNode instances can not be copied. " +
"Consider using frozen() instead.")
__deepcopy__ = __copy__
def invalidate(self):
"""
Invalidate this :class:`TransformNode` and triggers an
invalidation of its ancestors. Should be called any
time the transform changes.
"""
value = self.INVALID
if self.is_affine:
value = self.INVALID_AFFINE
return self._invalidate_internal(value, invalidating_node=self)
def _invalidate_internal(self, value, invalidating_node):
"""
Called by :meth:`invalidate` and subsequently ascends the transform
stack calling each TransformNode's _invalidate_internal method.
"""
# determine if this call will be an extension to the invalidation
# status. If not, then a shortcut means that we needn't invoke an
# invalidation up the transform stack as it will already have been
# invalidated.
# N.B This makes the invalidation sticky, once a transform has been
# invalidated as NON_AFFINE, then it will always be invalidated as
# NON_AFFINE even when triggered with a AFFINE_ONLY invalidation.
# In most cases this is not a problem (i.e. for interactive panning and
# zooming) and the only side effect will be on performance.
status_changed = self._invalid < value
if self.pass_through or status_changed:
self._invalid = value
for parent in self._parents.values():
parent._invalidate_internal(value=value,
invalidating_node=self)
def set_children(self, *children):
"""
Set the children of the transform, to let the invalidation
system know which transforms can invalidate this transform.
Should be called from the constructor of any transforms that
depend on other transforms.
"""
for child in children:
child._parents[id(self)] = self
if DEBUG:
_set_children = set_children
def set_children(self, *children):
self._set_children(*children)
self._children = children
set_children.__doc__ = _set_children.__doc__
def frozen(self):
"""
Returns a frozen copy of this transform node. The frozen copy
will not update when its children change. Useful for storing
a previously known state of a transform where
``copy.deepcopy()`` might normally be used.
"""
return self
if DEBUG:
def write_graphviz(self, fobj, highlight=[]):
"""
For debugging purposes.
Writes the transform tree rooted at 'self' to a graphviz "dot"
format file. This file can be run through the "dot" utility
to produce a graph of the transform tree.
Affine transforms are marked in blue. Bounding boxes are
marked in yellow.
*fobj*: A Python file-like object
Once the "dot" file has been created, it can be turned into a
png easily with::
$> dot -Tpng -o $OUTPUT_FILE $DOT_FILE
"""
seen = set()
def recurse(root):
if root in seen:
return
seen.add(root)
props = {}
label = root.__class__.__name__
if root._invalid:
label = '[%s]' % label
if root in highlight:
props['style'] = 'bold'
props['shape'] = 'box'
props['label'] = '"%s"' % label
props = ' '.join(['%s=%s' % (key, val)
for key, val
in props.iteritems()])
fobj.write('%s [%s];\n' %
(hash(root), props))
if hasattr(root, '_children'):
for child in root._children:
name = '?'
for key, val in root.__dict__.iteritems():
if val is child:
name = key
break
fobj.write('"%s" -> "%s" [label="%s", fontsize=10];\n'
% (hash(root),
hash(child),
name))
recurse(child)
fobj.write("digraph G {\n")
recurse(self)
fobj.write("}\n")
class BboxBase(TransformNode):
"""
This is the base class of all bounding boxes, and provides
read-only access to its data. A mutable bounding box is provided
by the :class:`Bbox` class.
The canonical representation is as two points, with no
restrictions on their ordering. Convenience properties are
provided to get the left, bottom, right and top edges and width
and height, but these are not stored explicitly.
"""
is_bbox = True
is_affine = True
#* Redundant: Removed for performance
#
# def __init__(self):
# TransformNode.__init__(self)
if DEBUG:
def _check(points):
if ma.isMaskedArray(points):
warnings.warn("Bbox bounds are a masked array.")
points = np.asarray(points)
if (points[1, 0] - points[0, 0] == 0 or
points[1, 1] - points[0, 1] == 0):
warnings.warn("Singular Bbox.")
_check = staticmethod(_check)
def frozen(self):
return Bbox(self.get_points().copy())
frozen.__doc__ = TransformNode.__doc__
def __array__(self, *args, **kwargs):
return self.get_points()
def is_unit(self):
"""
Returns True if the :class:`Bbox` is the unit bounding box
from (0, 0) to (1, 1).
"""
return list(self.get_points().flatten()) == [0., 0., 1., 1.]
def _get_x0(self):
return self.get_points()[0, 0]
x0 = property(_get_x0, None, None, """
(property) :attr:`x0` is the first of the pair of *x* coordinates that
define the bounding box. :attr:`x0` is not guaranteed to be
less than :attr:`x1`. If you require that, use :attr:`xmin`.""")
def _get_y0(self):
return self.get_points()[0, 1]
y0 = property(_get_y0, None, None, """
(property) :attr:`y0` is the first of the pair of *y* coordinates that
define the bounding box. :attr:`y0` is not guaranteed to be
less than :attr:`y1`. If you require that, use :attr:`ymin`.""")
def _get_x1(self):
return self.get_points()[1, 0]
x1 = property(_get_x1, None, None, """
(property) :attr:`x1` is the second of the pair of *x* coordinates
that define the bounding box. :attr:`x1` is not guaranteed to be
greater than :attr:`x0`. If you require that, use :attr:`xmax`.""")
def _get_y1(self):
return self.get_points()[1, 1]
y1 = property(_get_y1, None, None, """
(property) :attr:`y1` is the second of the pair of *y* coordinates
that define the bounding box. :attr:`y1` is not guaranteed to be
greater than :attr:`y0`. If you require that, use :attr:`ymax`.""")
def _get_p0(self):
return self.get_points()[0]
p0 = property(_get_p0, None, None, """
(property) :attr:`p0` is the first pair of (*x*, *y*) coordinates
that define the bounding box. It is not guaranteed to be the
bottom-left corner. For that, use :attr:`min`.""")
def _get_p1(self):
return self.get_points()[1]
p1 = property(_get_p1, None, None, """
(property) :attr:`p1` is the second pair of (*x*, *y*) coordinates
that define the bounding box. It is not guaranteed to be the
top-right corner. For that, use :attr:`max`.""")
def _get_xmin(self):
return min(self.get_points()[:, 0])
xmin = property(_get_xmin, None, None, """
(property) :attr:`xmin` is the left edge of the bounding box.""")
def _get_ymin(self):
return min(self.get_points()[:, 1])
ymin = property(_get_ymin, None, None, """
(property) :attr:`ymin` is the bottom edge of the bounding box.""")
def _get_xmax(self):
return max(self.get_points()[:, 0])
xmax = property(_get_xmax, None, None, """
(property) :attr:`xmax` is the right edge of the bounding box.""")
def _get_ymax(self):
return max(self.get_points()[:, 1])
ymax = property(_get_ymax, None, None, """
(property) :attr:`ymax` is the top edge of the bounding box.""")
def _get_min(self):
return [min(self.get_points()[:, 0]),
min(self.get_points()[:, 1])]
min = property(_get_min, None, None, """
(property) :attr:`min` is the bottom-left corner of the bounding
box.""")
def _get_max(self):
return [max(self.get_points()[:, 0]),
max(self.get_points()[:, 1])]
max = property(_get_max, None, None, """
(property) :attr:`max` is the top-right corner of the bounding box.""")
def _get_intervalx(self):
return self.get_points()[:, 0]
intervalx = property(_get_intervalx, None, None, """
(property) :attr:`intervalx` is the pair of *x* coordinates that define
the bounding box. It is not guaranteed to be sorted from left to
right.""")
def _get_intervaly(self):
return self.get_points()[:, 1]
intervaly = property(_get_intervaly, None, None, """
(property) :attr:`intervaly` is the pair of *y* coordinates that define
the bounding box. It is not guaranteed to be sorted from bottom to
top.""")
def _get_width(self):
points = self.get_points()
return points[1, 0] - points[0, 0]
width = property(_get_width, None, None, """
(property) The width of the bounding box. It may be negative if
:attr:`x1` < :attr:`x0`.""")
def _get_height(self):
points = self.get_points()
return points[1, 1] - points[0, 1]
height = property(_get_height, None, None, """
(property) The height of the bounding box. It may be negative if
:attr:`y1` < :attr:`y0`.""")
def _get_size(self):
points = self.get_points()
return points[1] - points[0]
size = property(_get_size, None, None, """
(property) The width and height of the bounding box. May be negative,
in the same way as :attr:`width` and :attr:`height`.""")
def _get_bounds(self):
x0, y0, x1, y1 = self.get_points().flatten()
return (x0, y0, x1 - x0, y1 - y0)
bounds = property(_get_bounds, None, None, """
(property) Returns (:attr:`x0`, :attr:`y0`, :attr:`width`,
:attr:`height`).""")
def _get_extents(self):
return self.get_points().flatten().copy()
extents = property(_get_extents, None, None, """
(property) Returns (:attr:`x0`, :attr:`y0`, :attr:`x1`,
:attr:`y1`).""")
def get_points(self):
return NotImplementedError()
def containsx(self, x):
"""
Returns True if *x* is between or equal to :attr:`x0` and
:attr:`x1`.
"""
x0, x1 = self.intervalx
return ((x0 < x1
and (x >= x0 and x <= x1))
or (x >= x1 and x <= x0))
def containsy(self, y):
"""
Returns True if *y* is between or equal to :attr:`y0` and
:attr:`y1`.
"""
y0, y1 = self.intervaly
return ((y0 < y1
and (y >= y0 and y <= y1))
or (y >= y1 and y <= y0))
def contains(self, x, y):
"""
Returns *True* if (*x*, *y*) is a coordinate inside the
bounding box or on its edge.
"""
return self.containsx(x) and self.containsy(y)
def overlaps(self, other):
"""
Returns True if this bounding box overlaps with the given
bounding box *other*.
"""
ax1, ay1, ax2, ay2 = self._get_extents()
bx1, by1, bx2, by2 = other._get_extents()
if ax2 < ax1:
ax2, ax1 = ax1, ax2
if ay2 < ay1:
ay2, ay1 = ay1, ay2
if bx2 < bx1:
bx2, bx1 = bx1, bx2
if by2 < by1:
by2, by1 = by1, by2
return not ((bx2 < ax1) or
(by2 < ay1) or
(bx1 > ax2) or
(by1 > ay2))
def fully_containsx(self, x):
"""
Returns True if *x* is between but not equal to :attr:`x0` and
:attr:`x1`.
"""
x0, x1 = self.intervalx
return ((x0 < x1
and (x > x0 and x < x1))
or (x > x1 and x < x0))
def fully_containsy(self, y):
"""
Returns True if *y* is between but not equal to :attr:`y0` and
:attr:`y1`.
"""
y0, y1 = self.intervaly
return ((y0 < y1
and (y > y0 and y < y1))
or (y > y1 and y < y0))
def fully_contains(self, x, y):
"""
Returns True if (*x*, *y*) is a coordinate inside the bounding
box, but not on its edge.
"""
return self.fully_containsx(x) \
and self.fully_containsy(y)
def fully_overlaps(self, other):
"""
Returns True if this bounding box overlaps with the given
bounding box *other*, but not on its edge alone.
"""
ax1, ay1, ax2, ay2 = self._get_extents()
bx1, by1, bx2, by2 = other._get_extents()
if ax2 < ax1:
ax2, ax1 = ax1, ax2
if ay2 < ay1:
ay2, ay1 = ay1, ay2
if bx2 < bx1:
bx2, bx1 = bx1, bx2
if by2 < by1:
by2, by1 = by1, by2
return not ((bx2 <= ax1) or
(by2 <= ay1) or
(bx1 >= ax2) or
(by1 >= ay2))
def transformed(self, transform):
"""
Return a new :class:`Bbox` object, statically transformed by
the given transform.
"""
return Bbox(transform.transform(self.get_points()))
def inverse_transformed(self, transform):
"""
Return a new :class:`Bbox` object, statically transformed by
the inverse of the given transform.
"""
return Bbox(transform.inverted().transform(self.get_points()))
coefs = {'C': (0.5, 0.5),
'SW': (0, 0),
'S': (0.5, 0),
'SE': (1.0, 0),
'E': (1.0, 0.5),
'NE': (1.0, 1.0),
'N': (0.5, 1.0),
'NW': (0, 1.0),
'W': (0, 0.5)}
def anchored(self, c, container=None):
"""
Return a copy of the :class:`Bbox`, shifted to position *c*
within a container.
*c*: may be either:
* a sequence (*cx*, *cy*) where *cx* and *cy* range from 0
to 1, where 0 is left or bottom and 1 is right or top
* a string:
- 'C' for centered
- 'S' for bottom-center
- 'SE' for bottom-left
- 'E' for left
- etc.
Optional argument *container* is the box within which the
:class:`Bbox` is positioned; it defaults to the initial
:class:`Bbox`.
"""
if container is None:
container = self
l, b, w, h = container.bounds
if isinstance(c, basestring):
cx, cy = self.coefs[c]
else:
cx, cy = c
L, B, W, H = self.bounds
return Bbox(self._points +
[(l + cx * (w - W)) - L,
(b + cy * (h - H)) - B])
def shrunk(self, mx, my):
"""
Return a copy of the :class:`Bbox`, shrunk by the factor *mx*
in the *x* direction and the factor *my* in the *y* direction.
The lower left corner of the box remains unchanged. Normally
*mx* and *my* will be less than 1, but this is not enforced.
"""
w, h = self.size
return Bbox([self._points[0],
self._points[0] + [mx * w, my * h]])
def shrunk_to_aspect(self, box_aspect, container=None, fig_aspect=1.0):
"""
Return a copy of the :class:`Bbox`, shrunk so that it is as
large as it can be while having the desired aspect ratio,
*box_aspect*. If the box coordinates are relative---that
is, fractions of a larger box such as a figure---then the
physical aspect ratio of that figure is specified with
*fig_aspect*, so that *box_aspect* can also be given as a
ratio of the absolute dimensions, not the relative dimensions.
"""
assert box_aspect > 0 and fig_aspect > 0
if container is None:
container = self
w, h = container.size
H = w * box_aspect / fig_aspect
if H <= h:
W = w
else:
W = h * fig_aspect / box_aspect
H = h
return Bbox([self._points[0],
self._points[0] + (W, H)])
def splitx(self, *args):
"""
e.g., ``bbox.splitx(f1, f2, ...)``
Returns a list of new :class:`Bbox` objects formed by
splitting the original one with vertical lines at fractional
positions *f1*, *f2*, ...
"""
boxes = []
xf = [0] + list(args) + [1]
x0, y0, x1, y1 = self._get_extents()
w = x1 - x0
for xf0, xf1 in zip(xf[:-1], xf[1:]):
boxes.append(Bbox([[x0 + xf0 * w, y0], [x0 + xf1 * w, y1]]))
return boxes
def splity(self, *args):
"""
e.g., ``bbox.splitx(f1, f2, ...)``
Returns a list of new :class:`Bbox` objects formed by
splitting the original one with horizontal lines at fractional
positions *f1*, *f2*, ...
"""
boxes = []
yf = [0] + list(args) + [1]
x0, y0, x1, y1 = self._get_extents()
h = y1 - y0
for yf0, yf1 in zip(yf[:-1], yf[1:]):
boxes.append(Bbox([[x0, y0 + yf0 * h], [x1, y0 + yf1 * h]]))
return boxes
def count_contains(self, vertices):
"""
Count the number of vertices contained in the :class:`Bbox`.
*vertices* is a Nx2 Numpy array.
"""
if len(vertices) == 0:
return 0
vertices = np.asarray(vertices)
x0, y0, x1, y1 = self._get_extents()
dx0 = np.sign(vertices[:, 0] - x0)
dy0 = np.sign(vertices[:, 1] - y0)
dx1 = np.sign(vertices[:, 0] - x1)
dy1 = np.sign(vertices[:, 1] - y1)
inside = (abs(dx0 + dx1) + abs(dy0 + dy1)) <= 2
return np.sum(inside)
def count_overlaps(self, bboxes):
"""
Count the number of bounding boxes that overlap this one.
bboxes is a sequence of :class:`BboxBase` objects
"""
return count_bboxes_overlapping_bbox(self, bboxes)
def expanded(self, sw, sh):
"""
Return a new :class:`Bbox` which is this :class:`Bbox`
expanded around its center by the given factors *sw* and
*sh*.
"""
width = self.width
height = self.height
deltaw = (sw * width - width) / 2.0
deltah = (sh * height - height) / 2.0
a = np.array([[-deltaw, -deltah], [deltaw, deltah]])
return Bbox(self._points + a)
def padded(self, p):
"""
Return a new :class:`Bbox` that is padded on all four sides by
the given value.
"""
points = self.get_points()
return Bbox(points + [[-p, -p], [p, p]])
def translated(self, tx, ty):
"""
Return a copy of the :class:`Bbox`, statically translated by
*tx* and *ty*.
"""
return Bbox(self._points + (tx, ty))
def corners(self):
"""
Return an array of points which are the four corners of this
rectangle. For example, if this :class:`Bbox` is defined by
the points (*a*, *b*) and (*c*, *d*), :meth:`corners` returns
(*a*, *b*), (*a*, *d*), (*c*, *b*) and (*c*, *d*).
"""
l, b, r, t = self.get_points().flatten()
return np.array([[l, b], [l, t], [r, b], [r, t]])
def rotated(self, radians):
"""
Return a new bounding box that bounds a rotated version of
this bounding box by the given radians. The new bounding box
is still aligned with the axes, of course.
"""
corners = self.corners()
corners_rotated = Affine2D().rotate(radians).transform(corners)
bbox = Bbox.unit()
bbox.update_from_data_xy(corners_rotated, ignore=True)
return bbox
@staticmethod
def union(bboxes):
"""
Return a :class:`Bbox` that contains all of the given bboxes.
"""
assert(len(bboxes))
if len(bboxes) == 1:
return bboxes[0]
x0 = np.inf
y0 = np.inf
x1 = -np.inf
y1 = -np.inf
for bbox in bboxes:
points = bbox.get_points()
xs = points[:, 0]
ys = points[:, 1]
x0 = min(x0, np.min(xs))
y0 = min(y0, np.min(ys))
x1 = max(x1, np.max(xs))
y1 = max(y1, np.max(ys))
return Bbox.from_extents(x0, y0, x1, y1)
class Bbox(BboxBase):
"""
A mutable bounding box.
"""
def __init__(self, points, **kwargs):
"""
*points*: a 2x2 numpy array of the form [[x0, y0], [x1, y1]]
If you need to create a :class:`Bbox` object from another form
of data, consider the static methods :meth:`unit`,
:meth:`from_bounds` and :meth:`from_extents`.
"""
BboxBase.__init__(self, **kwargs)
self._points = np.asarray(points, np.float_)
self._minpos = np.array([0.0000001, 0.0000001])
self._ignore = True
# it is helpful in some contexts to know if the bbox is a
# default or has been mutated; we store the orig points to
# support the mutated methods
self._points_orig = self._points.copy()
if DEBUG:
___init__ = __init__
def __init__(self, points, **kwargs):
self._check(points)
self.___init__(points, **kwargs)
def invalidate(self):
self._check(self._points)
TransformNode.invalidate(self)
_unit_values = np.array([[0.0, 0.0], [1.0, 1.0]], np.float_)
@staticmethod
def unit():
"""
(staticmethod) Create a new unit :class:`Bbox` from (0, 0) to
(1, 1).
"""
return Bbox(Bbox._unit_values.copy())
@staticmethod
def from_bounds(x0, y0, width, height):
"""
(staticmethod) Create a new :class:`Bbox` from *x0*, *y0*,
*width* and *height*.
*width* and *height* may be negative.
"""
return Bbox.from_extents(x0, y0, x0 + width, y0 + height)
@staticmethod
def from_extents(*args):
"""
(staticmethod) Create a new Bbox from *left*, *bottom*,
*right* and *top*.
The *y*-axis increases upwards.
"""
points = np.array(args, dtype=np.float_).reshape(2, 2)
return Bbox(points)
def __repr__(self):
return 'Bbox(%r)' % repr(self._points)
def ignore(self, value):
"""
Set whether the existing bounds of the box should be ignored
by subsequent calls to :meth:`update_from_data` or
:meth:`update_from_data_xy`.
*value*:
- When True, subsequent calls to :meth:`update_from_data`
will ignore the existing bounds of the :class:`Bbox`.
- When False, subsequent calls to :meth:`update_from_data`
will include the existing bounds of the :class:`Bbox`.
"""
self._ignore = value
def update_from_data(self, x, y, ignore=None):
"""
Update the bounds of the :class:`Bbox` based on the passed in
data. After updating, the bounds will have positive *width*
and *height*; *x0* and *y0* will be the minimal values.
*x*: a numpy array of *x*-values
*y*: a numpy array of *y*-values
*ignore*:
- when True, ignore the existing bounds of the :class:`Bbox`.
- when False, include the existing bounds of the :class:`Bbox`.
- when None, use the last value passed to :meth:`ignore`.
"""
warnings.warn(
"update_from_data requires a memory copy -- please replace with "
"update_from_data_xy")
xy = np.hstack((x.reshape((len(x), 1)), y.reshape((len(y), 1))))
return self.update_from_data_xy(xy, ignore)
def update_from_path(self, path, ignore=None, updatex=True, updatey=True):
"""
Update the bounds of the :class:`Bbox` based on the passed in
data. After updating, the bounds will have positive *width*
and *height*; *x0* and *y0* will be the minimal values.
*path*: a :class:`~matplotlib.path.Path` instance
*ignore*:
- when True, ignore the existing bounds of the :class:`Bbox`.
- when False, include the existing bounds of the :class:`Bbox`.
- when None, use the last value passed to :meth:`ignore`.
*updatex*: when True, update the x values
*updatey*: when True, update the y values
"""
if ignore is None:
ignore = self._ignore
if path.vertices.size == 0:
return
points, minpos, changed = update_path_extents(
path, None, self._points, self._minpos, ignore)
if changed:
self.invalidate()
if updatex:
self._points[:, 0] = points[:, 0]
self._minpos[0] = minpos[0]
if updatey:
self._points[:, 1] = points[:, 1]
self._minpos[1] = minpos[1]
def update_from_data_xy(self, xy, ignore=None, updatex=True, updatey=True):
"""
Update the bounds of the :class:`Bbox` based on the passed in
data. After updating, the bounds will have positive *width*
and *height*; *x0* and *y0* will be the minimal values.
*xy*: a numpy array of 2D points
*ignore*:
- when True, ignore the existing bounds of the :class:`Bbox`.
- when False, include the existing bounds of the :class:`Bbox`.
- when None, use the last value passed to :meth:`ignore`.
*updatex*: when True, update the x values
*updatey*: when True, update the y values
"""
if len(xy) == 0:
return
path = Path(xy)
self.update_from_path(path, ignore=ignore,
updatex=updatex, updatey=updatey)
def _set_x0(self, val):
self._points[0, 0] = val
self.invalidate()
x0 = property(BboxBase._get_x0, _set_x0)
def _set_y0(self, val):
self._points[0, 1] = val
self.invalidate()
y0 = property(BboxBase._get_y0, _set_y0)
def _set_x1(self, val):
self._points[1, 0] = val
self.invalidate()
x1 = property(BboxBase._get_x1, _set_x1)
def _set_y1(self, val):
self._points[1, 1] = val
self.invalidate()
y1 = property(BboxBase._get_y1, _set_y1)
def _set_p0(self, val):
self._points[0] = val
self.invalidate()
p0 = property(BboxBase._get_p0, _set_p0)
def _set_p1(self, val):
self._points[1] = val
self.invalidate()
p1 = property(BboxBase._get_p1, _set_p1)
def _set_intervalx(self, interval):
self._points[:, 0] = interval
self.invalidate()
intervalx = property(BboxBase._get_intervalx, _set_intervalx)
def _set_intervaly(self, interval):
self._points[:, 1] = interval
self.invalidate()
intervaly = property(BboxBase._get_intervaly, _set_intervaly)
def _set_bounds(self, bounds):
l, b, w, h = bounds
points = np.array([[l, b], [l + w, b + h]], np.float_)
if np.any(self._points != points):
self._points = points
self.invalidate()
bounds = property(BboxBase._get_bounds, _set_bounds)
def _get_minpos(self):
return self._minpos
minpos = property(_get_minpos)
def _get_minposx(self):
return self._minpos[0]
minposx = property(_get_minposx)
def _get_minposy(self):
return self._minpos[1]
minposy = property(_get_minposy)
def get_points(self):
"""
Get the points of the bounding box directly as a numpy array
of the form: [[x0, y0], [x1, y1]].
"""
self._invalid = 0
return self._points
def set_points(self, points):
"""
Set the points of the bounding box directly from a numpy array
of the form: [[x0, y0], [x1, y1]]. No error checking is
performed, as this method is mainly for internal use.
"""
if np.any(self._points != points):
self._points = points
self.invalidate()
def set(self, other):
"""
Set this bounding box from the "frozen" bounds of another
:class:`Bbox`.
"""
if np.any(self._points != other.get_points()):
self._points = other.get_points()
self.invalidate()
def mutated(self):
'return whether the bbox has changed since init'
return self.mutatedx() or self.mutatedy()
def mutatedx(self):
'return whether the x-limits have changed since init'
return (self._points[0, 0] != self._points_orig[0, 0] or
self._points[1, 0] != self._points_orig[1, 0])
def mutatedy(self):
'return whether the y-limits have changed since init'
return (self._points[0, 1] != self._points_orig[0, 1] or
self._points[1, 1] != self._points_orig[1, 1])
class TransformedBbox(BboxBase):
"""
A :class:`Bbox` that is automatically transformed by a given
transform. When either the child bounding box or transform
changes, the bounds of this bbox will update accordingly.
"""
def __init__(self, bbox, transform, **kwargs):
"""
*bbox*: a child :class:`Bbox`
*transform*: a 2D :class:`Transform`
"""
assert bbox.is_bbox
assert isinstance(transform, Transform)
assert transform.input_dims == 2
assert transform.output_dims == 2
BboxBase.__init__(self, **kwargs)
self._bbox = bbox
self._transform = transform
self.set_children(bbox, transform)
self._points = None
def __repr__(self):
return "TransformedBbox(%r, %r)" % (self._bbox, self._transform)
def get_points(self):
if self._invalid:
points = self._transform.transform(self._bbox.get_points())
points = np.ma.filled(points, 0.0)
self._points = points
self._invalid = 0
return self._points
get_points.__doc__ = Bbox.get_points.__doc__
if DEBUG:
_get_points = get_points
def get_points(self):
points = self._get_points()
self._check(points)
return points
class Transform(TransformNode):
"""
The base class of all :class:`TransformNode` instances that
actually perform a transformation.
All non-affine transformations should be subclasses of this class.
New affine transformations should be subclasses of
:class:`Affine2D`.
Subclasses of this class should override the following members (at
minimum):
- :attr:`input_dims`
- :attr:`output_dims`
- :meth:`transform`
- :attr:`is_separable`
- :attr:`has_inverse`
- :meth:`inverted` (if :attr:`has_inverse` is True)
If the transform needs to do something non-standard with
:class:`matplotlib.path.Path` objects, such as adding curves
where there were once line segments, it should override:
- :meth:`transform_path`
"""
input_dims = None
"""
The number of input dimensions of this transform.
Must be overridden (with integers) in the subclass.
"""
output_dims = None
"""
The number of output dimensions of this transform.
Must be overridden (with integers) in the subclass.
"""
has_inverse = False
"""True if this transform has a corresponding inverse transform."""
is_separable = False
"""True if this transform is separable in the x- and y- dimensions."""
def __add__(self, other):
"""
Composes two transforms together such that *self* is followed
by *other*.
"""
if isinstance(other, Transform):
return composite_transform_factory(self, other)
raise TypeError(
"Can not add Transform to object of type '%s'" % type(other))
def __radd__(self, other):
"""
Composes two transforms together such that *self* is followed
by *other*.
"""
if isinstance(other, Transform):
return composite_transform_factory(other, self)
raise TypeError(
"Can not add Transform to object of type '%s'" % type(other))
def __eq__(self, other):
# equality is based on transform object id. Hence:
# Transform() != Transform().
# Some classes, such as TransformWrapper & AffineBase, will override.
return self is other
def _iter_break_from_left_to_right(self):
"""
Returns an iterator breaking down this transform stack from left to
right recursively. If self == ((A, N), A) then the result will be an
iterator which yields I : ((A, N), A), followed by A : (N, A),
followed by (A, N) : (A), but not ((A, N), A) : I.
This is equivalent to flattening the stack then yielding
``flat_stack[:i], flat_stack[i:]`` where i=0..(n-1).
"""
yield IdentityTransform(), self
@property
def depth(self):
"""
Returns the number of transforms which have been chained
together to form this Transform instance.
.. note::
For the special case of a Composite transform, the maximum depth
of the two is returned.
"""
return 1
def contains_branch(self, other):
"""
Return whether the given transform is a sub-tree of this transform.
This routine uses transform equality to identify sub-trees, therefore
in many situations it is object id which will be used.
For the case where the given transform represents the whole
of this transform, returns True.
"""
if self.depth < other.depth:
return False
# check that a subtree is equal to other (starting from self)
for _, sub_tree in self._iter_break_from_left_to_right():
if sub_tree == other:
return True
return False
def contains_branch_seperately(self, other_transform):
"""
Returns whether the given branch is a sub-tree of this transform on
each seperate dimension.
A common use for this method is to identify if a transform is a blended
transform containing an axes' data transform. e.g.::
x_isdata, y_isdata = trans.contains_branch_seperately(ax.transData)
"""
if self.output_dims != 2:
raise ValueError('contains_branch_seperately only supports '
'transforms with 2 output dimensions')
# for a non-blended transform each seperate dimension is the same, so
# just return the appropriate shape.
return [self.contains_branch(other_transform)] * 2
def __sub__(self, other):
"""
Returns a transform stack which goes all the way down self's transform
stack, and then ascends back up other's stack. If it can, this is
optimised::
# normally
A - B == a + b.inverted()
# sometimes, when A contains the tree B there is no need to
# descend all the way down to the base of A (via B), instead we
# can just stop at B.
(A + B) - (B)^-1 == A
# similarly, when B contains tree A, we can avoid decending A at
# all, basically:
A - (A + B) == ((B + A) - A).inverted() or B^-1
For clarity, the result of ``(A + B) - B + B == (A + B)``.
"""
# we only know how to do this operation if other is a Transform.
if not isinstance(other, Transform):
return NotImplemented
for remainder, sub_tree in self._iter_break_from_left_to_right():
if sub_tree == other:
return remainder
for remainder, sub_tree in other._iter_break_from_left_to_right():
if sub_tree == self:
if not remainder.has_inverse:
raise ValueError("The shortcut cannot be computed since "
"other's transform includes a non-invertable component.")
return remainder.inverted()
# if we have got this far, then there was no shortcut possible
if other.has_inverse:
return self + other.inverted()
else:
raise ValueError('It is not possible to compute transA - transB '
'since transB cannot be inverted and there is no '
'shortcut possible.')
def __array__(self, *args, **kwargs):
"""
Array interface to get at this Transform's affine matrix.
"""
return self.get_affine().get_matrix()
def transform(self, values):
"""
Performs the transformation on the given array of values.
Accepts a numpy array of shape (N x :attr:`input_dims`) and
returns a numpy array of shape (N x :attr:`output_dims`).
"""
return self.transform_affine(self.transform_non_affine(values))
def transform_affine(self, values):
"""
Performs only the affine part of this transformation on the
given array of values.
``transform(values)`` is always equivalent to
``transform_affine(transform_non_affine(values))``.
In non-affine transformations, this is generally a no-op. In
affine transformations, this is equivalent to
``transform(values)``.
Accepts a numpy array of shape (N x :attr:`input_dims`) and
returns a numpy array of shape (N x :attr:`output_dims`).
"""
return self.get_affine().transform(values)
def transform_non_affine(self, values):
"""
Performs only the non-affine part of the transformation.
``transform(values)`` is always equivalent to
``transform_affine(transform_non_affine(values))``.
In non-affine transformations, this is generally equivalent to
``transform(values)``. In affine transformations, this is
always a no-op.
Accepts a numpy array of shape (N x :attr:`input_dims`) and
returns a numpy array of shape (N x :attr:`output_dims`).
"""
return values
def get_affine(self):
"""
Get the affine part of this transform.
"""
return IdentityTransform()
def get_matrix(self):
"""
Get the Affine transformation array for the affine part
of this transform.
"""
return self.get_affine().get_matrix()
def transform_point(self, point):
"""
A convenience function that returns the transformed copy of a
single point.
The point is given as a sequence of length :attr:`input_dims`.
The transformed point is returned as a sequence of length
:attr:`output_dims`.
"""
assert len(point) == self.input_dims
return self.transform(np.asarray([point]))[0]
def transform_path(self, path):
"""
Returns a transformed path.
*path*: a :class:`~matplotlib.path.Path` instance.
In some cases, this transform may insert curves into the path
that began as line segments.
"""
return self.transform_path_affine(self.transform_path_non_affine(path))
def transform_path_affine(self, path):
"""
Returns a path, transformed only by the affine part of
this transform.
*path*: a :class:`~matplotlib.path.Path` instance.
``transform_path(path)`` is equivalent to
``transform_path_affine(transform_path_non_affine(values))``.
"""
return self.get_affine().transform_path_affine(path)
def transform_path_non_affine(self, path):
"""
Returns a path, transformed only by the non-affine
part of this transform.
*path*: a :class:`~matplotlib.path.Path` instance.
``transform_path(path)`` is equivalent to
``transform_path_affine(transform_path_non_affine(values))``.
"""
return Path(self.transform_non_affine(path.vertices), path.codes,
path._interpolation_steps)
def transform_angles(self, angles, pts, radians=False, pushoff=1e-5):
"""
Performs transformation on a set of angles anchored at
specific locations.
The *angles* must be a column vector (i.e., numpy array).
The *pts* must be a two-column numpy array of x,y positions
(angle transforms currently only work in 2D). This array must
have the same number of rows as *angles*.
*radians* indicates whether or not input angles are given in
radians (True) or degrees (False; the default).
*pushoff* is the distance to move away from *pts* for
determining transformed angles (see discussion of method
below).
The transformed angles are returned in an array with the same
size as *angles*.
The generic version of this method uses a very generic
algorithm that transforms *pts*, as well as locations very
close to *pts*, to find the angle in the transformed system.
"""
# Must be 2D
if self.input_dims != 2 or self.output_dims != 2:
raise NotImplementedError('Only defined in 2D')
# pts must be array with 2 columns for x,y
assert pts.shape[1] == 2
# angles must be a column vector and have same number of
# rows as pts
assert np.prod(angles.shape) == angles.shape[0] == pts.shape[0]
# Convert to radians if desired
if not radians:
angles = angles / 180.0 * np.pi
# Move a short distance away
pts2 = pts + pushoff * np.c_[np.cos(angles), np.sin(angles)]
# Transform both sets of points
tpts = self.transform(pts)
tpts2 = self.transform(pts2)
# Calculate transformed angles
d = tpts2 - tpts
a = np.arctan2(d[:, 1], d[:, 0])
# Convert back to degrees if desired
if not radians:
a = a * 180.0 / np.pi
return a
def inverted(self):
"""
Return the corresponding inverse transformation.
The return value of this method should be treated as
temporary. An update to *self* does not cause a corresponding
update to its inverted copy.
``x === self.inverted().transform(self.transform(x))``
"""
raise NotImplementedError()
class TransformWrapper(Transform):
"""
A helper class that holds a single child transform and acts
equivalently to it.
This is useful if a node of the transform tree must be replaced at
run time with a transform of a different type. This class allows
that replacement to correctly trigger invalidation.
Note that :class:`TransformWrapper` instances must have the same
input and output dimensions during their entire lifetime, so the
child transform may only be replaced with another child transform
of the same dimensions.
"""
pass_through = True
def __init__(self, child):
"""
*child*: A class:`Transform` instance. This child may later
be replaced with :meth:`set`.
"""
assert isinstance(child, Transform)
Transform.__init__(self)
self.input_dims = child.input_dims
self.output_dims = child.output_dims
self._set(child)
self._invalid = 0
def __eq__(self, other):
return self._child.__eq__(other)
if DEBUG:
def __str__(self):
return str(self._child)
def __getstate__(self):
# only store the child
return {'child': self._child}
def __setstate__(self, state):
# re-initialise the TransformWrapper with the state's child
self.__init__(state['child'])
def __repr__(self):
return "TransformWrapper(%r)" % self._child
def frozen(self):
return self._child.frozen()
frozen.__doc__ = Transform.frozen.__doc__
def _set(self, child):
self._child = child
self.set_children(child)
self.transform = child.transform
self.transform_affine = child.transform_affine
self.transform_non_affine = child.transform_non_affine
self.transform_path = child.transform_path
self.transform_path_affine = child.transform_path_affine
self.transform_path_non_affine = child.transform_path_non_affine
self.get_affine = child.get_affine
self.inverted = child.inverted
self.get_matrix = child.get_matrix
# note we do not wrap other properties here since the transform's
# child can be changed with WrappedTransform.set and so checking
# is_affine and other such properties may be dangerous.
def set(self, child):
"""
Replace the current child of this transform with another one.
The new child must have the same number of input and output
dimensions as the current child.
"""
assert child.input_dims == self.input_dims
assert child.output_dims == self.output_dims
self._set(child)
self._invalid = 0
self.invalidate()
self._invalid = 0
def _get_is_affine(self):
return self._child.is_affine
is_affine = property(_get_is_affine)
def _get_is_separable(self):
return self._child.is_separable
is_separable = property(_get_is_separable)
def _get_has_inverse(self):
return self._child.has_inverse
has_inverse = property(_get_has_inverse)
class AffineBase(Transform):
"""
The base class of all affine transformations of any number of
dimensions.
"""
is_affine = True
def __init__(self, *args, **kwargs):
Transform.__init__(self, *args, **kwargs)
self._inverted = None
def __array__(self, *args, **kwargs):
# optimises the access of the transform matrix vs the superclass
return self.get_matrix()
@staticmethod
def _concat(a, b):
"""
Concatenates two transformation matrices (represented as numpy
arrays) together.
"""
return np.dot(b, a)
def __eq__(self, other):
if other.is_affine:
return np.all(self.get_matrix() == other.get_matrix())
return NotImplemented
def transform(self, values):
return self.transform_affine(values)
transform.__doc__ = Transform.transform.__doc__
def transform_affine(self, values):
raise NotImplementedError('Affine subclasses should override this '
'method.')
transform_affine.__doc__ = Transform.transform_affine.__doc__
def transform_non_affine(self, points):
return points
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def transform_path(self, path):
return self.transform_path_affine(path)
transform_path.__doc__ = Transform.transform_path.__doc__
def transform_path_affine(self, path):
return Path(self.transform_affine(path.vertices),
path.codes, path._interpolation_steps)
transform_path_affine.__doc__ = Transform.transform_path_affine.__doc__
def transform_path_non_affine(self, path):
return path
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
def get_affine(self):
return self
get_affine.__doc__ = Transform.get_affine.__doc__
class Affine2DBase(AffineBase):
"""
The base class of all 2D affine transformations.
2D affine transformations are performed using a 3x3 numpy array::
a c e
b d f
0 0 1
This class provides the read-only interface. For a mutable 2D
affine transformation, use :class:`Affine2D`.
Subclasses of this class will generally only need to override a
constructor and :meth:`get_matrix` that generates a custom 3x3 matrix.
"""
has_inverse = True
input_dims = 2
output_dims = 2
def frozen(self):
return Affine2D(self.get_matrix().copy())
frozen.__doc__ = AffineBase.frozen.__doc__
def _get_is_separable(self):
mtx = self.get_matrix()
return mtx[0, 1] == 0.0 and mtx[1, 0] == 0.0
is_separable = property(_get_is_separable)
def to_values(self):
"""
Return the values of the matrix as a sequence (a,b,c,d,e,f)
"""
mtx = self.get_matrix()
return tuple(mtx[:2].swapaxes(0, 1).flatten())
@staticmethod
def matrix_from_values(a, b, c, d, e, f):
"""
(staticmethod) Create a new transformation matrix as a 3x3
numpy array of the form::
a c e
b d f
0 0 1
"""
return np.array([[a, c, e], [b, d, f], [0.0, 0.0, 1.0]], np.float_)
def transform_affine(self, points):
mtx = self.get_matrix()
if isinstance(points, MaskedArray):
tpoints = affine_transform(points.data, mtx)
return ma.MaskedArray(tpoints, mask=ma.getmask(points))
return affine_transform(points, mtx)
def transform_point(self, point):
mtx = self.get_matrix()
return affine_transform(point, mtx)
transform_point.__doc__ = AffineBase.transform_point.__doc__
if DEBUG:
_transform_affine = transform_affine
def transform_affine(self, points):
# The major speed trap here is just converting to the
# points to an array in the first place. If we can use
# more arrays upstream, that should help here.
if (not ma.isMaskedArray(points) and
not isinstance(points, np.ndarray)):
warnings.warn(
('A non-numpy array of type %s was passed in for ' +
'transformation. Please correct this.')
% type(points))
return self._transform_affine(points)
transform_affine.__doc__ = AffineBase.transform_affine.__doc__
def inverted(self):
if self._inverted is None or self._invalid:
mtx = self.get_matrix()
shorthand_name = None
if self._shorthand_name:
shorthand_name = '(%s)-1' % self._shorthand_name
self._inverted = Affine2D(inv(mtx), shorthand_name=shorthand_name)
self._invalid = 0
return self._inverted
inverted.__doc__ = AffineBase.inverted.__doc__
class Affine2D(Affine2DBase):
"""
A mutable 2D affine transformation.
"""
def __init__(self, matrix=None, **kwargs):
"""
Initialize an Affine transform from a 3x3 numpy float array::
a c e
b d f
0 0 1
If *matrix* is None, initialize with the identity transform.
"""
Affine2DBase.__init__(self, **kwargs)
if matrix is None:
matrix = np.identity(3)
elif DEBUG:
matrix = np.asarray(matrix, np.float_)
assert matrix.shape == (3, 3)
self._mtx = matrix
self._invalid = 0
def __repr__(self):
return "Affine2D(%s)" % repr(self._mtx)
# def __cmp__(self, other):
# # XXX redundant. this only tells us eq.
# if (isinstance(other, Affine2D) and
# (self.get_matrix() == other.get_matrix()).all()):
# return 0
# return -1
@staticmethod
def from_values(a, b, c, d, e, f):
"""
(staticmethod) Create a new Affine2D instance from the given
values::
a c e
b d f
0 0 1
.
"""
return Affine2D(
np.array([a, c, e, b, d, f, 0.0, 0.0, 1.0], np.float_)
.reshape((3, 3)))
def get_matrix(self):
"""
Get the underlying transformation matrix as a 3x3 numpy array::
a c e
b d f
0 0 1
.
"""
self._invalid = 0
return self._mtx
def set_matrix(self, mtx):
"""
Set the underlying transformation matrix from a 3x3 numpy array::
a c e
b d f
0 0 1
.
"""
self._mtx = mtx
self.invalidate()
def set(self, other):
"""
Set this transformation from the frozen copy of another
:class:`Affine2DBase` object.
"""
assert isinstance(other, Affine2DBase)
self._mtx = other.get_matrix()
self.invalidate()
@staticmethod
def identity():
"""
(staticmethod) Return a new :class:`Affine2D` object that is
the identity transform.
Unless this transform will be mutated later on, consider using
the faster :class:`IdentityTransform` class instead.
"""
return Affine2D(np.identity(3))
def clear(self):
"""
Reset the underlying matrix to the identity transform.
"""
self._mtx = np.identity(3)
self.invalidate()
return self
def rotate(self, theta):
"""
Add a rotation (in radians) to this transform in place.
Returns *self*, so this method can easily be chained with more
calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate`
and :meth:`scale`.
"""
a = np.cos(theta)
b = np.sin(theta)
rotate_mtx = np.array(
[[a, -b, 0.0], [b, a, 0.0], [0.0, 0.0, 1.0]],
np.float_)
self._mtx = np.dot(rotate_mtx, self._mtx)
self.invalidate()
return self
def rotate_deg(self, degrees):
"""
Add a rotation (in degrees) to this transform in place.
Returns *self*, so this method can easily be chained with more
calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate`
and :meth:`scale`.
"""
return self.rotate(degrees * np.pi / 180.)
def rotate_around(self, x, y, theta):
"""
Add a rotation (in radians) around the point (x, y) in place.
Returns *self*, so this method can easily be chained with more
calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate`
and :meth:`scale`.
"""
return self.translate(-x, -y).rotate(theta).translate(x, y)
def rotate_deg_around(self, x, y, degrees):
"""
Add a rotation (in degrees) around the point (x, y) in place.
Returns *self*, so this method can easily be chained with more
calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate`
and :meth:`scale`.
"""
return self.translate(-x, -y).rotate_deg(degrees).translate(x, y)
def translate(self, tx, ty):
"""
Adds a translation in place.
Returns *self*, so this method can easily be chained with more
calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate`
and :meth:`scale`.
"""
translate_mtx = np.array(
[[1.0, 0.0, tx], [0.0, 1.0, ty], [0.0, 0.0, 1.0]],
np.float_)
self._mtx = np.dot(translate_mtx, self._mtx)
self.invalidate()
return self
def scale(self, sx, sy=None):
"""
Adds a scale in place.
If *sy* is None, the same scale is applied in both the *x*- and
*y*-directions.
Returns *self*, so this method can easily be chained with more
calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate`
and :meth:`scale`.
"""
if sy is None:
sy = sx
scale_mtx = np.array(
[[sx, 0.0, 0.0], [0.0, sy, 0.0], [0.0, 0.0, 1.0]],
np.float_)
self._mtx = np.dot(scale_mtx, self._mtx)
self.invalidate()
return self
def _get_is_separable(self):
mtx = self.get_matrix()
return mtx[0, 1] == 0.0 and mtx[1, 0] == 0.0
is_separable = property(_get_is_separable)
class IdentityTransform(Affine2DBase):
"""
A special class that does on thing, the identity transform, in a
fast way.
"""
_mtx = np.identity(3)
def frozen(self):
return self
frozen.__doc__ = Affine2DBase.frozen.__doc__
def __repr__(self):
return "IdentityTransform()"
def get_matrix(self):
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
def transform(self, points):
return points
transform.__doc__ = Affine2DBase.transform.__doc__
transform_affine = transform
transform_affine.__doc__ = Affine2DBase.transform_affine.__doc__
transform_non_affine = transform
transform_non_affine.__doc__ = Affine2DBase.transform_non_affine.__doc__
def transform_path(self, path):
return path
transform_path.__doc__ = Affine2DBase.transform_path.__doc__
transform_path_affine = transform_path
transform_path_affine.__doc__ = Affine2DBase.transform_path_affine.__doc__
transform_path_non_affine = transform_path
transform_path_non_affine.__doc__ = Affine2DBase.transform_path_non_affine.__doc__
def get_affine(self):
return self
get_affine.__doc__ = Affine2DBase.get_affine.__doc__
inverted = get_affine
inverted.__doc__ = Affine2DBase.inverted.__doc__
class BlendedGenericTransform(Transform):
"""
A "blended" transform uses one transform for the *x*-direction, and
another transform for the *y*-direction.
This "generic" version can handle any given child transform in the
*x*- and *y*-directions.
"""
input_dims = 2
output_dims = 2
is_separable = True
pass_through = True
def __init__(self, x_transform, y_transform, **kwargs):
"""
Create a new "blended" transform using *x_transform* to
transform the *x*-axis and *y_transform* to transform the
*y*-axis.
You will generally not call this constructor directly but use
the :func:`blended_transform_factory` function instead, which
can determine automatically which kind of blended transform to
create.
"""
# Here we ask: "Does it blend?"
Transform.__init__(self, **kwargs)
self._x = x_transform
self._y = y_transform
self.set_children(x_transform, y_transform)
self._affine = None
def __eq__(self, other):
# Note, this is an exact copy of BlendedAffine2D.__eq__
if isinstance(other, (BlendedAffine2D, BlendedGenericTransform)):
return (self._x == other._x) and (self._y == other._y)
elif self._x == self._y:
return self._x == other
else:
return NotImplemented
def contains_branch_seperately(self, transform):
# Note, this is an exact copy of BlendedAffine2D.contains_branch_seperately
return self._x.contains_branch(transform), self._y.contains_branch(transform)
@property
def depth(self):
return max([self._x.depth, self._y.depth])
def contains_branch(self, other):
# a blended transform cannot possibly contain a branch from two different transforms.
return False
def _get_is_affine(self):
return self._x.is_affine and self._y.is_affine
is_affine = property(_get_is_affine)
def _get_has_inverse(self):
return self._x.has_inverse and self._y.has_inverse
has_inverse = property(_get_has_inverse)
def frozen(self):
return blended_transform_factory(self._x.frozen(), self._y.frozen())
frozen.__doc__ = Transform.frozen.__doc__
def __repr__(self):
return "BlendedGenericTransform(%s,%s)" % (self._x, self._y)
def transform_non_affine(self, points):
if self._x.is_affine and self._y.is_affine:
return points
x = self._x
y = self._y
if x == y and x.input_dims == 2:
return x.transform_non_affine(points)
if x.input_dims == 2:
x_points = x.transform_non_affine(points)[:, 0:1]
else:
x_points = x.transform_non_affine(points[:, 0])
x_points = x_points.reshape((len(x_points), 1))
if y.input_dims == 2:
y_points = y.transform_non_affine(points)[:, 1:]
else:
y_points = y.transform_non_affine(points[:, 1])
y_points = y_points.reshape((len(y_points), 1))
if isinstance(x_points, MaskedArray) or isinstance(y_points, MaskedArray):
return ma.concatenate((x_points, y_points), 1)
else:
return np.concatenate((x_points, y_points), 1)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def inverted(self):
return BlendedGenericTransform(self._x.inverted(), self._y.inverted())
inverted.__doc__ = Transform.inverted.__doc__
def get_affine(self):
if self._invalid or self._affine is None:
if self._x == self._y:
self._affine = self._x.get_affine()
else:
x_mtx = self._x.get_affine().get_matrix()
y_mtx = self._y.get_affine().get_matrix()
# This works because we already know the transforms are
# separable, though normally one would want to set b and
# c to zero.
mtx = np.vstack((x_mtx[0], y_mtx[1], [0.0, 0.0, 1.0]))
self._affine = Affine2D(mtx)
self._invalid = 0
return self._affine
get_affine.__doc__ = Transform.get_affine.__doc__
class BlendedAffine2D(Affine2DBase):
"""
A "blended" transform uses one transform for the *x*-direction, and
another transform for the *y*-direction.
This version is an optimization for the case where both child
transforms are of type :class:`Affine2DBase`.
"""
is_separable = True
def __init__(self, x_transform, y_transform, **kwargs):
"""
Create a new "blended" transform using *x_transform* to
transform the *x*-axis and *y_transform* to transform the
*y*-axis.
Both *x_transform* and *y_transform* must be 2D affine
transforms.
You will generally not call this constructor directly but use
the :func:`blended_transform_factory` function instead, which
can determine automatically which kind of blended transform to
create.
"""
assert x_transform.is_affine
assert y_transform.is_affine
assert x_transform.is_separable
assert y_transform.is_separable
Transform.__init__(self, **kwargs)
self._x = x_transform
self._y = y_transform
self.set_children(x_transform, y_transform)
Affine2DBase.__init__(self)
self._mtx = None
def __eq__(self, other):
# Note, this is an exact copy of BlendedGenericTransform.__eq__
if isinstance(other, (BlendedAffine2D, BlendedGenericTransform)):
return (self._x == other._x) and (self._y == other._y)
elif self._x == self._y:
return self._x == other
else:
return NotImplemented
def contains_branch_seperately(self, transform):
# Note, this is an exact copy of BlendedTransform.contains_branch_seperately
return self._x.contains_branch(transform), self._y.contains_branch(transform)
def __repr__(self):
return "BlendedAffine2D(%s,%s)" % (self._x, self._y)
def get_matrix(self):
if self._invalid:
if self._x == self._y:
self._mtx = self._x.get_matrix()
else:
x_mtx = self._x.get_matrix()
y_mtx = self._y.get_matrix()
# This works because we already know the transforms are
# separable, though normally one would want to set b and
# c to zero.
self._mtx = np.vstack((x_mtx[0], y_mtx[1], [0.0, 0.0, 1.0]))
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
def blended_transform_factory(x_transform, y_transform):
"""
Create a new "blended" transform using *x_transform* to transform
the *x*-axis and *y_transform* to transform the *y*-axis.
A faster version of the blended transform is returned for the case
where both child transforms are affine.
"""
if (isinstance(x_transform, Affine2DBase)
and isinstance(y_transform, Affine2DBase)):
return BlendedAffine2D(x_transform, y_transform)
return BlendedGenericTransform(x_transform, y_transform)
class CompositeGenericTransform(Transform):
"""
A composite transform formed by applying transform *a* then
transform *b*.
This "generic" version can handle any two arbitrary
transformations.
"""
pass_through = True
def __init__(self, a, b, **kwargs):
"""
Create a new composite transform that is the result of
applying transform *a* then transform *b*.
You will generally not call this constructor directly but use
the :func:`composite_transform_factory` function instead,
which can automatically choose the best kind of composite
transform instance to create.
"""
assert a.output_dims == b.input_dims
self.input_dims = a.input_dims
self.output_dims = b.output_dims
Transform.__init__(self, **kwargs)
self._a = a
self._b = b
self.set_children(a, b)
is_affine = property(lambda self: self._a.is_affine and self._b.is_affine)
def frozen(self):
self._invalid = 0
frozen = composite_transform_factory(self._a.frozen(), self._b.frozen())
if not isinstance(frozen, CompositeGenericTransform):
return frozen.frozen()
return frozen
frozen.__doc__ = Transform.frozen.__doc__
def _invalidate_internal(self, value, invalidating_node):
# In some cases for a composite transform, an invalidating call to AFFINE_ONLY needs
# to be extended to invalidate the NON_AFFINE part too. These cases are when the right
# hand transform is non-affine and either:
# (a) the left hand transform is non affine
# (b) it is the left hand node which has triggered the invalidation
if value == Transform.INVALID_AFFINE \
and not self._b.is_affine \
and (not self._a.is_affine or invalidating_node is self._a):
value = Transform.INVALID
Transform._invalidate_internal(self, value=value,
invalidating_node=invalidating_node)
def __eq__(self, other):
if isinstance(other, (CompositeGenericTransform, CompositeAffine2D)):
return self is other or (self._a == other._a and self._b == other._b)
else:
return False
def _iter_break_from_left_to_right(self):
for lh_compliment, rh_compliment in self._a._iter_break_from_left_to_right():
yield lh_compliment, rh_compliment + self._b
for lh_compliment, rh_compliment in self._b._iter_break_from_left_to_right():
yield self._a + lh_compliment, rh_compliment
@property
def depth(self):
return self._a.depth + self._b.depth
def _get_is_affine(self):
return self._a.is_affine and self._b.is_affine
is_affine = property(_get_is_affine)
def _get_is_separable(self):
return self._a.is_separable and self._b.is_separable
is_separable = property(_get_is_separable)
if DEBUG:
def __str__(self):
return '(%s, %s)' % (self._a, self._b)
def __repr__(self):
return "CompositeGenericTransform(%r, %r)" % (self._a, self._b)
def transform_affine(self, points):
return self.get_affine().transform(points)
transform_affine.__doc__ = Transform.transform_affine.__doc__
def transform_non_affine(self, points):
if self._a.is_affine and self._b.is_affine:
return points
elif not self._a.is_affine and self._b.is_affine:
return self._a.transform_non_affine(points)
else:
return self._b.transform_non_affine(
self._a.transform(points))
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def transform_path_non_affine(self, path):
if self._a.is_affine and self._b.is_affine:
return path
elif not self._a.is_affine and self._b.is_affine:
return self._a.transform_path_non_affine(path)
else:
return self._b.transform_path_non_affine(
self._a.transform_path(path))
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
def get_affine(self):
if not self._b.is_affine:
return self._b.get_affine()
else:
return Affine2D(np.dot(self._b.get_affine().get_matrix(),
self._a.get_affine().get_matrix()))
get_affine.__doc__ = Transform.get_affine.__doc__
def inverted(self):
return CompositeGenericTransform(self._b.inverted(), self._a.inverted())
inverted.__doc__ = Transform.inverted.__doc__
def _get_has_inverse(self):
return self._a.has_inverse and self._b.has_inverse
has_inverse = property(_get_has_inverse)
class CompositeAffine2D(Affine2DBase):
"""
A composite transform formed by applying transform *a* then transform *b*.
This version is an optimization that handles the case where both *a*
and *b* are 2D affines.
"""
def __init__(self, a, b, **kwargs):
"""
Create a new composite transform that is the result of
applying transform *a* then transform *b*.
Both *a* and *b* must be instances of :class:`Affine2DBase`.
You will generally not call this constructor directly but use
the :func:`composite_transform_factory` function instead,
which can automatically choose the best kind of composite
transform instance to create.
"""
assert a.output_dims == b.input_dims
self.input_dims = a.input_dims
self.output_dims = b.output_dims
assert a.is_affine
assert b.is_affine
Affine2DBase.__init__(self, **kwargs)
self._a = a
self._b = b
self.set_children(a, b)
self._mtx = None
if DEBUG:
def __str__(self):
return '(%s, %s)' % (self._a, self._b)
@property
def depth(self):
return self._a.depth + self._b.depth
def _iter_break_from_left_to_right(self):
for lh_compliment, rh_compliment in self._a._iter_break_from_left_to_right():
yield lh_compliment, rh_compliment + self._b
for lh_compliment, rh_compliment in self._b._iter_break_from_left_to_right():
yield self._a + lh_compliment, rh_compliment
def __repr__(self):
return "CompositeAffine2D(%r, %r)" % (self._a, self._b)
def get_matrix(self):
if self._invalid:
self._mtx = np.dot(
self._b.get_matrix(),
self._a.get_matrix())
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
def composite_transform_factory(a, b):
"""
Create a new composite transform that is the result of applying
transform a then transform b.
Shortcut versions of the blended transform are provided for the
case where both child transforms are affine, or one or the other
is the identity transform.
Composite transforms may also be created using the '+' operator,
e.g.::
c = a + b
"""
# check to see if any of a or b are IdentityTransforms. We use
# isinstance here to guarantee that the transforms will *always*
# be IdentityTransforms. Since TransformWrappers are mutable,
# use of equality here would be wrong.
if isinstance(a, IdentityTransform):
return b
elif isinstance(b, IdentityTransform):
return a
elif isinstance(a, Affine2D) and isinstance(b, Affine2D):
return CompositeAffine2D(a, b)
return CompositeGenericTransform(a, b)
class BboxTransform(Affine2DBase):
"""
:class:`BboxTransform` linearly transforms points from one
:class:`Bbox` to another :class:`Bbox`.
"""
is_separable = True
def __init__(self, boxin, boxout, **kwargs):
"""
Create a new :class:`BboxTransform` that linearly transforms
points from *boxin* to *boxout*.
"""
assert boxin.is_bbox
assert boxout.is_bbox
Affine2DBase.__init__(self, **kwargs)
self._boxin = boxin
self._boxout = boxout
self.set_children(boxin, boxout)
self._mtx = None
self._inverted = None
def __repr__(self):
return "BboxTransform(%r, %r)" % (self._boxin, self._boxout)
def get_matrix(self):
if self._invalid:
inl, inb, inw, inh = self._boxin.bounds
outl, outb, outw, outh = self._boxout.bounds
x_scale = outw / inw
y_scale = outh / inh
if DEBUG and (x_scale == 0 or y_scale == 0):
raise ValueError("Transforming from or to a singular bounding box.")
self._mtx = np.array([[x_scale, 0.0 , (-inl*x_scale+outl)],
[0.0 , y_scale, (-inb*y_scale+outb)],
[0.0 , 0.0 , 1.0 ]],
np.float_)
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
class BboxTransformTo(Affine2DBase):
"""
:class:`BboxTransformTo` is a transformation that linearly
transforms points from the unit bounding box to a given
:class:`Bbox`.
"""
is_separable = True
def __init__(self, boxout, **kwargs):
"""
Create a new :class:`BboxTransformTo` that linearly transforms
points from the unit bounding box to *boxout*.
"""
assert boxout.is_bbox
Affine2DBase.__init__(self, **kwargs)
self._boxout = boxout
self.set_children(boxout)
self._mtx = None
self._inverted = None
def __repr__(self):
return "BboxTransformTo(%r)" % (self._boxout)
def get_matrix(self):
if self._invalid:
outl, outb, outw, outh = self._boxout.bounds
if DEBUG and (outw == 0 or outh == 0):
raise ValueError("Transforming to a singular bounding box.")
self._mtx = np.array([[outw, 0.0, outl],
[ 0.0, outh, outb],
[ 0.0, 0.0, 1.0]],
np.float_)
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
class BboxTransformToMaxOnly(BboxTransformTo):
"""
:class:`BboxTransformTo` is a transformation that linearly
transforms points from the unit bounding box to a given
:class:`Bbox` with a fixed upper left of (0, 0).
"""
def __repr__(self):
return "BboxTransformToMaxOnly(%r)" % (self._boxout)
def get_matrix(self):
if self._invalid:
xmax, ymax = self._boxout.max
if DEBUG and (xmax == 0 or ymax == 0):
raise ValueError("Transforming to a singular bounding box.")
self._mtx = np.array([[xmax, 0.0, 0.0],
[ 0.0, ymax, 0.0],
[ 0.0, 0.0, 1.0]],
np.float_)
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
class BboxTransformFrom(Affine2DBase):
"""
:class:`BboxTransformFrom` linearly transforms points from a given
:class:`Bbox` to the unit bounding box.
"""
is_separable = True
def __init__(self, boxin, **kwargs):
assert boxin.is_bbox
Affine2DBase.__init__(self, **kwargs)
self._boxin = boxin
self.set_children(boxin)
self._mtx = None
self._inverted = None
def __repr__(self):
return "BboxTransformFrom(%r)" % (self._boxin)
def get_matrix(self):
if self._invalid:
inl, inb, inw, inh = self._boxin.bounds
if DEBUG and (inw == 0 or inh == 0):
raise ValueError("Transforming from a singular bounding box.")
x_scale = 1.0 / inw
y_scale = 1.0 / inh
self._mtx = np.array([[x_scale, 0.0 , (-inl*x_scale)],
[0.0 , y_scale, (-inb*y_scale)],
[0.0 , 0.0 , 1.0 ]],
np.float_)
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
class ScaledTranslation(Affine2DBase):
"""
A transformation that translates by *xt* and *yt*, after *xt* and *yt*
have been transformad by the given transform *scale_trans*.
"""
def __init__(self, xt, yt, scale_trans, **kwargs):
Affine2DBase.__init__(self, **kwargs)
self._t = (xt, yt)
self._scale_trans = scale_trans
self.set_children(scale_trans)
self._mtx = None
self._inverted = None
def __repr__(self):
return "ScaledTranslation(%r)" % (self._t,)
def get_matrix(self):
if self._invalid:
xt, yt = self._scale_trans.transform_point(self._t)
self._mtx = np.array([[1.0, 0.0, xt],
[0.0, 1.0, yt],
[0.0, 0.0, 1.0]],
np.float_)
self._invalid = 0
self._inverted = None
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
class TransformedPath(TransformNode):
"""
A :class:`TransformedPath` caches a non-affine transformed copy of
the :class:`~matplotlib.path.Path`. This cached copy is
automatically updated when the non-affine part of the transform
changes.
.. note::
Paths are considered immutable by this class. Any update to the
path's vertices/codes will not trigger a transform recomputation.
"""
def __init__(self, path, transform):
"""
Create a new :class:`TransformedPath` from the given
:class:`~matplotlib.path.Path` and :class:`Transform`.
"""
assert isinstance(transform, Transform)
TransformNode.__init__(self)
self._path = path
self._transform = transform
self.set_children(transform)
self._transformed_path = None
self._transformed_points = None
def _revalidate(self):
# only recompute if the invalidation includes the non_affine part of the transform
if ((self._invalid & self.INVALID_NON_AFFINE == self.INVALID_NON_AFFINE)
or self._transformed_path is None):
self._transformed_path = \
self._transform.transform_path_non_affine(self._path)
self._transformed_points = \
Path(self._transform.transform_non_affine(self._path.vertices),
None, self._path._interpolation_steps)
self._invalid = 0
def get_transformed_points_and_affine(self):
"""
Return a copy of the child path, with the non-affine part of
the transform already applied, along with the affine part of
the path necessary to complete the transformation. Unlike
:meth:`get_transformed_path_and_affine`, no interpolation will
be performed.
"""
self._revalidate()
return self._transformed_points, self.get_affine()
def get_transformed_path_and_affine(self):
"""
Return a copy of the child path, with the non-affine part of
the transform already applied, along with the affine part of
the path necessary to complete the transformation.
"""
self._revalidate()
return self._transformed_path, self.get_affine()
def get_fully_transformed_path(self):
"""
Return a fully-transformed copy of the child path.
"""
self._revalidate()
return self._transform.transform_path_affine(self._transformed_path)
def get_affine(self):
return self._transform.get_affine()
def nonsingular(vmin, vmax, expander=0.001, tiny=1e-15, increasing=True):
'''
Modify the endpoints of a range as needed to avoid singularities.
*vmin*, *vmax*
the initial endpoints.
*tiny*
threshold for the ratio of the interval to the maximum absolute
value of its endpoints. If the interval is smaller than
this, it will be expanded. This value should be around
1e-15 or larger; otherwise the interval will be approaching
the double precision resolution limit.
*expander*
fractional amount by which *vmin* and *vmax* are expanded if
the original interval is too small, based on *tiny*.
*increasing*: [True | False]
If True (default), swap *vmin*, *vmax* if *vmin* > *vmax*
Returns *vmin*, *vmax*, expanded and/or swapped if necessary.
If either input is inf or NaN, or if both inputs are 0,
returns -*expander*, *expander*.
'''
if (not np.isfinite(vmin)) or (not np.isfinite(vmax)):
return -expander, expander
swapped = False
if vmax < vmin:
vmin, vmax = vmax, vmin
swapped = True
if vmax - vmin <= max(abs(vmin), abs(vmax)) * tiny:
if vmax == 0 and vmin == 0:
vmin = -expander
vmax = expander
else:
vmin -= expander*abs(vmin)
vmax += expander*abs(vmax)
if swapped and not increasing:
vmin, vmax = vmax, vmin
return vmin, vmax
def interval_contains(interval, val):
a, b = interval
return (
((a < b) and (a <= val and b >= val))
or (b <= val and a >= val))
def interval_contains_open(interval, val):
a, b = interval
return (
((a < b) and (a < val and b > val))
or (b < val and a > val))
def offset_copy(trans, fig=None, x=0.0, y=0.0, units='inches'):
'''
Return a new transform with an added offset.
args:
trans is any transform
kwargs:
fig is the current figure; it can be None if units are 'dots'
x, y give the offset
units is 'inches', 'points' or 'dots'
'''
if units == 'dots':
return trans + Affine2D().translate(x, y)
if fig is None:
raise ValueError('For units of inches or points a fig kwarg is needed')
if units == 'points':
x /= 72.0
y /= 72.0
elif not units == 'inches':
raise ValueError('units must be dots, points, or inches')
return trans + ScaledTranslation(x, y, fig.dpi_scale_trans)
| mit |
jblackburne/scikit-learn | doc/sphinxext/sphinx_gallery/notebook.py | 9 | 3565 | # -*- coding: utf-8 -*-
r"""
============================
Parser for Jupyter notebooks
============================
Class that holds the Ipython notebook information
"""
# Author: Óscar Nájera
# License: 3-clause BSD
from __future__ import division, absolute_import, print_function
import json
import os
import re
import sys
def ipy_notebook_skeleton():
"""Returns a dictionary with the elements of a Jupyter notebook"""
py_version = sys.version_info
notebook_skeleton = {
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python " + str(py_version[0]),
"language": "python",
"name": "python" + str(py_version[0])
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": py_version[0]
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython" + str(py_version[0]),
"version": '{0}.{1}.{2}'.format(*sys.version_info[:3])
}
},
"nbformat": 4,
"nbformat_minor": 0
}
return notebook_skeleton
def rst2md(text):
"""Converts the RST text from the examples docstrigs and comments
into markdown text for the IPython notebooks"""
top_heading = re.compile(r'^=+$\s^([\w\s-]+)^=+$', flags=re.M)
text = re.sub(top_heading, r'# \1', text)
math_eq = re.compile(r'^\.\. math::((?:.+)?(?:\n+^ .+)*)', flags=re.M)
text = re.sub(math_eq,
lambda match: r'$${0}$$'.format(match.group(1).strip()),
text)
inline_math = re.compile(r':math:`(.+)`')
text = re.sub(inline_math, r'$\1$', text)
return text
class Notebook(object):
"""Ipython notebook object
Constructs the file cell-by-cell and writes it at the end"""
def __init__(self, file_name, target_dir):
"""Declare the skeleton of the notebook
Parameters
----------
file_name : str
original script file name, .py extension will be renamed
target_dir: str
directory where notebook file is to be saved
"""
self.file_name = file_name.replace('.py', '.ipynb')
self.write_file = os.path.join(target_dir, self.file_name)
self.work_notebook = ipy_notebook_skeleton()
self.add_code_cell("%matplotlib inline")
def add_code_cell(self, code):
"""Add a code cell to the notebook
Parameters
----------
code : str
Cell content
"""
code_cell = {
"cell_type": "code",
"execution_count": None,
"metadata": {"collapsed": False},
"outputs": [],
"source": [code.strip()]
}
self.work_notebook["cells"].append(code_cell)
def add_markdown_cell(self, text):
"""Add a markdown cell to the notebook
Parameters
----------
code : str
Cell content
"""
markdown_cell = {
"cell_type": "markdown",
"metadata": {},
"source": [rst2md(text)]
}
self.work_notebook["cells"].append(markdown_cell)
def save_file(self):
"""Saves the notebook to a file"""
with open(self.write_file, 'w') as out_nb:
json.dump(self.work_notebook, out_nb, indent=2)
| bsd-3-clause |
sonalranjit/SECS | SECS_trace.py | 2 | 1609 | __author__ = 'sonal'
import numpy as np
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.axes_grid1 import make_axes_locatable
import os
from math import *
def polar_plot(grid, title):
#z = grid[:,8]
u = grid[:,8]
v = grid[:,9]
plt.figure(figsize=(18,18))
ax = plt.gca()
#m = Basemap(projection='npaeqd',boundinglat=20,lon_0=-100.,resolution='l')
m = Basemap(width=8000000, height=8000000, resolution='l', projection='lcc',\
lat_0=60,lon_0=-100.)
m.drawcoastlines()
m.drawparallels(np.arange(-80.,81,20.),labels=[1,0,0,0],fontsize=10)
m.drawmeridians(np.arange(-180.,181.,20.),labels=[0,0,0,1],fontsize=10)
x,y =m(grid[:,7],grid[:,6])
sc = m.scatter(x,y,s=abs(u),c=u,marker=',',cmap=cm.jet,alpha=0.9,edgecolors='none')
plt.title(title)
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
cb1 = plt.colorbar(sc,cax=cax)
cb1.set_label("mA/m",fontsize=18)
plt.savefig('GOCE_asc_EICSu_krigged_201104.png',bbox_inches='tight',pad_inches=0.2)
#plt.show()
def asc_desc(data):
asc = []
desc = []
lat = data[:,6]
for i in range(0,len(data)-1):
if lat[i+1] >= lat[i]:
asc.append(i)
else:
desc.append(i)
return asc, desc
SECS_data = np.loadtxt('EICS_201103_krigged.txt')
asc_idx, desc_idx= asc_desc(SECS_data)
asc_track = SECS_data[asc_idx,:]
desc_track = SECS_data[desc_idx,:]
polar_plot(asc_track,'GOCE Ascending EICS u component Krigged April, 2011') | gpl-2.0 |
rjonnal/zernike | __init__.py | 1 | 20006 | """This module contains functions for Zernike calculations. Mainly the private
function _zgen, a generator function for Zernike polynomials. The public
functions make use of _zgen to create height or slope maps in a unit
pupil, corresponding to individual Zernike terms.
Author: Ravi S. Jonnal / Werner Lab, UC Davis
Revision: 2.0 / 28 June 2014
"""
import numpy as np
from matplotlib import pyplot as plt
import sys
from time import sleep
import os
USE_CACHE_FILE = False
def fact(num):
"""Implementation of factorial function.
"""
# Check that the number is an integer.
assert(num%1==0)
# Check that $num\geq 0$.
assert(num>=0)
# Compute $num!$ recursively.
if num==0 or num==1:
return 1
else:
return num * fact(num-1)
def choose(a,b):
"""Binomial coefficient, implemented using
this module's factorial function.
See [here](http://www.encyclopediaofmath.org/index.php/Newton_binomial) for detail.
"""
assert(a>=b)
return fact(a)/(fact(b)*fact(a-b))
def splitEquation(eqStr,width,bookend):
if len(eqStr)<=width or len(eqStr)==0:
return eqStr
else:
spaceIndices = []
idx = 0
while idx>-1:
idx = eqStr.find(' ',idx+1)
spaceIndices.append(idx)
spaceIndices = spaceIndices[:-1]
idxList = [x for x in spaceIndices if x<width]
if len(idxList)==0:
return eqStr
else:
idx = idxList[-1]
head = eqStr[:idx]
innards = ' ' + bookend + '\n' + bookend
tail = splitEquation(eqStr[idx:],width,bookend)
test =head + innards + tail
return test
class Zernike:
def __init__(self):
if USE_CACHE_FILE:
cachedir = './cache/'
self._cachefn = os.path.join(cachedir,'zernike_cache.txt')
if not os.path.exists(cachedir):
os.makedirs(cachedir)
try:
self._termMatrix = np.loadtxt(self._cachefn).astype(np.int32)
except Exception as e:
print 'No term cache file. Creating.'
self._termMatrix = np.array([])
np.savetxt(self._cachefn,self._termMatrix)
# Make a dictionary of precomputed coefficients, using the cache file.
# This dictionary will be used to look up values when they exist in
# the dictionary, and will recompute them otherwise.
self._termDict = {}
if USE_CACHE_FILE:
for row in self._termMatrix:
n,m,kindIndex,s,j,k = row[:6]
t1,t2,t3,c,tXexp,tYexp = row[6:]
self._termDict[(n,m,kindIndex,s,j,k)] = (t1,t2,t3,c,tXexp,tYexp)
# The functions in this class can be asked for phase height,
# or partial x or partial y derivatives. 'Kind' refers to
# which of these is requested. Numerical encodings for 'kind'
# permit some arithmetical simplicity and generality
# (utilizing a number associated with the kind in a single
# equation, rather than having different sets of equations
# for each kind case).
self._kindDictionary = {}
self._kindDictionary['h'] = 0
self._kindDictionary['dx'] = 1
self._kindDictionary['dy'] = 2
def j2nm(self,j):
n = np.ceil((-3+np.sqrt(9+8*j))/2)
m = 2*j-n*(n+2)
return np.int(n),np.int(m)
def nm2j(self,n,m):
return np.int(n*(n+1)/2.0+(n+m)/2.0)
def _zeqn(self,n,m,kind='h',forceRecompute=False):
"""Return parameters sufficient for specifying a Zernike term
of desired order and azimuthal frequency.
Given an order (or degree) n and azimuthal frequency f, and x-
and y- rectangular (Cartesian) coordinates, produce parameters
necessary for constructing the appropriate Zernike
representation.
An individual polynomial has the format:
$$ Z_n^m = \sqrt{c} \Sigma^j\Sigma^k [a_{jk}X^jY^k] $$
This function returns a tuple ($c$,cdict). $c$ is the square
of the normalizing coefficient $\sqrt{c}$, and cdict contains
key-value pairs (($j$,$k$),$a$), mapping the $X$ and $Y$
exponents ($j$ and $k$, respectively) onto polynomial term
coefficients ($a$). The resulting structure can be used to
compute the wavefront height or slope for arbitrary pupil
coordinates, or to generate string representations of the
polynomials.
Zernike terms are only defined when n and m have the same
parity (both odd or both even).
Please see Schwiegerling lecture notes in
/doc/supporting_docs/ for eqn. references.
Args:
n (int): The Zernike order or degree.
m (int): The azimuthal frequency.
kind (str): 'h', 'dx', or 'dy', for height, partial x
derivative (slope) or partial y derivative,
respectively.
Returns:
params (tuple): (c,cdict), with c being the normalizing
coefficient c and cdict being the map of exponent pairs
onto inner coefficients.
"""
absm = np.abs(m)
kindIndex = self._kindDictionary[kind.lower()]
if USE_CACHE_FILE:
# open cache file in append mode:
self._cacheHandle = file(self._cachefn,'a')
# check that n and m are both even or both odd
if (float(n-absm))%2.0:
errString = 'zernike._zgen error: ' + \
'parity of n and m are different; n = %d, m = %d'%(n,m)
sys.exit(errString)
# check that n is non-negative:
if n<0:
errString = 'zernike._zgen error: ' + \
'n must be non-negative; n = %d'%n
sys.exit(errString)
# $|m|$ must be less than or equal to $n$.
if abs(m)>n:
errString = 'zernike._zgen error: ' + \
'|m| must be less than or equal to n, but n=%d and m=%d.'%(n,m)
sys.exit(errString)
# These are the squares of the outer coefficients. It's useful
# to keep them this way for _convertToString, since we'd
# prefer to print the $\sqrt{}$ rather than a truncated irrational
# number.
if m==0:
outerCoef = n+1
else:
outerCoef = 2*(n+1)
srange = range((n-absm)/2+1)
cdict = {}
for s in srange:
jrange = range(((n-absm)/2)-s+1)
for j in jrange:
# Subtract 1 from absm to determine range,
# only when m<0.
if m<0:
krange = range((absm-1)/2+1)
else:
krange = range(absm/2+1)
for k in krange:
# If m==0, k must also be 0;
# see eqn. 13c, 19c, and 20c, each of which
# only sum over s and j, not k.
if m==0:
assert(k==0)
# For m==0 cases, n/2 is used in coef denominator. Make
# sure that n is even, or else n/2 is not well-defined
# because n is an integer.
if m==0:
assert n%2==0
# Check to see if calculations are cached.
# If so, use cached values; if not, recalculate.
cached = self._termDict.has_key((n,m,kindIndex,s,j,k))
if cached and not forceRecompute:
t1,t2,t3,c,tXexp,tYexp = self._termDict[(n,m,kindIndex,s,j,k)]
else:
# The coefficient for each term in this
# polynomial has the format: $$\frac{t1n}{t1d1
# t1d2 t1d3} t2 t3$$. These six terms are
# computed here.
t1n = ((-1)**(s+k))*fact(n-s)
t1d1 = fact(s)
t1d2 = fact((n + absm)/2-s)
t1d3 = fact((n - absm)/2-s)
t1 = t1n/(t1d1*t1d2*t1d3)
t2 = choose((n - absm)/2 - s, j)
t3 = choose(absm, 2*k + (m<0))
if kind.lower()=='h':
# The (implied) coefficient of the $X^a Y^b$
# term at the end of eqns. 13a-c.
c = 1
tXexp = n - 2*(s+j+k) - (m<0)
tYexp = 2*(j+k) + (m<0)
elif kind.lower()=='dx':
# The coefficient of the $X^a Y^b$ term at
# the end of eqns. 19a-c.
c = (n - 2*(s+j+k) - (m<0))
# Could cacluate explicitly:
# $tXexp = X^{(n - 2*(s+j+k)- 1 - (m<0))}$
#
# However, piggy-backing on previous
# calculation of c speeds things up.
tXexp = c - 1
tYexp = 2*(j+k) + (m<0)
elif kind.lower()=='dy':
# The coefficient of the $X^a Y^b$ term at
# the end of eqns. 20a-c.
c = 2*(j+k) + (m<0)
tXexp = n - 2*(s+j+k) - (m<0)
tYexp = c - 1
else:
errString = 'zernike._zgen error: ' + \
'invalid kind \'%s\'; should be \'h\', \'dx\', or \'dy\'.'%kind
sys.exit(errString)
if not cached and USE_CACHE_FILE:
self._cacheHandle.write('%d\t'*12%(n,m,kindIndex,s,j,k,t1,t2,t3,c,tXexp,tYexp)+'\n')
ct123 = c*t1*t2*t3
# The key for the polynomial dictionary is the pair of X,Y
# coefficients.
termKey = (tXexp,tYexp)
# Leave this term out of the dictionary if its coefficient
# is 0.
if ct123:
# If we already have this term, add to its coefficient.
if cdict.has_key(termKey):
cdict[termKey] = cdict[termKey] + ct123
# If not, add it to the dictionary.
else:
cdict[termKey] = ct123
# Remove zeros to speed up computations later.
cdict = {key: value for key, value in cdict.items() if value}
return (outerCoef,cdict)
def _convertToString(self,params):
"""Return a string representation of a Zernike polynomial.
This function takes a tuple, consisting of a squared
normalizing coefficient and dictionary of inner coefficients
and exponents, provided by _zeqn, and returns a string
representation of the polynomial, with LaTeX- style markup.
Example: a params of (10, {(3,4): 7, (2,5): -1}) would produce a
two-term polynomial '\sqrt{10} [7 X^3 Y^4 - X^2 Y^5]', which could be used in LaTeX,
pandoc, markdown, MathJax, or Word with MathType, to produce:
$$ \sqrt{10} [7 X^3 Y^4 - X^2 Y^5] $$
Args:
params (tuple): A pair consisting of an outer coefficient
$c$ and a dictionary mapping tuples (xexp,yexp) of
exponents onto the corresponding term coefficients.
Returns:
string: A string representation of the polynomial.
"""
c = params[0]
cdict = params[1]
keys = sorted(cdict.keys(), key=lambda tup: (tup[0]+tup[1],tup[0]))[::-1]
outstr = ''
firstKey = True
for key in keys:
coef = cdict[key]
if coef>0:
sign = '+'
else:
sign = '-'
coef = abs(coef)
if coef<0 or not firstKey:
outstr = outstr + '%s'%sign
if coef>1 or (key[0]==0 and key[1]==0):
outstr = outstr + '%d'%coef
if key[0]:
outstr = outstr + 'X^{%d}'%key[0]
if key[1]:
outstr = outstr + 'Y^{%d}'%key[1]
firstKey = False
outstr = outstr + ' '
outstr = outstr.strip()
if np.sqrt(float(c))%1.0<.00001:
cstr = '%d'%(np.sqrt(c))
else:
cstr = '\sqrt{%d}'%(c)
if len(outstr):
outstr = '%s [%s]'%(cstr,outstr)
else:
outstr = '%s'%(cstr)
return outstr
def _convertToSurface(self,params,X,Y,mask=None):
"""Return a phase map specified by a Zernike polynomial.
This function takes a tuple, consisting of a squared
normalizing coefficient and dictionary of inner coefficients
and exponents, provided by _zeqn, and x- and y- rectangular
(Cartesian) coordinates, and produces a phase map.
This function works by evaluating the polynomial expressed by
params at each coordinate specified by X and Y.
Args:
params (tuple): A pair consisting of an outer coefficient
$c$ and a dictionary mapping tuples (xexp,yexp) of
exponents onto the corresponding term coefficients.
X (float): A scalar, vector, or matrix of X coordinates in unit pupil.
Y (float): A scalar, vector, or matrix of Y coordinates in unit pupil.
kind (str): 'h', 'dx', or 'dy', for height, partial x derivative (slope)
or partial y derivative, respectively.
Returns:
float: height, dx, or dy; returned structure same size as X and Y.
"""
# Check that shapes of X and Y are equal (not necessarily square).
if not (X.shape[0]==Y.shape[0] and \
X.shape[1]==Y.shape[1]):
errString = 'zernike.getSurface error: ' + \
'X and Y must have the same shape, but X is %d x %d'%(X.shape[0],X.shape[1]) + \
'and Y is %d x %d'%(Y.shape[0],Y.shape[1])
sys.exit(errString)
if mask is None:
mask = np.ones(X.shape)
params = self._zeqn(n,m,kind)
normalizer = np.sqrt(params[0])
matrix_out = np.zeros(X.shape)
for item in params[1].items():
matrix_out = matrix_out + item[1] * X**(item[0][0]) * Y**(item[0][1])
matrix_out = matrix_out * np.sqrt(normalizer)
matrix_out = matrix_out * mask
return matrix_out
def getSurface(self,n,m,X,Y,kind='h',mask=None):
"""Return a phase map specified by a Zernike order and azimuthal frequency.
Given an order (or degree) n and azimuthal frequency f, and x- and y-
rectangular (Cartesian) coordinates, produce a phase map of either height,
partial x derivative, or partial y derivative.
Zernike terms are only defined when n and m have the same parity (both odd
or both even).
The input X and Y values should be located inside a unit pupil, such that
$$\sqrt{X^2 + Y^2}\leq 1$$
Please see Schwiegerling lecture notes in /doc/supporting_docs/ for eqn.
references.
This function works by calling Zernike._zeqn to calculate the coefficients
and exponents of the polynomial, and then using the supplied X and Y
coordinates to produce the height map (or partial derivative).
Args:
n (int): The Zernike order or degree.
m (int): The azimuthal frequency.
X (float): A scalar, vector, or matrix of X coordinates in unit pupil.
Y (float): A scalar, vector, or matrix of Y coordinates in unit pupil.
kind (str): 'h', 'dx', or 'dy', for height, partial x derivative (slope)
or partial y derivative, respectively.
Returns:
float: height, dx, or dy; returned structure same size as X and Y.
"""
# Check that shapes of X and Y are equal (not necessarily square).
if not np.all(X.shape==Y.shape):
errString = 'zernike.getSurface error: ' + \
'X and Y must have the same shape, but X is %d x %d'%(X.shape[0],X.shape[1]) + \
'and Y is %d x %d'%(Y.shape[0],Y.shape[1])
sys.exit(errString)
if mask is None:
mask = np.ones(X.shape)
params = self._zeqn(n,m,kind)
normalizer = np.sqrt(params[0])
matrix_out = np.zeros(X.shape)
for item in params[1].items():
matrix_out = matrix_out + item[1] * X**(item[0][0]) * Y**(item[0][1])
matrix_out = matrix_out * normalizer
matrix_out = matrix_out * mask
return matrix_out
def getEquationString(self,n,m,kind='h',doubleDollar=False):
"""Return LaTeX-encoded of the Zernike polynomial specified by
order n, frequency m.
Args:
n (int): The Zernike order or degree.
m (int): The azimuthal frequency.
kind (str): 'h', 'dx', or 'dy', for height, partial x
derivative (slope) or partial y derivative,
respectively.
doubleDollar (bool): determines how to bookend the
polynomial string; True causes bookending with '$$', to
produce "display" math mode, whereas False would produce
a string suitable for inline use.
Returns:
str: a LaTeX representation of the Zernike polynomial
specified by n, m, and Kind.
"""
params = self._zeqn(n,m,kind)
rightString = self._convertToString(params)
if kind.lower()=='h':
leftString = 'Z^{%d}_{%d}'%(m,n)
elif kind.lower()=='dx':
leftString = '\\frac{\delta Z^{%d}_{%d}}{\delta x}'%(m,n)
elif kind.lower()=='dy':
leftString = '\\frac{\delta Z^{%d}_{%d}}{\delta y}'%(m,n)
else:
sys.exit('zernike.getEquationString: invalid kind %s'%kind)
if doubleDollar:
bookend = '$$'
else:
bookend = '$'
return '%s %s = %s %s'%(bookend,leftString,rightString,bookend)
def plotPolynomial(self,n,m,kind='h'):
"""Plot a polynomial surface specified by order n, frequency m, and kind.
Args:
n (int): The Zernike order or degree.
m (int): The azimuthal frequency.
kind (str): 'h', 'dx', or 'dy', for height, partial x
derivative (slope) or partial y derivative,
respectively.
Calling function/script required to provide a plotting context (e.g. pyplot.figure).
"""
from mpl_toolkits.mplot3d import Axes3D
N = 64
mask = np.zeros((N,N))
xx,yy = np.meshgrid(np.linspace(-1,1,N),np.linspace(-1,1,N))
d = np.sqrt(xx**2 + yy**2)
mask[np.where(d<1)] = 1
surface = self.getSurface(n,m,xx,yy,kind,mask)
surface = surface * mask
#plt.figure()
ax = plt.axes([0,.2,1,.8],projection='3d')
surf = ax.plot_wireframe(xx,yy,surface,rstride=1,cstride=1,color='k')
ax.view_init(elev=70., azim=40)
eqstr = self.getEquationString(n,m,kind)
eqstr = splitEquation(eqstr,160,'$')
print 'plotting %s'%eqstr
plt.axes([0,0,1,.2])
plt.xticks([])
plt.yticks([])
plt.box('off')
fontsize = 12
plt.text(0.5,0.5,eqstr,ha='center',va='center',fontsize=fontsize)
| gpl-2.0 |
B3AU/waveTree | examples/ensemble/plot_bias_variance.py | 6 | 7330 | """
============================================================
Single estimator versus bagging: bias-variance decomposition
============================================================
This example illustrates and compares the bias-variance decomposition of the
expected mean squared error of a single estimator against a bagging ensemble.
In regression, the expected mean squared error of an estimator can be
decomposed in terms of bias, variance and noise. On average over datasets of
the regression problem, the bias term measures the average amount by which the
predictions of the estimator differ from the predictions of the best possible
estimator for the problem (i.e., the Bayes model). The variance term measures
the variability of the predictions of the estimator when fit over different
instances LS of the problem. Finally, the noise measures the irreducible part
of the error which is due the variability in the data.
The upper left figure illustrates the predictions (in dark red) of a single
decision tree trained over a random dataset LS (the blue dots) of a toy 1d
regression problem. It also illustrates the predictions (in light red) of other
single decision trees trained over other (and different) randomly drawn
instances LS of the problem. Intuitively, the variance term here corresponds to
the width of the beam of predictions (in light red) of the individual
estimators. The larger the variance, the more sensitive are the predictions for
`x` to small changes in the training set. The bias term corresponds to the
difference between the average prediction of the estimator (in cyan) and the
best possible model (in dark blue). On this problem, we can thus observe that
the bias is quite low (both the cyan and the blue curves are close to each
other) while the variance is large (the red beam is rather wide).
The lower left figure plots the pointwise decomposition of the expected mean
squared error of a single decision tree. It confirms that the bias term (in
blue) is low while the variance is large (in green). It also illustrates the
noise part of the error which, as expected, appears to be constant and around
`0.01`.
The right figures correspond to the same plots but using instead a bagging
ensemble of decision trees. In both figures, we can observe that the bias term
is larger than in the previous case. In the upper right figure, the difference
between the average prediction (in cyan) and the best possible model is larger
(e.g., notice the offset around `x=2`). In the lower right figure, the bias
curve is also slightly higher than in the lower left figure. In terms of
variance however, the beam of predictions is narrower, which suggests that the
variance is lower. Indeed, as the lower right figure confirms, the variance
term (in green) is lower than for single decision trees. Overall, the bias-
variance decomposition is therefore no longer the same. The tradeoff is better
for bagging: averaging several decision trees fit on bootstrap copies of the
dataset slightly increases the bias term but allows for a larger reduction of
the variance, which results in a lower overall mean squared error (compare the
red curves int the lower figures). The script output also confirms this
intuition. The total error of the bagging ensemble is lower than the total
error of a single decision tree, and this difference indeed mainly stems from a
reduced variance.
For further details on bias-variance decomposition, see section 7.3 of [1]_.
References
----------
.. [1] T. Hastie, R. Tibshirani and J. Friedman,
"Elements of Statistical Learning", Springer, 2009.
"""
print(__doc__)
# Author: Gilles Louppe <g.louppe@gmail.com>
# License: BSD 3 clause
import numpy as np
from matplotlib import pyplot as plt
from sklearn.ensemble import BaggingRegressor
from sklearn.tree import DecisionTreeRegressor
# Settings
n_repeat = 50 # Number of iterations for computing expectations
n_train = 50 # Size of the training set
n_test = 1000 # Size of the test set
noise = 0.1 # Standard deviation of the noise
np.random.seed(0)
# Change this for exploring the bias-variance decomposition of other
# estimators. This should work well for estimators with high variance (e.g.,
# decision trees or KNN), but poorly for estimators with low variance (e.g.,
# linear models).
estimators = [("Tree", DecisionTreeRegressor()),
("Bagging(Tree)", BaggingRegressor(DecisionTreeRegressor()))]
n_estimators = len(estimators)
# Generate data
def f(x):
x = x.ravel()
return np.exp(-x ** 2) + 1.5 * np.exp(-(x - 2) ** 2)
def generate(n_samples, noise, n_repeat=1):
X = np.random.rand(n_samples) * 10 - 5
X = np.sort(X)
if n_repeat == 1:
y = f(X) + np.random.normal(0.0, noise, n_samples)
else:
y = np.zeros((n_samples, n_repeat))
for i in range(n_repeat):
y[:, i] = f(X) + np.random.normal(0.0, noise, n_samples)
X = X.reshape((n_samples, 1))
return X, y
X_train = []
y_train = []
for i in range(n_repeat):
X, y = generate(n_samples=n_train, noise=noise)
X_train.append(X)
y_train.append(y)
X_test, y_test = generate(n_samples=n_test, noise=noise, n_repeat=n_repeat)
# Loop over estimators to compare
for n, (name, estimator) in enumerate(estimators):
# Compute predictions
y_predict = np.zeros((n_test, n_repeat))
for i in xrange(n_repeat):
estimator.fit(X_train[i], y_train[i])
y_predict[:, i] = estimator.predict(X_test)
# Bias^2 + Variance + Noise decomposition of the mean squared error
y_error = np.zeros(n_test)
for i in range(n_repeat):
for j in range(n_repeat):
y_error += (y_test[:, j] - y_predict[:, i]) ** 2
y_error /= (n_repeat * n_repeat)
y_noise = np.var(y_test, axis=1)
y_bias = (f(X_test) - np.mean(y_predict, axis=1)) ** 2
y_var = np.var(y_predict, axis=1)
print("{0}: {1:.4f} (error) = {2:.4f} (bias^2) "
" + {3:.4f} (var) + {4:.4f} (noise)".format(name,
np.mean(y_error),
np.mean(y_bias),
np.mean(y_var),
np.mean(y_noise)))
# Plot figures
plt.subplot(2, n_estimators, n + 1)
plt.plot(X_test, f(X_test), "b", label="$f(x)$")
plt.plot(X_train[0], y_train[0], ".b", label="LS ~ $y = f(x)+noise$")
for i in range(n_repeat):
if i == 0:
plt.plot(X_test, y_predict[:, i], "r", label="$\^y(x)$")
else:
plt.plot(X_test, y_predict[:, i], "r", alpha=0.05)
plt.plot(X_test, np.mean(y_predict, axis=1), "c",
label="$\mathbb{E}_{LS} \^y(x)$")
plt.xlim([-5, 5])
plt.title(name)
if n == 0:
plt.legend(loc="upper left", prop={"size": 11})
plt.subplot(2, n_estimators, n_estimators + n + 1)
plt.plot(X_test, y_error, "r", label="$error(x)$")
plt.plot(X_test, y_bias, "b", label="$bias^2(x)$"),
plt.plot(X_test, y_var, "g", label="$variance(x)$"),
plt.plot(X_test, y_noise, "c", label="$noise(x)$")
plt.xlim([-5, 5])
plt.ylim([0, 0.1])
if n == 0:
plt.legend(loc="upper left", prop={"size": 11})
plt.show()
| bsd-3-clause |
RuthAngus/LSST-max | code/GP_periodogram.py | 1 | 1066 | from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
from GProtation import make_plot, lnprob, neglnlike
import emcee
import time
import george
from george.kernels import ExpSquaredKernel, ExpSine2Kernel
import scipy.optimize as spo
def GP_periodogram(x, y, yerr, p_init, plims, N):
"""
This function takes a light curves and attempts to produce a GP periodogram.
It returns the value of the highest peak.
The kernel hyperparameters are optimised over a grid of periods.
This is also a "profile likelihood".
x, y, yerr: the light curve.
p_init: the initial guess for the period.
plims: the (log) boundaries for the grid.
N: the number of grid points.
"""
# create the grid
periods = np.linspace(np.exp(plims[0], np.exp(plims[1], 10)
# initial hyperparameters
if __name__ == "__main__":
# fake data
x = np.arange(0, 10, 100)
p = 2
err = .1
y = np.sin(2*np.pi*(1./p)*x) + np.random.randn(100)*err
yerr = np.ones_like(y) * err
p_init, plims = 2, np.log(.1, 5)
GP_periodogram(x, y, yerr, p_init, plims, 10)
| mit |
locksmithone/qcnsim | tag/20140102/doc/validations/weibull/weibullGenerator.py | 3 | 3655 | import numpy
#import scipy
import matplotlib.pyplot
import math
def weibullGenerator(scale, shape, start, end, step):
'''
Generates Weibull sample lists per the parameters.
Returns two lists of X and Y values distributed per Weibull.
'''
weibullSamplesY = []
weibullSamplesX = []
for i in numpy.arange(start, end, step):
weibullSamplesY.append((shape/scale)*((i/scale)**(shape-1.0))*(math.exp(-(i/scale)**shape)))
weibullSamplesX.append(i)
return weibullSamplesX, weibullSamplesY
def readValuesFromFile(filename):
'''
Reads values from a file and returns a list of floats.
'''
yValues = [] # Y values to be read from file.
fileHandle = open(filename, 'r') # Opens file for reading.
#yValues= list(fileHandle) # Read all values into yValues.
for line in fileHandle:
yValues.append(float(line.rstrip()))
fileHandle.close()
return yValues
# Now construct a map of parameters per Weibull samples.
# Key is filename with samples, value is list of lists:
# list1 is weibullGenerator parameters to generate a Weibull graph from matplotlib,
# list2 is set of parameters to plot the samples from the filename.
weibullParameterMap = {
'weibull_Scale1.0_Shape5.0.csv': [[1.0,5.0,0.0,3.0,.01], [0.0,3.0,0.0,2.0]],
'weibull_Scale1.0_Shape1.0.csv': [[1.0,1.0,0.0,3.0,.01], [0.0,3.0,0.0,1.0]],
'weibull_Scale1.0_Shape2.0.csv': [[1.0,2.0,0.0,3.0,.01], [0.0,3.0,0.0,0.9]],
'weibull_Scale1.0_Shape0.5.csv': [[1.0,0.5,0.0,3.0,.01], [0.0,3.0,0.0,5.0]]
}
# Iterate through dictionary and generate graphs.
for filename, parameters in weibullParameterMap.items():
weibullSamplesX, weibullSamplesY = weibullGenerator(parameters[0][0], parameters[0][1],
parameters[0][2], parameters[0][3],
parameters[0][4])
print("Parameters: ", parameters)
matplotlib.pyplot.figure()
matplotlib.pyplot.plot(weibullSamplesX, weibullSamplesY)
matplotlib.pyplot.grid(True)
matplotlib.pyplot.xlabel("x values")
matplotlib.pyplot.ylabel("Probability")
matplotlib.pyplot.title('Weibull pdf: ' + str(parameters[0]))
matplotlib.pyplot.savefig(filename + '_pdf.png')
matplotlib.pyplot.show()
#matplotlib.pyplot.close()
ySamples = readValuesFromFile(filename)
matplotlib.pyplot.figure()
matplotlib.pyplot.hist(ySamples, bins=300, range=(parameters[1][0], parameters[1][1]),
normed=True, color='r')
matplotlib.pyplot.axis(parameters[1])
matplotlib.pyplot.grid(True)
matplotlib.pyplot.xlabel("x values")
matplotlib.pyplot.ylabel("Probability")
matplotlib.pyplot.title('Samples from ' + filename)
matplotlib.pyplot.savefig(filename + '_sample.png')
matplotlib.pyplot.show()
#matplotlib.pyplot.close()
print("*** Done! ***")
##print (weibullGenerator(1.0,5.0,0.0,3.0,.001))
#weibullSamplesX, weibullSamplesY = weibullGenerator(1.0,5.0,0.0,3.0,.001)
#matplotlib.pyplot.figure()
##matplotlib.pyplot.hist(weibullSamplesY, 100)
#matplotlib.pyplot.plot(weibullSamplesX, weibullSamplesY)
#matplotlib.pyplot.grid(True)
#matplotlib.pyplot.show()
##matplotlib.pyplot.close()
#print("Done Figure 1.")
#ySamples = readValuesFromFile('weibull_Scale1.0_Shape5.0.csv')
#print("Done reading.")
##print (ySamples)
#matplotlib.pyplot.figure()
#matplotlib.pyplot.hist(ySamples, 500)
#matplotlib.pyplot.axis([0.0,3.0,0.0,650])
#matplotlib.pyplot.grid(True)
#matplotlib.pyplot.show()
##matplotlib.pyplot.close()
#print("Done Figure 2.")
| lgpl-2.1 |
ccd-utexas/OLD-MAID | ProEMOnline.py | 2 | 57911 | # -*- coding: utf-8 -*-
"""
This scripts sets an initial layout for the ProEMOnline software. It uses the
PyQtGraph dockarea system and was designed from the dockarea.py example.
Keaton wrote this.
"""
#Import everything you'll need
from __future__ import absolute_import, division
import pyqtgraph as pg
from pyqtgraph.Qt import QtCore, QtGui
import numpy as np
import pickle #for saving layouts
from functools import partial
from glob import glob
from scipy import stats
from scipy.optimize import curve_fit
from scipy.fftpack import fft,fftfreq
import pandas as pd
import os
import subprocess
import csv
import sys
import time
import datetime as dt
import dateutil.parser
from astropy.io import fits
from scipy.interpolate import interp1d
import scipy.ndimage.filters as filters
from astropy.stats import biweight_location, biweight_midvariance
from photutils import daofind
from photutils import CircularAperture, CircularAnnulus, aperture_photometry
from pyqtgraph.dockarea import *
from bs4 import BeautifulSoup
import matplotlib.pyplot as plt
# Local modules.
import read_spe
#Return a string of the current time
def timestring():
date = dt.datetime.now()
return date.strftime('%Y%m%d_%Hh%Mm%Ss')
#Function to save a screenshot
def saveScreenshot():
ssfilename=os.path.splitext(spefile)[0]+'_'+timestring()+'.png'
log("Writing screenshot to file "+ssfilename,2)
p=QtGui.QPixmap.grabWidget(area)
writeout = p.save(ssfilename, 'png')
if not writeout: log("Saving screenshot failed!",3)
#### BEGIN PROGRAM ####
#The organization and behavoir of the program are as follows:
#This program operates in four stages.
#Stage 0 - Program Initialized, waiting to open SPE file.
#Stage 1 - SPE file open, stars are being selected
#Stage 2 - Online data reduction and aperture photometry/plotting is being done.
#Stage 3 - End of data acquisition detected. Final data written to file. Timestamps verified. Log saved. Weather/time log data saved.
# -> revert back to Stage 0.
stage=0 #start at 0
def stagechange(num):
global stage
if num in range(4):
log("Program stage = "+str(num),1)
stage=num
else: log("Attempt to change stage to invalid value ("+str(num)+")",3)
#### STAGE 0 ####
#Set up the general GUI aspects
defaultdir = 'D:/sync_to_White_Dwarf_Archive/'#where to search for SPE files
#Set up main window with menu items
class WithMenu(QtGui.QMainWindow):
def __init__(self):
super(WithMenu, self).__init__()
self.initUI()
def initUI(self):
#SETUP THE MENUBAR!
#Note: Exit is protected on Mac. This works on Windows.
exitAction = QtGui.QAction('Exit', self)
exitAction.setShortcut('Ctrl+Q')
exitAction.setStatusTip('Exit application')
exitAction.triggered.connect(QtGui.qApp.quit)
#Open SPE
openFile = QtGui.QAction('&Open SPE', self)
openFile.setShortcut('Ctrl+O')
openFile.setStatusTip('Open SPE File')
#openFile.setCheckable(True)
openFile.triggered.connect(self.openSPE)
#Run Photometry
runPhot = QtGui.QAction('&Run Photometry', self)
runPhot.setShortcut('Ctrl+R')
runPhot.setStatusTip('Run Aperture Photometry on Frames')
runPhot.triggered.connect(self.run)
#Update FT
updateFT = QtGui.QAction('&Update FT', self)
updateFT.setShortcut('Ctrl+U')
updateFT.setStatusTip('Update Fourier Transform with Current Light Curve')
updateFT.triggered.connect(self.updateFTfunct)
#Run Autoguider
autoguide = QtGui.QAction('Feed to &Autoguider', self)
autoguide.setShortcut('Ctrl+A')
autoguide.setStatusTip('Send most recently acquired frame to Guide82')
autoguide.triggered.connect(self.toAutoguider)
#Load dark for science frames
loadDark = QtGui.QAction('Load Darks', self)
loadDark.setStatusTip('Open SPE Calibrations for Dark Subtracting Science Images')
loadDark.triggered.connect(self.openDark)
#Load dark for flat frames
loadDarkForFlats = QtGui.QAction('Load Darks for Flats', self)
loadDarkForFlats.setStatusTip('Open SPE Calibrations for Dark Subtracting Flat Images')
loadDarkForFlats.triggered.connect(self.openDarkForFlats)
#Load flat
loadFlat = QtGui.QAction('Load Flats', self)
loadFlat.setStatusTip('Open SPE Calibrations for Flatfielding Science Images')
loadFlat.triggered.connect(self.openFlat)
#Restore points
restorePoints = QtGui.QAction('Restore Points', self)
restorePoints.setStatusTip('Return All Previously Discarded Points to the Light Curve.')
restorePoints.triggered.connect(self.restorePts)
#undo recenly selected bad point
undo = QtGui.QAction('Undo Bad Point Selection', self)
undo.setShortcut('Ctrl+Z')
undo.setStatusTip('Return Most Recently Discarded Point to the Light Curve.')
undo.triggered.connect(self.undoBad)
#Save Layout
saveLayout = QtGui.QAction('Save Layout', self)
saveLayout.setStatusTip('Save the current dock layout')
saveLayout.triggered.connect(self.saveLayout)
#Load Layout
loadLayout = QtGui.QAction('Load Layout', self)
loadLayout.setStatusTip('Load a saved dock layout')
loadLayout.triggered.connect(self.loadLayout)
#changeSmoothing
changeSmoothing = QtGui.QAction('Change Smoothing', self)
changeSmoothing.setStatusTip('Change Light Curve Smoothing Parameters.')
changeSmoothing.triggered.connect(self.changeSmooth)
#save screenshot
screenshot = QtGui.QAction('Save Screenshot', self)
screenshot.setStatusTip('Save a Screenshot of the Main Window.')
savescreenshot = partial(saveScreenshot)
screenshot.triggered.connect(savescreenshot)
#Menubar
menubar = self.menuBar()
#File Menu
fileMenu = menubar.addMenu('File')
fileMenu.addAction(openFile)
fileMenu.addAction(runPhot)
fileMenu.addAction(updateFT)
fileMenu.addAction(autoguide)
fileMenu.addAction(exitAction)
#Calibrations Menu
calibrationsMenu = menubar.addMenu('Calibrations')
calibrationsMenu.addAction(loadDark)
calibrationsMenu.addAction(loadDarkForFlats)
calibrationsMenu.addAction(loadFlat)
#Interactions menu
interactionsMenu = menubar.addMenu('Interact')
interactionsMenu.addAction(restorePoints)
interactionsMenu.addAction(undo)
self.changeApertureMenu = interactionsMenu.addMenu('Select Aperture Size')
self.changeCompStarMenu = interactionsMenu.addMenu('Select Comp Star for Division')
interactionsMenu.addAction(changeSmoothing)
#Layout Menu
layoutMenu = menubar.addMenu('Layout')
layoutMenu.addAction(saveLayout)
layoutMenu.addAction(loadLayout)
#Output Menu
outputMenu = menubar.addMenu('Output')
outputMenu.addAction(screenshot)
#Functions to save and load layouts
layoutsDir = './layouts/'
layoutsExt = '.p'
def saveLayout(self):
layoutName, ok = QtGui.QInputDialog.getText(self, 'Save layout',
'Enter name for this layout:')
if ok:
#Save dict in pickle format
pickle.dump( area.saveState(), open( self.layoutsDir+layoutName+self.layoutsExt, "wb" ) )
def loadLayout(self):
layouts = glob(self.layoutsDir+'*'+self.layoutsExt)
if len(layouts) == 0:
_ = QtGui.QMessageBox.warning(self,'Load layout','No saved layouts found.')
else:
layouts = [layout[len(self.layoutsDir):-1*len(self.layoutsExt)] for layout in layouts]
layout, ok = QtGui.QInputDialog().getItem(self,'Load layout','Select layout: ',layouts)
if ok:
state = pickle.load(open(self.layoutsDir+layout+self.layoutsExt, "rb" ) )
area.restoreState(state)
#Function to open SPE files to operate on.
def openSPE(self):
'''
Select a new target SPE file to work on.
Open dialog box, select file, verify that it is a SPE file.
'''
global defaultdir,rundir
fname = str(QtGui.QFileDialog.getOpenFileName(self, 'Open SPE file',
defaultdir,filter='Data (*.spe)'))
if fname[-4:]=='.spe':
log("Opening file "+fname,1)
#Set the default directory to a couple levels up from this file
rundir = os.path.dirname(fname)
defaultdir = os.path.dirname(rundir)
#set target log text as filename to start
targetEdit.setText(os.path.basename(fname)[:-4])
#This needs to trigger a major chain of events
stage1(fname)
else: log("Invalid file type (must be SPE).",3)
#Update the FT at user's command
def updateFTfunct(self):
global framenum
updateft(i=framenum)
def toAutoguider(self):
if spefile != '':
log("Opening separate program to send incoming data to Guide82.",2)
subprocess.Popen(["python",os.path.join(os.path.dirname(os.path.abspath(__file__)),'toAutoguider.py'),spefile])
else:
log("Open SPE file first before trying to send data to Guide82.",3)
#Load Dark frames
def openDark(self):
global dark, darkExists, darkExp, darkDark
fname = str(QtGui.QFileDialog.getOpenFileName(self, 'Open dark file',
defaultdir,filter='Data (*.spe *.fits)'))
if fname[-4:]=='.spe':
log("Opening dark file "+fname,1)
dspe = read_spe.File(fname)
num_darks=dspe.get_num_frames()
#get all frames in SPE file
#stack as 3D numpy array
(frames,_)=dspe.get_frame(0)
frames=np.array([frames])
for i in range(1,num_darks):
(thisframe,_)=dspe.get_frame(i)
frames=np.concatenate((frames,[thisframe]),0)
dark=np.median(frames,axis=0)
darkExists = True
log("Mean dark counts: "+str(np.mean(dark)))
processframe()
displayFrame(autoscale=True,markstars=False)
#Write out master dark file as fits
#Set up header
prihdr = fits.Header()
prihdr['OBJECT'] = 'dark'
prihdr['IMAGETYP'] = 'dark'
prihdr['REDUCED'] = dt.datetime.now().isoformat()
prihdr['COMMENT'] = "Reduced by Keaton Bell's OLD MAID Software"
if hasattr(dspe, 'footer_metadata'):
footer_metadata = BeautifulSoup(dspe.footer_metadata, "xml")
ts_begin = footer_metadata.find(name='TimeStamp', event='ExposureStarted').attrs['absoluteTime']
dt_begin = dateutil.parser.parse(ts_begin)
prihdr['TICKRATE'] = int(footer_metadata.find(name='TimeStamp', event='ExposureStarted').attrs['resolution'])
prihdr['DATE-OBS'] = str(dt_begin.isoformat())
prihdr['XBINNING'] = footer_metadata.find(name="SensorMapping").attrs['xBinning']
prihdr['YBINNING'] = footer_metadata.find(name="SensorMapping").attrs['yBinning']
prihdr['INSTRUME'] = footer_metadata.find(name="Camera").attrs['model']
prihdr['TRIGGER'] = footer_metadata.find(name='TriggerResponse').text
prihdr['COMMENT'] = "SPE file has footer metadata"
darkExp=np.round(float(footer_metadata.find(name='ExposureTime').text)/1000.)
if darkExp != exptime:
log("Exp times for dark and science frames do not match!",3)
log("Exposure time for dark: "+str(darkExp)+" s")
prihdr['EXPTIME'] = str(float(footer_metadata.find(name='ExposureTime').text)/1000.)
#prihdr['SOFTWARE'] = footer_metadata.find(name='Origin')
prihdr['SHUTTER'] = footer_metadata.find(name='Mode').text
if footer_metadata.find(name='Mode').text != 'AlwaysClosed':
prihdr['WARNING'] = 'Shutter not closed for dark frame.'
log("Shutter not closed for dark frame.",3)
else:
darkDark=True
else:
prihdr['WARNING'] = "No XML footer metadata."
log("No XML footer metadata.",3)
#Set up fits object
hdu = fits.PrimaryHDU(dark,header=prihdr)
darkpath = os.path.dirname(fname)
fitsfilename = 'master_'+os.path.basename(fname).split('.spe')[0]+'.fits'
log("Writing master dark as "+fitsfilename)
hdu.writeto(os.path.join(darkpath, fitsfilename),clobber=True)
#Close SPE
dspe.close()
#option to load as fits
elif fname[-5:]=='.fits':
log("Opening dark file "+fname,1)
hdulist = fits.open(fname)
prihdr = hdulist[0].header
dark=hdulist[0].data
darkExp = np.round(float(prihdr['EXPTIME']))
if darkExp != exptime:
log("Exp times for dark and science frames do not match!",3)
log("Exposure time for dark: "+str(darkExp)+" s")
log("Mean dark counts: "+str(np.mean(dark)))
if prihdr['SHUTTER'] != 'AlwaysClosed':
prihdr['WARNING'] = 'Shutter not closed for dark frame.'
log("Shutter not closed for dark frame.",3)
else:
darkDark=True
darkExists = True
processframe()
displayFrame(autoscale=True,markstars=False)
hdulist.close()
else: log("Invalid file type (must be SPE or FITS).",3)
#Load Dark frames for flat calibration
def openDarkForFlats(self):
global darkForFlat, darkForFlatExists, darkForFlatExp, darkForFlatDark
fname = str(QtGui.QFileDialog.getOpenFileName(self, 'Open SPE dark for flat calibration',
defaultdir,filter='Data (*.spe *.fits)'))
if fname[-4:]=='.spe':
log("Opening dark file "+fname+" for flat calibration.",1)
dspe = read_spe.File(str(fname))
num_darks=dspe.get_num_frames()
#get all frames in SPE file
#stack as 3D numpy array
(frames,_)=dspe.get_frame(0)
frames=np.array([frames])
for i in range(1,num_darks):
(thisframe,_)=dspe.get_frame(i)
frames=np.concatenate((frames,[thisframe]),0)
darkForFlat=np.median(frames,axis=0)
darkForFlatExists = True
log("Mean dark counts for flat: "+str(np.mean(darkForFlat)))
#Write out master dark file as fits
#Set up header
prihdr = fits.Header()
prihdr['OBJECT'] = 'dark'
prihdr['IMAGETYP'] = 'dark'
prihdr['REDUCED'] = dt.datetime.now().isoformat()
prihdr['COMMENT'] = "Reduced by Keaton Bell's OLD MAID Software"
if hasattr(dspe, 'footer_metadata'):
footer_metadata = BeautifulSoup(dspe.footer_metadata, "xml")
ts_begin = footer_metadata.find(name='TimeStamp', event='ExposureStarted').attrs['absoluteTime']
dt_begin = dateutil.parser.parse(ts_begin)
prihdr['TICKRATE'] = int(footer_metadata.find(name='TimeStamp', event='ExposureStarted').attrs['resolution'])
prihdr['DATE-OBS'] = str(dt_begin.isoformat())
prihdr['XBINNING'] = footer_metadata.find(name="SensorMapping").attrs['xBinning']
prihdr['YBINNING'] = footer_metadata.find(name="SensorMapping").attrs['yBinning']
prihdr['INSTRUME'] = footer_metadata.find(name="Camera").attrs['model']
prihdr['TRIGGER'] = footer_metadata.find(name='TriggerResponse').text
prihdr['COMMENT'] = "SPE file has footer metadata"
darkForFlatExp=np.round(float(footer_metadata.find(name='ExposureTime').text)/1000.)
log("Exposure time for dark for flat: "+str(darkForFlatExp)+" s")
prihdr['EXPTIME'] = str(float(footer_metadata.find(name='ExposureTime').text)/1000.)
#prihdr['SOFTWARE'] = footer_metadata.find(name='Origin')
prihdr['SHUTTER'] = footer_metadata.find(name='Mode').text
if footer_metadata.find(name='Mode').text != 'AlwaysClosed':
prihdr['WARNING'] = 'Shutter not closed for dark frame.'
log("Shutter not closed for dark frame.",3)
else:
darkForFlatDark=True
else:
prihdr['WARNING'] = "No XML footer metadata."
log("No XML footer metadata.",3)
#Set up fits object
hdu = fits.PrimaryHDU(darkForFlat,header=prihdr)
darkpath = os.path.dirname(fname)
fitsfilename = 'master_'+os.path.basename(fname).split('.spe')[0]+'.fits'
log("Writing master dark as "+fitsfilename)
hdu.writeto(os.path.join(darkpath, fitsfilename),clobber=True)
#Close SPE
dspe.close()
#Option to load as Fits
elif fname[-5:]=='.fits':
log("Opening dark file "+fname+" for flat calibration.",1)
hdulist = fits.open(fname)
prihdr = hdulist[0].header
darkForFlat=hdulist[0].data
darkForFlatExp = np.round(float(prihdr['EXPTIME']))
log("Exposure time for dark for flat: "+str(darkForFlatExp)+" s")
log("Mean dark counts: "+str(np.mean(darkForFlat)))
if prihdr['SHUTTER'] != 'AlwaysClosed':
prihdr['WARNING'] = 'Shutter not closed for dark frame.'
log("Shutter not closed for dark frame for flat.",3)
else:
darkForFlatDark=True
darkForFlatExists = True
processframe()
displayFrame(autoscale=True,markstars=False)
hdulist.close()
else: log("Invalid file type (must be SPE or FITS).",3)
#Load Flat frames
def openFlat(self):
global flat, flatExists, flatReduced
fname = str(QtGui.QFileDialog.getOpenFileName(self, 'Open SPE flat file',
defaultdir,filter='Data (*.spe *.fits)'))
if fname[-4:]=='.spe':
if darkForFlatExists == False:
log("Import dark for reducting flats before importing flat SPE file.",3)
else:
log("Opening flat file "+fname,1)
fspe = read_spe.File(fname)
num_flats=fspe.get_num_frames()
#get all frames in SPE file
#stack as 3D numpy array
(frames,_)=fspe.get_frame(0)
modes=[]
frames = frames - darkForFlat
modes.append(stats.mode(frames.flatten())[0][0])
frames=np.array([frames/modes[0]])
for i in range(1,num_flats):
(thisframe,_)=fspe.get_frame(i)
thisframe = thisframe-darkForFlat
#modes.append(stats.mode(thisframe.flatten())[0][0])
modes.append(np.median(thisframe.flatten()))
frames=np.concatenate((frames,[thisframe/modes[i]]),0)
flat=np.median(frames,axis=0)
flatExists=True
log("Median flat counts: "+str(np.median(modes)))
processframe()
displayFrame(autoscale=True,markstars=False)
#Write out fits file
#Set up header
prihdr = fits.Header()
prihdr['OBJECT'] = 'flat'
prihdr['IMAGETYP'] = 'flat'
if hasattr(fspe, 'footer_metadata'):
footer_metadata = BeautifulSoup(fspe.footer_metadata, "xml")
ts_begin = footer_metadata.find(name='TimeStamp', event='ExposureStarted').attrs['absoluteTime']
dt_begin = dateutil.parser.parse(ts_begin)
prihdr['TICKRATE'] = int(footer_metadata.find(name='TimeStamp', event='ExposureStarted').attrs['resolution'])
prihdr['DATE-OBS'] = str(dt_begin.isoformat())
prihdr['XBINNING'] = footer_metadata.find(name="SensorMapping").attrs['xBinning']
prihdr['YBINNING'] = footer_metadata.find(name="SensorMapping").attrs['yBinning']
prihdr['INSTRUME'] = footer_metadata.find(name="Camera").attrs['model']
prihdr['TRIGGER'] = footer_metadata.find(name='TriggerResponse').text
prihdr['MODE'] = 1 #normalized
prihdr['COMMENT'] = "SPE file has footer metadata"
prihdr['EXPTIME'] = str(float(footer_metadata.find(name='ExposureTime').text)/1000.)
flatexptime = np.round(float(footer_metadata.find(name='ExposureTime').text)/1000.)
#check that dark exp time matches flat
if flatexptime == darkForFlatExp:
flatReduced = True
else:
log("Exp times for dark and flat do not match!",3)
if darkForFlatExp == 0:
log("Bias being used for flat subtraction.",1)
flatReduced=True
#prihdr['SOFTWARE'] = footer_metadata.find(name='Origin')
prihdr['SHUTTER'] = footer_metadata.find(name='Mode').text
prihdr['REDUCED'] = dt.datetime.now().isoformat()
else:
prihdr['WARNING'] = "No XML footer metadata."
log("No XML footer metadata.",3)
#Set up fits object
#Only write flat if properly dark subtracted:
if darkForFlatDark and flatReduced:
hdu = fits.PrimaryHDU(flat,header=prihdr)
flatpath = os.path.dirname(fname)
fitsfilename = 'master_'+os.path.basename(fname).split('.spe')[0]+'.fits'
log("Writing master flat as "+fitsfilename)
hdu.writeto(os.path.join(flatpath, fitsfilename),clobber=True)
#Close SPE
fspe.close()
#Option to load as Fits
elif fname[-5:]=='.fits':
log("Opening flat file "+fname,1)
hdulist = fits.open(fname)
prihdr = hdulist[0].header
flat=hdulist[0].data
flatExists = True
flatmode= float(prihdr["mode"])
if flatmode == 1: #Properly normalized?
flatReduced=True
else:
log("Mode of master flat is "+str(flatmode)+". Not properly normalized?",3)
processframe()
displayFrame(autoscale=True,markstars=False)
hdulist.close()
else: log("Invalid file type (must be SPE).",3)
#Restore previously "bad" points
def restorePts(self):
global bad
log("Deselecting "+str(len(bad))+" points.")
bad=[]
updatelcs(i=framenum)
#Undo most recently selected "bad" point
def undoBad(self):
global bad
_ = bad.pop()
#Set up aperture size menu options
def setupApsizeMenu(self):
for size in apsizes:
self.changeApertureMenu.addAction(str(size)+' pixels',lambda s=size: setApSize(s))
#Set up comp star selection menu options
def addCompStarOption(self,i):
self.changeCompStarMenu.addAction('Comp Star #'+str(i),lambda s=i: setCompStar(s))
#Change Smoothing parameters
def changeSmooth(self):
kernel.openKernelDialog()
#Run Photometry
def run(self):
#Do aperture photometry on selected stars
global numstars, selectingstars
if stage == 1:
if len(stars) == 0:
log("No stars selected. Select stars before running.",3)
else:
numstars = len(stars)
#Write original coordinates and seeing to phot_coords.orig
f = open(rundir+'/phot_coords.orig', 'w')
for j,star in enumerate(stars):
f.write('{:.2f} {:.2f} {:.2f}\n'.format(star[0],star[1],seeing[j]))
f.close()
selectingstars=False
stage2()
#Confirm Quit
def closeEvent(self, event):
reply = QtGui.QMessageBox.question(self, 'Message',
"Really quit?", QtGui.QMessageBox.Yes |
QtGui.QMessageBox.No, QtGui.QMessageBox.No)
if reply == QtGui.QMessageBox.Yes:
event.accept()
else:
event.ignore()
# Make the App have a window and dock area.
app = QtGui.QApplication([])
win = WithMenu()
area = DockArea()
win.setCentralWidget(area)
win.resize(1500,800)
win.setWindowTitle('OLD MAID Software')
## Set up each of the docks (to hold the widgets)
d1 = Dock("Observing Log", size=(500,500))
d2 = Dock("Process Log", size=(500,500))
d3 = Dock("Fourier Transform", size=(500,500))
d4 = Dock("Smoothed Light Curve", size=(1000,250))
d5 = Dock("Image", size=(500,500))
d6 = Dock("Divided Light Curve", size=(1000,250))
d7 = Dock("Raw Counts", size=(500,250))
d8 = Dock("Sky Brightness", size=(1000,250))
d9 = Dock("Seeing", size=(1000,250))
#Define initial layout
area.addDock(d4, 'left')
area.addDock(d1, 'right',d4)
area.addDock(d6, 'above', d4)
area.addDock(d9, 'bottom', d4)
area.addDock(d8, 'above', d9)
area.addDock(d7, 'above', d8)
area.addDock(d5, 'bottom',d1)
area.addDock(d2, 'bottom', d5)
area.addDock(d3, 'bottom', d7)
area.moveDock(d5,'right',d3)
#Define and place widgets into the docks
## First dock holds the Observing Log
#Type of widget: Form
w1 = pg.LayoutWidget()
#Name the form elements
observer = QtGui.QLabel('Observer')
target = QtGui.QLabel('Target')
filt = QtGui.QLabel('Filter')
logtext = QtGui.QLabel('Log')
#Define the types of fields
observerEdit = QtGui.QLineEdit()
targetEdit = QtGui.QLineEdit()
filtEdit = QtGui.QComboBox()
filtEdit.addItems(["BG40","u'","g'","r'","i'","z'","Other"])
logEdit = QtGui.QTextEdit()
logEdit.setText("WARNING: None of these log fields are saved!")
#Put the fields in the form
w1.addWidget(observer, 1, 0)
w1.addWidget(observerEdit, 1, 1)
w1.addWidget(target, 2, 0)
w1.addWidget(targetEdit, 2, 1)
w1.addWidget(filt, 3, 0)
w1.addWidget(filtEdit, 3, 1)
w1.addWidget(logtext, 4, 0)
w1.addWidget(logEdit, 4, 1, 6, 1)
#Put the widget in the dock
d1.addWidget(w1)
## Process Log
# Records activity.
w2 = pg.LayoutWidget()
processLog = QtGui.QTextEdit()
processLog.setReadOnly(True)
w2.addWidget(processLog, 0, 0, 6, 1)
d2.addWidget(w2)
# This widget need special functions to get messages:
def log(text,level=0):
'''log messages to the process log and log file
text is the message for the log
level indicated how important it is:
level=0: Routine background process: gray text;
level=1: User influenced action: black text;
level=2: Major change: bold black;
level=3: Warning message: bold red;
'''
text=str(text)
colors = ['darkgray','black','black','red']
prefix = ['','','','WARNING: ']
fontweight = [50,50,75,75]
if level in range(4):
processLog.setTextColor(QtGui.QColor(colors[level]))
processLog.setFontWeight(fontweight[level])
processLog.append(prefix[level]+text)
else: log('Level assigned to message "'+text+'" out of range.',level=3)
## Light Curve
# It's a plot
w6 = pg.PlotWidget(title="Divided Light Curve",labels={'left': 'rel. flux', 'bottom': 'time (s)'})
# Set up plot components
# Raw points
s1 = pg.ScatterPlotItem(brush=(255,0,0), pen='w',symbol='o')
# Bad (ignored) points #Not currently displayed since it causes scaling issues.
#s2 = pg.ScatterPlotItem(brush=(255,0,0), pen='b',symbol='o')
# Connecting lines
l1 = pg.PlotCurveItem()
#Add components to plot widget.
w6.addItem(s1)
#w6.addItem(s2)
w6.addItem(l1)
#Add widget to dock
d6.addWidget(w6)
# Make points change color when clicked
def clicked(plot, points):
global bad
for p in points:
if p.pos()[0]/exptime in bad:
bad.remove(p.pos()[0]/exptime)
else:
bad.append(p.pos()[0]/exptime)
updatelcs(i=framenum)
s1.sigClicked.connect(clicked)
#s2.sigClicked.connect(clicked)
## Smoothed Light Curve
w4 = pg.PlotWidget(title="Smoothed Light Curve",labels={'left': 'smoothed flux', 'bottom': 'time (s)'})
ss1 = pg.ScatterPlotItem(brush=(255,0,0), pen='w',symbol='o')
sl1 = pg.PlotCurveItem()
w4.addItem(ss1)
w4.addItem(sl1)
d4.addWidget(w4)
## Raw Star/Sky Counts
w7 = pg.PlotWidget(title="Raw Star Counts",labels={'left': 'flux summed in aperture', 'bottom': 'time (s)'})
d7.addWidget(w7)
#Hold the individual plot items in this list once they are created:
rawcounts=[]
## Sky
w8 = pg.PlotWidget(title="Sky Brightness",labels={'left': 'median sky counts', 'bottom': 'time (s)'})
sky = pg.PlotCurveItem()
w8.addItem(sky)
d8.addWidget(w8)
## Seeing
w9 = pg.PlotWidget(title="Seeing",labels={'left': 'FWHM (pixels)', 'bottom': 'time (s)'})
d9.addWidget(w9)
gridlines = pg.GridItem()
w9.addItem(gridlines)
#Hold the individual plot items in this list once they are created:
seeingplots = []
## Fourier Transform
w3 = pg.PlotWidget(title="Fourier Transform",labels={'left': 'amplitude (mma)', 'bottom': 'freq (muHz)'})
ft = w3.plot(pen='y')
d3.addWidget(w3)
## Image
w5 = pg.ImageView()
w5.ui.roiBtn.hide()
#w5.ui.normBtn.hide() #Causing trouble on windows
#Define function for selecting stars. (must be defined before linking the click action)
def click(event):#Linked to image click event
global stars, seeing
if event.button() == 1 and selectingstars:
event.accept()
pos = event.pos()
#x and y are swapped in the GUI!
x=pos.x()
y=pos.y()
#log('Clicked at ({:.2f}, {:.2f})'.format(x,y),level=0)
#improve coordinates
dx,dy,newseeing = improvecoords(x,y)
#round originals so original position *within* pixel doesn't affect answer
newcoords=[np.floor(x)+dx,np.floor(y)+dy]
stars.append(newcoords)
seeing.append(newseeing)
#make menuoption for comp star selection
if len(stars) > 1: win.addCompStarOption(len(stars)-1)
#Mark stars in image display
targs.setData([p[0] for p in stars],[p[1] for p in stars])
targs.setPen(pencolors[0:len(stars)])
#Set up plot for raw counts and seeing:
rawcounts.append(pg.ScatterPlotItem(pen=pencolors[len(stars)-1],symbol='o',size=1))
seeingplots.append(pg.PlotCurveItem(pen=seeingcolors[len(stars)-1]))
log('Star selected at ({:.2f}, {:.2f})'.format(newcoords[0],newcoords[1]),level=1)
elif event.button() == 2:
event.accept()#Passed on to other functionality if not accepted.
print "RIGHT!"
w5.getImageItem().mouseClickEvent = click #Function defined below
#w5.keyPressEvent = moveCircles # Seems to be the right thing for detecting frame changes,
#But I can't connect to it without overriding other behavior. May need to subclass this.
#Set up plot for apertures around stars
#print QtGui.QColor.colorNames() for available names.
stringcolors=['red','green','blue','magenta','orange','yellow',
'darkred','darkgreen','darkblue','darkmagenta','darkorange','darkgoldenrod',
'hotpink','seagreen','skyblue','salmon','brown','lightyellow']
pencolors = [pg.mkPen(QtGui.QColor(c), width=3) for c in stringcolors]
seeingcolors = [pg.mkPen(QtGui.QColor(c), width=1.5) for c in stringcolors]
targs = pg.ScatterPlotItem(brush=None, pen=pencolors[0],symbol='o',pxMode=False,size=8)
w5.addItem(targs)
#Add widget to dock
d5.addWidget(w5)
## Show the program!
win.show()
win.raise_()
#win.activateWindow()
# I think everything is set up enough to start doing stuff
# Send initial message to process log.
log("ProEMOnline initialized",2)
#log("Development version. Do not trust.",3)
stagechange(0)
log("Open SPE file to begin analysis.",1)
#### STAGE 1 ####
# Stage 1 starts when a SPE file is loaded.
# It's the "getting everything set up" stage
# Since the SPE file is loaded by the menu action, this will be one big
# function that is called on the new image.
#First define all the variables everything will need access to:
#These will be called into action as global variables.
#SPE Filename
spefile = ''
#SPE Data
spe=[]
#SPE file directory
rundir=''
#Does SPE have a footer?
hasFooter=False
#Number of frames in currently read spe file
numframes=0
#Exposure time for science frames
exptime=1. #If it can't be figured out, plots are in terms of frame #
#Dark data
dark = []
darkExists=False
darkExp=0 #exp time should match spe exptime
darkDark=False #shutter closed?
darkForFlat = []
darkForFlatExists=False
darkForFlatExp=0
darkForFlatDark=False
#Flat data
flat = []
flatExists=False
flatReduced=False #proper dark subtracted?
#Flag whether full reductions are being done (*correct* darks and flat)
#Number of last *reduced* (photometry measures) frame
framenum=-1 #none yet
#Flag to indicate whether we are currently selecting stars in the frame:
selectingstars = False
#Number of stars to do photometry on (target first)
numstars = 0 #0 means we haven't selected stars yet.
#Star coords
stars = [] #list of list of list of coords
#Image data:
img=[] #only hold current image to save tiem
#And another version to look nice
displayimg=[] #only hold current image to save tiem
#Keep track of "Bad" points
bad=[]
#Elapsed timestamps
rawtimes=[] #start of timestamp
#Search radius (box for now), improve later
pixdist=10 #(super)pixels
#List of median background counts:
backmed=[]
#List of background variances
backvar=[]
#Seeing for each star,frame:
seeing=[]
#Binning
binning=4
def stage1(fname):
#Load SPE File
#Access needed global vars
global spefile,spe,binning,exptime,dark,flat
#Announce Stage 1
stagechange(1)
#Record SPE filename this once
spefile = fname
#Read in SPE data
spe = read_spe.File(spefile)
binning = 1024/spe.get_frame(0)[0].shape[0]
log(str(spe.get_num_frames()) + ' frames read in.')
exptime=getexptime(spe)
log('Inferred exposure time: '+str(exptime)+' s')
if hasattr(spe, 'footer_metadata'):
#log('SPE file has footer.')
exptime=np.round(float(BeautifulSoup(spe.footer_metadata, "xml").find(name='ExposureTime').text)/1000.)
#log('Exposute time from footer: '+str(exptime)+' s')
#now display the first frame
processframe()
displayFrame(autoscale=True,markstars=False)
#Load calibration frames and set up
log("Please load dark, flat, and dark for flat files",1)
dark = np.zeros(img[0].shape)
flat = np.ones(img[0].shape)
#Select stars:
selectstars()
#spe.close() #In real version we'll close spe
win.setupApsizeMenu()
#Determine the exposuretime of a SPE file without a footer
def getexptime(thisspe):
#Input open SPE file
#don't read lots of frames in large files
numtoread = min([thisspe.get_num_frames(),11])
tstamps = np.zeros(numtoread)
for f in range(numtoread):
tstamps[f] = spe.get_frame(f)[1]['time_stamp_exposure_started']
timediff = tstamps[1:numtoread]-tstamps[:numtoread-1]
return np.round(np.median(timediff/1e6))
#Define all the stuff that needs to be done to each incoming frame
def processframe(i=0):
global img,displayimg,rawtimes,backmed,backvar,framenum
(thisframe,thistime) = spe.get_frame(i)
#calibrate (doesn't do anything if calibration frames are not available):
if darkExists: thisframe=(thisframe-dark)
if flatExists: thisframe=thisframe/flat
#read in frame
img=np.transpose(thisframe)
backgroundmed,backgroundvar=charbackground()
#append stuff to global variables
#Replace if this frame already exists, otherwise append
if i <= framenum: #replace
#log('Re-processing frame '+str(i)+' of '+str(framenum))
rawtimes[i]=thistime['time_stamp_exposure_started']
backmed[i]=backgroundmed
backvar[i]=backgroundvar
else: #append
#log('Processing frame '+str(i)+' of '+str(framenum))
rawtimes.append(thistime['time_stamp_exposure_started'])
backmed.append(backgroundmed)
backvar.append(backgroundvar)
#make display image
newdisplayimg=np.copy(img)
newdisplayimg[0,0]=0
imgvals = newdisplayimg.flatten()
img99percentile = np.percentile(imgvals,99)
newdisplayimg[newdisplayimg > img99percentile] = img99percentile
#log("Framenum: "+str(framenum),2)
#Replace if this frame already exists, otherwise append
displayimg=newdisplayimg
framenum=i
#Function to characterize the background to find stellar centroids accurately
#This should be done for each frame as it's read in
def charbackground():
"""Characterize the image background, median and variance
for frame currenly held in img
"""
backgroundmed = biweight_location(img)
backgroundvar = biweight_midvariance(img)
return backgroundmed, backgroundvar
#show the image to the widget
def displayFrame(autoscale=False,markstars=True):
"""Display an RBG image
i is index to display
Autoscale optional.
Return nothing.
"""
#Make sure i is in range
if autoscale:
#lowlevel=np.min(thisimg[thisimg > 0])
lowlevel=np.min(displayimg)
if np.sum(displayimg > 0) > 100:
lowlevel=np.percentile(displayimg[displayimg > 0],3)
highlevel=np.max(displayimg)-1
w5.setImage(np.array(displayimg),autoRange=True,levels=[lowlevel,highlevel],)
else:
w5.setImage(np.array(displayimg),autoRange=False,autoLevels=False)
#Draw position circles:
if markstars and len(stars) > 0:
targs.setData([p[0] for p in stars[framenum]],[p[1] for p in stars[framenum]])
targs.setSize(2.*apsizes[apsizeindex])
targs.setPen(pencolors[0:numstars])
def selectstars():
'''Select stars in the current frame.
Click to select any number in the first image.
Click to select numstars in later images to get following back on track.
'''
global selectingstars
selectingstars = True
def gaussian(x, A, sigma):
#Define a gaussian for finding FWHM
return A*np.exp(-(x)**2/(2.*sigma**2))
def improvecoords(x,y,i=framenum,pixdist=pixdist,fwhm=4.0,sigma=5.):
"""Improve stellar centroid position from guess value. (one at a time)
#return the adjustment than needs to be made in x and y directions
#also calculate the FWHM seeing
"""
#x=(1024/binning)-x
#y=(1024/binning)-y
#Keep track of motion
delta = np.zeros(2)
#Get image subregion around guess position
#Need to be careful not to ask for out-of-range indexes near a border
x0=x-pixdist
y0=y-pixdist
xdist=2*pixdist
ydist=2*pixdist
if x0 < 0: #if near the left edge
x0 = 0 #subregion from near given position
delta[0] += pixdist-x #adjust delta accordingly
if y0 < 0: #same in the y direction
y0 = 0
delta[1] += pixdist-y
if x+pixdist > img.shape[0]:
xdist = img.shape[0]-x+pixdist
if y+pixdist > img.shape[1]:
ydist = img.shape[1]-y+pixdist
subdata=img[x0:x0+xdist,y0:y0+ydist]
#print subdata.shape
sources = daofind(subdata - backmed[i], sigma*backvar[i], fwhm,
sharplo=0.1, sharphi=1.5, roundlo=-2.0, roundhi=2.0)
#From what I can tell, daofind returns x and y swapped, so fix it
returnedx = sources['ycentroid']
returnedy = sources['xcentroid']
thisseeing = np.nan
if len(sources) != 0:
strongsignal= np.argmax(sources['peak'])
delta[0]+=returnedx[strongsignal]-pixdist
delta[1]+=returnedy[strongsignal]-pixdist
#Fit with a gaussian
seeingdata = subdata.flatten() - backmed[i]
dist = []
for j in np.arange(subdata.shape[1])+0.5:
for k in np.arange(subdata.shape[0])+0.5:
dist.append(np.sqrt((returnedy[strongsignal]-k)**2.
+(returnedx[strongsignal]-j)**2.))
dist=np.array(dist).flatten()#distance between new coord and pixel centers
#plt.scatter(dist,seeingdata)
try: #ignores error if max iterations is hit
p0=[1000.,4.]#initial guesses
popt,_ = curve_fit(gaussian,np.append(dist,dist*-1.),np.append(seeingdata,seeingdata),p0=p0)
thisseeing = np.abs(popt[-1])*2.3548
#plt.plot(np.arange(0,10,.1),gaussian(np.arange(0,10,.1),popt[0],popt[1]))
except RuntimeError:
print "ERROR: gaussian fit did not converge for a star in frame "+str(i)
#plt.show()
else:
delta=np.zeros(2)
#also measure the seeing in this step:
#check that unique source found
'''
if len(sources) == 0:
log("Frame #"+str(i),1)
log("WARNING: no sources found in searched region near ({:.2f}, {:.2f}).".format(x,y))
#delta = [0,0] in this case
else:
if len(sources) > 1:
log("Frame #"+str(i),1)
log("WARNING: non-unique solution found for target near ({:.2f}, {:.2f}).".format(x,y))
log(str(len(sources))+" signals in window. Using brightest.")
#Take brightest star found
'''
#handle stars that were not found #Move this outside this function
"""
if [0,0] in delta and follow:
meandeltax=np.mean(delta[np.where(delta[:,0] != 0),0])
meandeltay=np.mean(delta[np.where(delta[:,1] != 0),1])
delta[np.where(delta[:,0] == 0)] += [meandeltax,meandeltay]
"""
return delta[0],delta[1],thisseeing
#### STAGE 2 ####
#Aperture details (provide a way to change these!)
apsizes=np.arange(1,11)
apsizeindex=3
r_in = 16. #inner sky annulus radius #change in terms of binning eventually
r_out = 24. #outer sky annulus radius #change in terms of binning eventually
def setApSize(size):
global apsizeindex
log("Aperture size set to "+str(size)+" pixels.",1)
#log("(Updates on next frame.)")
if size in apsizes:
apsizeindex=np.where(apsizes == size)[0][0]
targs.setSize(2*size)# Currently doesn't update until next click/frame
if stage > 1:
updatelcs(i=framenum)
compstar = 1 #which star to divide by
def setCompStar(s):
global compstar
compstar = s
log("Now dividing by comparsion star #"+str(s),1)
updatelcs(framenum)
#Phot results: variables to hold light curves and uncertainties
photresults=np.array([])
#Run the stage 2 loop
def stage2():
global stars,seeing, spe, stage, hasFooter
stagechange(2)
#Add plot items for raw counts panel to plot
for splot in rawcounts: w7.addItem(splot)
for splot in seeingplots: w9.addItem(splot)
#Make stars array an array of arrays of star coord arrays (yikes)
# i.e, it needs to get pushed a level deeper
stars=[stars]
#same with seeing
seeing=np.array([seeing])
#Run photometry on the first frame
dophot(0)
updatelcs(i=0)
updatehack()
#Start timer that looks for new data
timer2.start(min(exptime*1000.,5000.))# shorter of exptime and 5 sec
timer3.start(1.*60*1000)#update every 1 minutes
#This currently freezes up the UI. Need to thread, but not enough time
#to implement this currently. Use a hack for now
'''
#Run the loop:
fsize_spe_old = 0
while not hasFooter:
#Update only if there's new data
fsize_spe_new = os.path.getsize(spefile)
if fsize_spe_new > fsize_spe_old:
spe = read_spe.File(spefile)
numframes = spe.get_num_frames()
log('Processing frames '+str(framenum)+'-'+str(numframes),1)
while framenum < numframes:
nextframe()
if hasattr(spe, 'footer_metadata'):
hasFooter = True
log('SPE footer detected. Data acquisition complete.',2)
stagechange(3)
spe.close()
fsize_spe_old = fsize_spe_new
'''
fsize_spe_old = 0#Keep track if new spe file is larger that old one
def updatehack():
global spe, hasFooter, numframes,fsize_spe_old
#Only look for new data if not currently processing new data
if not timer.isActive():
#Update only if there's new data
fsize_spe_new = os.path.getsize(spefile)
if fsize_spe_new > fsize_spe_old and stage ==2:
spe = read_spe.File(spefile)
numframes = spe.get_num_frames()
if framenum+1==numframes-1:log('Processing frame '+str(framenum+1))
else: log('Processing frames '+str(framenum+1)+'-'+str(numframes-1),1)
timer.start(100)
#Update plots
updatelcs(i=framenum)
if hasattr(spe, 'footer_metadata'):
hasFooter = True
timer3.stop()
fsize_spe_old = fsize_spe_new
def nextframehack():
#call nextframe until you're caught up
global framenum,spe
nextframe()
updatelcs(i=framenum)
if framenum >= numframes-1:
timer.stop()
updateft(i=framenum)
if hasFooter:
log('SPE footer detected. Data acquisition complete.',2)
stagechange(3)
log("Image processing complete",2)
writetimestamps()
displayFrame(autoscale=True)
spe.close()
#This timer catches up on photometry
timer = pg.QtCore.QTimer()#set up timer to avoid while loop
timer.timeout.connect(nextframehack)
#This timer checks for new data
timer2 = pg.QtCore.QTimer()
timer2.timeout.connect(updatehack)
#For demo purposes, read in the next frame of the spe file each time this is called
def nextframe():
global stars, seeing
#if stage == 2:
oldcoords = stars[framenum]
processframe(i=framenum+1) #Frame num increases here.
newcoords=[]
newseeing=[]
for coord in oldcoords:
dx,dy,thisseeing = improvecoords(coord[0],coord[1],i=framenum)
newcoords.append([np.floor(coord[0])+.5+dx,np.floor(coord[1])+.5+dy])
newseeing.append(thisseeing)
stars.append(newcoords)
seeing = np.append(seeing,[newseeing],axis=0)
#Show the frame
displayFrame(autoscale=True,markstars=True)
#Perform photometry
dophot(i=framenum)
#Update light curves
#updatelcs(i=framenum) #only after all the new photometry is done.
def dophot(i):
'''Do photometric measurements.
Stars have been selected. Do aperture photometry on given frame
'''
global photresults
#print "dophot(i) called with i="+str(i)
#Do the aperture photometry
#The aperture_photometry() function can do many stars at once
#But you must first do a background subtraction
#We're going to save a lot of information in this step:
#Total counts and uncertainty for every aperture size for every star
#And eventually for every frame...
#Note that the photometry package seems to reference x and y coords
#as the tranpose of what we've been using. Switch the order here:
coords = [star[::-1] for star in stars[i]]
thisphotometry = np.zeros((len(coords),len(apsizes)))
for n in range(numstars):
#Loop through the stars in the image
#annulus_aperture = CircularAnnulus(coords[n], r_in=r_in, r_out=r_out)
#print aperture_photometry(img[i],annulus_aperture).keys()
#background_mean = aperture_photometry(img[i],annulus_aperture)['aperture_sum'][0]/annulus_aperture.area()
#NOTE on the above line: This should really be a median!
#Issue 161 on photutils https://github.com/astropy/photutils/issues/161 is open as of 09/28/15
gain = 12.63 #? From PI Certificate of Performance for "traditional 5MHz gain." Confirm this value!
#loop through aperture sizes
for j,size in enumerate(apsizes):
aperture = CircularAperture(np.array(coords[n]), r=size)
#phot = aperture_photometry(x-background_mean,aperture,error=backgroundvar,gain=gain)
#Why am I getting negative numbers?
#phot = aperture_photometry(img[i]-np.median(img),aperture)
phot = aperture_photometry(img-backmed[i],aperture)
thisphotometry[n,j]=phot['aperture_sum'][0]
#print "photometry ",thisphotometry
if i == 0:
photresults = np.array([thisphotometry])
else:
#print "photresults dimensions are "+str(photresults.shape)
#print "trying to append shape "+str(thisphotometry.shape)
photresults = np.append(photresults,[thisphotometry],axis=0)
#print "photresults dimensions are "+str(photresults.shape)
#yay. This deserves to all be checked very carefully, especially since the gain only affects uncertainty and not overall counts.
#Allow different kernel types:
kerneltypes = ['Uniform','Epanechnikov']
#set up a dialog to change the kernel details:
class KernelDialog(QtGui.QDialog):
def __init__(self, parent=None):
super(KernelDialog, self).__init__(parent)
typeLabel = QtGui.QLabel("Kernel &type")
self.typeEdit = QtGui.QComboBox()
self.typeEdit.addItems(kerneltypes)
#self.typeEdit.setCurrentIndex(currentind)
typeLabel.setBuddy(self.typeEdit)
widthLabel = QtGui.QLabel("Kernel &width")
self.widthEdit = QtGui.QSpinBox()
self.widthEdit.setMinimum(2)
self.widthEdit.setMaximum(200)
#self.widthEdit.setValue(currentwidth)
widthLabel.setBuddy(self.widthEdit)
self.buttons = QtGui.QDialogButtonBox(QtGui.QDialogButtonBox.Ok | QtGui.QDialogButtonBox.Cancel,
QtCore.Qt.Horizontal, self)
self.buttons.accepted.connect(self.accept)
self.buttons.rejected.connect(self.reject)
grid = QtGui.QGridLayout(self)
grid.addWidget(typeLabel,0,0)
grid.addWidget(self.typeEdit,0,1)
grid.addWidget(widthLabel,1,0)
grid.addWidget(self.widthEdit,1,1)
grid.addWidget(self.buttons, 3, 0)
self.setLayout(grid)
self.setWindowTitle("Define Smoothing Kernel")
def kernelFormat(self):
kerneltype=int(self.typeEdit.currentIndex())
width=int(self.widthEdit.value())
return (kerneltype,width)
@staticmethod
def getKernelFormat(parent = None):
dialog = KernelDialog(parent)
result = dialog.exec_()
kerneltype,width = dialog.kernelFormat()
return (kerneltype,width, result == QtGui.QDialog.Accepted)
#set up a class that holds all the smoothing kernel information
class smoothingkernel:
"""Holds all smoothing kernel info"""
kerneltype = 0
width = 10 #points
kernel=[]
types = kerneltypes
def setkernel(self,kerneltype,width):
if kerneltype == 1: #Epanechnikov
u=(2.*np.arange(width)/(float(width)-1.))-0.5
self.kernel = 0.75*(1.-u**2.)
self.kernel /= np.sum(self.kernel)
log("Using "+self.types[kerneltype]+" smoothing kernel of width "+str(width))
elif kerneltype == 0: #Uniform
self.kernel = np.ones(width)/float(width)
log("Using "+self.types[kerneltype]+" smoothing kernel of width "+str(width))
def openKernelDialog(self):
dkerneltype,dwidth,daccepted = KernelDialog.getKernelFormat()
if daccepted and (dkerneltype in range(len(kerneltypes))) and (dwidth > 1):
self.setkernel(dkerneltype,dwidth)
def __init__(self):
self.setkernel(0,10)
#set up the kernel object
kernel=smoothingkernel()
#Update display.
def updatelcs(i):
#Identify which points to include/exclude, up to frame i
goodmask=np.ones(i+1, np.bool)
goodmask[bad] = False
badmask = np.zeros(i+1, np.bool)
badmask[bad] = True
targdivided = photresults[:i+1,0,apsizeindex]/photresults[:i+1,compstar,apsizeindex]
times = np.arange(i+1)#Multiply by exptime for timestamps
goodfluxnorm=targdivided[goodmask[:i+1]]/np.abs(np.mean(targdivided[goodmask[:i+1]]))
s1.setData(exptime*times[goodmask[:i+1]],goodfluxnorm)
#s2.setData(times[badmask[:i]],targdivided[badmask[:i]])
l1.setData(exptime*times[goodmask[:i+1]],goodfluxnorm)
#sl1.setData(times[goodmask[:i]],fluxsmoothed[goodmask[:i]])
#Raw Counts:
for j,splot in enumerate(rawcounts): splot.setData(exptime*times,photresults[:,j,apsizeindex])
#Seeing:
for j,splot in enumerate(seeingplots[::-1]): splot.setData(exptime*times,seeing[:,j])
#Sky brightness
sky.setData(exptime*times,backmed)
def updateftfromtimer():
updateft(i=framenum)
def updateft(i=framenum):
oversample=10. #Oversampling factor
goodmask=np.ones(i+1, np.bool)
goodmask[bad] = False
targdivided = photresults[:i+1,0,apsizeindex]/photresults[:i+1,compstar,apsizeindex]
goodfluxnorm=targdivided[goodmask[:i+1]]/np.abs(np.mean(targdivided[goodmask[:i+1]]))
times = np.arange(i+1)#Multiply by exptime for timestamps
#Fourier Transform and smoothed lc
if goodmask.sum() > 2:
#This all requires at least two points
#Only update once per file read-in
interped = interp1d(exptime*times[goodmask[:i+1]],goodfluxnorm-1.)
xnew = np.arange(exptime*min(times[goodmask[:i]]),exptime*max(times[goodmask[:i+1]]),exptime)
ynew = interped(xnew)
#calculate FT
amp = 2.*np.abs(fft(ynew,n=len(ynew)*oversample))#FFT
amp /= float(len(ynew))
freq = fftfreq(len(amp),d=exptime)
pos = freq>=0 # keep positive part
ft.setData(1e6*freq[pos],1e3*amp[pos])
#Smoothed LC
#Update if there are enough points:
if len(ynew) > kernel.width:
fluxsmoothed=np.convolve(ynew,kernel.kernel,mode='same')
ss1.setData(xnew,fluxsmoothed)
#This timer recomputes the FT and smoothed lc infrequently
timer3 = pg.QtCore.QTimer()
timer3.timeout.connect(updateftfromtimer)
''' Not implemented yet!
#To keep the GUI from locking up, computationally intensive processes must
#be done in a thread. Set up that thread here:
class Stage2Thread(QtCore.QThread):
setTime = QtCore.pyqtSignal(int,int)
iteration = QtCore.pyqtSignal(threading.Event, int)
def run(self):
self.setTime.emit(0,300)
for i in range(300):
time.sleep(0.05)
event = threading.Event()
self.iteration.emit(event, i)
event.wait()
'''
#Write timestamps
def writetimestamps():
fpath_csv = os.path.splitext(spefile)[0]+'_timestamps.csv'
log("Writing absolute timestamps to file "+fpath_csv,2)
if hasattr(spe, 'footer_metadata'):
footer_metadata = BeautifulSoup(spe.footer_metadata, "xml")
trigger_response = footer_metadata.find(name='TriggerResponse').text
ts_begin = footer_metadata.find(name='TimeStamp', event='ExposureStarted').attrs['absoluteTime']
dt_begin = dateutil.parser.parse(ts_begin)
ticks_per_second = int(footer_metadata.find(name='TimeStamp', event='ExposureStarted').attrs['resolution'])
else:
log(("No XML footer metadata.\n" +
"Unknown trigger response.\n" +
"Using file creation time as absolute timestamp.\n" +
"Assuming 1E6 ticks per seconds."),3)
trigger_response = ""
dt_begin = dt.datetime.utcfromtimestamp(os.path.getctime(fpath_spe))
ticks_per_second = 1E6
idx_metadata_map = {}
for idx in xrange(spe.get_num_frames()):
(frame, metadata) = spe.get_frame(idx)
idx_metadata_map[idx] = metadata
df_metadata = pd.DataFrame.from_dict(idx_metadata_map, orient='index')
df_metadata = df_metadata.set_index(keys='frame_tracking_number')
df_metadata = df_metadata[['time_stamp_exposure_started', 'time_stamp_exposure_ended']].applymap(lambda x: x / ticks_per_second)
df_metadata = df_metadata[['time_stamp_exposure_started', 'time_stamp_exposure_ended']].applymap(lambda x : dt_begin + dt.timedelta(seconds=x))
df_metadata[['diff_time_stamp_exposure_started', 'diff_time_stamp_exposure_ended']] = df_metadata - df_metadata.shift()
log("Trigger response = {tr}".format(tr=trigger_response))
log("Absolute timestamp = {dt_begin}".format(dt_begin=dt_begin))
log("Ticks per second = {tps}".format(tps=ticks_per_second))
df_metadata.head()
# Write out as CSV to source directory of SPE file.
df_metadata.to_csv(fpath_csv, quoting=csv.QUOTE_NONNUMERIC)
saveScreenshot()
## Start Qt event loop unless running in interactive mode or using pyside.
if __name__ == '__main__':
if (sys.flags.interactive != 1) or not hasattr(QtCore, 'PYQT_VERSION'):
if len(sys.argv) > 1:
defaultdir = sys.argv[1]
QtGui.QApplication.instance().exec_()
| mit |
rajathkumarmp/numpy | numpy/fft/fftpack.py | 72 | 45497 | """
Discrete Fourier Transforms
Routines in this module:
fft(a, n=None, axis=-1)
ifft(a, n=None, axis=-1)
rfft(a, n=None, axis=-1)
irfft(a, n=None, axis=-1)
hfft(a, n=None, axis=-1)
ihfft(a, n=None, axis=-1)
fftn(a, s=None, axes=None)
ifftn(a, s=None, axes=None)
rfftn(a, s=None, axes=None)
irfftn(a, s=None, axes=None)
fft2(a, s=None, axes=(-2,-1))
ifft2(a, s=None, axes=(-2, -1))
rfft2(a, s=None, axes=(-2,-1))
irfft2(a, s=None, axes=(-2, -1))
i = inverse transform
r = transform of purely real data
h = Hermite transform
n = n-dimensional transform
2 = 2-dimensional transform
(Note: 2D routines are just nD routines with different default
behavior.)
The underlying code for these functions is an f2c-translated and modified
version of the FFTPACK routines.
"""
from __future__ import division, absolute_import, print_function
__all__ = ['fft', 'ifft', 'rfft', 'irfft', 'hfft', 'ihfft', 'rfftn',
'irfftn', 'rfft2', 'irfft2', 'fft2', 'ifft2', 'fftn', 'ifftn']
from numpy.core import (array, asarray, zeros, swapaxes, shape, conjugate,
take, sqrt)
from . import fftpack_lite as fftpack
_fft_cache = {}
_real_fft_cache = {}
def _raw_fft(a, n=None, axis=-1, init_function=fftpack.cffti,
work_function=fftpack.cfftf, fft_cache=_fft_cache):
a = asarray(a)
if n is None:
n = a.shape[axis]
if n < 1:
raise ValueError("Invalid number of FFT data points (%d) specified."
% n)
try:
# Thread-safety note: We rely on list.pop() here to atomically
# retrieve-and-remove a wsave from the cache. This ensures that no
# other thread can get the same wsave while we're using it.
wsave = fft_cache.setdefault(n, []).pop()
except (IndexError):
wsave = init_function(n)
if a.shape[axis] != n:
s = list(a.shape)
if s[axis] > n:
index = [slice(None)]*len(s)
index[axis] = slice(0, n)
a = a[index]
else:
index = [slice(None)]*len(s)
index[axis] = slice(0, s[axis])
s[axis] = n
z = zeros(s, a.dtype.char)
z[index] = a
a = z
if axis != -1:
a = swapaxes(a, axis, -1)
r = work_function(a, wsave)
if axis != -1:
r = swapaxes(r, axis, -1)
# As soon as we put wsave back into the cache, another thread could pick it
# up and start using it, so we must not do this until after we're
# completely done using it ourselves.
fft_cache[n].append(wsave)
return r
def _unitary(norm):
if norm not in (None, "ortho"):
raise ValueError("Invalid norm value %s, should be None or \"ortho\"."
% norm)
return norm is not None
def fft(a, n=None, axis=-1, norm=None):
"""
Compute the one-dimensional discrete Fourier Transform.
This function computes the one-dimensional *n*-point discrete Fourier
Transform (DFT) with the efficient Fast Fourier Transform (FFT)
algorithm [CT].
Parameters
----------
a : array_like
Input array, can be complex.
n : int, optional
Length of the transformed axis of the output.
If `n` is smaller than the length of the input, the input is cropped.
If it is larger, the input is padded with zeros. If `n` is not given,
the length of the input along the axis specified by `axis` is used.
axis : int, optional
Axis over which to compute the FFT. If not given, the last axis is
used.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axis
indicated by `axis`, or the last one if `axis` is not specified.
Raises
------
IndexError
if `axes` is larger than the last axis of `a`.
See Also
--------
numpy.fft : for definition of the DFT and conventions used.
ifft : The inverse of `fft`.
fft2 : The two-dimensional FFT.
fftn : The *n*-dimensional FFT.
rfftn : The *n*-dimensional FFT of real input.
fftfreq : Frequency bins for given FFT parameters.
Notes
-----
FFT (Fast Fourier Transform) refers to a way the discrete Fourier
Transform (DFT) can be calculated efficiently, by using symmetries in the
calculated terms. The symmetry is highest when `n` is a power of 2, and
the transform is therefore most efficient for these sizes.
The DFT is defined, with the conventions used in this implementation, in
the documentation for the `numpy.fft` module.
References
----------
.. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the
machine calculation of complex Fourier series," *Math. Comput.*
19: 297-301.
Examples
--------
>>> np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8))
array([ -3.44505240e-16 +1.14383329e-17j,
8.00000000e+00 -5.71092652e-15j,
2.33482938e-16 +1.22460635e-16j,
1.64863782e-15 +1.77635684e-15j,
9.95839695e-17 +2.33482938e-16j,
0.00000000e+00 +1.66837030e-15j,
1.14383329e-17 +1.22460635e-16j,
-1.64863782e-15 +1.77635684e-15j])
>>> import matplotlib.pyplot as plt
>>> t = np.arange(256)
>>> sp = np.fft.fft(np.sin(t))
>>> freq = np.fft.fftfreq(t.shape[-1])
>>> plt.plot(freq, sp.real, freq, sp.imag)
[<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>]
>>> plt.show()
In this example, real input has an FFT which is Hermitian, i.e., symmetric
in the real part and anti-symmetric in the imaginary part, as described in
the `numpy.fft` documentation.
"""
a = asarray(a).astype(complex)
if n is None:
n = a.shape[axis]
output = _raw_fft(a, n, axis, fftpack.cffti, fftpack.cfftf, _fft_cache)
if _unitary(norm):
output *= 1 / sqrt(n)
return output
def ifft(a, n=None, axis=-1, norm=None):
"""
Compute the one-dimensional inverse discrete Fourier Transform.
This function computes the inverse of the one-dimensional *n*-point
discrete Fourier transform computed by `fft`. In other words,
``ifft(fft(a)) == a`` to within numerical accuracy.
For a general description of the algorithm and definitions,
see `numpy.fft`.
The input should be ordered in the same way as is returned by `fft`,
i.e., ``a[0]`` should contain the zero frequency term,
``a[1:n/2+1]`` should contain the positive-frequency terms, and
``a[n/2+1:]`` should contain the negative-frequency terms, in order of
decreasingly negative frequency. See `numpy.fft` for details.
Parameters
----------
a : array_like
Input array, can be complex.
n : int, optional
Length of the transformed axis of the output.
If `n` is smaller than the length of the input, the input is cropped.
If it is larger, the input is padded with zeros. If `n` is not given,
the length of the input along the axis specified by `axis` is used.
See notes about padding issues.
axis : int, optional
Axis over which to compute the inverse DFT. If not given, the last
axis is used.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axis
indicated by `axis`, or the last one if `axis` is not specified.
Raises
------
IndexError
If `axes` is larger than the last axis of `a`.
See Also
--------
numpy.fft : An introduction, with definitions and general explanations.
fft : The one-dimensional (forward) FFT, of which `ifft` is the inverse
ifft2 : The two-dimensional inverse FFT.
ifftn : The n-dimensional inverse FFT.
Notes
-----
If the input parameter `n` is larger than the size of the input, the input
is padded by appending zeros at the end. Even though this is the common
approach, it might lead to surprising results. If a different padding is
desired, it must be performed before calling `ifft`.
Examples
--------
>>> np.fft.ifft([0, 4, 0, 0])
array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j])
Create and plot a band-limited signal with random phases:
>>> import matplotlib.pyplot as plt
>>> t = np.arange(400)
>>> n = np.zeros((400,), dtype=complex)
>>> n[40:60] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20,)))
>>> s = np.fft.ifft(n)
>>> plt.plot(t, s.real, 'b-', t, s.imag, 'r--')
[<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>]
>>> plt.legend(('real', 'imaginary'))
<matplotlib.legend.Legend object at 0x...>
>>> plt.show()
"""
# The copy may be required for multithreading.
a = array(a, copy=True, dtype=complex)
if n is None:
n = a.shape[axis]
unitary = _unitary(norm)
output = _raw_fft(a, n, axis, fftpack.cffti, fftpack.cfftb, _fft_cache)
return output * (1 / (sqrt(n) if unitary else n))
def rfft(a, n=None, axis=-1, norm=None):
"""
Compute the one-dimensional discrete Fourier Transform for real input.
This function computes the one-dimensional *n*-point discrete Fourier
Transform (DFT) of a real-valued array by means of an efficient algorithm
called the Fast Fourier Transform (FFT).
Parameters
----------
a : array_like
Input array
n : int, optional
Number of points along transformation axis in the input to use.
If `n` is smaller than the length of the input, the input is cropped.
If it is larger, the input is padded with zeros. If `n` is not given,
the length of the input along the axis specified by `axis` is used.
axis : int, optional
Axis over which to compute the FFT. If not given, the last axis is
used.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axis
indicated by `axis`, or the last one if `axis` is not specified.
If `n` is even, the length of the transformed axis is ``(n/2)+1``.
If `n` is odd, the length is ``(n+1)/2``.
Raises
------
IndexError
If `axis` is larger than the last axis of `a`.
See Also
--------
numpy.fft : For definition of the DFT and conventions used.
irfft : The inverse of `rfft`.
fft : The one-dimensional FFT of general (complex) input.
fftn : The *n*-dimensional FFT.
rfftn : The *n*-dimensional FFT of real input.
Notes
-----
When the DFT is computed for purely real input, the output is
Hermitian-symmetric, i.e. the negative frequency terms are just the complex
conjugates of the corresponding positive-frequency terms, and the
negative-frequency terms are therefore redundant. This function does not
compute the negative frequency terms, and the length of the transformed
axis of the output is therefore ``n//2 + 1``.
When ``A = rfft(a)`` and fs is the sampling frequency, ``A[0]`` contains
the zero-frequency term 0*fs, which is real due to Hermitian symmetry.
If `n` is even, ``A[-1]`` contains the term representing both positive
and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely
real. If `n` is odd, there is no term at fs/2; ``A[-1]`` contains
the largest positive frequency (fs/2*(n-1)/n), and is complex in the
general case.
If the input `a` contains an imaginary part, it is silently discarded.
Examples
--------
>>> np.fft.fft([0, 1, 0, 0])
array([ 1.+0.j, 0.-1.j, -1.+0.j, 0.+1.j])
>>> np.fft.rfft([0, 1, 0, 0])
array([ 1.+0.j, 0.-1.j, -1.+0.j])
Notice how the final element of the `fft` output is the complex conjugate
of the second element, for real input. For `rfft`, this symmetry is
exploited to compute only the non-negative frequency terms.
"""
# The copy may be required for multithreading.
a = array(a, copy=True, dtype=float)
output = _raw_fft(a, n, axis, fftpack.rffti, fftpack.rfftf,
_real_fft_cache)
if _unitary(norm):
output *= 1 / sqrt(a.shape[axis])
return output
def irfft(a, n=None, axis=-1, norm=None):
"""
Compute the inverse of the n-point DFT for real input.
This function computes the inverse of the one-dimensional *n*-point
discrete Fourier Transform of real input computed by `rfft`.
In other words, ``irfft(rfft(a), len(a)) == a`` to within numerical
accuracy. (See Notes below for why ``len(a)`` is necessary here.)
The input is expected to be in the form returned by `rfft`, i.e. the
real zero-frequency term followed by the complex positive frequency terms
in order of increasing frequency. Since the discrete Fourier Transform of
real input is Hermitian-symmetric, the negative frequency terms are taken
to be the complex conjugates of the corresponding positive frequency terms.
Parameters
----------
a : array_like
The input array.
n : int, optional
Length of the transformed axis of the output.
For `n` output points, ``n//2+1`` input points are necessary. If the
input is longer than this, it is cropped. If it is shorter than this,
it is padded with zeros. If `n` is not given, it is determined from
the length of the input along the axis specified by `axis`.
axis : int, optional
Axis over which to compute the inverse FFT. If not given, the last
axis is used.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : ndarray
The truncated or zero-padded input, transformed along the axis
indicated by `axis`, or the last one if `axis` is not specified.
The length of the transformed axis is `n`, or, if `n` is not given,
``2*(m-1)`` where ``m`` is the length of the transformed axis of the
input. To get an odd number of output points, `n` must be specified.
Raises
------
IndexError
If `axis` is larger than the last axis of `a`.
See Also
--------
numpy.fft : For definition of the DFT and conventions used.
rfft : The one-dimensional FFT of real input, of which `irfft` is inverse.
fft : The one-dimensional FFT.
irfft2 : The inverse of the two-dimensional FFT of real input.
irfftn : The inverse of the *n*-dimensional FFT of real input.
Notes
-----
Returns the real valued `n`-point inverse discrete Fourier transform
of `a`, where `a` contains the non-negative frequency terms of a
Hermitian-symmetric sequence. `n` is the length of the result, not the
input.
If you specify an `n` such that `a` must be zero-padded or truncated, the
extra/removed values will be added/removed at high frequencies. One can
thus resample a series to `m` points via Fourier interpolation by:
``a_resamp = irfft(rfft(a), m)``.
Examples
--------
>>> np.fft.ifft([1, -1j, -1, 1j])
array([ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j])
>>> np.fft.irfft([1, -1j, -1])
array([ 0., 1., 0., 0.])
Notice how the last term in the input to the ordinary `ifft` is the
complex conjugate of the second term, and the output has zero imaginary
part everywhere. When calling `irfft`, the negative frequencies are not
specified, and the output array is purely real.
"""
# The copy may be required for multithreading.
a = array(a, copy=True, dtype=complex)
if n is None:
n = (a.shape[axis] - 1) * 2
unitary = _unitary(norm)
output = _raw_fft(a, n, axis, fftpack.rffti, fftpack.rfftb,
_real_fft_cache)
return output * (1 / (sqrt(n) if unitary else n))
def hfft(a, n=None, axis=-1, norm=None):
"""
Compute the FFT of a signal which has Hermitian symmetry (real spectrum).
Parameters
----------
a : array_like
The input array.
n : int, optional
Length of the transformed axis of the output.
For `n` output points, ``n//2+1`` input points are necessary. If the
input is longer than this, it is cropped. If it is shorter than this,
it is padded with zeros. If `n` is not given, it is determined from
the length of the input along the axis specified by `axis`.
axis : int, optional
Axis over which to compute the FFT. If not given, the last
axis is used.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : ndarray
The truncated or zero-padded input, transformed along the axis
indicated by `axis`, or the last one if `axis` is not specified.
The length of the transformed axis is `n`, or, if `n` is not given,
``2*(m-1)`` where ``m`` is the length of the transformed axis of the
input. To get an odd number of output points, `n` must be specified.
Raises
------
IndexError
If `axis` is larger than the last axis of `a`.
See also
--------
rfft : Compute the one-dimensional FFT for real input.
ihfft : The inverse of `hfft`.
Notes
-----
`hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the
opposite case: here the signal has Hermitian symmetry in the time domain
and is real in the frequency domain. So here it's `hfft` for which
you must supply the length of the result if it is to be odd:
``ihfft(hfft(a), len(a)) == a``, within numerical accuracy.
Examples
--------
>>> signal = np.array([1, 2, 3, 4, 3, 2])
>>> np.fft.fft(signal)
array([ 15.+0.j, -4.+0.j, 0.+0.j, -1.-0.j, 0.+0.j, -4.+0.j])
>>> np.fft.hfft(signal[:4]) # Input first half of signal
array([ 15., -4., 0., -1., 0., -4.])
>>> np.fft.hfft(signal, 6) # Input entire signal and truncate
array([ 15., -4., 0., -1., 0., -4.])
>>> signal = np.array([[1, 1.j], [-1.j, 2]])
>>> np.conj(signal.T) - signal # check Hermitian symmetry
array([[ 0.-0.j, 0.+0.j],
[ 0.+0.j, 0.-0.j]])
>>> freq_spectrum = np.fft.hfft(signal)
>>> freq_spectrum
array([[ 1., 1.],
[ 2., -2.]])
"""
# The copy may be required for multithreading.
a = array(a, copy=True, dtype=complex)
if n is None:
n = (a.shape[axis] - 1) * 2
unitary = _unitary(norm)
return irfft(conjugate(a), n, axis) * (sqrt(n) if unitary else n)
def ihfft(a, n=None, axis=-1, norm=None):
"""
Compute the inverse FFT of a signal which has Hermitian symmetry.
Parameters
----------
a : array_like
Input array.
n : int, optional
Length of the inverse FFT.
Number of points along transformation axis in the input to use.
If `n` is smaller than the length of the input, the input is cropped.
If it is larger, the input is padded with zeros. If `n` is not given,
the length of the input along the axis specified by `axis` is used.
axis : int, optional
Axis over which to compute the inverse FFT. If not given, the last
axis is used.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axis
indicated by `axis`, or the last one if `axis` is not specified.
If `n` is even, the length of the transformed axis is ``(n/2)+1``.
If `n` is odd, the length is ``(n+1)/2``.
See also
--------
hfft, irfft
Notes
-----
`hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the
opposite case: here the signal has Hermitian symmetry in the time domain
and is real in the frequency domain. So here it's `hfft` for which
you must supply the length of the result if it is to be odd:
``ihfft(hfft(a), len(a)) == a``, within numerical accuracy.
Examples
--------
>>> spectrum = np.array([ 15, -4, 0, -1, 0, -4])
>>> np.fft.ifft(spectrum)
array([ 1.+0.j, 2.-0.j, 3.+0.j, 4.+0.j, 3.+0.j, 2.-0.j])
>>> np.fft.ihfft(spectrum)
array([ 1.-0.j, 2.-0.j, 3.-0.j, 4.-0.j])
"""
# The copy may be required for multithreading.
a = array(a, copy=True, dtype=float)
if n is None:
n = a.shape[axis]
unitary = _unitary(norm)
output = conjugate(rfft(a, n, axis))
return output * (1 / (sqrt(n) if unitary else n))
def _cook_nd_args(a, s=None, axes=None, invreal=0):
if s is None:
shapeless = 1
if axes is None:
s = list(a.shape)
else:
s = take(a.shape, axes)
else:
shapeless = 0
s = list(s)
if axes is None:
axes = list(range(-len(s), 0))
if len(s) != len(axes):
raise ValueError("Shape and axes have different lengths.")
if invreal and shapeless:
s[-1] = (a.shape[axes[-1]] - 1) * 2
return s, axes
def _raw_fftnd(a, s=None, axes=None, function=fft, norm=None):
a = asarray(a)
s, axes = _cook_nd_args(a, s, axes)
itl = list(range(len(axes)))
itl.reverse()
for ii in itl:
a = function(a, n=s[ii], axis=axes[ii], norm=norm)
return a
def fftn(a, s=None, axes=None, norm=None):
"""
Compute the N-dimensional discrete Fourier Transform.
This function computes the *N*-dimensional discrete Fourier Transform over
any number of axes in an *M*-dimensional array by means of the Fast Fourier
Transform (FFT).
Parameters
----------
a : array_like
Input array, can be complex.
s : sequence of ints, optional
Shape (length of each transformed axis) of the output
(`s[0]` refers to axis 0, `s[1]` to axis 1, etc.).
This corresponds to `n` for `fft(x, n)`.
Along any axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used.
axes : sequence of ints, optional
Axes over which to compute the FFT. If not given, the last ``len(s)``
axes are used, or all axes if `s` is also not specified.
Repeated indices in `axes` means that the transform over that axis is
performed multiple times.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by `axes`, or by a combination of `s` and `a`,
as explained in the parameters section above.
Raises
------
ValueError
If `s` and `axes` have different length.
IndexError
If an element of `axes` is larger than than the number of axes of `a`.
See Also
--------
numpy.fft : Overall view of discrete Fourier transforms, with definitions
and conventions used.
ifftn : The inverse of `fftn`, the inverse *n*-dimensional FFT.
fft : The one-dimensional FFT, with definitions and conventions used.
rfftn : The *n*-dimensional FFT of real input.
fft2 : The two-dimensional FFT.
fftshift : Shifts zero-frequency terms to centre of array
Notes
-----
The output, analogously to `fft`, contains the term for zero frequency in
the low-order corner of all axes, the positive frequency terms in the
first half of all axes, the term for the Nyquist frequency in the middle
of all axes and the negative frequency terms in the second half of all
axes, in order of decreasingly negative frequency.
See `numpy.fft` for details, definitions and conventions used.
Examples
--------
>>> a = np.mgrid[:3, :3, :3][0]
>>> np.fft.fftn(a, axes=(1, 2))
array([[[ 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]],
[[ 9.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]],
[[ 18.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]]])
>>> np.fft.fftn(a, (2, 2), axes=(0, 1))
array([[[ 2.+0.j, 2.+0.j, 2.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]],
[[-2.+0.j, -2.+0.j, -2.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j]]])
>>> import matplotlib.pyplot as plt
>>> [X, Y] = np.meshgrid(2 * np.pi * np.arange(200) / 12,
... 2 * np.pi * np.arange(200) / 34)
>>> S = np.sin(X) + np.cos(Y) + np.random.uniform(0, 1, X.shape)
>>> FS = np.fft.fftn(S)
>>> plt.imshow(np.log(np.abs(np.fft.fftshift(FS))**2))
<matplotlib.image.AxesImage object at 0x...>
>>> plt.show()
"""
return _raw_fftnd(a, s, axes, fft, norm)
def ifftn(a, s=None, axes=None, norm=None):
"""
Compute the N-dimensional inverse discrete Fourier Transform.
This function computes the inverse of the N-dimensional discrete
Fourier Transform over any number of axes in an M-dimensional array by
means of the Fast Fourier Transform (FFT). In other words,
``ifftn(fftn(a)) == a`` to within numerical accuracy.
For a description of the definitions and conventions used, see `numpy.fft`.
The input, analogously to `ifft`, should be ordered in the same way as is
returned by `fftn`, i.e. it should have the term for zero frequency
in all axes in the low-order corner, the positive frequency terms in the
first half of all axes, the term for the Nyquist frequency in the middle
of all axes and the negative frequency terms in the second half of all
axes, in order of decreasingly negative frequency.
Parameters
----------
a : array_like
Input array, can be complex.
s : sequence of ints, optional
Shape (length of each transformed axis) of the output
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
This corresponds to ``n`` for ``ifft(x, n)``.
Along any axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used. See notes for issue on `ifft` zero padding.
axes : sequence of ints, optional
Axes over which to compute the IFFT. If not given, the last ``len(s)``
axes are used, or all axes if `s` is also not specified.
Repeated indices in `axes` means that the inverse transform over that
axis is performed multiple times.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by `axes`, or by a combination of `s` or `a`,
as explained in the parameters section above.
Raises
------
ValueError
If `s` and `axes` have different length.
IndexError
If an element of `axes` is larger than than the number of axes of `a`.
See Also
--------
numpy.fft : Overall view of discrete Fourier transforms, with definitions
and conventions used.
fftn : The forward *n*-dimensional FFT, of which `ifftn` is the inverse.
ifft : The one-dimensional inverse FFT.
ifft2 : The two-dimensional inverse FFT.
ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning
of array.
Notes
-----
See `numpy.fft` for definitions and conventions used.
Zero-padding, analogously with `ifft`, is performed by appending zeros to
the input along the specified dimension. Although this is the common
approach, it might lead to surprising results. If another form of zero
padding is desired, it must be performed before `ifftn` is called.
Examples
--------
>>> a = np.eye(4)
>>> np.fft.ifftn(np.fft.fftn(a, axes=(0,)), axes=(1,))
array([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])
Create and plot an image with band-limited frequency content:
>>> import matplotlib.pyplot as plt
>>> n = np.zeros((200,200), dtype=complex)
>>> n[60:80, 20:40] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20, 20)))
>>> im = np.fft.ifftn(n).real
>>> plt.imshow(im)
<matplotlib.image.AxesImage object at 0x...>
>>> plt.show()
"""
return _raw_fftnd(a, s, axes, ifft, norm)
def fft2(a, s=None, axes=(-2, -1), norm=None):
"""
Compute the 2-dimensional discrete Fourier Transform
This function computes the *n*-dimensional discrete Fourier Transform
over any axes in an *M*-dimensional array by means of the
Fast Fourier Transform (FFT). By default, the transform is computed over
the last two axes of the input array, i.e., a 2-dimensional FFT.
Parameters
----------
a : array_like
Input array, can be complex
s : sequence of ints, optional
Shape (length of each transformed axis) of the output
(`s[0]` refers to axis 0, `s[1]` to axis 1, etc.).
This corresponds to `n` for `fft(x, n)`.
Along each axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used.
axes : sequence of ints, optional
Axes over which to compute the FFT. If not given, the last two
axes are used. A repeated index in `axes` means the transform over
that axis is performed multiple times. A one-element sequence means
that a one-dimensional FFT is performed.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by `axes`, or the last two axes if `axes` is not given.
Raises
------
ValueError
If `s` and `axes` have different length, or `axes` not given and
``len(s) != 2``.
IndexError
If an element of `axes` is larger than than the number of axes of `a`.
See Also
--------
numpy.fft : Overall view of discrete Fourier transforms, with definitions
and conventions used.
ifft2 : The inverse two-dimensional FFT.
fft : The one-dimensional FFT.
fftn : The *n*-dimensional FFT.
fftshift : Shifts zero-frequency terms to the center of the array.
For two-dimensional input, swaps first and third quadrants, and second
and fourth quadrants.
Notes
-----
`fft2` is just `fftn` with a different default for `axes`.
The output, analogously to `fft`, contains the term for zero frequency in
the low-order corner of the transformed axes, the positive frequency terms
in the first half of these axes, the term for the Nyquist frequency in the
middle of the axes and the negative frequency terms in the second half of
the axes, in order of decreasingly negative frequency.
See `fftn` for details and a plotting example, and `numpy.fft` for
definitions and conventions used.
Examples
--------
>>> a = np.mgrid[:5, :5][0]
>>> np.fft.fft2(a)
array([[ 50.0 +0.j , 0.0 +0.j , 0.0 +0.j ,
0.0 +0.j , 0.0 +0.j ],
[-12.5+17.20477401j, 0.0 +0.j , 0.0 +0.j ,
0.0 +0.j , 0.0 +0.j ],
[-12.5 +4.0614962j , 0.0 +0.j , 0.0 +0.j ,
0.0 +0.j , 0.0 +0.j ],
[-12.5 -4.0614962j , 0.0 +0.j , 0.0 +0.j ,
0.0 +0.j , 0.0 +0.j ],
[-12.5-17.20477401j, 0.0 +0.j , 0.0 +0.j ,
0.0 +0.j , 0.0 +0.j ]])
"""
return _raw_fftnd(a, s, axes, fft, norm)
def ifft2(a, s=None, axes=(-2, -1), norm=None):
"""
Compute the 2-dimensional inverse discrete Fourier Transform.
This function computes the inverse of the 2-dimensional discrete Fourier
Transform over any number of axes in an M-dimensional array by means of
the Fast Fourier Transform (FFT). In other words, ``ifft2(fft2(a)) == a``
to within numerical accuracy. By default, the inverse transform is
computed over the last two axes of the input array.
The input, analogously to `ifft`, should be ordered in the same way as is
returned by `fft2`, i.e. it should have the term for zero frequency
in the low-order corner of the two axes, the positive frequency terms in
the first half of these axes, the term for the Nyquist frequency in the
middle of the axes and the negative frequency terms in the second half of
both axes, in order of decreasingly negative frequency.
Parameters
----------
a : array_like
Input array, can be complex.
s : sequence of ints, optional
Shape (length of each axis) of the output (``s[0]`` refers to axis 0,
``s[1]`` to axis 1, etc.). This corresponds to `n` for ``ifft(x, n)``.
Along each axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used. See notes for issue on `ifft` zero padding.
axes : sequence of ints, optional
Axes over which to compute the FFT. If not given, the last two
axes are used. A repeated index in `axes` means the transform over
that axis is performed multiple times. A one-element sequence means
that a one-dimensional FFT is performed.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by `axes`, or the last two axes if `axes` is not given.
Raises
------
ValueError
If `s` and `axes` have different length, or `axes` not given and
``len(s) != 2``.
IndexError
If an element of `axes` is larger than than the number of axes of `a`.
See Also
--------
numpy.fft : Overall view of discrete Fourier transforms, with definitions
and conventions used.
fft2 : The forward 2-dimensional FFT, of which `ifft2` is the inverse.
ifftn : The inverse of the *n*-dimensional FFT.
fft : The one-dimensional FFT.
ifft : The one-dimensional inverse FFT.
Notes
-----
`ifft2` is just `ifftn` with a different default for `axes`.
See `ifftn` for details and a plotting example, and `numpy.fft` for
definition and conventions used.
Zero-padding, analogously with `ifft`, is performed by appending zeros to
the input along the specified dimension. Although this is the common
approach, it might lead to surprising results. If another form of zero
padding is desired, it must be performed before `ifft2` is called.
Examples
--------
>>> a = 4 * np.eye(4)
>>> np.fft.ifft2(a)
array([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],
[ 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],
[ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])
"""
return _raw_fftnd(a, s, axes, ifft, norm)
def rfftn(a, s=None, axes=None, norm=None):
"""
Compute the N-dimensional discrete Fourier Transform for real input.
This function computes the N-dimensional discrete Fourier Transform over
any number of axes in an M-dimensional real array by means of the Fast
Fourier Transform (FFT). By default, all axes are transformed, with the
real transform performed over the last axis, while the remaining
transforms are complex.
Parameters
----------
a : array_like
Input array, taken to be real.
s : sequence of ints, optional
Shape (length along each transformed axis) to use from the input.
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
The final element of `s` corresponds to `n` for ``rfft(x, n)``, while
for the remaining axes, it corresponds to `n` for ``fft(x, n)``.
Along any axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used.
axes : sequence of ints, optional
Axes over which to compute the FFT. If not given, the last ``len(s)``
axes are used, or all axes if `s` is also not specified.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex ndarray
The truncated or zero-padded input, transformed along the axes
indicated by `axes`, or by a combination of `s` and `a`,
as explained in the parameters section above.
The length of the last axis transformed will be ``s[-1]//2+1``,
while the remaining transformed axes will have lengths according to
`s`, or unchanged from the input.
Raises
------
ValueError
If `s` and `axes` have different length.
IndexError
If an element of `axes` is larger than than the number of axes of `a`.
See Also
--------
irfftn : The inverse of `rfftn`, i.e. the inverse of the n-dimensional FFT
of real input.
fft : The one-dimensional FFT, with definitions and conventions used.
rfft : The one-dimensional FFT of real input.
fftn : The n-dimensional FFT.
rfft2 : The two-dimensional FFT of real input.
Notes
-----
The transform for real input is performed over the last transformation
axis, as by `rfft`, then the transform over the remaining axes is
performed as by `fftn`. The order of the output is as for `rfft` for the
final transformation axis, and as for `fftn` for the remaining
transformation axes.
See `fft` for details, definitions and conventions used.
Examples
--------
>>> a = np.ones((2, 2, 2))
>>> np.fft.rfftn(a)
array([[[ 8.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j]],
[[ 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j]]])
>>> np.fft.rfftn(a, axes=(2, 0))
array([[[ 4.+0.j, 0.+0.j],
[ 4.+0.j, 0.+0.j]],
[[ 0.+0.j, 0.+0.j],
[ 0.+0.j, 0.+0.j]]])
"""
# The copy may be required for multithreading.
a = array(a, copy=True, dtype=float)
s, axes = _cook_nd_args(a, s, axes)
a = rfft(a, s[-1], axes[-1], norm)
for ii in range(len(axes)-1):
a = fft(a, s[ii], axes[ii], norm)
return a
def rfft2(a, s=None, axes=(-2, -1), norm=None):
"""
Compute the 2-dimensional FFT of a real array.
Parameters
----------
a : array
Input array, taken to be real.
s : sequence of ints, optional
Shape of the FFT.
axes : sequence of ints, optional
Axes over which to compute the FFT.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : ndarray
The result of the real 2-D FFT.
See Also
--------
rfftn : Compute the N-dimensional discrete Fourier Transform for real
input.
Notes
-----
This is really just `rfftn` with different default behavior.
For more details see `rfftn`.
"""
return rfftn(a, s, axes, norm)
def irfftn(a, s=None, axes=None, norm=None):
"""
Compute the inverse of the N-dimensional FFT of real input.
This function computes the inverse of the N-dimensional discrete
Fourier Transform for real input over any number of axes in an
M-dimensional array by means of the Fast Fourier Transform (FFT). In
other words, ``irfftn(rfftn(a), a.shape) == a`` to within numerical
accuracy. (The ``a.shape`` is necessary like ``len(a)`` is for `irfft`,
and for the same reason.)
The input should be ordered in the same way as is returned by `rfftn`,
i.e. as for `irfft` for the final transformation axis, and as for `ifftn`
along all the other axes.
Parameters
----------
a : array_like
Input array.
s : sequence of ints, optional
Shape (length of each transformed axis) of the output
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
number of input points used along this axis, except for the last axis,
where ``s[-1]//2+1`` points of the input are used.
Along any axis, if the shape indicated by `s` is smaller than that of
the input, the input is cropped. If it is larger, the input is padded
with zeros. If `s` is not given, the shape of the input along the
axes specified by `axes` is used.
axes : sequence of ints, optional
Axes over which to compute the inverse FFT. If not given, the last
`len(s)` axes are used, or all axes if `s` is also not specified.
Repeated indices in `axes` means that the inverse transform over that
axis is performed multiple times.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : ndarray
The truncated or zero-padded input, transformed along the axes
indicated by `axes`, or by a combination of `s` or `a`,
as explained in the parameters section above.
The length of each transformed axis is as given by the corresponding
element of `s`, or the length of the input in every axis except for the
last one if `s` is not given. In the final transformed axis the length
of the output when `s` is not given is ``2*(m-1)`` where ``m`` is the
length of the final transformed axis of the input. To get an odd
number of output points in the final axis, `s` must be specified.
Raises
------
ValueError
If `s` and `axes` have different length.
IndexError
If an element of `axes` is larger than than the number of axes of `a`.
See Also
--------
rfftn : The forward n-dimensional FFT of real input,
of which `ifftn` is the inverse.
fft : The one-dimensional FFT, with definitions and conventions used.
irfft : The inverse of the one-dimensional FFT of real input.
irfft2 : The inverse of the two-dimensional FFT of real input.
Notes
-----
See `fft` for definitions and conventions used.
See `rfft` for definitions and conventions used for real input.
Examples
--------
>>> a = np.zeros((3, 2, 2))
>>> a[0, 0, 0] = 3 * 2 * 2
>>> np.fft.irfftn(a)
array([[[ 1., 1.],
[ 1., 1.]],
[[ 1., 1.],
[ 1., 1.]],
[[ 1., 1.],
[ 1., 1.]]])
"""
# The copy may be required for multithreading.
a = array(a, copy=True, dtype=complex)
s, axes = _cook_nd_args(a, s, axes, invreal=1)
for ii in range(len(axes)-1):
a = ifft(a, s[ii], axes[ii], norm)
a = irfft(a, s[-1], axes[-1], norm)
return a
def irfft2(a, s=None, axes=(-2, -1), norm=None):
"""
Compute the 2-dimensional inverse FFT of a real array.
Parameters
----------
a : array_like
The input array
s : sequence of ints, optional
Shape of the inverse FFT.
axes : sequence of ints, optional
The axes over which to compute the inverse fft.
Default is the last two axes.
norm : {None, "ortho"}, optional
.. versionadded:: 1.10.0
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : ndarray
The result of the inverse real 2-D FFT.
See Also
--------
irfftn : Compute the inverse of the N-dimensional FFT of real input.
Notes
-----
This is really `irfftn` with different defaults.
For more details see `irfftn`.
"""
return irfftn(a, s, axes, norm)
| bsd-3-clause |
cactusbin/nyt | matplotlib/examples/axes_grid/demo_curvelinear_grid2.py | 15 | 1839 | import numpy as np
#from matplotlib.path import Path
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid.grid_helper_curvelinear import GridHelperCurveLinear
from mpl_toolkits.axes_grid.axislines import Subplot
import mpl_toolkits.axes_grid.angle_helper as angle_helper
def curvelinear_test1(fig):
"""
grid for custom transform.
"""
def tr(x, y):
sgn = np.sign(x)
x, y = np.abs(np.asarray(x)), np.asarray(y)
return sgn*x**.5, y
def inv_tr(x,y):
sgn = np.sign(x)
x, y = np.asarray(x), np.asarray(y)
return sgn*x**2, y
extreme_finder = angle_helper.ExtremeFinderCycle(20, 20,
lon_cycle = None,
lat_cycle = None,
lon_minmax = None, #(0, np.inf),
lat_minmax = None,
)
grid_helper = GridHelperCurveLinear((tr, inv_tr),
extreme_finder=extreme_finder)
ax1 = Subplot(fig, 111, grid_helper=grid_helper)
# ax1 will have a ticks and gridlines defined by the given
# transform (+ transData of the Axes). Note that the transform of
# the Axes itself (i.e., transData) is not affected by the given
# transform.
fig.add_subplot(ax1)
ax1.imshow(np.arange(25).reshape(5,5),
vmax = 50, cmap=plt.cm.gray_r,
interpolation="nearest",
origin="lower")
# tick density
grid_helper.grid_finder.grid_locator1._nbins = 6
grid_helper.grid_finder.grid_locator2._nbins = 6
if 1:
fig = plt.figure(1, figsize=(7, 4))
fig.clf()
curvelinear_test1(fig)
plt.show()
| unlicense |
shear/rppy | test_ruger_hti.py | 2 | 2682 | # -*- coding: utf-8 -*-
"""
Created on Mon Aug 3 17:24:04 2015
@author: Sean
"""
import rppy
import numpy as np
import matplotlib.pyplot as plt
p1 = 2000
vp1 = 3000
vs1 = 1500
e1 = 0.0
d1 = 0.0
y1 = 0.0
p2 = 2200
vp2 = 4000
vs2 = 2000
y2 = 0.1
d2 = 0.1
e2 = 0.1
theta = 30
phi = np.arange(0, 90, 1)
phit = np.array([1.2500, 4.9342, 8.6184, 11.842, 15.526, 19.211, 22.664,
25.888, 28.421, 30.724, 34.638, 38.092, 41.546, 45.461,
49.375, 53.289, 56.974, 60.888, 65.493, 69.408, 73.783,
79.079, 84.375, 89.211])
exp = np.array([0.19816, 0.19816, 0.19678, 0.19539, 0.19263, 0.19056,
0.18711, 0.18365, 0.18020, 0.17813, 0.17329, 0.16845,
0.16431, 0.15878, 0.15326, 0.14842, 0.14359, 0.13875,
0.13391, 0.12977, 0.12632, 0.12286, 0.12079, 0.12010])
Rpp = np.zeros(np.shape(phi))
Rpo = np.zeros(np.shape(phi))
Rpk = np.zeros(np.shape(phi))
for ind, phiv in enumerate(phi):
Rpp[ind] = rppy.reflectivity.ruger_hti(vp1, vs1, p1, e1, d1, y1,
vp2, vs2, p2, e2, d2, y2,
theta, phiv)
Rpo[ind] = rppy.reflectivity.exact_ortho(rppy.reflectivity.Cij(vp1, vs1, p1, 0, 0, 0, e1, d1, y1, 0), p1,
rppy.reflectivity.Cij(vp2, vs2, p2, 0, 0, 0, e2, d2, y2, 0), p2,
0, 0, phiv, theta)
Rpk[ind] = rppy.reflectivity.vavrycuk_psencik_hti(vp1, vs1, p1, e1, d1, y1,
vp2, vs2, p2, e2, d2, y1,
phiv, theta)
plt.figure(1)
plt.plot(phi, Rpp, phi, Rpo, phi, Rpk)
plt.show()
theta = np.arange(0, 60, 1)
phi = 45
Rpp = np.zeros(np.shape(theta))
Rpo = np.zeros(np.shape(theta))
Rpk = np.zeros(np.shape(theta))
Rpa = np.zeros(np.shape(theta))
for ind, thetav in enumerate(theta):
Rpp[ind] = rppy.reflectivity.ruger_hti(vp1, vs1, p1, e1, d1, y1,
vp2, vs2, p2, e2, d2, y1,
thetav, phi)
Rpk[ind] = rppy.reflectivity.vavrycuk_psencik_hti(vp1, vs1, p1, e1, d1, y1,
vp2, vs2, p2, e2, d2, y1,
phi, thetav)
Rpo = rppy.reflectivity.zoeppritz(vp1, vs1, p1, vp2, vs2, p2, theta)
Rpa = rppy.reflectivity.aki_richards(vp1, vs1, p1, vp2, vs2, p2, theta)
plt.figure(2)
plt.plot(theta, Rpp, theta, Rpo, theta, Rpk, theta, Rpa)
plt.xlim([0, 60])
plt.ylim([0.125, 0.275])
plt.legend(['Ruger', 'Zoe', 'Vavrycuk', 'A-R'])
plt.show()
| bsd-2-clause |
andnovar/ggplot | ggplot/scales/scale_colour_gradient.py | 12 | 2017 | from __future__ import (absolute_import, division, print_function,
unicode_literals)
from .scale import scale
from copy import deepcopy
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap, rgb2hex, ColorConverter
def colors_at_breaks(cmap, breaks=[0, 0.25, 0.5, 0.75, 1.]):
return [rgb2hex(cmap(bb)[:3]) for bb in breaks]
class scale_colour_gradient(scale):
"""
Specify a two- or three-point gradient.
Parameters
----------
name : Name of an existing gradient scheme
limits : list of the upper and lower bounds of the gradient
low : colour at the lower bound of the gradient
mid : colour at the middle of the gradient
high : Colour at the upper bound of the gradient
Examples
--------
>>> from ggplot import *
>>> diamons_premium = diamonds[diamonds.cut=='Premium']
>>> gg = ggplot(diamons_premium, aes(x='depth', y='carat', colour='price')) + \\
... geom_point()
>>> print(gg + scale_colour_gradient(low='red', mid='white', high='blue', limits=[4000,6000]) + \\
... ggtitle('With red-blue gradient'))
>>> print(gg + ggtitle('With standard gradient'))
"""
VALID_SCALES = ['name', 'limits', 'low', 'mid', 'high']
def __radd__(self, gg):
gg = deepcopy(gg)
if self.name:
gg.color_label = self.name
if not (self.limits is None):
gg.color_limits = self.limits
color_spectrum = []
if self.low:
color_spectrum.append(self.low)
if self.mid:
color_spectrum.append(self.mid)
if self.high:
color_spectrum.append(self.high)
if self.low and self.high:
gradient2n = LinearSegmentedColormap.from_list('gradient2n', color_spectrum)
plt.cm.register_cmap(cmap=gradient2n)
# add them back to ggplot
gg.color_scale = colors_at_breaks(gradient2n)
gg.colormap = gradient2n
return gg
| bsd-2-clause |
felipessalvatore/CNNexample | src/tunning/fc.py | 1 | 2217 | import os
import sys
from random import randint
import numpy as np
import inspect
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
currentdir = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))
parentdir = os.path.dirname(currentdir)
sys.path.insert(0, parentdir)
from util import run_test, get_data_4d, get_time
from CNN import CNNModel, train_model, check_valid
from DataHolder import DataHolder
from Config import Config
train_dataset, train_labels, valid_dataset, valid_labels, test_dataset, test_labels = get_data_4d()
my_dataholder = DataHolder(train_dataset,
train_labels,
valid_dataset,
valid_labels,
test_dataset,
test_labels)
FC = [5, 10, 15, 20, 30, 40, 60, 200]
number_of_exp = len(FC)
results = []
duration = []
info = []
for i, fc in enumerate(FC):
print("\n ({0} of {1})".format(i + 1, number_of_exp))
my_config = Config(tunning=True, hidden_nodes_1=3 * fc,
hidden_nodes_2=2 * fc,
hidden_nodes_3=fc)
attrs = vars(my_config)
config_info = ["%s: %s" % item for item in attrs.items()]
info.append(config_info)
my_model = CNNModel(my_config, my_dataholder)
train_model(my_model, my_dataholder, 10001, 1000, False)
current_dur = get_time(train_model, 10001)
score = check_valid(my_model)
results.append(score)
duration.append(current_dur)
best_result = max(list(zip(results, FC, duration, info)))
result_string = """In an experiment with {0} fully connected sizes
the best one is {1} with valid accuracy = {2}.
\nThe training takes {3:.2f} seconds using the following params:
\n{4}""".format(number_of_exp,
best_result[1],
best_result[0],
best_result[2],
best_result[3])
file = open("final.txt", "w")
file.write(result_string)
file.close()
plt.plot(FC, results)
plt.xlabel("hidden_nodes_3")
plt.ylabel("valid acc")
plt.savefig("fc.png")
plt.clf()
plt.plot(FC, duration)
plt.xlabel("hidden_nodes_3")
plt.ylabel("duration (s)")
plt.savefig("fc_du.png")
plt.clf()
| mit |
hdmetor/scikit-learn | examples/mixture/plot_gmm_selection.py | 248 | 3223 | """
=================================
Gaussian Mixture Model Selection
=================================
This example shows that model selection can be performed with
Gaussian Mixture Models using information-theoretic criteria (BIC).
Model selection concerns both the covariance type
and the number of components in the model.
In that case, AIC also provides the right result (not shown to save time),
but BIC is better suited if the problem is to identify the right model.
Unlike Bayesian procedures, such inferences are prior-free.
In that case, the model with 2 components and full covariance
(which corresponds to the true generative model) is selected.
"""
print(__doc__)
import itertools
import numpy as np
from scipy import linalg
import matplotlib.pyplot as plt
import matplotlib as mpl
from sklearn import mixture
# Number of samples per component
n_samples = 500
# Generate random sample, two components
np.random.seed(0)
C = np.array([[0., -0.1], [1.7, .4]])
X = np.r_[np.dot(np.random.randn(n_samples, 2), C),
.7 * np.random.randn(n_samples, 2) + np.array([-6, 3])]
lowest_bic = np.infty
bic = []
n_components_range = range(1, 7)
cv_types = ['spherical', 'tied', 'diag', 'full']
for cv_type in cv_types:
for n_components in n_components_range:
# Fit a mixture of Gaussians with EM
gmm = mixture.GMM(n_components=n_components, covariance_type=cv_type)
gmm.fit(X)
bic.append(gmm.bic(X))
if bic[-1] < lowest_bic:
lowest_bic = bic[-1]
best_gmm = gmm
bic = np.array(bic)
color_iter = itertools.cycle(['k', 'r', 'g', 'b', 'c', 'm', 'y'])
clf = best_gmm
bars = []
# Plot the BIC scores
spl = plt.subplot(2, 1, 1)
for i, (cv_type, color) in enumerate(zip(cv_types, color_iter)):
xpos = np.array(n_components_range) + .2 * (i - 2)
bars.append(plt.bar(xpos, bic[i * len(n_components_range):
(i + 1) * len(n_components_range)],
width=.2, color=color))
plt.xticks(n_components_range)
plt.ylim([bic.min() * 1.01 - .01 * bic.max(), bic.max()])
plt.title('BIC score per model')
xpos = np.mod(bic.argmin(), len(n_components_range)) + .65 +\
.2 * np.floor(bic.argmin() / len(n_components_range))
plt.text(xpos, bic.min() * 0.97 + .03 * bic.max(), '*', fontsize=14)
spl.set_xlabel('Number of components')
spl.legend([b[0] for b in bars], cv_types)
# Plot the winner
splot = plt.subplot(2, 1, 2)
Y_ = clf.predict(X)
for i, (mean, covar, color) in enumerate(zip(clf.means_, clf.covars_,
color_iter)):
v, w = linalg.eigh(covar)
if not np.any(Y_ == i):
continue
plt.scatter(X[Y_ == i, 0], X[Y_ == i, 1], .8, color=color)
# Plot an ellipse to show the Gaussian component
angle = np.arctan2(w[0][1], w[0][0])
angle = 180 * angle / np.pi # convert to degrees
v *= 4
ell = mpl.patches.Ellipse(mean, v[0], v[1], 180 + angle, color=color)
ell.set_clip_box(splot.bbox)
ell.set_alpha(.5)
splot.add_artist(ell)
plt.xlim(-10, 10)
plt.ylim(-3, 6)
plt.xticks(())
plt.yticks(())
plt.title('Selected GMM: full model, 2 components')
plt.subplots_adjust(hspace=.35, bottom=.02)
plt.show()
| bsd-3-clause |
sauloal/cnidaria | scripts/venv/lib/python2.7/site-packages/mpl_toolkits/axisartist/axisline_style.py | 8 | 5277 | from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
from matplotlib.patches import _Style, FancyArrowPatch
from matplotlib.transforms import IdentityTransform
from matplotlib.path import Path
import numpy as np
class _FancyAxislineStyle:
class SimpleArrow(FancyArrowPatch):
"""
The artist class that will be returned for SimpleArrow style.
"""
_ARROW_STYLE = "->"
def __init__(self, axis_artist, line_path, transform,
line_mutation_scale):
self._axis_artist = axis_artist
self._line_transform = transform
self._line_path = line_path
self._line_mutation_scale = line_mutation_scale
FancyArrowPatch.__init__(self,
path=self._line_path,
arrowstyle=self._ARROW_STYLE,
arrow_transmuter=None,
patchA=None,
patchB=None,
shrinkA=0.,
shrinkB=0.,
mutation_scale=line_mutation_scale,
mutation_aspect=None,
transform=IdentityTransform(),
)
def set_line_mutation_scale(self, scale):
self.set_mutation_scale(scale*self._line_mutation_scale)
def _extend_path(self, path, mutation_size=10):
"""
Extend the path to make a room for drawing arrow.
"""
from matplotlib.bezier import get_cos_sin
x0, y0 = path.vertices[-2]
x1, y1 = path.vertices[-1]
cost, sint = get_cos_sin(x0, y0, x1, y1)
d = mutation_size * 1.
x2, y2 = x1 + cost*d, y1+sint*d
if path.codes is None:
_path = Path(np.concatenate([path.vertices, [[x2, y2]]]))
else:
_path = Path(np.concatenate([path.vertices, [[x2, y2]]]),
np.concatenate([path.codes, [Path.LINETO]]))
return _path
def set_path(self, path):
self._line_path = path
def draw(self, renderer):
"""
Draw the axis line.
1) transform the path to the display coordinate.
2) extend the path to make a room for arrow
3) update the path of the FancyArrowPatch.
4) draw
"""
path_in_disp = self._line_transform.transform_path(self._line_path)
mutation_size = self.get_mutation_scale() #line_mutation_scale()
extented_path = self._extend_path(path_in_disp,
mutation_size=mutation_size)
self._path_original = extented_path
FancyArrowPatch.draw(self, renderer)
class FilledArrow(SimpleArrow):
"""
The artist class that will be returned for SimpleArrow style.
"""
_ARROW_STYLE = "-|>"
class AxislineStyle(_Style):
"""
:class:`AxislineStyle` is a container class which defines style classes
for AxisArtists.
An instance of any axisline style class is an callable object,
whose call signature is ::
__call__(self, axis_artist, path, transform)
When called, this should return a mpl artist with following
methods implemented. ::
def set_path(self, path):
# set the path for axisline.
def set_line_mutation_scale(self, scale):
# set the scale
def draw(self, renderer):
# draw
"""
_style_list = {}
class _Base(object):
# The derived classes are required to be able to be initialized
# w/o arguments, i.e., all its argument (except self) must have
# the default values.
def __init__(self):
"""
initialization.
"""
super(AxislineStyle._Base, self).__init__()
def __call__(self, axis_artist, transform):
"""
Given the AxisArtist instance, and transform for the path
(set_path method), return the mpl artist for drawing the axis line.
"""
return self.new_line(axis_artist, transform)
class SimpleArrow(_Base):
"""
A simple arrow.
"""
ArrowAxisClass = _FancyAxislineStyle.SimpleArrow
def __init__(self, size=1):
"""
*size*
size of the arrow as a fraction of the ticklabel size.
"""
self.size = size
super(AxislineStyle.SimpleArrow, self).__init__()
def new_line(self, axis_artist, transform):
linepath = Path([(0,0), (0, 1)])
axisline = self.ArrowAxisClass(axis_artist, linepath, transform,
line_mutation_scale=self.size)
return axisline
_style_list["->"] = SimpleArrow
class FilledArrow(SimpleArrow):
ArrowAxisClass = _FancyAxislineStyle.FilledArrow
_style_list["-|>"] = FilledArrow
| mit |
mjudsp/Tsallis | examples/plot_isotonic_regression.py | 303 | 1767 | """
===================
Isotonic Regression
===================
An illustration of the isotonic regression on generated data. The
isotonic regression finds a non-decreasing approximation of a function
while minimizing the mean squared error on the training data. The benefit
of such a model is that it does not assume any form for the target
function such as linearity. For comparison a linear regression is also
presented.
"""
print(__doc__)
# Author: Nelle Varoquaux <nelle.varoquaux@gmail.com>
# Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Licence: BSD
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
from sklearn.linear_model import LinearRegression
from sklearn.isotonic import IsotonicRegression
from sklearn.utils import check_random_state
n = 100
x = np.arange(n)
rs = check_random_state(0)
y = rs.randint(-50, 50, size=(n,)) + 50. * np.log(1 + np.arange(n))
###############################################################################
# Fit IsotonicRegression and LinearRegression models
ir = IsotonicRegression()
y_ = ir.fit_transform(x, y)
lr = LinearRegression()
lr.fit(x[:, np.newaxis], y) # x needs to be 2d for LinearRegression
###############################################################################
# plot result
segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]
lc = LineCollection(segments, zorder=0)
lc.set_array(np.ones(len(y)))
lc.set_linewidths(0.5 * np.ones(n))
fig = plt.figure()
plt.plot(x, y, 'r.', markersize=12)
plt.plot(x, y_, 'g.-', markersize=12)
plt.plot(x, lr.predict(x[:, np.newaxis]), 'b-')
plt.gca().add_collection(lc)
plt.legend(('Data', 'Isotonic Fit', 'Linear Fit'), loc='lower right')
plt.title('Isotonic regression')
plt.show()
| bsd-3-clause |
ansobolev/regCMPostProc | src/plot.py | 1 | 2816 | #!/usr/bin/env python
# RegCM postprocessing tool
# Copyright (C) 2014 Aliou, Addisu, Kanhu, Andrey
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
import matplotlib.pyplot as plt
import cartopy
import cartopy.crs as ccrs
import cartopy.feature as cfeature
from value import Value
class Plotter(object):
def __init__(self, value):
self._value = value
self.lat, self.lon = value.latlon
def plot(self, coastlines=True,
countries=True,
places=True,
title=None,
levels = None):
if levels is not None:
l_min, l_max = levels
l = (l_max - l_min) / 10
levels = range(l_min, l_max + l, l)
projection = ccrs.PlateCarree()
self.fig, self.ax = plt.subplots(subplot_kw={'projection': projection})
if coastlines:
self.ax.coastlines('10m')
if countries:
countries = cfeature.NaturalEarthFeature(
scale='110m', category='cultural', name='admin_0_countries')
self.ax.add_feature(countries, color='r', alpha=0.1)
if places:
places = cfeature.NaturalEarthFeature(
scale='110m', category='cultural', name='populated_places')
self.ax.add_feature(places, color='b', hatch='o')
cx = self.ax.contourf(self.lon, self.lat, self._value.data, transform=ccrs.PlateCarree(),cmap='bwr', levels=levels)
# To mask out OCEAN or LAND
#ax.add_feature(cfeature.OCEAN)
#ax.add_feature(cfeature.LAND)
self.ax.gridlines(crs=ccrs.PlateCarree(), draw_labels=True,
linewidth=1, color='blue', alpha=0.5, linestyle='-')
self.fig.colorbar(cx)
times = self._value.limits['time']
plt.title(self._value.title + ' [' + self._value.units + ']\n' +
'mean between ' + str(times[0]) + ' and ' + str(times[1]) + '\n')
def show(self):
plt.show()
def save(self, filename, format):
plt.savefig(filename + '.' + format)
def close(self):
plt.close(self.fig)
if __name__ == "__main__":
pass | gpl-3.0 |
wmvanvliet/mne-python | examples/time_frequency/plot_source_power_spectrum.py | 19 | 1959 | """
======================================================
Compute source power spectral density (PSD) in a label
======================================================
Returns an STC file containing the PSD (in dB) of each of the sources
within a label.
"""
# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#
# License: BSD (3-clause)
import matplotlib.pyplot as plt
import mne
from mne import io
from mne.datasets import sample
from mne.minimum_norm import read_inverse_operator, compute_source_psd
print(__doc__)
###############################################################################
# Set parameters
data_path = sample.data_path()
raw_fname = data_path + '/MEG/sample/sample_audvis_raw.fif'
fname_inv = data_path + '/MEG/sample/sample_audvis-meg-oct-6-meg-inv.fif'
fname_label = data_path + '/MEG/sample/labels/Aud-lh.label'
# Setup for reading the raw data
raw = io.read_raw_fif(raw_fname, verbose=False)
events = mne.find_events(raw, stim_channel='STI 014')
inverse_operator = read_inverse_operator(fname_inv)
raw.info['bads'] = ['MEG 2443', 'EEG 053']
# picks MEG gradiometers
picks = mne.pick_types(raw.info, meg=True, eeg=False, eog=True,
stim=False, exclude='bads')
tmin, tmax = 0, 120 # use the first 120s of data
fmin, fmax = 4, 100 # look at frequencies between 4 and 100Hz
n_fft = 2048 # the FFT size (n_fft). Ideally a power of 2
label = mne.read_label(fname_label)
stc = compute_source_psd(raw, inverse_operator, lambda2=1. / 9., method="dSPM",
tmin=tmin, tmax=tmax, fmin=fmin, fmax=fmax,
pick_ori="normal", n_fft=n_fft, label=label,
dB=True)
stc.save('psd_dSPM')
###############################################################################
# View PSD of sources in label
plt.plot(stc.times, stc.data.T)
plt.xlabel('Frequency (Hz)')
plt.ylabel('PSD (dB)')
plt.title('Source Power Spectrum (PSD)')
plt.show()
| bsd-3-clause |
destijl/forensicartifacts | frontend/thirdparty/networkx-1.9/examples/graph/napoleon_russian_campaign.py | 44 | 3216 | #!/usr/bin/env python
"""
Minard's data from Napoleon's 1812-1813 Russian Campaign.
http://www.math.yorku.ca/SCS/Gallery/minard/minard.txt
"""
__author__ = """Aric Hagberg (hagberg@lanl.gov)"""
# Copyright (C) 2006 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
import string
import networkx as nx
def minard_graph():
data1="""\
24.0,54.9,340000,A,1
24.5,55.0,340000,A,1
25.5,54.5,340000,A,1
26.0,54.7,320000,A,1
27.0,54.8,300000,A,1
28.0,54.9,280000,A,1
28.5,55.0,240000,A,1
29.0,55.1,210000,A,1
30.0,55.2,180000,A,1
30.3,55.3,175000,A,1
32.0,54.8,145000,A,1
33.2,54.9,140000,A,1
34.4,55.5,127100,A,1
35.5,55.4,100000,A,1
36.0,55.5,100000,A,1
37.6,55.8,100000,A,1
37.7,55.7,100000,R,1
37.5,55.7,98000,R,1
37.0,55.0,97000,R,1
36.8,55.0,96000,R,1
35.4,55.3,87000,R,1
34.3,55.2,55000,R,1
33.3,54.8,37000,R,1
32.0,54.6,24000,R,1
30.4,54.4,20000,R,1
29.2,54.3,20000,R,1
28.5,54.2,20000,R,1
28.3,54.3,20000,R,1
27.5,54.5,20000,R,1
26.8,54.3,12000,R,1
26.4,54.4,14000,R,1
25.0,54.4,8000,R,1
24.4,54.4,4000,R,1
24.2,54.4,4000,R,1
24.1,54.4,4000,R,1"""
data2="""\
24.0,55.1,60000,A,2
24.5,55.2,60000,A,2
25.5,54.7,60000,A,2
26.6,55.7,40000,A,2
27.4,55.6,33000,A,2
28.7,55.5,33000,R,2
29.2,54.2,30000,R,2
28.5,54.1,30000,R,2
28.3,54.2,28000,R,2"""
data3="""\
24.0,55.2,22000,A,3
24.5,55.3,22000,A,3
24.6,55.8,6000,A,3
24.6,55.8,6000,R,3
24.2,54.4,6000,R,3
24.1,54.4,6000,R,3"""
cities="""\
24.0,55.0,Kowno
25.3,54.7,Wilna
26.4,54.4,Smorgoni
26.8,54.3,Moiodexno
27.7,55.2,Gloubokoe
27.6,53.9,Minsk
28.5,54.3,Studienska
28.7,55.5,Polotzk
29.2,54.4,Bobr
30.2,55.3,Witebsk
30.4,54.5,Orscha
30.4,53.9,Mohilow
32.0,54.8,Smolensk
33.2,54.9,Dorogobouge
34.3,55.2,Wixma
34.4,55.5,Chjat
36.0,55.5,Mojaisk
37.6,55.8,Moscou
36.6,55.3,Tarantino
36.5,55.0,Malo-Jarosewii"""
c={}
for line in cities.split('\n'):
x,y,name=line.split(',')
c[name]=(float(x),float(y))
g=[]
for data in [data1,data2,data3]:
G=nx.Graph()
i=0
G.pos={} # location
G.pop={} # size
last=None
for line in data.split('\n'):
x,y,p,r,n=line.split(',')
G.pos[i]=(float(x),float(y))
G.pop[i]=int(p)
if last is None:
last=i
else:
G.add_edge(i,last,{r:int(n)})
last=i
i=i+1
g.append(G)
return g,c
if __name__ == "__main__":
(g,city)=minard_graph()
try:
import matplotlib.pyplot as plt
plt.figure(1,figsize=(11,5))
plt.clf()
colors=['b','g','r']
for G in g:
c=colors.pop(0)
node_size=[int(G.pop[n]/300.0) for n in G]
nx.draw_networkx_edges(G,G.pos,edge_color=c,width=4,alpha=0.5)
nx.draw_networkx_nodes(G,G.pos,node_size=node_size,node_color=c,alpha=0.5)
nx.draw_networkx_nodes(G,G.pos,node_size=5,node_color='k')
for c in city:
x,y=city[c]
plt.text(x,y+0.1,c)
plt.savefig("napoleon_russian_campaign.png")
except ImportError:
pass
| apache-2.0 |
zarafagroupware/python-zarafa | scripts/z-barplot.py | 2 | 1667 | #!/usr/bin/env python
import zarafa
import matplotlib.pyplot as plt
def opt_args():
parser = zarafa.parser('skpc')
parser.add_option('--save', dest='save', action='store', help='Save plot to file (png)')
return parser.parse_args()
def b2m(bytes):
return (bytes / 1024) / 1024
def main():
options, args = opt_args()
users = list(zarafa.Server(options).users())
width = 0.35 # the width of the bars
fig, ax = plt.subplots()
ind = range(0, len(users))
data = [b2m(user.store.size) for user in users]
rects1 = ax.bar(ind, data, width, color='r')
data = [len(list(user.store.folders())) for user in users]
rects2 = ax.bar([offset + width for offset in ind], data, width, color='g')
data =[sum(folder.count for folder in user.store.folders()) for user in users]
rects3 = ax.bar([offset + width * 2 for offset in ind], data, width, color='b')
ax.legend( (rects1[0], rects2[0], rects3[0]), ('Store size (Mb)', 'Folders', 'Items') )
ax.set_ylabel('Values')
ax.set_title('Store size, Folder, Items per user')
ax.set_xticks([offset + width for offset in ind])
ax.set_xticklabels([user.name for user in users])
def autolabel(rects):
# attach some text labels
for rect in rects:
height = rect.get_height()
ax.text(rect.get_x()+rect.get_width()/2., 1.05*height, '%d'%int(height),
ha='center', va='bottom')
autolabel(rects1)
autolabel(rects2)
autolabel(rects3)
if options.save:
plt.savefig(options.save)
else:
plt.show()
if __name__ == '__main__':
main()
| agpl-3.0 |
pap/nupic | external/linux32/lib/python2.6/site-packages/matplotlib/fontconfig_pattern.py | 72 | 6429 | """
A module for parsing and generating fontconfig patterns.
See the `fontconfig pattern specification
<http://www.fontconfig.org/fontconfig-user.html>`_ for more
information.
"""
# Author : Michael Droettboom <mdroe@stsci.edu>
# License : matplotlib license (PSF compatible)
# This class is defined here because it must be available in:
# - The old-style config framework (:file:`rcsetup.py`)
# - The traits-based config framework (:file:`mpltraits.py`)
# - The font manager (:file:`font_manager.py`)
# It probably logically belongs in :file:`font_manager.py`, but
# placing it in any of these places would have created cyclical
# dependency problems, or an undesired dependency on traits even
# when the traits-based config framework is not used.
import re
from matplotlib.pyparsing import Literal, ZeroOrMore, \
Optional, Regex, StringEnd, ParseException, Suppress
family_punc = r'\\\-:,'
family_unescape = re.compile(r'\\([%s])' % family_punc).sub
family_escape = re.compile(r'([%s])' % family_punc).sub
value_punc = r'\\=_:,'
value_unescape = re.compile(r'\\([%s])' % value_punc).sub
value_escape = re.compile(r'([%s])' % value_punc).sub
class FontconfigPatternParser:
"""A simple pyparsing-based parser for fontconfig-style patterns.
See the `fontconfig pattern specification
<http://www.fontconfig.org/fontconfig-user.html>`_ for more
information.
"""
_constants = {
'thin' : ('weight', 'light'),
'extralight' : ('weight', 'light'),
'ultralight' : ('weight', 'light'),
'light' : ('weight', 'light'),
'book' : ('weight', 'book'),
'regular' : ('weight', 'regular'),
'normal' : ('weight', 'normal'),
'medium' : ('weight', 'medium'),
'demibold' : ('weight', 'demibold'),
'semibold' : ('weight', 'semibold'),
'bold' : ('weight', 'bold'),
'extrabold' : ('weight', 'extra bold'),
'black' : ('weight', 'black'),
'heavy' : ('weight', 'heavy'),
'roman' : ('slant', 'normal'),
'italic' : ('slant', 'italic'),
'oblique' : ('slant', 'oblique'),
'ultracondensed' : ('width', 'ultra-condensed'),
'extracondensed' : ('width', 'extra-condensed'),
'condensed' : ('width', 'condensed'),
'semicondensed' : ('width', 'semi-condensed'),
'expanded' : ('width', 'expanded'),
'extraexpanded' : ('width', 'extra-expanded'),
'ultraexpanded' : ('width', 'ultra-expanded')
}
def __init__(self):
family = Regex(r'([^%s]|(\\[%s]))*' %
(family_punc, family_punc)) \
.setParseAction(self._family)
size = Regex(r"([0-9]+\.?[0-9]*|\.[0-9]+)") \
.setParseAction(self._size)
name = Regex(r'[a-z]+') \
.setParseAction(self._name)
value = Regex(r'([^%s]|(\\[%s]))*' %
(value_punc, value_punc)) \
.setParseAction(self._value)
families =(family
+ ZeroOrMore(
Literal(',')
+ family)
).setParseAction(self._families)
point_sizes =(size
+ ZeroOrMore(
Literal(',')
+ size)
).setParseAction(self._point_sizes)
property =( (name
+ Suppress(Literal('='))
+ value
+ ZeroOrMore(
Suppress(Literal(','))
+ value)
)
| name
).setParseAction(self._property)
pattern =(Optional(
families)
+ Optional(
Literal('-')
+ point_sizes)
+ ZeroOrMore(
Literal(':')
+ property)
+ StringEnd()
)
self._parser = pattern
self.ParseException = ParseException
def parse(self, pattern):
"""
Parse the given fontconfig *pattern* and return a dictionary
of key/value pairs useful for initializing a
:class:`font_manager.FontProperties` object.
"""
props = self._properties = {}
try:
self._parser.parseString(pattern)
except self.ParseException, e:
raise ValueError("Could not parse font string: '%s'\n%s" % (pattern, e))
self._properties = None
return props
def _family(self, s, loc, tokens):
return [family_unescape(r'\1', str(tokens[0]))]
def _size(self, s, loc, tokens):
return [float(tokens[0])]
def _name(self, s, loc, tokens):
return [str(tokens[0])]
def _value(self, s, loc, tokens):
return [value_unescape(r'\1', str(tokens[0]))]
def _families(self, s, loc, tokens):
self._properties['family'] = [str(x) for x in tokens]
return []
def _point_sizes(self, s, loc, tokens):
self._properties['size'] = [str(x) for x in tokens]
return []
def _property(self, s, loc, tokens):
if len(tokens) == 1:
if tokens[0] in self._constants:
key, val = self._constants[tokens[0]]
self._properties.setdefault(key, []).append(val)
else:
key = tokens[0]
val = tokens[1:]
self._properties.setdefault(key, []).extend(val)
return []
parse_fontconfig_pattern = FontconfigPatternParser().parse
def generate_fontconfig_pattern(d):
"""
Given a dictionary of key/value pairs, generates a fontconfig
pattern string.
"""
props = []
families = ''
size = ''
for key in 'family style variant weight stretch file size'.split():
val = getattr(d, 'get_' + key)()
if val is not None and val != []:
if type(val) == list:
val = [value_escape(r'\\\1', str(x)) for x in val if x is not None]
if val != []:
val = ','.join(val)
props.append(":%s=%s" % (key, val))
return ''.join(props)
| agpl-3.0 |
sevenian3/ChromaStarPy | solartest.py | 1 | 6462 | # -*- coding: utf-8 -*-
"""
Created on Wed Aug 30 10:54:21 2017
@author: ishort
"""
#plotting:
import matplotlib
import matplotlib.pyplot as plt
#%matplotlib inline
import pylab
#General file for printing ad hoc quantities
#dbgHandle = open("debug.out", 'w')
#Get the data
dataPath = "SolFluxAtlas2005/"
#outPath = absPath + "Outputs/"
numStr = ""
num = 0.0
wavStr = ""
flxStr = ""
inLine = ""
fields = [" " for i in range(2)]
#with open("", 'r', encoding='utf-8') as inputHandle:
inFile = dataPath + "fluxspliced.2005"
with open(inFile, 'r') as inputHandle:
#Expects number of records on first lines, then white space delimited columns of
#wavelengths in nm and continuum rectified fluxes
inLine = inputHandle.readline() #Special one-line header
print(inLine)
fields = inLine.split()
numStr = fields[0].strip() #first field is number of following records
num = int(numStr)
waveSun = [0.0 for i in range(num)]
fluxSun = [0.0 for i in range(num)]
for i in range(num):
inLine = inputHandle.readline()
fields = inLine.split()
wavStr = fields[0].strip(); flxStr = fields[1].strip()
waveSun[i] = float(wavStr); fluxSun[i] = float(flxStr)
pylab.plot(waveSun, fluxSun, color='black')
#Now get the synthetic spectrum pre-computed with ChromaStarPy
modelPath = "Outputs/"
#outPath = absPath + "Outputs/"
numStr = ""
num = 0.0
wavStr = ""
flxStr = ""
inLine = " "
#fields = [" " for i in range(2)]
"""
runVers = "pyLoop"
#Model atmosphere
teffStr = "5777.0"
loggStr = "4.44"
logZStr = "0.0"
massStarStr = "1.0"
xiTStr = "1.0"
logHeFeStr = "0.0"
logCOStr = "0.0"
logAlphaFeStr = "0.0"
#Spectrum synthesis
lambdaStartStr = "390.0"
lambdaStopStr = "400.0"
lineThreshStr = "-3.0"
voigtThreshStr = "-3.0"
logGammaColStr = "0.5"
logKapFudgeStr = "0.0"
macroVStr = "1.0"
rotVStr = "2.0"
rotIStr = "90.0"
RVStr = "0.0"
strucStem = "Teff" + teffStr + "Logg" + loggStr + "Z" + logZStr + "M" + massStarStr+"xiT"+xiTStr + \
"HeFe" + logHeFeStr + "CO" + logCOStr + "AlfFe" + logAlphaFeStr + "v" + runVers
strucFile = "struc." + strucStem + ".out"
specFile = "spec." + strucStem + "L"+lambdaStartStr+"-"+lambdaStopStr+"xiT"+xiTStr+"LThr"+lineThreshStr+ \
"GamCol"+logGammaColStr+"Mac"+macroVStr+"Rot"+rotVStr+"-"+rotIStr+"RV"+RVStr + ".out"
#with open("", 'r', encoding='utf-8') as inputHandle:
inFile = modelPath + specFile;
"""
project = "Project"
runVers = "Run"
teff = 5777.0
logg = 4.44
log10ZScale = 0.0
lambdaStart = 390.0
lambdaStop = 400.0
fileStem = project + "-"\
+ str(round(teff, 7)) + "-" + str(round(logg, 3)) + "-" + str(round(log10ZScale, 3))\
+ "-" + str(round(lambdaStart, 5)) + "-" + str(round(lambdaStop, 5))\
+ "-" + runVers
inFile = modelPath + fileStem + ".spec.txt"
invnAir = 1.0 / 1.000277 #// reciprocal of refractive index of air at STP
#numStr = fields[0].strip() #first field is number of following records
#num = int(numStr)
waveMod = []
fluxMod = []
wav = 0.0 #//initialization
wavStr = ""
lblStr = ""
with open(inFile, 'r') as inputHandle:
#Expects number of records on first lines, then white space delimited columns of
#wavelengths in nm and continuum rectified fluxes
inLine = inputHandle.readline() #line of header
print(inLine)
inLine = inputHandle.readline()
print(inLine)
fields = inLine.split()
#number of line IDs is last field:
numLineIdsStr = fields[len(fields)-1]
numLineIds = int(numLineIdsStr) - 1 # to be on safe side
print("Recovered that there are " + numLineIdsStr + " lines to ID")
inLine = inputHandle.readline()
print(inLine)
fields = inLine.split()
#number of wavelengths in spectrum is last field:
numWavsStr = fields[len(fields)-1]
numWavs = int(numWavsStr) # to be on safe side
print("Recovered that there are " + numWavsStr + " wavelengths")
#One more line of header
inLine = inputHandle.readline() #line of header
print(inLine)
waveMod = [0.0 for i in range(numWavs)]
fluxMod = [0.0 for i in range(numWavs)]
#Get the synthetic spectrum
for i in range(numWavs):
inLine = inputHandle.readline()
fields = inLine.split()
wavStr = fields[0].strip(); flxStr = fields[1].strip()
wav = invnAir * float(wavStr)
waveMod[i] = wav
fluxMod[i] = float(flxStr)
waveIds = [0.0 for i in range(numLineIds)]
lblIds = ["" for i in range(numLineIds)]
#Get the line IDs
#Expects four white-space-delimited fields:
# wavelength, element, ion. stage, and rounded wavelength
#Another line of header for line id section
inLine = inputHandle.readline() #line of header
print(inLine)
for i in range(numLineIds):
inLine = inputHandle.readline()
fields = inLine.split()
wavStr = fields[0].strip()
wav = invnAir * float(wavStr)
waveIds[i] = wav
lblStr = fields[1].strip() + " " + fields[2].strip() + " " + fields[3].strip()
lblIds[i] = lblStr
"""
#If we do NOT know number of records:
#for i in inputHandle: #doesn't work - 0 iterations
while (inLine != ""):
inLine = inputHandle.readline()
if not inLine:
break
#print(inLine)
fields = inLine.split()
wavStr = fields[0].strip(); flxStr = fields[1].strip()
wav = invnAir * float(wavStr)
waveMod.append(wav)
fluxMod.append(float(flxStr))
"""
#plot the spectrum
#plt.title('Synthetic spectrum')
plt.ylabel('$F_\lambda/F^C_\lambda$')
plt.xlabel('$\lambda$ (nm)')
xMin = min(waveMod)
xMax = max(waveMod)
pylab.xlim(xMin, xMax)
pylab.ylim(0.0, 1.6)
pylab.plot(waveMod, fluxMod, color="gray")
#add the line IDs
for i in range(numLineIds):
if "Ca II" in lblIds[i]:
thisLam = waveIds[i]
thisLbl = lblIds[i]
xPoint = [thisLam, thisLam]
yPoint = [1.05, 1.1]
pylab.plot(xPoint, yPoint, color='black')
pylab.text(thisLam, 1.5, thisLbl, rotation=270)
#Save as encapsulated postscript (eps) for LaTex
epsName = fileStem + ".eps"
plt.savefig(epsName, format='eps', dpi=1000) | mit |
OrkoHunter/networkx | examples/graph/atlas.py | 54 | 2609 | #!/usr/bin/env python
"""
Atlas of all graphs of 6 nodes or less.
"""
__author__ = """Aric Hagberg (hagberg@lanl.gov)"""
# Copyright (C) 2004 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
import networkx as nx
from networkx.generators.atlas import *
from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic as isomorphic
import random
def atlas6():
""" Return the atlas of all connected graphs of 6 nodes or less.
Attempt to check for isomorphisms and remove.
"""
Atlas=graph_atlas_g()[0:208] # 208
# remove isolated nodes, only connected graphs are left
U=nx.Graph() # graph for union of all graphs in atlas
for G in Atlas:
zerodegree=[n for n in G if G.degree(n)==0]
for n in zerodegree:
G.remove_node(n)
U=nx.disjoint_union(U,G)
# list of graphs of all connected components
C=nx.connected_component_subgraphs(U)
UU=nx.Graph()
# do quick isomorphic-like check, not a true isomorphism checker
nlist=[] # list of nonisomorphic graphs
for G in C:
# check against all nonisomorphic graphs so far
if not iso(G,nlist):
nlist.append(G)
UU=nx.disjoint_union(UU,G) # union the nonisomorphic graphs
return UU
def iso(G1, glist):
"""Quick and dirty nonisomorphism checker used to check isomorphisms."""
for G2 in glist:
if isomorphic(G1,G2):
return True
return False
if __name__ == '__main__':
import networkx as nx
G=atlas6()
print("graph has %d nodes with %d edges"\
%(nx.number_of_nodes(G),nx.number_of_edges(G)))
print(nx.number_connected_components(G),"connected components")
try:
from networkx import graphviz_layout
except ImportError:
raise ImportError("This example needs Graphviz and either PyGraphviz or Pydot")
import matplotlib.pyplot as plt
plt.figure(1,figsize=(8,8))
# layout graphs with positions using graphviz neato
pos=nx.graphviz_layout(G,prog="neato")
# color nodes the same in each connected subgraph
C=nx.connected_component_subgraphs(G)
for g in C:
c=[random.random()]*nx.number_of_nodes(g) # random color...
nx.draw(g,
pos,
node_size=40,
node_color=c,
vmin=0.0,
vmax=1.0,
with_labels=False
)
plt.savefig("atlas.png",dpi=75)
| bsd-3-clause |
herilalaina/scikit-learn | examples/feature_selection/plot_f_test_vs_mi.py | 82 | 1671 | """
===========================================
Comparison of F-test and mutual information
===========================================
This example illustrates the differences between univariate F-test statistics
and mutual information.
We consider 3 features x_1, x_2, x_3 distributed uniformly over [0, 1], the
target depends on them as follows:
y = x_1 + sin(6 * pi * x_2) + 0.1 * N(0, 1), that is the third features is
completely irrelevant.
The code below plots the dependency of y against individual x_i and normalized
values of univariate F-tests statistics and mutual information.
As F-test captures only linear dependency, it rates x_1 as the most
discriminative feature. On the other hand, mutual information can capture any
kind of dependency between variables and it rates x_2 as the most
discriminative feature, which probably agrees better with our intuitive
perception for this example. Both methods correctly marks x_3 as irrelevant.
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from sklearn.feature_selection import f_regression, mutual_info_regression
np.random.seed(0)
X = np.random.rand(1000, 3)
y = X[:, 0] + np.sin(6 * np.pi * X[:, 1]) + 0.1 * np.random.randn(1000)
f_test, _ = f_regression(X, y)
f_test /= np.max(f_test)
mi = mutual_info_regression(X, y)
mi /= np.max(mi)
plt.figure(figsize=(15, 5))
for i in range(3):
plt.subplot(1, 3, i + 1)
plt.scatter(X[:, i], y, edgecolor='black', s=20)
plt.xlabel("$x_{}$".format(i + 1), fontsize=14)
if i == 0:
plt.ylabel("$y$", fontsize=14)
plt.title("F-test={:.2f}, MI={:.2f}".format(f_test[i], mi[i]),
fontsize=16)
plt.show()
| bsd-3-clause |
ryandougherty/mwa-capstone | MWA_Tools/build/matplotlib/lib/mpl_examples/misc/font_indexing.py | 4 | 1299 | """
A little example that shows how the various indexing into the font
tables relate to one another. Mainly for mpl developers....
"""
import matplotlib
from matplotlib.ft2font import FT2Font, KERNING_DEFAULT, KERNING_UNFITTED, KERNING_UNSCALED
#fname = '/usr/share/fonts/sfd/FreeSans.ttf'
fname = matplotlib.get_data_path() + '/fonts/ttf/Vera.ttf'
font = FT2Font(fname)
font.set_charmap(0)
codes = font.get_charmap().items()
#dsu = [(ccode, glyphind) for ccode, glyphind in codes]
#dsu.sort()
#for ccode, glyphind in dsu:
# try: name = font.get_glyph_name(glyphind)
# except RuntimeError: pass
# else: print '% 4d % 4d %s %s'%(glyphind, ccode, hex(int(ccode)), name)
# make a charname to charcode and glyphind dictionary
coded = {}
glyphd = {}
for ccode, glyphind in codes:
name = font.get_glyph_name(glyphind)
coded[name] = ccode
glyphd[name] = glyphind
code = coded['A']
glyph = font.load_char(code)
#print glyph.bbox
print glyphd['A'], glyphd['V'], coded['A'], coded['V']
print 'AV', font.get_kerning(glyphd['A'], glyphd['V'], KERNING_DEFAULT)
print 'AV', font.get_kerning(glyphd['A'], glyphd['V'], KERNING_UNFITTED)
print 'AV', font.get_kerning(glyphd['A'], glyphd['V'], KERNING_UNSCALED)
print 'AV', font.get_kerning(glyphd['A'], glyphd['T'], KERNING_UNSCALED)
| gpl-2.0 |
scipy/scipy | scipy/odr/models.py | 19 | 7660 | """ Collection of Model instances for use with the odrpack fitting package.
"""
import numpy as np
from scipy.odr.odrpack import Model
__all__ = ['Model', 'exponential', 'multilinear', 'unilinear', 'quadratic',
'polynomial']
def _lin_fcn(B, x):
a, b = B[0], B[1:]
b.shape = (b.shape[0], 1)
return a + (x*b).sum(axis=0)
def _lin_fjb(B, x):
a = np.ones(x.shape[-1], float)
res = np.concatenate((a, x.ravel()))
res.shape = (B.shape[-1], x.shape[-1])
return res
def _lin_fjd(B, x):
b = B[1:]
b = np.repeat(b, (x.shape[-1],)*b.shape[-1], axis=0)
b.shape = x.shape
return b
def _lin_est(data):
# Eh. The answer is analytical, so just return all ones.
# Don't return zeros since that will interfere with
# ODRPACK's auto-scaling procedures.
if len(data.x.shape) == 2:
m = data.x.shape[0]
else:
m = 1
return np.ones((m + 1,), float)
def _poly_fcn(B, x, powers):
a, b = B[0], B[1:]
b.shape = (b.shape[0], 1)
return a + np.sum(b * np.power(x, powers), axis=0)
def _poly_fjacb(B, x, powers):
res = np.concatenate((np.ones(x.shape[-1], float),
np.power(x, powers).flat))
res.shape = (B.shape[-1], x.shape[-1])
return res
def _poly_fjacd(B, x, powers):
b = B[1:]
b.shape = (b.shape[0], 1)
b = b * powers
return np.sum(b * np.power(x, powers-1), axis=0)
def _exp_fcn(B, x):
return B[0] + np.exp(B[1] * x)
def _exp_fjd(B, x):
return B[1] * np.exp(B[1] * x)
def _exp_fjb(B, x):
res = np.concatenate((np.ones(x.shape[-1], float), x * np.exp(B[1] * x)))
res.shape = (2, x.shape[-1])
return res
def _exp_est(data):
# Eh.
return np.array([1., 1.])
class _MultilinearModel(Model):
r"""
Arbitrary-dimensional linear model
This model is defined by :math:`y=\beta_0 + \sum_{i=1}^m \beta_i x_i`
Examples
--------
We can calculate orthogonal distance regression with an arbitrary
dimensional linear model:
>>> from scipy import odr
>>> x = np.linspace(0.0, 5.0)
>>> y = 10.0 + 5.0 * x
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, odr.multilinear)
>>> output = odr_obj.run()
>>> print(output.beta)
[10. 5.]
"""
def __init__(self):
super().__init__(
_lin_fcn, fjacb=_lin_fjb, fjacd=_lin_fjd, estimate=_lin_est,
meta={'name': 'Arbitrary-dimensional Linear',
'equ': 'y = B_0 + Sum[i=1..m, B_i * x_i]',
'TeXequ': r'$y=\beta_0 + \sum_{i=1}^m \beta_i x_i$'})
multilinear = _MultilinearModel()
def polynomial(order):
"""
Factory function for a general polynomial model.
Parameters
----------
order : int or sequence
If an integer, it becomes the order of the polynomial to fit. If
a sequence of numbers, then these are the explicit powers in the
polynomial.
A constant term (power 0) is always included, so don't include 0.
Thus, polynomial(n) is equivalent to polynomial(range(1, n+1)).
Returns
-------
polynomial : Model instance
Model instance.
Examples
--------
We can fit an input data using orthogonal distance regression (ODR) with
a polynomial model:
>>> import matplotlib.pyplot as plt
>>> from scipy import odr
>>> x = np.linspace(0.0, 5.0)
>>> y = np.sin(x)
>>> poly_model = odr.polynomial(3) # using third order polynomial model
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, poly_model)
>>> output = odr_obj.run() # running ODR fitting
>>> poly = np.poly1d(output.beta[::-1])
>>> poly_y = poly(x)
>>> plt.plot(x, y, label="input data")
>>> plt.plot(x, poly_y, label="polynomial ODR")
>>> plt.legend()
>>> plt.show()
"""
powers = np.asarray(order)
if powers.shape == ():
# Scalar.
powers = np.arange(1, powers + 1)
powers.shape = (len(powers), 1)
len_beta = len(powers) + 1
def _poly_est(data, len_beta=len_beta):
# Eh. Ignore data and return all ones.
return np.ones((len_beta,), float)
return Model(_poly_fcn, fjacd=_poly_fjacd, fjacb=_poly_fjacb,
estimate=_poly_est, extra_args=(powers,),
meta={'name': 'Sorta-general Polynomial',
'equ': 'y = B_0 + Sum[i=1..%s, B_i * (x**i)]' % (len_beta-1),
'TeXequ': r'$y=\beta_0 + \sum_{i=1}^{%s} \beta_i x^i$' %
(len_beta-1)})
class _ExponentialModel(Model):
r"""
Exponential model
This model is defined by :math:`y=\beta_0 + e^{\beta_1 x}`
Examples
--------
We can calculate orthogonal distance regression with an exponential model:
>>> from scipy import odr
>>> x = np.linspace(0.0, 5.0)
>>> y = -10.0 + np.exp(0.5*x)
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, odr.exponential)
>>> output = odr_obj.run()
>>> print(output.beta)
[-10. 0.5]
"""
def __init__(self):
super().__init__(_exp_fcn, fjacd=_exp_fjd, fjacb=_exp_fjb,
estimate=_exp_est,
meta={'name': 'Exponential',
'equ': 'y= B_0 + exp(B_1 * x)',
'TeXequ': r'$y=\beta_0 + e^{\beta_1 x}$'})
exponential = _ExponentialModel()
def _unilin(B, x):
return x*B[0] + B[1]
def _unilin_fjd(B, x):
return np.ones(x.shape, float) * B[0]
def _unilin_fjb(B, x):
_ret = np.concatenate((x, np.ones(x.shape, float)))
_ret.shape = (2,) + x.shape
return _ret
def _unilin_est(data):
return (1., 1.)
def _quadratic(B, x):
return x*(x*B[0] + B[1]) + B[2]
def _quad_fjd(B, x):
return 2*x*B[0] + B[1]
def _quad_fjb(B, x):
_ret = np.concatenate((x*x, x, np.ones(x.shape, float)))
_ret.shape = (3,) + x.shape
return _ret
def _quad_est(data):
return (1.,1.,1.)
class _UnilinearModel(Model):
r"""
Univariate linear model
This model is defined by :math:`y = \beta_0 x + \beta_1`
Examples
--------
We can calculate orthogonal distance regression with an unilinear model:
>>> from scipy import odr
>>> x = np.linspace(0.0, 5.0)
>>> y = 1.0 * x + 2.0
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, odr.unilinear)
>>> output = odr_obj.run()
>>> print(output.beta)
[1. 2.]
"""
def __init__(self):
super().__init__(_unilin, fjacd=_unilin_fjd, fjacb=_unilin_fjb,
estimate=_unilin_est,
meta={'name': 'Univariate Linear',
'equ': 'y = B_0 * x + B_1',
'TeXequ': '$y = \\beta_0 x + \\beta_1$'})
unilinear = _UnilinearModel()
class _QuadraticModel(Model):
r"""
Quadratic model
This model is defined by :math:`y = \beta_0 x^2 + \beta_1 x + \beta_2`
Examples
--------
We can calculate orthogonal distance regression with a quadratic model:
>>> from scipy import odr
>>> x = np.linspace(0.0, 5.0)
>>> y = 1.0 * x ** 2 + 2.0 * x + 3.0
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, odr.quadratic)
>>> output = odr_obj.run()
>>> print(output.beta)
[1. 2. 3.]
"""
def __init__(self):
super().__init__(
_quadratic, fjacd=_quad_fjd, fjacb=_quad_fjb, estimate=_quad_est,
meta={'name': 'Quadratic',
'equ': 'y = B_0*x**2 + B_1*x + B_2',
'TeXequ': '$y = \\beta_0 x^2 + \\beta_1 x + \\beta_2'})
quadratic = _QuadraticModel()
| bsd-3-clause |
abhijeet-talaulikar/Automatic-Helmet-Detection | K-Fold/Logistic_Regression.py | 1 | 2663 | import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics import roc_curve, auc
from sklearn.model_selection import KFold
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import *
from timeit import default_timer as timer
from random import randint
from sklearn.feature_selection import *
from sklearn.decomposition import PCA
helmet_data = np.genfromtxt ('helmet.csv', delimiter=",")
face_data = np.genfromtxt ('face.csv', delimiter=",")
data_full = np.concatenate((helmet_data, face_data), 0)
np.random.shuffle(data_full) #shuffle the tuples
#feature reduction (on HOG part)
#gain, j = mutual_info_classif(data_full[:, 8:-1], data_full[:, -1], discrete_features='auto', n_neighbors=3, copy=True, random_state=None), 0
#for i in np.arange(len(gain)):
# if gain[i] <= 0.001:
# data_full = np.delete(data_full, 8+i-j, 1)
# j += 1
#data = np.copy(data_full)
#principal component analysis
pca = PCA(n_components=150)
data = pca.fit_transform(data_full[:, 8:-1])
data = np.concatenate((data_full[:, 0:8], data, np.array([data_full[:, -1]]).T), axis=1)
precision, recall, f1, accuracy, support, fn, roc_auc = 0, 0, 0, 0, 0, 0, 0
colors = ['cyan', 'indigo', 'seagreen', 'yellow', 'blue', 'darkorange']
k = 10
kf = KFold(n_splits = k)
start = timer()
for train, test in kf.split(data):
X_train, X_test = data[train, 0:-1], data[test, 0:-1]
y_train, y_test = data[train, -1], data[test, -1]
clf = LogisticRegression().fit(X_train, y_train)
y_pred = clf.predict(X_test)
#ROC curve
y_prob = clf.predict_proba(X_test)[:,1]
fpr, tpr, thresholds = roc_curve(y_test, y_prob, pos_label=1)
roc_auc += auc(fpr, tpr)
plt.plot(fpr, tpr, color=colors[randint(0, len(colors)-1)])
precision += precision_score(y_test, y_pred, average = 'macro')
recall += recall_score(y_test, y_pred, average = 'macro')
f1 += f1_score(y_test, y_pred, average = 'macro')
accuracy += accuracy_score(y_test, y_pred)
y = y_test - y_pred
fn += sum(y[y > 0]) / len(y_test)
end = timer()
precision /= k
recall /= k
f1 /= k
accuracy /= k
fn /= k
print("Precision \t: %s" % round(precision, 4))
print("Recall \t\t: %s" % round(recall, 4))
print("F1 \t\t: %s" % round(f1, 4))
print("Accuracy \t: %s" % round(accuracy, 4))
print("False Neg \t: %s%%" % round(fn * 100, 4))
print("Mean AUC \t: %s" % round(roc_auc / k, 4))
print("\nExecution time: %s ms" % round((end - start) * 1000, 4))
#ROC curve
plt.title('Logistic Regression (AUC = %s)' % round(roc_auc, 4))
plt.legend(loc='lower right')
plt.plot([0,1],[0,1],'r--')
plt.xlim([-0.05,1.0])
plt.ylim([0.0,1.05])
plt.ylabel('True Positive Rate')
plt.xlabel('False Positive Rate')
plt.show()
| gpl-3.0 |
aabadie/scikit-learn | benchmarks/bench_plot_neighbors.py | 101 | 6469 | """
Plot the scaling of the nearest neighbors algorithms with k, D, and N
"""
from time import time
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import ticker
from sklearn import neighbors, datasets
def get_data(N, D, dataset='dense'):
if dataset == 'dense':
np.random.seed(0)
return np.random.random((N, D))
elif dataset == 'digits':
X = datasets.load_digits().data
i = np.argsort(X[0])[::-1]
X = X[:, i]
return X[:N, :D]
else:
raise ValueError("invalid dataset: %s" % dataset)
def barplot_neighbors(Nrange=2 ** np.arange(1, 11),
Drange=2 ** np.arange(7),
krange=2 ** np.arange(10),
N=1000,
D=64,
k=5,
leaf_size=30,
dataset='digits'):
algorithms = ('kd_tree', 'brute', 'ball_tree')
fiducial_values = {'N': N,
'D': D,
'k': k}
#------------------------------------------------------------
# varying N
N_results_build = dict([(alg, np.zeros(len(Nrange)))
for alg in algorithms])
N_results_query = dict([(alg, np.zeros(len(Nrange)))
for alg in algorithms])
for i, NN in enumerate(Nrange):
print("N = %i (%i out of %i)" % (NN, i + 1, len(Nrange)))
X = get_data(NN, D, dataset)
for algorithm in algorithms:
nbrs = neighbors.NearestNeighbors(n_neighbors=min(NN, k),
algorithm=algorithm,
leaf_size=leaf_size)
t0 = time()
nbrs.fit(X)
t1 = time()
nbrs.kneighbors(X)
t2 = time()
N_results_build[algorithm][i] = (t1 - t0)
N_results_query[algorithm][i] = (t2 - t1)
#------------------------------------------------------------
# varying D
D_results_build = dict([(alg, np.zeros(len(Drange)))
for alg in algorithms])
D_results_query = dict([(alg, np.zeros(len(Drange)))
for alg in algorithms])
for i, DD in enumerate(Drange):
print("D = %i (%i out of %i)" % (DD, i + 1, len(Drange)))
X = get_data(N, DD, dataset)
for algorithm in algorithms:
nbrs = neighbors.NearestNeighbors(n_neighbors=k,
algorithm=algorithm,
leaf_size=leaf_size)
t0 = time()
nbrs.fit(X)
t1 = time()
nbrs.kneighbors(X)
t2 = time()
D_results_build[algorithm][i] = (t1 - t0)
D_results_query[algorithm][i] = (t2 - t1)
#------------------------------------------------------------
# varying k
k_results_build = dict([(alg, np.zeros(len(krange)))
for alg in algorithms])
k_results_query = dict([(alg, np.zeros(len(krange)))
for alg in algorithms])
X = get_data(N, DD, dataset)
for i, kk in enumerate(krange):
print("k = %i (%i out of %i)" % (kk, i + 1, len(krange)))
for algorithm in algorithms:
nbrs = neighbors.NearestNeighbors(n_neighbors=kk,
algorithm=algorithm,
leaf_size=leaf_size)
t0 = time()
nbrs.fit(X)
t1 = time()
nbrs.kneighbors(X)
t2 = time()
k_results_build[algorithm][i] = (t1 - t0)
k_results_query[algorithm][i] = (t2 - t1)
plt.figure(figsize=(8, 11))
for (sbplt, vals, quantity,
build_time, query_time) in [(311, Nrange, 'N',
N_results_build,
N_results_query),
(312, Drange, 'D',
D_results_build,
D_results_query),
(313, krange, 'k',
k_results_build,
k_results_query)]:
ax = plt.subplot(sbplt, yscale='log')
plt.grid(True)
tick_vals = []
tick_labels = []
bottom = 10 ** np.min([min(np.floor(np.log10(build_time[alg])))
for alg in algorithms])
for i, alg in enumerate(algorithms):
xvals = 0.1 + i * (1 + len(vals)) + np.arange(len(vals))
width = 0.8
c_bar = plt.bar(xvals, build_time[alg] - bottom,
width, bottom, color='r')
q_bar = plt.bar(xvals, query_time[alg],
width, build_time[alg], color='b')
tick_vals += list(xvals + 0.5 * width)
tick_labels += ['%i' % val for val in vals]
plt.text((i + 0.02) / len(algorithms), 0.98, alg,
transform=ax.transAxes,
ha='left',
va='top',
bbox=dict(facecolor='w', edgecolor='w', alpha=0.5))
plt.ylabel('Time (s)')
ax.xaxis.set_major_locator(ticker.FixedLocator(tick_vals))
ax.xaxis.set_major_formatter(ticker.FixedFormatter(tick_labels))
for label in ax.get_xticklabels():
label.set_rotation(-90)
label.set_fontsize(10)
title_string = 'Varying %s' % quantity
descr_string = ''
for s in 'NDk':
if s == quantity:
pass
else:
descr_string += '%s = %i, ' % (s, fiducial_values[s])
descr_string = descr_string[:-2]
plt.text(1.01, 0.5, title_string,
transform=ax.transAxes, rotation=-90,
ha='left', va='center', fontsize=20)
plt.text(0.99, 0.5, descr_string,
transform=ax.transAxes, rotation=-90,
ha='right', va='center')
plt.gcf().suptitle("%s data set" % dataset.capitalize(), fontsize=16)
plt.figlegend((c_bar, q_bar), ('construction', 'N-point query'),
'upper right')
if __name__ == '__main__':
barplot_neighbors(dataset='digits')
barplot_neighbors(dataset='dense')
plt.show()
| bsd-3-clause |
charman2/rsas | examples/unsteady.py | 1 | 5254 | # -*- coding: utf-8 -*-
"""Storage selection (SAS) functions: example with multiple fluxes out at steady state
Runs the rSAS model for a synthetic dataset with one flux in and
multiple fluxes out and steady state flow
Theory is presented in:
Harman, C. J. (2014), Time-variable transit time distributions and transport:
Theory and application to storage-dependent transport of chloride in a watershed,
Water Resour. Res., 51, doi:10.1002/2014WR015707.
"""
from __future__ import division
import rsas
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
# Initializes the random number generator so we always get the same result
np.random.seed(0)
# =====================================
# Load the input data
# =====================================
data = pd.read_csv('Q1.csv', index_col=0, parse_dates=[1])
# length of the dataset
N = len(data)
# The individual timeseries can be pulled out of the dataframe
S = data['S'].values
J = data['J'].values
Q = data['Q1'].values
C_J = data['C_J'].values-2
C_Q1 = data['C_Q1'].values
ST_min = data['ST_min'].values
ST_max = data['ST_max'].values
# =========================
# Parameters needed by rsas
# =========================
# The concentration of water older than the start of observations
C_old = ((J*C_J)[J>0]).sum()/((J)[J>0]).sum()
# =========================
# Create the rsas functions
# =========================
S_dead = 10.
#lam = 0.
# Uniform
# Parameters for the rSAS function
Q_rSAS_fun_type = 'uniform'
ST_min = np.zeros(N)
ST_max = S + S_dead
Q_rSAS_fun_parameters = np.c_[ST_min, ST_max]
rSAS_fun_Q1 = rsas.create_function(Q_rSAS_fun_type, Q_rSAS_fun_parameters)
rSAS_fun = [rSAS_fun_Q1]
# Kumaraswami
## Parameters for the rSAS function
#Q_rSAS_fun_type = 'kumaraswami'
#ST_min = np.ones(N) * 0.
#ST_max = S + S_dead
#a = np.maximum(0.01, 2. + lam * (S - S.mean())/S.std())
#b = np.ones(N) * 5.
#Q_rSAS_fun_parameters = np.c_[a, b, ST_min, ST_max]
#rSAS_fun_Q1 = rsas.create_function(Q_rSAS_fun_type, Q_rSAS_fun_parameters)
#rSAS_fun = [rSAS_fun_Q1]
# =================
# Initial condition
# =================
# Unknown initial age distribution, so just set this to zeros
ST_init = np.zeros(N + 1)
# =============
# Run the model
# =============
# Run it
outputs = rsas.solve(J, Q, rSAS_fun, ST_init=ST_init,
mode='RK4', dt = 1., n_substeps=3, C_J=C_J, C_old=[C_old], verbose=False, debug=False)
# Let's pull these out to make the outputs from rsas crystal clear
# State variables: age-ranked storage of water and solutes
# ROWS of ST, MS are T - ages
# COLUMNS of ST, MS are t - times
# LAYERS of MS are s - solutes
ST = outputs['ST']
MS = outputs['MS'][:,:,0]
# Timestep-averaged backwards TTD
# ROWS of PQ are T - ages
# COLUMNS of PQ are t - times
# LAYERS of PQ are q - fluxes
PQ1m = outputs['PQ'][:,:,0]
# Timestep-averaged outflow concentration
# ROWS of C_Q are t - times
# COLUMNS of PQ are q - fluxes
C_Q1m1 = outputs['C_Q'][:,0,0]
# Timestep averaged solute load out
# ROWS of MQ are T - ages
# COLUMNS of MQ are t - times
# LAYERS of MQ are q - fluxes
# Last dimension of MS are s - solutes
MQ1m = outputs['MQ'][:,:,0,0]
#%%
# ==================================
# Plot the rSAS function
# ==================================
STx = np.linspace(0,S.max()+S_dead,100)
Omega = np.r_[[rSAS_fun_Q1.cdf_i(STx,i) for i in range(N)]].T
import matplotlib.cm as cm
fig = plt.figure(0)
plt.clf()
for i in range(N):
plt.plot(STx, Omega[:,i], lw=1, color=cm.jet((S[i]-S.min())/S.ptp()))
plt.ylim((0,1))
plt.ylabel('$\Omega_Q(T)$')
plt.xlabel('age-ranked storage $S_T$')
plt.title('Cumulative rSAS function')
#%%
# ==================================
# Plot the transit time distribution
# ==================================
fig = plt.figure(1)
plt.clf()
plt.plot(PQ1m, lw=1)
plt.ylim((0,1))
plt.ylabel('$P_Q(T)$')
plt.xlabel('age $T$')
plt.title('Cumulative transit time distribution')
#%%
# =====================================================================
# Outflow concentration estimated using several different TTD
# =====================================================================
# Lets get the instantaneous value of the TTD at the end of each timestep
PQ1i = np.zeros((N+1, N+1))
PQ1i[:,0] = rSAS_fun_Q1.cdf_i(ST[:,0],0)
PQ1i[:,1:] = np.r_[[rSAS_fun_Q1.cdf_i(ST[:,i+1],i) for i in range(N)]].T
# Use the transit time distribution and input timeseries to estimate
# the output timeseries for the instantaneous and timestep-averaged cases
C_Q1i, C_Q1i_raw, Q1i_observed_fraction = rsas.transport(PQ1i, C_J, C_old)
C_Q1m2, C_Q1m2_raw, Q1m2_observed_fraction = rsas.transport(PQ1m, C_J, C_old)
# Plot the results
fig = plt.figure(2)
plt.clf()
plt.step(data['datetime'], C_Q1m1, 'g', ls='--', label='mean rsas internal', lw=2, where='post')
plt.step(data['datetime'], C_Q1m2, 'b', ls=':', label='mean rsas.transport', lw=2, where='post')
plt.step(data['datetime'], C_Q1m2_raw, '0.5', ls=':', label='mean rsas.transport (obs part)', lw=2, where='post')
plt.plot(data['datetime'], C_Q1i, 'b:o', label='inst. rsas.transport', lw=1)
#plt.plot(data['datetime'], data['C_Q1'], 'r.', label='observed', lw=2)
plt.ylim((-2, 0))
plt.legend(loc=0)
plt.ylabel('Concentration [-]')
plt.xlabel('time')
plt.title('Outflow concentration')
plt.show()
| mit |
keflavich/pyspeckit | docs/conf.py | 4 | 12272 | # -*- coding: utf-8 -*-
# Licensed under a 3-clause BSD style license - see LICENSE.rst
#
# Astropy documentation build configuration file.
#
# This file is execfile()d with the current directory set to its containing dir.
#
# Note that not all possible configuration values are present in this file.
#
# All configuration values have a default. Some values are defined in
# the global Astropy configuration which is loaded here before anything else.
# See astropy.sphinx.conf for which values are set there.
# If extensions (or modules to document with autodoc) are in another directory,
# add these directories to sys.path here. If the directory is relative to the
# documentation root, use os.path.abspath to make it absolute, like shown here.
# sys.path.insert(0, os.path.abspath('..'))
# IMPORTANT: the above commented section was generated by sphinx-quickstart, but
# is *NOT* appropriate for astropy or Astropy affiliated packages. It is left
# commented out with this explanation to make it clear why this should not be
# done. If the sys.path entry above is added, when the astropy.sphinx.conf
# import occurs, it will import the *source* version of astropy instead of the
# version installed (if invoked as "make html" or directly with sphinx), or the
# version in the build directory (if "python setup.py build_sphinx" is used).
# Thus, any C-extensions that are needed to build the documentation will *not*
# be accessible, and the documentation will not build correctly.
import datetime
import os
import sys
try:
from sphinx_astropy.conf.v1 import * # noqa
except ImportError:
print('ERROR: the documentation requires the sphinx-astropy package to be'
' installed')
sys.exit(1)
# Get configuration information from setup.cfg
try:
from ConfigParser import ConfigParser
except ImportError:
from configparser import ConfigParser
conf = ConfigParser()
conf.read([os.path.join(os.path.dirname(__file__), '..', 'setup.cfg')])
setup_cfg = dict(conf.items('metadata'))
# -- General configuration ----------------------------------------------------
# If your documentation needs a minimal Sphinx version, state it here.
#needs_sphinx = '1.2'
# -*- coding: utf-8 -*-
try:
import numpy
except ImportError:
print("Failed to import numpy")
# If extensions (or modules to document with autodoc) are in another directory,
# add these directories to sys.path here. If the directory is relative to the
# documentation root, use os.path.abspath to make it absolute, like shown here.
rootpath = os.path.abspath(os.path.join(os.path.dirname(__file__), '..'))
sys.path.insert(0, rootpath)
#import numpydoc
#sys.path.insert(0, os.path.split(numpydoc.__file__)[0])
sys.path.insert(0, rootpath+"/docs/sphinxext/")
sys.path.append(os.path.abspath('sphinxext'))
sys.path.append(os.path.abspath('.'))
print("rootpath: ",rootpath)
# -- General configuration -----------------------------------------------------
# If your documentation needs a minimal Sphinx version, state it here.
#needs_sphinx = '1.0'
#sys.path.insert(0, os.path.abspath('.'))
# Add any Sphinx extension module names here, as strings. They can be extensions
# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
extensions += ['edit_on_github', 'edit_on_bitbucket']
# Add any paths that contain templates here, relative to this directory.
templates_path = ['_templates']
# The suffix of source filenames.
source_suffix = '.rst'
# The encoding of source files.
#source_encoding = 'utf-8-sig'
# The master toctree document.
master_doc = 'index'
html_sidebars = {'**':['globaltoc.html', 'localtoc.html', 'relations.html',
'sourcelink.html', 'searchbox.html']}
# General information about the project.
project = 'pyspeckit'
copyright = '2011, Adam Ginsburg and coauthors'
# This does not *have* to match the package name, but typically does
project = setup_cfg['package_name']
author = setup_cfg['author']
copyright = '{0}, {1}'.format(
datetime.datetime.now().year, setup_cfg['author'])
# The version info for the project you're documenting, acts as replacement for
# |version| and |release|, also used in various other places throughout the
# built documents.
# read the docs mocks
__import__(setup_cfg['package_name'])
package = sys.modules[setup_cfg['package_name']]
class Mock(object):
def __init__(self, *args, **kwargs):
pass
def __call__(self, *args, **kwargs):
return Mock()
@classmethod
def __getattr__(cls, name):
if name in ('__file__', '__path__'):
return '/dev/null'
elif name[0] == name[0].upper():
return type(name, (), {})
else:
return Mock()
MOCK_MODULES = {'matplotlib', 'matplotlib.pyplot', 'matplotlib.figure',
'matplotlib.widgets', 'matplotlib.cbook', 'pyfits', 'scipy',
'scipy', 'pyfits', 'pytest',
'scipy.interpolate', 'scipy.ndimage', 'pywcs', 'matplotlib',
'matplotlib.pyplot', 'h5py', 'atpy','progressbar'}
for mod_name in MOCK_MODULES:
if mod_name not in sys.modules:
sys.modules[mod_name] = Mock()
for mod_name in MOCK_MODULES:
sys.modules[mod_name] = Mock()
# The short X.Y version.
#import pyspeckit
#version = pyspeckit.__version__
## The full version, including alpha/beta/rc tags.
#release = pyspeckit.__version__
#
# The short X.Y version.
version = package.__version__.split('-', 1)[0]
# The full version, including alpha/beta/rc tags.
release = package.__version__
# The language for content autogenerated by Sphinx. Refer to documentation
# for a list of supported languages.
#language = None
# There are two options for replacing |today|: either, you set today to some
# non-false value, then it is used:
#today = ''
# Else, today_fmt is used as the format for a strftime call.
#today_fmt = '%B %d, %Y'
# List of patterns, relative to source directory, that match files and
# directories to ignore when looking for source files.
exclude_patterns = ['_build','_static','_template']
# The reST default role (used for this markup: `text`) to use for all documents.
default_role = 'obj'
# If true, '()' will be appended to :func: etc. cross-reference text.
#add_function_parentheses = True
# If true, the current module name will be prepended to all description
# unit titles (such as .. function::).
#add_module_names = True
# If true, sectionauthor and moduleauthor directives will be shown in the
# output. They are ignored by default.
#show_authors = False
# The name of the Pygments (syntax highlighting) style to use.
pygments_style = 'sphinx'
# A list of ignored prefixes for module index sorting.
#modindex_common_prefix = []
# -- Options for HTML output ---------------------------------------------------
# The theme to use for HTML and HTML Help pages. See the documentation for
# a list of builtin themes.
html_theme = 'agogo'
html_style = 'extra.css'
# Theme options are theme-specific and customize the look and feel of a theme
# further. For a list of options available for each theme, see the
# documentation.
#html_theme_options = {}
html_theme_options = dict(
pagewidth = '1000px',
documentwidth = '760px',
sidebarwidth = '200px',
nosidebar=False,
headerbg="#666666",
headercolor1="#000000",
headercolor2="#000000",
headerlinkcolor="#FF9522",
linkcolor="#4a8f43",
textalign='left',
)
# Add any paths that contain custom themes here, relative to this directory.
#html_theme_path = []
# The name for this set of Sphinx documents. If None, it defaults to
# "<project> v<release> documentation".
#html_title = None
# The name for this set of Sphinx documents. If None, it defaults to
# "<project> v<release> documentation".
html_title = '{0} v{1}'.format(project, release)
# A shorter title for the navigation bar. Default is the same as html_title.
#html_short_title = None
# The name of an image file (relative to this directory) to place at the top
# of the sidebar.
html_logo = "images/logo.png"
# The name of an image file (within the static path) to use as favicon of the
# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
# pixels large.
html_favicon = "images/logo.ico"
# Add any paths that contain custom static files (such as style sheets) here,
# relative to this directory. They are copied after the builtin static files,
# so a file named "default.css" will overwrite the builtin "default.css".
html_static_path = ['_static','_static/extra.css','_static/scipy.css','_static/astropy.css']
# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
# using the given strftime format.
html_last_updated_fmt = '%b %d, %Y'
# If true, SmartyPants will be used to convert quotes and dashes to
# typographically correct entities.
#html_use_smartypants = True
# Custom sidebar templates, maps document names to template names.
#html_sidebars = {}
# Additional templates that should be rendered to pages, maps page names to
# template names.
#html_additional_pages = {}
# If false, no module index is generated.
#html_domain_indices = True
# If false, no index is generated.
#html_use_index = True
# If true, the index is split into individual pages for each letter.
#html_split_index = False
# If true, links to the reST sources are added to the pages.
html_show_sourcelink = True
# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
html_show_sphinx = True
# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
#html_show_copyright = True
# If true, an OpenSearch description file will be output, and all pages will
# contain a <link> tag referring to it. The value of this option must be the
# base URL from which the finished HTML is served.
#html_use_opensearch = ''
# This is the file name suffix for HTML files (e.g. ".xhtml").
#html_file_suffix = None
# Output file base name for HTML help builder.
htmlhelp_basename = 'pyspeckitdoc'
htmlhelp_basename = project + 'doc'
# -- Options for LaTeX output --------------------------------------------------
# The paper size ('letter' or 'a4').
#latex_paper_size = 'letter'
# The font size ('10pt', '11pt' or '12pt').
#latex_font_size = '10pt'
# Grouping the document tree into LaTeX files. List of tuples
# (source start file, target name, title, author, documentclass [howto/manual]).
latex_documents = [
('index', 'pyspeckit.tex', 'pyspeckit Documentation',
'Adam Ginsburg and coauthors', 'manual'),
]
latex_documents = [('index', project + '.tex', project + ' Documentation',
author, 'manual')]
# The name of an image file (relative to this directory) to place at the top of
# the title page.
#latex_logo = None
# For "manual" documents, if this is true, then toplevel headings are parts,
# not chapters.
#latex_use_parts = False
# If true, show page references after internal links.
#latex_show_pagerefs = False
# If true, show URL addresses after external links.
#latex_show_urls = False
# Additional stuff for the LaTeX preamble.
#latex_preamble = ''
# Documents to append as an appendix to all manuals.
#latex_appendices = []
# If false, no module index is generated.
#latex_domain_indices = True
# Try to make autoclass include both __init__ and Class docstrings
autoclass_content = 'both'
# -- Options for manual page output --------------------------------------------
# One entry per manual page. List of tuples
# (source start file, name, description, authors, manual section).
man_pages = [('index', project.lower(), project + ' Documentation',
[author], 1)]
## -- Options for the edit_on_github extension ----------------------------------------
if eval(setup_cfg.get('edit_on_github')):
extensions += ['edit_on_github']
versionmod = __import__(setup_cfg['package_name'] + '.version')
edit_on_github_project = setup_cfg['github_project']
if versionmod.version.release:
edit_on_github_branch = "v" + versionmod.version.version
else:
edit_on_github_branch = "master"
edit_on_github_source_root = ""
edit_on_github_doc_root = "docs"
edit_on_bitbucket_project = "pyspeckit/pyspeckit"
edit_on_bitbucket_source_root = ""
edit_on_bitbucket_doc_root = "doc"
| mit |
cauchycui/scikit-learn | examples/linear_model/plot_ols_ridge_variance.py | 387 | 2060 | #!/usr/bin/python
# -*- coding: utf-8 -*-
"""
=========================================================
Ordinary Least Squares and Ridge Regression Variance
=========================================================
Due to the few points in each dimension and the straight
line that linear regression uses to follow these points
as well as it can, noise on the observations will cause
great variance as shown in the first plot. Every line's slope
can vary quite a bit for each prediction due to the noise
induced in the observations.
Ridge regression is basically minimizing a penalised version
of the least-squared function. The penalising `shrinks` the
value of the regression coefficients.
Despite the few data points in each dimension, the slope
of the prediction is much more stable and the variance
in the line itself is greatly reduced, in comparison to that
of the standard linear regression
"""
print(__doc__)
# Code source: Gaël Varoquaux
# Modified for documentation by Jaques Grobler
# License: BSD 3 clause
import numpy as np
import matplotlib.pyplot as plt
from sklearn import linear_model
X_train = np.c_[.5, 1].T
y_train = [.5, 1]
X_test = np.c_[0, 2].T
np.random.seed(0)
classifiers = dict(ols=linear_model.LinearRegression(),
ridge=linear_model.Ridge(alpha=.1))
fignum = 1
for name, clf in classifiers.items():
fig = plt.figure(fignum, figsize=(4, 3))
plt.clf()
plt.title(name)
ax = plt.axes([.12, .12, .8, .8])
for _ in range(6):
this_X = .1 * np.random.normal(size=(2, 1)) + X_train
clf.fit(this_X, y_train)
ax.plot(X_test, clf.predict(X_test), color='.5')
ax.scatter(this_X, y_train, s=3, c='.5', marker='o', zorder=10)
clf.fit(X_train, y_train)
ax.plot(X_test, clf.predict(X_test), linewidth=2, color='blue')
ax.scatter(X_train, y_train, s=30, c='r', marker='+', zorder=10)
ax.set_xticks(())
ax.set_yticks(())
ax.set_ylim((0, 1.6))
ax.set_xlabel('X')
ax.set_ylabel('y')
ax.set_xlim(0, 2)
fignum += 1
plt.show()
| bsd-3-clause |
18padx08/PPTex | PPTexEnv_x86_64/lib/python2.7/site-packages/matplotlib/tests/test_transforms.py | 9 | 19984 | from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
from six.moves import xrange, zip
import unittest
from nose.tools import assert_equal, assert_raises
import numpy.testing as np_test
from numpy.testing import assert_almost_equal
from matplotlib.transforms import Affine2D, BlendedGenericTransform
from matplotlib.path import Path
from matplotlib.scale import LogScale
from matplotlib.testing.decorators import cleanup, image_comparison
import numpy as np
import matplotlib.transforms as mtrans
import matplotlib.pyplot as plt
import matplotlib.path as mpath
import matplotlib.patches as mpatches
@cleanup
def test_non_affine_caching():
class AssertingNonAffineTransform(mtrans.Transform):
"""
This transform raises an assertion error when called when it
shouldn't be and self.raise_on_transform is True.
"""
input_dims = output_dims = 2
is_affine = False
def __init__(self, *args, **kwargs):
mtrans.Transform.__init__(self, *args, **kwargs)
self.raise_on_transform = False
self.underlying_transform = mtrans.Affine2D().scale(10, 10)
def transform_path_non_affine(self, path):
if self.raise_on_transform:
assert False, ('Invalidated affine part of transform '
'unnecessarily.')
return self.underlying_transform.transform_path(path)
transform_path = transform_path_non_affine
def transform_non_affine(self, path):
if self.raise_on_transform:
assert False, ('Invalidated affine part of transform '
'unnecessarily.')
return self.underlying_transform.transform(path)
transform = transform_non_affine
my_trans = AssertingNonAffineTransform()
ax = plt.axes()
plt.plot(list(xrange(10)), transform=my_trans + ax.transData)
plt.draw()
# enable the transform to raise an exception if it's non-affine transform
# method is triggered again.
my_trans.raise_on_transform = True
ax.transAxes.invalidate()
plt.draw()
@cleanup
def test_external_transform_api():
class ScaledBy(object):
def __init__(self, scale_factor):
self._scale_factor = scale_factor
def _as_mpl_transform(self, axes):
return mtrans.Affine2D().scale(self._scale_factor) + axes.transData
ax = plt.axes()
line, = plt.plot(list(xrange(10)), transform=ScaledBy(10))
ax.set_xlim(0, 100)
ax.set_ylim(0, 100)
# assert that the top transform of the line is the scale transform.
np.testing.assert_allclose(line.get_transform()._a.get_matrix(),
mtrans.Affine2D().scale(10).get_matrix())
@image_comparison(baseline_images=['pre_transform_data'])
def test_pre_transform_plotting():
# a catch-all for as many as possible plot layouts which handle pre-transforming the data
# NOTE: The axis range is important in this plot. It should be x10 what the data suggests it should be
ax = plt.axes()
times10 = mtrans.Affine2D().scale(10)
ax.contourf(np.arange(48).reshape(6, 8), transform=times10 + ax.transData)
ax.pcolormesh(np.linspace(0, 4, 7),
np.linspace(5.5, 8, 9),
np.arange(48).reshape(8, 6),
transform=times10 + ax.transData)
ax.scatter(np.linspace(0, 10), np.linspace(10, 0),
transform=times10 + ax.transData)
x = np.linspace(8, 10, 20)
y = np.linspace(1, 5, 20)
u = 2*np.sin(x) + np.cos(y[:, np.newaxis])
v = np.sin(x) - np.cos(y[:, np.newaxis])
df = 25. / 30. # Compatibility factor for old test image
ax.streamplot(x, y, u, v, transform=times10 + ax.transData,
density=(df, df), linewidth=u**2 + v**2)
# reduce the vector data down a bit for barb and quiver plotting
x, y = x[::3], y[::3]
u, v = u[::3, ::3], v[::3, ::3]
ax.quiver(x, y + 5, u, v, transform=times10 + ax.transData)
ax.barbs(x - 3, y + 5, u**2, v**2, transform=times10 + ax.transData)
@cleanup
def test_contour_pre_transform_limits():
ax = plt.axes()
xs, ys = np.meshgrid(np.linspace(15, 20, 15), np.linspace(12.4, 12.5, 20))
ax.contourf(xs, ys, np.log(xs * ys), transform=mtrans.Affine2D().scale(0.1) + ax.transData)
expected = np.array([[ 1.5 , 1.24],
[ 2. , 1.25]])
assert_almost_equal(expected, ax.dataLim.get_points())
@cleanup
def test_pcolor_pre_transform_limits():
# Based on test_contour_pre_transform_limits()
ax = plt.axes()
xs, ys = np.meshgrid(np.linspace(15, 20, 15), np.linspace(12.4, 12.5, 20))
ax.pcolor(xs, ys, np.log(xs * ys), transform=mtrans.Affine2D().scale(0.1) + ax.transData)
expected = np.array([[ 1.5 , 1.24],
[ 2. , 1.25]])
assert_almost_equal(expected, ax.dataLim.get_points())
@cleanup
def test_pcolormesh_pre_transform_limits():
# Based on test_contour_pre_transform_limits()
ax = plt.axes()
xs, ys = np.meshgrid(np.linspace(15, 20, 15), np.linspace(12.4, 12.5, 20))
ax.pcolormesh(xs, ys, np.log(xs * ys), transform=mtrans.Affine2D().scale(0.1) + ax.transData)
expected = np.array([[ 1.5 , 1.24],
[ 2. , 1.25]])
assert_almost_equal(expected, ax.dataLim.get_points())
def test_Affine2D_from_values():
points = np.array([ [0,0],
[10,20],
[-1,0],
])
t = mtrans.Affine2D.from_values(1,0,0,0,0,0)
actual = t.transform(points)
expected = np.array( [[0,0],[10,0],[-1,0]] )
assert_almost_equal(actual,expected)
t = mtrans.Affine2D.from_values(0,2,0,0,0,0)
actual = t.transform(points)
expected = np.array( [[0,0],[0,20],[0,-2]] )
assert_almost_equal(actual,expected)
t = mtrans.Affine2D.from_values(0,0,3,0,0,0)
actual = t.transform(points)
expected = np.array( [[0,0],[60,0],[0,0]] )
assert_almost_equal(actual,expected)
t = mtrans.Affine2D.from_values(0,0,0,4,0,0)
actual = t.transform(points)
expected = np.array( [[0,0],[0,80],[0,0]] )
assert_almost_equal(actual,expected)
t = mtrans.Affine2D.from_values(0,0,0,0,5,0)
actual = t.transform(points)
expected = np.array( [[5,0],[5,0],[5,0]] )
assert_almost_equal(actual,expected)
t = mtrans.Affine2D.from_values(0,0,0,0,0,6)
actual = t.transform(points)
expected = np.array( [[0,6],[0,6],[0,6]] )
assert_almost_equal(actual,expected)
def test_clipping_of_log():
# issue 804
M,L,C = Path.MOVETO, Path.LINETO, Path.CLOSEPOLY
points = [ (0.2, -99), (0.4, -99), (0.4, 20), (0.2, 20), (0.2, -99) ]
codes = [ M, L, L, L, C ]
path = Path(points, codes)
# something like this happens in plotting logarithmic histograms
trans = BlendedGenericTransform(Affine2D(),
LogScale.Log10Transform('clip'))
tpath = trans.transform_path_non_affine(path)
result = tpath.iter_segments(trans.get_affine(),
clip=(0, 0, 100, 100),
simplify=False)
tpoints, tcodes = list(zip(*result))
# Because y coordinate -99 is outside the clip zone, the first
# line segment is effectively removed. That means that the closepoly
# operation must be replaced by a move to the first point.
assert np.allclose(tcodes, [ M, M, L, L, L ])
class NonAffineForTest(mtrans.Transform):
"""
A class which looks like a non affine transform, but does whatever
the given transform does (even if it is affine). This is very useful
for testing NonAffine behaviour with a simple Affine transform.
"""
is_affine = False
output_dims = 2
input_dims = 2
def __init__(self, real_trans, *args, **kwargs):
self.real_trans = real_trans
r = mtrans.Transform.__init__(self, *args, **kwargs)
def transform_non_affine(self, values):
return self.real_trans.transform(values)
def transform_path_non_affine(self, path):
return self.real_trans.transform_path(path)
class BasicTransformTests(unittest.TestCase):
def setUp(self):
self.ta1 = mtrans.Affine2D(shorthand_name='ta1').rotate(np.pi / 2)
self.ta2 = mtrans.Affine2D(shorthand_name='ta2').translate(10, 0)
self.ta3 = mtrans.Affine2D(shorthand_name='ta3').scale(1, 2)
self.tn1 = NonAffineForTest(mtrans.Affine2D().translate(1, 2), shorthand_name='tn1')
self.tn2 = NonAffineForTest(mtrans.Affine2D().translate(1, 2), shorthand_name='tn2')
self.tn3 = NonAffineForTest(mtrans.Affine2D().translate(1, 2), shorthand_name='tn3')
# creates a transform stack which looks like ((A, (N, A)), A)
self.stack1 = (self.ta1 + (self.tn1 + self.ta2)) + self.ta3
# creates a transform stack which looks like (((A, N), A), A)
self.stack2 = self.ta1 + self.tn1 + self.ta2 + self.ta3
# creates a transform stack which is a subset of stack2
self.stack2_subset = self.tn1 + self.ta2 + self.ta3
# when in debug, the transform stacks can produce dot images:
# self.stack1.write_graphviz(file('stack1.dot', 'w'))
# self.stack2.write_graphviz(file('stack2.dot', 'w'))
# self.stack2_subset.write_graphviz(file('stack2_subset.dot', 'w'))
def test_transform_depth(self):
assert_equal(self.stack1.depth, 4)
assert_equal(self.stack2.depth, 4)
assert_equal(self.stack2_subset.depth, 3)
def test_left_to_right_iteration(self):
stack3 = (self.ta1 + (self.tn1 + (self.ta2 + self.tn2))) + self.ta3
# stack3.write_graphviz(file('stack3.dot', 'w'))
target_transforms = [stack3,
(self.tn1 + (self.ta2 + self.tn2)) + self.ta3,
(self.ta2 + self.tn2) + self.ta3,
self.tn2 + self.ta3,
self.ta3,
]
r = [rh for _, rh in stack3._iter_break_from_left_to_right()]
self.assertEqual(len(r), len(target_transforms))
for target_stack, stack in zip(target_transforms, r):
self.assertEqual(target_stack, stack)
def test_transform_shortcuts(self):
self.assertEqual(self.stack1 - self.stack2_subset, self.ta1)
self.assertEqual(self.stack2 - self.stack2_subset, self.ta1)
assert_equal((self.stack2_subset - self.stack2),
self.ta1.inverted(),
)
assert_equal((self.stack2_subset - self.stack2).depth, 1)
assert_raises(ValueError, self.stack1.__sub__, self.stack2)
aff1 = self.ta1 + (self.ta2 + self.ta3)
aff2 = self.ta2 + self.ta3
self.assertEqual(aff1 - aff2, self.ta1)
self.assertEqual(aff1 - self.ta2, aff1 + self.ta2.inverted())
self.assertEqual(self.stack1 - self.ta3, self.ta1 + (self.tn1 + self.ta2))
self.assertEqual(self.stack2 - self.ta3, self.ta1 + self.tn1 + self.ta2)
self.assertEqual((self.ta2 + self.ta3) - self.ta3 + self.ta3, self.ta2 + self.ta3)
def test_contains_branch(self):
r1 = (self.ta2 + self.ta1)
r2 = (self.ta2 + self.ta1)
self.assertEqual(r1, r2)
self.assertNotEqual(r1, self.ta1)
self.assertTrue(r1.contains_branch(r2))
self.assertTrue(r1.contains_branch(self.ta1))
self.assertFalse(r1.contains_branch(self.ta2))
self.assertFalse(r1.contains_branch((self.ta2 + self.ta2)))
self.assertEqual(r1, r2)
self.assertTrue(self.stack1.contains_branch(self.ta3))
self.assertTrue(self.stack2.contains_branch(self.ta3))
self.assertTrue(self.stack1.contains_branch(self.stack2_subset))
self.assertTrue(self.stack2.contains_branch(self.stack2_subset))
self.assertFalse(self.stack2_subset.contains_branch(self.stack1))
self.assertFalse(self.stack2_subset.contains_branch(self.stack2))
self.assertTrue(self.stack1.contains_branch((self.ta2 + self.ta3)))
self.assertTrue(self.stack2.contains_branch((self.ta2 + self.ta3)))
self.assertFalse(self.stack1.contains_branch((self.tn1 + self.ta2)))
def test_affine_simplification(self):
# tests that a transform stack only calls as much is absolutely necessary
# "non-affine" allowing the best possible optimization with complex
# transformation stacks.
points = np.array([[0, 0], [10, 20], [np.nan, 1], [-1, 0]], dtype=np.float64)
na_pts = self.stack1.transform_non_affine(points)
all_pts = self.stack1.transform(points)
na_expected = np.array([[1., 2.], [-19., 12.],
[np.nan, np.nan], [1., 1.]], dtype=np.float64)
all_expected = np.array([[11., 4.], [-9., 24.],
[np.nan, np.nan], [11., 2.]], dtype=np.float64)
# check we have the expected results from doing the affine part only
np_test.assert_array_almost_equal(na_pts, na_expected)
# check we have the expected results from a full transformation
np_test.assert_array_almost_equal(all_pts, all_expected)
# check we have the expected results from doing the transformation in two steps
np_test.assert_array_almost_equal(self.stack1.transform_affine(na_pts), all_expected)
# check that getting the affine transformation first, then fully transforming using that
# yields the same result as before.
np_test.assert_array_almost_equal(self.stack1.get_affine().transform(na_pts), all_expected)
# check that the affine part of stack1 & stack2 are equivalent (i.e. the optimization
# is working)
expected_result = (self.ta2 + self.ta3).get_matrix()
result = self.stack1.get_affine().get_matrix()
np_test.assert_array_equal(expected_result, result)
result = self.stack2.get_affine().get_matrix()
np_test.assert_array_equal(expected_result, result)
class TestTransformPlotInterface(unittest.TestCase):
def tearDown(self):
plt.close()
def test_line_extent_axes_coords(self):
# a simple line in axes coordinates
ax = plt.axes()
ax.plot([0.1, 1.2, 0.8], [0.9, 0.5, 0.8], transform=ax.transAxes)
np.testing.assert_array_equal(ax.dataLim.get_points(), np.array([[np.inf, np.inf], [-np.inf, -np.inf]]))
def test_line_extent_data_coords(self):
# a simple line in data coordinates
ax = plt.axes()
ax.plot([0.1, 1.2, 0.8], [0.9, 0.5, 0.8], transform=ax.transData)
np.testing.assert_array_equal(ax.dataLim.get_points(), np.array([[ 0.1, 0.5], [ 1.2, 0.9]]))
def test_line_extent_compound_coords1(self):
# a simple line in data coordinates in the y component, and in axes coordinates in the x
ax = plt.axes()
trans = mtrans.blended_transform_factory(ax.transAxes, ax.transData)
ax.plot([0.1, 1.2, 0.8], [35, -5, 18], transform=trans)
np.testing.assert_array_equal(ax.dataLim.get_points(), np.array([[ np.inf, -5.], [ -np.inf, 35.]]))
plt.close()
def test_line_extent_predata_transform_coords(self):
# a simple line in (offset + data) coordinates
ax = plt.axes()
trans = mtrans.Affine2D().scale(10) + ax.transData
ax.plot([0.1, 1.2, 0.8], [35, -5, 18], transform=trans)
np.testing.assert_array_equal(ax.dataLim.get_points(), np.array([[1., -50.], [12., 350.]]))
plt.close()
def test_line_extent_compound_coords2(self):
# a simple line in (offset + data) coordinates in the y component, and in axes coordinates in the x
ax = plt.axes()
trans = mtrans.blended_transform_factory(ax.transAxes, mtrans.Affine2D().scale(10) + ax.transData)
ax.plot([0.1, 1.2, 0.8], [35, -5, 18], transform=trans)
np.testing.assert_array_equal(ax.dataLim.get_points(), np.array([[ np.inf, -50.], [ -np.inf, 350.]]))
plt.close()
def test_line_extents_affine(self):
ax = plt.axes()
offset = mtrans.Affine2D().translate(10, 10)
plt.plot(list(xrange(10)), transform=offset + ax.transData)
expeted_data_lim = np.array([[0., 0.], [9., 9.]]) + 10
np.testing.assert_array_almost_equal(ax.dataLim.get_points(),
expeted_data_lim)
def test_line_extents_non_affine(self):
ax = plt.axes()
offset = mtrans.Affine2D().translate(10, 10)
na_offset = NonAffineForTest(mtrans.Affine2D().translate(10, 10))
plt.plot(list(xrange(10)), transform=offset + na_offset + ax.transData)
expeted_data_lim = np.array([[0., 0.], [9., 9.]]) + 20
np.testing.assert_array_almost_equal(ax.dataLim.get_points(),
expeted_data_lim)
def test_pathc_extents_non_affine(self):
ax = plt.axes()
offset = mtrans.Affine2D().translate(10, 10)
na_offset = NonAffineForTest(mtrans.Affine2D().translate(10, 10))
pth = mpath.Path(np.array([[0, 0], [0, 10], [10, 10], [10, 0]]))
patch = mpatches.PathPatch(pth, transform=offset + na_offset + ax.transData)
ax.add_patch(patch)
expeted_data_lim = np.array([[0., 0.], [10., 10.]]) + 20
np.testing.assert_array_almost_equal(ax.dataLim.get_points(),
expeted_data_lim)
def test_pathc_extents_affine(self):
ax = plt.axes()
offset = mtrans.Affine2D().translate(10, 10)
pth = mpath.Path(np.array([[0, 0], [0, 10], [10, 10], [10, 0]]))
patch = mpatches.PathPatch(pth, transform=offset + ax.transData)
ax.add_patch(patch)
expeted_data_lim = np.array([[0., 0.], [10., 10.]]) + 10
np.testing.assert_array_almost_equal(ax.dataLim.get_points(),
expeted_data_lim)
def test_line_extents_for_non_affine_transData(self):
ax = plt.axes(projection='polar')
# add 10 to the radius of the data
offset = mtrans.Affine2D().translate(0, 10)
plt.plot(list(xrange(10)), transform=offset + ax.transData)
# the data lim of a polar plot is stored in coordinates
# before a transData transformation, hence the data limits
# are not what is being shown on the actual plot.
expeted_data_lim = np.array([[0., 0.], [9., 9.]]) + [0, 10]
np.testing.assert_array_almost_equal(ax.dataLim.get_points(),
expeted_data_lim)
def test_bbox_intersection():
bbox_from_ext = mtrans.Bbox.from_extents
inter = mtrans.Bbox.intersection
from numpy.testing import assert_array_equal as assert_a_equal
def assert_bbox_eq(bbox1, bbox2):
assert_a_equal(bbox1.bounds, bbox2.bounds)
r1 = bbox_from_ext(0, 0, 1, 1)
r2 = bbox_from_ext(0.5, 0.5, 1.5, 1.5)
r3 = bbox_from_ext(0.5, 0, 0.75, 0.75)
r4 = bbox_from_ext(0.5, 1.5, 1, 2.5)
r5 = bbox_from_ext(1, 1, 2, 2)
# self intersection -> no change
assert_bbox_eq(inter(r1, r1), r1)
# simple intersection
assert_bbox_eq(inter(r1, r2), bbox_from_ext(0.5, 0.5, 1, 1))
# r3 contains r2
assert_bbox_eq(inter(r1, r3), r3)
# no intersection
assert_equal(inter(r1, r4), None)
# single point
assert_bbox_eq(inter(r1, r5), bbox_from_ext(1, 1, 1, 1))
@cleanup
def test_log_transform():
# Tests that the last line runs without exception (previously the
# transform would fail if one of the axes was logarithmic).
fig, ax = plt.subplots()
ax.set_yscale('log')
ax.transData.transform((1,1))
if __name__=='__main__':
import nose
nose.runmodule(argv=['-s','--with-doctest'], exit=False)
| mit |
samuelstjean/dipy | scratch/very_scratch/diffusion_sphere_stats.py | 20 | 18082 | import nibabel
import os
import numpy as np
import dipy as dp
#import dipy.core.generalized_q_sampling as dgqs
import dipy.reconst.gqi as dgqs
import dipy.reconst.dti as ddti
import dipy.reconst.recspeed as rp
import dipy.io.pickles as pkl
import scipy as sp
from matplotlib.mlab import find
#import dipy.core.sphere_plots as splots
import dipy.core.sphere_stats as sphats
import dipy.core.geometry as geometry
import get_vertices as gv
#old SimData files
'''
results_SNR030_1fibre
results_SNR030_1fibre+iso
results_SNR030_2fibres_15deg
results_SNR030_2fibres_30deg
results_SNR030_2fibres_60deg
results_SNR030_2fibres_90deg
results_SNR030_2fibres+iso_15deg
results_SNR030_2fibres+iso_30deg
results_SNR030_2fibres+iso_60deg
results_SNR030_2fibres+iso_90deg
results_SNR030_isotropic
'''
#fname='/home/ian/Data/SimData/results_SNR030_1fibre'
''' file has one row for every voxel, every voxel is repeating 1000
times with the same noise level , then we have 100 different
directions. 1000 * 100 is the number of all rows.
The 100 conditions are given by 10 polar angles (in degrees) 0, 20, 40, 60, 80,
80, 60, 40, 20 and 0, and each of these with longitude angle 0, 40, 80,
120, 160, 200, 240, 280, 320, 360.
'''
#new complete SimVoxels files
simdata = ['fibres_2_SNR_80_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_60_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_40_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_40_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_20_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_100_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_20_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_40_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_60_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_100_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_1_SNR_60_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_80_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_100_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_100_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_80_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_60_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_40_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_80_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_20_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_60_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_1_SNR_100_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_1_SNR_100_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_20_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_1_SNR_20_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_40_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_20_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_80_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_1_SNR_80_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_20_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_60_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_100_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_80_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_60_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_20_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_100_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_1_SNR_20_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_80_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_1_SNR_80_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_100_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_1_SNR_40_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_1_SNR_60_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_40_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_60_angle_30_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_40_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_60_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_80_angle_15_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_1_SNR_40_angle_00_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_100_angle_60_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00',
'fibres_2_SNR_40_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_1_diso_0.7',
'fibres_2_SNR_20_angle_90_l1_1.4_l2_0.35_l3_0.35_iso_0_diso_00']
simdir = '/home/ian/Data/SimVoxels/'
def gq_tn_calc_save():
for simfile in simdata:
dataname = simfile
print dataname
sim_data=np.loadtxt(simdir+dataname)
marta_table_fname='/home/ian/Data/SimData/Dir_and_bvals_DSI_marta.txt'
b_vals_dirs=np.loadtxt(marta_table_fname)
bvals=b_vals_dirs[:,0]*1000
gradients=b_vals_dirs[:,1:]
gq = dgqs.GeneralizedQSampling(sim_data,bvals,gradients)
gqfile = simdir+'gq/'+dataname+'.pkl'
pkl.save_pickle(gqfile,gq)
'''
gq.IN gq.__doc__ gq.glob_norm_param
gq.QA gq.__init__ gq.odf
gq.__class__ gq.__module__ gq.q2odf_params
'''
tn = ddti.Tensor(sim_data,bvals,gradients)
tnfile = simdir+'tn/'+dataname+'.pkl'
pkl.save_pickle(tnfile,tn)
'''
tn.ADC tn.__init__ tn._getevals
tn.B tn.__module__ tn._getevecs
tn.D tn.__new__ tn._getndim
tn.FA tn.__reduce__ tn._getshape
tn.IN tn.__reduce_ex__ tn._setevals
tn.MD tn.__repr__ tn._setevecs
tn.__class__ tn.__setattr__ tn.adc
tn.__delattr__ tn.__sizeof__ tn.evals
tn.__dict__ tn.__str__ tn.evecs
tn.__doc__ tn.__subclasshook__ tn.fa
tn.__format__ tn.__weakref__ tn.md
tn.__getattribute__ tn._evals tn.ndim
tn.__getitem__ tn._evecs tn.shape
tn.__hash__ tn._getD
'''
''' file has one row for every voxel, every voxel is repeating 1000
times with the same noise level , then we have 100 different
directions. 100 * 1000 is the number of all rows.
At the moment this module is hardwired to the use of the EDS362
spherical mesh. I am assumung (needs testing) that directions 181 to 361
are the antipodal partners of directions 0 to 180. So when counting the
number of different vertices that occur as maximal directions we wll map
the indices modulo 181.
'''
def analyze_maxima(indices, max_dirs, subsets):
'''This calculates the eigenstats for each of the replicated batches
of the simulation data
'''
results = []
for direction in subsets:
batch = max_dirs[direction,:,:]
index_variety = np.array([len(set(np.remainder(indices[direction,:],181)))])
#normed_centroid, polar_centroid, centre, b1 = sphats.eigenstats(batch)
centre, b1 = sphats.eigenstats(batch)
# make azimuth be in range (0,360) rather than (-180,180)
centre[1] += 360*(centre[1] < 0)
#results.append(np.concatenate((normed_centroid, polar_centroid, centre, b1, index_variety)))
results.append(np.concatenate((centre, b1, index_variety)))
return results
#dt_first_directions = tn.evecs[:,:,0].reshape((100,1000,3))
# these are the principal directions for the full set of simulations
#gq_tn_calc_save()
#eds=np.load(os.path.join(os.path.dirname(dp.__file__),'core','matrices','evenly_distributed_sphere_362.npz'))
from dipy.data import get_sphere
odf_vertices,odf_faces=get_sphere('symmetric362')
#odf_vertices=eds['vertices']
def run_comparisons(sample_data=35):
for simfile in [simdata[sample_data]]:
dataname = simfile
print dataname
sim_data=np.loadtxt(simdir+dataname)
gqfile = simdir+'gq/'+dataname+'.pkl'
gq = pkl.load_pickle(gqfile)
tnfile = simdir+'tn/'+dataname+'.pkl'
tn = pkl.load_pickle(tnfile)
dt_first_directions_in=odf_vertices[tn.IN]
dt_indices = tn.IN.reshape((100,1000))
dt_results = analyze_maxima(dt_indices, dt_first_directions_in.reshape((100,1000,3)),range(10,90))
gq_indices = np.array(gq.IN[:,0],dtype='int').reshape((100,1000))
gq_first_directions_in=odf_vertices[np.array(gq.IN[:,0],dtype='int')]
#print gq_first_directions_in.shape
gq_results = analyze_maxima(gq_indices, gq_first_directions_in.reshape((100,1000,3)),range(10,90))
#for gqi see example dicoms_2_tracks gq.IN[:,0]
np.set_printoptions(precision=3, suppress=True, linewidth=200, threshold=5000)
out = open('/home/ian/Data/SimVoxels/Out/'+'***_'+dataname,'w')
#print np.vstack(dt_results).shape, np.vstack(gq_results).shape
results = np.hstack((np.vstack(dt_results), np.vstack(gq_results)))
#print results.shape
#results = np.vstack(dt_results)
print >> out, results[:,:]
out.close()
#up = dt_batch[:,2]>= 0
#splots.plot_sphere(dt_batch[up], 'batch '+str(direction))
#splots.plot_lambert(dt_batch[up],'batch '+str(direction), centre)
#spread = gq.q2odf_params e,v = np.linalg.eigh(np.dot(spread,spread.transpose())) effective_dimension = len(find(np.cumsum(e) > 0.05*np.sum(e))) #95%
#rotated = np.dot(dt_batch,evecs)
#rot_evals, rot_evecs = np.linalg.eig(np.dot(rotated.T,rotated)/rotated.shape[0])
#eval_order = np.argsort(rot_evals)
#rotated = rotated[:,eval_order]
#up = rotated[:,2]>= 0
#splot.plot_sphere(rotated[up],'first1000')
#splot.plot_lambert(rotated[up],'batch '+str(direction))
def run_gq_sims(sample_data=[35,23,46,39,40,10,37,27,21,20]):
results = []
out = open('/home/ian/Data/SimVoxels/Out/'+'npa+fa','w')
for j in range(len(sample_data)):
sample = sample_data[j]
simfile = simdata[sample]
dataname = simfile
print dataname
sim_data=np.loadtxt(simdir+dataname)
marta_table_fname='/home/ian/Data/SimData/Dir_and_bvals_DSI_marta.txt'
b_vals_dirs=np.loadtxt(marta_table_fname)
bvals=b_vals_dirs[:,0]*1000
gradients=b_vals_dirs[:,1:]
for j in np.vstack((np.arange(100)*1000,np.arange(100)*1000+1)).T.ravel():
# 0,1,1000,1001,2000,2001,...
s = sim_data[j,:]
gqs = dp.GeneralizedQSampling(s.reshape((1,102)),bvals,gradients,Lambda=3.5)
tn = dp.Tensor(s.reshape((1,102)),bvals,gradients,fit_method='LS')
t0, t1, t2, npa = gqs.npa(s, width = 5)
print >> out, dataname, j, npa, tn.fa()[0]
'''
for (i,o) in enumerate(gqs.odf(s)):
print i,o
for (i,o) in enumerate(gqs.odf_vertices):
print i,o
'''
#o = gqs.odf(s)
#v = gqs.odf_vertices
#pole = v[t0[0]]
#eqv = dgqs.equatorial_zone_vertices(v, pole, 5)
#print 'Number of equatorial vertices: ', len(eqv)
#print np.max(o[eqv]),np.min(o[eqv])
#cos_e_pole = [np.dot(pole.T, v[i]) for i in eqv]
#print np.min(cos1), np.max(cos1)
#print 'equatorial max in equatorial vertices:', t1[0] in eqv
#x = np.cross(v[t0[0]],v[t1[0]])
#x = x/np.sqrt(np.sum(x**2))
#print x
#ptchv = dgqs.patch_vertices(v, x, 5)
#print len(ptchv)
#eqp = eqv[np.argmin([np.abs(np.dot(v[t1[0]].T,v[p])) for p in eqv])]
#print (eqp, o[eqp])
#print t2[0] in ptchv, t2[0] in eqv
#print np.dot(pole.T, v[t1[0]]), np.dot(pole.T, v[t2[0]])
#print ptchv[np.argmin([o[v] for v in ptchv])]
#gq_indices = np.array(gq.IN[:,0],dtype='int').reshape((100,1000))
#gq_first_directions_in=odf_vertices[np.array(gq.IN[:,0],dtype='int')]
#print gq_first_directions_in.shape
#gq_results = analyze_maxima(gq_indices, gq_first_directions_in.reshape((100,1000,3)),range(100))
#for gqi see example dicoms_2_tracks gq.IN[:,0]
#np.set_printoptions(precision=6, suppress=True, linewidth=200, threshold=5000)
#out = open('/home/ian/Data/SimVoxels/Out/'+'+++_'+dataname,'w')
#results = np.hstack((np.vstack(dt_results), np.vstack(gq_results)))
#results = np.vstack(dt_results)
#print >> out, results[:,:]
out.close()
def run_small_data():
#smalldir = '/home/ian/Devel/dipy/dipy/data/'
smalldir = '/home/eg309/Devel/dipy/dipy/data/'
# from os.path import join as opj
# bvals=np.load(opj(os.path.dirname(__file__), \
# 'data','small_64D.bvals.npy'))
bvals=np.load(smalldir+'small_64D.bvals.npy')
# gradients=np.load(opj(os.path.dirname(__file__), \
# 'data','small_64D.gradients.npy'))
gradients=np.load(smalldir+'small_64D.gradients.npy')
# img =ni.load(os.path.join(os.path.dirname(__file__),\
# 'data','small_64D.nii'))
img=nibabel.load(smalldir+'small_64D.nii')
small_data=img.get_data()
print 'real_data', small_data.shape
gqsmall = dgqs.GeneralizedQSampling(small_data,bvals,gradients)
tnsmall = ddti.Tensor(small_data,bvals,gradients)
x,y,z,a,b=tnsmall.evecs.shape
evecs=tnsmall.evecs
xyz=x*y*z
evecs = evecs.reshape(xyz,3,3)
#vs = np.sign(evecs[:,2,:])
#print vs.shape
#print np.hstack((vs,vs,vs)).reshape(1000,3,3).shape
#evecs = np.hstack((vs,vs,vs)).reshape(1000,3,3)
#print evecs.shape
evals=tnsmall.evals
evals = evals.reshape(xyz,3)
#print evals.shape
#print('GQS in %d' %(t2-t1))
'''
eds=np.load(opj(os.path.dirname(__file__),\
'..','matrices',\
'evenly_distributed_sphere_362.npz'))
'''
from dipy.data import get_sphere
odf_vertices,odf_faces=get_sphere('symmetric362')
#odf_vertices=eds['vertices']
#odf_faces=eds['faces']
#Yeh et.al, IEEE TMI, 2010
#calculate the odf using GQI
scaling=np.sqrt(bvals*0.01506) # 0.01506 = 6*D where D is the free
#water diffusion coefficient
#l_values sqrt(6 D tau) D free water
#diffusion coefficiet and tau included in the b-value
tmp=np.tile(scaling,(3,1))
b_vector=gradients.T*tmp
Lambda = 1.2 # smoothing parameter - diffusion sampling length
q2odf_params=np.sinc(np.dot(b_vector.T, odf_vertices.T) * Lambda/np.pi)
#implements equation no. 9 from Yeh et.al.
S=small_data.copy()
x,y,z,g=S.shape
S=S.reshape(x*y*z,g)
QA = np.zeros((x*y*z,5))
IN = np.zeros((x*y*z,5))
FA = tnsmall.fa().reshape(x*y*z)
fwd = 0
#Calculate Quantitative Anisotropy and find the peaks and the indices
#for every voxel
summary = {}
summary['vertices'] = odf_vertices
v = odf_vertices.shape[0]
summary['faces'] = odf_faces
f = odf_faces.shape[0]
for (i,s) in enumerate(S):
#print 'Volume %d' % i
istr = str(i)
summary[istr] = {}
t0, t1, t2, npa = gqsmall.npa(s, width = 5)
summary[istr]['triple']=(t0,t1,t2)
summary[istr]['npa']=npa
odf = Q2odf(s,q2odf_params)
peaks,inds=rp.peak_finding(odf,odf_faces)
fwd=max(np.max(odf),fwd)
#peaks = peaks - np.min(odf)
n_peaks=min(len(peaks),5)
peak_heights = [odf[i] for i in inds[:n_peaks]]
#QA[i][:l] = peaks[:n_peaks]
IN[i][:n_peaks] = inds[:n_peaks]
summary[istr]['odf'] = odf
summary[istr]['peaks'] = peaks
summary[istr]['inds'] = inds
summary[istr]['evecs'] = evecs[i,:,:]
summary[istr]['evals'] = evals[i,:]
summary[istr]['n_peaks'] = n_peaks
summary[istr]['peak_heights'] = peak_heights
# summary[istr]['fa'] = tnsmall.fa()[0]
summary[istr]['fa'] = FA[i]
'''
QA/=fwd
QA=QA.reshape(x,y,z,5)
IN=IN.reshape(x,y,z,5)
'''
peaks_1 = [i for i in range(1000) if summary[str(i)]['n_peaks']==1]
peaks_2 = [i for i in range(1000) if summary[str(i)]['n_peaks']==2]
peaks_3 = [i for i in range(1000) if summary[str(i)]['n_peaks']==3]
#peaks_2 = [i for i in range(1000) if len(summary[str(i)]['inds'])==2]
#peaks_3 = [i for i in range(1000) if len(summary[str(i)]['inds'])==3]
print '#voxels with 1, 2, 3 peaks', len(peaks_1),len(peaks_2),len(peaks_3)
return FA, summary
def Q2odf(s,q2odf_params):
''' construct odf for a voxel '''
odf=np.dot(s,q2odf_params)
return odf
#run_comparisons()
#run_gq_sims()
FA, summary = run_small_data()
peaks_1 = [i for i in range(1000) if summary[str(i)]['n_peaks']==1]
peaks_2 = [i for i in range(1000) if summary[str(i)]['n_peaks']==2]
peaks_3 = [i for i in range(1000) if summary[str(i)]['n_peaks']==3]
fa_npa_1 = [[summary[str(i)]['fa'], summary[str(i)]['npa'], summary[str(i)]['peak_heights']] for i in peaks_1]
fa_npa_2 = [[summary[str(i)]['fa'], summary[str(i)]['npa'], summary[str(i)]['peak_heights']] for i in peaks_2]
fa_npa_3 = [[summary[str(i)]['fa'], summary[str(i)]['npa'], summary[str(i)]['peak_heights']] for i in peaks_3]
| bsd-3-clause |
blab/antibody-response-pulse | bcell-array/code/Virus_Bcell_IgM_IgG_Landscape.py | 1 | 11385 |
# coding: utf-8
# # Antibody Response Pulse
# https://github.com/blab/antibody-response-pulse
#
# ### B-cells evolution --- cross-reactive antibody response after influenza virus infection or vaccination
# ### Adaptive immune response for repeated infection
# In[1]:
'''
author: Alvason Zhenhua Li
date: 04/09/2015
'''
get_ipython().magic(u'matplotlib inline')
import numpy as np
import matplotlib.pyplot as plt
import os
import alva_machinery_event_OAS_new as alva
AlvaFontSize = 23
AlvaFigSize = (15, 5)
numberingFig = 0
# equation plotting
dir_path = '/Users/al/Desktop/GitHub/antibody-response-pulse/bcell-array/figure'
file_name = 'Virus-Bcell-IgM-IgG'
figure_name = '-equation'
file_suffix = '.png'
save_figure = os.path.join(dir_path, file_name + figure_name + file_suffix)
numberingFig = numberingFig + 1
plt.figure(numberingFig, figsize=(12, 5))
plt.axis('off')
plt.title(r'$ Virus-Bcell-IgM-IgG \ equations \ (antibody-response \ for \ repeated-infection) $'
, fontsize = AlvaFontSize)
plt.text(0, 7.0/9, r'$ \frac{\partial V_n(t)}{\partial t} = +\mu_{v} V_{n}(t)(1 - \frac{V_n(t)}{V_{max}}) - \phi_{m} M_{n}(t) V_{n}(t) - \phi_{g} G_{n}(t) V_{n}(t) $'
, fontsize = 1.2*AlvaFontSize)
plt.text(0, 5.0/9, r'$ \frac{\partial B_n(t)}{\partial t} = +\mu_{b}V_{n}(t)(1 - \frac{V_n(t)}{V_{max}}) + (\beta_{m} + \beta_{g}) V_{n}(t) B_{n}(t) - \mu_{b} B_{n}(t) + m_b V_{n}(t)\frac{B_{i-1}(t) - 2B_i(t) + B_{i+1}(t)}{(\Delta i)^2} $'
, fontsize = 1.2*AlvaFontSize)
plt.text(0, 3.0/9,r'$ \frac{\partial M_n(t)}{\partial t} = +\xi_{m} B_{n}(t) - \phi_{m} M_{n}(t) V_{n}(t) - \mu_{m} M_{n}(t) $'
, fontsize = 1.2*AlvaFontSize)
plt.text(0, 1.0/9,r'$ \frac{\partial G_n(t)}{\partial t} = +\xi_{g} B_{n}(t) - \phi_{g} G_{n}(t) V_{n}(t) - \mu_{g} G_{n}(t) + m_a V_{n}(t)\frac{G_{i-1}(t) - 2G_i(t) + G_{i+1}(t)}{(\Delta i)^2} $'
, fontsize = 1.2*AlvaFontSize)
plt.savefig(save_figure, dpi = 100)
plt.show()
# define the V-M-G partial differential equations
def dVdt_array(VBMGxt = [], *args):
# naming
V = VBMGxt[0]
B = VBMGxt[1]
M = VBMGxt[2]
G = VBMGxt[3]
x_totalPoint = VBMGxt.shape[1]
# there are n dSdt
dV_dt_array = np.zeros(x_totalPoint)
# each dSdt with the same equation form
dV_dt_array[:] = +inRateV*V[:]*(1 - V[:]/maxV) - killRateVm*M[:]*V[:] - killRateVg*G[:]*V[:]
return(dV_dt_array)
def dBdt_array(VBMGxt = [], *args):
# naming
V = VBMGxt[0]
B = VBMGxt[1]
M = VBMGxt[2]
G = VBMGxt[3]
x_totalPoint = VBMGxt.shape[1]
# there are n dSdt
dB_dt_array = np.zeros(x_totalPoint)
# each dSdt with the same equation form
Bcopy = np.copy(B)
centerX = Bcopy[:]
leftX = np.roll(Bcopy[:], 1)
rightX = np.roll(Bcopy[:], -1)
leftX[0] = centerX[0]
rightX[-1] = centerX[-1]
dB_dt_array[:] = +inRateB*V[:]*(1 - V[:]/maxV) + (actRateBm + alva.event_active + alva.event_OAS_B)*V[:]*B[:] - outRateB*B[:] + mutatRateB*V[:]*(leftX[:] - 2*centerX[:] + rightX[:])/(dx**2)
return(dB_dt_array)
def dMdt_array(VBMGxt = [], *args):
# naming
V = VBMGxt[0]
B = VBMGxt[1]
M = VBMGxt[2]
G = VBMGxt[3]
x_totalPoint = VBMGxt.shape[1]
# there are n dSdt
dM_dt_array = np.zeros(x_totalPoint)
# each dSdt with the same equation form
dM_dt_array[:] = +inRateM*B[:] - consumeRateM*M[:]*V[:] - outRateM*M[:]
return(dM_dt_array)
def dGdt_array(VBMGxt = [], *args):
# naming
V = VBMGxt[0]
B = VBMGxt[1]
M = VBMGxt[2]
G = VBMGxt[3]
x_totalPoint = VBMGxt.shape[1]
# there are n dSdt
dG_dt_array = np.zeros(x_totalPoint)
# each dSdt with the same equation form
Gcopy = np.copy(G)
centerX = Gcopy[:]
leftX = np.roll(Gcopy[:], 1)
rightX = np.roll(Gcopy[:], -1)
leftX[0] = centerX[0]
rightX[-1] = centerX[-1]
dG_dt_array[:] = +(inRateG + alva.event_OAS)*B[:] - consumeRateG*G[:]*V[:] - outRateG*G[:] + mutatRateA*(leftX[:] - 2*centerX[:] + rightX[:])/(dx**2)
return(dG_dt_array)
# In[2]:
# setting parameter
timeUnit = 'year'
if timeUnit == 'hour':
hour = float(1)
day = float(24)
elif timeUnit == 'day':
day = float(1)
hour = float(1)/24
elif timeUnit == 'year':
year = float(1)
day = float(1)/365
hour = float(1)/24/365
maxV = float(50) # max virus/micro-liter
inRateV = 0.2/hour # in-rate of virus
killRateVm = 0.0003/hour # kill-rate of virus by antibody-IgM
killRateVg = killRateVm # kill-rate of virus by antibody-IgG
inRateB = 0.06/hour # in-rate of B-cell
outRateB = inRateB/8 # out-rate of B-cell
actRateBm = killRateVm # activation rate of naive B-cell
inRateM = 0.16/hour # in-rate of antibody-IgM from naive B-cell
outRateM = inRateM/1 # out-rate of antibody-IgM from naive B-cell
consumeRateM = killRateVm # consume-rate of antibody-IgM by cleaning virus
inRateG = inRateM/10 # in-rate of antibody-IgG from memory B-cell
outRateG = outRateM/250 # out-rate of antibody-IgG from memory B-cell
consumeRateG = killRateVg # consume-rate of antibody-IgG by cleaning virus
mutatRateB = 0.00002/hour # B-cell mutation rate
mutatRateA = 0.0002/hour # mutation rate
# time boundary and griding condition
minT = float(0)
maxT = float(10*12*30*day)
totalPoint_T = int(6*10**3 + 1)
gT = np.linspace(minT, maxT, totalPoint_T)
spacingT = np.linspace(minT, maxT, num = totalPoint_T, retstep = True)
gT = spacingT[0]
dt = spacingT[1]
# space boundary and griding condition
minX = float(0)
maxX = float(9)
totalPoint_X = int(maxX - minX + 1)
gX = np.linspace(minX, maxX, totalPoint_X)
gridingX = np.linspace(minX, maxX, num = totalPoint_X, retstep = True)
gX = gridingX[0]
dx = gridingX[1]
gV_array = np.zeros([totalPoint_X, totalPoint_T])
gB_array = np.zeros([totalPoint_X, totalPoint_T])
gM_array = np.zeros([totalPoint_X, totalPoint_T])
gG_array = np.zeros([totalPoint_X, totalPoint_T])
# initial output condition
#gV_array[1, 0] = float(2)
#[pre-parameter, post-parameter, recovered-day, OAS+, OSA-, origin_virus]
actRateBg_1st = 0.0002/hour # activation rate of memory B-cell at 1st time (pre-)
actRateBg_2nd = actRateBg_1st*10 # activation rate of memory B-cell at 2nd time (post-)
origin_virus = int(2)
current_virus = int(6)
event_parameter = np.array([[actRateBg_1st,
actRateBg_2nd,
14*day,
+5/hour,
-actRateBm - actRateBg_1st + (actRateBm + actRateBg_1st)/1.3,
origin_virus,
current_virus]])
# [viral population, starting time] ---first
infection_period = 12*30*day
viral_population = np.zeros(int(maxX + 1))
viral_population[origin_virus:current_virus + 1] = 3
infection_starting_time = np.arange(int(maxX + 1))*infection_period
event_1st = np.zeros([int(maxX + 1), 2])
event_1st[:, 0] = viral_population
event_1st[:, 1] = infection_starting_time
print ('event_1st = {:}'.format(event_1st))
# [viral population, starting time] ---2nd]
viral_population = np.zeros(int(maxX + 1))
viral_population[origin_virus:current_virus + 1] = 0
infection_starting_time = np.arange(int(maxX + 1))*0
event_2nd = np.zeros([int(maxX + 1), 2])
event_2nd[:, 0] = viral_population
event_2nd[:, 1] = infection_starting_time
print ('event_2nd = {:}'.format(event_2nd))
event_table = np.array([event_parameter, event_1st, event_2nd])
# Runge Kutta numerical solution
pde_array = np.array([dVdt_array, dBdt_array, dMdt_array, dGdt_array])
initial_Out = np.array([gV_array, gB_array, gM_array, gG_array])
gOut_array = alva.AlvaRungeKutta4XT(pde_array, initial_Out, minX, maxX, totalPoint_X, minT, maxT, totalPoint_T, event_table)
# plotting
gV = gOut_array[0]
gB = gOut_array[1]
gM = gOut_array[2]
gG = gOut_array[3]
numberingFig = numberingFig + 1
for i in range(totalPoint_X):
figure_name = '-response-%i'%(i)
figure_suffix = '.png'
save_figure = os.path.join(dir_path, file_name + figure_name + file_suffix)
plt.figure(numberingFig, figsize = AlvaFigSize)
plt.plot(gT, gV[i], color = 'red', label = r'$ V_{%i}(t) $'%(i), linewidth = 3.0, alpha = 0.5)
plt.plot(gT, gM[i], color = 'blue', label = r'$ IgM_{%i}(t) $'%(i), linewidth = 3.0, alpha = 0.5)
plt.plot(gT, gG[i], color = 'green', label = r'$ IgG_{%i}(t) $'%(i), linewidth = 3.0, alpha = 0.5)
plt.plot(gT, gM[i] + gG[i], color = 'gray', linewidth = 5.0, alpha = 0.5, linestyle = 'dashed'
, label = r'$ IgM_{%i}(t) + IgG_{%i}(t) $'%(i, i))
plt.grid(True, which = 'both')
plt.title(r'$ Antibody \ from \ Virus-{%i} $'%(i), fontsize = AlvaFontSize)
plt.xlabel(r'$time \ (%s)$'%(timeUnit), fontsize = AlvaFontSize)
plt.ylabel(r'$ Neutralization \ \ titer $', fontsize = AlvaFontSize)
plt.xlim([minT, maxT])
plt.xticks(fontsize = AlvaFontSize*0.6)
plt.yticks(fontsize = AlvaFontSize*0.6)
plt.ylim([2**0, 2**12])
plt.yscale('log', basey = 2)
plt.legend(loc = (1,0), fontsize = AlvaFontSize)
plt.savefig(save_figure, dpi = 100, bbox_inches='tight')
plt.show()
# In[3]:
# Normalization stacked graph
numberingFig = numberingFig + 1
plt.figure(numberingFig, figsize = AlvaFigSize)
plt.stackplot(gT, gM + gG, alpha = 0.3)
plt.title(r'$ Stacked-graph \ of \ Antibody $', fontsize = AlvaFontSize)
plt.xlabel(r'$time \ (%s)$'%(timeUnit), fontsize = AlvaFontSize)
plt.ylabel(r'$ Neutralization \ \ titer $', fontsize = AlvaFontSize)
plt.xticks(fontsize = AlvaFontSize*0.6)
plt.yticks(fontsize = AlvaFontSize*0.6)
plt.ylim([2**0, 2**12])
plt.yscale('log', basey = 2)
plt.grid(True)
plt.show()
# In[4]:
# expected peak of the antibody response
totalColor = current_virus - origin_virus + 1
AlvaColor = [plt.get_cmap('rainbow')(float(i)/(totalColor)) for i in range(1, totalColor + 1)]
sample_time = 90*day
# plotting
figure_name = '-landscape'
figure_suffix = '.png'
save_figure = os.path.join(dir_path, file_name + figure_name + file_suffix)
numberingFig = numberingFig + 1
plt.figure(numberingFig, figsize = (12, 9))
for i in range(origin_virus, current_virus + 1):
detect_xn = current_virus + 2 - i
if detect_xn == origin_virus:
virus_label = '$ origin-virus $'
elif detect_xn == current_virus:
virus_label = '$ current-virus $'
else: virus_label = '$ {:}th-virus $'.format(detect_xn - origin_virus + 1)
detect_time = int(totalPoint_T/(maxT - minT)*(detect_xn*infection_period + sample_time))
plt.plot(gX, gM[:, detect_time] + gG[:, detect_time], marker = 'o', markersize = 20
, color = AlvaColor[detect_xn - origin_virus], label = virus_label)
plt.fill_between(gX, gM[:, detect_time] + gG[:, detect_time], facecolor = AlvaColor[detect_xn - origin_virus]
, alpha = 0.5)
plt.grid(True, which = 'both')
plt.title(r'$ Antibody \ Landscape $', fontsize = AlvaFontSize)
plt.xlabel(r'$ Virus \ space \ (Antigenic-distance) $', fontsize = AlvaFontSize)
plt.ylabel(r'$ Neutralization \ \ titer $', fontsize = AlvaFontSize)
plt.xlim([minX, maxX])
plt.xticks(fontsize = AlvaFontSize)
plt.yticks(fontsize = AlvaFontSize)
plt.ylim([2**0, 2**9])
plt.yscale('log', basey = 2)
plt.legend(loc = (1,0), fontsize = AlvaFontSize)
plt.savefig(save_figure, dpi = 100, bbox_inches='tight')
plt.show()
# In[ ]:
| gpl-2.0 |
only4hj/fast-rcnn | lib/roi_data_layer/minibatch.py | 1 | 22641 | # --------------------------------------------------------
# Fast R-CNN
# Copyright (c) 2015 Microsoft
# Licensed under The MIT License [see LICENSE for details]
# Written by Ross Girshick
# --------------------------------------------------------
"""Compute minibatch blobs for training a Fast R-CNN network."""
import numpy as np
import numpy.random as npr
import cv2
from fast_rcnn.config import cfg
from utils.blob import prep_im_for_blob, im_list_to_blob
from utils.model import last_conv_size
from roi_data_layer.roidb import prepare_one_roidb_rpn, prepare_one_roidb_frcnn
from roidb import clear_one_roidb
def get_minibatch(roidb, num_classes, bbox_means, bbox_stds, proposal_file):
"""Given a roidb, construct a minibatch sampled from it."""
num_images = len(roidb)
# Sample random scales to use for each image in this batch
random_scale_inds = npr.randint(0, high=len(cfg.TRAIN.SCALES),
size=num_images)
assert(cfg.TRAIN.BATCH_SIZE % num_images == 0), \
'num_images ({}) must divide BATCH_SIZE ({})'. \
format(num_images, cfg.TRAIN.BATCH_SIZE)
rois_per_image = cfg.TRAIN.BATCH_SIZE / num_images
fg_rois_per_image = np.round(cfg.TRAIN.FG_FRACTION * rois_per_image)
# Get the input image blob, formatted for caffe
im_blob, im_scales, processed_ims = _get_image_blob(roidb, random_scale_inds)
if 'model_to_use' in roidb[0] and roidb[0]['model_to_use'] == 'rpn':
conv_h, scale_h = last_conv_size(im_blob.shape[2], cfg.MODEL_NAME)
conv_w, scale_w = last_conv_size(im_blob.shape[3], cfg.MODEL_NAME)
# Now, build the region of interest and label blobs
rois_blob = np.zeros((0, 5), dtype=np.float32)
labels_blob = np.zeros((0, 9, conv_h, conv_w), dtype=np.float32)
bbox_targets_blob = np.zeros((0, 36, conv_h, conv_w), dtype=np.float32)
bbox_loss_blob = np.zeros(bbox_targets_blob.shape, dtype=np.float32)
all_overlaps = []
for im_i in xrange(num_images):
if cfg.TRAIN.LAZY_PREPARING_ROIDB:
prepare_one_roidb_rpn(roidb[im_i],
processed_ims[im_i].shape[0],
processed_ims[im_i].shape[1],
im_scales[im_i])
# Normalize bbox_targets
if cfg.TRAIN.NORMALIZE_BBOX:
bbox_targets = roidb[im_i]['bbox_targets']
cls_inds = np.where(bbox_targets[:, 0] > 0)[0]
if cls_inds.size > 0:
bbox_targets[cls_inds, 1:] -= bbox_means[0, :]
bbox_targets[cls_inds, 1:] /= bbox_stds[0, :]
labels, overlaps, im_rois, bbox_targets, bbox_loss \
= _sample_rois_rpn(roidb[im_i], fg_rois_per_image, rois_per_image,
num_classes, conv_h, conv_w)
# Add to RoIs blob
if im_rois != None:
batch_ind = im_i * np.ones((im_rois.shape[0], 1))
rois_blob_this_image = np.hstack((batch_ind, im_rois))
rois_blob = np.vstack((rois_blob, rois_blob_this_image))
# Add to labels, bbox targets, and bbox loss blobs
labels_blob = np.vstack((labels_blob, labels))
bbox_targets_blob = np.vstack((bbox_targets_blob, bbox_targets))
bbox_loss_blob = np.vstack((bbox_loss_blob, bbox_loss))
# For debug visualizations
#_vis_minibatch_rpn(im_blob, conv_h, conv_w, rois_blob, labels_blob, roidb, bbox_targets_blob, bbox_loss_blob)
blobs = {'data': im_blob,
'labels': labels_blob}
else:
# Now, build the region of interest and label blobs
rois_blob = np.zeros((0, 5), dtype=np.float32)
labels_blob = np.zeros((0), dtype=np.float32)
bbox_targets_blob = np.zeros((0, 4 * num_classes), dtype=np.float32)
bbox_loss_blob = np.zeros(bbox_targets_blob.shape, dtype=np.float32)
all_overlaps = []
for im_i in xrange(num_images):
if cfg.TRAIN.LAZY_PREPARING_ROIDB:
prepare_one_roidb_frcnn(roidb[im_i], proposal_file, num_classes)
# Normalize bbox_targets
if cfg.TRAIN.NORMALIZE_BBOX:
bbox_targets = roidb[im_i]['bbox_targets']
for cls in xrange(1, num_classes):
cls_inds = np.where(bbox_targets[:, 0] == cls)[0]
bbox_targets[cls_inds, 1:] -= bbox_means[cls, :]
bbox_targets[cls_inds, 1:] /= bbox_stds[cls, :]
labels, overlaps, im_rois, bbox_targets, bbox_loss \
= _sample_rois(roidb[im_i], fg_rois_per_image, rois_per_image,
num_classes)
# Add to RoIs blob
rois = _project_im_rois(im_rois, im_scales[im_i])
batch_ind = im_i * np.ones((rois.shape[0], 1))
rois_blob_this_image = np.hstack((batch_ind, rois))
rois_blob = np.vstack((rois_blob, rois_blob_this_image))
# Add to labels, bbox targets, and bbox loss blobs
labels_blob = np.hstack((labels_blob, labels))
bbox_targets_blob = np.vstack((bbox_targets_blob, bbox_targets))
bbox_loss_blob = np.vstack((bbox_loss_blob, bbox_loss))
#all_overlaps = np.hstack((all_overlaps, overlaps))
# For debug visualizations
#_vis_minibatch(im_blob, rois_blob, labels_blob, all_overlaps)
blobs = {'data': im_blob,
'rois': rois_blob,
'labels': labels_blob}
if cfg.TRAIN.BBOX_REG:
blobs['bbox_targets'] = bbox_targets_blob
blobs['bbox_loss_weights'] = bbox_loss_blob
return blobs
def clear_minibatch(roidb):
num_images = len(roidb)
for im_i in xrange(num_images):
clear_one_roidb(roidb[im_i])
def _sample_rois(roidb, fg_rois_per_image, rois_per_image, num_classes):
"""Generate a random sample of RoIs comprising foreground and background
examples.
"""
# label = class RoI has max overlap with
labels = roidb['max_classes']
overlaps = roidb['max_overlaps']
rois = roidb['boxes']
# Select foreground RoIs as those with >= FG_THRESH overlap
fg_inds = np.where(overlaps >= cfg.TRAIN.FG_THRESH)[0]
# Guard against the case when an image has fewer than fg_rois_per_image
# foreground RoIs
fg_rois_per_this_image = np.minimum(fg_rois_per_image, fg_inds.size)
# Sample foreground regions without replacement
if fg_inds.size > 0:
fg_inds = npr.choice(fg_inds, size=fg_rois_per_this_image,
replace=False)
# Select background RoIs as those within [BG_THRESH_LO, BG_THRESH_HI)
bg_inds = np.where((overlaps < cfg.TRAIN.BG_THRESH_HI) &
(overlaps >= cfg.TRAIN.BG_THRESH_LO))[0]
# Compute number of background RoIs to take from this image (guarding
# against there being fewer than desired)
bg_rois_per_this_image = rois_per_image - fg_rois_per_this_image
bg_rois_per_this_image = np.minimum(bg_rois_per_this_image,
bg_inds.size)
# Sample foreground regions without replacement
if bg_inds.size > 0:
bg_inds = npr.choice(bg_inds, size=bg_rois_per_this_image,
replace=False)
# The indices that we're selecting (both fg and bg)
keep_inds = np.append(fg_inds, bg_inds)
# Select sampled values from various arrays:
labels = labels[keep_inds]
# Clamp labels for the background RoIs to 0
labels[fg_rois_per_this_image:] = 0
overlaps = overlaps[keep_inds]
rois = rois[keep_inds]
bbox_targets, bbox_loss_weights = \
_get_bbox_regression_labels(roidb['bbox_targets'][keep_inds, :],
num_classes)
return labels, overlaps, rois, bbox_targets, bbox_loss_weights
def get_img_rect(img_height, img_width, conv_height, conv_width, axis1, axis2, axis3):
anchors = np.array([[128*2, 128*1], [128*1, 128*1], [128*1, 128*2],
[256*2, 256*1], [256*1, 256*1], [256*1, 256*2],
[512*2, 512*1], [512*1, 512*1], [512*1, 512*2]])
scale_width = img_width / conv_width
scale_height = img_height / conv_height
img_center_x = img_width * axis3 / conv_width + scale_width / 2
img_center_y = img_height * axis2 / conv_height + scale_height / 2
anchor_size = anchors[axis1]
img_x1 = img_center_x - anchor_size[0] / 2
img_x2 = img_center_x + anchor_size[0] / 2
img_y1 = img_center_y - anchor_size[1] / 2
img_y2 = img_center_y + anchor_size[1] / 2
return [img_x1, img_y1, img_x2, img_y2]
def _sample_rois_rpn(roidb, fg_rois_per_image, rois_per_image, num_classes,
union_conv_height, union_conv_width):
"""Generate a random sample of RoIs comprising foreground and background
examples.
"""
# label = class RoI has max overlap with
labels = roidb['max_classes']
new_labels = np.zeros(labels.shape, dtype=np.int16)
new_labels.fill(-1)
bbox_target = roidb['bbox_targets']
new_bbox_target = np.zeros(bbox_target.shape, dtype=np.float32)
conv_width = roidb['conv_width']
conv_height = roidb['conv_height']
# Select foreground RoIs as those with >= FG_THRESH overlap
fg_inds = np.where(labels > 0)[0]
# Guard against the case when an image has fewer than fg_rois_per_image
# foreground RoIs
fg_rois_per_this_image = np.minimum(fg_rois_per_image, fg_inds.size)
# Sample foreground regions without replacement
if fg_inds.size > 0:
fg_inds = npr.choice(fg_inds, size=fg_rois_per_this_image,
replace=False)
# Select background RoIs as those within [BG_THRESH_LO, BG_THRESH_HI)
bg_inds = np.where(labels == 0)[0]
# Compute number of background RoIs to take from this image (guarding
# against there being fewer than desired)
bg_rois_per_this_image = rois_per_image - fg_rois_per_this_image
bg_rois_per_this_image = np.minimum(bg_rois_per_this_image,
bg_inds.size)
# Sample foreground regions without replacement
if bg_inds.size > 0:
bg_inds = npr.choice(bg_inds, size=bg_rois_per_this_image,
replace=False)
new_labels[fg_inds] = 1
new_labels[bg_inds] = 0
if 'rois' in roidb:
rois = roidb['rois'][fg_inds]
else:
rois = None
"""
print 'labels.shape %s' % labels.shape
print 'bbox_target.shape %s' % (bbox_target.shape, )
for fg_ind in fg_inds:
print 'label : %s ' % labels[fg_ind]
print 'bbox_target : %s ' % bbox_target[fg_ind]
axis1 = fg_ind / conv_height / conv_width
axis2 = fg_ind / conv_width % conv_height
axis3 = fg_ind % conv_width
im = cv2.imread(roidb['image'])
target_size = cfg.TRAIN.SCALES[0]
im, im_scale = prep_im_for_blob(im, 0, target_size,
cfg.TRAIN.MAX_SIZE,
cfg.TRAIN.MIN_SIZE)
img_height = im.shape[2]
img_width = im.shape[3]
proposal_rects = get_img_rect(img_height, img_width, conv_height, conv_width, axis1, axis2, axis3)
for proposal_rect in proposal_rects:
plt.imshow(im)
for ground_rect in ground_rects:
plt.gca().add_patch(
plt.Rectangle((ground_rect[0], ground_rect[1]), ground_rect[2] - ground_rect[0],
ground_rect[3] - ground_rect[1], fill=False,
edgecolor='b', linewidth=3)
)
plt.gca().add_patch(
plt.Rectangle((proposal_rect[0], proposal_rect[1]), proposal_rect[2] - proposal_rect[0],
proposal_rect[3] - proposal_rect[1], fill=False,
edgecolor='g', linewidth=3)
)
plt.gca().add_patch(
plt.Rectangle((pred_rect[0], pred_rect[1]), pred_rect[2] - pred_rect[0],
pred_rect[3] - pred_rect[1], fill=False,
edgecolor='r', linewidth=3)
)
plt.show(block=False)
raw_input("")
plt.close()
"""
new_bbox_target[fg_inds] = bbox_target[fg_inds]
new_bbox_target, bbox_loss_weights = \
_get_bbox_regression_labels_rpn(new_bbox_target,
num_classes, labels)
"""
print 'label no 1 : %s' % len(np.where(new_labels == 1)[0])
print 'new_bbox_target no 1 : %s' % len(np.where(new_bbox_target != 0)[0])
print 'bbox_loss_weights no 1 : %s' % len(np.where(bbox_loss_weights > 0)[0])
"""
new_labels = new_labels.reshape((1, 9, conv_height, conv_width))
new_bbox_target = new_bbox_target.reshape((1, 9, conv_height, conv_width, 4))
new_bbox_target = new_bbox_target.transpose(0, 1, 4, 2, 3)
new_bbox_target = new_bbox_target.reshape((1, 36, conv_height, conv_width))
bbox_loss_weights = bbox_loss_weights.reshape((1, 9, conv_height, conv_width, 4))
bbox_loss_weights = bbox_loss_weights.transpose(0, 1, 4, 2, 3)
bbox_loss_weights = bbox_loss_weights.reshape((1, 36, conv_height, conv_width))
output_labels = np.zeros((1, 9, union_conv_height, union_conv_width))
output_bbox_targets = np.zeros((1, 36, union_conv_height, union_conv_width))
output_bbox_loss_weights = np.zeros((1, 36, union_conv_height, union_conv_width))
output_labels.fill(-1)
output_labels[:, :, 0:conv_height, 0:conv_width] = new_labels
output_bbox_targets[:, :, 0:conv_height, 0:conv_width] = new_bbox_target
output_bbox_loss_weights[:, :, 0:conv_height, 0:conv_width] = bbox_loss_weights
"""
for fg_ind in fg_inds:
if fg_ind == 6510:
axis1 = fg_ind / conv_height / conv_width
axis2 = fg_ind / conv_width % conv_height
axis3 = fg_ind % conv_width
print ''
print 'conv_size : %s, %s' % (conv_height, conv_width)
print 'axis : %s, %s, %s' % (axis1, axis2, axis3)
print 'output_labels[%s] : %s' % (fg_ind, output_labels[0, axis1, axis2, axis3])
print 'output_bbox_targets[%s] : %s' % (fg_ind, output_bbox_targets[0, axis1*4:axis1*4+4, axis2, axis3])
print 'output_bbox_loss_weights[%s] : %s' % (fg_ind, output_bbox_loss_weights[0, axis1*4:axis1*4+4, axis2, axis3])
"""
"""
# Generate positive rois based on index for debugging
anchors = [[128*2, 128*1], [128*1, 128*1], [128*1, 128*2],
[256*2, 256*1], [256*1, 256*1], [256*1, 256*2],
[512*2, 512*1], [512*1, 512*1], [512*1, 512*2]]
conv_scale_width = roidb['conv_scale_width']
conv_scale_height = roidb['conv_scale_height']
rois = np.zeros((len(fg_inds), 4), dtype=np.int16)
for i, fg_ind in enumerate(fg_inds):
center_x = fg_ind % conv_width
center_y = (fg_ind - center_x) / conv_width % conv_height
anchor = fg_ind / conv_height / conv_width
anchor_w = anchors[anchor][0]
anchor_h = anchors[anchor][1]
x1 = center_x * conv_scale_width - anchor_w / 2
y1 = center_y * conv_scale_height - anchor_h / 2
x2 = x1 + anchor_w
y2 = y1 + anchor_h
rois[i, :] = x1, y1, x2, y2
"""
"""
pos_labels = np.where(new_labels == 1)
i = 0
for d0, d1, d2, d3 in zip(pos_labels[0], pos_labels[1], pos_labels[2], pos_labels[3]):
print '[%s] label : %s, bbox_target : %s, bbox_loss_weights : %s' % (i, new_labels[d0, d1, d2, d3],
new_bbox_target[d0, d1*4 : d1*4+4, d2, d3],
bbox_loss_weights[d0, d1*4 : d1*4+4, d2, d3])
i += 1
"""
"""
print 'label no 2 : %s' % len(np.where(output_labels == 1)[0])
print 'new_bbox_target no 2 : %s' % len(np.where(output_bbox_targets != 0)[0])
print 'bbox_loss_weights no 2 : %s' % len(np.where(output_bbox_loss_weights > 0)[0])
"""
return output_labels, None, rois, output_bbox_targets, output_bbox_loss_weights
def _get_image_blob(roidb, scale_inds):
"""Builds an input blob from the images in the roidb at the specified
scales.
"""
num_images = len(roidb)
processed_ims = []
im_scales = []
for i in xrange(num_images):
im = cv2.imread(roidb[i]['image'])
if roidb[i]['flipped']:
im = im[:, ::-1, :]
target_size = cfg.TRAIN.SCALES[scale_inds[i]]
im, im_scale = prep_im_for_blob(im, cfg.PIXEL_MEANS, target_size,
cfg.TRAIN.MAX_SIZE,
cfg.TRAIN.MIN_SIZE)
im_scales.append(im_scale)
processed_ims.append(im)
# Create a blob to hold the input images
blob = im_list_to_blob(processed_ims)
return blob, im_scales, processed_ims
def _project_im_rois(im_rois, im_scale_factor):
"""Project image RoIs into the rescaled training image."""
rois = im_rois * im_scale_factor
return rois
def _get_bbox_regression_labels(bbox_target_data, num_classes):
"""Bounding-box regression targets are stored in a compact form in the
roidb.
This function expands those targets into the 4-of-4*K representation used
by the network (i.e. only one class has non-zero targets). The loss weights
are similarly expanded.
Returns:
bbox_target_data (ndarray): N x 4K blob of regression targets
bbox_loss_weights (ndarray): N x 4K blob of loss weights
"""
clss = bbox_target_data[:, 0]
bbox_targets = np.zeros((clss.size, 4 * num_classes), dtype=np.float32)
bbox_loss_weights = np.zeros(bbox_targets.shape, dtype=np.float32)
inds = np.where(clss > 0)[0]
for ind in inds:
cls = clss[ind]
start = 4 * cls
end = start + 4
bbox_targets[ind, start:end] = bbox_target_data[ind, 1:]
bbox_loss_weights[ind, start:end] = [1., 1., 1., 1.]
return bbox_targets, bbox_loss_weights
def _get_bbox_regression_labels_rpn(bbox_target_data, num_classes, labels):
"""Bounding-box regression targets are stored in a compact form in the
roidb.
This function expands those targets into the 4-of-4*K representation used
by the network (i.e. only one class has non-zero targets). The loss weights
are similarly expanded.
Returns:
bbox_target_data (ndarray): N x 4K blob of regression targets
bbox_loss_weights (ndarray): N x 4K blob of loss weights
"""
clss = bbox_target_data[:, 0]
bbox_targets = np.zeros((clss.size, 4), dtype=np.float32)
bbox_loss_weights = np.zeros(bbox_targets.shape, dtype=np.float32)
inds = np.where(clss > 0)[0]
#print ''
#print 'len(inds) : %s' % len(inds)
for ind in inds:
bbox_targets[ind, :] = bbox_target_data[ind, 1:]
bbox_loss_weights[ind, :] = [1., 1., 1., 1.]
#print 'bbox_targets[ind, :] : %s - %s ' % (bbox_target_data[ind, 0], bbox_targets[ind, :])
return bbox_targets, bbox_loss_weights
def _vis_minibatch(im_blob, rois_blob, labels_blob, overlaps):
"""Visualize a mini-batch for debugging."""
import matplotlib.pyplot as plt
for i in xrange(rois_blob.shape[0]):
rois = rois_blob[i, :]
im_ind = rois[0]
roi = rois[1:]
im = im_blob[im_ind, :, :, :].transpose((1, 2, 0)).copy()
im += cfg.PIXEL_MEANS
im = im[:, :, (2, 1, 0)]
im = im.astype(np.uint8)
cls = labels_blob[i]
plt.imshow(im)
print 'class: ', cls, ' overlap: ', overlaps[i]
plt.gca().add_patch(
plt.Rectangle((roi[0], roi[1]), roi[2] - roi[0],
roi[3] - roi[1], fill=False,
edgecolor='r', linewidth=3)
)
plt.show()
def _vis_minibatch_rpn(im_blob, conv_h, conv_w, rois_blob, labels_blob, roidb, bbox_targets_blob, bbox_loss_blob):
"""Visualize a mini-batch for debugging."""
import matplotlib.pyplot as plt
for i in xrange(len(roidb)):
# DJDJ
#if roidb[i]['image'].endswith('000009.jpg') == False:
# continue
print 'image : %s' % roidb[i]['image']
resized_gt_boxes = roidb[int(i)]['resized_gt_boxes']
im = im_blob[i, :, :, :].transpose((1, 2, 0)).copy()
im += cfg.PIXEL_MEANS
im = im[:, :, (2, 1, 0)]
im = im.astype(np.uint8)
for j in range(9):
for k in range(labels_blob.shape[2]):
for l in range(labels_blob.shape[3]):
label = labels_blob[i][j][k][l]
if label == -1:
continue
elif label == 1:
color = 'g'
elif label == 0:
#color = 'y'
continue
plt.imshow(im)
for resized_gt_box in resized_gt_boxes:
resized_gt_box = resized_gt_box.astype(np.int)
plt.gca().add_patch(
plt.Rectangle((resized_gt_box[0], resized_gt_box[1]), resized_gt_box[2] - resized_gt_box[0],
resized_gt_box[3] - resized_gt_box[1], fill=False,
edgecolor='b', linewidth=3)
)
proposal_rects = get_img_rect(im.shape[0], im.shape[1], conv_h, conv_w, j, k, l)
plt.gca().add_patch(
plt.Rectangle((proposal_rects[0], proposal_rects[1]), proposal_rects[2] - proposal_rects[0],
proposal_rects[3] - proposal_rects[1], fill=False,
edgecolor=color, linewidth=3)
)
plt.show(block=False)
raw_input("")
plt.close()
| mit |
rodluger/everest | docs/mcmc.py | 1 | 2721 | """MCMC example for transit fitting."""
import matplotlib.pyplot as pl
from everest import Everest, TransitModel
import numpy as np
import emcee
from tqdm import tqdm
from corner import corner
def lnprior(x):
"""Return the log prior given parameter vector `x`."""
per, t0, b = x
if b < -1 or b > 1:
return -np.inf
elif per < 7 or per > 10:
return -np.inf
elif t0 < 1978 or t0 > 1979:
return -np.inf
else:
return 0.
def lnlike(x, star):
"""Return the log likelihood given parameter vector `x`."""
ll = lnprior(x)
if np.isinf(ll):
return ll, (np.nan, np.nan)
per, t0, b = x
model = TransitModel('b', per=per, t0=t0, b=b, rhos=10.)(star.time)
like, d, vard = star.lnlike(model, full_output=True)
ll += like
return ll, (d,)
# Initialize the everest model
star = Everest(201635569)
# Set up the MCMC sampler
params = ['Period (days)', r't$_0$ (BJD - 2456811)', 'Impact parameter']
blobs = ['Depth (%)']
nsteps = 1000
nburn = 300
nwalk = 10
ndim = len(params)
nblobs = len(blobs)
sampler = emcee.EnsembleSampler(nwalk, ndim, lnlike, args=[star])
x0 = [[8.368 + 0.01 * np.random.randn(),
1978.4513 + 0.01 * np.random.randn(),
0. + 0.1 * np.random.randn()] for k in range(nwalk)]
blobs0 = [[0.] for k in range(nwalk)]
# Run!
for i in tqdm(sampler.sample(x0, iterations=nsteps, blobs0=blobs0),
total=nsteps):
pass
# Add the blobs to the chain for plotting
chain = np.concatenate((sampler.chain,
np.array(sampler.blobs).swapaxes(0, 1)), axis=2)
# Re-scale the transit time for prettier axes labels
chain[:, :, 1] -= 1978.
# Take the absolute value of the impact parameter for plotting
chain[:, :, 2] = np.abs(chain[:, :, 2])
# Re-scale the transit depth as a percentage
chain[:, :, 3] *= 100.
# Plot the chains
fig1, ax = pl.subplots(ndim + nblobs, figsize=(6, 7))
fig1.suptitle("K2-14b", fontsize=16, fontweight='bold')
ax[-1].set_xlabel("Iteration", fontsize=14)
for n in range(ndim + nblobs):
for k in range(nwalk):
ax[n].plot(chain[k, :, n], alpha=0.3, lw=1)
ax[n].set_ylabel((params + blobs)[n], fontsize=9)
ax[n].margins(0, None)
ax[n].axvline(nburn, color='b', alpha=0.5, lw=1, ls='--')
fig1.savefig("k2-14b_chains.png", bbox_inches='tight')
# Plot the posterior distributions
samples = chain[:, nburn:, :].reshape(-1, ndim + nblobs)
fig2 = corner(samples, labels=params + blobs)
fig2.suptitle("K2-14b", fontsize=16, fontweight='bold')
fig2.set_size_inches(6, 6)
for ax in fig2.axes:
for tick in ax.get_xticklabels() + ax.get_yticklabels():
tick.set_fontsize(7)
fig2.savefig("k2-14b_corner.png", bbox_inches='tight')
| mit |
cxcsds/ciao-contrib | crates_contrib/images.py | 1 | 4630 | #
# Copyright (C) 2012, 2015, 2016, 2019
# Smithsonian Astrophysical Observatory
#
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
#
"""
Image-specific Crates routines.
At present there is only one routine - imextent.
"""
from pytransform import LINEAR2DTransform
__all__ = ('imextent', )
def imextent(img, xmin, xmax, ymin, ymax, limits='center'):
"""Create a linear transform for the image axes.
Returns a 2D linear transform object that represents the
mapping from "pixel" units (e.g. logical values) to
a linearly scaled system (offset and scale change, no
rotation). One use of this is to mimic the extent
argument from matplotlib's imshow command, as discussed
in the examples below.
Parameters
----------
img : 2D NumPy array
xmin, xmax, ymin, ymax : float
The coordinates of the lower-left and upper-right
corners of the image in the transformed (non-logical)
system.
limits : {'center', 'edge'}
Do the coordinates (xmin, ..., ymax) refer to the
center of the pixels, or their edges. In FITS convention,
the bottom-left pixel is centered on 1,1 and the top-right
pixel is nx,ny (for a nx by ny grid). With limits='center'
xmin,xmax refers to the center of the lower-left pixel
(i.e. 1,1 in FITS terminology) whereas with limits='edge'
it refers to the bottom-left corner (0.5,0.5 in FITS).
Returns
-------
tr : pytransform.LINEAR2DTransform
The transform object containing the coordinate mapping.
Notes
-----
The logical coordinate system follows the FITS standard, so the
first pixel is (1,1) and not (0,0), and the X axis values are
given first.
Examples
--------
The following example creates a 40 pixel wide by 20 pixel high
image, zi, where the X axis goes from 40 to 60 and the Y
axis 10 to 20. The imextent call creates a transform object.
>>> yi, xi = np.mgrid[10:20:20j, 40:60:40j]
>>> zi = 100.0 / np.sqrt((xi - 45.62) ** 2 + (yi - 14.7) ** 2)
>>> tr = imextent(zi, 40, 60, 10, 20)
The transform object can be used to convert between logical
coordinates (where 1,1 refers to the center of the lower-left
pixel) and the data coordinates:
>>> print(tr.apply([[1,1], [40,20]]))
[[40 10]
[60 20]]
and the invert method goes from data to logical coordinates:
>>> print(tr.invert([[45.0, 15.0]]))
[[ 10.75 10.5 ]]
The following examples use a 4 pixel by 3 pixel image:
>>> img = np.arange(0, 12).reshape(3, 4)
The default value for the limits argument is 'center', which
means that the given coordinates - in this case 10,-10 and
13,-6 - refer to the center of the bottom-left and top-right
pixels:
>>> tr_cen = imextent(img, 10, 13, -10, -6, limits='center')
The alternative is limits='edge', where 10,-10 refers to the
bottom-left corner of the image and 13,-6 refers to the
top-right corner:
>>> tr_edge = imextent(img, 10, 13, -10, -6, limits='edge')
>>> print(tr_cen.apply([[1.0, 1.0]]))
[[ 10. -10.]]
>>> print(tr_edge.apply([[1.0, 1.0]]))
[[ 10.375 -9.33333333]]
"""
try:
(ny, nx) = img.shape
except AttributeError:
raise ValueError("First argument has no shape attribute.")
dx = (xmax - xmin) * 1.0
dy = (ymax - ymin) * 1.0
if limits == 'center':
dx /= (nx - 1.0)
dy /= (ny - 1.0)
x0 = xmin - dx
y0 = ymin - dy
elif limits == 'edge':
dx /= nx
dy /= ny
x0 = xmin - dx / 2.0
y0 = ymin - dy / 2.0
else:
raise ValueError("limits must be 'center' or 'edge', not '{}'".format(limits))
tr = LINEAR2DTransform()
tr.get_parameter('ROTATION').set_value(0.0)
tr.get_parameter('SCALE').set_value([dx, dy])
tr.get_parameter('OFFSET').set_value([x0, y0])
return tr
| gpl-3.0 |
rasbt/python-machine-learning-book | code/optional-py-scripts/ch05.py | 1 | 19830 | # Sebastian Raschka, 2015 (http://sebastianraschka.com)
# Python Machine Learning - Code Examples
#
# Chapter 5 - Compressing Data via Dimensionality Reduction
#
# S. Raschka. Python Machine Learning. Packt Publishing Ltd., 2015.
# GitHub Repo: https://github.com/rasbt/python-machine-learning-book
#
# License: MIT
# https://github.com/rasbt/python-machine-learning-book/blob/master/LICENSE.txt
import pandas as pd
import numpy as np
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from sklearn.linear_model import LogisticRegression
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
from sklearn.datasets import make_moons
from sklearn.datasets import make_circles
from sklearn.decomposition import KernelPCA
from scipy.spatial.distance import pdist, squareform
from scipy import exp
from scipy.linalg import eigh
from matplotlib.ticker import FormatStrFormatter
# for sklearn 0.18's alternative syntax
from distutils.version import LooseVersion as Version
from sklearn import __version__ as sklearn_version
if Version(sklearn_version) < '0.18':
from sklearn.grid_search import train_test_split
from sklearn.lda import LDA
else:
from sklearn.model_selection import train_test_split
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
#############################################################################
print(50 * '=')
print('Section: Unsupervised dimensionality reduction'
' via principal component analysis')
print(50 * '-')
df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/'
'machine-learning-databases/wine/wine.data',
header=None)
df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash',
'Alcalinity of ash', 'Magnesium', 'Total phenols',
'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins',
'Color intensity', 'Hue',
'OD280/OD315 of diluted wines', 'Proline']
print('Wine data excerpt:\n\n:', df_wine.head())
X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values
X_train, X_test, y_train, y_test = \
train_test_split(X, y, test_size=0.3, random_state=0)
sc = StandardScaler()
X_train_std = sc.fit_transform(X_train)
X_test_std = sc.transform(X_test)
cov_mat = np.cov(X_train_std.T)
eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)
print('\nEigenvalues \n%s' % eigen_vals)
#############################################################################
print(50 * '=')
print('Section: Total and explained variance')
print(50 * '-')
tot = sum(eigen_vals)
var_exp = [(i / tot) for i in sorted(eigen_vals, reverse=True)]
cum_var_exp = np.cumsum(var_exp)
plt.bar(range(1, 14), var_exp, alpha=0.5, align='center',
label='individual explained variance')
plt.step(range(1, 14), cum_var_exp, where='mid',
label='cumulative explained variance')
plt.ylabel('Explained variance ratio')
plt.xlabel('Principal components')
plt.legend(loc='best')
# plt.tight_layout()
# plt.savefig('./figures/pca1.png', dpi=300)
plt.show()
#############################################################################
print(50 * '=')
print('Section: Feature Transformation')
print(50 * '-')
# Make a list of (eigenvalue, eigenvector) tuples
eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i])
for i in range(len(eigen_vals))]
# Sort the (eigenvalue, eigenvector) tuples from high to low
eigen_pairs.sort(reverse=True)
w = np.hstack((eigen_pairs[0][1][:, np.newaxis],
eigen_pairs[1][1][:, np.newaxis]))
print('Matrix W:\n', w)
X_train_pca = X_train_std.dot(w)
colors = ['r', 'b', 'g']
markers = ['s', 'x', 'o']
for l, c, m in zip(np.unique(y_train), colors, markers):
plt.scatter(X_train_pca[y_train == l, 0],
X_train_pca[y_train == l, 1],
c=c, label=l, marker=m)
plt.xlabel('PC 1')
plt.ylabel('PC 2')
plt.legend(loc='lower left')
# plt.tight_layout()
# plt.savefig('./figures/pca2.png', dpi=300)
plt.show()
print('Dot product:\n', X_train_std[0].dot(w))
#############################################################################
print(50 * '=')
print('Section: Principal component analysis in scikit-learn')
print(50 * '-')
pca = PCA()
X_train_pca = pca.fit_transform(X_train_std)
print('Variance explained ratio:\n', pca.explained_variance_ratio_)
plt.bar(range(1, 14), pca.explained_variance_ratio_, alpha=0.5, align='center')
plt.step(range(1, 14), np.cumsum(pca.explained_variance_ratio_), where='mid')
plt.ylabel('Explained variance ratio')
plt.xlabel('Principal components')
plt.show()
pca = PCA(n_components=2)
X_train_pca = pca.fit_transform(X_train_std)
X_test_pca = pca.transform(X_test_std)
plt.scatter(X_train_pca[:, 0], X_train_pca[:, 1])
plt.xlabel('PC 1')
plt.ylabel('PC 2')
plt.show()
def plot_decision_regions(X, y, classifier, resolution=0.02):
# setup marker generator and color map
markers = ('s', 'x', 'o', '^', 'v')
colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')
cmap = ListedColormap(colors[:len(np.unique(y))])
# plot the decision surface
x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1
x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),
np.arange(x2_min, x2_max, resolution))
Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
Z = Z.reshape(xx1.shape)
plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)
plt.xlim(xx1.min(), xx1.max())
plt.ylim(xx2.min(), xx2.max())
# plot class samples
for idx, cl in enumerate(np.unique(y)):
plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1],
alpha=0.8, c=cmap(idx),
marker=markers[idx], label=cl)
lr = LogisticRegression()
lr = lr.fit(X_train_pca, y_train)
plot_decision_regions(X_train_pca, y_train, classifier=lr)
plt.xlabel('PC 1')
plt.ylabel('PC 2')
plt.legend(loc='lower left')
# plt.tight_layout()
# plt.savefig('./figures/pca3.png', dpi=300)
plt.show()
plot_decision_regions(X_test_pca, y_test, classifier=lr)
plt.xlabel('PC 1')
plt.ylabel('PC 2')
plt.legend(loc='lower left')
# plt.tight_layout()
# plt.savefig('./figures/pca4.png', dpi=300)
plt.show()
pca = PCA(n_components=None)
X_train_pca = pca.fit_transform(X_train_std)
print('Explaind variance ratio:\n', pca.explained_variance_ratio_)
#############################################################################
print(50 * '=')
print('Section: Supervised data compression via linear discriminant analysis'
' - Computing the scatter matrices')
print(50 * '-')
np.set_printoptions(precision=4)
mean_vecs = []
for label in range(1, 4):
mean_vecs.append(np.mean(X_train_std[y_train == label], axis=0))
print('MV %s: %s\n' % (label, mean_vecs[label - 1]))
d = 13 # number of features
S_W = np.zeros((d, d))
for label, mv in zip(range(1, 4), mean_vecs):
class_scatter = np.zeros((d, d)) # scatter matrix for each class
for row in X_train_std[y_train == label]:
row, mv = row.reshape(d, 1), mv.reshape(d, 1) # make column vectors
class_scatter += (row - mv).dot((row - mv).T)
S_W += class_scatter # sum class scatter matrices
print('Within-class scatter matrix: %sx%s' % (S_W.shape[0], S_W.shape[1]))
print('Class label distribution: %s'
% np.bincount(y_train)[1:])
d = 13 # number of features
S_W = np.zeros((d, d))
for label, mv in zip(range(1, 4), mean_vecs):
class_scatter = np.cov(X_train_std[y_train == label].T)
S_W += class_scatter
print('Scaled within-class scatter matrix: %sx%s' % (S_W.shape[0],
S_W.shape[1]))
mean_overall = np.mean(X_train_std, axis=0)
d = 13 # number of features
S_B = np.zeros((d, d))
for i, mean_vec in enumerate(mean_vecs):
n = X_train[y_train == i + 1, :].shape[0]
mean_vec = mean_vec.reshape(d, 1) # make column vector
mean_overall = mean_overall.reshape(d, 1) # make column vector
S_B += n * (mean_vec - mean_overall).dot((mean_vec - mean_overall).T)
print('Between-class scatter matrix: %sx%s' % (S_B.shape[0], S_B.shape[1]))
#############################################################################
print(50 * '=')
print('Section: Selecting linear discriminants for the new feature subspace')
print(50 * '-')
eigen_vals, eigen_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))
# Make a list of (eigenvalue, eigenvector) tuples
eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i])
for i in range(len(eigen_vals))]
# Sort the (eigenvalue, eigenvector) tuples from high to low
eigen_pairs = sorted(eigen_pairs, key=lambda k: k[0], reverse=True)
# Visually confirm that the list is correctly sorted by decreasing eigenvalues
print('Eigenvalues in decreasing order:\n')
for eigen_val in eigen_pairs:
print(eigen_val[0])
tot = sum(eigen_vals.real)
discr = [(i / tot) for i in sorted(eigen_vals.real, reverse=True)]
cum_discr = np.cumsum(discr)
plt.bar(range(1, 14), discr, alpha=0.5, align='center',
label='individual "discriminability"')
plt.step(range(1, 14), cum_discr, where='mid',
label='cumulative "discriminability"')
plt.ylabel('"discriminability" ratio')
plt.xlabel('Linear Discriminants')
plt.ylim([-0.1, 1.1])
plt.legend(loc='best')
# plt.tight_layout()
# plt.savefig('./figures/lda1.png', dpi=300)
plt.show()
w = np.hstack((eigen_pairs[0][1][:, np.newaxis].real,
eigen_pairs[1][1][:, np.newaxis].real))
print('Matrix W:\n', w)
#############################################################################
print(50 * '=')
print('Section: Projecting samples onto the new feature space')
print(50 * '-')
X_train_lda = X_train_std.dot(w)
colors = ['r', 'b', 'g']
markers = ['s', 'x', 'o']
for l, c, m in zip(np.unique(y_train), colors, markers):
plt.scatter(X_train_lda[y_train == l, 0] * (-1),
X_train_lda[y_train == l, 1] * (-1),
c=c, label=l, marker=m)
plt.xlabel('LD 1')
plt.ylabel('LD 2')
plt.legend(loc='lower right')
# plt.tight_layout()
# plt.savefig('./figures/lda2.png', dpi=300)
plt.show()
#############################################################################
print(50 * '=')
print('Section: LDA via scikit-learn')
print(50 * '-')
lda = LDA(n_components=2)
X_train_lda = lda.fit_transform(X_train_std, y_train)
lr = LogisticRegression()
lr = lr.fit(X_train_lda, y_train)
plot_decision_regions(X_train_lda, y_train, classifier=lr)
plt.xlabel('LD 1')
plt.ylabel('LD 2')
plt.legend(loc='lower left')
# plt.tight_layout()
# plt.savefig('./images/lda3.png', dpi=300)
plt.show()
X_test_lda = lda.transform(X_test_std)
plot_decision_regions(X_test_lda, y_test, classifier=lr)
plt.xlabel('LD 1')
plt.ylabel('LD 2')
plt.legend(loc='lower left')
# plt.tight_layout()
# plt.savefig('./images/lda4.png', dpi=300)
plt.show()
#############################################################################
print(50 * '=')
print('Section: Implementing a kernel principal component analysis in Python')
print(50 * '-')
def rbf_kernel_pca(X, gamma, n_components):
"""
RBF kernel PCA implementation.
Parameters
------------
X: {NumPy ndarray}, shape = [n_samples, n_features]
gamma: float
Tuning parameter of the RBF kernel
n_components: int
Number of principal components to return
Returns
------------
X_pc: {NumPy ndarray}, shape = [n_samples, k_features]
Projected dataset
"""
# Calculate pairwise squared Euclidean distances
# in the MxN dimensional dataset.
sq_dists = pdist(X, 'sqeuclidean')
# Convert pairwise distances into a square matrix.
mat_sq_dists = squareform(sq_dists)
# Compute the symmetric kernel matrix.
K = exp(-gamma * mat_sq_dists)
# Center the kernel matrix.
N = K.shape[0]
one_n = np.ones((N, N)) / N
K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)
# Obtaining eigenpairs from the centered kernel matrix
# numpy.eigh returns them in sorted order
eigvals, eigvecs = eigh(K)
# Collect the top k eigenvectors (projected samples)
X_pc = np.column_stack((eigvecs[:, -i]
for i in range(1, n_components + 1)))
return X_pc
#############################################################################
print(50 * '=')
print('Section: Example 1: Separating half-moon shapes')
print(50 * '-')
X, y = make_moons(n_samples=100, random_state=123)
plt.scatter(X[y == 0, 0], X[y == 0, 1], color='red', marker='^', alpha=0.5)
plt.scatter(X[y == 1, 0], X[y == 1, 1], color='blue', marker='o', alpha=0.5)
# plt.tight_layout()
# plt.savefig('./figures/half_moon_1.png', dpi=300)
plt.show()
scikit_pca = PCA(n_components=2)
X_spca = scikit_pca.fit_transform(X)
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))
ax[0].scatter(X_spca[y == 0, 0], X_spca[y == 0, 1],
color='red', marker='^', alpha=0.5)
ax[0].scatter(X_spca[y == 1, 0], X_spca[y == 1, 1],
color='blue', marker='o', alpha=0.5)
ax[1].scatter(X_spca[y == 0, 0], np.zeros((50, 1)) + 0.02,
color='red', marker='^', alpha=0.5)
ax[1].scatter(X_spca[y == 1, 0], np.zeros((50, 1)) - 0.02,
color='blue', marker='o', alpha=0.5)
ax[0].set_xlabel('PC1')
ax[0].set_ylabel('PC2')
ax[1].set_ylim([-1, 1])
ax[1].set_yticks([])
ax[1].set_xlabel('PC1')
# plt.tight_layout()
# plt.savefig('./figures/half_moon_2.png', dpi=300)
plt.show()
X_kpca = rbf_kernel_pca(X, gamma=15, n_components=2)
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))
ax[0].scatter(X_kpca[y == 0, 0], X_kpca[y == 0, 1],
color='red', marker='^', alpha=0.5)
ax[0].scatter(X_kpca[y == 1, 0], X_kpca[y == 1, 1],
color='blue', marker='o', alpha=0.5)
ax[1].scatter(X_kpca[y == 0, 0], np.zeros((50, 1)) + 0.02,
color='red', marker='^', alpha=0.5)
ax[1].scatter(X_kpca[y == 1, 0], np.zeros((50, 1)) - 0.02,
color='blue', marker='o', alpha=0.5)
ax[0].set_xlabel('PC1')
ax[0].set_ylabel('PC2')
ax[1].set_ylim([-1, 1])
ax[1].set_yticks([])
ax[1].set_xlabel('PC1')
ax[0].xaxis.set_major_formatter(FormatStrFormatter('%0.1f'))
ax[1].xaxis.set_major_formatter(FormatStrFormatter('%0.1f'))
# plt.tight_layout()
# plt.savefig('./figures/half_moon_3.png', dpi=300)
plt.show()
#############################################################################
print(50 * '=')
print('Section: Example 2: Separating concentric circles')
print(50 * '-')
X, y = make_circles(n_samples=1000, random_state=123, noise=0.1, factor=0.2)
plt.scatter(X[y == 0, 0], X[y == 0, 1], color='red', marker='^', alpha=0.5)
plt.scatter(X[y == 1, 0], X[y == 1, 1], color='blue', marker='o', alpha=0.5)
# plt.tight_layout()
# plt.savefig('./figures/circles_1.png', dpi=300)
plt.show()
scikit_pca = PCA(n_components=2)
X_spca = scikit_pca.fit_transform(X)
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))
ax[0].scatter(X_spca[y == 0, 0], X_spca[y == 0, 1],
color='red', marker='^', alpha=0.5)
ax[0].scatter(X_spca[y == 1, 0], X_spca[y == 1, 1],
color='blue', marker='o', alpha=0.5)
ax[1].scatter(X_spca[y == 0, 0], np.zeros((500, 1)) + 0.02,
color='red', marker='^', alpha=0.5)
ax[1].scatter(X_spca[y == 1, 0], np.zeros((500, 1)) - 0.02,
color='blue', marker='o', alpha=0.5)
ax[0].set_xlabel('PC1')
ax[0].set_ylabel('PC2')
ax[1].set_ylim([-1, 1])
ax[1].set_yticks([])
ax[1].set_xlabel('PC1')
# plt.tight_layout()
# plt.savefig('./figures/circles_2.png', dpi=300)
plt.show()
X_kpca = rbf_kernel_pca(X, gamma=15, n_components=2)
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))
ax[0].scatter(X_kpca[y == 0, 0], X_kpca[y == 0, 1],
color='red', marker='^', alpha=0.5)
ax[0].scatter(X_kpca[y == 1, 0], X_kpca[y == 1, 1],
color='blue', marker='o', alpha=0.5)
ax[1].scatter(X_kpca[y == 0, 0], np.zeros((500, 1)) + 0.02,
color='red', marker='^', alpha=0.5)
ax[1].scatter(X_kpca[y == 1, 0], np.zeros((500, 1)) - 0.02,
color='blue', marker='o', alpha=0.5)
ax[0].set_xlabel('PC1')
ax[0].set_ylabel('PC2')
ax[1].set_ylim([-1, 1])
ax[1].set_yticks([])
ax[1].set_xlabel('PC1')
# plt.tight_layout()
# plt.savefig('./figures/circles_3.png', dpi=300)
plt.show()
#############################################################################
print(50 * '=')
print('Section: Projecting new data points')
print(50 * '-')
def rbf_kernel_pca(X, gamma, n_components):
"""
RBF kernel PCA implementation.
Parameters
------------
X: {NumPy ndarray}, shape = [n_samples, n_features]
gamma: float
Tuning parameter of the RBF kernel
n_components: int
Number of principal components to return
Returns
------------
X_pc: {NumPy ndarray}, shape = [n_samples, k_features]
Projected dataset
lambdas: list
Eigenvalues
"""
# Calculate pairwise squared Euclidean distances
# in the MxN dimensional dataset.
sq_dists = pdist(X, 'sqeuclidean')
# Convert pairwise distances into a square matrix.
mat_sq_dists = squareform(sq_dists)
# Compute the symmetric kernel matrix.
K = exp(-gamma * mat_sq_dists)
# Center the kernel matrix.
N = K.shape[0]
one_n = np.ones((N, N)) / N
K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)
# Obtaining eigenpairs from the centered kernel matrix
# numpy.eigh returns them in sorted order
eigvals, eigvecs = eigh(K)
# Collect the top k eigenvectors (projected samples)
alphas = np.column_stack((eigvecs[:, -i]
for i in range(1, n_components + 1)))
# Collect the corresponding eigenvalues
lambdas = [eigvals[-i] for i in range(1, n_components + 1)]
return alphas, lambdas
X, y = make_moons(n_samples=100, random_state=123)
alphas, lambdas = rbf_kernel_pca(X, gamma=15, n_components=1)
x_new = X[25]
print('New data point x_new:', x_new)
x_proj = alphas[25] # original projection
print('Original projection x_proj:', x_proj)
def project_x(x_new, X, gamma, alphas, lambdas):
pair_dist = np.array([np.sum((x_new - row)**2) for row in X])
k = np.exp(-gamma * pair_dist)
return k.dot(alphas / lambdas)
# projection of the "new" datapoint
x_reproj = project_x(x_new, X, gamma=15, alphas=alphas, lambdas=lambdas)
print('Reprojection x_reproj:', x_reproj)
plt.scatter(alphas[y == 0, 0], np.zeros((50)),
color='red', marker='^', alpha=0.5)
plt.scatter(alphas[y == 1, 0], np.zeros((50)),
color='blue', marker='o', alpha=0.5)
plt.scatter(x_proj, 0, color='black',
label='original projection of point X[25]', marker='^', s=100)
plt.scatter(x_reproj, 0, color='green',
label='remapped point X[25]', marker='x', s=500)
plt.legend(scatterpoints=1)
# plt.tight_layout()
# plt.savefig('./figures/reproject.png', dpi=300)
plt.show()
#############################################################################
print(50 * '=')
print('Section: Kernel principal component analysis in scikit-learn')
print(50 * '-')
X, y = make_moons(n_samples=100, random_state=123)
scikit_kpca = KernelPCA(n_components=2, kernel='rbf', gamma=15)
X_skernpca = scikit_kpca.fit_transform(X)
plt.scatter(X_skernpca[y == 0, 0], X_skernpca[y == 0, 1],
color='red', marker='^', alpha=0.5)
plt.scatter(X_skernpca[y == 1, 0], X_skernpca[y == 1, 1],
color='blue', marker='o', alpha=0.5)
plt.xlabel('PC1')
plt.ylabel('PC2')
# plt.tight_layout()
# plt.savefig('./figures/scikit_kpca.png', dpi=300)
plt.show()
| mit |
LewBurton/sklearn_pycon2015 | notebooks/fig_code/sgd_separator.py | 54 | 1148 | import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import SGDClassifier
from sklearn.datasets.samples_generator import make_blobs
def plot_sgd_separator():
# we create 50 separable points
X, Y = make_blobs(n_samples=50, centers=2,
random_state=0, cluster_std=0.60)
# fit the model
clf = SGDClassifier(loss="hinge", alpha=0.01,
n_iter=200, fit_intercept=True)
clf.fit(X, Y)
# plot the line, the points, and the nearest vectors to the plane
xx = np.linspace(-1, 5, 10)
yy = np.linspace(-1, 5, 10)
X1, X2 = np.meshgrid(xx, yy)
Z = np.empty(X1.shape)
for (i, j), val in np.ndenumerate(X1):
x1 = val
x2 = X2[i, j]
p = clf.decision_function([x1, x2])
Z[i, j] = p[0]
levels = [-1.0, 0.0, 1.0]
linestyles = ['dashed', 'solid', 'dashed']
colors = 'k'
ax = plt.axes()
ax.contour(X1, X2, Z, levels, colors=colors, linestyles=linestyles)
ax.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired)
ax.axis('tight')
if __name__ == '__main__':
plot_sgd_separator()
plt.show()
| bsd-3-clause |
sodafree/backend | build/ipython/IPython/frontend/terminal/console/app.py | 3 | 5217 | """ A minimal application using the ZMQ-based terminal IPython frontend.
This is not a complete console app, as subprocess will not be able to receive
input, there is no real readline support, among other limitations.
Authors:
* Min RK
* Paul Ivanov
"""
#-----------------------------------------------------------------------------
# Imports
#-----------------------------------------------------------------------------
import signal
import sys
import time
from IPython.frontend.terminal.ipapp import TerminalIPythonApp, frontend_flags as term_flags
from IPython.utils.traitlets import (
Dict, List, Unicode, Int, CaselessStrEnum, CBool, Any
)
from IPython.utils.warn import warn,error
from IPython.zmq.ipkernel import IPKernelApp
from IPython.zmq.session import Session, default_secure
from IPython.zmq.zmqshell import ZMQInteractiveShell
from IPython.frontend.consoleapp import (
IPythonConsoleApp, app_aliases, app_flags, aliases, app_aliases, flags
)
from IPython.frontend.terminal.console.interactiveshell import ZMQTerminalInteractiveShell
#-----------------------------------------------------------------------------
# Globals
#-----------------------------------------------------------------------------
_examples = """
ipython console # start the ZMQ-based console
ipython console --existing # connect to an existing ipython session
"""
#-----------------------------------------------------------------------------
# Flags and Aliases
#-----------------------------------------------------------------------------
# copy flags from mixin:
flags = dict(flags)
# start with mixin frontend flags:
frontend_flags = dict(app_flags)
# add TerminalIPApp flags:
frontend_flags.update(term_flags)
# disable quick startup, as it won't propagate to the kernel anyway
frontend_flags.pop('quick')
# update full dict with frontend flags:
flags.update(frontend_flags)
# copy flags from mixin
aliases = dict(aliases)
# start with mixin frontend flags
frontend_aliases = dict(app_aliases)
# load updated frontend flags into full dict
aliases.update(frontend_aliases)
# get flags&aliases into sets, and remove a couple that
# shouldn't be scrubbed from backend flags:
frontend_aliases = set(frontend_aliases.keys())
frontend_flags = set(frontend_flags.keys())
#-----------------------------------------------------------------------------
# Classes
#-----------------------------------------------------------------------------
class ZMQTerminalIPythonApp(TerminalIPythonApp, IPythonConsoleApp):
name = "ipython-console"
"""Start a terminal frontend to the IPython zmq kernel."""
description = """
The IPython terminal-based Console.
This launches a Console application inside a terminal.
The Console supports various extra features beyond the traditional
single-process Terminal IPython shell, such as connecting to an
existing ipython session, via:
ipython console --existing
where the previous session could have been created by another ipython
console, an ipython qtconsole, or by opening an ipython notebook.
"""
examples = _examples
classes = [ZMQTerminalInteractiveShell] + IPythonConsoleApp.classes
flags = Dict(flags)
aliases = Dict(aliases)
frontend_aliases = Any(frontend_aliases)
frontend_flags = Any(frontend_flags)
subcommands = Dict()
def parse_command_line(self, argv=None):
super(ZMQTerminalIPythonApp, self).parse_command_line(argv)
self.build_kernel_argv(argv)
def init_shell(self):
IPythonConsoleApp.initialize(self)
# relay sigint to kernel
signal.signal(signal.SIGINT, self.handle_sigint)
self.shell = ZMQTerminalInteractiveShell.instance(config=self.config,
display_banner=False, profile_dir=self.profile_dir,
ipython_dir=self.ipython_dir, kernel_manager=self.kernel_manager)
def init_gui_pylab(self):
# no-op, because we don't want to import matplotlib in the frontend.
pass
def handle_sigint(self, *args):
if self.shell._executing:
if self.kernel_manager.has_kernel:
# interrupt already gets passed to subprocess by signal handler.
# Only if we prevent that should we need to explicitly call
# interrupt_kernel, until which time, this would result in a
# double-interrupt:
# self.kernel_manager.interrupt_kernel()
pass
else:
self.shell.write_err('\n')
error("Cannot interrupt kernels we didn't start.\n")
else:
# raise the KeyboardInterrupt if we aren't waiting for execution,
# so that the interact loop advances, and prompt is redrawn, etc.
raise KeyboardInterrupt
def init_code(self):
# no-op in the frontend, code gets run in the backend
pass
def launch_new_instance():
"""Create and run a full blown IPython instance"""
app = ZMQTerminalIPythonApp.instance()
app.initialize()
app.start()
if __name__ == '__main__':
launch_new_instance()
| bsd-3-clause |
dudulianangang/vps | EneConsTest.py | 1 | 5969 | import sdf
import matplotlib.pyplot as plt
import numpy as np
import matplotlib as mpl
plt.style.use('seaborn-white')
# plt.rcParams['font.family'] = 'sans-serif'
# plt.rcParams['font.sans-serif'] = 'Tahoma'
# # plt.rcParams['font.monospace'] = 'Ubuntu Mono'
plt.rcParams['font.size'] = 16
# plt.rcParams['axes.labelsize'] = 10
# plt.rcParams['axes.labelweight'] = 'bold'
# plt.rcParams['xtick.labelsize'] = 8
# plt.rcParams['ytick.labelsize'] = 8
# plt.rcParams['legend.fontsize'] = 10
# plt.rcParams['figure.titlesize'] = 12
# constants for normalization
n0 = 1.8e20
me = 9.1e-31
qe = 1.6e-19
ep = 8.9e-12
c = 3e8
wp = np.sqrt(n0*qe*qe/me/ep)
ld = c/wp
e0 = me*c*wp/qe
b0 = e0/c
tt = 1/wp
ts = 50*5
te = 1500
pct = 100
en0 = me*c**2
en1 = 0.5*ep*ld**2
# simulation domain
nx = 3500
ny = 3500
lx = 3500
ly = 3500
# figure domain (set by grid)
grid_min_x = 0
grid_max_x = nx
grid_min_y = 0
grid_max_y = ny
Gx = np.linspace(0,lx,nx)
Gy = np.linspace(0,ly,ny)
gx = Gx[grid_min_x:grid_max_x+1]
gy = Gy[grid_min_y:grid_max_y+1]
# figure parameters
# fs = 24
jetcmap = plt.cm.get_cmap("rainbow", 9) #generate a jet map with 10 values
jet_vals = jetcmap(np.arange(9)) #extract those values as an array
jet_vals[0] = [1.0, 1, 1.0, 1] #change the first value
newcmap = mpl.colors.LinearSegmentedColormap.from_list("newjet", jet_vals)
# define array
EneBmE = np.ones(7)
EneBmI = np.ones(7)
EneBgE = np.ones(7)
EneBgI = np.ones(7)
sex = np.ones(7)
sey = np.ones(7)
sez = np.ones(7)
sbx = np.ones(7)
sby = np.ones(7)
sbz = np.ones(7)
TpeC1 = np.ones(7)
TpeS1 = np.ones(7)
TfeC1 = np.ones(7)
TfeS1 = np.ones(7)
TpeC2 = np.ones(7)
TpeS2 = np.ones(7)
TfeC2 = np.ones(7)
TfeS2 = np.ones(7)
TeC1 = np.ones(7)
TeS1 = np.ones(7)
TeC2 = np.ones(7)
TeS2 = np.ones(7)
time = np.ones(7)
# plot function
file = '/Volumes/yaowp2016/'
folder = 'nj'
for i in range(7):
ii = i*5
time[i] = i*ts
fname = file+folder+'/6'+str(ii).zfill(4)+'.sdf'
datafile = sdf.read(fname)
GamBmE = datafile.Particles_Gamma_subset_ele1_ele_bm.data
GamBmI = datafile.Particles_Gamma_subset_ion1_ion_bm.data
GamBgE = datafile.Particles_Gamma_subset_ele1_ele_e.data
GamBgI = datafile.Particles_Gamma_subset_ion1_ion_e.data
WgtBmE = datafile.Particles_Weight_subset_ele1_ele_bm.data
WgtBmI = datafile.Particles_Weight_subset_ion1_ion_bm.data
WgtBgE = datafile.Particles_Weight_subset_ele1_ele_e.data
WgtBgI = datafile.Particles_Weight_subset_ion1_ion_e.data
EneBmE[i] = np.sum((GamBmE-1)*en0*np.mean(WgtBmE))*pct
EneBmI[i] = np.sum((GamBmI-1)*en0*np.mean(WgtBmI))*pct
EneBgE[i] = np.sum((GamBgE-1)*en0*np.mean(WgtBgE))*pct
EneBgI[i] = np.sum((GamBgI-1)*en0*np.mean(WgtBgI))*pct
fname = file+folder+'/'+str(ii).zfill(4)+'.sdf'
datafile = sdf.read(fname)
Ex = datafile.Electric_Field_Ex.data
Ey = datafile.Electric_Field_Ey.data
Ez = datafile.Electric_Field_Ez.data
Bx = datafile.Magnetic_Field_Bx.data*c
By = datafile.Magnetic_Field_By.data*c
Bz = datafile.Magnetic_Field_Bz.data*c
sex[i] = np.sum(Ex**2)*en1
sey[i] = np.sum(Ey**2)*en1
sez[i] = np.sum(Ez**2)*en1
sbx[i] = np.sum(Bx**2)*en1
sby[i] = np.sum(By**2)*en1
sbz[i] = np.sum(Bz**2)*en1
TpeC1[i] = EneBmE[i]+EneBmI[i]+EneBgE[i]+EneBgI[i]
TfeC1[i] = sex[i]+sey[i]+sez[i]+sbx[i]+sby[i]+sbz[i]
TfeS1[i] = datafile.Total_Field_Energy_in_Simulation__J_.data
TpeS1[i] = datafile.Total_Particle_Energy_in_Simulation__J_.data
folder = 'nj_non'
for i in range(7):
ii = i*5
time[i] = i*ts
fname = file+folder+'/6'+str(ii).zfill(4)+'.sdf'
datafile = sdf.read(fname)
GamBmE = datafile.Particles_Gamma_subset_ele1_ele_bm.data
GamBmI = datafile.Particles_Gamma_subset_ion1_ion_bm.data
GamBgE = datafile.Particles_Gamma_subset_ele1_ele_e.data
GamBgI = datafile.Particles_Gamma_subset_ion1_ion_e.data
WgtBmE = datafile.Particles_Weight_subset_ele1_ele_bm.data
WgtBmI = datafile.Particles_Weight_subset_ion1_ion_bm.data
WgtBgE = datafile.Particles_Weight_subset_ele1_ele_e.data
WgtBgI = datafile.Particles_Weight_subset_ion1_ion_e.data
EneBmE[i] = np.sum((GamBmE-1)*en0*np.mean(WgtBmE))*pct
EneBmI[i] = np.sum((GamBmI-1)*en0*np.mean(WgtBmI))*pct
EneBgE[i] = np.sum((GamBgE-1)*en0*np.mean(WgtBgE))*pct
EneBgI[i] = np.sum((GamBgI-1)*en0*np.mean(WgtBgI))*pct
fname = file+folder+'/'+str(ii).zfill(4)+'.sdf'
datafile = sdf.read(fname)
Ex = datafile.Electric_Field_Ex.data
Ey = datafile.Electric_Field_Ey.data
Ez = datafile.Electric_Field_Ez.data
Bx = datafile.Magnetic_Field_Bx.data*c
By = datafile.Magnetic_Field_By.data*c
Bz = datafile.Magnetic_Field_Bz.data*c
sex[i] = np.sum(Ex**2)*en1
sey[i] = np.sum(Ey**2)*en1
sez[i] = np.sum(Ez**2)*en1
sbx[i] = np.sum(Bx**2)*en1
sby[i] = np.sum(By**2)*en1
sbz[i] = np.sum(Bz**2)*en1
TpeC2[i] = EneBmE[i]+EneBmI[i]+EneBgE[i]+EneBgI[i]
TfeC2[i] = sex[i]+sey[i]+sez[i]+sbx[i]+sby[i]+sbz[i]
TfeS2[i] = datafile.Total_Field_Energy_in_Simulation__J_.data
TpeS2[i] = datafile.Total_Particle_Energy_in_Simulation__J_.data
TeC1 = TpeC1+TfeC1
TeS1 = TpeS1+TfeS1
TeC2 = TpeC2+TfeC2
TeS2 = TpeS2+TfeS2
np.save('tpec1.npy', TpeC1)
np.save('tpes1.npy', TpeS1)
np.save('tfec1.npy', TfeC1)
np.save('tfes1.npy', TfeS1)
np.save('tpec2.npy', TpeC2)
np.save('tpes2.npy', TpeS2)
np.save('tfec2.npy', TfeC2)
np.save('tfes2.npy', TfeS2)
np.save('tec1.npy', TeC1)
np.save('tes1.npy', TeS1)
np.save('tec2.npy', TeC2)
np.save('tes2.npy', TeS2)
# plt.figure(figsize=(8,5))
# ax = plt.subplot()
# ax.plot(time, TpeC1,'r-', lw=2, label='tbc-cal')
# ax.plot(time, TpeS1,'r--', lw=2, label='tbc-sys')
# ax.plot(time, TpeC2,'b-', lw=2, label='pbc-cal')
# ax.plot(time, TpeS2,'b--', lw=2, label='pbc-sys')
# plt.xlabel('time($\omega_{pe}^{-1}$)',fontsize=24)
# plt.ylabel('energy($J$)',fontsize=24)
# plt.legend(loc='best', numpoints=1, fancybox=True)
# plt.title('total system energy',fontsize=32,fontstyle='normal')
# plt.show()
# plt.savefig(file+folder+'/plots/'+'TotalEnergyComp.png',bbox_inches='tight') # n means normalized
# plt.close()
| apache-2.0 |
pleoni/game-of-life | plot/old/test_perf_mpi/life_perf_compilers.py | 1 | 1863 | import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from numpy import *
import sys
import datetime
datafile1="life_host_icc.out"
datafile2="life_host_gnu.out"
datafile3="life_host_pgi.out"
if len(sys.argv) > 1:
datafile=sys.argv[1]
plotfile="compilers_perf_eurora.png"
data1 = loadtxt(datafile1)
data2 = loadtxt(datafile2)
data3 = loadtxt(datafile3)
today = datetime.date.today()
fig = plt.figure() # apre una nuova figura
top = fig.add_subplot(211)
bottom = fig.add_subplot(212)
############# TOP
ICC_C1000 = data1[where((data1[:,0]==1) & (data1[:,5]==1000) ),:][0] # mpi 1 - Comp 1000
ICC_C0 = data1[where((data1[:,0]==1) & (data1[:,5]==0) ),:][0] # mpi 1 - comp 0
GNU_C1000 = data2[where((data2[:,0]==1) & (data2[:,5]==1000) ),:][0] # mpi 1 - Comp 1000
GNU_C0 = data2[where((data2[:,0]==1) & (data2[:,5]==0) ),:][0] # mpi 1 - comp 0
PGI_C1000 = data3[where((data3[:,0]==1) & (data3[:,5]==1000) ),:][0] # mpi 1 - Comp 1000
PGI_C0 = data3[where((data3[:,0]==1) & (data3[:,5]==0) ),:][0] # mpi 1 - comp 0
top.set_title(str(today) + ' life_hpc2 on eurora - NCOMP=1000')
top.grid()
top.set_xlabel('Lattice Size')
top.set_ylabel('time')
#top.set_yscale('log')
#top.legend()
top.plot(ICC_C1000[:,3],ICC_C1000[:,8],'-xr',GNU_C1000[:,3],GNU_C1000[:,8],'-xg',PGI_C1000[:,3],PGI_C1000[:,8],'-xc');
top.legend(('icc','gnu','pgi'), loc = 'upper left', shadow = False, prop={'size':9})
############# BOTTOM
bottom.set_title(str(today) + ' life_hpc2 on eurora - NCOMP=0')
bottom.grid()
bottom.set_xlabel('Lattice size')
bottom.set_ylabel('time')
bottom.plot(ICC_C0[:,3],ICC_C0[:,8],'-xr',GNU_C0[:,3],GNU_C0[:,8],'-xg',PGI_C0[:,3],PGI_C0[:,8],'-xc');
bottom.legend(('icc','gnu','pgi'), loc = 'upper left', shadow = False, prop={'size':9})
plt.subplots_adjust(hspace=0.5)
plt.savefig(plotfile)
#plt.show()
| gpl-2.0 |
DistrictDataLabs/yellowbrick | yellowbrick/classifier/rocauc.py | 1 | 29053 | # yellowbrick.classifier.rocauc
# Implements visual ROC/AUC curves for classification evaluation.
#
# Author: Rebecca Bilbro
# Author: Benjamin Bengfort
# Author: Neal Humphrey
# Created: Tue May 03 18:15:42 2017 -0400
#
# Copyright (C) 2016 The scikit-yb developers
# For license information, see LICENSE.txt
#
# ID: rocauc.py [5388065] neal@nhumphrey.com $
"""
Implements visual ROC/AUC curves for classification evaluation.
"""
##########################################################################
## Imports
##########################################################################
import numpy as np
from sklearn.metrics import auc, roc_curve
from sklearn.preprocessing import label_binarize
from sklearn.utils.multiclass import type_of_target
from yellowbrick.exceptions import ModelError
from yellowbrick.style.palettes import LINE_COLOR
from yellowbrick.exceptions import YellowbrickValueError
from yellowbrick.classifier.base import ClassificationScoreVisualizer
# Dictionary keys for ROCAUC
MACRO = "macro"
MICRO = "micro"
# Target Type Constants
BINARY = "binary"
MULTICLASS = "multiclass"
##########################################################################
## ROCAUC Visualizer
##########################################################################
class ROCAUC(ClassificationScoreVisualizer):
"""
Receiver Operating Characteristic (ROC) curves are a measure of a
classifier's predictive quality that compares and visualizes the tradeoff
between the models' sensitivity and specificity. The ROC curve displays
the true positive rate on the Y axis and the false positive rate on the
X axis on both a global average and per-class basis. The ideal point is
therefore the top-left corner of the plot: false positives are zero and
true positives are one.
This leads to another metric, area under the curve (AUC), a computation
of the relationship between false positives and true positives. The higher
the AUC, the better the model generally is. However, it is also important
to inspect the "steepness" of the curve, as this describes the
maximization of the true positive rate while minimizing the false positive
rate. Generalizing "steepness" usually leads to discussions about
convexity, which we do not get into here.
Parameters
----------
estimator : estimator
A scikit-learn estimator that should be a classifier. If the model is
not a classifier, an exception is raised. If the internal model is not
fitted, it is fit when the visualizer is fitted, unless otherwise specified
by ``is_fitted``.
ax : matplotlib Axes, default: None
The axes to plot the figure on. If not specified the current axes will be
used (or generated if required).
micro : bool, default: True
Plot the micro-averages ROC curve, computed from the sum of all true
positives and false positives across all classes. Micro is not defined
for binary classification problems with estimators with only a
decision_function method.
macro : bool, default: True
Plot the macro-averages ROC curve, which simply takes the average of
curves across all classes. Macro is not defined for binary
classification problems with estimators with only a decision_function
method.
per_class : bool, default: True
Plot the ROC curves for each individual class. This should be set
to false if only the macro or micro average curves are required. For true
binary classifiers, setting per_class=False will plot the positive class
ROC curve, and per_class=True will use ``1-P(1)`` to compute the curve of
the negative class if only a decision_function method exists on the estimator.
binary : bool, default: False
This argument quickly resets the visualizer for true binary classification
by updating the micro, macro, and per_class arguments to False (do not use
in conjunction with those other arguments). Note that this is not a true
hyperparameter to the visualizer, it just collects other parameters into
a single, simpler argument.
classes : list of str, defult: None
The class labels to use for the legend ordered by the index of the sorted
classes discovered in the ``fit()`` method. Specifying classes in this
manner is used to change the class names to a more specific format or
to label encoded integer classes. Some visualizers may also use this
field to filter the visualization for specific classes. For more advanced
usage specify an encoder rather than class labels.
encoder : dict or LabelEncoder, default: None
A mapping of classes to human readable labels. Often there is a mismatch
between desired class labels and those contained in the target variable
passed to ``fit()`` or ``score()``. The encoder disambiguates this mismatch
ensuring that classes are labeled correctly in the visualization.
is_fitted : bool or str, default="auto"
Specify if the wrapped estimator is already fitted. If False, the estimator
will be fit when the visualizer is fit, otherwise, the estimator will not be
modified. If "auto" (default), a helper method will check if the estimator
is fitted before fitting it again.
force_model : bool, default: False
Do not check to ensure that the underlying estimator is a classifier. This
will prevent an exception when the visualizer is initialized but may result
in unexpected or unintended behavior.
kwargs : dict
Keyword arguments passed to the visualizer base classes.
Attributes
----------
classes_ : ndarray of shape (n_classes,)
The class labels observed while fitting.
class_count_ : ndarray of shape (n_classes,)
Number of samples encountered for each class during fitting.
score_ : float
An evaluation metric of the classifier on test data produced when
``score()`` is called. This metric is between 0 and 1 -- higher scores are
generally better. For classifiers, this score is usually accuracy, but
if micro or macro is specified this returns an F1 score.
target_type_ : string
Specifies if the detected classification target was binary or multiclass.
Notes
-----
ROC curves are typically used in binary classification, and in fact the
Scikit-Learn ``roc_curve`` metric is only able to perform metrics for
binary classifiers. As a result it is necessary to binarize the output or
to use one-vs-rest or one-vs-all strategies of classification. The
visualizer does its best to handle multiple situations, but exceptions can
arise from unexpected models or outputs.
Another important point is the relationship of class labels specified on
initialization to those drawn on the curves. The classes are not used to
constrain ordering or filter curves; the ROC computation happens on the
unique values specified in the target vector to the ``score`` method. To
ensure the best quality visualization, do not use a LabelEncoder for this
and do not pass in class labels.
.. seealso::
http://scikit-learn.org/stable/auto_examples/model_selection/plot_roc.html
.. todo:: Allow the class list to filter the curves on the visualization.
Examples
--------
>>> from yellowbrick.classifier import ROCAUC
>>> from sklearn.linear_model import LogisticRegression
>>> from sklearn.model_selection import train_test_split
>>> data = load_data("occupancy")
>>> features = ["temp", "relative humidity", "light", "C02", "humidity"]
>>> X_train, X_test, y_train, y_test = train_test_split(X, y)
>>> oz = ROCAUC(LogisticRegression())
>>> oz.fit(X_train, y_train)
>>> oz.score(X_test, y_test)
>>> oz.show()
"""
def __init__(
self,
estimator,
ax=None,
micro=True,
macro=True,
per_class=True,
binary=False,
classes=None,
encoder=None,
is_fitted="auto",
force_model=False,
**kwargs
):
super(ROCAUC, self).__init__(
estimator,
ax=ax,
classes=classes,
encoder=encoder,
is_fitted=is_fitted,
force_model=force_model,
**kwargs
)
# Set the visual parameters for ROCAUC
# NOTE: the binary flag breaks our API since it's really just a meta parameter
# for micro, macro, and per_class. We knew this going in, but did it anyway.
self.binary = binary
if self.binary:
self.micro = False
self.macro = False
self.per_class = False
else:
self.micro = micro
self.macro = macro
self.per_class = per_class
def fit(self, X, y=None):
"""
Fit the classification model.
"""
# The target determines what kind of estimator is fit
ttype = type_of_target(y)
if ttype.startswith(MULTICLASS):
self.target_type_ = MULTICLASS
elif ttype.startswith(BINARY):
self.target_type_ = BINARY
else:
raise YellowbrickValueError(
(
"{} does not support target type '{}', "
"please provide a binary or multiclass single-output target"
).format(self.__class__.__name__, ttype)
)
# Fit the model and return self
return super(ROCAUC, self).fit(X, y)
def score(self, X, y=None):
"""
Generates the predicted target values using the Scikit-Learn
estimator.
Parameters
----------
X : ndarray or DataFrame of shape n x m
A matrix of n instances with m features
y : ndarray or Series of length n
An array or series of target or class values
Returns
-------
score_ : float
Global accuracy unless micro or macro scores are requested.
"""
# Call super to check if fitted and to compute self.score_
# NOTE: this sets score to the base score if neither macro nor micro
super(ROCAUC, self).score(X, y)
# Compute the predictions for the test data
y_pred = self._get_y_scores(X)
if self.target_type_ == BINARY:
# For binary, per_class must be True to draw micro/macro curves
if (self.micro or self.macro) and not self.per_class:
raise ModelError(
"no curves will be drawn; ",
"set per_class=True or micro=False and macro=False.",
)
# For binary, if predictions are returned in shape (n,), micro and macro
# curves are not defined
if (self.micro or self.macro) and len(y_pred.shape) == 1:
raise ModelError(
"no curves will be drawn; set binary=True.",
)
if self.target_type_ == MULTICLASS:
# If it's multiclass classification, at least one of micro, macro, or
# per_class must be True
if not self.micro and not self.macro and not self.per_class:
raise YellowbrickValueError(
"no curves will be drawn; specify micro, macro, or per_class"
)
# Classes may be label encoded so only use what's in y to compute.
# The self.classes_ attribute will be used as names for labels.
classes = np.unique(y)
n_classes = len(classes)
# Store the false positive rate, true positive rate and curve info.
self.fpr = dict()
self.tpr = dict()
self.roc_auc = dict()
# If the decision is binary draw only ROC curve for the positive class
if self.target_type_ is BINARY and not self.per_class:
# In this case predict_proba returns an array of shape (n, 2) which
# specifies the probabilities of both the negative and positive classes.
if len(y_pred.shape) == 2 and y_pred.shape[1] == 2:
self.fpr[BINARY], self.tpr[BINARY], _ = roc_curve(y, y_pred[:, 1])
else:
# decision_function returns array of shape (n,), so plot it directly
self.fpr[BINARY], self.tpr[BINARY], _ = roc_curve(y, y_pred)
self.roc_auc[BINARY] = auc(self.fpr[BINARY], self.tpr[BINARY])
# Per-class binary decisions may have to have the negative class curve computed
elif self.target_type_ is BINARY and self.per_class:
# draw a curve for class 1 (the positive class)
if len(y_pred.shape) == 2 and y_pred.shape[1] == 2:
# predict_proba returns array of shape (n, 2), so use
# probability of class 1 to compute ROC
self.fpr[1], self.tpr[1], _ = roc_curve(y, y_pred[:, 1])
else:
# decision_function returns array of shape (n,)
self.fpr[1], self.tpr[1], _ = roc_curve(y, y_pred)
self.roc_auc[1] = auc(self.fpr[1], self.tpr[1])
# draw a curve for class 0 (the negative class)
if len(y_pred.shape) == 2 and y_pred.shape[1] == 2:
# predict_proba returns array of shape (n, 2), so use
# probability of class 0 to compute ROC
self.fpr[0], self.tpr[0], _ = roc_curve(1 - y, y_pred[:, 0])
else:
# decision_function returns array of shape (n,).
# To draw a ROC curve for class 0 we swap the classes 0 and 1 in y
# and reverse classifiers predictions y_pred.
self.fpr[0], self.tpr[0], _ = roc_curve(1 - y, -y_pred)
self.roc_auc[0] = auc(self.fpr[0], self.tpr[0])
else:
# Otherwise compute the ROC curve and ROC area for each class
for i, c in enumerate(classes):
self.fpr[i], self.tpr[i], _ = roc_curve(y, y_pred[:, i], pos_label=c)
self.roc_auc[i] = auc(self.fpr[i], self.tpr[i])
# Compute micro average
if self.micro:
self._score_micro_average(y, y_pred, classes, n_classes)
# Compute macro average
if self.macro:
self._score_macro_average(n_classes)
# Draw the Curves
self.draw()
# Set score to micro average if specified
if self.micro:
self.score_ = self.roc_auc[MICRO]
# Set score to macro average if not micro
if self.macro:
self.score_ = self.roc_auc[MACRO]
return self.score_
def draw(self):
"""
Renders ROC-AUC plot.
Called internally by score, possibly more than once
Returns
-------
ax : the axis with the plotted figure
"""
colors = self.class_colors_[0 : len(self.classes_)]
n_classes = len(colors)
# If it's a binary decision, plot the single ROC curve
if self.target_type_ == BINARY and not self.per_class:
self.ax.plot(
self.fpr[BINARY],
self.tpr[BINARY],
label="ROC for binary decision, AUC = {:0.2f}".format(
self.roc_auc[BINARY]
),
)
# If per-class plotting is requested, plot ROC curves for each class
if self.per_class:
for i, color in zip(range(n_classes), colors):
self.ax.plot(
self.fpr[i],
self.tpr[i],
color=color,
label="ROC of class {}, AUC = {:0.2f}".format(
self.classes_[i], self.roc_auc[i]
),
)
# If requested, plot the ROC curve for the micro average
if self.micro:
self.ax.plot(
self.fpr[MICRO],
self.tpr[MICRO],
linestyle="--",
color=self.class_colors_[len(self.classes_) - 1],
label="micro-average ROC curve, AUC = {:0.2f}".format(
self.roc_auc["micro"]
),
)
# If requested, plot the ROC curve for the macro average
if self.macro:
self.ax.plot(
self.fpr[MACRO],
self.tpr[MACRO],
linestyle="--",
color=self.class_colors_[len(self.classes_) - 1],
label="macro-average ROC curve, AUC = {:0.2f}".format(
self.roc_auc["macro"]
),
)
# Plot the line of no discrimination to compare the curve to.
self.ax.plot([0, 1], [0, 1], linestyle=":", c=LINE_COLOR)
return self.ax
def finalize(self, **kwargs):
"""
Sets a title and axis labels of the figures and ensures the axis limits
are scaled between the valid ROCAUC score values.
Parameters
----------
kwargs: generic keyword arguments.
Notes
-----
Generally this method is called from show and not directly by the user.
"""
# Set the title and add the legend
self.set_title("ROC Curves for {}".format(self.name))
self.ax.legend(loc="lower right", frameon=True)
# Set the limits for the ROC/AUC (always between 0 and 1)
self.ax.set_xlim([0.0, 1.0])
self.ax.set_ylim([0.0, 1.0])
# Set x and y axis labels
self.ax.set_ylabel("True Positive Rate")
self.ax.set_xlabel("False Positive Rate")
def _get_y_scores(self, X):
"""
The ``roc_curve`` metric requires target scores that can either be the
probability estimates of the positive class, confidence values or non-
thresholded measure of decisions (as returned by "decision_function").
This method computes the scores by resolving the estimator methods
that retreive these values.
.. todo:: implement confidence values metric.
Parameters
----------
X : ndarray or DataFrame of shape n x m
A matrix of n instances with m features -- generally the test data
that is associated with y_true values.
"""
# The resolution order of scoring functions
attrs = ("predict_proba", "decision_function")
# Return the first resolved function
for attr in attrs:
try:
method = getattr(self.estimator, attr, None)
if method:
return method(X)
except AttributeError:
# Some Scikit-Learn estimators have both probability and
# decision functions but override __getattr__ and raise an
# AttributeError on access.
# Note that because of the ordering of our attrs above,
# estimators with both will *only* ever use probability.
continue
# If we've gotten this far, raise an error
raise ModelError(
"ROCAUC requires estimators with predict_proba or "
"decision_function methods."
)
def _score_micro_average(self, y, y_pred, classes, n_classes):
"""
Compute the micro average scores for the ROCAUC curves.
"""
# Convert y to binarized array for micro and macro scores
y = label_binarize(y, classes=classes)
if n_classes == 2:
y = np.hstack((1 - y, y))
# Compute micro-average
self.fpr[MICRO], self.tpr[MICRO], _ = roc_curve(y.ravel(), y_pred.ravel())
self.roc_auc[MICRO] = auc(self.fpr[MICRO], self.tpr[MICRO])
def _score_macro_average(self, n_classes):
"""
Compute the macro average scores for the ROCAUC curves.
"""
# Gather all FPRs
all_fpr = np.unique(np.concatenate([self.fpr[i] for i in range(n_classes)]))
avg_tpr = np.zeros_like(all_fpr)
# Compute the averages per class
for i in range(n_classes):
avg_tpr += np.interp(all_fpr, self.fpr[i], self.tpr[i])
# Finalize the average
avg_tpr /= n_classes
# Store the macro averages
self.fpr[MACRO] = all_fpr
self.tpr[MACRO] = avg_tpr
self.roc_auc[MACRO] = auc(self.fpr[MACRO], self.tpr[MACRO])
##########################################################################
## Quick method for ROCAUC
##########################################################################
def roc_auc(
estimator,
X_train,
y_train,
X_test=None,
y_test=None,
ax=None,
micro=True,
macro=True,
per_class=True,
binary=False,
classes=None,
encoder=None,
is_fitted="auto",
force_model=False,
show=True,
**kwargs
):
"""ROCAUC
Receiver Operating Characteristic (ROC) curves are a measure of a
classifier's predictive quality that compares and visualizes the tradeoff
between the models' sensitivity and specificity. The ROC curve displays
the true positive rate on the Y axis and the false positive rate on the
X axis on both a global average and per-class basis. The ideal point is
therefore the top-left corner of the plot: false positives are zero and
true positives are one.
This leads to another metric, area under the curve (AUC), a computation
of the relationship between false positives and true positives. The higher
the AUC, the better the model generally is. However, it is also important
to inspect the "steepness" of the curve, as this describes the
maximization of the true positive rate while minimizing the false positive
rate. Generalizing "steepness" usually leads to discussions about
convexity, which we do not get into here.
Parameters
----------
estimator : estimator
A scikit-learn estimator that should be a classifier. If the model is
not a classifier, an exception is raised. If the internal model is not
fitted, it is fit when the visualizer is fitted, unless otherwise specified
by ``is_fitted``.
X_train : array-like, 2D
The table of instance data or independent variables that describe the outcome of
the dependent variable, y. Used to fit the visualizer and also to score the
visualizer if test splits are not specified.
y_train : array-like, 2D
The vector of target data or the dependent variable predicted by X. Used to fit
the visualizer and also to score the visualizer if test splits not specified.
X_test: array-like, 2D, default: None
The table of instance data or independent variables that describe the outcome of
the dependent variable, y. Used to score the visualizer if specified.
y_test: array-like, 1D, default: None
The vector of target data or the dependent variable predicted by X.
Used to score the visualizer if specified.
ax : matplotlib Axes, default: None
The axes to plot the figure on. If not specified the current axes will be
used (or generated if required).
test_size : float, default=0.2
The percentage of the data to reserve as test data.
random_state : int or None, default=None
The value to seed the random number generator for shuffling data.
micro : bool, default: True
Plot the micro-averages ROC curve, computed from the sum of all true
positives and false positives across all classes. Micro is not defined
for binary classification problems with estimators with only a
decision_function method.
macro : bool, default: True
Plot the macro-averages ROC curve, which simply takes the average of
curves across all classes. Macro is not defined for binary
classification problems with estimators with only a decision_function
method.
per_class : bool, default: True
Plot the ROC curves for each individual class. This should be set
to false if only the macro or micro average curves are required. For true
binary classifiers, setting per_class=False will plot the positive class
ROC curve, and per_class=True will use ``1-P(1)`` to compute the curve of
the negative class if only a decision_function method exists on the estimator.
binary : bool, default: False
This argument quickly resets the visualizer for true binary classification
by updating the micro, macro, and per_class arguments to False (do not use
in conjunction with those other arguments). Note that this is not a true
hyperparameter to the visualizer, it just collects other parameters into
a single, simpler argument.
classes : list of str, defult: None
The class labels to use for the legend ordered by the index of the sorted
classes discovered in the ``fit()`` method. Specifying classes in this
manner is used to change the class names to a more specific format or
to label encoded integer classes. Some visualizers may also use this
field to filter the visualization for specific classes. For more advanced
usage specify an encoder rather than class labels.
encoder : dict or LabelEncoder, default: None
A mapping of classes to human readable labels. Often there is a mismatch
between desired class labels and those contained in the target variable
passed to ``fit()`` or ``score()``. The encoder disambiguates this mismatch
ensuring that classes are labeled correctly in the visualization.
is_fitted : bool or str, default="auto"
Specify if the wrapped estimator is already fitted. If False, the estimator
will be fit when the visualizer is fit, otherwise, the estimator will not be
modified. If "auto" (default), a helper method will check if the estimator
is fitted before fitting it again.
force_model : bool, default: False
Do not check to ensure that the underlying estimator is a classifier. This
will prevent an exception when the visualizer is initialized but may result
in unexpected or unintended behavior.
show: bool, default: True
If True, calls ``show()``, which in turn calls ``plt.show()`` however you cannot
call ``plt.savefig`` from this signature, nor ``clear_figure``. If False, simply
calls ``finalize()``
kwargs : dict
Keyword arguments passed to the visualizer base classes.
Notes
-----
ROC curves are typically used in binary classification, and in fact the
Scikit-Learn ``roc_curve`` metric is only able to perform metrics for
binary classifiers. As a result it is necessary to binarize the output or
to use one-vs-rest or one-vs-all strategies of classification. The
visualizer does its best to handle multiple situations, but exceptions can
arise from unexpected models or outputs.
Another important point is the relationship of class labels specified on
initialization to those drawn on the curves. The classes are not used to
constrain ordering or filter curves; the ROC computation happens on the
unique values specified in the target vector to the ``score`` method. To
ensure the best quality visualization, do not use a LabelEncoder for this
and do not pass in class labels.
.. seealso:: https://bit.ly/2IORWO2
.. todo:: Allow the class list to filter the curves on the visualization.
Examples
--------
>>> from yellowbrick.classifier import ROCAUC
>>> from sklearn.linear_model import LogisticRegression
>>> data = load_data("occupancy")
>>> features = ["temp", "relative humidity", "light", "C02", "humidity"]
>>> X = data[features].values
>>> y = data.occupancy.values
>>> roc_auc(LogisticRegression(), X, y)
Returns
-------
viz : ROCAUC
Returns the fitted, finalized visualizer object
"""
# Instantiate the visualizer
visualizer = ROCAUC(
estimator=estimator,
ax=ax,
micro=micro,
macro=macro,
per_class=per_class,
binary=binary,
classes=classes,
encoder=encoder,
is_fitted=is_fitted,
force_model=force_model,
**kwargs
)
# Fit and transform the visualizer (calls draw)
visualizer.fit(X_train, y_train, **kwargs)
# Scores the visualizer with X_test and y_test if provided,
# X_train, y_train if not provided
if X_test is not None and y_test is not None:
visualizer.score(X_test, y_test)
else:
visualizer.score(X_train, y_train)
if show:
visualizer.show()
else:
visualizer.finalize()
# Return the visualizer
return visualizer
| apache-2.0 |
Wonjuseo/Project101 | others/sine_RNN.py | 1 | 4425 | import tensorflow as tf
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.utils import shuffle
def sin(x, T=100):
return np.sin(2.0*np.pi*x/T)
def problem(T=100,ampl=0.05):
x = np.arange(0,2*T+1)
noise = ampl*np.random.uniform(low=-1.0,high=1.0,size=len(x))
return sin(x) + noise
class EarlyStopping():
def __init__(self,patience=0,verbose=0):
self._step = 0
self._loss = float('inf')
self.patience = patience
self.verbose = verbose
def validate(self,loss):
if self._loss <loss:
self._step+=1
if self._step>self.patience:
if self.verbose:
print('early stopping')
return True
else:
self._step = 0
self._loss = loss
return False
def inference(x,n_batch,maxlen=None,n_hidden=None,n_out=None):
def weight_variable(shape):
initial = tf.truncated_normal(shape,stddev=0.01)
return tf.Variable(initial)
def bias_variable(shape):
initial = tf.zeros(shape,dtype=tf.float32)
return tf.Variable(initial)
cell = tf.contrib.rnn.GRUCell(n_hidden)
initial_state = cell.zero_state(n_batch,tf.float32)
state = initial_state
outputs= []
with tf.variable_scope('RNN'):
for t in range(maxlen):
if t>0:
tf.get_variable_scope().reuse_variables()
(cell_output,state) = cell(x[:,t,:],state)
outputs.append(cell_output)
output = outputs[-1]
V = weight_variable([n_hidden,n_out])
c = bias_variable([n_out])
y = tf.matmul(output,V)+c
return y
def loss(y,t):
mse = tf.reduce_mean(tf.square(y-t))
return mse
def training(loss):
optimizer = tf.train.AdamOptimizer(learning_rate=0.001,beta1=0.9,beta2=0.999)
train_step = optimizer.minimize(loss)
return train_step
T=100
sine_data = problem(T)
length = 2*T
maxlen = 25
data = []
target = []
for i in range(0,length-maxlen+1):
data.append(sine_data[i:i+maxlen])
target.append(sine_data[i+maxlen])
X = np.array(data).reshape(len(data),maxlen,1) # 1 dimension
Y = np.array(target).reshape(len(data),1)
X = np.zeros((len(data),maxlen,1),dtype=float)
Y = np.zeros((len(data),1),dtype=float)
for i, seq in enumerate(data):
for t, value in enumerate(seq):
X[i,t,0] = value
Y[i,0] = target[i]
train_data = int(len(data)*0.9)
test_data = len(data)-train_data
X_train, X_test, Y_train, Y_test = train_test_split(X,Y,test_size=test_data)
n_in = len(X[0][0])
n_hidden = 20
n_out = len(Y[0])
x = tf.placeholder(tf.float32,shape=[None,maxlen,n_in])
t = tf.placeholder(tf.float32,shape=[None,n_out])
n_batch = tf.placeholder(tf.int32)
y = inference(x,n_batch,maxlen=maxlen,n_hidden=n_hidden,n_out=n_out)
loss_fun = loss(y,t)
train_step = training(loss_fun)
epochs = 500
batch_size = 10
init = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init)
n_batches = train_data//batch_size
early_stopping = EarlyStopping(patience=10,verbose=1)
history = {'val_loss':[],'val_acc':[]}
for epoch in range(epochs):
X_, Y_ = shuffle(X_train,Y_train)
for i in range(n_batches):
start = i*batch_size
end = start + batch_size
sess.run(train_step,feed_dict={x:X_[start:end],t:Y_[start:end],n_batch:batch_size})
val_loss = loss_fun.eval(session=sess,feed_dict={x:X_test,t:Y_test,n_batch:test_data})
history['val_loss'].append(val_loss)
print('epochs:',epoch,'validation_loss:',val_loss)
#if early_stopping.validate(val_loss):
# break
truncate = maxlen
Z = X[:1]
original = [sine_data[i] for i in range(maxlen)]
predicted = [None for i in range(maxlen)]
for i in range(length-maxlen+1):
z_=Z[-1:]
y_=y.eval(session=sess,feed_dict={x:Z[-1:],n_batch:1})
sequence_ = np.concatenate((z_.reshape(maxlen,n_in)[1:],y_),axis=0).reshape(1,maxlen,n_in)
Z = np.append(Z,sequence_,axis=0)
predicted.append(y_.reshape(-1))
import matplotlib.pyplot as plt
plt.rc('font',family='serif')
plt.figure()
plt.plot(problem(T,ampl=0),linestyle='dotted',color='#aaaaaa')
plt.plot(original,linestyle='dashed',color='black')
plt.plot(predicted,color='black')
plt.show()
| apache-2.0 |
Srisai85/scikit-learn | examples/linear_model/plot_iris_logistic.py | 283 | 1678 | #!/usr/bin/python
# -*- coding: utf-8 -*-
"""
=========================================================
Logistic Regression 3-class Classifier
=========================================================
Show below is a logistic-regression classifiers decision boundaries on the
`iris <http://en.wikipedia.org/wiki/Iris_flower_data_set>`_ dataset. The
datapoints are colored according to their labels.
"""
print(__doc__)
# Code source: Gaël Varoquaux
# Modified for documentation by Jaques Grobler
# License: BSD 3 clause
import numpy as np
import matplotlib.pyplot as plt
from sklearn import linear_model, datasets
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features.
Y = iris.target
h = .02 # step size in the mesh
logreg = linear_model.LogisticRegression(C=1e5)
# we create an instance of Neighbours Classifier and fit the data.
logreg.fit(X, Y)
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
Z = logreg.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.figure(1, figsize=(4, 3))
plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=Y, edgecolors='k', cmap=plt.cm.Paired)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.xticks(())
plt.yticks(())
plt.show()
| bsd-3-clause |
nagordon/mechpy | mechpy/composites.py | 1 | 71681 | # coding: utf-8
'''
Module for composite material analysis
Hyer-Stress Analysis of Fiber-Reinforced Composite Materials
Herakovich-Mechanics of Fibrous Composites
Daniel-Engineering Mechanics of Composite Materials
Kollar-Mechanics of COmposite Structures
NASA- Basic Mechancis of Lamianted Composites
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19950009349.pdf
TODO:
* transverse shear stress reddy pg 136 or daniel pg 139
* include line loads (Qx,Qy) for combined loading
* calculate capability of panel based on margin
'''
#==============================================================================
# Import Modules
#==============================================================================
from __future__ import print_function, division
__author__ = 'Neal Gordon <nealagordon@gmail.com>'
__date__ = '2016-12-02'
__version__ = 0.1
from copy import copy
from numpy import pi, zeros, ones, linspace, arange, array, sin, cos, sqrt, pi
from numpy.linalg import solve, inv
#from scipy import linalg
import numpy as np
#np.set_printoptions(suppress=False,precision=2) # suppress scientific notation
np.set_printoptions(precision=3, linewidth=200)#, threshold=np.inf)
import scipy
from scipy.spatial import ConvexHull
#np.set_printoptions(formatter={'float': lambda x: "{:.2f}".format(x)})
import pandas as pd
import sympy as sp
from sympy import Function, dsolve, Eq, Derivative, symbols, pprint
from sympy.plotting import plot3d
#from sympy import cos, sin
#sp.init_printing(use_latex='mathjax')
#sp.init_printing(wrap_line=False, pretty_print=True)
import matplotlib as mpl
mpl.rcParams['figure.figsize'] = (8,5)
mpl.rcParams['font.size'] = 12
mpl.rcParams['legend.fontsize'] = 14
import matplotlib.pyplot as plt
from matplotlib.pyplot import plot,figure,xlim,ylim,title,legend, \
grid, show, xlabel,ylabel, tight_layout
from mpl_toolkits.mplot3d import axes3d
# if using ipython console, turn off inline plotting
#mpl.use('Qt5Agg')
# inline plotting
from IPython import get_ipython
#get_ipython().magic('matplotlib inline')
###disable inline plotting
try:
get_ipython().magic('matplotlib')
except:
pass
from IPython.display import display
import os
plt.close('all')
#==============================================================================
# Functions
#==============================================================================
def import_matprops(mymaterial=['T300_5208','AL_7075']):
'''
import material properties
'''
matprops = pd.read_csv(os.path.join(os.path.dirname(__file__), "compositematerials.csv"), index_col=0)
if mymaterial==[] or mymaterial=='':
print(matprops.columns.tolist())
mat = matprops[mymaterial]
#mat.applymap(lambda x:np.float(x))
mat = mat.applymap(lambda x:pd.to_numeric(x, errors='ignore'))
return mat
def Sf(E1,E2,nu12,G12):
'''transversely isptropic compliance matrix. pg 58 herakovich'''
nu21 = E2*nu12/E1
S = array([[1/E1, -nu21/E2, 0],
[-nu12/E1, 1/E2, 0],
[0, 0, 1/G12]])
return S
def S6f(E1,E2,E3,nu12,nu13,nu23,G12,G13,G23):
'''
daniel pg 74
transversely isotropic compliance matrix.
For transversly isotropic
E2=E3, nu12=nu13,G12=G13,G23=E2/(2(1+nu23))
'''
S6 = array( [[ 1/E1, -nu12/E1, -nu12/E1, 0, 0, 0],
[-nu12/E1, 1/E2, -nu23/E2, 0, 0, 0],
[-nu12/E1, -nu23/E2, 1/E2, 0, 0, 0],
[ 0, 0, 0, 1/G23, 0, 0],
[ 0, 0, 0, 0, 1/G13, 0],
[ 0, 0, 0, 0, 0, 1/G12]])
return S6
def C6f(E1,E2,E3,nu12,nu13,nu23,G12,G13,G23):
'''
daniel pg 74
transversely isotropic stiffness matrix.
'''
C6 = inv(S6f(E1,E2,E3,nu12,nu13,nu23,G12,G13,G23))
return C6
def Qf(E1,E2,nu12,G12):
'''transversly isptropic compliance matrix. pg 58 herakovich
G12 = E1/(2*(1+nu12)) if isotropic'''
nu21 = E2*nu12/E1
Q = array([[E1/(1-nu12*nu21), E2*nu12/(1-nu12*nu21), 0],
[ E2*nu12/(1-nu12*nu21), E2/(1-nu12*nu21), 0],
[0, 0, G12]])
return Q
def T61(th):
'''Stress
th=ply angle in degrees
voight notation for stress tranform. sigma1 = T1 @ sigmax
reddy pg 91'''
n = sin(th*pi/180)
m = cos(th*pi/180)
T1 = array( [[m**2, n**2, 0, 0, 0, 2*m*n],
[n**2, m**2, 0, 0, 0,-2*m*n],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, m,-n, 0],
[0, 0, 0, n, m, 0],
[-m*n, m*n, 0, 0, 0,(m**2-n**2)]])
return T1
def T62(th):
'''Strain
voight notation for strain transform. epsilon1 = T2 @ epsilonx
th=ply angle in degrees
reddy pg 91
'''
n = sin(th*pi/180)
m = cos(th*pi/180)
T2 = array( [[m**2, n**2, 0, 0, 0, m*n],
[n**2, m**2, 0, 0, 0,-m*n],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, m,-n, 0],
[0, 0, 0, n, m, 0],
[-2*m*n, 2*m*n, 0, 0, 0,(m**2-n**2)]])
return T2
def T1(th):
'''Stress Transform for Plane Stress
th=ply angle in degrees
voight notation for stress tranform. sigma1 = T1 @ sigmax
recall T1(th)**-1 == T1(-th)'''
n = sin(th*pi/180)
m = cos(th*pi/180)
T1 = array( [[m**2, n**2, 2*m*n],
[n**2, m**2,-2*m*n],
[-m*n, m*n,(m**2-n**2)]])
return T1
def T2(th):
'''Strain Transform for Plane Stress
th=ply angle in degrees
voight notation for strain transform. epsilon1 = T2 @ epsilonx'''
n = sin(th*pi/180)
m = cos(th*pi/180)
T2 = array( [[m**2, n**2, m*n],
[n**2, m**2,-m*n],
[-2*m*n, 2*m*n, (m**2-n**2)]])
return T2
def T1s(th):
'''Symbolic Stress Transform for Plane Stress
th=ply angle in degrees
voight notation for stress tranform. sigma1 = T1 @ sigmax
recall T1(th)**-1 == T1(-th)'''
n = sp.sin(th*sp.pi/180)
m = sp.cos(th*sp.pi/180)
T1 = sp.Matrix( [[m**2, n**2, 2*m*n],
[n**2, m**2,-2*m*n],
[-m*n, m*n,(m**2-n**2)]])
return T1
def T2s(th):
'''Symbolic Strain Transform for Plane Stress
th=ply angle in degrees
voight notation for strain transform. epsilon1 = T2 @ epsilonx'''
n = sp.sin(th*sp.pi/180)
m = sp.cos(th*sp.pi/180)
T2 = sp.Matrix( [[m**2, n**2, m*n],
[n**2, m**2,-m*n],
[-2*m*n, 2*m*n, (m**2-n**2)]])
return T2
def failure_envelope():
# failure envelopes
# max stress criteria
# 1 direction in first row
# 2 direction in second row
# failure strength in compression
#Fc = matrix([[-1250.0, -600.0],
# [-200.0, -120.0]]) # ksi
#
##failure strength in tension
#Ft = matrix([[1500, 1000]
# [50, 30]]) # ksi
#
##Failure strength in shear
#Fs = matrix( [100, 70] ) # Shear
Fc1 = [-1250, -600] # Compression 1 direction
Fc2 = [-200, -120] # Compression 2 direction
Ft1 = [1500, 1000] # Tension 1 direction
Ft2 = [50, 30] # Tension 2 direction
Fs = [100, 70] # Shear
# F1 = Ft(1);
# F2 = Ft(1);
# F6 = Fs(1);
for c in range(2):# mattype
factor = 1.25
# right
plot( [Ft1[c], Ft1[c]], [Fc2[c], Ft2[c]])
# left
plot( [Fc1[c], Fc1[c]] , [Fc2[c], Ft2[c]])
# top
plot( [Fc1[c], Ft1[c]] , [Ft2[c], Ft2[c]])
# bottom
plot( [Fc1[c], Ft1[c]] , [Fc2[c], Fc2[c]])
# center horizontal
plot( [Fc1[c], Ft1[c]] , [0, 0])
# center vertical
plot( [0, 0] , [Fc2[c], Ft2[c]])
#xlim([min(Fc1) max(Ft1)]*factor)
#ylim([min(Fc2) max(Ft2)]*factor)
xlabel('$\sigma_1,ksi$')
ylabel('$\sigma_2,ksi$')
title('failure envelope with Max-Stress Criteria')
def material_plots(materials = ['Carbon_cloth_AGP3705H']):
'''
plotting composite properties
Sf(E1,E2,nu12,G12)
'''
# plt.rcParams['figure.figsize'] = (10, 8)
# plt.rcParams['font.size'] = 14
# plt.rcParams['legend.fontsize'] = 14
plyangle = arange(-45, 45.1, 0.1)
h = 1 # lamina thickness
layupname='[0]'
mat = import_matprops(materials)
Ex = mat[materials[0]].E1
Ey = mat[materials[0]].E2
nuxy = mat[materials[0]].nu12
Gxy = mat[materials[0]].G12
# layupname = '[0, 45, 45, 0]'
# Ex= 2890983.38
# Ey= 2844063.06
# nuxy= 0.27
# Gxy= 1129326.25
# h = 0.0600
plt.close('all')
S = Sf(Ex,Ey,nuxy,Gxy)
C = inv(S)
C11 = [(inv(T1(th)) @ C @ T2(th))[0,0] for th in plyangle]
C22 = [(inv(T1(th)) @ C @ T2(th))[1,1] for th in plyangle]
C33 = [(inv(T1(th)) @ C @ T2(th))[2,2] for th in plyangle]
C12 = [(inv(T1(th)) @ C @ T2(th))[0,1] for th in plyangle]
Exbar = zeros(len(plyangle))
Eybar = zeros(len(plyangle))
Gxybar = zeros(len(plyangle))
Q = Qf(Ex,Ey,nuxy,Gxy)
Qbar = zeros((len(plyangle),3,3))
for i,th in enumerate(plyangle):
Qbar[i] = solve(T1(th), Q) @ T2(th)
#Qbar = [solve(T1(th),Q) @ T2(th) for th in plyangle]
Qbar11 = Qbar[:,0,0]
Qbar22 = Qbar[:,1,1]
Qbar66 = Qbar[:,2,2]
Qbar12 = Qbar[:,0,1]
Qbar16 = Qbar[:,0,2]
Qbar26 = Qbar[:,1,2]
Aij = Qbar*h
# laminate Stiffness
# | Exbar Eybar Gxybar |
# A = | vxybar vyxbar etasxbar |
# | etaxsbar etaysbar etasybar |
# laminate Comnpliance
aij = zeros((len(plyangle),3,3))
for i, _Aij in enumerate(Aij):
aij[i] = inv(_Aij)
# material properties for whole laminate (Daniel, pg183)
Exbar = [1/(h*_aij[0,0]) for _aij in aij]
Eybar = [1/(h*_aij[1,1]) for _aij in aij]
Gxybar = [1/(h*_aij[2,2]) for _aij in aij]
# Global Stress
s_xy = array([[100],
[10],
[5]])
# local ply stress
s_12 = np.zeros((3,len(plyangle)))
for i,th in enumerate(plyangle):
#s_12[:,i] = np.transpose(T1(th) @ s_xy)[0] # local stresses
s_12[:,[i]] = T1(th) @ s_xy
# Plotting
figure()#, figsize=(10,8))
plot(plyangle, C11, plyangle, C22, plyangle, C33, plyangle, C12)
legend(['$\overline{C}_{11}$','$\overline{C}_{22}$', '$\overline{C}_{44}$', '$\overline{C}_{66}$'])
title('Transversly Isotropic Stiffness properties of carbon fiber T300_5208')
xlabel("$\Theta$")
ylabel('$\overline{C}_{ii}$, ksi')
grid()
figure()#, figsize=(10,8))
plot(plyangle, Exbar, label = r"Modulus: $E_x$")
plot(plyangle, Eybar, label = r"Modulus: $E_y$")
plot(plyangle, Gxybar, label = r"Modulus: $G_{xy}$")
title("Constitutive Properties in various angles")
xlabel("$\Theta$")
ylabel("modulus, psi")
legend()
grid()
figure()#,figsize=(10,8))
plot(plyangle, s_12[0,:], label = '$\sigma_{11},ksi$' )
plot(plyangle, s_12[1,:], label = '$\sigma_{22},ksi$' )
plot(plyangle, s_12[2,:], label = '$\sigma_{12},ksi$' )
legend(loc='lower left')
xlabel("$\Theta$")
ylabel("Stress, ksi")
grid()
# plot plyangle as a function of time
figure()#,figsize=(10,8))
plot(plyangle,Qbar11, label = "Qbar11")
plot(plyangle,Qbar22, label = "Qbar22")
plot(plyangle,Qbar66, label = "Qbar66")
legend(loc='lower left')
xlabel("$\Theta$")
ylabel('Q')
grid()
# plot plyangle as a function of time
figure()#,figsize=(10,8))
plot(plyangle,Qbar12, label = "Qbar12")
plot(plyangle,Qbar16, label = "Qbar16")
plot(plyangle,Qbar26, label = "Qbar26")
legend(loc='lower left')
xlabel("$\Theta$")
ylabel('Q')
grid()
titlename = 'Laminate Properties varying angle for {} {}'.format(materials[0], layupname)
#df = pd.DataFrame({'plyangle':plyangle, 'Exbar':Exbar, 'Eybar':Eybar,'Gxybar':Gxybar})
#print(df)
#df.to_csv(titlename+'.csv')
plt.figure(figsize=(9,6))
plot(plyangle, Exbar, label = r"Modulus: $E_x$")
plot(plyangle, Eybar, label = r"Modulus: $E_y$")
plot(plyangle, Gxybar, label = r"Modulus: $G_{xy}$")
title(titlename)
xlabel("$\Theta$")
ylabel("modulus, psi")
legend(loc='best')
grid()
#plt.savefig(titlename+'.png')
show()
def laminate_gen(lamthk=1.5, symang=[45,0,90], plyratio=2.0, matrixlayers=False, balancedsymmetric=True):
'''
## function created to quickly create laminates based on given parameters
lamthk=1.5 # total #thickness of laminate
symang = [45,0,90, 30] #symmertic ply angle
plyratio=2.0 # lamina/matrix ratio
matrixlayers=False # add matrix layers between lamina plys
nonsym=False # symmetric
mat = material type, as in different plies, matrix layer, uni tapes, etc
#ply ratio can be used to vary the ratio of thickness between a matrix ply
and lamina ply. if the same thickness is desired, plyratio = 1,
if lamina is 2x as thick as matrix plyratio = 2
'''
if matrixlayers:
nply = (len(symang)*2+1)*2
nm = nply-len(symang)*2
nf = len(symang)*2
tm = lamthk / (plyratio*nf + nm)
tf = tm*plyratio
plyangle = zeros(nply//2)
mat = 2*ones(nply//2) # orthotropic fiber and matrix = 1, isotropic matrix=2,
mat[1:-1:2] = 1 # [2 if x%2 else 1 for x in range(nply//2) ]
plyangle[1:-1:2] = symang[:] # make a copy
thk = tm*ones(nply//2)
thk[2:2:-1] = tf
lamang = list(symang) + list(symang[::-1])
plyangle = list(plyangle) + list(plyangle[::-1])
mat = list(mat) + list(mat[::-1])
thk = list(thk) + list(thk[::-1])
else: # no matrix layers, ignore ratio
if balancedsymmetric:
nply = len(symang)*2
mat = list(3*np.ones(nply))
thk = list(lamthk/nply*np.ones(nply))
lamang = list(symang) + list(symang[::-1])
plyangle = list(symang) + list(symang[::-1])
else:
nply = len(symang)
mat =[1]*nply
thk = list(lamthk/nply*np.ones(nply))
lamang = symang[:]
plyangle = symang[:]
return thk,plyangle,mat,lamang
def make_quasi(n0=4,n45=4):
#n0 = 4
#n45 = 13
#
#ply0 = [0]*n0
#ply45 = [45]*n45
#plyangle = []
#from itertools import zip_longest
#for x,y in zip_longest(ply0,ply45):
# if len(plyangle)<min(len(ply0),len(ply45))*2:
# plyangle.append(x)
# plyangle.append(y)
# else:
# plyangle.append(x)
# plyangle.reverse()
# plyangle.append(y)
#plyangle = [x for x in plyangle if x is not None]
#plyangle
ntot = n45+n0
plyangle = [45]*int(n45)
for p in [0]*int(n0):
plyangle.append(p)
plyangle.reverse()
return plyangle
#@xw.func
def laminate_calcs(NM,ek,q0,plyangle,plymatindex,materials,platedim, zoffset,SF,plots,prints):
'''
code to compute composite properties, applied mechanical and thermal loads
and stress and strain
inputs
NM # force/moments lbs/in
ek # strain, curvature in/in
q0 = pressure
plyangle # angle for each ply
plymatindex # material for each ply
materials # list materials used,
general outline for computing elastic properties of composites
1) Determine engineering properties of unidirectional laminate. E1, E2, nu12, G12
2) Calculate ply stiffnesses Q11, Q22, Q12, Q66 in the principal/local coordinate system
3) Determine Fiber orientation of each ply
4) Calculate the transformed stiffness Qxy in the global coordinate system
5) Determine the through-thicknesses of each ply
6) Determine the laminate stiffness Matrix (ABD)
7) Calculate the laminate compliance matrix by inverting the ABD matrix
8) Calculate the laminate engineering properties
# Stress Strain Relationship for a laminate, with Q=reduced stiffness matrix
|sx | |Qbar11 Qbar12 Qbar16| |ex +z*kx |
|sy |=|Qbar12 Qbar22 Qbar26|=|ey +z*ky |
|sxy| |Qbar16 Qbar26 Qbar66| |exy+z*kxy|
# Herakovich pg 84
Qbar = inv(T1) @ Q @ T2 == solve(T1, Q) @ T2
transformation reminders - see Herakovich for details
sig1 = T1*sigx
sigx = inv(T1)*sig1
eps1 = T2*epsx
epsx = inv(T2)*epsx
sigx = inv(T1)*Q*T2*epsx
Qbar = inv(T1)*Q*T2
Sbar = inv(T2)*inv(Q)*T2
Notes, core transverse direction is G13, ribbon direction is G23
a_width = 50 # plate width (inches or meters)
b_length = 50 # laminate length, inches or meters
'''
#==========================================================================
# Initialize python settings
#==========================================================================
#get_ipython().magic('matplotlib')
plt.close('all')
plt.rcParams['figure.figsize'] = (12, 8)
plt.rcParams['font.size'] = 13
#plt.rcParams['legend.fontsize'] = 14
#==========================================================================
# Define composite properties
#==========================================================================
assert(len(plyangle)==len(plymatindex))
a_width, b_length = platedim
# either apply strains or loads , lb/in
Nx_, Ny_, Nxy_, Mx_, My_, Mxy_ = NM
NMbarapp = array([[Nx_],[Ny_],[Nxy_],[Mx_],[My_],[Mxy_]])
ex_, ey_, exy_, kx_, ky_, kxy_ = ek
epsilonbarapp = array([[ex_],[ey_],[exy_],[kx_],[ky_],[kxy_]])
Ti = 0 # initial temperature (C)
Tf = 0 # final temperature (C)
#SF = 1.0 # safety factor
#==========================================================================
# Import Material Properties
#==========================================================================
mat = import_matprops(materials)
#mat = import_matprops(['E-Glass Epoxy cloth','rohacell2lb']) # Herakovich
alphaf = lambda mat: array([[mat.alpha1], [mat.alpha2], [0]])
''' to get ply material info, use as follows
alpha = alphaf(mat[materials[plymatindex[i]]])
mat[materials[1]].E2
'''
laminatethk = array([mat[materials[i]].plythk for i in plymatindex ])
nply = len(laminatethk) # number of plies
H = np.sum(laminatethk) # plate thickness
# area = a_width*H
z = zeros(nply+1)
zmid = zeros(nply)
z[0] = -H/2
for i in range(nply):
z[i+1] = z[i] + laminatethk[i]
zmid[i] = z[i] + laminatethk[i]/2
#==========================================================================
# ABD Matrix Compute
#==========================================================================
# Reduced stiffness matrix for a plane stress ply in principal coordinates
# calcluating Q from the Compliance matrix may cause cancE1ation errors
A = zeros((3,3)); B = zeros((3,3)); D = zeros((3,3))
for i in range(nply): # = nply
Q = Qf(mat[materials[plymatindex[i]]].E1, mat[materials[plymatindex[i]]].E2, mat[materials[plymatindex[i]]].nu12, mat[materials[plymatindex[i]]].G12 )
Qbar = solve(T1(plyangle[i]), Q) @ T2(plyangle[i]) # inv(T1(plyangle[i])) @ Q @ T2(plyangle[i])
A += Qbar*(z[i+1]-z[i])
# coupling stiffness
B += (1/2)*Qbar*(z[i+1]**2-z[i]**2)
# bending or flexural laminate stiffness relating moments to curvatures
D += (1/3)*Qbar*(z[i+1]**3-z[i]**3)
#Cbar6 = T61 @ C6 @ np.transpose(T61)
# laminate stiffness matrix
ABD = zeros((6,6))
ABD[0:3,0:3] = A
ABD[0:3,3:6] = B + zoffset*A
ABD[3:6,0:3] = B + zoffset*A
ABD[3:6,3:6] = D + 2*zoffset*B + zoffset**2*A
# laminatee compliance
abcd = inv(ABD)
a = abcd[0:3,0:3]
#==========================================================================
# Laminate Properties
#==========================================================================
# effective laminate shear coupling coefficients
etasxbar = a[0,2]/a[2,2]
etasybar = a[1,2]/a[2,2]
etaxsbar = a[2,0]/a[0,0]
etaysbar = a[2,1]/a[1,1]
# laminate engineer properties
Exbar = 1 / (H*a[0,0])
Eybar = 1 / (H*a[1,1])
Gxybar = 1 / (H*a[2,2])
nuxybar = -a[0,1]/a[0,0]
nuyxbar = -a[0,1]/a[1,1]
# TODO: validate results, does not appear to be correct
# strain centers, pg 72, NASA-Basic mechanics of lamianted composites
# added divide by zero epsilon
z_eps0_x = -B[0,0] / (D[0,0] + 1e-16)
z_eps0_y = -B[0,1] / (D[0,1] + 1e-16)
z_eps0_xy = -B[0,2] / (D[0,2] + 1e-16)
z_sc = -B[2,2] / (D[2,2] +1e-16) # shear center
# --------------------- Double Check ---------------------
# # Laminate compliance matrix
# LamComp = array([ [1/Exbar, -nuyxbar/Eybar, etasxbar/Gxybar],
# [-nuxybar/Exbar, 1/Eybar , etasybar/Gxybar],
# [etaxsbar/Exbar, etaysbar/Eybar, 1/Gxybar]] )
# # Daniel pg 183
# # combines applied loads and applied strains
# strain_laminate = LamComp @ Nxyzapplied[:3]/H + strainxyzapplied[:3]
# Nxyz = A @ strain_laminate
# stress_laminate = Nxyz/H
# --------------------------------------------------------
#==========================================================================
# Pressure Load
#==========================================================================
#==========================================================================
# pressure displacement and moments
#==========================================================================
D11,D12,D22,D66 = D[0,0], D[0,1], D[1,1], D[2,2]
B11 = B[0,0]
A11, A12 = A[0,0], A[0,1]
# reddy pg 247 Navier displacement solution for a simply supported plate
s = b_length/a_width
x = a_width/2
y = b_length/2
# 5.2.8, reddy, or hyer 13.123
terms = 5
w0 = 0
for m in range(1,terms,2):
for n in range(1,terms,2):
dmn = pi**4/b_length**4 * (D11*m**4*s**4 + 2*(D12 + 2*D66)*m**2*n**2*s**2 + D22*n**4)
alpha = m*pi/a_width
beta = n*pi/b_length
# for uniformly distributed loads, m,n = 1,3,5,...
Qmn = 16*q0/(pi**2*m*n)
Wmn = Qmn/dmn
w0 += Wmn * sin(alpha*x) * sin(beta*y)
w0_simplesupport = w0
# 5.2.12a, reddy
# mid span moments
Mxq=Myq=Mxyq=0
for m in range(1,terms,2):
for n in range(1,terms,2):
dmn = pi**4/b_length**4 * (D11*m**4*s**4 + 2*(D12 + 2*D66)*m**2*n**2*s**2 + D22*n**4)
alpha = m*pi/a_width
beta = n*pi/b_length
# for uniformly distributed loads, m,n = 1,3,5,...
Qmn = 16*q0/(pi**2*m*n)
Wmn = Qmn/dmn
Mxq += (D11*alpha**2 + D12*beta**2 ) * Wmn * sin(m*pi*x/a_width) * sin(n*pi*y/b_length)
Myq += (D12*alpha**2 + D22*beta**2 ) * Wmn * sin(m*pi*x/a_width) * sin(n*pi*y/b_length)
Mxyq += alpha*beta*D66 * Wmn * cos(m*pi*x/a_width) * cos(n*pi*y/b_length)
Mxyq = -2*Mxyq
NMq = [[0],[0],[0],[Mxq],[Myq],[Mxyq]]
# hyer, x-pin-pin, y-free-free plate reaction forces, pg 619
# Forces and Moments across the width of the plate
A11R = A11*(1-B11**2/(A11*D11))
D11R = D11*(1-B11**2/(A11*D11))
Nxq0 = lambda x: B11/D11 * q0 * a_width**2 /12
Nyq0 = lambda x: B11 * A12*q0 * a_width**2 / (D11*A11R*12) * (6*(x/a_width)**2-1/2)
Nxyq0 = lambda x: 0
Mxq0 = lambda x: q0 * a_width**2/8 * (1-4*(x/a_width)**2)
Myq0 = lambda x: D12 * q0 * a_width**2 / (D11R*8) * ((1-2*B11**2/(3*A11*D11))-(4*(x/a_width)**2))
Mxyq0 = lambda x: 0
# clamped plate 5.4.11, reddy
#w0_clamped = ( 49 * q0*a_width**4 * (x/a_width - (x/a_width)**2 )**2 * (y/b_length - (y/b_length)**2)**2) / (8 * (7*D11+4*(D12 + 2*D66)*s**2 + 7*D22*s**4) )
# reddy, 5.4.12
w0_clamped = 0.00342 * (q0*a_width**4) / (D11+0.5714*(D12+2*D66)*s**2+D22*s**4)
# reddy, 5.4.15
#w0_clamped = 0.00348 * (q0*a_width**4) / (D11*b_length**4+0.6047*(D12+2*D66)*s**2+D22*s**4)
# reddy 5.4.15, for isotropic D11=D
w0_clamped_isotropic = 0.00134*q0*a_width**4/D11
#==========================================================================
# Applied Loads and pressure loads
#==========================================================================
NMbarapptotal = NMbarapp + NMq + ABD @ epsilonbarapp
#==========================================================================
# Thermal Loads
#==========================================================================
'''
if the material is isotropic and unconstrained, then no thermal stresses
will be experienced. If there are constraints, then the material will experience
thermally induced stresses. As with orthotropic materials, various directions will have
different stresses, and when stacked in various orientations, stresses can be
unintuitive and complicated. Global Thermal strains are subtracted from applied strains
# 1) determine the free unrestrained thermal strains in each layer, alphabar
'''
dT = Tf-Ti
Nhatth= zeros((3,1)) # unit thermal force in global CS
Mhatth = zeros((3,1)) # unit thermal moment in global CS
alphabar = zeros((3,nply)) # global ply CTE
for i in range(nply): # = nply
Q = Qf(mat[materials[plymatindex[i]]].E1, mat[materials[plymatindex[i]]].E2, mat[materials[plymatindex[i]]].nu12, mat[materials[plymatindex[i]]].G12 )
alpha = alphaf(mat[materials[plymatindex[i]]])
Qbar = inv(T1(plyangle[i])) @ Q @ T2(plyangle[i])
alphabar[:,[i]] = solve(T2(plyangle[i]), alpha)
#alphabar[:,[i]] = inv(T2(plyangle[i])) @ alpha # Convert to global CS
Nhatth += Qbar @ (alphabar[:,[i]])*(z[i+1] - z[i]) # Hyer method for calculating thermal unit loads
Mhatth += 0.5*Qbar@(alphabar[:,[i]])*(z[i+1]**2-z[i]**2)
NMhatth = np.vstack((Nhatth,Mhatth))
NMbarth = NMhatth*dT # resultant thermal loads
# Laminate CTE
epsilonhatth = abcd@NMhatth # laminate CTE
# applied loads and thermal loads
epsilonbarapp = abcd @ NMbarapptotal
epsilonbarth = abcd @ NMbarth # resultant thermal strains
epsilonbartotal = epsilonbarapp + epsilonbarth
# Composite respone from applied mechanical loads and strains. Average
# properties only. Used to compare results from tensile test.
#epsilon_laminate = abcd@NMbarapptotal
#sigma_laminate = ABD@epsilon_laminate/H
epsilon_laminate = epsilonbartotal[:]
sigma_laminate = ABD@epsilonbartotal/H
alpha_laminate = a@Nhatth
# determine thermal load and applied loads or strains Hyer pg 435,452
Nx = NMbarapptotal[0,0]*a_width # units kiloNewtons, total load as would be applied in a tensile test
Ny = NMbarapptotal[1,0]*b_length # units kN
#==========================================================================
# Thermal and mechanical local and global stresses at the ply interface
#==========================================================================
# Declare variables for plotting
epsilon_app = zeros((3,2*nply))
sigma_app = zeros((3,2*nply))
epsilonbar_app = zeros((3,2*nply))
sigmabar_app = zeros((3,2*nply))
epsilon_th = zeros((3,2*nply))
sigma_th = zeros((3,2*nply))
epsilonbar_th = zeros((3,2*nply))
sigmabar_th = zeros((3,2*nply))
epsilon = zeros((3,2*nply))
epsilonbar = zeros((3,2*nply))
sigma = zeros((3,2*nply))
sigmabar = zeros((3,2*nply))
for i,k in enumerate(range(0,2*nply,2)):
# stress is calcuated at top and bottom of each ply
Q = Qf(mat[materials[plymatindex[i]]].E1, mat[materials[plymatindex[i]]].E2, mat[materials[plymatindex[i]]].nu12, mat[materials[plymatindex[i]]].G12 )
Qbar = inv(T1(plyangle[i])) @ Q @ T2(plyangle[i])
### transverse shear, herakovich pg 254
#Q44 = mat[materials[plymatindex[i]]].G23
#Q55 = mat[materials[plymatindex[i]]].G13
#Qbar44 = Q44*cos(plyangle[i])**2+Q55*sin(plyangle[i])**2
#Qbar55 = Q55*cos(plyangle[i])**2 + Q44*sin(plyangle[i])**2
#Qbar45 = (Q55-Q44)*cos(plyangle[i])*sin(plyangle[i])
#epsilontransverse = array([[gammayz],[gammaxz]])
#sigmatransverse = array([[Qbar44, Qbar45],[Qbar45, Qbar55]]) @ epsilontransverse
# Global stresses and strains, applied load only
epsbarapp1 = epsilonbarapp[0:3] + z[i]*epsilonbarapp[3:7]
epsbarapp2 = epsilonbarapp[0:3] + z[i+1]*epsilonbarapp[3:7]
sigbarapp1 = Qbar @ epsbarapp1
sigbarapp2 = Qbar @ epsbarapp2
# Local stresses and strains, appplied load only
epsapp1 = T2(plyangle[i]) @ epsbarapp1
epsapp2 = T2(plyangle[i]) @ epsbarapp2
sigapp1 = Q @ epsapp1
sigapp2 = Q @ epsapp2
# Interface Stresses and Strains
epsilon_app[:,k:k+2] = np.column_stack((epsapp1,epsapp2))
epsilonbar_app[:,k:k+2] = np.column_stack((epsbarapp1,epsbarapp2))
sigma_app[:,k:k+2] = np.column_stack((sigapp1,sigapp2))
sigmabar_app[:,k:k+2] = np.column_stack((sigbarapp1,sigbarapp2))
# Global stress and strains, thermal loading only
epsbarth1 = epsilonbarth[0:3] + z[i]*epsilonbarth[3:7] - dT*alphabar[:,[i]]
epsbarth2 = epsilonbarth[0:3] + z[i+1]*epsilonbarth[3:7] - dT*alphabar[:,[i]]
sigbarth1 = Qbar @ epsbarth1
sigbarth2 = Qbar @ epsbarth2
# Local stress and strains, thermal loading only
epsth1 = T2(plyangle[i]) @ epsbarth1
epsth2 = T2(plyangle[i]) @ epsbarth2
sigth1 = Q @ epsth1
sigth2 = Q @ epsth2
# Interface Stresses and Strains
epsilon_th[:,k:k+2] = np.column_stack((epsth1,epsth2))
epsilonbar_th[:,k:k+2] = np.column_stack((epsbarth1+dT*alphabar[:,[i]],epsbarth2+dT*alphabar[:,[i]])) # remove the local thermal loads for plotting. only use local thermal strains for calculating stress
sigma_th[:,k:k+2] = np.column_stack((sigth1,sigth2))
sigmabar_th[:,k:k+2] = np.column_stack((sigbarth1,sigbarth2))
# TOTAL global stresses and strains, applied and thermal
epsbar1 = epsbarapp1 + epsbarth1
epsbar2 = epsbarapp2 + epsbarth2
sigbar1 = Qbar @ epsbar1
sigbar2 = Qbar @ epsbar2
# TOTAL local stresses and strains , applied and thermal
eps1 = T2(plyangle[i]) @ epsbar1
eps2 = T2(plyangle[i]) @ epsbar2
sig1 = Q @ eps1
sig2 = Q @ eps2
# Interface Stresses and Strains
epsilon[:,k:k+2] = np.column_stack((eps1,eps2))
epsilonbar[:,k:k+2] = np.column_stack((epsbar1+dT*alphabar[:,[i]],epsbar2+dT*alphabar[:,[i]])) # remove the local thermal loads for plotting. only use local thermal strains for calculating stress
sigma[:,k:k+2] = np.column_stack((sig1,sig2))
sigmabar[:,k:k+2] = np.column_stack((sigbar1,sigbar2))
#==========================================================================
# Strength Failure Calculations
#==========================================================================
# Strength Ratio
STRENGTHRATIO_MAXSTRESS = zeros((3,2*nply))
# Failure Index
FAILUREINDEX_MAXSTRESS = zeros((3,2*nply))
STRENGTHRATIO_TSAIWU = zeros((nply))
for i,k in enumerate(range(0,2*nply,2)):
# stress
s1 = sigma[0,k]
s2 = sigma[1,k]
s12 = np.abs(sigma[2,k])
# strength
F1 = mat[materials[plymatindex[i]]].F1t if s1 > 0 else mat[materials[plymatindex[i]]].F1c
F2 = mat[materials[plymatindex[i]]].F2t if s2 > 0 else mat[materials[plymatindex[i]]].F2c
F12 = mat[materials[plymatindex[i]]].F12
# Max Stress failure index ,failure if > 1, then fail, FI = 1/SR
FAILUREINDEX_MAXSTRESS[0,k:k+2] = s1 / F1
FAILUREINDEX_MAXSTRESS[1,k:k+2] = s2 / F2
FAILUREINDEX_MAXSTRESS[2,k:k+2] = s12 / F12
# Tsai Wu, failure occures when > 1
F1t = mat[materials[plymatindex[i]]].F1t
F1c = mat[materials[plymatindex[i]]].F1c
F2t = mat[materials[plymatindex[i]]].F2t
F2c = mat[materials[plymatindex[i]]].F2c
F12 = mat[materials[plymatindex[i]]].F12
# inhomogeneous Tsai-Wu criterion # from Daniel
# http://www2.mae.ufl.edu/haftka/composites/mcdaniel-nonhomogenous.pdf
f1 = 1/F1t + 1/F1c
f2 = 1/F2t + 1/F2c
f11 = -1/(F1t*F1c)
f22 = -1/(F2t*F2c)
f66 = 1/F12**2
f12 = -0.5*sqrt(f11*f22)
#TW = f1*s1 + f2*s2 + f11*s1**2 + f22*s2**2 + f66*s12**2 + 2*f12*s1*s2
# polynomial to solve. Added a machine epsilon to avoid divide by zero errors
lam1 = f11*s1**2 + f22*s2**2 + f66*s12**2 + 2*f12*s1*s2 + 1e-16
lam2 = f1*s1 + f2*s2 + 1e-16
lam3 = -1
# smallest positive root
roots = array([(-lam2+sqrt(lam2**2-4*lam1*lam3)) / (2*lam1) ,
(-lam2-sqrt(lam2**2-4*lam1*lam3)) / (2*lam1)] )
STRENGTHRATIO_TSAIWU[i] = roots[roots>=0].min() # strength ratio
# f1 = 1/F1t - 1/F1c
# f2 = 1/F2t - 1/F2c
# f11 = 1/(F1t*F1c)
# f22 = 1/(F2t*F2c)
# f66 = 1/F12**2
# STRENGTHRATIO_TSAIWU[i] = 2 / (f1*s2 + f2*s2 + sqrt((f1*s1+f2*s2)**2+4*(f11*s1**2+f22*s2**2+f66*s12**2)))
### Apply safety factors
FAILUREINDEX_MAXSTRESS = FAILUREINDEX_MAXSTRESS * SF
STRENGTHRATIO_TSAIWU = STRENGTHRATIO_TSAIWU / SF
###
MARGINSAFETY_TSAIWU = STRENGTHRATIO_TSAIWU-1 # margin of safety
# strength ratio for max stress, if < 1, then fail, SR = 1/FI
STRENGTHRATIO_MAXSTRESS = 1/(FAILUREINDEX_MAXSTRESS+1e-16)
# margin of safety based on max stress criteria
MARGINSAFETY_MAXSTRESS = STRENGTHRATIO_MAXSTRESS-1
# minimum margin of safety for Max stress failure
MARGINSAFETY_MAXSTRESS_min = MARGINSAFETY_MAXSTRESS.min().min()
FAILUREINDEX_MAXSTRESS_max = FAILUREINDEX_MAXSTRESS.max().max()
# minimum margin of safety of both Tsai-Wu and Max Stress
#MARGINSAFETY_MAXSTRESS_min = np.minimum(MARGINSAFETY_MAXSTRESS.min().min(), MARGINSAFETY_TSAIWU.min() )
# find critial values for all failure criteria
#MARGINSAFETY_MAXSTRESS = MARGINSAFETY_MAXSTRESS[~np.isinf(MARGINSAFETY_MAXSTRESS)] # remove inf
#MARGINSAFETY_TSAIWU = MARGINSAFETY_TSAIWU[~np.isinf(MARGINSAFETY_TSAIWU)] # remove inf
#==========================================================================
# Buckling Failure Calculations
#==========================================================================
''' Buckling of Clamped plates under shear load, reddy, 5.6.17'''
k11 = 537.181*D11/a_width**4 + 324.829*(D12+2*D66)/(a_width**2*b_length**2) + 537.181*D22/b_length**4
k12 = 23.107/(a_width*b_length)
k22 = 3791.532*D11/a_width**4 + 4227.255*(D12+2*D66)/(a_width**2*b_length**2) + 3791.532*D22/b_length**4
Nxycrit0 = 1/k12*np.sqrt(k11*k22)
FI_clamped_shear_buckling = (abs(Nxy_)*SF) / Nxycrit0 # failure if > 1
MS_clamped_shear_buckling = 1/(FI_clamped_shear_buckling+1e-16)-1
'''Kassapoglous pg 126,137
simply supported plate buckling, assumes Nx>0 is compression
Nxcrit0 is the axial load that causes buckling
Nxycrit0 is the shear load that cause buckling
Nxcrit is the axial load part of a combined load that causes buckling
Nxycrit is the shear load part of a combined load that causes buckling
'''
# no buckling issues if Nx is positive
# buckling calcuations assumes Nx compression is positive.
Nx__ = abs(Nx_) if Nx_ < 0 else np.float64(0)
Nxy__ = np.float64(0) if Nxy_ == 0 else abs(Nxy_) # assume shear in 1 direction although both directions are ok
# Nxy=0
Nxcrit0 = pi**2/a_width**2 * (D11 + 2*(D12 + 2*D66)*a_width**2/b_length**2 + D22*a_width**4/b_length**4)
# Nx=0
Nxycrit0 = 9*pi**4*b_length / (32*a_width**3) * (D11 + 2*(D12 + 2*D66)*a_width**2/b_length**2 + D22*a_width**4/b_length**4)
FI_Nxy0_buckling, FI_Nx0_buckling, FI_Nx_buckling, FI_Nxy_buckling = 0,0,0,0
if Nx__ == 0 or Nxy__ == 0:
FI_Nxy0_buckling = (Nxy__*SF)/Nxycrit0
FI_Nx0_buckling = (Nx__*SF)/Nxcrit0
else:
# interaction term
k = Nxy__ / Nx__
Nxcrit = min( abs((pi**2/a_width**2) * (D11 + 2*(D12 + 2*D66)*a_width**2/b_length**2 +D22*a_width**4/b_length**4 ) / (2-8192*a_width**2*k**2/(81*b_length**2*pi**4)) * (5 + sqrt(9 + 65536*a_width**2*k**2/(81*pi**4*b_length**2)))) ,
abs((pi**2/a_width**2) * (D11 + 2*(D12 + 2*D66)*a_width**2/b_length**2 +D22*a_width**4/b_length**4 ) / (2-8192*a_width**2*k**2/(81*b_length**2*pi**4)) * (5 - sqrt(9 + 65536*a_width**2*k**2/(81*pi**4*b_length**2)))) )
Nxycrit = Nxycrit0*sqrt(1-Nxcrit/Nxcrit0)
# interactive calc
FI_Nx_buckling = (Nx__ *SF)/Nxcrit
FI_Nxy_buckling = (Nxy__*SF)/Nxycrit
FI_combinedload_simplesupport_buckle = max([FI_Nxy0_buckling,
FI_Nx0_buckling,
FI_Nx_buckling,
FI_Nxy_buckling] )
MS_min_buckling = 1/(FI_combinedload_simplesupport_buckle+1e-16)-1
#==========================================================================
# Facesheet Wrinkling
#==========================================================================
#==========================================================================
# principal lamainte stresses
#==========================================================================
sigma_principal_laminate = np.linalg.eig(array([[sigma_laminate[0,0],sigma_laminate[2,0],0],
[sigma_laminate[2,0],sigma_laminate[1,0],0],
[0,0,0]]))[0]
tauxy_p = sigma_laminate[2,0]
sigmax_p = sigma_laminate[0,0]
sigmay_p = sigma_laminate[1,0]
thetap = 0.5 * np.arctan( 2*tauxy_p / ((sigmax_p-sigmay_p+1e-16))) * 180/np.pi
#==========================================================================
# Printing Results
#==========================================================================
if prints:
print('--------------- laminate1 Stress analysis of fibers----------')
print('(z-) plyangles (z+)'); print(plyangle)
print('(z-) plymatindex (z+)'); print(plymatindex)
print('ply layers') ; print(z)
print('lamiante thickness, H = {:.4f}'.format(H))
#print('x- zero strain laminate center, z_eps0_x = {:.4f}'.format(z_eps0_x))
#print('y- zero strain laminate center, z_eps0_y = {:.4f}'.format(z_eps0_y))
#print('xy-zero strain laminate center, z_eps0_xy = {:.4f}'.format(z_eps0_xy))
#print('shear center laminate center, z_sc = {:.4f}'.format(z_sc))
print('Applied Loads'); print(NM)
print('ABD=');print(ABD)
print('Ex= {:.2f}'.format(Exbar) )
print('Ey= {:.2f}'.format(Eybar) )
print('nuxy= {:.2f}'.format(nuxybar) )
print('Gxy= {:.2f}'.format(Gxybar) )
print('epsilon_laminate') ; print(epsilon_laminate)
print('sigma_laminate') ; print(sigma_laminate)
print('sigma_principal_laminate') ; print(sigma_principal_laminate)
print('principal_angle = {:.2f} deg'.format(thetap))
print('NMbarapp') ; print(NMbarapp)
print('sigma') ; print(sigma)
print('\nMax Stress Percent Margin of Safety, failure < 0, minimum = {:.4f}'.format( MARGINSAFETY_MAXSTRESS_min ) )
print(MARGINSAFETY_MAXSTRESS)
print('\nTsai-Wu Percent Margin of Safety, failure < 0, minimum = {:.4f}'.format(MARGINSAFETY_TSAIWU.min()))
print(MARGINSAFETY_TSAIWU)
print('\nmaximum failure index = {:.4f}'.format( FAILUREINDEX_MAXSTRESS_max ))
print(FAILUREINDEX_MAXSTRESS)
print('\nBuckling MS for Nxy only for clamped edges = {:.4f}\n'.format(MS_clamped_shear_buckling))
# print('---- Individual Buckling Failure Index (fail>1) combined loads and simple support -----')
# print('FI_Nxy0 = {:.2f}'.format(FI_Nxy0_buckling) )
# print('FI_Nx0 = {:.2f}'.format(FI_Nx0_buckling) )
# print('---- Interactive Buckling Failure Index (fail>1) combined loads and simple support -----')
# print('FI_Nx = {:.2f}'.format(FI_Nx_buckling) )
# print('FI_Nxy = {:.2f}'.format(FI_Nxy_buckling) )
# print('---- Buckling Failure Index (fail>1) combined loads and simple support -----')
# print(FI_combinedload_simplesupport_buckle)
print('buckling combined loads and simple support MS = {:.4f}\n'.format((MS_min_buckling)))
print('Mx_midspan = {:.2f}'.format(Mxq) )
print('My_midspan = {:.2f}'.format(Myq) )
print('Mxy_midspan = {:.2f}'.format(Mxyq) )
print('w0_simplesupport = {:.6f}'.format(w0_simplesupport) )
print('w0_clamped = {:.6f}'.format(w0_clamped) )
print('w0_clamped_isotropic= {:.6f}'.format(w0_clamped_isotropic) )
#display(sp.Matrix(sigmabar))
#==========================================================================
# Plotting
#==========================================================================
if plots:
windowwidth = 800
windowheight = 450
zplot = zeros(2*nply)
for i,k in enumerate(range(0,2*nply,2)): # = nply
zplot[k:k+2] = z[i:i+2]
#legendlab = ['total','thermal','applied','laminate']
# global stresses and strains
mylw = 1.5 #linewidth
# Global Stresses and Strains
f1, ((ax1,ax2,ax3), (ax4,ax5,ax6)) = plt.subplots(2,3, sharex='row', sharey=True)
f1.canvas.set_window_title('Global Stress and Strain of %s laminate' % (plyangle))
stresslabel = ['$\sigma_x$','$\sigma_y$','$\\tau_{xy}$']
strainlabel = ['$\epsilon_x$','$\epsilon_y$','$\gamma_{xy}$']
for i,ax in enumerate([ax1,ax2,ax3]):
## the top axes
ax.set_ylabel('thickness,z')
ax.set_xlabel(strainlabel[i])
ax.set_title(' Ply Strain '+strainlabel[i])
ax.ticklabel_format(axis='x', style='sci', scilimits=(1,4)) # scilimits=(-2,2))
ax.plot(epsilonbar[i,:], zplot, color='blue', lw=mylw, label='total')
ax.plot(epsilonbar_th[i,:], zplot, color='red', lw=mylw, alpha=0.75, linestyle='--', label='thermal')
ax.plot(epsilonbar_app[i,:], zplot, color='green', lw=mylw, alpha=0.75,linestyle='-.', label='applied')
ax.plot([epsilon_laminate[i], epsilon_laminate[i]],[np.min(z) , np.max(z)], color='black', lw=mylw, label='laminate')
ax.grid(True)
#ax.set_xticks(linspace( min(ax.get_xticks()) , max(ax.get_xticks()) ,6))
for i,ax in enumerate([ax4,ax5,ax6]):
ax.set_ylabel('thickness,z')
ax.set_xlabel(stresslabel[i])
ax.set_title(' Ply Stress '+stresslabel[i])
ax.ticklabel_format(axis='x', style='sci', scilimits=(-3,3)) # scilimits=(-2,2))
ax.plot(sigmabar[i,:], zplot, color='blue', lw=mylw, label='total')
ax.plot(sigmabar_th[i,:], zplot, color='red', lw=mylw, alpha=0.75,linestyle='--', label='thermal')
ax.plot(sigmabar_app[i,:], zplot, color='green', lw=mylw, alpha=0.75,linestyle='-.', label='applied')
ax.plot([sigma_laminate[i], sigma_laminate[i]],[np.min(z) , np.max(z)], color='black', lw=mylw, label='laminate')
ax.grid(True)
leg = legend(fancybox=True) ; leg.get_frame().set_alpha(0.3)
tight_layout()
try:
mngr = plt.get_current_fig_manager()
mngr.window.setGeometry(25,50,windowwidth,windowheight)
except:
pass
f1.show()
#plt.savefig('global-stresses-strains.png')
### Local Stresses and Strains
f2, ((ax1,ax2,ax3), (ax4,ax5,ax6)) = plt.subplots(2,3, sharex='row', sharey=True)
f2.canvas.set_window_title('Local Stress and Strain of %s laminate' % (plyangle))
stresslabel = ['$\sigma_1$','$\sigma_2$','$\\tau_{12}$']
strainlabel = ['$\epsilon_1$','$\epsilon_2$','$\gamma_{12}$']
strengthplot = [ [ [F1t,F1t],[zplot.min(), zplot.max()], [F1c, F1c],[zplot.min(), zplot.max()] ] ,
[ [F2t,F2t],[zplot.min(), zplot.max()], [F2c, F2c],[zplot.min(), zplot.max()] ] ,
[ [F12,F12],[zplot.min(), zplot.max()], [-F12,-F12],[zplot.min(), zplot.max()] ] ]
for i,ax in enumerate([ax1,ax2,ax3]):
## the top axes
ax.set_ylabel('thickness,z')
ax.set_xlabel(strainlabel[i])
ax.set_title(' Ply Strain '+strainlabel[i])
ax.ticklabel_format(axis='x', style='sci', scilimits=(1,4)) # scilimits=(-2,2))
ax.plot(epsilon[i,:], zplot, color='blue', lw=mylw, label='total')
ax.plot(epsilon_th[i,:], zplot, color='red', lw=mylw, alpha=0.75,linestyle='--', label='thermal')
ax.plot(epsilon_app[i,:], zplot, color='green', lw=mylw, alpha=0.75,linestyle='-.', label='applied')
ax.plot([epsilon_laminate[i], epsilon_laminate[i]],[np.min(z) , np.max(z)], color='black', lw=mylw, label='laminate')
ax.grid(True)
for i,ax in enumerate([ax4,ax5,ax6]):
ax.set_ylabel('thickness,z')
ax.set_xlabel(stresslabel[i])
ax.set_title(' Ply Stress '+stresslabel[i])
ax.ticklabel_format(axis='x', style='sci', scilimits=(-3,3)) # scilimits=(-2,2))
ax.plot(sigma[i,:], zplot, color='blue', lw=mylw, label='total')
ax.plot(sigma_th[i,:], zplot, color='red', lw=mylw, alpha=0.75,linestyle='--', label='thermal')
ax.plot(sigma_app[i,:], zplot, color='green', lw=mylw, alpha=0.75,linestyle='-.', label='applied')
ax.plot([sigma_laminate[i], sigma_laminate[i]],[np.min(z) , np.max(z)], color='black', lw=mylw, label='laminate')
### plots strengths
#ax.plot(strengthplot[i][0],strengthplot[i][1], color='yellow', lw=mylw)
ax.grid(True)
leg = legend(fancybox=True) ; leg.get_frame().set_alpha(0.3)
tight_layout()
try:
mngr = plt.get_current_fig_manager()
mngr.window.setGeometry(windowwidth+50,50,windowwidth,windowheight)
except:
pass
f2.show()
#plt.savefig('local-stresses-strains.png')
### Failure
f3, ((ax1,ax2,ax3)) = plt.subplots(1,3, sharex=True, sharey=True)
f3.canvas.set_window_title('Failure Index(failure if > 1), %s laminate' % (plyangle))
stresslabel = ['$\sigma_1/F_1$','$\sigma_2/F_2$','$\\tau_{12}/F_{12}$']
for i,ax in enumerate([ax1,ax2,ax3]):
## the top axes
ax.set_ylabel('thickness,z')
ax.set_xlabel(stresslabel[i])
#ax.set_title(' Ply Strain at $\epsilon=%f$' % (epsxapp*100))
ax.ticklabel_format(axis='x', style='sci', scilimits=(1,4)) # scilimits=(-2,2))
ax.plot(FAILUREINDEX_MAXSTRESS[i,:], zplot, color='blue', lw=mylw, label='total')
ax.grid(True)
ax.set_title('Failure Index, fail if > 1')
#leg = legend(fancybox=True) ; leg.get_frame().set_alpha(0.3)
tight_layout()
try:
mngr = plt.get_current_fig_manager()
mngr.window.setGeometry(25,windowheight+100,windowwidth,windowheight)
except:
pass
f2.show()
#plt.savefig('local-stresses-strains.png')
### warpage
res = 100
Xplt,Yplt = np.meshgrid(np.linspace(-a_width/2,a_width/2,res), np.linspace(-b_length/2,b_length/2,res))
epsx = epsilon_laminate[0,0]
epsy = epsilon_laminate[1,0]
epsxy = epsilon_laminate[2,0]
kapx = epsilon_laminate[3,0]
kapy = epsilon_laminate[4,0]
kapxy = epsilon_laminate[5,0]
### dispalcement
w = -0.5*(kapx*Xplt**2 + kapy*Yplt**2 + kapxy*Xplt*Yplt)
u = epsx*Xplt # pg 451 hyer
fig = plt.figure('plate-warpage')
ax = fig.gca(projection='3d')
ax.plot_surface(Xplt, Yplt, w+zmid[0], cmap=mpl.cm.jet, alpha=0.3)
###ax.auto_scale_xyz([-(a_width/2)*1.1, (a_width/2)*1.1], [(b_length/2)*1.1, (b_length/2)*1.1], [-1e10, 1e10])
ax.set_xlabel('plate width,y-direction,in')
ax.set_ylabel('plate length,x-direction, in')
ax.set_zlabel('warpage,in')
#ax.set_zlim(-0.01, 0.04)
#mngr = plt.get_current_fig_manager() ; mngr.window.setGeometry(450,550,600, 450)
try:
mngr = plt.get_current_fig_manager()
mngr.window.setGeometry(windowwidth+50,windowheight+100,windowwidth,windowheight)
except:
pass
plt.show()
#plt.savefig('plate-warpage')
return MARGINSAFETY_MAXSTRESS_min, FAILUREINDEX_MAXSTRESS_max
def plate():
'''
composite plate mechanics
TODO - results need vetted
'''
#==========================================================================
# Initialize
#==========================================================================
get_ipython().magic('matplotlib')
plt.close('all')
plt.rcParams['figure.figsize'] = (12, 8)
plt.rcParams['font.size'] = 13
#plt.rcParams['legend.fontsize'] = 14
#==========================================================================
# Import Material Properties
#==========================================================================
plythk = 0.0025
plyangle = array([0,90,-45,45,0]) * np.pi/180 # angle for each ply
nply = len(plyangle) # number of plies
laminatethk = np.zeros(nply) + plythk
H = sum(laminatethk) # plate thickness
# Create z dimensions of laminate
z_ = np.linspace(-H/2, H/2, nply+1)
a = 20 # plate width;
b = 10 # plate height
q0_ = 5.7 # plate load;
# Transversly isotropic material properties
E1 = 150e9
E2 = 12.1e9
nu12 = 0.248
G12 = 4.4e9
nu23 = 0.458
G23 = E2 / (2*(1+nu23))
# Failure Strengths
F1t = 1500e6
F1c = -1250e6
F2t = 50e6
F2c = -200e6
F12t = 100e6
F12c = -100e6
Strength = np.array([[F1t, F1c],
[F2t, F2c],
[F12t, F12c]])
th = sp.symbols('th')
# Stiffnes matrix in material coordinates
Cijm6 = inv(Sij6)
# reduced stiffness in structural
Cij = sp.Matrix([[Cij6[0,0], Cij6[0,1], 0],
[Cij6[0,1], Cij6[1,1], 0],
[0, 0, Cij6[5,5] ]] )
Tij = sp.Matrix([[cos(th)**2, sin(th)**2, 2*sin(th)*cos(th)],
[sin(th)**2, cos(th)**2, -2*sin(th)*cos(th)],
[-cos(th)*sin(th), sin(th)*cos(th), (cos(th)**2-sin(th)**2)]])
## Cylindrical Bending of a laminated plate
# displacement in w (z direction)
from sympy.abc import x
f = Function('f')
eq = dsolve(2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x), f(x), hint = '1st_homogeneous_coeff_best', simplify=False)
pprint(eq)
#==============================================================================
th,x,y,z,q0,C1,C2,C3,C4,C5,C6,C7,A11,B11,D11,A16,B16 = symbols('th x y z q0 C1 C2 C3 C4 C5 C6 C7 A11 B11 D11 A16 B16')
wfun = Function('wfun')
ufun = Function('ufun')
## EQ 4.4.1a
eq1 = A11*ufun(x).diff(x,2) - B11*wfun(x).diff(x,3)
#eq1 = A11*diff(ufun,x,2) - B11*diff(wfun,x,3); # C5 C1
## EQ 4.4.1b
#eq2 = A16*diff(ufun,x,2) - B16*diff(wfun,x,3); # C5 C1
eq2 = A16*ufun(x).diff(x,2) - B16*wfun(x).diff(x,3)
## EQ 4.4.1c
#eq3 = B11*diff(ufun,x,3) - D11*diff(wfun,x,4) + q0;
eq3 = B11*ufun(x).diff(x,3) - D11*wfun(x).diff(x,4) + q0
################## python conversion eded here ################################
# solve eq1 eq2 and eq3 to get the w and u functions
# displacement in w (z direction) from eq1,eq2,eq3
wfun = A11*q0*x**4 / (4*(6*B11**2-6*A11*D11)) + C1 + C2*x + C3*x**2 + C4*x**3 # C1 C2 C3 C4
# displacement in u (x direction) from eq1,eq2,eq3
ufun = B11*q0*x**3 / (6*(B11**2-A11*D11)) + C7 + x*C6 + 3*B11*x**2*C5/A11 # C5 C6 C7
# Cij6.evalf(subs={th:plyangle[i]}) * (z_[i+1]**3-z_[i]**3)
# cond1 -> w(0)=0 at x(0), roller
C1sol = sp.solve(wfun.subs(x,0), C1)[0] # = 0
# cond2 -> angle at dw/dx at x(0) is 0, cantilever
C2sol = sp.solve(wfun.diff(x).subs(x,0),C2)[0] # = 0
# cond3 -> w(z) = 0 at x(a), roller
C4sol1 = sp.solve(wfun.subs({x:a,C1:C1sol,C2:C2sol}),C4)[0] # C3
# cond4 u = 0 at x = 0
C7sol = sp.solve(ufun.subs(x,0),C7)[0] #=0
# u=0 at x = a
C5sol1 = sp.solve(ufun.subs({x:a, C7:C7sol}),C5)[0] #C6
# cond 5 EQ 4.4.14a Myy = 0 @ x(a) (Mxx , B11 D11) (Myy, B12 D12) roller no moment
C6sol1 = sp.solve( ( ((B11*ufun.diff(x)+0.5*wfun.diff(x)**2 ) - D11*wfun.diff(x,2)).subs({x:a, C1:C1sol, C2:C2sol, C4:C4sol1, C5:C5sol1, C7:C7sol})), C6)[0] # C6 C3
# EQ 4.4.13a, Nxx = 0 @ x(0) roller has no Nxx
C6sol2 = sp.solve( ((A11* ufun.diff(x) + 0.5*wfun.diff(x)**2)-B11*wfun.diff(x,2)).subs({x:a, C1:C1sol, C2:C2sol, C4:C4sol1, C5:C5sol1, C7:C7sol}),C6)[0] # C6 C3
C3sol = sp.solve(C6sol1 - C6sol2,C3)[0]
C4sol = C4sol1.subs(C3,C3sol)
C6sol = sp.simplify(C6sol2.subs(C3,C3sol))
C5sol = sp.simplify(C5sol1.subs(C6,C6sol))
# substitute integration constants with actual values( _ is actual number)
C1_ = copy(C1sol)
C2_ = copy(C2sol)
C7_ = copy(C7sol)
C3_ = C3sol.subs({q0:q0_, A11:Aij[0,0], B11:Bij[0,0], D11:Dij[0,0]})
C4_ = C4sol.subs({q0:q0_, A11:Aij[0,0], B11:Bij[0,0], D11:Dij[0,0]})
C5_ = C5sol.subs({q0:q0_, A11:Aij[0,0], B11:Bij[0,0], D11:Dij[0,0]})
C6_ = C6sol.subs({q0:q0_, A11:Aij[0,0], B11:Bij[0,0], D11:Dij[0,0]})
# function w(x) vertical displacement w along z with actual vaules
wsol = wfun.subs({q0:q0_, C1:C1_, C2:C2_, C3:C3_, C4:C4_, A11:Aij[0,0], B11:Bij[0,0], D11:Dij[0,0]})
# function u(x) horizontal displacement u along x with actual vaules
usol = ufun.subs({q0:q0_, C5:C5_, C6:C6_, C7:C7_, A11:Aij[0,0], B11:Bij[0,0], D11:Dij[0,0]})
# 3d plots
plot3d(wsol,(x,0,a), (y,0,b))
plt.xlabel('x')
plt.ylabel('y')
plt.title('Cylindrical Bending -Displacement of a plate With CLPT')
## Strain calculation
# eq 3.3.8 (pg 116 reddy (pdf = 138))
epstotal = array([[usol.diff(x) + 0.5* wsol.diff(x)**5 - z*wsol.diff(x,2)],[0],[0]])
epsx = epstotal[0,0]
## Calculating and plotting Stress in each layer
res = 8 # accuracy of finding max and min stress
xplot = linspace(0,a,res)
yplot = linspace(0,b,res)
G0 = sp.symbols('G0')
Globalminstress = np.zeros((3, nply))
Globalmaxstress = np.zeros((3, nply))
for kstress in range(3): # stress state s_x, s_y, s_xz
plt.figure(kstress+1)
for klay in range(nply): # loop through all layers
thplot = plyangle[klay]
zplot = linspace(z_[klay],z_[klay+1],res)
stressplot = np.zeros((len(zplot),len(xplot)))
## Calc Stresses
if kstress == 2:
# Shear stresses
G0_ = -sp.integrate(s_stress[0].diff(x),z)+G0
# solve for shear stresses from s_1
s_xz = sp.solve(G0_,G0)[0]
# out of plane shear S_xz does not need to be transformed ??
plot3d(s_xz, (x,0, a), (z, z_[klay], z_[klay+1]) )
else:
# normal stresses
# Cij = reduced structural stiffness in strictural coordinates 3x3
# stress in structural coordinates
s_stress = Cij.subs(th,thplot) @ epstotal
# stressin material coordinates
m_stress = Tij.subs(th,thplot) @ s_stress
#ezsurf(m_stress(kstress),[0,a,z_(klay),z_(klay+1)])
## find max stress in each layer
ii=0
for i in xplot:
jj=0
for j in zplot:
if kstress == 2:
stressplot[ii,jj] = s_xz.subs({x:i, z:j})
else:
stressplot[ii,jj] = m_stress[kstress].subs({x:i, z:j})
jj+=jj
ii+=ii
Globalminstress[kstress,klay] = np.min(stressplot)
Globalmaxstress[kstress,klay] = np.max(stressplot)
#
plt.title('\sigma_%i' % kstress)
## Plot max stress and failure strength
plt.figure()
for i in range(3):
plt.subplot(1, 3, i+1)
plt.bar(range(nply), Globalmaxstress[i,:])
plt.bar(range(nply), Globalminstress[i,:])
plt.scatter(range(nply),np.ones(nply) * Strength[i,0])
plt.scatter(range(nply),np.ones(nply) * Strength[i,1])
plt.xlabel('layer')
plt.title('\sigma%i' % i)
def plate_navier():
'''
composite plate bending with navier solution
TODO - code needs to be converted from matlab
'''
## Plate a*b*h simply supported under q = q0 CLPT
pass
'''
q0,a,b,m,n,x,y = sp.symbols('q0 a b m n x y')
Qmn = 4/(a*b)*sp.integrate( sp.integrate( q0*sp.sin(m*pi*x/a)*sp.sin(n*pi*y/b),(x,0,a)) ,(y,0,b))
dmn = pi**4 / b**4 * (DTij(1,1)*m**4*(b/a)**4 + 2* (DTij(1,2)+2*DTij(6,6)) *m**2*n**2*(b/a)**2 + DTij(2,2)*n**4)
Wmn = Qmn/dmn;
w0 = Wmn * sin(m*pi*x/a) * sin(n*pi*y/b);
w0_ = subs(w0,[q0 a b],[-q0_ a_ b_] );
figure
w0sum = 0;
for n_ = 1:10
for m_ = 1:10
w0sum = w0sum + subs(w0_,[n m],[n_ m_]);
end
end
w0sum;
% xplot = linspace(0,a_,res);
% yplot = linspace(0,b_,res);
ii=1;
for i = xplot
jj=1;
for j = yplot
w0plot(ii,jj) = subs(w0sum,[x y],[i j]);
jj=jj+1;
end
ii=ii+1;
end
surf(xplot,yplot,w0plot)
colorbar
set(gca,'PlotBoxAspectRatio',[2 1 1]);
xlabel('length a, u(x)')
ylabel('length b, v(y)')
zlabel('w(z)')
'''
class laminate(object):
"""
IN-WORK - laminate object for composite material analysis
"""
# constructor
def __init__(self, plyangle, matindex, matname):
# run when laminate is instantiated
# loads materials used
self.plyangle = plyangle
self.matindex = matindex
self.matname = matname
self.__mat = self.__import_matprops(matname)
# create a simple function to handle CTE properties
def __alphaf(self, mat):
return array([[mat.alpha1], [mat.alpha2], [0]])
self.laminatethk = array([self.__mat[matname[i]].plythk for i in matindex ])
self.nply = len(self.laminatethk) # number of plies
self.H = np.sum(self.laminatethk) # plate thickness
# area = a_width*H
z = zeros(self.nply+1)
zmid = zeros(self.nply)
z[0] = -self.H/2
for i in range(self.nply):
z[i+1] = z[i] + self.laminatethk[i]
zmid[i] = z[i] + self.laminatethk[i]/2
self.z = z
self.zmid = zmid
self.__abdmatrix()
def __Qf(self, E1,E2,nu12,G12):
'''transversly isptropic compliance matrix. pg 58 herakovich
G12 = E1/(2*(1+nu12)) if isotropic'''
nu21 = E2*nu12/E1
Q = array([[E1/(1-nu12*nu21), E2*nu12/(1-nu12*nu21), 0],
[ E2*nu12/(1-nu12*nu21), E2/(1-nu12*nu21), 0],
[0, 0, G12]])
return Q
def __T1(self, th):
'''Stress Transform for Plane Stress
th=ply angle in degrees
voight notation for stress tranform. sigma1 = T1 @ sigmax
recall T1(th)**-1 == T1(-th)'''
n = sin(th*pi/180)
m = cos(th*pi/180)
T1 = array( [[m**2, n**2, 2*m*n],
[n**2, m**2,-2*m*n],
[-m*n, m*n,(m**2-n**2)]])
return T1
def __T2(self, th):
'''Strain Transform for Plane Stress
th=ply angle in degrees
voight notation for strain transform. epsilon1 = T2 @ epsilonx'''
n = sin(th*pi/180)
m = cos(th*pi/180)
T2 = array( [[m**2, n**2, m*n],
[n**2, m**2,-m*n],
[-2*m*n, 2*m*n, (m**2-n**2)]])
return T2
# private method
def __abdmatrix(self):
'''used within the object but not accessible outside'''
#==========================================================================
# ABD Matrix Compute
#==========================================================================
# Reduced stiffness matrix for a plane stress ply in principal coordinates
# calcluating Q from the Compliance matrix may cause cancE1ation errors
A = zeros((3,3)); B = zeros((3,3)); D = zeros((3,3))
for i in range(self.nply): # = nply
Q = self.__Qf(self.__mat[self.matname[self.matindex[i]]].E1,
self.__mat[self.matname[self.matindex[i]]].E2,
self.__mat[self.matname[self.matindex[i]]].nu12,
self.__mat[self.matname[self.matindex[i]]].G12 )
Qbar = inv(self.__T1(self.plyangle[i])) @ Q @ self.__T2(self.plyangle[i]) # solve(T1(plyangle[i]), Q) @ T2(plyangle[i])
A += Qbar*(self.z[i+1]-self.z[i])
# coupling stiffness
B += (1/2)*Qbar*(self.z[i+1]**2-self.z[i]**2)
# bending or flexural laminate stiffness relating moments to curvatures
D += (1/3)*Qbar*(self.z[i+1]**3-self.z[i]**3)
# laminate stiffness matrix
ABD = zeros((6,6))
ABD[0:3,0:3] = A
ABD[0:3,3:6] = B
ABD[3:6,0:3] = B
ABD[3:6,3:6] = D
self.ABD = ABD
# method
def available_materials(self):
'''show the materials available in the library'''
matprops = pd.read_csv(os.path.join(os.path.dirname(__file__), "compositematerials.csv"), index_col=0)
print('---available materials---')
for k in matprops.columns.tolist():
print(k)
print('-------------------------')
# private method to be used internally
def __import_matprops(self, mymaterial=['T300_5208','AL_7075']):
'''
import material properties
'''
matprops = pd.read_csv(os.path.join(os.path.dirname(__file__), "compositematerials.csv"), index_col=0)
if mymaterial==[] or mymaterial=='':
print(matprops.columns.tolist())
mat = matprops[mymaterial]
#mat.applymap(lambda x:np.float(x))
mat = mat.applymap(lambda x:pd.to_numeric(x, errors='ignore'))
return mat
def failure_envelope_laminate(Nx,Ny,Nxy,Mx,My,Mxy,q0,mymat,layup):
'''
find the miniumu margin give load conditions
'''
# create a 45 carbon cloth panel with a 0.5 inch rohacell core
_, FAILUREINDEX_MAXSTRESS_max = laminate_calcs(NM=[Nx,Ny,Nxy,Mx,My,Mxy],
ek=[0,0,0,0,0,0],
q0=q0,
plyangle= layup,
plymatindex=[0,0,0,0],
materials = [mymat],
platedim=[10,10],
zoffset=0,
SF=1.0,
plots=0,
prints=0)
return FAILUREINDEX_MAXSTRESS_max
def plot_single_max_failure_loads(mymat='E-Glass Epoxy fabric M10E-3783', mylayup=[0,45,45,0] ):
'''
loops through and tries to find a load that is close to 0 and then
attempts to find the root (ie margin=0)
older version used newton method for root finding
scipy.optimize.newton(laminate_min, guess)
TODO: Current calculation is stupid using random points to plot. fix it
by use FI, failure index instead of margin to generate a
linear relationship and envelope
'''
#laminate_min = lambda N: failure_envelope_laminate(N,0,0,0,0,0,0)
loadnamelist = ['Nx','Ny','Nxy','Mx','My','Mxy','q0']
laminate_min_list = []
laminate_min_list.append(lambda N: failure_envelope_laminate(N,0,0,0,0,0,0,mymat,mylayup))
laminate_min_list.append(lambda N: failure_envelope_laminate(0,N,0,0,0,0,0,mymat,mylayup))
laminate_min_list.append(lambda N: failure_envelope_laminate(0,0,N,0,0,0,0,mymat,mylayup))
laminate_min_list.append(lambda N: failure_envelope_laminate(0,0,0,N,0,0,0,mymat,mylayup))
laminate_min_list.append(lambda N: failure_envelope_laminate(0,0,0,0,N,0,0,mymat,mylayup))
laminate_min_list.append(lambda N: failure_envelope_laminate(0,0,0,0,0,N,0,mymat,mylayup))
laminate_min_list.append(lambda N: failure_envelope_laminate(0,0,0,0,0,0,N,mymat,mylayup))
envelope_loads = []
N_t = array([0,1])
N_c = array([0,-1])
for loadname,laminate_min in zip(loadnamelist,laminate_min_list):
# tension
FI = [laminate_min(N) for N in N_t]
m = (FI[1]-FI[0]) / (N_t[1] - N_t[0])
b = FI[1]-m*N_t[1]
N_crit_t = (1-b) / m
# compression
FI = [laminate_min(N) for N in N_c]
m = (FI[1]-FI[0]) / (N_c[1] - N_c[0])
b = FI[1]-m*N_c[1]
N_crit_c = (1-b) / m
envelope_loads.append('{} = {:.1f} , {:.1f}'.format(loadname,N_crit_t, N_crit_c))
print('------------- enveloped loads for {} {} -----------------'.format(mylayup, mymat))
for k in envelope_loads:
print(k)
# plot envelope
Nx_env = []
Nxy_env = []
laminate_min = lambda N: failure_envelope_laminate(N,0,0,0,0,0,0,mymat,mylayup)
# compression
FI = [laminate_min(N) for N in N_c]
m = (FI[1]-FI[0]) / (N_c[1] - N_c[0])
b = FI[1]-m*N_c[1]
Nx_env.append( (1-b) / m )
Nxy_env.append( 0 )
# tension
FI = [laminate_min(N) for N in N_t]
m = (FI[1]-FI[0]) / (N_t[1] - N_t[0])
b = FI[1]-m*N_t[1]
Nx_env.append( (1-b) / m )
Nxy_env.append( 0 )
laminate_min = lambda N: failure_envelope_laminate(0,0,N,0,0,0,0,mymat,mylayup)
# compression
FI = [laminate_min(N) for N in N_c]
m = (FI[1]-FI[0]) / (N_c[1] - N_c[0])
b = FI[1]-m*N_c[1]
Nxy_env.append( (1-b) / m )
Nx_env.append( 0 )
# tension
FI = [laminate_min(N) for N in N_t]
m = (FI[1]-FI[0]) / (N_t[1] - N_t[0])
b = FI[1]-m*N_t[1]
Nxy_env.append( (1-b) / m )
Nx_env.append( 0 )
laminate_min_Nx_Nxy_func = lambda Nx,Nxy: failure_envelope_laminate(Nx,0,Nxy,0,0,0,0,mymat,mylayup)
n = 500
f = 1.25 # < 1
# arr1 = np.random.randint(Nx_env[0]-abs(Nx_env[0]*f),Nx_env[0]+abs(Nx_env[0])*f,n)
# arr2 = np.random.randint(Nx_env[1]-abs(Nx_env[1]*f),Nx_env[1]+abs(Nx_env[1])*f,n)
# Nx_r = np.concatenate((arr1, arr2))
#
# arr1 = np.random.randint(Nxy_env[2]-abs(Nxy_env[2])*f,Nxy_env[2]+abs(Nxy_env[2])*f,n)
# arr2 = np.random.randint(Nxy_env[3]-abs(Nxy_env[3])*f,Nxy_env[3]+abs(Nxy_env[3])*f,n)
# Nxy_r = np.concatenate((arr1, arr2))
Nx_r = np.random.randint(Nx_env[0]*f,Nx_env[1]*f, n)
Nxy_r = np.random.randint(Nxy_env[2]*f,Nxy_env[3]*f, n)
for Nx_ri, Nxy_ri in zip(Nx_r, Nxy_r):
FI = laminate_min_Nx_Nxy_func(Nx_ri, Nxy_ri)
if FI < 1:
Nx_env.append(Nx_ri)
Nxy_env.append(Nxy_ri)
points = array([ [x,xy] for x,xy in zip(Nx_env, Nxy_env)])
hull = scipy.spatial.ConvexHull(points)
plot(points[:,0], points[:,1], 'bo')
for simplex in hull.simplices:
plot(points[simplex, 0], points[simplex, 1], 'k-')
xlabel('Nx, lb/in')
ylabel('Nxy, lb/in')
title('Failure envelope')
return envelope_loads
def my_laminate_with_loading():
# loads lbs/in
Nx = 50
Ny = 0
Nxy = 0
Mx = 0
My = 0
Mxy = 0
q0 = 0 # pressure
# Qx = 0
# Qy = 0
a_width = 50
b_length = 3.14*6.75
## sandwich laminate
# plyangle= [45,45,0, 45,45],
# plymatindex=[0, 0, 1, 0, 0],
# create a 45 carbon cloth panel with a 0.5 inch rohacell core
laminate_calcs(NM=[Nx,Ny,Nxy,Mx,My,Mxy],
ek=[0,0,0,0,0,0],
q0=q0,
plyangle= [0,60,-60,-60,60,0],
plymatindex=[0,0,0,0,0,0],
materials = ['E-Glass Epoxy Uni'],
platedim=[a_width,b_length],
zoffset=0,
SF=2.0,
plots=0,
prints=1)
if __name__=='__main__':
#plot_single_max_failure_loads()
#plot_failure_index()
my_laminate_with_loading()
#material_plots(['E-Glass Epoxy fabric M10E-3783'])
#plate()
#plot_Nx_Nxy_failure_envelope(['Carbon_cloth_AGP3705H'])
#plot_single_max_failure_loads()
# # reload modules
# import importlib ; importlib.reload
# from composites import laminate
# plyangle = [0,45]
# matindex = [0,0]
# matname = ['graphite-polymer_SI']
# lam1 = laminate(plyangle, matindex, matname)
# lam1.ABD
| mit |
guziy/basemap | setup.py | 1 | 6013 | from __future__ import (absolute_import, division, print_function)
import glob
import io
import os
import sys
from setuptools.dist import Distribution
if sys.version_info < (2, 6):
raise SystemExit("""matplotlib and the basemap toolkit require Python 2.6 or later.""")
# Do not require numpy for just querying the package
# Taken from the netcdf-python setup file (which took it from h5py setup file).
inc_dirs = []
if any('--' + opt in sys.argv for opt in Distribution.display_option_names +
['help-commands', 'help']) or sys.argv[1] == 'egg_info':
from setuptools import setup, Extension
else:
import numpy
# Use numpy versions if they are available.
from numpy.distutils.core import setup, Extension
# append numpy include dir.
inc_dirs.append(numpy.get_include())
def get_install_requirements(path):
path = os.path.join(os.path.dirname(__file__), path)
with io.open(path, encoding='utf-8') as fp:
content = fp.read()
return [req for req in content.split("\n")
if req != '' and not req.startswith('#')]
def checkversion(GEOS_dir):
"""check geos C-API header file (geos_c.h)"""
try:
f = open(os.path.join(GEOS_dir, 'include', 'geos_c.h'))
except IOError:
return None
geos_version = None
for line in f:
if line.startswith('#define GEOS_VERSION'):
geos_version = line.split()[2]
return geos_version
# get location of geos lib from environment variable if it is set.
if 'GEOS_DIR' in os.environ:
GEOS_dir = os.environ.get('GEOS_DIR')
else:
# set GEOS_dir manually here if automatic detection fails.
GEOS_dir = None
user_home = os.path.expanduser('~')
geos_search_locations = [user_home, os.path.join(user_home, 'local'),
'/usr', '/usr/local', '/sw', '/opt', '/opt/local']
if GEOS_dir is None:
# if GEOS_dir not set, check a few standard locations.
GEOS_dirs = geos_search_locations
for direc in GEOS_dirs:
geos_version = checkversion(direc)
sys.stdout.write('checking for GEOS lib in %s ....\n' % direc)
if geos_version is None or geos_version < '"3.1.1"':
continue
else:
sys.stdout.write('GEOS lib (version %s) found in %s\n' %\
(geos_version[1:-1],direc))
GEOS_dir = direc
break
else:
geos_version = checkversion(GEOS_dir)
if GEOS_dir is None:
raise SystemExit("""
Can't find geos library in standard locations ('%s').
Please install the corresponding packages using your
systems software management system (e.g. for Debian Linux do:
'apt-get install libgeos-3.3.3 libgeos-c1 libgeos-dev' and/or
set the environment variable GEOS_DIR to point to the location
where geos is installed (for example, if geos_c.h
is in /usr/local/include, and libgeos_c is in /usr/local/lib,
set GEOS_DIR to /usr/local), or edit the setup.py script
manually and set the variable GEOS_dir (right after the line
that says "set GEOS_dir manually here".""" % "', '".join(geos_search_locations))
else:
geos_include_dirs=[os.path.join(GEOS_dir,'include')] + inc_dirs
geos_library_dirs=[os.path.join(GEOS_dir,'lib'),os.path.join(GEOS_dir,'lib64')]
packages = ['mpl_toolkits','mpl_toolkits.basemap']
namespace_packages = ['mpl_toolkits']
package_dirs = {'':'lib'}
# can't install _geoslib in mpl_toolkits.basemap namespace,
# or Basemap objects won't be pickleable.
# don't use runtime_library_dirs on windows (workaround
# for a distutils bug - http://bugs.python.org/issue2437).
if sys.platform == 'win32':
runtime_lib_dirs = []
else:
runtime_lib_dirs = geos_library_dirs
extensions = [ Extension("_geoslib",['src/_geoslib.c'],
library_dirs=geos_library_dirs,
runtime_library_dirs=runtime_lib_dirs,
include_dirs=geos_include_dirs,
libraries=['geos_c']) ]
# Specify all the required mpl data
pathout =\
os.path.join('lib',os.path.join('mpl_toolkits',os.path.join('basemap','data')))
datafiles = glob.glob(os.path.join(pathout,'*'))
datafiles = [os.path.join('data',os.path.basename(f)) for f in datafiles]
package_data = {'mpl_toolkits.basemap':datafiles}
install_requires = get_install_requirements("requirements.txt")
__version__ = "1.2.1"
setup(
name = "basemap",
version = __version__,
description = "Plot data on map projections with matplotlib",
long_description = """
An add-on toolkit for matplotlib that lets you plot data
on map projections with coastlines, lakes, rivers and political boundaries.
See http://matplotlib.org/basemap/users/examples.html for
examples of what it can do.""",
url = "https://matplotlib.org/basemap/",
download_url = "https://github.com/matplotlib/basemap/archive/v{0}rel.tar.gz".format(__version__),
author = "Jeff Whitaker",
author_email = "jeffrey.s.whitaker@noaa.gov",
maintainer = "Ben Root",
maintainer_email = "ben.v.root@gmail.com",
install_requires = install_requires,
platforms = ["any"],
license = "OSI Approved",
keywords = ["python","plotting","plots","graphs","charts","GIS","mapping","map projections","maps"],
classifiers = ["Development Status :: 5 - Production/Stable",
"Intended Audience :: Science/Research",
"License :: OSI Approved",
"Programming Language :: Python",
"Programming Language :: Python :: 3",
"Topic :: Scientific/Engineering :: Visualization",
"Topic :: Software Development :: Libraries :: Python Modules",
"Operating System :: OS Independent"],
packages = packages,
namespace_packages = namespace_packages,
package_dir = package_dirs,
ext_modules = extensions,
package_data = package_data
)
| gpl-2.0 |
chugunovyar/factoryForBuild | env/lib/python2.7/site-packages/matplotlib/sphinxext/mathmpl.py | 12 | 3822 | from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
import os
import sys
from hashlib import md5
from docutils import nodes
from docutils.parsers.rst import directives
import warnings
from matplotlib import rcParams
from matplotlib.mathtext import MathTextParser
rcParams['mathtext.fontset'] = 'cm'
mathtext_parser = MathTextParser("Bitmap")
# Define LaTeX math node:
class latex_math(nodes.General, nodes.Element):
pass
def fontset_choice(arg):
return directives.choice(arg, ['cm', 'stix', 'stixsans'])
options_spec = {'fontset': fontset_choice}
def math_role(role, rawtext, text, lineno, inliner,
options={}, content=[]):
i = rawtext.find('`')
latex = rawtext[i+1:-1]
node = latex_math(rawtext)
node['latex'] = latex
node['fontset'] = options.get('fontset', 'cm')
return [node], []
math_role.options = options_spec
def math_directive(name, arguments, options, content, lineno,
content_offset, block_text, state, state_machine):
latex = ''.join(content)
node = latex_math(block_text)
node['latex'] = latex
node['fontset'] = options.get('fontset', 'cm')
return [node]
# This uses mathtext to render the expression
def latex2png(latex, filename, fontset='cm'):
latex = "$%s$" % latex
orig_fontset = rcParams['mathtext.fontset']
rcParams['mathtext.fontset'] = fontset
if os.path.exists(filename):
depth = mathtext_parser.get_depth(latex, dpi=100)
else:
try:
depth = mathtext_parser.to_png(filename, latex, dpi=100)
except:
warnings.warn("Could not render math expression %s" % latex,
Warning)
depth = 0
rcParams['mathtext.fontset'] = orig_fontset
sys.stdout.write("#")
sys.stdout.flush()
return depth
# LaTeX to HTML translation stuff:
def latex2html(node, source):
inline = isinstance(node.parent, nodes.TextElement)
latex = node['latex']
name = 'math-%s' % md5(latex.encode()).hexdigest()[-10:]
destdir = os.path.join(setup.app.builder.outdir, '_images', 'mathmpl')
if not os.path.exists(destdir):
os.makedirs(destdir)
dest = os.path.join(destdir, '%s.png' % name)
path = '/'.join((setup.app.builder.imgpath, 'mathmpl'))
depth = latex2png(latex, dest, node['fontset'])
if inline:
cls = ''
else:
cls = 'class="center" '
if inline and depth != 0:
style = 'style="position: relative; bottom: -%dpx"' % (depth + 1)
else:
style = ''
return '<img src="%s/%s.png" %s%s/>' % (path, name, cls, style)
def setup(app):
setup.app = app
# Add visit/depart methods to HTML-Translator:
def visit_latex_math_html(self, node):
source = self.document.attributes['source']
self.body.append(latex2html(node, source))
def depart_latex_math_html(self, node):
pass
# Add visit/depart methods to LaTeX-Translator:
def visit_latex_math_latex(self, node):
inline = isinstance(node.parent, nodes.TextElement)
if inline:
self.body.append('$%s$' % node['latex'])
else:
self.body.extend(['\\begin{equation}',
node['latex'],
'\\end{equation}'])
def depart_latex_math_latex(self, node):
pass
app.add_node(latex_math,
html=(visit_latex_math_html, depart_latex_math_html),
latex=(visit_latex_math_latex, depart_latex_math_latex))
app.add_role('math', math_role)
app.add_directive('math', math_directive,
True, (0, 0, 0), **options_spec)
metadata = {'parallel_read_safe': True, 'parallel_write_safe': True}
return metadata
| gpl-3.0 |
pylayers/pylayers | pylayers/antprop/examples/ex_signature.py | 3 | 3411 | #!/usr/bin/python
#-*- coding:Utf-8 -*-
import matplotlib.pyplot as plt
import numpy as np
import networkx as nx
from pylayers.gis.layout import *
from pylayers.antprop.signature import *
# load the layout graphs
def showr2(L,r2d,tx,rx,k,l):
col = ['r','b','g','c','m','k','y']
r = r2d[str(k)]
pts = r['pt']
sig = r['sig']
fig,ax = showsig(L,sig[:,:,l],tx,rx)
sh = np.shape(pts)
x = np.hstack((tx[0],pts[0,:,l],rx[0]))
y = np.hstack((tx[1],pts[1,:,l],rx[1]))
plt.plot(x,y,col[k])
plt.title(sig[:,:,l])
return fig,ax
def showr2d(L,r2d,tx,rx):
"""
r2d['pt'] : nd,ni,nr
"""
L.display['thin']=True
col = ['r','b','g','c','m','k','y']
fig,ax = L.showGs()
for k in r2d:
r = r2d[k]
pts = r['pt']
sh = np.shape(pts)
for r in range(sh[2]):
x = np.hstack((tx[0],pts[0,:,r],rx[0]))
y = np.hstack((tx[1],pts[1,:,r],rx[1]))
plt.plot(x,y,col[eval(k)])
return fig,ax
def showsig(L,s,tx,rx):
L.display['thin']=True
fig,ax = L.showGs()
L.display['thin']=False
L.display['edlabel']=True
fig,ax = L.showGs(fig=fig,ax=ax,edlist=s[0,:],width=4)
plt.plot(tx[0],tx[1],'x')
plt.plot(rx[0],rx[1],'+')
plt.title(str(s[0,:])+str(s[1,:]))
L.display['edlabel']=False
return fig,ax
strucname = 'TA-Office'
#strucname = 'defstr'
L = Layout(strucname+'.ini')
L.boundary()
print L.ax
try:
L.dumpr()
except:
L.build()
L.dumpw()
#tx = np.array([8., 8., 1.])
#rx = np.array([30., 11., 2.])
#tx = np.array([1., 0., 1.])
#rx = np.array([8., -1.5, 2.])
#L = Layout('TA-Office.str')
#L.build()
tx = np.array([20, 8, 1])
rx = np.array([35, 6, 2])
S = Signatures(L, tx, rx)
print "Calcul signatures"
#s1 = S.get_sigslist(tx, rx)
s1 = S.run(tx,rx,2)
print "Fin calcul signatures"
#print "signatures --> rayons "
#r2d = S.sigs2rays(s1)
r2d = S.rays(s1)
##print "fin signatures --> rayons "
##
#r22 = r2d['2']
#pt2 = r22['pt']
#sig2 = r22['sig']
#pt2 = np.swapaxes(pt2,0,2)
#pt2 = np.swapaxes(pt2,1,2)
#tx2 = np.kron(np.ones(2),tx).reshape(2,3,1)
#rx2 = np.kron(np.ones(2),rx).reshape(2,3,1)
#tx2[:,2,:]=0
#rx2[:,2,:]=0
#pt = np.concatenate((tx2,pt2,rx2),axis=2)
#vsi = pt[:, :, 1:] - pt[:,:,:-1]
#si = np.sqrt(np.sum(vsi*vsi, axis=1))
#alpha = np.cumsum(si,axis=1)
#c = alpha[:,-1].reshape(2,1)
#alpha = alpha/c
#pt[:,2,1:]= tx[2]+alpha*(rx[2]-tx[2])
#
#
showr2d(L,r2d,tx,rx)
print "rayons 2D --> rayons3D "
#rays3d = S.ray2D3D(r2d)
#print "fin rayons 2D --> rayons3D "
##
#S.show3(rays=rays3d,strucname=strucname)
##
##
##
#s = np.array([[5,1,8],[1,1,2]])
#sig = Signature(s)
#rsig = sig.sig2ray(L,tx[0:2],rx[0:2])
#sig.ev(L)
#M = sig.image(tx[0:2])
#Y = sig.backtrace(tx[0:2],rx[0:2],M)
#plt.plot(M[0,:],M[1,:],'ob')
#plt.plot(Y[0,:],Y[1,:],'xk')
#fig,ax = showr2(L,r2d,tx[0:2],rx[0:2],3,4)
#plt.show()
#room8 = L.Gt.node[8]
#polyg8 = room8['polyg']
#vnodes8 = room8['vnodes']
#udeg1 = []
#udeg2 = []
#for ik, inode in enumerate(vnodes8):
# deg = L.Gs.degree(inode)
# if vnodes8[0] < 0:
# index = ik / 2
# else:
# index = (ik - 1) / 2
# if inode < 0:
# if deg == 2:
# udeg2.append(index)
# if deg == 1:
# udeg1.append(index) # warning not used
#Gv = polyg8.buildGv(show=True,udeg2=udeg2)
#L.showGs()
#nx.draw_networkx_edges(L.dGv[8],L.Gs.pos,nx.edges(L.dGv[8],nbunch=[47]))
| mit |
matbra/bokeh | examples/compat/mpl/listcollection.py | 34 | 1602 | from matplotlib.collections import LineCollection
import matplotlib.pyplot as plt
import numpy as np
from bokeh import mpl
from bokeh.plotting import output_file, show
def make_segments(x, y):
'''
Create list of line segments from x and y coordinates.
'''
points = np.array([x, y]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
return segments
def colorline(x, y, colors=None, linewidth=3, alpha=1.0):
'''
Plot a line with segments.
Optionally, specify segments colors and segments widths.
'''
# Make a list of colors cycling through the rgbcmyk series.
# You have several ways to input the colors:
# colors = ['r','g','b','c','y','m','k']
# colors = ['red','green','blue','cyan','yellow','magenta','black']
# colors = ['#ff0000', '#008000', '#0000ff', '#00bfbf', '#bfbf00', '#bf00bf', '#000000']
# colors = [(1.0, 0.0, 0.0, 1.0), (0.0, 0.5, 0.0, 1.0), (0.0, 0.0, 1.0, 1.0), (0.0, 0.75, 0.75, 1.0),
# (0.75, 0.75, 0, 1.0), (0.75, 0, 0.75, 1.0), (0.0, 0.0, 0.0, 1.0)]
colors = ['r', 'g', 'b', 'c', 'y', 'm', 'k']
widths = [5, 10, 20, 40, 20, 10, 5]
segments = make_segments(x, y)
lc = LineCollection(segments, colors=colors, linewidth=widths, alpha=alpha)
ax = plt.gca()
ax.add_collection(lc)
return lc
# Colored sine wave
x = np.linspace(0, 4 * np.pi, 100)
y = np.sin(x)
colorline(x, y)
plt.title("MPL support for ListCollection in Bokeh")
plt.xlim(x.min(), x.max())
plt.ylim(-1.0, 1.0)
output_file("listcollection.html")
show(mpl.to_bokeh())
| bsd-3-clause |
eduardoneira/SistemasDistribuidos_TPFinal | CentroMonitoreoCiudad/FaceRecognizer/modules/old_feature_matcher.py | 1 | 4628 | #!/bin/python3
import numpy as np
import cv2
import base64
import pdb
from tkinter import *
from matplotlib import pyplot as plt
class FeatureMatcher:
__PORC_DISTANCE = 0.7
def __init__(self,feature_extractor='SURF',upright=True,min_match_count=10,threshold=400):
self.MIN_MATCH_COUNT = min_match_count
self.__create_feature_extractor(feature_extractor,upright,threshold)
FLANN_INDEX_KDTREE = 0
index_params = dict(algorithm = FLANN_INDEX_KDTREE, trees = 5)
search_params = dict(checks = 200)
self.flann = cv2.FlannBasedMatcher(index_params, search_params)
def __create_feature_extractor(self,feature_extractor,upright,threshold):
if feature_extractor == 'SURF':
self.feature_finder = cv2.xfeatures2d.SURF_create(threshold,extended=True)
self.feature_finder.setUpright(upright)
elif feature_extractor == 'SIFT':
self.feature_finder = cv2.xfeatures2d.SIFT_create(edgeThreshold=20,sigma=1.1)
elif feature_extractor == 'ORB':
self.feature_finder = cv2.ORB_create()
else:
raise 'Feature extractor no encontrado'
def compare(self,img1,img2):
self.features_img1 = self.find_features(img1)
self.features_img2 = self.find_features(img2)
pdb.set_trace()
return self.flann.knnMatch(self.features_img1[1],self.features_img2[1],k=2)
def compare_base64(self,image1_base64,image2_base64):
img1 = self.base64_to_img(image1_base64)
img2 = self.base64_to_img(image2_base64)
return self.compare(img1,img2)
def are_similar(self,img1,img2):
self.good_matches = []
for m,n in self.compare(img1,img2):
if m.distance < self.__PORC_DISTANCE*n.distance:
self.good_matches.append(m)
return (len(self.good_matches) > self.MIN_MATCH_COUNT)
def find_features(self,img):
return self.feature_finder.detectAndCompute(img,None)
def bytes_to_img(self,image_bytes):
nparr = np.fromstring(image_bytes, np.uint8)
return cv2.imdecode(nparr, 0)
def base64_to_img(self,image_base64):
return self.bytes_to_img(base64.b64decode(image_base64))
def compare_and_draw_base64(self,img1,img2):
self.compare_and_draw(self.base64_to_img(img1),self.base64_to_img(img2))
def compare_and_draw(self,img1,img2):
# if self.are_similar(img1,img2):
# src_pts = np.float32([ self.features_img1[0][m.queryIdx].pt for m in self.good_matches ]).reshape(-1,1,2)
# dst_pts = np.float32([ self.features_img2[0][m.trainIdx].pt for m in self.good_matches ]).reshape(-1,1,2)
# M, mask = cv2.findHomography(src_pts,dst_pts,cv2.RANSAC,5.0)
# matchesMask = mask.ravel().tolist()
# h,w = img1.shape
# pts = np.float32([ [0,0],[0,h-1],[w-1,h-1],[w-1,0] ]).reshape(-1,1,2)
# dst = cv2.perspectiveTransform(pts,M)
# img2 = cv2.polylines(img2,[np.int32(dst)],True,255,3,cv2.LINE_AA)
# else:
# print("Not enough matches are found - %d/%d" % (len(self.good_matches),self.MIN_MATCH_COUNT))
# matchesMask = None
# draw_params = dict(matchColor = (0,255,0),
# singlePointColor = (255,0,0),
# matchesMask = matchesMask,
# flags = 2)
# img3 = cv2.drawMatchesKnn(img1,self.features_img1[0],img2,self.features_img2[0],self.good_matches,None,**draw_params)
# plt.imshow(img3,'gray'),plt.show()
hash1 = self.find_features(img1)
hash2 = self.find_features(img2)
matches = self.flann.knnMatch(hash1[1],hash2[1],k=2)
good = []
for m,n in matches:
if m.distance < 0.95*n.distance:
good.append(m)
print(len(good))
if len(good)>self.MIN_MATCH_COUNT:
src_pts = np.float32([ hash1[0][m.queryIdx].pt for m in good ]).reshape(-1,1,2)
dst_pts = np.float32([ hash2[0][m.trainIdx].pt for m in good ]).reshape(-1,1,2)
M, mask = cv2.findHomography(src_pts, dst_pts, cv2.RANSAC,5.0)
matchesMask = mask.ravel().tolist()
h,w = img1.shape
pts = np.float32([ [0,0],[0,h-1],[w-1,h-1],[w-1,0] ]).reshape(-1,1,2)
dst = cv2.perspectiveTransform(pts,M)
img2 = cv2.polylines(img2,[np.int32(dst)],True,255,3, cv2.LINE_AA)
else:
print( "Not enough matches are found - {}/{}".format(len(good), self.MIN_MATCH_COUNT) )
matchesMask = None
draw_params = dict(matchColor = (0,255,0), # draw matches in green color
singlePointColor = (255,0,0),
matchesMask = matchesMask, # draw only inliers
flags = 2)
img3 = cv2.drawMatches(img1,hash1[0],img2,hash2[0],good,None,**draw_params)
plt.imshow(img3, 'gray'),plt.show() | gpl-3.0 |
DTOcean/dtocean-core | tests/test_data_definitions_simplepie.py | 1 | 2601 | import pytest
import matplotlib.pyplot as plt
from aneris.control.factory import InterfaceFactory
from dtocean_core.core import (AutoFileInput,
AutoFileOutput,
AutoPlot,
Core)
from dtocean_core.data import CoreMetaData
from dtocean_core.data.definitions import SimplePie
def test_SimplePie_available():
new_core = Core()
all_objs = new_core.control._store._structures
assert "SimplePie" in all_objs.keys()
def test_SimplePie():
meta = CoreMetaData({"identifier": "test",
"structure": "test",
"title": "test",
"types": ["float"]})
test = SimplePie()
raw = {"a": 0, "b": 1}
a = test.get_data(raw, meta)
b = test.get_value(a)
assert b["a"] == 0
assert b["b"] == 1
def test_get_None():
test = SimplePie()
result = test.get_value(None)
assert result is None
@pytest.mark.parametrize("fext", [".csv", ".xls", ".xlsx"])
def test_SimplePie_auto_file(tmpdir, fext):
test_path = tmpdir.mkdir("sub").join("test{}".format(fext))
test_path_str = str(test_path)
raw = {"a": 0, "b": 1}
meta = CoreMetaData({"identifier": "test",
"structure": "test",
"title": "test",
"types": ["float"]})
test = SimplePie()
fout_factory = InterfaceFactory(AutoFileOutput)
FOutCls = fout_factory(meta, test)
fout = FOutCls()
fout._path = test_path_str
fout.data.result = test.get_data(raw, meta)
fout.connect()
assert len(tmpdir.listdir()) == 1
fin_factory = InterfaceFactory(AutoFileInput)
FInCls = fin_factory(meta, test)
fin = FInCls()
fin._path = test_path_str
fin.connect()
result = test.get_data(fin.data.result, meta)
assert result["a"] == 0
assert result["b"] == 1
def test_SimplePie_auto_plot():
raw = {"a": 0, "b": 1}
meta = CoreMetaData({"identifier": "test",
"structure": "test",
"title": "test",
"types": ["float"]})
test = SimplePie()
fout_factory = InterfaceFactory(AutoPlot)
PlotCls = fout_factory(meta, test)
plot = PlotCls()
plot.data.result = test.get_data(raw, meta)
plot.meta.result = meta
plot.connect()
assert len(plt.get_fignums()) == 1
plt.close("all")
| gpl-3.0 |
buntyke/GPy | GPy/core/gp.py | 8 | 37031 | # Copyright (c) 2012-2014, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
import sys
from .. import kern
from .model import Model
from .parameterization import ObsAr
from .mapping import Mapping
from .. import likelihoods
from ..inference.latent_function_inference import exact_gaussian_inference, expectation_propagation
from .parameterization.variational import VariationalPosterior
import logging
import warnings
from GPy.util.normalizer import MeanNorm
logger = logging.getLogger("GP")
class GP(Model):
"""
General purpose Gaussian process model
:param X: input observations
:param Y: output observations
:param kernel: a GPy kernel, defaults to rbf+white
:param likelihood: a GPy likelihood
:param inference_method: The :class:`~GPy.inference.latent_function_inference.LatentFunctionInference` inference method to use for this GP
:rtype: model object
:param Norm normalizer:
normalize the outputs Y.
Prediction will be un-normalized using this normalizer.
If normalizer is None, we will normalize using MeanNorm.
If normalizer is False, no normalization will be done.
.. Note:: Multiple independent outputs are allowed using columns of Y
"""
def __init__(self, X, Y, kernel, likelihood, mean_function=None, inference_method=None, name='gp', Y_metadata=None, normalizer=False):
super(GP, self).__init__(name)
assert X.ndim == 2
if isinstance(X, (ObsAr, VariationalPosterior)):
self.X = X.copy()
else: self.X = ObsAr(X)
self.num_data, self.input_dim = self.X.shape
assert Y.ndim == 2
logger.info("initializing Y")
if normalizer is True:
self.normalizer = MeanNorm()
elif normalizer is False:
self.normalizer = None
else:
self.normalizer = normalizer
if self.normalizer is not None:
self.normalizer.scale_by(Y)
self.Y_normalized = ObsAr(self.normalizer.normalize(Y))
self.Y = Y
elif isinstance(Y, np.ndarray):
self.Y = ObsAr(Y)
self.Y_normalized = self.Y
else:
self.Y = Y
if Y.shape[0] != self.num_data:
#There can be cases where we want inputs than outputs, for example if we have multiple latent
#function values
warnings.warn("There are more rows in your input data X, \
than in your output data Y, be VERY sure this is what you want")
_, self.output_dim = self.Y.shape
assert ((Y_metadata is None) or isinstance(Y_metadata, dict))
self.Y_metadata = Y_metadata
assert isinstance(kernel, kern.Kern)
#assert self.input_dim == kernel.input_dim
self.kern = kernel
assert isinstance(likelihood, likelihoods.Likelihood)
self.likelihood = likelihood
#handle the mean function
self.mean_function = mean_function
if mean_function is not None:
assert isinstance(self.mean_function, Mapping)
assert mean_function.input_dim == self.input_dim
assert mean_function.output_dim == self.output_dim
self.link_parameter(mean_function)
#find a sensible inference method
logger.info("initializing inference method")
if inference_method is None:
if isinstance(likelihood, likelihoods.Gaussian) or isinstance(likelihood, likelihoods.MixedNoise):
inference_method = exact_gaussian_inference.ExactGaussianInference()
else:
inference_method = expectation_propagation.EP()
print("defaulting to ", inference_method, "for latent function inference")
self.inference_method = inference_method
logger.info("adding kernel and likelihood as parameters")
self.link_parameter(self.kern)
self.link_parameter(self.likelihood)
self.posterior = None
# The predictive variable to be used to predict using the posterior object's
# woodbury_vector and woodbury_inv is defined as predictive_variable
# as long as the posterior has the right woodbury entries.
# It is the input variable used for the covariance between
# X_star and the posterior of the GP.
# This is usually just a link to self.X (full GP) or self.Z (sparse GP).
# Make sure to name this variable and the predict functions will "just work"
# In maths the predictive variable is:
# K_{xx} - K_{xp}W_{pp}^{-1}K_{px}
# W_{pp} := \texttt{Woodbury inv}
# p := _predictive_variable
@property
def _predictive_variable(self):
return self.X
def set_XY(self, X=None, Y=None):
"""
Set the input / output data of the model
This is useful if we wish to change our existing data but maintain the same model
:param X: input observations
:type X: np.ndarray
:param Y: output observations
:type Y: np.ndarray
"""
self.update_model(False)
if Y is not None:
if self.normalizer is not None:
self.normalizer.scale_by(Y)
self.Y_normalized = ObsAr(self.normalizer.normalize(Y))
self.Y = Y
else:
self.Y = ObsAr(Y)
self.Y_normalized = self.Y
if X is not None:
if self.X in self.parameters:
# LVM models
if isinstance(self.X, VariationalPosterior):
assert isinstance(X, type(self.X)), "The given X must have the same type as the X in the model!"
self.unlink_parameter(self.X)
self.X = X
self.link_parameter(self.X)
else:
self.unlink_parameter(self.X)
from ..core import Param
self.X = Param('latent mean',X)
self.link_parameter(self.X)
else:
self.X = ObsAr(X)
self.update_model(True)
def set_X(self,X):
"""
Set the input data of the model
:param X: input observations
:type X: np.ndarray
"""
self.set_XY(X=X)
def set_Y(self,Y):
"""
Set the output data of the model
:param X: output observations
:type X: np.ndarray
"""
self.set_XY(Y=Y)
def parameters_changed(self):
"""
Method that is called upon any changes to :class:`~GPy.core.parameterization.param.Param` variables within the model.
In particular in the GP class this method reperforms inference, recalculating the posterior and log marginal likelihood and gradients of the model
.. warning::
This method is not designed to be called manually, the framework is set up to automatically call this method upon changes to parameters, if you call
this method yourself, there may be unexpected consequences.
"""
self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.likelihood, self.Y_normalized, self.mean_function, self.Y_metadata)
self.likelihood.update_gradients(self.grad_dict['dL_dthetaL'])
self.kern.update_gradients_full(self.grad_dict['dL_dK'], self.X)
if self.mean_function is not None:
self.mean_function.update_gradients(self.grad_dict['dL_dm'], self.X)
def log_likelihood(self):
"""
The log marginal likelihood of the model, :math:`p(\mathbf{y})`, this is the objective function of the model being optimised
"""
return self._log_marginal_likelihood
def _raw_predict(self, Xnew, full_cov=False, kern=None):
"""
For making predictions, does not account for normalization or likelihood
full_cov is a boolean which defines whether the full covariance matrix
of the prediction is computed. If full_cov is False (default), only the
diagonal of the covariance is returned.
.. math::
p(f*|X*, X, Y) = \int^{\inf}_{\inf} p(f*|f,X*)p(f|X,Y) df
= N(f*| K_{x*x}(K_{xx} + \Sigma)^{-1}Y, K_{x*x*} - K_{xx*}(K_{xx} + \Sigma)^{-1}K_{xx*}
\Sigma := \texttt{Likelihood.variance / Approximate likelihood covariance}
"""
if kern is None:
kern = self.kern
Kx = kern.K(self._predictive_variable, Xnew)
mu = np.dot(Kx.T, self.posterior.woodbury_vector)
if len(mu.shape)==1:
mu = mu.reshape(-1,1)
if full_cov:
Kxx = kern.K(Xnew)
if self.posterior.woodbury_inv.ndim == 2:
var = Kxx - np.dot(Kx.T, np.dot(self.posterior.woodbury_inv, Kx))
elif self.posterior.woodbury_inv.ndim == 3: # Missing data
var = np.empty((Kxx.shape[0],Kxx.shape[1],self.posterior.woodbury_inv.shape[2]))
from ..util.linalg import mdot
for i in range(var.shape[2]):
var[:, :, i] = (Kxx - mdot(Kx.T, self.posterior.woodbury_inv[:, :, i], Kx))
var = var
else:
Kxx = kern.Kdiag(Xnew)
if self.posterior.woodbury_inv.ndim == 2:
var = (Kxx - np.sum(np.dot(self.posterior.woodbury_inv.T, Kx) * Kx, 0))[:,None]
elif self.posterior.woodbury_inv.ndim == 3: # Missing data
var = np.empty((Kxx.shape[0],self.posterior.woodbury_inv.shape[2]))
for i in range(var.shape[1]):
var[:, i] = (Kxx - (np.sum(np.dot(self.posterior.woodbury_inv[:, :, i].T, Kx) * Kx, 0)))
var = var
#add in the mean function
if self.mean_function is not None:
mu += self.mean_function.f(Xnew)
return mu, var
def predict(self, Xnew, full_cov=False, Y_metadata=None, kern=None):
"""
Predict the function(s) at the new point(s) Xnew.
:param Xnew: The points at which to make a prediction
:type Xnew: np.ndarray (Nnew x self.input_dim)
:param full_cov: whether to return the full covariance matrix, or just
the diagonal
:type full_cov: bool
:param Y_metadata: metadata about the predicting point to pass to the likelihood
:param kern: The kernel to use for prediction (defaults to the model
kern). this is useful for examining e.g. subprocesses.
:returns: (mean, var):
mean: posterior mean, a Numpy array, Nnew x self.input_dim
var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew.
This is to allow for different normalizations of the output dimensions.
Note: If you want the predictive quantiles (e.g. 95% confidence interval) use :py:func:"~GPy.core.gp.GP.predict_quantiles".
"""
#predict the latent function values
mu, var = self._raw_predict(Xnew, full_cov=full_cov, kern=kern)
if self.normalizer is not None:
mu, var = self.normalizer.inverse_mean(mu), self.normalizer.inverse_variance(var)
# now push through likelihood
mean, var = self.likelihood.predictive_values(mu, var, full_cov, Y_metadata=Y_metadata)
return mean, var
def predict_quantiles(self, X, quantiles=(2.5, 97.5), Y_metadata=None, kern=None):
"""
Get the predictive quantiles around the prediction at X
:param X: The points at which to make a prediction
:type X: np.ndarray (Xnew x self.input_dim)
:param quantiles: tuple of quantiles, default is (2.5, 97.5) which is the 95% interval
:type quantiles: tuple
:param kern: optional kernel to use for prediction
:type predict_kw: dict
:returns: list of quantiles for each X and predictive quantiles for interval combination
:rtype: [np.ndarray (Xnew x self.output_dim), np.ndarray (Xnew x self.output_dim)]
"""
m, v = self._raw_predict(X, full_cov=False, kern=kern)
if self.normalizer is not None:
m, v = self.normalizer.inverse_mean(m), self.normalizer.inverse_variance(v)
return self.likelihood.predictive_quantiles(m, v, quantiles, Y_metadata=Y_metadata)
def predictive_gradients(self, Xnew):
"""
Compute the derivatives of the predicted latent function with respect to X*
Given a set of points at which to predict X* (size [N*,Q]), compute the
derivatives of the mean and variance. Resulting arrays are sized:
dmu_dX* -- [N*, Q ,D], where D is the number of output in this GP (usually one).
Note that this is not the same as computing the mean and variance of the derivative of the function!
dv_dX* -- [N*, Q], (since all outputs have the same variance)
:param X: The points at which to get the predictive gradients
:type X: np.ndarray (Xnew x self.input_dim)
:returns: dmu_dX, dv_dX
:rtype: [np.ndarray (N*, Q ,D), np.ndarray (N*,Q) ]
"""
dmu_dX = np.empty((Xnew.shape[0],Xnew.shape[1],self.output_dim))
for i in range(self.output_dim):
dmu_dX[:,:,i] = self.kern.gradients_X(self.posterior.woodbury_vector[:,i:i+1].T, Xnew, self.X)
# gradients wrt the diagonal part k_{xx}
dv_dX = self.kern.gradients_X(np.eye(Xnew.shape[0]), Xnew)
#grads wrt 'Schur' part K_{xf}K_{ff}^{-1}K_{fx}
alpha = -2.*np.dot(self.kern.K(Xnew, self.X),self.posterior.woodbury_inv)
dv_dX += self.kern.gradients_X(alpha, Xnew, self.X)
return dmu_dX, dv_dX
def predict_jacobian(self, Xnew, kern=None, full_cov=True):
"""
Compute the derivatives of the posterior of the GP.
Given a set of points at which to predict X* (size [N*,Q]), compute the
mean and variance of the derivative. Resulting arrays are sized:
dL_dX* -- [N*, Q ,D], where D is the number of output in this GP (usually one).
Note that this is the mean and variance of the derivative,
not the derivative of the mean and variance! (See predictive_gradients for that)
dv_dX* -- [N*, Q], (since all outputs have the same variance)
If there is missing data, it is not implemented for now, but
there will be one output variance per output dimension.
:param X: The points at which to get the predictive gradients.
:type X: np.ndarray (Xnew x self.input_dim)
:param kern: The kernel to compute the jacobian for.
:param boolean full_cov: whether to return the full covariance of the jacobian.
:returns: dmu_dX, dv_dX
:rtype: [np.ndarray (N*, Q ,D), np.ndarray (N*,Q,(D)) ]
Note: We always return sum in input_dim gradients, as the off-diagonals
in the input_dim are not needed for further calculations.
This is a compromise for increase in speed. Mathematically the jacobian would
have another dimension in Q.
"""
if kern is None:
kern = self.kern
mean_jac = np.empty((Xnew.shape[0],Xnew.shape[1],self.output_dim))
for i in range(self.output_dim):
mean_jac[:,:,i] = kern.gradients_X(self.posterior.woodbury_vector[:,i:i+1].T, Xnew, self._predictive_variable)
dK_dXnew_full = np.empty((self._predictive_variable.shape[0], Xnew.shape[0], Xnew.shape[1]))
for i in range(self._predictive_variable.shape[0]):
dK_dXnew_full[i] = kern.gradients_X([[1.]], Xnew, self._predictive_variable[[i]])
if full_cov:
dK2_dXdX = kern.gradients_XX([[1.]], Xnew)
else:
dK2_dXdX = kern.gradients_XX_diag([[1.]], Xnew)
def compute_cov_inner(wi):
if full_cov:
# full covariance gradients:
var_jac = dK2_dXdX - np.einsum('qnm,miq->niq', dK_dXnew_full.T.dot(wi), dK_dXnew_full)
else:
var_jac = dK2_dXdX - np.einsum('qim,miq->iq', dK_dXnew_full.T.dot(wi), dK_dXnew_full)
return var_jac
if self.posterior.woodbury_inv.ndim == 3: # Missing data:
if full_cov:
var_jac = np.empty((Xnew.shape[0],Xnew.shape[0],Xnew.shape[1],self.output_dim))
for d in range(self.posterior.woodbury_inv.shape[2]):
var_jac[:, :, :, d] = compute_cov_inner(self.posterior.woodbury_inv[:, :, d])
else:
var_jac = np.empty((Xnew.shape[0],Xnew.shape[1],self.output_dim))
for d in range(self.posterior.woodbury_inv.shape[2]):
var_jac[:, :, d] = compute_cov_inner(self.posterior.woodbury_inv[:, :, d])
else:
var_jac = compute_cov_inner(self.posterior.woodbury_inv)
return mean_jac, var_jac
def predict_wishard_embedding(self, Xnew, kern=None, mean=True, covariance=True):
"""
Predict the wishard embedding G of the GP. This is the density of the
input of the GP defined by the probabilistic function mapping f.
G = J_mean.T*J_mean + output_dim*J_cov.
:param array-like Xnew: The points at which to evaluate the magnification.
:param :py:class:`~GPy.kern.Kern` kern: The kernel to use for the magnification.
Supplying only a part of the learning kernel gives insights into the density
of the specific kernel part of the input function. E.g. one can see how dense the
linear part of a kernel is compared to the non-linear part etc.
"""
if kern is None:
kern = self.kern
mu_jac, var_jac = self.predict_jacobian(Xnew, kern, full_cov=False)
mumuT = np.einsum('iqd,ipd->iqp', mu_jac, mu_jac)
Sigma = np.zeros(mumuT.shape)
if var_jac.ndim == 3:
Sigma[(slice(None), )+np.diag_indices(Xnew.shape[1], 2)] = var_jac.sum(-1)
else:
Sigma[(slice(None), )+np.diag_indices(Xnew.shape[1], 2)] = self.output_dim*var_jac
G = 0.
if mean:
G += mumuT
if covariance:
G += Sigma
return G
def predict_magnification(self, Xnew, kern=None, mean=True, covariance=True):
"""
Predict the magnification factor as
sqrt(det(G))
for each point N in Xnew
"""
G = self.predict_wishard_embedding(Xnew, kern, mean, covariance)
from ..util.linalg import jitchol
mag = np.empty(Xnew.shape[0])
for n in range(Xnew.shape[0]):
try:
mag[n] = np.sqrt(np.exp(2*np.sum(np.log(np.diag(jitchol(G[n, :, :]))))))
except:
mag[n] = np.sqrt(np.linalg.det(G[n, :, :]))
return mag
def posterior_samples_f(self,X,size=10, full_cov=True):
"""
Samples the posterior GP at the points X.
:param X: The points at which to take the samples.
:type X: np.ndarray (Nnew x self.input_dim)
:param size: the number of a posteriori samples.
:type size: int.
:param full_cov: whether to return the full covariance matrix, or just the diagonal.
:type full_cov: bool.
:returns: fsim: set of simulations
:rtype: np.ndarray (N x samples)
"""
m, v = self._raw_predict(X, full_cov=full_cov)
if self.normalizer is not None:
m, v = self.normalizer.inverse_mean(m), self.normalizer.inverse_variance(v)
v = v.reshape(m.size,-1) if len(v.shape)==3 else v
if not full_cov:
fsim = np.random.multivariate_normal(m.flatten(), np.diag(v.flatten()), size).T
else:
fsim = np.random.multivariate_normal(m.flatten(), v, size).T
return fsim
def posterior_samples(self, X, size=10, full_cov=False, Y_metadata=None):
"""
Samples the posterior GP at the points X.
:param X: the points at which to take the samples.
:type X: np.ndarray (Nnew x self.input_dim.)
:param size: the number of a posteriori samples.
:type size: int.
:param full_cov: whether to return the full covariance matrix, or just the diagonal.
:type full_cov: bool.
:param noise_model: for mixed noise likelihood, the noise model to use in the samples.
:type noise_model: integer.
:returns: Ysim: set of simulations, a Numpy array (N x samples).
"""
fsim = self.posterior_samples_f(X, size, full_cov=full_cov)
Ysim = self.likelihood.samples(fsim, Y_metadata=Y_metadata)
return Ysim
def plot_f(self, plot_limits=None, which_data_rows='all',
which_data_ycols='all', fixed_inputs=[],
levels=20, samples=0, fignum=None, ax=None, resolution=None,
plot_raw=True,
linecol=None,fillcol=None, Y_metadata=None, data_symbol='kx',
apply_link=False):
"""
Plot the GP's view of the world, where the data is normalized and before applying a likelihood.
This is a call to plot with plot_raw=True.
Data will not be plotted in this, as the GP's view of the world
may live in another space, or units then the data.
Can plot only part of the data and part of the posterior functions
using which_data_rowsm which_data_ycols.
:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
:type plot_limits: np.array
:param which_data_rows: which of the training data to plot (default all)
:type which_data_rows: 'all' or a slice object to slice model.X, model.Y
:param which_data_ycols: when the data has several columns (independant outputs), only plot these
:type which_data_ycols: 'all' or a list of integers
:param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
:type fixed_inputs: a list of tuples
:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
:type resolution: int
:param levels: number of levels to plot in a contour plot.
:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
:type levels: int
:param samples: the number of a posteriori samples to plot
:type samples: int
:param fignum: figure to plot on.
:type fignum: figure number
:param ax: axes to plot on.
:type ax: axes handle
:param linecol: color of line to plot [Tango.colorsHex['darkBlue']]
:type linecol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
:param fillcol: color of fill [Tango.colorsHex['lightBlue']]
:type fillcol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
:param Y_metadata: additional data associated with Y which may be needed
:type Y_metadata: dict
:param data_symbol: symbol as used matplotlib, by default this is a black cross ('kx')
:type data_symbol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) alongside marker type, as is standard in matplotlib.
:param apply_link: if there is a link function of the likelihood, plot the link(f*) rather than f*
:type apply_link: boolean
"""
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
from ..plotting.matplot_dep import models_plots
kw = {}
if linecol is not None:
kw['linecol'] = linecol
if fillcol is not None:
kw['fillcol'] = fillcol
return models_plots.plot_fit(self, plot_limits, which_data_rows,
which_data_ycols, fixed_inputs,
levels, samples, fignum, ax, resolution,
plot_raw=plot_raw, Y_metadata=Y_metadata,
data_symbol=data_symbol, apply_link=apply_link, **kw)
def plot(self, plot_limits=None, which_data_rows='all',
which_data_ycols='all', fixed_inputs=[],
levels=20, samples=0, fignum=None, ax=None, resolution=None,
plot_raw=False, linecol=None,fillcol=None, Y_metadata=None,
data_symbol='kx', predict_kw=None, plot_training_data=True, samples_y=0, apply_link=False):
"""
Plot the posterior of the GP.
- In one dimension, the function is plotted with a shaded region identifying two standard deviations.
- In two dimsensions, a contour-plot shows the mean predicted function
- In higher dimensions, use fixed_inputs to plot the GP with some of the inputs fixed.
Can plot only part of the data and part of the posterior functions
using which_data_rowsm which_data_ycols.
:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
:type plot_limits: np.array
:param which_data_rows: which of the training data to plot (default all)
:type which_data_rows: 'all' or a slice object to slice model.X, model.Y
:param which_data_ycols: when the data has several columns (independant outputs), only plot these
:type which_data_ycols: 'all' or a list of integers
:param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
:type fixed_inputs: a list of tuples
:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
:type resolution: int
:param levels: number of levels to plot in a contour plot.
:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
:type levels: int
:param samples: the number of a posteriori samples to plot, p(f*|y)
:type samples: int
:param fignum: figure to plot on.
:type fignum: figure number
:param ax: axes to plot on.
:type ax: axes handle
:param linecol: color of line to plot [Tango.colorsHex['darkBlue']]
:type linecol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
:param fillcol: color of fill [Tango.colorsHex['lightBlue']]
:type fillcol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
:param Y_metadata: additional data associated with Y which may be needed
:type Y_metadata: dict
:param data_symbol: symbol as used matplotlib, by default this is a black cross ('kx')
:type data_symbol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) alongside marker type, as is standard in matplotlib.
:param plot_training_data: whether or not to plot the training points
:type plot_training_data: boolean
:param samples_y: the number of a posteriori samples to plot, p(y*|y)
:type samples_y: int
:param apply_link: if there is a link function of the likelihood, plot the link(f*) rather than f*, when plotting posterior samples f
:type apply_link: boolean
"""
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
from ..plotting.matplot_dep import models_plots
kw = {}
if linecol is not None:
kw['linecol'] = linecol
if fillcol is not None:
kw['fillcol'] = fillcol
return models_plots.plot_fit(self, plot_limits, which_data_rows,
which_data_ycols, fixed_inputs,
levels, samples, fignum, ax, resolution,
plot_raw=plot_raw, Y_metadata=Y_metadata,
data_symbol=data_symbol, predict_kw=predict_kw,
plot_training_data=plot_training_data, samples_y=samples_y, apply_link=apply_link, **kw)
def plot_data(self, which_data_rows='all',
which_data_ycols='all', visible_dims=None,
fignum=None, ax=None, data_symbol='kx'):
"""
Plot the training data
- For higher dimensions than two, use fixed_inputs to plot the data points with some of the inputs fixed.
Can plot only part of the data
using which_data_rows and which_data_ycols.
:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
:type plot_limits: np.array
:param which_data_rows: which of the training data to plot (default all)
:type which_data_rows: 'all' or a slice object to slice model.X, model.Y
:param which_data_ycols: when the data has several columns (independant outputs), only plot these
:type which_data_ycols: 'all' or a list of integers
:param visible_dims: an array specifying the input dimensions to plot (maximum two)
:type visible_dims: a numpy array
:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
:type resolution: int
:param levels: number of levels to plot in a contour plot.
:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
:type levels: int
:param samples: the number of a posteriori samples to plot, p(f*|y)
:type samples: int
:param fignum: figure to plot on.
:type fignum: figure number
:param ax: axes to plot on.
:type ax: axes handle
:param linecol: color of line to plot [Tango.colorsHex['darkBlue']]
:type linecol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
:param fillcol: color of fill [Tango.colorsHex['lightBlue']]
:type fillcol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) as is standard in matplotlib
:param data_symbol: symbol as used matplotlib, by default this is a black cross ('kx')
:type data_symbol: color either as Tango.colorsHex object or character ('r' is red, 'g' is green) alongside marker type, as is standard in matplotlib.
"""
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
from ..plotting.matplot_dep import models_plots
kw = {}
return models_plots.plot_data(self, which_data_rows,
which_data_ycols, visible_dims,
fignum, ax, data_symbol, **kw)
def errorbars_trainset(self, which_data_rows='all',
which_data_ycols='all', fixed_inputs=[], fignum=None, ax=None,
linecol=None, data_symbol='kx', predict_kw=None, plot_training_data=True,lw=None):
"""
Plot the posterior error bars corresponding to the training data
- For higher dimensions than two, use fixed_inputs to plot the data points with some of the inputs fixed.
Can plot only part of the data
using which_data_rows and which_data_ycols.
:param which_data_rows: which of the training data to plot (default all)
:type which_data_rows: 'all' or a slice object to slice model.X, model.Y
:param which_data_ycols: when the data has several columns (independant outputs), only plot these
:type which_data_rows: 'all' or a list of integers
:param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
:type fixed_inputs: a list of tuples
:param fignum: figure to plot on.
:type fignum: figure number
:param ax: axes to plot on.
:type ax: axes handle
:param plot_training_data: whether or not to plot the training points
:type plot_training_data: boolean
"""
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
from ..plotting.matplot_dep import models_plots
kw = {}
if lw is not None:
kw['lw'] = lw
return models_plots.errorbars_trainset(self, which_data_rows, which_data_ycols, fixed_inputs,
fignum, ax, linecol, data_symbol,
predict_kw, plot_training_data, **kw)
def plot_magnification(self, labels=None, which_indices=None,
resolution=50, ax=None, marker='o', s=40,
fignum=None, legend=True,
plot_limits=None,
aspect='auto', updates=False, plot_inducing=True, kern=None, **kwargs):
import sys
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
from ..plotting.matplot_dep import dim_reduction_plots
return dim_reduction_plots.plot_magnification(self, labels, which_indices,
resolution, ax, marker, s,
fignum, plot_inducing, legend,
plot_limits, aspect, updates, **kwargs)
def input_sensitivity(self, summarize=True):
"""
Returns the sensitivity for each dimension of this model
"""
return self.kern.input_sensitivity(summarize=summarize)
def optimize(self, optimizer=None, start=None, **kwargs):
"""
Optimize the model using self.log_likelihood and self.log_likelihood_gradient, as well as self.priors.
kwargs are passed to the optimizer. They can be:
:param max_f_eval: maximum number of function evaluations
:type max_f_eval: int
:messages: whether to display during optimisation
:type messages: bool
:param optimizer: which optimizer to use (defaults to self.preferred optimizer), a range of optimisers can be found in :module:`~GPy.inference.optimization`, they include 'scg', 'lbfgs', 'tnc'.
:type optimizer: string
"""
self.inference_method.on_optimization_start()
try:
super(GP, self).optimize(optimizer, start, **kwargs)
except KeyboardInterrupt:
print("KeyboardInterrupt caught, calling on_optimization_end() to round things up")
self.inference_method.on_optimization_end()
raise
def infer_newX(self, Y_new, optimize=True):
"""
Infer X for the new observed data *Y_new*.
:param Y_new: the new observed data for inference
:type Y_new: numpy.ndarray
:param optimize: whether to optimize the location of new X (True by default)
:type optimize: boolean
:return: a tuple containing the posterior estimation of X and the model that optimize X
:rtype: (:class:`~GPy.core.parameterization.variational.VariationalPosterior` and numpy.ndarray, :class:`~GPy.core.model.Model`)
"""
from ..inference.latent_function_inference.inferenceX import infer_newX
return infer_newX(self, Y_new, optimize=optimize)
def log_predictive_density(self, x_test, y_test, Y_metadata=None):
"""
Calculation of the log predictive density
.. math:
p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
:param x_test: test locations (x_{*})
:type x_test: (Nx1) array
:param y_test: test observations (y_{*})
:type y_test: (Nx1) array
:param Y_metadata: metadata associated with the test points
"""
mu_star, var_star = self._raw_predict(x_test)
return self.likelihood.log_predictive_density(y_test, mu_star, var_star, Y_metadata=Y_metadata)
def log_predictive_density_sampling(self, x_test, y_test, Y_metadata=None, num_samples=1000):
"""
Calculation of the log predictive density by sampling
.. math:
p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
:param x_test: test locations (x_{*})
:type x_test: (Nx1) array
:param y_test: test observations (y_{*})
:type y_test: (Nx1) array
:param Y_metadata: metadata associated with the test points
:param num_samples: number of samples to use in monte carlo integration
:type num_samples: int
"""
mu_star, var_star = self._raw_predict(x_test)
return self.likelihood.log_predictive_density_sampling(y_test, mu_star, var_star, Y_metadata=Y_metadata, num_samples=num_samples)
| mit |
sinhrks/scikit-learn | examples/manifold/plot_lle_digits.py | 138 | 8594 | """
=============================================================================
Manifold learning on handwritten digits: Locally Linear Embedding, Isomap...
=============================================================================
An illustration of various embeddings on the digits dataset.
The RandomTreesEmbedding, from the :mod:`sklearn.ensemble` module, is not
technically a manifold embedding method, as it learn a high-dimensional
representation on which we apply a dimensionality reduction method.
However, it is often useful to cast a dataset into a representation in
which the classes are linearly-separable.
t-SNE will be initialized with the embedding that is generated by PCA in
this example, which is not the default setting. It ensures global stability
of the embedding, i.e., the embedding does not depend on random
initialization.
"""
# Authors: Fabian Pedregosa <fabian.pedregosa@inria.fr>
# Olivier Grisel <olivier.grisel@ensta.org>
# Mathieu Blondel <mathieu@mblondel.org>
# Gael Varoquaux
# License: BSD 3 clause (C) INRIA 2011
print(__doc__)
from time import time
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import offsetbox
from sklearn import (manifold, datasets, decomposition, ensemble,
discriminant_analysis, random_projection)
digits = datasets.load_digits(n_class=6)
X = digits.data
y = digits.target
n_samples, n_features = X.shape
n_neighbors = 30
#----------------------------------------------------------------------
# Scale and visualize the embedding vectors
def plot_embedding(X, title=None):
x_min, x_max = np.min(X, 0), np.max(X, 0)
X = (X - x_min) / (x_max - x_min)
plt.figure()
ax = plt.subplot(111)
for i in range(X.shape[0]):
plt.text(X[i, 0], X[i, 1], str(digits.target[i]),
color=plt.cm.Set1(y[i] / 10.),
fontdict={'weight': 'bold', 'size': 9})
if hasattr(offsetbox, 'AnnotationBbox'):
# only print thumbnails with matplotlib > 1.0
shown_images = np.array([[1., 1.]]) # just something big
for i in range(digits.data.shape[0]):
dist = np.sum((X[i] - shown_images) ** 2, 1)
if np.min(dist) < 4e-3:
# don't show points that are too close
continue
shown_images = np.r_[shown_images, [X[i]]]
imagebox = offsetbox.AnnotationBbox(
offsetbox.OffsetImage(digits.images[i], cmap=plt.cm.gray_r),
X[i])
ax.add_artist(imagebox)
plt.xticks([]), plt.yticks([])
if title is not None:
plt.title(title)
#----------------------------------------------------------------------
# Plot images of the digits
n_img_per_row = 20
img = np.zeros((10 * n_img_per_row, 10 * n_img_per_row))
for i in range(n_img_per_row):
ix = 10 * i + 1
for j in range(n_img_per_row):
iy = 10 * j + 1
img[ix:ix + 8, iy:iy + 8] = X[i * n_img_per_row + j].reshape((8, 8))
plt.imshow(img, cmap=plt.cm.binary)
plt.xticks([])
plt.yticks([])
plt.title('A selection from the 64-dimensional digits dataset')
#----------------------------------------------------------------------
# Random 2D projection using a random unitary matrix
print("Computing random projection")
rp = random_projection.SparseRandomProjection(n_components=2, random_state=42)
X_projected = rp.fit_transform(X)
plot_embedding(X_projected, "Random Projection of the digits")
#----------------------------------------------------------------------
# Projection on to the first 2 principal components
print("Computing PCA projection")
t0 = time()
X_pca = decomposition.TruncatedSVD(n_components=2).fit_transform(X)
plot_embedding(X_pca,
"Principal Components projection of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Projection on to the first 2 linear discriminant components
print("Computing Linear Discriminant Analysis projection")
X2 = X.copy()
X2.flat[::X.shape[1] + 1] += 0.01 # Make X invertible
t0 = time()
X_lda = discriminant_analysis.LinearDiscriminantAnalysis(n_components=2).fit_transform(X2, y)
plot_embedding(X_lda,
"Linear Discriminant projection of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Isomap projection of the digits dataset
print("Computing Isomap embedding")
t0 = time()
X_iso = manifold.Isomap(n_neighbors, n_components=2).fit_transform(X)
print("Done.")
plot_embedding(X_iso,
"Isomap projection of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Locally linear embedding of the digits dataset
print("Computing LLE embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='standard')
t0 = time()
X_lle = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_lle,
"Locally Linear Embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Modified Locally linear embedding of the digits dataset
print("Computing modified LLE embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='modified')
t0 = time()
X_mlle = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_mlle,
"Modified Locally Linear Embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# HLLE embedding of the digits dataset
print("Computing Hessian LLE embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='hessian')
t0 = time()
X_hlle = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_hlle,
"Hessian Locally Linear Embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# LTSA embedding of the digits dataset
print("Computing LTSA embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='ltsa')
t0 = time()
X_ltsa = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_ltsa,
"Local Tangent Space Alignment of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# MDS embedding of the digits dataset
print("Computing MDS embedding")
clf = manifold.MDS(n_components=2, n_init=1, max_iter=100)
t0 = time()
X_mds = clf.fit_transform(X)
print("Done. Stress: %f" % clf.stress_)
plot_embedding(X_mds,
"MDS embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Random Trees embedding of the digits dataset
print("Computing Totally Random Trees embedding")
hasher = ensemble.RandomTreesEmbedding(n_estimators=200, random_state=0,
max_depth=5)
t0 = time()
X_transformed = hasher.fit_transform(X)
pca = decomposition.TruncatedSVD(n_components=2)
X_reduced = pca.fit_transform(X_transformed)
plot_embedding(X_reduced,
"Random forest embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# Spectral embedding of the digits dataset
print("Computing Spectral embedding")
embedder = manifold.SpectralEmbedding(n_components=2, random_state=0,
eigen_solver="arpack")
t0 = time()
X_se = embedder.fit_transform(X)
plot_embedding(X_se,
"Spectral embedding of the digits (time %.2fs)" %
(time() - t0))
#----------------------------------------------------------------------
# t-SNE embedding of the digits dataset
print("Computing t-SNE embedding")
tsne = manifold.TSNE(n_components=2, init='pca', random_state=0)
t0 = time()
X_tsne = tsne.fit_transform(X)
plot_embedding(X_tsne,
"t-SNE embedding of the digits (time %.2fs)" %
(time() - t0))
plt.show()
| bsd-3-clause |
yaojenkuo/stockflow | ctrls/CandleDrawer.py | 2 | 3513 | #!/bin/python
# -*- coding: utf-8 -*-
import numpy as np
from settings import *
from datetime import datetime
from ctrls.Reader import Reader
import matplotlib.pyplot as plt
from matplotlib.finance import candlestick_ohlc
class CandleDrawer():
'''畫出近 n 天 K 線圖＋Ma20布林通道+高低通道+量'''
def _getBooleanBand(self, series):
bool_next = []# 近 n 天和 Moving Average 的分佈
bool_up_series = []# boolean band 上界
ma_series = []# boolean band 中間
bool_down_series = []# boolean band 上界
for i in xrange(CANDLE_BOOL_NUM, len(series)):
ma_series.append(np.mean(series[i - CANDLE_BOOL_NUM:i]))
# Boolean Band
# 近 n 天和 Moving Average 的分佈
bool_next.append(series[i] - ma_series[-1])
if len(bool_next) > CANDLE_BOOL_NUM: bool_next.pop(0)
# 通道大小
bool_width = 2 * np.std(bool_next)
bool_up_series.append(ma_series[-1] + bool_width)
bool_down_series.append(ma_series[-1] - bool_width)
return bool_up_series, ma_series, bool_down_series
def _getFigTitle(self, number):
t = datetime.now()
return ('%s, Update: %s/%s/%s %s:%s:%s' % (number,
str(t.year), str(t.month),str(t.day),
str(t.hour), str(t.minute), str(t.second))
)
def draw(self, number, length = CANDLE_FIG_LENGTH):
reader = Reader(number)
series = [[] for x in xrange(7)]
# Candle Stick
candle_sticks = []
idx = -1
while True:
idx +=1
row = reader.getInput()
if row == None: break
for i in [1, 3, 4, 5, 6]:
series[i].append(float(row[i]))
# matplotlib 的 candlestick_ohlc 依序放入 [編號, 收盤, 最高, 最低, 開盤] 會畫出 K 線圖
candle_sticks.append((
idx,
float(row[6]),
float(row[4]),
float(row[5]),
float(row[3])
))
bool_up_series, ma_series, bool_down_series = self._getBooleanBand(series[6])
# Draw Figure
line_width = CANDLE_FIG_LINE_WIDTH
fig, axarr = plt.subplots(2, sharex=True)
candlestick_ohlc(axarr[0], candle_sticks[-length:], width=CANDLE_STICK_WIDTH)
x_axis = range(len(series[6]))
# set zorder 讓 candlestick 可以在上面
axarr[0].plot(x_axis[-length:], ma_series[-length:], c='#00ff00', ls='-', lw=line_width, zorder=-5)
axarr[0].plot(x_axis[-length:], bool_up_series[-length:], c='#ff0000', ls='-', lw=line_width, zorder=-4)
axarr[0].plot(x_axis[-length:], bool_down_series[-length:], c='#0000ff', ls='-', lw=line_width, zorder=-3)
axarr[0].plot(x_axis[-length:], series[4][-length:], c='#ff3399', ls='-', lw=line_width, zorder=-2)
axarr[0].plot(x_axis[-length:], series[5][-length:], c='#0099ff', ls='-', lw=line_width, zorder=-1)
axarr[0].set_title(self._getFigTitle(number))
axarr[1].plot(x_axis[-length:], series[1][-length:], c='#000000', ls='-', lw=line_width)
# set figure arguments
fig.set_size_inches(FIGURE_WIDTH, FIGURE_HEIGHT)
# output figure
fig.savefig(CANDLE_FIG_PATH+'/'+number+'.png', dpi=FIGURE_DPI)
plt.clf()
plt.close('all')
| mit |
PatrickChrist/scikit-learn | examples/svm/plot_svm_anova.py | 250 | 2000 | """
=================================================
SVM-Anova: SVM with univariate feature selection
=================================================
This example shows how to perform univariate feature before running a SVC
(support vector classifier) to improve the classification scores.
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets, feature_selection, cross_validation
from sklearn.pipeline import Pipeline
###############################################################################
# Import some data to play with
digits = datasets.load_digits()
y = digits.target
# Throw away data, to be in the curse of dimension settings
y = y[:200]
X = digits.data[:200]
n_samples = len(y)
X = X.reshape((n_samples, -1))
# add 200 non-informative features
X = np.hstack((X, 2 * np.random.random((n_samples, 200))))
###############################################################################
# Create a feature-selection transform and an instance of SVM that we
# combine together to have an full-blown estimator
transform = feature_selection.SelectPercentile(feature_selection.f_classif)
clf = Pipeline([('anova', transform), ('svc', svm.SVC(C=1.0))])
###############################################################################
# Plot the cross-validation score as a function of percentile of features
score_means = list()
score_stds = list()
percentiles = (1, 3, 6, 10, 15, 20, 30, 40, 60, 80, 100)
for percentile in percentiles:
clf.set_params(anova__percentile=percentile)
# Compute cross-validation score using all CPUs
this_scores = cross_validation.cross_val_score(clf, X, y, n_jobs=1)
score_means.append(this_scores.mean())
score_stds.append(this_scores.std())
plt.errorbar(percentiles, score_means, np.array(score_stds))
plt.title(
'Performance of the SVM-Anova varying the percentile of features selected')
plt.xlabel('Percentile')
plt.ylabel('Prediction rate')
plt.axis('tight')
plt.show()
| bsd-3-clause |
NEONScience/NEON-Data-Skills | tutorials/Python/Lidar/lidar-biomass/calc-biomass_py/calc-biomass_py.py | 1 | 20510 | #!/usr/bin/env python
# coding: utf-8
# ---
# syncID: e6ccf19a4b454ca594388eeaa88ebe12
# title: "Calculate Vegetation Biomass from LiDAR Data in Python"
# description: "Learn to calculate the biomass of standing vegetation using a canopy height model data product."
# dateCreated: 2017-06-21
# authors: Tristan Goulden
# contributors: Donal O'Leary
# estimatedTime: 1 hour
# packagesLibraries: numpy, gdal, matplotlib, matplotlib.pyplot, os
# topics: lidar,remote-sensing
# languagesTool: python
# dataProduct: DP1.10098.001, DP3.30015.001,
# code1: https://raw.githubusercontent.com/NEONScience/NEON-Data-Skills/main/tutorials/Python/Lidar/lidar-biomass/calc-biomass_py/calc-biomass_py.ipynb
# tutorialSeries: intro-lidar-py-series
# urlTitle: calc-biomass-py
# ---
# <div id="ds-objectives" markdown="1">
#
# In this tutorial, we will calculate the biomass for a section of the SJER site. We
# will be using the Canopy Height Model discrete LiDAR data product as well as NEON
# field data on vegetation data. This tutorial will calculate Biomass for individual
# trees in the forest.
#
# ### Objectives
# After completing this tutorial, you will be able to:
#
# * Learn how to apply a guassian smoothing fernal for high-frequency spatial filtering
# * Apply a watershed segmentation algorithm for delineating tree crowns
# * Calculate biomass predictor variables from a CHM
# * Setup training data for Biomass predictions
# * Apply a Random Forest machine learning approach to calculate biomass
#
#
# ### Install Python Packages
#
# * **numpy**
# * **gdal**
# * **matplotlib**
# * **matplotlib.pyplot**
# * **os**
#
#
# ### Download Data
#
# If you have already downloaded the data set for the Data Institute, you have the
# data for this tutorial within the SJER directory. If you would like to just
# download the data for this tutorial use the following link.
#
# <a href="https://neondata.sharefile.com/d-s58db39240bf49ac8" class="link--button link--arrow">
# Download the Biomass Calculation teaching data subset</a>
#
# </div>
# In this tutorial, we will calculate the biomass for a section of the SJER site. We
# will be using the Canopy Height Model discrete LiDAR data product as well as NEON
# field data on vegetation data. This tutorial will calculate Biomass for individual
# trees in the forest.
#
# The calculation of biomass consists of four primary steps:
#
# 1. Delineating individual tree crowns
# 2. Calculating predictor variables for all individuals
# 3. Collecting training data
# 4. Applying a regression model to estiamte biomass from predictors
#
# In this tutorial we will use a watershed segmentation algorithm for delineating
# tree crowns (step 1) and and a Random Forest (RF) machine learning algorithm for
# relating the predictor variables to biomass (part 4). The predictor variables were
# selected following suggestions by Gleason et al. (2012) and biomass estimates were
# determined from DBH (diamter at breast height) measurements following relationships
# given in Jenkins et al. (2003).
#
# ## Get Started
#
# First, we need to specify the directory where we will find and save the data needed for this tutorial. You will need to change this line to suit your local machine. I have decided to save my data in the following directory:
# In[1]:
data_path = '/Users/olearyd/Git/data/'
# Next, we will import several of the typical libraries.
# In[2]:
import numpy as np
import os
import gdal, osr
import matplotlib.pyplot as plt
import sys
from scipy import ndimage as ndi
get_ipython().run_line_magic('matplotlib', 'inline')
# Next, we will add libraries from skilearn which will help with the watershed delination, determination of predictor variables and random forest algorithm
# In[3]:
#Import biomass specific libraries
from skimage.morphology import watershed
from skimage.feature import peak_local_max
from skimage.measure import regionprops
from sklearn.ensemble import RandomForestRegressor
# ## Define functions
#
# Now we will define a few functions that allow us to more easily work with the NEON data.
#
# * `plot_band_array`: function to plot NEON spatial data.
# In[4]:
#Define plot band array function
def plot_band_array(band_array,image_extent,title,cmap_title,colormap,colormap_limits):
plt.imshow(band_array,extent=image_extent)
cbar = plt.colorbar(); plt.set_cmap(colormap); plt.clim(colormap_limits)
cbar.set_label(cmap_title,rotation=270,labelpad=20)
plt.title(title); ax = plt.gca()
ax.ticklabel_format(useOffset=False, style='plain')
rotatexlabels = plt.setp(ax.get_xticklabels(),rotation=90)
# * `array2raster`: function to output geotiff files.
# In[5]:
def array2raster(newRasterfn,rasterOrigin,pixelWidth,pixelHeight,array,epsg):
cols = array.shape[1]
rows = array.shape[0]
originX = rasterOrigin[0]
originY = rasterOrigin[1]
driver = gdal.GetDriverByName('GTiff')
outRaster = driver.Create(newRasterfn, cols, rows, 1, gdal.GDT_Float32)
outRaster.SetGeoTransform((originX, pixelWidth, 0, originY, 0, pixelHeight))
outband = outRaster.GetRasterBand(1)
outband.WriteArray(array)
outRasterSRS = osr.SpatialReference()
outRasterSRS.ImportFromEPSG(epsg)
outRaster.SetProjection(outRasterSRS.ExportToWkt())
outband.FlushCache()
# * `raster2array`: function to conver rasters to an array.
# In[6]:
def raster2array(geotif_file):
metadata = {}
dataset = gdal.Open(geotif_file)
metadata['array_rows'] = dataset.RasterYSize
metadata['array_cols'] = dataset.RasterXSize
metadata['bands'] = dataset.RasterCount
metadata['driver'] = dataset.GetDriver().LongName
metadata['projection'] = dataset.GetProjection()
metadata['geotransform'] = dataset.GetGeoTransform()
mapinfo = dataset.GetGeoTransform()
metadata['pixelWidth'] = mapinfo[1]
metadata['pixelHeight'] = mapinfo[5]
metadata['ext_dict'] = {}
metadata['ext_dict']['xMin'] = mapinfo[0]
metadata['ext_dict']['xMax'] = mapinfo[0] + dataset.RasterXSize/mapinfo[1]
metadata['ext_dict']['yMin'] = mapinfo[3] + dataset.RasterYSize/mapinfo[5]
metadata['ext_dict']['yMax'] = mapinfo[3]
metadata['extent'] = (metadata['ext_dict']['xMin'],metadata['ext_dict']['xMax'],
metadata['ext_dict']['yMin'],metadata['ext_dict']['yMax'])
if metadata['bands'] == 1:
raster = dataset.GetRasterBand(1)
metadata['noDataValue'] = raster.GetNoDataValue()
metadata['scaleFactor'] = raster.GetScale()
# band statistics
metadata['bandstats'] = {} # make a nested dictionary to store band stats in same
stats = raster.GetStatistics(True,True)
metadata['bandstats']['min'] = round(stats[0],2)
metadata['bandstats']['max'] = round(stats[1],2)
metadata['bandstats']['mean'] = round(stats[2],2)
metadata['bandstats']['stdev'] = round(stats[3],2)
array = dataset.GetRasterBand(1).ReadAsArray(0,0,
metadata['array_cols'],
metadata['array_rows']).astype(np.float)
array[array==int(metadata['noDataValue'])]=np.nan
array = array/metadata['scaleFactor']
return array, metadata
elif metadata['bands'] > 1:
print('More than one band ... need to modify function for case of multiple bands')
# * `crown_geometric_volume_pth`: function to get tree crown volumn.
# In[7]:
def crown_geometric_volume_pth(tree_data,min_tree_height,pth):
p = np.percentile(tree_data, pth)
tree_data_pth = [v if v < p else p for v in tree_data]
crown_geometric_volume_pth = np.sum(tree_data_pth - min_tree_height)
return crown_geometric_volume_pth, p
# * `get_predictors`: function to get the trees from the biomass data.
# In[8]:
def get_predictors(tree,chm_array, labels):
indexes_of_tree = np.asarray(np.where(labels==tree.label)).T
tree_crown_heights = chm_array[indexes_of_tree[:,0],indexes_of_tree[:,1]]
full_crown = np.sum(tree_crown_heights - np.min(tree_crown_heights))
crown50, p50 = crown_geometric_volume_pth(tree_crown_heights,tree.min_intensity,50)
crown60, p60 = crown_geometric_volume_pth(tree_crown_heights,tree.min_intensity,60)
crown70, p70 = crown_geometric_volume_pth(tree_crown_heights,tree.min_intensity,70)
return [tree.label,
np.float(tree.area),
tree.major_axis_length,
tree.max_intensity,
tree.min_intensity,
p50, p60, p70,
full_crown, crown50, crown60, crown70]
# ## Canopy Height Data
#
# With everything set up, we can now start working with our data by define the file path to our CHM file. Note that you will need to change this and subsequent filepaths according to your local machine.
# In[9]:
chm_file = data_path+'NEON_D17_SJER_DP3_256000_4106000_CHM.tif'
# When we output the results, we will want to include the same file information as the input, so we will gather the file name information.
# In[10]:
#Get info from chm file for outputting results
just_chm_file = os.path.basename(chm_file)
just_chm_file_split = just_chm_file.split(sep="_")
# Now we will get the CHM data...
# In[11]:
chm_array, chm_array_metadata = raster2array(chm_file)
# ..., plot it, and save the figure.
# In[12]:
#Plot the original CHM
plt.figure(1)
#Plot the CHM figure
plot_band_array(chm_array,chm_array_metadata['extent'],
'Canopy height Model',
'Canopy height (m)',
'Greens',[0, 9])
plt.savefig(data_path+just_chm_file[0:-4]+'_CHM.png',dpi=300,orientation='landscape',
bbox_inches='tight',
pad_inches=0.1)
# It looks like SJER primarily has low vegetation with scattered taller trees.
#
# ## Create Filtered CHM
#
# Now we will use a Gaussian smoothing kernal (convolution) across the data set to remove spurious high vegetation points. This will help ensure we are finding the treetops properly before running the watershed segmentation algorithm.
#
# For different forest types it may be necessary to change the input parameters. Information on the function can be found in the <a href="https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.ndimage.filters.gaussian_filter.html" target="_blank">SciPy documentation</a>.
#
# Of most importance are the second and fifth inputs. The second input defines the standard deviation of the Gaussian smoothing kernal. Too large a value will apply too much smoothing, too small and some spurious high points may be left behind. The fifth, the truncate value, controls after how many standard deviations the Gaussian kernal will get cut off (since it theoretically goes to infinity).
# In[13]:
#Smooth the CHM using a gaussian filter to remove spurious points
chm_array_smooth = ndi.gaussian_filter(chm_array,2,
mode='constant',cval=0,truncate=2.0)
chm_array_smooth[chm_array==0] = 0
# Now save a copy of filtered CHM. We will later use this in our code, so we'll output it into our data directory.
# In[14]:
#Save the smoothed CHM
array2raster(data_path+'chm_filter.tif',
(chm_array_metadata['ext_dict']['xMin'],chm_array_metadata['ext_dict']['yMax']),
1,-1,
np.array(chm_array_smooth,dtype=float),
32611)
# ## Determine local maximums
#
# Now we will run an algorithm to determine local maximums within the image. Setting indices to 'False' returns a raster of the maximum points, as opposed to a list of coordinates. The footprint parameter is an area where only a single peak can be found. This should be approximately the size of the smallest tree. Information on more sophisticated methods to define the window can be found in Chen (2006).
# In[15]:
#Calculate local maximum points in the smoothed CHM
local_maxi = peak_local_max(chm_array_smooth,indices=False, footprint=np.ones((5, 5)))
# Our new object `local_maxi` is an array of boolean values where each pixel is identified as either being the local maximum (`True`) or not being the local maximum (`False`).
# In[16]:
local_maxi
# This is very helpful, but it can be difficult to visualizee boolean values using our typical numeric plotting procedures as defined in the `plot_band_array` function above. Therefore, we will need to convert this boolean array to an numeric format to use this function. Booleans convert easily to integers with values of `False=0` and `True=1` using the `.astype(int)` method.
# In[17]:
local_maxi.astype(int)
# Next ,we can plot the raster of local maximums bo coercing the boolean array into an array ofintegers inline. The following figure shows the difference in finding local maximums for a filtered vs. non-filtered CHM.
#
# We will save the graphics (.png) in an outputs folder sister to our working directory and data outputs (.tif) to our data directory.
# In[18]:
#Plot the local maximums
plt.figure(2)
plot_band_array(local_maxi.astype(int),chm_array_metadata['extent'],
'Maximum',
'Maxi',
'Greys',
[0, 1])
plt.savefig(data_path+just_chm_file[0:-4]+ '_Maximums.png',
dpi=300,orientation='landscape',
bbox_inches='tight',pad_inches=0.1)
array2raster(data_path+'maximum.tif',
(chm_array_metadata['ext_dict']['xMin'],chm_array_metadata['ext_dict']['yMax']),
1,-1,np.array(local_maxi,dtype=np.float32),32611)
# If we were to look at the overlap between the tree crowns and the local maxima from each method, it would appear a bit like this raster.
#
# <figure>
# <a href="https://raw.githubusercontent.com/NEONScience/NEON-Data-Skills/main/graphics/raster-general/raster-classification-filter-vs-nonfilter.jpg">
# <img src="https://raw.githubusercontent.com/NEONScience/NEON-Data-Skills/main/graphics/raster-general/raster-classification-filter-vs-nonfilter.jpg"></a>
# <figcaption> The difference in finding local maximums for a filtered vs.
# non-filtered CHM.
# Source: National Ecological Observatory Network (NEON)
# </figcaption>
# </figure>
#
#
# Apply labels to all of the local maximum points
# In[19]:
#Identify all the maximum points
markers = ndi.label(local_maxi)[0]
# Next we will create a mask layer of all of the vegetation points so that the watershed segmentation will only occur on the trees and not extend into the surrounding ground points. Since 0 represent ground points in the CHM, setting the mask to 1 where the CHM is not zero will define the mask
# In[20]:
#Create a CHM mask so the segmentation will only occur on the trees
chm_mask = chm_array_smooth
chm_mask[chm_array_smooth != 0] = 1
# ## Watershed segmentation
#
# As in a river system, a watershed is divided by a ridge that divides areas. Here our watershed are the individual tree canopies and the ridge is the delineation between each one.
#
# <figure>
# <a href="https://raw.githubusercontent.com/NEONScience/NEON-Data-Skills/main/graphics/raster-general/raster-classification-watershed-segments.png">
# <img src="https://raw.githubusercontent.com/NEONScience/NEON-Data-Skills/main/graphics/raster-general/raster-classification-watershed-segments.png"></a>
# <figcaption> A raster classified based on watershed segmentation.
# Source: National Ecological Observatory Network (NEON)
# </figcaption>
# </figure>
#
# Next, we will perform the watershed segmentation which produces a raster of labels.
# In[21]:
#Perfrom watershed segmentation
labels = watershed(chm_array_smooth, markers, mask=chm_mask)
labels_for_plot = labels.copy()
labels_for_plot = np.array(labels_for_plot,dtype = np.float32)
labels_for_plot[labels_for_plot==0] = np.nan
max_labels = np.max(labels)
# In[22]:
#Plot the segments
plot_band_array(labels_for_plot,chm_array_metadata['extent'],
'Crown Segmentation','Tree Crown Number',
'Spectral',[0, max_labels])
plt.savefig(data_path+just_chm_file[0:-4]+'_Segmentation.png',
dpi=300,orientation='landscape',
bbox_inches='tight',pad_inches=0.1)
array2raster(data_path+'labels.tif',
(chm_array_metadata['ext_dict']['xMin'],
chm_array_metadata['ext_dict']['yMax']),
1,-1,np.array(labels,dtype=float),32611)
# Now we will get several properties of the individual trees will be used as predictor variables.
# In[23]:
#Get the properties of each segment
tree_properties = regionprops(labels,chm_array)
# Now we will get the predictor variables to match the (soon to be loaded) training data using the function defined above. The first column will be segment IDs, the rest will be the predictor variables.
# In[24]:
predictors_chm = np.array([get_predictors(tree, chm_array, labels) for tree in tree_properties])
X = predictors_chm[:,1:]
tree_ids = predictors_chm[:,0]
# ## Training data
#
# We now bring in the training data file which is a simple CSV file with no header. The first column is biomass, and the remaining columns are the same predictor variables defined above. The tree diameter and max height are defined in the NEON vegetation structure data along with the tree DBH. The field validated values are used for training, while the other were determined from the CHM and camera images by manually delineating the tree crowns and pulling out the relevant information from the CHM.
#
# Biomass was calculated from DBH according to the formulas in Jenkins et al. (2003).
#
# If you didn't download this training dataset above, you can <a href="https://neondata.sharefile.com/share/view/cdc8242e24ad4517/fobd4959-4cf0-44ab-acc6-0695a04a1afc" target="_blank">Download the training dataset CSV here</a>.
# In[25]:
#Define the file of training data
training_data_file = data_path+'SJER_Biomass_Training.csv'
#Read in the training data from a CSV file
training_data = np.genfromtxt(training_data_file,delimiter=',')
#Grab the biomass (Y) from the first line
biomass = training_data[:,0]
#Grab the biomass prdeictors from the remaining lines
biomass_predictors = training_data[:,1:12]
# ## Random Forest classifiers
#
# We can then define parameters of the Random Forest classifier and fit the predictor variables from the training data to the Biomass estaimtes.
# In[26]:
#Define paraemters for Random forest regressor
max_depth = 30
#Define regressor rules
regr_rf = RandomForestRegressor(max_depth=max_depth, random_state=2)
#Fit the biomass to regressor variables
regr_rf.fit(biomass_predictors,biomass)
# We now apply the Random Forest model to the predictor variables to retreive biomass
# In[27]:
#Apply the model to the predictors
estimated_biomass = regr_rf.predict(X)
# For outputting a raster, copy the labels raster to a biomass raster, then cycle through the segments and assign the biomass estimate to each individual tree segment.
# In[28]:
#Set an out raster with the same size as the labels
biomass_map = np.array((labels),dtype=float)
#Assign the appropriate biomass to the labels
biomass_map[biomass_map==0] = np.nan
for tree_id, biomass_of_tree_id in zip(tree_ids, estimated_biomass):
biomass_map[biomass_map == tree_id] = biomass_of_tree_id
# ## Calc Biomass
# Collect some of the biomass statistics and then plot the results and save an output geotiff.
# In[29]:
#Get biomass stats for plotting
mean_biomass = np.mean(estimated_biomass)
std_biomass = np.std(estimated_biomass)
min_biomass = np.min(estimated_biomass)
sum_biomass = np.sum(estimated_biomass)
print('Sum of biomass is ',sum_biomass,' kg')
#Plot the biomass!
plt.figure(5)
plot_band_array(biomass_map,chm_array_metadata['extent'],
'Biomass (kg)','Biomass (kg)',
'winter',
[min_biomass+std_biomass, mean_biomass+std_biomass*3])
plt.savefig(data_path+just_chm_file_split[0]+'_'+just_chm_file_split[1]+'_'+just_chm_file_split[2]+'_'+just_chm_file_split[3]+'_'+just_chm_file_split[4]+'_'+just_chm_file_split[5]+'_'+'Biomass.png',
dpi=300,orientation='landscape',
bbox_inches='tight',
pad_inches=0.1)
array2raster(data_path+'biomass.tif',
(chm_array_metadata['ext_dict']['xMin'],chm_array_metadata['ext_dict']['yMax']),
1,-1,np.array(biomass_map,dtype=float),32611)
# In[ ]:
| agpl-3.0 |
antoinecarme/pyaf | setup.py | 1 | 1126 | from setuptools import setup
from setuptools import find_packages
with open("README.md", "r") as fh:
pyaf_long_description = fh.read()
setup(name='pyaf',
version='3.0-RC1',
description='Python Automatic Forecasting',
long_description=pyaf_long_description,
long_description_content_type="text/markdown",
author='Antoine CARME',
author_email='antoine.carme@laposte.net',
url='https://github.com/antoinecarme/pyaf',
license='BSD 3-clause',
packages=find_packages(include=['pyaf', 'pyaf.*']),
python_requires='>=3',
classifiers=['Development Status :: 5 - Production/Stable',
'Programming Language :: Python :: 3'],
keywords='arx automatic-forecasting autoregressive benchmark cycle decomposition exogenous forecasting heroku hierarchical-forecasting horizon jupyter pandas python scikit-learn seasonal time-series transformation trend web-service',
install_requires=[
'scipy',
'pandas',
'sklearn',
'matplotlib',
'pydot',
'dill',
'sqlalchemy'
])
| bsd-3-clause |
saimn/astropy | astropy/visualization/wcsaxes/frame.py | 8 | 10649 | # Licensed under a 3-clause BSD style license - see LICENSE.rst
import abc
from collections import OrderedDict
import numpy as np
from matplotlib import rcParams
from matplotlib.lines import Line2D, Path
from matplotlib.patches import PathPatch
__all__ = ['RectangularFrame1D', 'Spine', 'BaseFrame', 'RectangularFrame', 'EllipticalFrame']
class Spine:
"""
A single side of an axes.
This does not need to be a straight line, but represents a 'side' when
determining which part of the frame to put labels and ticks on.
"""
def __init__(self, parent_axes, transform):
self.parent_axes = parent_axes
self.transform = transform
self.data = None
self.pixel = None
self.world = None
@property
def data(self):
return self._data
@data.setter
def data(self, value):
if value is None:
self._data = None
self._pixel = None
self._world = None
else:
self._data = value
self._pixel = self.parent_axes.transData.transform(self._data)
with np.errstate(invalid='ignore'):
self._world = self.transform.transform(self._data)
self._update_normal()
@property
def pixel(self):
return self._pixel
@pixel.setter
def pixel(self, value):
if value is None:
self._data = None
self._pixel = None
self._world = None
else:
self._data = self.parent_axes.transData.inverted().transform(self._data)
self._pixel = value
self._world = self.transform.transform(self._data)
self._update_normal()
@property
def world(self):
return self._world
@world.setter
def world(self, value):
if value is None:
self._data = None
self._pixel = None
self._world = None
else:
self._data = self.transform.transform(value)
self._pixel = self.parent_axes.transData.transform(self._data)
self._world = value
self._update_normal()
def _update_normal(self):
# Find angle normal to border and inwards, in display coordinate
dx = self.pixel[1:, 0] - self.pixel[:-1, 0]
dy = self.pixel[1:, 1] - self.pixel[:-1, 1]
self.normal_angle = np.degrees(np.arctan2(dx, -dy))
def _halfway_x_y_angle(self):
"""
Return the x, y, normal_angle values halfway along the spine
"""
x_disp, y_disp = self.pixel[:, 0], self.pixel[:, 1]
# Get distance along the path
d = np.hstack([0., np.cumsum(np.sqrt(np.diff(x_disp) ** 2 + np.diff(y_disp) ** 2))])
xcen = np.interp(d[-1] / 2., d, x_disp)
ycen = np.interp(d[-1] / 2., d, y_disp)
# Find segment along which the mid-point lies
imin = np.searchsorted(d, d[-1] / 2.) - 1
# Find normal of the axis label facing outwards on that segment
normal_angle = self.normal_angle[imin] + 180.
return xcen, ycen, normal_angle
class SpineXAligned(Spine):
"""
A single side of an axes, aligned with the X data axis.
This does not need to be a straight line, but represents a 'side' when
determining which part of the frame to put labels and ticks on.
"""
@property
def data(self):
return self._data
@data.setter
def data(self, value):
if value is None:
self._data = None
self._pixel = None
self._world = None
else:
self._data = value
self._pixel = self.parent_axes.transData.transform(self._data)
with np.errstate(invalid='ignore'):
self._world = self.transform.transform(self._data[:,0:1])
self._update_normal()
@property
def pixel(self):
return self._pixel
@pixel.setter
def pixel(self, value):
if value is None:
self._data = None
self._pixel = None
self._world = None
else:
self._data = self.parent_axes.transData.inverted().transform(self._data)
self._pixel = value
self._world = self.transform.transform(self._data[:,0:1])
self._update_normal()
class BaseFrame(OrderedDict, metaclass=abc.ABCMeta):
"""
Base class for frames, which are collections of
:class:`~astropy.visualization.wcsaxes.frame.Spine` instances.
"""
spine_class = Spine
def __init__(self, parent_axes, transform, path=None):
super().__init__()
self.parent_axes = parent_axes
self._transform = transform
self._linewidth = rcParams['axes.linewidth']
self._color = rcParams['axes.edgecolor']
self._path = path
for axis in self.spine_names:
self[axis] = self.spine_class(parent_axes, transform)
@property
def origin(self):
ymin, ymax = self.parent_axes.get_ylim()
return 'lower' if ymin < ymax else 'upper'
@property
def transform(self):
return self._transform
@transform.setter
def transform(self, value):
self._transform = value
for axis in self:
self[axis].transform = value
def _update_patch_path(self):
self.update_spines()
x, y = [], []
for axis in self:
x.append(self[axis].data[:, 0])
y.append(self[axis].data[:, 1])
vertices = np.vstack([np.hstack(x), np.hstack(y)]).transpose()
if self._path is None:
self._path = Path(vertices)
else:
self._path.vertices = vertices
@property
def patch(self):
self._update_patch_path()
return PathPatch(self._path, transform=self.parent_axes.transData,
facecolor=rcParams['axes.facecolor'], edgecolor='white')
def draw(self, renderer):
for axis in self:
x, y = self[axis].pixel[:, 0], self[axis].pixel[:, 1]
line = Line2D(x, y, linewidth=self._linewidth, color=self._color, zorder=1000)
line.draw(renderer)
def sample(self, n_samples):
self.update_spines()
spines = OrderedDict()
for axis in self:
data = self[axis].data
p = np.linspace(0., 1., data.shape[0])
p_new = np.linspace(0., 1., n_samples)
spines[axis] = self.spine_class(self.parent_axes, self.transform)
spines[axis].data = np.array([np.interp(p_new, p, d) for d in data.T]).transpose()
return spines
def set_color(self, color):
"""
Sets the color of the frame.
Parameters
----------
color : str
The color of the frame.
"""
self._color = color
def get_color(self):
return self._color
def set_linewidth(self, linewidth):
"""
Sets the linewidth of the frame.
Parameters
----------
linewidth : float
The linewidth of the frame in points.
"""
self._linewidth = linewidth
def get_linewidth(self):
return self._linewidth
@abc.abstractmethod
def update_spines(self):
raise NotImplementedError("")
class RectangularFrame1D(BaseFrame):
"""
A classic rectangular frame.
"""
spine_names = 'bt'
spine_class = SpineXAligned
def update_spines(self):
xmin, xmax = self.parent_axes.get_xlim()
ymin, ymax = self.parent_axes.get_ylim()
self['b'].data = np.array(([xmin, ymin], [xmax, ymin]))
self['t'].data = np.array(([xmax, ymax], [xmin, ymax]))
def _update_patch_path(self):
self.update_spines()
xmin, xmax = self.parent_axes.get_xlim()
ymin, ymax = self.parent_axes.get_ylim()
x = [xmin, xmax, xmax, xmin, xmin]
y = [ymin, ymin, ymax, ymax, ymin]
vertices = np.vstack([np.hstack(x), np.hstack(y)]).transpose()
if self._path is None:
self._path = Path(vertices)
else:
self._path.vertices = vertices
def draw(self, renderer):
xmin, xmax = self.parent_axes.get_xlim()
ymin, ymax = self.parent_axes.get_ylim()
x = [xmin, xmax, xmax, xmin, xmin]
y = [ymin, ymin, ymax, ymax, ymin]
line = Line2D(x, y, linewidth=self._linewidth, color=self._color, zorder=1000,
transform=self.parent_axes.transData)
line.draw(renderer)
class RectangularFrame(BaseFrame):
"""
A classic rectangular frame.
"""
spine_names = 'brtl'
def update_spines(self):
xmin, xmax = self.parent_axes.get_xlim()
ymin, ymax = self.parent_axes.get_ylim()
self['b'].data = np.array(([xmin, ymin], [xmax, ymin]))
self['r'].data = np.array(([xmax, ymin], [xmax, ymax]))
self['t'].data = np.array(([xmax, ymax], [xmin, ymax]))
self['l'].data = np.array(([xmin, ymax], [xmin, ymin]))
class EllipticalFrame(BaseFrame):
"""
An elliptical frame.
"""
spine_names = 'chv'
def update_spines(self):
xmin, xmax = self.parent_axes.get_xlim()
ymin, ymax = self.parent_axes.get_ylim()
xmid = 0.5 * (xmax + xmin)
ymid = 0.5 * (ymax + ymin)
dx = xmid - xmin
dy = ymid - ymin
theta = np.linspace(0., 2 * np.pi, 1000)
self['c'].data = np.array([xmid + dx * np.cos(theta),
ymid + dy * np.sin(theta)]).transpose()
self['h'].data = np.array([np.linspace(xmin, xmax, 1000),
np.repeat(ymid, 1000)]).transpose()
self['v'].data = np.array([np.repeat(xmid, 1000),
np.linspace(ymin, ymax, 1000)]).transpose()
def _update_patch_path(self):
"""Override path patch to include only the outer ellipse,
not the major and minor axes in the middle."""
self.update_spines()
vertices = self['c'].data
if self._path is None:
self._path = Path(vertices)
else:
self._path.vertices = vertices
def draw(self, renderer):
"""Override to draw only the outer ellipse,
not the major and minor axes in the middle.
FIXME: we may want to add a general method to give the user control
over which spines are drawn."""
axis = 'c'
x, y = self[axis].pixel[:, 0], self[axis].pixel[:, 1]
line = Line2D(x, y, linewidth=self._linewidth, color=self._color, zorder=1000)
line.draw(renderer)
| bsd-3-clause |
mne-tools/mne-tools.github.io | 0.11/_downloads/plot_evoked_topomap.py | 18 | 1498 | """
========================================
Plotting topographic maps of evoked data
========================================
Load evoked data and plot topomaps for selected time points.
"""
# Authors: Christian Brodbeck <christianbrodbeck@nyu.edu>
# Tal Linzen <linzen@nyu.edu>
# Denis A. Engeman <denis.engemann@gmail.com>
#
# License: BSD (3-clause)
import numpy as np
import matplotlib.pyplot as plt
from mne.datasets import sample
from mne import read_evokeds
print(__doc__)
path = sample.data_path()
fname = path + '/MEG/sample/sample_audvis-ave.fif'
# load evoked and subtract baseline
condition = 'Left Auditory'
evoked = read_evokeds(fname, condition=condition, baseline=(None, 0))
# set time instants in seconds (from 50 to 150ms in a step of 10ms)
times = np.arange(0.05, 0.15, 0.01)
# If times is set to None only 10 regularly spaced topographies will be shown
# plot magnetometer data as topomaps
evoked.plot_topomap(times, ch_type='mag')
# compute a 50 ms bin to stabilize topographies
evoked.plot_topomap(times, ch_type='mag', average=0.05)
# plot gradiometer data (plots the RMS for each pair of gradiometers)
evoked.plot_topomap(times, ch_type='grad')
# plot magnetometer data as topomap at 1 time point : 100 ms
# and add channel labels and title
evoked.plot_topomap(0.1, ch_type='mag', show_names=True, colorbar=False,
size=6, res=128, title='Auditory response')
plt.subplots_adjust(left=0.01, right=0.99, bottom=0.01, top=0.88)
| bsd-3-clause |
nikitasingh981/scikit-learn | examples/semi_supervised/plot_label_propagation_versus_svm_iris.py | 50 | 2378 | """
=====================================================================
Decision boundary of label propagation versus SVM on the Iris dataset
=====================================================================
Comparison for decision boundary generated on iris dataset
between Label Propagation and SVM.
This demonstrates Label Propagation learning a good boundary
even with a small amount of labeled data.
"""
print(__doc__)
# Authors: Clay Woolam <clay@woolam.org>
# License: BSD
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn import svm
from sklearn.semi_supervised import label_propagation
rng = np.random.RandomState(0)
iris = datasets.load_iris()
X = iris.data[:, :2]
y = iris.target
# step size in the mesh
h = .02
y_30 = np.copy(y)
y_30[rng.rand(len(y)) < 0.3] = -1
y_50 = np.copy(y)
y_50[rng.rand(len(y)) < 0.5] = -1
# we create an instance of SVM and fit out data. We do not scale our
# data since we want to plot the support vectors
ls30 = (label_propagation.LabelSpreading().fit(X, y_30),
y_30)
ls50 = (label_propagation.LabelSpreading().fit(X, y_50),
y_50)
ls100 = (label_propagation.LabelSpreading().fit(X, y), y)
rbf_svc = (svm.SVC(kernel='rbf').fit(X, y), y)
# create a mesh to plot in
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
# title for the plots
titles = ['Label Spreading 30% data',
'Label Spreading 50% data',
'Label Spreading 100% data',
'SVC with rbf kernel']
color_map = {-1: (1, 1, 1), 0: (0, 0, .9), 1: (1, 0, 0), 2: (.8, .6, 0)}
for i, (clf, y_train) in enumerate((ls30, ls50, ls100, rbf_svc)):
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]x[y_min, y_max].
plt.subplot(2, 2, i + 1)
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.contourf(xx, yy, Z, cmap=plt.cm.Paired)
plt.axis('off')
# Plot also the training points
colors = [color_map[y] for y in y_train]
plt.scatter(X[:, 0], X[:, 1], c=colors, cmap=plt.cm.Paired)
plt.title(titles[i])
plt.text(.90, 0, "Unlabeled points are colored white")
plt.show()
| bsd-3-clause |
DongjunLee/kino-bot | kino/slack/plot.py | 1 | 2684 | from matplotlib import pyplot as plt
import matplotlib.dates as dt
import seaborn
seaborn.set()
import datetime
class Plot(object):
def __init__(self):
pass
def make_bar(
x,
y,
f_name,
title=None,
legend=None,
x_label=None,
y_label=None,
x_ticks=None,
y_ticks=None,
):
fig = plt.figure()
if title is not None:
plt.title(title, fontsize=16)
if x_label is not None:
plt.ylabel(x_label)
if y_label is not None:
plt.xlabel(y_label)
if x_ticks is not None:
plt.xticks(x, x_ticks)
if y_ticks is not None:
plt.yticks(y_ticks)
plt.bar(x, y, align="center")
if legend is not None:
plt.legend(legend)
plt.savefig(f_name)
plt.close(fig)
def make_line(
x,
y,
f_name,
title=None,
legend=None,
x_label=None,
y_label=None,
x_ticks=None,
y_ticks=None,
):
fig = plt.figure()
if title is not None:
plt.title(title, fontsize=16)
if x_label is not None:
plt.ylabel(x_label)
if y_label is not None:
plt.xlabel(y_label)
if x_ticks is not None:
plt.xticks(x, x_ticks)
if y_ticks is not None:
plt.yticks(y_ticks)
if isinstance(y[0], list):
for data in y:
plt.plot(x, data)
else:
plt.plot(x, y)
if legend is not None:
plt.legend(legend)
plt.savefig(f_name)
plt.close(fig)
def make_efficiency_date(
total_data,
avg_data,
f_name,
title=None,
x_label=None,
y_label=None,
x_ticks=None,
y_ticks=None,
):
fig = plt.figure()
if title is not None:
plt.title(title, fontsize=16)
if x_label is not None:
plt.ylabel(x_label)
if y_label is not None:
plt.xlabel(y_label)
v_date = []
v_val = []
for data in total_data:
dates = dt.date2num(datetime.datetime.strptime(data[0], "%H:%M"))
to_int = round(float(data[1]))
plt.plot_date(dates, data[1], color=plt.cm.brg(to_int))
for data in avg_data:
dates = dt.date2num(datetime.datetime.strptime(data[0], "%H:%M"))
v_date.append(dates)
v_val.append(data[1])
plt.plot_date(v_date, v_val, "^y-", label="Average")
plt.legend()
plt.savefig(f_name)
plt.close(fig)
| mit |
sylvchev/mdla | examples/example_benchmark_performance.py | 1 | 6309 | """Benchmarking dictionary learning algorithms on random dataset"""
from multiprocessing import cpu_count
from time import time
import matplotlib.pyplot as plt
import numpy as np
from numpy import array
from numpy.linalg import norm
from numpy.random import permutation, rand, randint, randn
from mdla import MiniBatchMultivariateDictLearning, MultivariateDictLearning
# TODO:
# investigate perf break from pydico
def benchmarking_plot(figname, pst, plot_sep, minibatchRange, mprocessRange):
_ = plt.figure(figsize=(15, 10))
bar_width = 0.35
_ = plt.bar(
np.array([0]),
pst[0],
bar_width,
color="b",
label="Online, no multiprocessing (baseline)",
)
index = [0]
for i in range(1, plot_sep[1]):
if i == 1:
_ = plt.bar(
np.array([i + 1]),
pst[i],
bar_width,
color="r",
label="Online with minibatch",
)
else:
_ = plt.bar(np.array([i + 1]), pst[i], bar_width, color="r")
index.append(i + 1)
for _ in range(plot_sep[1], plot_sep[2]):
if i == plot_sep[1]:
_ = plt.bar(
np.array([i + 2]),
pst[i],
bar_width,
label="Batch with multiprocessing",
color="magenta",
)
else:
_ = plt.bar(np.array([i + 2]), pst[i], bar_width, color="magenta")
index.append(i + 2)
plt.ylabel("Time per iteration (s)")
plt.title("Processing time for online and batch processing")
tick = [""]
tick.extend(map(str, minibatchRange))
tick.extend(map(str, mprocessRange))
plt.xticks(index, tuple(tick))
plt.legend()
plt.savefig(figname + ".png")
def _generate_testbed(
kernel_init_len,
n_nonzero_coefs,
n_kernels,
n_samples=10,
n_features=5,
n_dims=3,
snr=1000,
):
"""Generate a dataset from a random dictionary
Generate a random dictionary and a dataset, where samples are combination of
n_nonzero_coefs dictionary atoms. Noise is added, based on SNR value, with
1000 indicated that no noise should be added.
Return the dictionary, the dataset and an array indicated how atoms are combined
to obtain each sample
"""
print("Dictionary sampled from uniform distribution")
dico = [rand(kernel_init_len, n_dims) for i in range(n_kernels)]
for i in range(len(dico)):
dico[i] /= norm(dico[i], "fro")
signals = list()
decomposition = list()
for _ in range(n_samples):
s = np.zeros(shape=(n_features, n_dims))
d = np.zeros(shape=(n_nonzero_coefs, 3))
rk = permutation(range(n_kernels))
for j in range(n_nonzero_coefs):
k_idx = rk[j]
k_amplitude = 3.0 * rand() + 1.0
k_offset = randint(n_features - kernel_init_len + 1)
s[k_offset : k_offset + kernel_init_len, :] += k_amplitude * dico[k_idx]
d[j, :] = array([k_amplitude, k_offset, k_idx])
decomposition.append(d)
noise = randn(n_features, n_dims)
if snr == 1000:
alpha = 0
else:
ps = norm(s, "fro")
pn = norm(noise, "fro")
alpha = ps / (pn * 10 ** (snr / 20.0))
signals.append(s + alpha * noise)
signals = np.array(signals)
return dico, signals, decomposition
rng_global = np.random.RandomState(1)
n_samples, n_dims = 1500, 1
n_features = kernel_init_len = 5
n_nonzero_coefs = 3
n_kernels, max_iter, learning_rate = 50, 10, 1.5
n_jobs, batch_size = -1, None
iter_time, plot_separator, it_separator = list(), list(), 0
generating_dict, X, code = _generate_testbed(
kernel_init_len, n_nonzero_coefs, n_kernels, n_samples, n_features, n_dims
)
# Online without mini-batch
print(
"Processing ",
max_iter,
"iterations in online mode, " "without multiprocessing:",
end="",
)
batch_size, n_jobs = n_samples, 1
learned_dict = MiniBatchMultivariateDictLearning(
n_kernels=n_kernels,
batch_size=batch_size,
n_iter=max_iter,
n_nonzero_coefs=n_nonzero_coefs,
n_jobs=n_jobs,
learning_rate=learning_rate,
kernel_init_len=kernel_init_len,
verbose=1,
dict_init=None,
random_state=rng_global,
)
ts = time()
learned_dict = learned_dict.fit(X)
iter_time.append((time() - ts) / max_iter)
it_separator += 1
plot_separator.append(it_separator)
# Online with mini-batch
minibatch_range = [cpu_count()]
minibatch_range.extend([cpu_count() * i for i in range(3, 10, 2)])
n_jobs = -1
for mb in minibatch_range:
print(
"\nProcessing ",
max_iter,
"iterations in online mode, with ",
"minibatch size",
mb,
"and",
cpu_count(),
"processes:",
end="",
)
batch_size = mb
learned_dict = MiniBatchMultivariateDictLearning(
n_kernels=n_kernels,
batch_size=batch_size,
n_iter=max_iter,
n_nonzero_coefs=n_nonzero_coefs,
n_jobs=n_jobs,
learning_rate=learning_rate,
kernel_init_len=kernel_init_len,
verbose=1,
dict_init=None,
random_state=rng_global,
)
ts = time()
learned_dict = learned_dict.fit(X)
iter_time.append((time() - ts) / max_iter)
it_separator += 1
plot_separator.append(it_separator)
# Batch learning
mp_range = range(1, cpu_count() + 1)
for p in mp_range:
print(
"\nProcessing ",
max_iter,
"iterations in batch mode, with",
p,
"processes:",
end="",
)
n_jobs = p
learned_dict = MultivariateDictLearning(
n_kernels=n_kernels,
max_iter=max_iter,
verbose=1,
n_nonzero_coefs=n_nonzero_coefs,
n_jobs=n_jobs,
learning_rate=learning_rate,
kernel_init_len=kernel_init_len,
dict_init=None,
random_state=rng_global,
)
ts = time()
learned_dict = learned_dict.fit(X)
iter_time.append((time() - ts) / max_iter)
it_separator += 1
plot_separator.append(it_separator)
print("Done benchmarking")
figname = "minibatch-performance"
print("Plotting results in", figname)
benchmarking_plot(figname, iter_time, plot_separator, minibatch_range, mp_range)
print("Exiting.")
| gpl-3.0 |
david-ragazzi/nupic | external/linux32/lib/python2.6/site-packages/matplotlib/axes.py | 69 | 259904 | from __future__ import division, generators
import math, sys, warnings, datetime, new
import numpy as np
from numpy import ma
import matplotlib
rcParams = matplotlib.rcParams
import matplotlib.artist as martist
import matplotlib.axis as maxis
import matplotlib.cbook as cbook
import matplotlib.collections as mcoll
import matplotlib.colors as mcolors
import matplotlib.contour as mcontour
import matplotlib.dates as mdates
import matplotlib.font_manager as font_manager
import matplotlib.image as mimage
import matplotlib.legend as mlegend
import matplotlib.lines as mlines
import matplotlib.mlab as mlab
import matplotlib.patches as mpatches
import matplotlib.quiver as mquiver
import matplotlib.scale as mscale
import matplotlib.table as mtable
import matplotlib.text as mtext
import matplotlib.ticker as mticker
import matplotlib.transforms as mtransforms
iterable = cbook.iterable
is_string_like = cbook.is_string_like
def _process_plot_format(fmt):
"""
Process a matlab(TM) style color/line style format string. Return a
(*linestyle*, *color*) tuple as a result of the processing. Default
values are ('-', 'b'). Example format strings include:
* 'ko': black circles
* '.b': blue dots
* 'r--': red dashed lines
.. seealso::
:func:`~matplotlib.Line2D.lineStyles` and
:func:`~matplotlib.pyplot.colors`:
for all possible styles and color format string.
"""
linestyle = None
marker = None
color = None
# Is fmt just a colorspec?
try:
color = mcolors.colorConverter.to_rgb(fmt)
return linestyle, marker, color # Yes.
except ValueError:
pass # No, not just a color.
# handle the multi char special cases and strip them from the
# string
if fmt.find('--')>=0:
linestyle = '--'
fmt = fmt.replace('--', '')
if fmt.find('-.')>=0:
linestyle = '-.'
fmt = fmt.replace('-.', '')
if fmt.find(' ')>=0:
linestyle = 'None'
fmt = fmt.replace(' ', '')
chars = [c for c in fmt]
for c in chars:
if c in mlines.lineStyles:
if linestyle is not None:
raise ValueError(
'Illegal format string "%s"; two linestyle symbols' % fmt)
linestyle = c
elif c in mlines.lineMarkers:
if marker is not None:
raise ValueError(
'Illegal format string "%s"; two marker symbols' % fmt)
marker = c
elif c in mcolors.colorConverter.colors:
if color is not None:
raise ValueError(
'Illegal format string "%s"; two color symbols' % fmt)
color = c
else:
raise ValueError(
'Unrecognized character %c in format string' % c)
if linestyle is None and marker is None:
linestyle = rcParams['lines.linestyle']
if linestyle is None:
linestyle = 'None'
if marker is None:
marker = 'None'
return linestyle, marker, color
def set_default_color_cycle(clist):
"""
Change the default cycle of colors that will be used by the plot
command. This must be called before creating the
:class:`Axes` to which it will apply; it will
apply to all future axes.
*clist* is a sequence of mpl color specifiers
"""
_process_plot_var_args.defaultColors = clist[:]
rcParams['lines.color'] = clist[0]
class _process_plot_var_args:
"""
Process variable length arguments to the plot command, so that
plot commands like the following are supported::
plot(t, s)
plot(t1, s1, t2, s2)
plot(t1, s1, 'ko', t2, s2)
plot(t1, s1, 'ko', t2, s2, 'r--', t3, e3)
an arbitrary number of *x*, *y*, *fmt* are allowed
"""
defaultColors = ['b','g','r','c','m','y','k']
def __init__(self, axes, command='plot'):
self.axes = axes
self.command = command
self._clear_color_cycle()
def _clear_color_cycle(self):
self.colors = _process_plot_var_args.defaultColors[:]
# if the default line color is a color format string, move it up
# in the que
try: ind = self.colors.index(rcParams['lines.color'])
except ValueError:
self.firstColor = rcParams['lines.color']
else:
self.colors[0], self.colors[ind] = self.colors[ind], self.colors[0]
self.firstColor = self.colors[0]
self.Ncolors = len(self.colors)
self.count = 0
def set_color_cycle(self, clist):
self.colors = clist[:]
self.firstColor = self.colors[0]
self.Ncolors = len(self.colors)
self.count = 0
def _get_next_cycle_color(self):
if self.count==0:
color = self.firstColor
else:
color = self.colors[int(self.count % self.Ncolors)]
self.count += 1
return color
def __call__(self, *args, **kwargs):
if self.axes.xaxis is not None and self.axes.yaxis is not None:
xunits = kwargs.pop( 'xunits', self.axes.xaxis.units)
yunits = kwargs.pop( 'yunits', self.axes.yaxis.units)
if xunits!=self.axes.xaxis.units:
self.axes.xaxis.set_units(xunits)
if yunits!=self.axes.yaxis.units:
self.axes.yaxis.set_units(yunits)
ret = self._grab_next_args(*args, **kwargs)
return ret
def set_lineprops(self, line, **kwargs):
assert self.command == 'plot', 'set_lineprops only works with "plot"'
for key, val in kwargs.items():
funcName = "set_%s"%key
if not hasattr(line,funcName):
raise TypeError, 'There is no line property "%s"'%key
func = getattr(line,funcName)
func(val)
def set_patchprops(self, fill_poly, **kwargs):
assert self.command == 'fill', 'set_patchprops only works with "fill"'
for key, val in kwargs.items():
funcName = "set_%s"%key
if not hasattr(fill_poly,funcName):
raise TypeError, 'There is no patch property "%s"'%key
func = getattr(fill_poly,funcName)
func(val)
def _xy_from_y(self, y):
if self.axes.yaxis is not None:
b = self.axes.yaxis.update_units(y)
if b: return np.arange(len(y)), y, False
if not ma.isMaskedArray(y):
y = np.asarray(y)
if len(y.shape) == 1:
y = y[:,np.newaxis]
nr, nc = y.shape
x = np.arange(nr)
if len(x.shape) == 1:
x = x[:,np.newaxis]
return x,y, True
def _xy_from_xy(self, x, y):
if self.axes.xaxis is not None and self.axes.yaxis is not None:
bx = self.axes.xaxis.update_units(x)
by = self.axes.yaxis.update_units(y)
# right now multicol is not supported if either x or y are
# unit enabled but this can be fixed..
if bx or by: return x, y, False
x = ma.asarray(x)
y = ma.asarray(y)
if len(x.shape) == 1:
x = x[:,np.newaxis]
if len(y.shape) == 1:
y = y[:,np.newaxis]
nrx, ncx = x.shape
nry, ncy = y.shape
assert nrx == nry, 'Dimensions of x and y are incompatible'
if ncx == ncy:
return x, y, True
if ncx == 1:
x = np.repeat(x, ncy, axis=1)
if ncy == 1:
y = np.repeat(y, ncx, axis=1)
assert x.shape == y.shape, 'Dimensions of x and y are incompatible'
return x, y, True
def _plot_1_arg(self, y, **kwargs):
assert self.command == 'plot', 'fill needs at least 2 arguments'
ret = []
x, y, multicol = self._xy_from_y(y)
if multicol:
for j in xrange(y.shape[1]):
color = self._get_next_cycle_color()
seg = mlines.Line2D(x, y[:,j],
color = color,
axes=self.axes,
)
self.set_lineprops(seg, **kwargs)
ret.append(seg)
else:
color = self._get_next_cycle_color()
seg = mlines.Line2D(x, y,
color = color,
axes=self.axes,
)
self.set_lineprops(seg, **kwargs)
ret.append(seg)
return ret
def _plot_2_args(self, tup2, **kwargs):
ret = []
if is_string_like(tup2[1]):
assert self.command == 'plot', ('fill needs at least 2 non-string '
'arguments')
y, fmt = tup2
x, y, multicol = self._xy_from_y(y)
linestyle, marker, color = _process_plot_format(fmt)
def makeline(x, y):
_color = color
if _color is None:
_color = self._get_next_cycle_color()
seg = mlines.Line2D(x, y,
color=_color,
linestyle=linestyle, marker=marker,
axes=self.axes,
)
self.set_lineprops(seg, **kwargs)
ret.append(seg)
if multicol:
for j in xrange(y.shape[1]):
makeline(x[:,j], y[:,j])
else:
makeline(x, y)
return ret
else:
x, y = tup2
x, y, multicol = self._xy_from_xy(x, y)
def makeline(x, y):
color = self._get_next_cycle_color()
seg = mlines.Line2D(x, y,
color=color,
axes=self.axes,
)
self.set_lineprops(seg, **kwargs)
ret.append(seg)
def makefill(x, y):
x = self.axes.convert_xunits(x)
y = self.axes.convert_yunits(y)
facecolor = self._get_next_cycle_color()
seg = mpatches.Polygon(np.hstack(
(x[:,np.newaxis],y[:,np.newaxis])),
facecolor = facecolor,
fill=True,
closed=closed
)
self.set_patchprops(seg, **kwargs)
ret.append(seg)
if self.command == 'plot':
func = makeline
else:
closed = kwargs.get('closed', True)
func = makefill
if multicol:
for j in xrange(y.shape[1]):
func(x[:,j], y[:,j])
else:
func(x, y)
return ret
def _plot_3_args(self, tup3, **kwargs):
ret = []
x, y, fmt = tup3
x, y, multicol = self._xy_from_xy(x, y)
linestyle, marker, color = _process_plot_format(fmt)
def makeline(x, y):
_color = color
if _color is None:
_color = self._get_next_cycle_color()
seg = mlines.Line2D(x, y,
color=_color,
linestyle=linestyle, marker=marker,
axes=self.axes,
)
self.set_lineprops(seg, **kwargs)
ret.append(seg)
def makefill(x, y):
facecolor = color
x = self.axes.convert_xunits(x)
y = self.axes.convert_yunits(y)
seg = mpatches.Polygon(np.hstack(
(x[:,np.newaxis],y[:,np.newaxis])),
facecolor = facecolor,
fill=True,
closed=closed
)
self.set_patchprops(seg, **kwargs)
ret.append(seg)
if self.command == 'plot':
func = makeline
else:
closed = kwargs.get('closed', True)
func = makefill
if multicol:
for j in xrange(y.shape[1]):
func(x[:,j], y[:,j])
else:
func(x, y)
return ret
def _grab_next_args(self, *args, **kwargs):
remaining = args
while 1:
if len(remaining)==0: return
if len(remaining)==1:
for seg in self._plot_1_arg(remaining[0], **kwargs):
yield seg
remaining = []
continue
if len(remaining)==2:
for seg in self._plot_2_args(remaining, **kwargs):
yield seg
remaining = []
continue
if len(remaining)==3:
if not is_string_like(remaining[2]):
raise ValueError, 'third arg must be a format string'
for seg in self._plot_3_args(remaining, **kwargs):
yield seg
remaining=[]
continue
if is_string_like(remaining[2]):
for seg in self._plot_3_args(remaining[:3], **kwargs):
yield seg
remaining=remaining[3:]
else:
for seg in self._plot_2_args(remaining[:2], **kwargs):
yield seg
remaining=remaining[2:]
class Axes(martist.Artist):
"""
The :class:`Axes` contains most of the figure elements:
:class:`~matplotlib.axis.Axis`, :class:`~matplotlib.axis.Tick`,
:class:`~matplotlib.lines.Line2D`, :class:`~matplotlib.text.Text`,
:class:`~matplotlib.patches.Polygon`, etc., and sets the
coordinate system.
The :class:`Axes` instance supports callbacks through a callbacks
attribute which is a :class:`~matplotlib.cbook.CallbackRegistry`
instance. The events you can connect to are 'xlim_changed' and
'ylim_changed' and the callback will be called with func(*ax*)
where *ax* is the :class:`Axes` instance.
"""
name = "rectilinear"
_shared_x_axes = cbook.Grouper()
_shared_y_axes = cbook.Grouper()
def __str__(self):
return "Axes(%g,%g;%gx%g)" % tuple(self._position.bounds)
def __init__(self, fig, rect,
axisbg = None, # defaults to rc axes.facecolor
frameon = True,
sharex=None, # use Axes instance's xaxis info
sharey=None, # use Axes instance's yaxis info
label='',
**kwargs
):
"""
Build an :class:`Axes` instance in
:class:`~matplotlib.figure.Figure` *fig* with
*rect=[left, bottom, width, height]* in
:class:`~matplotlib.figure.Figure` coordinates
Optional keyword arguments:
================ =========================================
Keyword Description
================ =========================================
*adjustable* [ 'box' | 'datalim' ]
*alpha* float: the alpha transparency
*anchor* [ 'C', 'SW', 'S', 'SE', 'E', 'NE', 'N',
'NW', 'W' ]
*aspect* [ 'auto' | 'equal' | aspect_ratio ]
*autoscale_on* [ *True* | *False* ] whether or not to
autoscale the *viewlim*
*axis_bgcolor* any matplotlib color, see
:func:`~matplotlib.pyplot.colors`
*axisbelow* draw the grids and ticks below the other
artists
*cursor_props* a (*float*, *color*) tuple
*figure* a :class:`~matplotlib.figure.Figure`
instance
*frame_on* a boolean - draw the axes frame
*label* the axes label
*navigate* [ *True* | *False* ]
*navigate_mode* [ 'PAN' | 'ZOOM' | None ] the navigation
toolbar button status
*position* [left, bottom, width, height] in
class:`~matplotlib.figure.Figure` coords
*sharex* an class:`~matplotlib.axes.Axes` instance
to share the x-axis with
*sharey* an class:`~matplotlib.axes.Axes` instance
to share the y-axis with
*title* the title string
*visible* [ *True* | *False* ] whether the axes is
visible
*xlabel* the xlabel
*xlim* (*xmin*, *xmax*) view limits
*xscale* [%(scale)s]
*xticklabels* sequence of strings
*xticks* sequence of floats
*ylabel* the ylabel strings
*ylim* (*ymin*, *ymax*) view limits
*yscale* [%(scale)s]
*yticklabels* sequence of strings
*yticks* sequence of floats
================ =========================================
""" % {'scale': ' | '.join([repr(x) for x in mscale.get_scale_names()])}
martist.Artist.__init__(self)
if isinstance(rect, mtransforms.Bbox):
self._position = rect
else:
self._position = mtransforms.Bbox.from_bounds(*rect)
self._originalPosition = self._position.frozen()
self.set_axes(self)
self.set_aspect('auto')
self._adjustable = 'box'
self.set_anchor('C')
self._sharex = sharex
self._sharey = sharey
if sharex is not None:
self._shared_x_axes.join(self, sharex)
if sharex._adjustable == 'box':
sharex._adjustable = 'datalim'
#warnings.warn(
# 'shared axes: "adjustable" is being changed to "datalim"')
self._adjustable = 'datalim'
if sharey is not None:
self._shared_y_axes.join(self, sharey)
if sharey._adjustable == 'box':
sharey._adjustable = 'datalim'
#warnings.warn(
# 'shared axes: "adjustable" is being changed to "datalim"')
self._adjustable = 'datalim'
self.set_label(label)
self.set_figure(fig)
# this call may differ for non-sep axes, eg polar
self._init_axis()
if axisbg is None: axisbg = rcParams['axes.facecolor']
self._axisbg = axisbg
self._frameon = frameon
self._axisbelow = rcParams['axes.axisbelow']
self._hold = rcParams['axes.hold']
self._connected = {} # a dict from events to (id, func)
self.cla()
# funcs used to format x and y - fall back on major formatters
self.fmt_xdata = None
self.fmt_ydata = None
self.set_cursor_props((1,'k')) # set the cursor properties for axes
self._cachedRenderer = None
self.set_navigate(True)
self.set_navigate_mode(None)
if len(kwargs): martist.setp(self, **kwargs)
if self.xaxis is not None:
self._xcid = self.xaxis.callbacks.connect('units finalize',
self.relim)
if self.yaxis is not None:
self._ycid = self.yaxis.callbacks.connect('units finalize',
self.relim)
def get_window_extent(self, *args, **kwargs):
'''
get the axes bounding box in display space; *args* and
*kwargs* are empty
'''
return self.bbox
def _init_axis(self):
"move this out of __init__ because non-separable axes don't use it"
self.xaxis = maxis.XAxis(self)
self.yaxis = maxis.YAxis(self)
self._update_transScale()
def set_figure(self, fig):
"""
Set the class:`~matplotlib.axes.Axes` figure
accepts a class:`~matplotlib.figure.Figure` instance
"""
martist.Artist.set_figure(self, fig)
self.bbox = mtransforms.TransformedBbox(self._position, fig.transFigure)
#these will be updated later as data is added
self.dataLim = mtransforms.Bbox.unit()
self.viewLim = mtransforms.Bbox.unit()
self.transScale = mtransforms.TransformWrapper(
mtransforms.IdentityTransform())
self._set_lim_and_transforms()
def _set_lim_and_transforms(self):
"""
set the *dataLim* and *viewLim*
:class:`~matplotlib.transforms.Bbox` attributes and the
*transScale*, *transData*, *transLimits* and *transAxes*
transformations.
"""
self.transAxes = mtransforms.BboxTransformTo(self.bbox)
# Transforms the x and y axis separately by a scale factor
# It is assumed that this part will have non-linear components
self.transScale = mtransforms.TransformWrapper(
mtransforms.IdentityTransform())
# An affine transformation on the data, generally to limit the
# range of the axes
self.transLimits = mtransforms.BboxTransformFrom(
mtransforms.TransformedBbox(self.viewLim, self.transScale))
# The parentheses are important for efficiency here -- they
# group the last two (which are usually affines) separately
# from the first (which, with log-scaling can be non-affine).
self.transData = self.transScale + (self.transLimits + self.transAxes)
self._xaxis_transform = mtransforms.blended_transform_factory(
self.axes.transData, self.axes.transAxes)
self._yaxis_transform = mtransforms.blended_transform_factory(
self.axes.transAxes, self.axes.transData)
def get_xaxis_transform(self):
"""
Get the transformation used for drawing x-axis labels, ticks
and gridlines. The x-direction is in data coordinates and the
y-direction is in axis coordinates.
.. note::
This transformation is primarily used by the
:class:`~matplotlib.axis.Axis` class, and is meant to be
overridden by new kinds of projections that may need to
place axis elements in different locations.
"""
return self._xaxis_transform
def get_xaxis_text1_transform(self, pad_points):
"""
Get the transformation used for drawing x-axis labels, which
will add the given amount of padding (in points) between the
axes and the label. The x-direction is in data coordinates
and the y-direction is in axis coordinates. Returns a
3-tuple of the form::
(transform, valign, halign)
where *valign* and *halign* are requested alignments for the
text.
.. note::
This transformation is primarily used by the
:class:`~matplotlib.axis.Axis` class, and is meant to be
overridden by new kinds of projections that may need to
place axis elements in different locations.
"""
return (self._xaxis_transform +
mtransforms.ScaledTranslation(0, -1 * pad_points / 72.0,
self.figure.dpi_scale_trans),
"top", "center")
def get_xaxis_text2_transform(self, pad_points):
"""
Get the transformation used for drawing the secondary x-axis
labels, which will add the given amount of padding (in points)
between the axes and the label. The x-direction is in data
coordinates and the y-direction is in axis coordinates.
Returns a 3-tuple of the form::
(transform, valign, halign)
where *valign* and *halign* are requested alignments for the
text.
.. note::
This transformation is primarily used by the
:class:`~matplotlib.axis.Axis` class, and is meant to be
overridden by new kinds of projections that may need to
place axis elements in different locations.
"""
return (self._xaxis_transform +
mtransforms.ScaledTranslation(0, pad_points / 72.0,
self.figure.dpi_scale_trans),
"bottom", "center")
def get_yaxis_transform(self):
"""
Get the transformation used for drawing y-axis labels, ticks
and gridlines. The x-direction is in axis coordinates and the
y-direction is in data coordinates.
.. note::
This transformation is primarily used by the
:class:`~matplotlib.axis.Axis` class, and is meant to be
overridden by new kinds of projections that may need to
place axis elements in different locations.
"""
return self._yaxis_transform
def get_yaxis_text1_transform(self, pad_points):
"""
Get the transformation used for drawing y-axis labels, which
will add the given amount of padding (in points) between the
axes and the label. The x-direction is in axis coordinates
and the y-direction is in data coordinates. Returns a 3-tuple
of the form::
(transform, valign, halign)
where *valign* and *halign* are requested alignments for the
text.
.. note::
This transformation is primarily used by the
:class:`~matplotlib.axis.Axis` class, and is meant to be
overridden by new kinds of projections that may need to
place axis elements in different locations.
"""
return (self._yaxis_transform +
mtransforms.ScaledTranslation(-1 * pad_points / 72.0, 0,
self.figure.dpi_scale_trans),
"center", "right")
def get_yaxis_text2_transform(self, pad_points):
"""
Get the transformation used for drawing the secondary y-axis
labels, which will add the given amount of padding (in points)
between the axes and the label. The x-direction is in axis
coordinates and the y-direction is in data coordinates.
Returns a 3-tuple of the form::
(transform, valign, halign)
where *valign* and *halign* are requested alignments for the
text.
.. note::
This transformation is primarily used by the
:class:`~matplotlib.axis.Axis` class, and is meant to be
overridden by new kinds of projections that may need to
place axis elements in different locations.
"""
return (self._yaxis_transform +
mtransforms.ScaledTranslation(pad_points / 72.0, 0,
self.figure.dpi_scale_trans),
"center", "left")
def _update_transScale(self):
self.transScale.set(
mtransforms.blended_transform_factory(
self.xaxis.get_transform(), self.yaxis.get_transform()))
if hasattr(self, "lines"):
for line in self.lines:
line._transformed_path.invalidate()
def get_position(self, original=False):
'Return the a copy of the axes rectangle as a Bbox'
if original:
return self._originalPosition.frozen()
else:
return self._position.frozen()
def set_position(self, pos, which='both'):
"""
Set the axes position with::
pos = [left, bottom, width, height]
in relative 0,1 coords, or *pos* can be a
:class:`~matplotlib.transforms.Bbox`
There are two position variables: one which is ultimately
used, but which may be modified by :meth:`apply_aspect`, and a
second which is the starting point for :meth:`apply_aspect`.
Optional keyword arguments:
*which*
========== ====================
value description
========== ====================
'active' to change the first
'original' to change the second
'both' to change both
========== ====================
"""
if not isinstance(pos, mtransforms.BboxBase):
pos = mtransforms.Bbox.from_bounds(*pos)
if which in ('both', 'active'):
self._position.set(pos)
if which in ('both', 'original'):
self._originalPosition.set(pos)
def reset_position(self):
'Make the original position the active position'
pos = self.get_position(original=True)
self.set_position(pos, which='active')
def _set_artist_props(self, a):
'set the boilerplate props for artists added to axes'
a.set_figure(self.figure)
if not a.is_transform_set():
a.set_transform(self.transData)
a.set_axes(self)
def _gen_axes_patch(self):
"""
Returns the patch used to draw the background of the axes. It
is also used as the clipping path for any data elements on the
axes.
In the standard axes, this is a rectangle, but in other
projections it may not be.
.. note::
Intended to be overridden by new projection types.
"""
return mpatches.Rectangle((0.0, 0.0), 1.0, 1.0)
def cla(self):
'Clear the current axes'
# Note: this is called by Axes.__init__()
self.xaxis.cla()
self.yaxis.cla()
self.ignore_existing_data_limits = True
self.callbacks = cbook.CallbackRegistry(('xlim_changed',
'ylim_changed'))
if self._sharex is not None:
# major and minor are class instances with
# locator and formatter attributes
self.xaxis.major = self._sharex.xaxis.major
self.xaxis.minor = self._sharex.xaxis.minor
x0, x1 = self._sharex.get_xlim()
self.set_xlim(x0, x1, emit=False)
self.xaxis.set_scale(self._sharex.xaxis.get_scale())
else:
self.xaxis.set_scale('linear')
if self._sharey is not None:
self.yaxis.major = self._sharey.yaxis.major
self.yaxis.minor = self._sharey.yaxis.minor
y0, y1 = self._sharey.get_ylim()
self.set_ylim(y0, y1, emit=False)
self.yaxis.set_scale(self._sharey.yaxis.get_scale())
else:
self.yaxis.set_scale('linear')
self._autoscaleon = True
self._update_transScale() # needed?
self._get_lines = _process_plot_var_args(self)
self._get_patches_for_fill = _process_plot_var_args(self, 'fill')
self._gridOn = rcParams['axes.grid']
self.lines = []
self.patches = []
self.texts = []
self.tables = []
self.artists = []
self.images = []
self.legend_ = None
self.collections = [] # collection.Collection instances
self.grid(self._gridOn)
props = font_manager.FontProperties(size=rcParams['axes.titlesize'])
self.titleOffsetTrans = mtransforms.ScaledTranslation(
0.0, 5.0 / 72.0, self.figure.dpi_scale_trans)
self.title = mtext.Text(
x=0.5, y=1.0, text='',
fontproperties=props,
verticalalignment='bottom',
horizontalalignment='center',
)
self.title.set_transform(self.transAxes + self.titleOffsetTrans)
self.title.set_clip_box(None)
self._set_artist_props(self.title)
# the patch draws the background of the axes. we want this to
# be below the other artists; the axesPatch name is
# deprecated. We use the frame to draw the edges so we are
# setting the edgecolor to None
self.patch = self.axesPatch = self._gen_axes_patch()
self.patch.set_figure(self.figure)
self.patch.set_facecolor(self._axisbg)
self.patch.set_edgecolor('None')
self.patch.set_linewidth(0)
self.patch.set_transform(self.transAxes)
# the frame draws the border around the axes and we want this
# above. this is a place holder for a more sophisticated
# artist that might just draw a left, bottom frame, or a
# centered frame, etc the axesFrame name is deprecated
self.frame = self.axesFrame = self._gen_axes_patch()
self.frame.set_figure(self.figure)
self.frame.set_facecolor('none')
self.frame.set_edgecolor(rcParams['axes.edgecolor'])
self.frame.set_linewidth(rcParams['axes.linewidth'])
self.frame.set_transform(self.transAxes)
self.frame.set_zorder(2.5)
self.axison = True
self.xaxis.set_clip_path(self.patch)
self.yaxis.set_clip_path(self.patch)
self._shared_x_axes.clean()
self._shared_y_axes.clean()
def clear(self):
'clear the axes'
self.cla()
def set_color_cycle(self, clist):
"""
Set the color cycle for any future plot commands on this Axes.
clist is a list of mpl color specifiers.
"""
self._get_lines.set_color_cycle(clist)
def ishold(self):
'return the HOLD status of the axes'
return self._hold
def hold(self, b=None):
"""
call signature::
hold(b=None)
Set the hold state. If *hold* is *None* (default), toggle the
*hold* state. Else set the *hold* state to boolean value *b*.
Examples:
* toggle hold:
>>> hold()
* turn hold on:
>>> hold(True)
* turn hold off
>>> hold(False)
When hold is True, subsequent plot commands will be added to
the current axes. When hold is False, the current axes and
figure will be cleared on the next plot command
"""
if b is None:
self._hold = not self._hold
else:
self._hold = b
def get_aspect(self):
return self._aspect
def set_aspect(self, aspect, adjustable=None, anchor=None):
"""
*aspect*
======== ================================================
value description
======== ================================================
'auto' automatic; fill position rectangle with data
'normal' same as 'auto'; deprecated
'equal' same scaling from data to plot units for x and y
num a circle will be stretched such that the height
is num times the width. aspect=1 is the same as
aspect='equal'.
======== ================================================
*adjustable*
========= ============================
value description
========= ============================
'box' change physical size of axes
'datalim' change xlim or ylim
========= ============================
*anchor*
===== =====================
value description
===== =====================
'C' centered
'SW' lower left corner
'S' middle of bottom edge
'SE' lower right corner
etc.
===== =====================
"""
if aspect in ('normal', 'auto'):
self._aspect = 'auto'
elif aspect == 'equal':
self._aspect = 'equal'
else:
self._aspect = float(aspect) # raise ValueError if necessary
if adjustable is not None:
self.set_adjustable(adjustable)
if anchor is not None:
self.set_anchor(anchor)
def get_adjustable(self):
return self._adjustable
def set_adjustable(self, adjustable):
"""
ACCEPTS: [ 'box' | 'datalim' ]
"""
if adjustable in ('box', 'datalim'):
if self in self._shared_x_axes or self in self._shared_y_axes:
if adjustable == 'box':
raise ValueError(
'adjustable must be "datalim" for shared axes')
self._adjustable = adjustable
else:
raise ValueError('argument must be "box", or "datalim"')
def get_anchor(self):
return self._anchor
def set_anchor(self, anchor):
"""
*anchor*
===== ============
value description
===== ============
'C' Center
'SW' bottom left
'S' bottom
'SE' bottom right
'E' right
'NE' top right
'N' top
'NW' top left
'W' left
===== ============
"""
if anchor in mtransforms.Bbox.coefs.keys() or len(anchor) == 2:
self._anchor = anchor
else:
raise ValueError('argument must be among %s' %
', '.join(mtransforms.BBox.coefs.keys()))
def get_data_ratio(self):
"""
Returns the aspect ratio of the raw data.
This method is intended to be overridden by new projection
types.
"""
xmin,xmax = self.get_xbound()
xsize = max(math.fabs(xmax-xmin), 1e-30)
ymin,ymax = self.get_ybound()
ysize = max(math.fabs(ymax-ymin), 1e-30)
return ysize/xsize
def apply_aspect(self, position=None):
'''
Use :meth:`_aspect` and :meth:`_adjustable` to modify the
axes box or the view limits.
'''
if position is None:
position = self.get_position(original=True)
aspect = self.get_aspect()
if aspect == 'auto':
self.set_position( position , which='active')
return
if aspect == 'equal':
A = 1
else:
A = aspect
#Ensure at drawing time that any Axes involved in axis-sharing
# does not have its position changed.
if self in self._shared_x_axes or self in self._shared_y_axes:
if self._adjustable == 'box':
self._adjustable = 'datalim'
warnings.warn(
'shared axes: "adjustable" is being changed to "datalim"')
figW,figH = self.get_figure().get_size_inches()
fig_aspect = figH/figW
if self._adjustable == 'box':
box_aspect = A * self.get_data_ratio()
pb = position.frozen()
pb1 = pb.shrunk_to_aspect(box_aspect, pb, fig_aspect)
self.set_position(pb1.anchored(self.get_anchor(), pb), 'active')
return
# reset active to original in case it had been changed
# by prior use of 'box'
self.set_position(position, which='active')
xmin,xmax = self.get_xbound()
xsize = max(math.fabs(xmax-xmin), 1e-30)
ymin,ymax = self.get_ybound()
ysize = max(math.fabs(ymax-ymin), 1e-30)
l,b,w,h = position.bounds
box_aspect = fig_aspect * (h/w)
data_ratio = box_aspect / A
y_expander = (data_ratio*xsize/ysize - 1.0)
#print 'y_expander', y_expander
# If y_expander > 0, the dy/dx viewLim ratio needs to increase
if abs(y_expander) < 0.005:
#print 'good enough already'
return
dL = self.dataLim
xr = 1.05 * dL.width
yr = 1.05 * dL.height
xmarg = xsize - xr
ymarg = ysize - yr
Ysize = data_ratio * xsize
Xsize = ysize / data_ratio
Xmarg = Xsize - xr
Ymarg = Ysize - yr
xm = 0 # Setting these targets to, e.g., 0.05*xr does not seem to help.
ym = 0
#print 'xmin, xmax, ymin, ymax', xmin, xmax, ymin, ymax
#print 'xsize, Xsize, ysize, Ysize', xsize, Xsize, ysize, Ysize
changex = (self in self._shared_y_axes
and self not in self._shared_x_axes)
changey = (self in self._shared_x_axes
and self not in self._shared_y_axes)
if changex and changey:
warnings.warn("adjustable='datalim' cannot work with shared "
"x and y axes")
return
if changex:
adjust_y = False
else:
#print 'xmarg, ymarg, Xmarg, Ymarg', xmarg, ymarg, Xmarg, Ymarg
if xmarg > xm and ymarg > ym:
adjy = ((Ymarg > 0 and y_expander < 0)
or (Xmarg < 0 and y_expander > 0))
else:
adjy = y_expander > 0
#print 'y_expander, adjy', y_expander, adjy
adjust_y = changey or adjy #(Ymarg > xmarg)
if adjust_y:
yc = 0.5*(ymin+ymax)
y0 = yc - Ysize/2.0
y1 = yc + Ysize/2.0
self.set_ybound((y0, y1))
#print 'New y0, y1:', y0, y1
#print 'New ysize, ysize/xsize', y1-y0, (y1-y0)/xsize
else:
xc = 0.5*(xmin+xmax)
x0 = xc - Xsize/2.0
x1 = xc + Xsize/2.0
self.set_xbound((x0, x1))
#print 'New x0, x1:', x0, x1
#print 'New xsize, ysize/xsize', x1-x0, ysize/(x1-x0)
def axis(self, *v, **kwargs):
'''
Convenience method for manipulating the x and y view limits
and the aspect ratio of the plot.
*kwargs* are passed on to :meth:`set_xlim` and
:meth:`set_ylim`
'''
if len(v)==1 and is_string_like(v[0]):
s = v[0].lower()
if s=='on': self.set_axis_on()
elif s=='off': self.set_axis_off()
elif s in ('equal', 'tight', 'scaled', 'normal', 'auto', 'image'):
self.set_autoscale_on(True)
self.set_aspect('auto')
self.autoscale_view()
# self.apply_aspect()
if s=='equal':
self.set_aspect('equal', adjustable='datalim')
elif s == 'scaled':
self.set_aspect('equal', adjustable='box', anchor='C')
self.set_autoscale_on(False) # Req. by Mark Bakker
elif s=='tight':
self.autoscale_view(tight=True)
self.set_autoscale_on(False)
elif s == 'image':
self.autoscale_view(tight=True)
self.set_autoscale_on(False)
self.set_aspect('equal', adjustable='box', anchor='C')
else:
raise ValueError('Unrecognized string %s to axis; '
'try on or off' % s)
xmin, xmax = self.get_xlim()
ymin, ymax = self.get_ylim()
return xmin, xmax, ymin, ymax
try: v[0]
except IndexError:
emit = kwargs.get('emit', True)
xmin = kwargs.get('xmin', None)
xmax = kwargs.get('xmax', None)
xmin, xmax = self.set_xlim(xmin, xmax, emit)
ymin = kwargs.get('ymin', None)
ymax = kwargs.get('ymax', None)
ymin, ymax = self.set_ylim(ymin, ymax, emit)
return xmin, xmax, ymin, ymax
v = v[0]
if len(v) != 4:
raise ValueError('v must contain [xmin xmax ymin ymax]')
self.set_xlim([v[0], v[1]])
self.set_ylim([v[2], v[3]])
return v
def get_child_artists(self):
"""
Return a list of artists the axes contains.
.. deprecated:: 0.98
"""
raise DeprecationWarning('Use get_children instead')
def get_frame(self):
'Return the axes Rectangle frame'
warnings.warn('use ax.patch instead', DeprecationWarning)
return self.patch
def get_legend(self):
'Return the legend.Legend instance, or None if no legend is defined'
return self.legend_
def get_images(self):
'return a list of Axes images contained by the Axes'
return cbook.silent_list('AxesImage', self.images)
def get_lines(self):
'Return a list of lines contained by the Axes'
return cbook.silent_list('Line2D', self.lines)
def get_xaxis(self):
'Return the XAxis instance'
return self.xaxis
def get_xgridlines(self):
'Get the x grid lines as a list of Line2D instances'
return cbook.silent_list('Line2D xgridline', self.xaxis.get_gridlines())
def get_xticklines(self):
'Get the xtick lines as a list of Line2D instances'
return cbook.silent_list('Text xtickline', self.xaxis.get_ticklines())
def get_yaxis(self):
'Return the YAxis instance'
return self.yaxis
def get_ygridlines(self):
'Get the y grid lines as a list of Line2D instances'
return cbook.silent_list('Line2D ygridline', self.yaxis.get_gridlines())
def get_yticklines(self):
'Get the ytick lines as a list of Line2D instances'
return cbook.silent_list('Line2D ytickline', self.yaxis.get_ticklines())
#### Adding and tracking artists
def has_data(self):
'''Return *True* if any artists have been added to axes.
This should not be used to determine whether the *dataLim*
need to be updated, and may not actually be useful for
anything.
'''
return (
len(self.collections) +
len(self.images) +
len(self.lines) +
len(self.patches))>0
def add_artist(self, a):
'Add any :class:`~matplotlib.artist.Artist` to the axes'
a.set_axes(self)
self.artists.append(a)
self._set_artist_props(a)
a.set_clip_path(self.patch)
a._remove_method = lambda h: self.artists.remove(h)
def add_collection(self, collection, autolim=True):
'''
add a :class:`~matplotlib.collections.Collection` instance
to the axes
'''
label = collection.get_label()
if not label:
collection.set_label('collection%d'%len(self.collections))
self.collections.append(collection)
self._set_artist_props(collection)
collection.set_clip_path(self.patch)
if autolim:
if collection._paths and len(collection._paths):
self.update_datalim(collection.get_datalim(self.transData))
collection._remove_method = lambda h: self.collections.remove(h)
def add_line(self, line):
'''
Add a :class:`~matplotlib.lines.Line2D` to the list of plot
lines
'''
self._set_artist_props(line)
line.set_clip_path(self.patch)
self._update_line_limits(line)
if not line.get_label():
line.set_label('_line%d'%len(self.lines))
self.lines.append(line)
line._remove_method = lambda h: self.lines.remove(h)
def _update_line_limits(self, line):
p = line.get_path()
if p.vertices.size > 0:
self.dataLim.update_from_path(p, self.ignore_existing_data_limits,
updatex=line.x_isdata,
updatey=line.y_isdata)
self.ignore_existing_data_limits = False
def add_patch(self, p):
"""
Add a :class:`~matplotlib.patches.Patch` *p* to the list of
axes patches; the clipbox will be set to the Axes clipping
box. If the transform is not set, it will be set to
:attr:`transData`.
"""
self._set_artist_props(p)
p.set_clip_path(self.patch)
self._update_patch_limits(p)
self.patches.append(p)
p._remove_method = lambda h: self.patches.remove(h)
def _update_patch_limits(self, patch):
'update the data limits for patch *p*'
# hist can add zero height Rectangles, which is useful to keep
# the bins, counts and patches lined up, but it throws off log
# scaling. We'll ignore rects with zero height or width in
# the auto-scaling
if (isinstance(patch, mpatches.Rectangle) and
(patch.get_width()==0 or patch.get_height()==0)):
return
vertices = patch.get_path().vertices
if vertices.size > 0:
xys = patch.get_patch_transform().transform(vertices)
if patch.get_data_transform() != self.transData:
transform = (patch.get_data_transform() +
self.transData.inverted())
xys = transform.transform(xys)
self.update_datalim(xys, updatex=patch.x_isdata,
updatey=patch.y_isdata)
def add_table(self, tab):
'''
Add a :class:`~matplotlib.tables.Table` instance to the
list of axes tables
'''
self._set_artist_props(tab)
self.tables.append(tab)
tab.set_clip_path(self.patch)
tab._remove_method = lambda h: self.tables.remove(h)
def relim(self):
'recompute the data limits based on current artists'
# Collections are deliberately not supported (yet); see
# the TODO note in artists.py.
self.dataLim.ignore(True)
self.ignore_existing_data_limits = True
for line in self.lines:
self._update_line_limits(line)
for p in self.patches:
self._update_patch_limits(p)
def update_datalim(self, xys, updatex=True, updatey=True):
'Update the data lim bbox with seq of xy tups or equiv. 2-D array'
# if no data is set currently, the bbox will ignore its
# limits and set the bound to be the bounds of the xydata.
# Otherwise, it will compute the bounds of it's current data
# and the data in xydata
if iterable(xys) and not len(xys): return
if not ma.isMaskedArray(xys):
xys = np.asarray(xys)
self.dataLim.update_from_data_xy(xys, self.ignore_existing_data_limits,
updatex=updatex, updatey=updatey)
self.ignore_existing_data_limits = False
def update_datalim_numerix(self, x, y):
'Update the data lim bbox with seq of xy tups'
# if no data is set currently, the bbox will ignore it's
# limits and set the bound to be the bounds of the xydata.
# Otherwise, it will compute the bounds of it's current data
# and the data in xydata
if iterable(x) and not len(x): return
self.dataLim.update_from_data(x, y, self.ignore_existing_data_limits)
self.ignore_existing_data_limits = False
def update_datalim_bounds(self, bounds):
'''
Update the datalim to include the given
:class:`~matplotlib.transforms.Bbox` *bounds*
'''
self.dataLim.set(mtransforms.Bbox.union([self.dataLim, bounds]))
def _process_unit_info(self, xdata=None, ydata=None, kwargs=None):
'look for unit *kwargs* and update the axis instances as necessary'
if self.xaxis is None or self.yaxis is None: return
#print 'processing', self.get_geometry()
if xdata is not None:
# we only need to update if there is nothing set yet.
if not self.xaxis.have_units():
self.xaxis.update_units(xdata)
#print '\tset from xdata', self.xaxis.units
if ydata is not None:
# we only need to update if there is nothing set yet.
if not self.yaxis.have_units():
self.yaxis.update_units(ydata)
#print '\tset from ydata', self.yaxis.units
# process kwargs 2nd since these will override default units
if kwargs is not None:
xunits = kwargs.pop( 'xunits', self.xaxis.units)
if xunits!=self.xaxis.units:
#print '\tkw setting xunits', xunits
self.xaxis.set_units(xunits)
# If the units being set imply a different converter,
# we need to update.
if xdata is not None:
self.xaxis.update_units(xdata)
yunits = kwargs.pop('yunits', self.yaxis.units)
if yunits!=self.yaxis.units:
#print '\tkw setting yunits', yunits
self.yaxis.set_units(yunits)
# If the units being set imply a different converter,
# we need to update.
if ydata is not None:
self.yaxis.update_units(ydata)
def in_axes(self, mouseevent):
'''
return *True* if the given *mouseevent* (in display coords)
is in the Axes
'''
return self.patch.contains(mouseevent)[0]
def get_autoscale_on(self):
"""
Get whether autoscaling is applied on plot commands
"""
return self._autoscaleon
def set_autoscale_on(self, b):
"""
Set whether autoscaling is applied on plot commands
accepts: [ *True* | *False* ]
"""
self._autoscaleon = b
def autoscale_view(self, tight=False, scalex=True, scaley=True):
"""
autoscale the view limits using the data limits. You can
selectively autoscale only a single axis, eg, the xaxis by
setting *scaley* to *False*. The autoscaling preserves any
axis direction reversal that has already been done.
"""
# if image data only just use the datalim
if not self._autoscaleon: return
if scalex:
xshared = self._shared_x_axes.get_siblings(self)
dl = [ax.dataLim for ax in xshared]
bb = mtransforms.BboxBase.union(dl)
x0, x1 = bb.intervalx
if scaley:
yshared = self._shared_y_axes.get_siblings(self)
dl = [ax.dataLim for ax in yshared]
bb = mtransforms.BboxBase.union(dl)
y0, y1 = bb.intervaly
if (tight or (len(self.images)>0 and
len(self.lines)==0 and
len(self.patches)==0)):
if scalex:
self.set_xbound(x0, x1)
if scaley:
self.set_ybound(y0, y1)
return
if scalex:
XL = self.xaxis.get_major_locator().view_limits(x0, x1)
self.set_xbound(XL)
if scaley:
YL = self.yaxis.get_major_locator().view_limits(y0, y1)
self.set_ybound(YL)
#### Drawing
def draw(self, renderer=None, inframe=False):
"Draw everything (plot lines, axes, labels)"
if renderer is None:
renderer = self._cachedRenderer
if renderer is None:
raise RuntimeError('No renderer defined')
if not self.get_visible(): return
renderer.open_group('axes')
self.apply_aspect()
# the patch draws the background rectangle -- the frame below
# will draw the edges
if self.axison and self._frameon:
self.patch.draw(renderer)
artists = []
if len(self.images)<=1 or renderer.option_image_nocomposite():
for im in self.images:
im.draw(renderer)
else:
# make a composite image blending alpha
# list of (mimage.Image, ox, oy)
mag = renderer.get_image_magnification()
ims = [(im.make_image(mag),0,0)
for im in self.images if im.get_visible()]
l, b, r, t = self.bbox.extents
width = mag*((round(r) + 0.5) - (round(l) - 0.5))
height = mag*((round(t) + 0.5) - (round(b) - 0.5))
im = mimage.from_images(height,
width,
ims)
im.is_grayscale = False
l, b, w, h = self.bbox.bounds
# composite images need special args so they will not
# respect z-order for now
renderer.draw_image(
round(l), round(b), im, self.bbox,
self.patch.get_path(),
self.patch.get_transform())
artists.extend(self.collections)
artists.extend(self.patches)
artists.extend(self.lines)
artists.extend(self.texts)
artists.extend(self.artists)
if self.axison and not inframe:
if self._axisbelow:
self.xaxis.set_zorder(0.5)
self.yaxis.set_zorder(0.5)
else:
self.xaxis.set_zorder(2.5)
self.yaxis.set_zorder(2.5)
artists.extend([self.xaxis, self.yaxis])
if not inframe: artists.append(self.title)
artists.extend(self.tables)
if self.legend_ is not None:
artists.append(self.legend_)
# the frame draws the edges around the axes patch -- we
# decouple these so the patch can be in the background and the
# frame in the foreground.
if self.axison and self._frameon:
artists.append(self.frame)
dsu = [ (a.zorder, i, a) for i, a in enumerate(artists)
if not a.get_animated() ]
dsu.sort()
for zorder, i, a in dsu:
a.draw(renderer)
renderer.close_group('axes')
self._cachedRenderer = renderer
def draw_artist(self, a):
"""
This method can only be used after an initial draw which
caches the renderer. It is used to efficiently update Axes
data (axis ticks, labels, etc are not updated)
"""
assert self._cachedRenderer is not None
a.draw(self._cachedRenderer)
def redraw_in_frame(self):
"""
This method can only be used after an initial draw which
caches the renderer. It is used to efficiently update Axes
data (axis ticks, labels, etc are not updated)
"""
assert self._cachedRenderer is not None
self.draw(self._cachedRenderer, inframe=True)
def get_renderer_cache(self):
return self._cachedRenderer
def __draw_animate(self):
# ignore for now; broken
if self._lastRenderer is None:
raise RuntimeError('You must first call ax.draw()')
dsu = [(a.zorder, a) for a in self.animated.keys()]
dsu.sort()
renderer = self._lastRenderer
renderer.blit()
for tmp, a in dsu:
a.draw(renderer)
#### Axes rectangle characteristics
def get_frame_on(self):
"""
Get whether the axes rectangle patch is drawn
"""
return self._frameon
def set_frame_on(self, b):
"""
Set whether the axes rectangle patch is drawn
ACCEPTS: [ *True* | *False* ]
"""
self._frameon = b
def get_axisbelow(self):
"""
Get whether axis below is true or not
"""
return self._axisbelow
def set_axisbelow(self, b):
"""
Set whether the axis ticks and gridlines are above or below most artists
ACCEPTS: [ *True* | *False* ]
"""
self._axisbelow = b
def grid(self, b=None, **kwargs):
"""
call signature::
grid(self, b=None, **kwargs)
Set the axes grids on or off; *b* is a boolean
If *b* is *None* and ``len(kwargs)==0``, toggle the grid state. If
*kwargs* are supplied, it is assumed that you want a grid and *b*
is thus set to *True*
*kawrgs* are used to set the grid line properties, eg::
ax.grid(color='r', linestyle='-', linewidth=2)
Valid :class:`~matplotlib.lines.Line2D` kwargs are
%(Line2D)s
"""
if len(kwargs): b = True
self.xaxis.grid(b, **kwargs)
self.yaxis.grid(b, **kwargs)
grid.__doc__ = cbook.dedent(grid.__doc__) % martist.kwdocd
def ticklabel_format(self, **kwargs):
"""
Convenience method for manipulating the ScalarFormatter
used by default for linear axes.
Optional keyword arguments:
============ =====================================
Keyword Description
============ =====================================
*style* [ 'sci' (or 'scientific') | 'plain' ]
plain turns off scientific notation
*scilimits* (m, n), pair of integers; if *style*
is 'sci', scientific notation will
be used for numbers outside the range
10`-m`:sup: to 10`n`:sup:.
Use (0,0) to include all numbers.
*axis* [ 'x' | 'y' | 'both' ]
============ =====================================
Only the major ticks are affected.
If the method is called when the
:class:`~matplotlib.ticker.ScalarFormatter` is not the
:class:`~matplotlib.ticker.Formatter` being used, an
:exc:`AttributeError` will be raised.
"""
style = kwargs.pop('style', '').lower()
scilimits = kwargs.pop('scilimits', None)
if scilimits is not None:
try:
m, n = scilimits
m+n+1 # check that both are numbers
except (ValueError, TypeError):
raise ValueError("scilimits must be a sequence of 2 integers")
axis = kwargs.pop('axis', 'both').lower()
if style[:3] == 'sci':
sb = True
elif style in ['plain', 'comma']:
sb = False
if style == 'plain':
cb = False
else:
cb = True
raise NotImplementedError, "comma style remains to be added"
elif style == '':
sb = None
else:
raise ValueError, "%s is not a valid style value"
try:
if sb is not None:
if axis == 'both' or axis == 'x':
self.xaxis.major.formatter.set_scientific(sb)
if axis == 'both' or axis == 'y':
self.yaxis.major.formatter.set_scientific(sb)
if scilimits is not None:
if axis == 'both' or axis == 'x':
self.xaxis.major.formatter.set_powerlimits(scilimits)
if axis == 'both' or axis == 'y':
self.yaxis.major.formatter.set_powerlimits(scilimits)
except AttributeError:
raise AttributeError(
"This method only works with the ScalarFormatter.")
def set_axis_off(self):
"""turn off the axis"""
self.axison = False
def set_axis_on(self):
"""turn on the axis"""
self.axison = True
def get_axis_bgcolor(self):
'Return the axis background color'
return self._axisbg
def set_axis_bgcolor(self, color):
"""
set the axes background color
ACCEPTS: any matplotlib color - see
:func:`~matplotlib.pyplot.colors`
"""
self._axisbg = color
self.patch.set_facecolor(color)
### data limits, ticks, tick labels, and formatting
def invert_xaxis(self):
"Invert the x-axis."
left, right = self.get_xlim()
self.set_xlim(right, left)
def xaxis_inverted(self):
'Returns True if the x-axis is inverted.'
left, right = self.get_xlim()
return right < left
def get_xbound(self):
"""
Returns the x-axis numerical bounds where::
lowerBound < upperBound
"""
left, right = self.get_xlim()
if left < right:
return left, right
else:
return right, left
def set_xbound(self, lower=None, upper=None):
"""
Set the lower and upper numerical bounds of the x-axis.
This method will honor axes inversion regardless of parameter order.
"""
if upper is None and iterable(lower):
lower,upper = lower
old_lower,old_upper = self.get_xbound()
if lower is None: lower = old_lower
if upper is None: upper = old_upper
if self.xaxis_inverted():
if lower < upper:
self.set_xlim(upper, lower)
else:
self.set_xlim(lower, upper)
else:
if lower < upper:
self.set_xlim(lower, upper)
else:
self.set_xlim(upper, lower)
def get_xlim(self):
"""
Get the x-axis range [*xmin*, *xmax*]
"""
return tuple(self.viewLim.intervalx)
def set_xlim(self, xmin=None, xmax=None, emit=True, **kwargs):
"""
call signature::
set_xlim(self, *args, **kwargs)
Set the limits for the xaxis
Returns the current xlimits as a length 2 tuple: [*xmin*, *xmax*]
Examples::
set_xlim((valmin, valmax))
set_xlim(valmin, valmax)
set_xlim(xmin=1) # xmax unchanged
set_xlim(xmax=1) # xmin unchanged
Keyword arguments:
*ymin*: scalar
the min of the ylim
*ymax*: scalar
the max of the ylim
*emit*: [ True | False ]
notify observers of lim change
ACCEPTS: len(2) sequence of floats
"""
if xmax is None and iterable(xmin):
xmin,xmax = xmin
self._process_unit_info(xdata=(xmin, xmax))
if xmin is not None:
xmin = self.convert_xunits(xmin)
if xmax is not None:
xmax = self.convert_xunits(xmax)
old_xmin,old_xmax = self.get_xlim()
if xmin is None: xmin = old_xmin
if xmax is None: xmax = old_xmax
xmin, xmax = mtransforms.nonsingular(xmin, xmax, increasing=False)
xmin, xmax = self.xaxis.limit_range_for_scale(xmin, xmax)
self.viewLim.intervalx = (xmin, xmax)
if emit:
self.callbacks.process('xlim_changed', self)
# Call all of the other x-axes that are shared with this one
for other in self._shared_x_axes.get_siblings(self):
if other is not self:
other.set_xlim(self.viewLim.intervalx, emit=False)
if (other.figure != self.figure and
other.figure.canvas is not None):
other.figure.canvas.draw_idle()
return xmin, xmax
def get_xscale(self):
'return the xaxis scale string: %s' % (
", ".join(mscale.get_scale_names()))
return self.xaxis.get_scale()
def set_xscale(self, value, **kwargs):
"""
call signature::
set_xscale(value)
Set the scaling of the x-axis: %(scale)s
ACCEPTS: [%(scale)s]
Different kwargs are accepted, depending on the scale:
%(scale_docs)s
"""
self.xaxis.set_scale(value, **kwargs)
self.autoscale_view()
self._update_transScale()
set_xscale.__doc__ = cbook.dedent(set_xscale.__doc__) % {
'scale': ' | '.join([repr(x) for x in mscale.get_scale_names()]),
'scale_docs': mscale.get_scale_docs().strip()}
def get_xticks(self, minor=False):
'Return the x ticks as a list of locations'
return self.xaxis.get_ticklocs(minor=minor)
def set_xticks(self, ticks, minor=False):
"""
Set the x ticks with list of *ticks*
ACCEPTS: sequence of floats
"""
return self.xaxis.set_ticks(ticks, minor=minor)
def get_xmajorticklabels(self):
'Get the xtick labels as a list of Text instances'
return cbook.silent_list('Text xticklabel',
self.xaxis.get_majorticklabels())
def get_xminorticklabels(self):
'Get the xtick labels as a list of Text instances'
return cbook.silent_list('Text xticklabel',
self.xaxis.get_minorticklabels())
def get_xticklabels(self, minor=False):
'Get the xtick labels as a list of Text instances'
return cbook.silent_list('Text xticklabel',
self.xaxis.get_ticklabels(minor=minor))
def set_xticklabels(self, labels, fontdict=None, minor=False, **kwargs):
"""
call signature::
set_xticklabels(labels, fontdict=None, minor=False, **kwargs)
Set the xtick labels with list of strings *labels*. Return a
list of axis text instances.
*kwargs* set the :class:`~matplotlib.text.Text` properties.
Valid properties are
%(Text)s
ACCEPTS: sequence of strings
"""
return self.xaxis.set_ticklabels(labels, fontdict,
minor=minor, **kwargs)
set_xticklabels.__doc__ = cbook.dedent(
set_xticklabels.__doc__) % martist.kwdocd
def invert_yaxis(self):
"Invert the y-axis."
left, right = self.get_ylim()
self.set_ylim(right, left)
def yaxis_inverted(self):
'Returns True if the y-axis is inverted.'
left, right = self.get_ylim()
return right < left
def get_ybound(self):
"Return y-axis numerical bounds in the form of lowerBound < upperBound"
left, right = self.get_ylim()
if left < right:
return left, right
else:
return right, left
def set_ybound(self, lower=None, upper=None):
"""Set the lower and upper numerical bounds of the y-axis.
This method will honor axes inversion regardless of parameter order.
"""
if upper is None and iterable(lower):
lower,upper = lower
old_lower,old_upper = self.get_ybound()
if lower is None: lower = old_lower
if upper is None: upper = old_upper
if self.yaxis_inverted():
if lower < upper:
self.set_ylim(upper, lower)
else:
self.set_ylim(lower, upper)
else:
if lower < upper:
self.set_ylim(lower, upper)
else:
self.set_ylim(upper, lower)
def get_ylim(self):
"""
Get the y-axis range [*ymin*, *ymax*]
"""
return tuple(self.viewLim.intervaly)
def set_ylim(self, ymin=None, ymax=None, emit=True, **kwargs):
"""
call signature::
set_ylim(self, *args, **kwargs):
Set the limits for the yaxis; v = [ymin, ymax]::
set_ylim((valmin, valmax))
set_ylim(valmin, valmax)
set_ylim(ymin=1) # ymax unchanged
set_ylim(ymax=1) # ymin unchanged
Keyword arguments:
*ymin*: scalar
the min of the ylim
*ymax*: scalar
the max of the ylim
*emit*: [ True | False ]
notify observers of lim change
Returns the current ylimits as a length 2 tuple
ACCEPTS: len(2) sequence of floats
"""
if ymax is None and iterable(ymin):
ymin,ymax = ymin
if ymin is not None:
ymin = self.convert_yunits(ymin)
if ymax is not None:
ymax = self.convert_yunits(ymax)
old_ymin,old_ymax = self.get_ylim()
if ymin is None: ymin = old_ymin
if ymax is None: ymax = old_ymax
ymin, ymax = mtransforms.nonsingular(ymin, ymax, increasing=False)
ymin, ymax = self.yaxis.limit_range_for_scale(ymin, ymax)
self.viewLim.intervaly = (ymin, ymax)
if emit:
self.callbacks.process('ylim_changed', self)
# Call all of the other y-axes that are shared with this one
for other in self._shared_y_axes.get_siblings(self):
if other is not self:
other.set_ylim(self.viewLim.intervaly, emit=False)
if (other.figure != self.figure and
other.figure.canvas is not None):
other.figure.canvas.draw_idle()
return ymin, ymax
def get_yscale(self):
'return the xaxis scale string: %s' % (
", ".join(mscale.get_scale_names()))
return self.yaxis.get_scale()
def set_yscale(self, value, **kwargs):
"""
call signature::
set_yscale(value)
Set the scaling of the y-axis: %(scale)s
ACCEPTS: [%(scale)s]
Different kwargs are accepted, depending on the scale:
%(scale_docs)s
"""
self.yaxis.set_scale(value, **kwargs)
self.autoscale_view()
self._update_transScale()
set_yscale.__doc__ = cbook.dedent(set_yscale.__doc__) % {
'scale': ' | '.join([repr(x) for x in mscale.get_scale_names()]),
'scale_docs': mscale.get_scale_docs().strip()}
def get_yticks(self, minor=False):
'Return the y ticks as a list of locations'
return self.yaxis.get_ticklocs(minor=minor)
def set_yticks(self, ticks, minor=False):
"""
Set the y ticks with list of *ticks*
ACCEPTS: sequence of floats
Keyword arguments:
*minor*: [ False | True ]
Sets the minor ticks if True
"""
return self.yaxis.set_ticks(ticks, minor=minor)
def get_ymajorticklabels(self):
'Get the xtick labels as a list of Text instances'
return cbook.silent_list('Text yticklabel',
self.yaxis.get_majorticklabels())
def get_yminorticklabels(self):
'Get the xtick labels as a list of Text instances'
return cbook.silent_list('Text yticklabel',
self.yaxis.get_minorticklabels())
def get_yticklabels(self, minor=False):
'Get the xtick labels as a list of Text instances'
return cbook.silent_list('Text yticklabel',
self.yaxis.get_ticklabels(minor=minor))
def set_yticklabels(self, labels, fontdict=None, minor=False, **kwargs):
"""
call signature::
set_yticklabels(labels, fontdict=None, minor=False, **kwargs)
Set the ytick labels with list of strings *labels*. Return a list of
:class:`~matplotlib.text.Text` instances.
*kwargs* set :class:`~matplotlib.text.Text` properties for the labels.
Valid properties are
%(Text)s
ACCEPTS: sequence of strings
"""
return self.yaxis.set_ticklabels(labels, fontdict,
minor=minor, **kwargs)
set_yticklabels.__doc__ = cbook.dedent(
set_yticklabels.__doc__) % martist.kwdocd
def xaxis_date(self, tz=None):
"""Sets up x-axis ticks and labels that treat the x data as dates.
*tz* is the time zone to use in labeling dates. Defaults to rc value.
"""
xmin, xmax = self.dataLim.intervalx
if xmin==0.:
# no data has been added - let's set the default datalim.
# We should probably use a better proxy for the datalim
# have been updated than the ignore setting
dmax = today = datetime.date.today()
dmin = today-datetime.timedelta(days=10)
self._process_unit_info(xdata=(dmin, dmax))
dmin, dmax = self.convert_xunits([dmin, dmax])
self.viewLim.intervalx = dmin, dmax
self.dataLim.intervalx = dmin, dmax
locator = self.xaxis.get_major_locator()
if not isinstance(locator, mdates.DateLocator):
locator = mdates.AutoDateLocator(tz)
self.xaxis.set_major_locator(locator)
# the autolocator uses the viewlim to pick the right date
# locator, but it may not have correct viewlim before an
# autoscale. If the viewlim is still zero..1, set it to the
# datalim and the autoscaler will update it on request
if self.viewLim.intervalx[0]==0.:
self.viewLim.intervalx = tuple(self.dataLim.intervalx)
locator.refresh()
formatter = self.xaxis.get_major_formatter()
if not isinstance(formatter, mdates.DateFormatter):
formatter = mdates.AutoDateFormatter(locator, tz)
self.xaxis.set_major_formatter(formatter)
def yaxis_date(self, tz=None):
"""Sets up y-axis ticks and labels that treat the y data as dates.
*tz* is the time zone to use in labeling dates. Defaults to rc value.
"""
ymin, ymax = self.dataLim.intervaly
if ymin==0.:
# no data has been added - let's set the default datalim.
# We should probably use a better proxy for the datalim
# have been updated than the ignore setting
dmax = today = datetime.date.today()
dmin = today-datetime.timedelta(days=10)
self._process_unit_info(ydata=(dmin, dmax))
dmin, dmax = self.convert_yunits([dmin, dmax])
self.viewLim.intervaly = dmin, dmax
self.dataLim.intervaly = dmin, dmax
locator = self.yaxis.get_major_locator()
if not isinstance(locator, mdates.DateLocator):
locator = mdates.AutoDateLocator(tz)
self.yaxis.set_major_locator(locator)
# the autolocator uses the viewlim to pick the right date
# locator, but it may not have correct viewlim before an
# autoscale. If the viewlim is still zero..1, set it to the
# datalim and the autoscaler will update it on request
if self.viewLim.intervaly[0]==0.:
self.viewLim.intervaly = tuple(self.dataLim.intervaly)
locator.refresh()
formatter = self.xaxis.get_major_formatter()
if not isinstance(formatter, mdates.DateFormatter):
formatter = mdates.AutoDateFormatter(locator, tz)
self.yaxis.set_major_formatter(formatter)
def format_xdata(self, x):
"""
Return *x* string formatted. This function will use the attribute
self.fmt_xdata if it is callable, else will fall back on the xaxis
major formatter
"""
try: return self.fmt_xdata(x)
except TypeError:
func = self.xaxis.get_major_formatter().format_data_short
val = func(x)
return val
def format_ydata(self, y):
"""
Return y string formatted. This function will use the
:attr:`fmt_ydata` attribute if it is callable, else will fall
back on the yaxis major formatter
"""
try: return self.fmt_ydata(y)
except TypeError:
func = self.yaxis.get_major_formatter().format_data_short
val = func(y)
return val
def format_coord(self, x, y):
'return a format string formatting the *x*, *y* coord'
if x is None:
x = '???'
if y is None:
y = '???'
xs = self.format_xdata(x)
ys = self.format_ydata(y)
return 'x=%s, y=%s'%(xs,ys)
#### Interactive manipulation
def can_zoom(self):
"""
Return *True* if this axes support the zoom box
"""
return True
def get_navigate(self):
"""
Get whether the axes responds to navigation commands
"""
return self._navigate
def set_navigate(self, b):
"""
Set whether the axes responds to navigation toolbar commands
ACCEPTS: [ True | False ]
"""
self._navigate = b
def get_navigate_mode(self):
"""
Get the navigation toolbar button status: 'PAN', 'ZOOM', or None
"""
return self._navigate_mode
def set_navigate_mode(self, b):
"""
Set the navigation toolbar button status;
.. warning::
this is not a user-API function.
"""
self._navigate_mode = b
def start_pan(self, x, y, button):
"""
Called when a pan operation has started.
*x*, *y* are the mouse coordinates in display coords.
button is the mouse button number:
* 1: LEFT
* 2: MIDDLE
* 3: RIGHT
.. note::
Intended to be overridden by new projection types.
"""
self._pan_start = cbook.Bunch(
lim = self.viewLim.frozen(),
trans = self.transData.frozen(),
trans_inverse = self.transData.inverted().frozen(),
bbox = self.bbox.frozen(),
x = x,
y = y
)
def end_pan(self):
"""
Called when a pan operation completes (when the mouse button
is up.)
.. note::
Intended to be overridden by new projection types.
"""
del self._pan_start
def drag_pan(self, button, key, x, y):
"""
Called when the mouse moves during a pan operation.
*button* is the mouse button number:
* 1: LEFT
* 2: MIDDLE
* 3: RIGHT
*key* is a "shift" key
*x*, *y* are the mouse coordinates in display coords.
.. note::
Intended to be overridden by new projection types.
"""
def format_deltas(key, dx, dy):
if key=='control':
if(abs(dx)>abs(dy)):
dy = dx
else:
dx = dy
elif key=='x':
dy = 0
elif key=='y':
dx = 0
elif key=='shift':
if 2*abs(dx) < abs(dy):
dx=0
elif 2*abs(dy) < abs(dx):
dy=0
elif(abs(dx)>abs(dy)):
dy=dy/abs(dy)*abs(dx)
else:
dx=dx/abs(dx)*abs(dy)
return (dx,dy)
p = self._pan_start
dx = x - p.x
dy = y - p.y
if dx == 0 and dy == 0:
return
if button == 1:
dx, dy = format_deltas(key, dx, dy)
result = p.bbox.translated(-dx, -dy) \
.transformed(p.trans_inverse)
elif button == 3:
try:
dx = -dx / float(self.bbox.width)
dy = -dy / float(self.bbox.height)
dx, dy = format_deltas(key, dx, dy)
if self.get_aspect() != 'auto':
dx = 0.5 * (dx + dy)
dy = dx
alpha = np.power(10.0, (dx, dy))
start = p.trans_inverse.transform_point((p.x, p.y))
lim_points = p.lim.get_points()
result = start + alpha * (lim_points - start)
result = mtransforms.Bbox(result)
except OverflowError:
warnings.warn('Overflow while panning')
return
self.set_xlim(*result.intervalx)
self.set_ylim(*result.intervaly)
def get_cursor_props(self):
"""
return the cursor propertiess as a (*linewidth*, *color*)
tuple, where *linewidth* is a float and *color* is an RGBA
tuple
"""
return self._cursorProps
def set_cursor_props(self, *args):
"""
Set the cursor property as::
ax.set_cursor_props(linewidth, color)
or::
ax.set_cursor_props((linewidth, color))
ACCEPTS: a (*float*, *color*) tuple
"""
if len(args)==1:
lw, c = args[0]
elif len(args)==2:
lw, c = args
else:
raise ValueError('args must be a (linewidth, color) tuple')
c =mcolors.colorConverter.to_rgba(c)
self._cursorProps = lw, c
def connect(self, s, func):
"""
Register observers to be notified when certain events occur. Register
with callback functions with the following signatures. The function
has the following signature::
func(ax) # where ax is the instance making the callback.
The following events can be connected to:
'xlim_changed','ylim_changed'
The connection id is is returned - you can use this with
disconnect to disconnect from the axes event
"""
raise DeprecationWarning('use the callbacks CallbackRegistry instance '
'instead')
def disconnect(self, cid):
'disconnect from the Axes event.'
raise DeprecationWarning('use the callbacks CallbackRegistry instance '
'instead')
def get_children(self):
'return a list of child artists'
children = []
children.append(self.xaxis)
children.append(self.yaxis)
children.extend(self.lines)
children.extend(self.patches)
children.extend(self.texts)
children.extend(self.tables)
children.extend(self.artists)
children.extend(self.images)
if self.legend_ is not None:
children.append(self.legend_)
children.extend(self.collections)
children.append(self.title)
children.append(self.patch)
children.append(self.frame)
return children
def contains(self,mouseevent):
"""Test whether the mouse event occured in the axes.
Returns T/F, {}
"""
if callable(self._contains): return self._contains(self,mouseevent)
return self.patch.contains(mouseevent)
def pick(self, *args):
"""
call signature::
pick(mouseevent)
each child artist will fire a pick event if mouseevent is over
the artist and the artist has picker set
"""
if len(args)>1:
raise DeprecationWarning('New pick API implemented -- '
'see API_CHANGES in the src distribution')
martist.Artist.pick(self,args[0])
def __pick(self, x, y, trans=None, among=None):
"""
Return the artist under point that is closest to the *x*, *y*.
If *trans* is *None*, *x*, and *y* are in window coords,
(0,0 = lower left). Otherwise, *trans* is a
:class:`~matplotlib.transforms.Transform` that specifies the
coordinate system of *x*, *y*.
The selection of artists from amongst which the pick function
finds an artist can be narrowed using the optional keyword
argument *among*. If provided, this should be either a sequence
of permitted artists or a function taking an artist as its
argument and returning a true value if and only if that artist
can be selected.
Note this algorithm calculates distance to the vertices of the
polygon, so if you want to pick a patch, click on the edge!
"""
# MGDTODO: Needs updating
if trans is not None:
xywin = trans.transform_point((x,y))
else:
xywin = x,y
def dist_points(p1, p2):
'return the distance between two points'
x1, y1 = p1
x2, y2 = p2
return math.sqrt((x1-x2)**2+(y1-y2)**2)
def dist_x_y(p1, x, y):
'*x* and *y* are arrays; return the distance to the closest point'
x1, y1 = p1
return min(np.sqrt((x-x1)**2+(y-y1)**2))
def dist(a):
if isinstance(a, Text):
bbox = a.get_window_extent()
l,b,w,h = bbox.bounds
verts = (l,b), (l,b+h), (l+w,b+h), (l+w, b)
xt, yt = zip(*verts)
elif isinstance(a, Patch):
path = a.get_path()
tverts = a.get_transform().transform_path(path)
xt, yt = zip(*tverts)
elif isinstance(a, mlines.Line2D):
xdata = a.get_xdata(orig=False)
ydata = a.get_ydata(orig=False)
xt, yt = a.get_transform().numerix_x_y(xdata, ydata)
return dist_x_y(xywin, np.asarray(xt), np.asarray(yt))
artists = self.lines + self.patches + self.texts
if callable(among):
artists = filter(test, artists)
elif iterable(among):
amongd = dict([(k,1) for k in among])
artists = [a for a in artists if a in amongd]
elif among is None:
pass
else:
raise ValueError('among must be callable or iterable')
if not len(artists): return None
ds = [ (dist(a),a) for a in artists]
ds.sort()
return ds[0][1]
#### Labelling
def get_title(self):
"""
Get the title text string.
"""
return self.title.get_text()
def set_title(self, label, fontdict=None, **kwargs):
"""
call signature::
set_title(label, fontdict=None, **kwargs):
Set the title for the axes.
kwargs are Text properties:
%(Text)s
ACCEPTS: str
.. seealso::
:meth:`text`:
for information on how override and the optional args work
"""
default = {
'fontsize':rcParams['axes.titlesize'],
'verticalalignment' : 'bottom',
'horizontalalignment' : 'center'
}
self.title.set_text(label)
self.title.update(default)
if fontdict is not None: self.title.update(fontdict)
self.title.update(kwargs)
return self.title
set_title.__doc__ = cbook.dedent(set_title.__doc__) % martist.kwdocd
def get_xlabel(self):
"""
Get the xlabel text string.
"""
label = self.xaxis.get_label()
return label.get_text()
def set_xlabel(self, xlabel, fontdict=None, **kwargs):
"""
call signature::
set_xlabel(xlabel, fontdict=None, **kwargs)
Set the label for the xaxis.
Valid kwargs are Text properties:
%(Text)s
ACCEPTS: str
.. seealso::
:meth:`text`:
for information on how override and the optional args work
"""
label = self.xaxis.get_label()
label.set_text(xlabel)
if fontdict is not None: label.update(fontdict)
label.update(kwargs)
return label
set_xlabel.__doc__ = cbook.dedent(set_xlabel.__doc__) % martist.kwdocd
def get_ylabel(self):
"""
Get the ylabel text string.
"""
label = self.yaxis.get_label()
return label.get_text()
def set_ylabel(self, ylabel, fontdict=None, **kwargs):
"""
call signature::
set_ylabel(ylabel, fontdict=None, **kwargs)
Set the label for the yaxis
Valid kwargs are Text properties:
%(Text)s
ACCEPTS: str
.. seealso::
:meth:`text`:
for information on how override and the optional args work
"""
label = self.yaxis.get_label()
label.set_text(ylabel)
if fontdict is not None: label.update(fontdict)
label.update(kwargs)
return label
set_ylabel.__doc__ = cbook.dedent(set_ylabel.__doc__) % martist.kwdocd
def text(self, x, y, s, fontdict=None,
withdash=False, **kwargs):
"""
call signature::
text(x, y, s, fontdict=None, **kwargs)
Add text in string *s* to axis at location *x*, *y*, data
coordinates.
Keyword arguments:
*fontdict*:
A dictionary to override the default text properties.
If *fontdict* is *None*, the defaults are determined by your rc
parameters.
*withdash*: [ False | True ]
Creates a :class:`~matplotlib.text.TextWithDash` instance
instead of a :class:`~matplotlib.text.Text` instance.
Individual keyword arguments can be used to override any given
parameter::
text(x, y, s, fontsize=12)
The default transform specifies that text is in data coords,
alternatively, you can specify text in axis coords (0,0 is
lower-left and 1,1 is upper-right). The example below places
text in the center of the axes::
text(0.5, 0.5,'matplotlib',
horizontalalignment='center',
verticalalignment='center',
transform = ax.transAxes)
You can put a rectangular box around the text instance (eg. to
set a background color) by using the keyword *bbox*. *bbox* is
a dictionary of :class:`matplotlib.patches.Rectangle`
properties. For example::
text(x, y, s, bbox=dict(facecolor='red', alpha=0.5))
Valid kwargs are :class:`matplotlib.text.Text` properties:
%(Text)s
"""
default = {
'verticalalignment' : 'bottom',
'horizontalalignment' : 'left',
#'verticalalignment' : 'top',
'transform' : self.transData,
}
# At some point if we feel confident that TextWithDash
# is robust as a drop-in replacement for Text and that
# the performance impact of the heavier-weight class
# isn't too significant, it may make sense to eliminate
# the withdash kwarg and simply delegate whether there's
# a dash to TextWithDash and dashlength.
if withdash:
t = mtext.TextWithDash(
x=x, y=y, text=s,
)
else:
t = mtext.Text(
x=x, y=y, text=s,
)
self._set_artist_props(t)
t.update(default)
if fontdict is not None: t.update(fontdict)
t.update(kwargs)
self.texts.append(t)
t._remove_method = lambda h: self.texts.remove(h)
#if t.get_clip_on(): t.set_clip_box(self.bbox)
if 'clip_on' in kwargs: t.set_clip_box(self.bbox)
return t
text.__doc__ = cbook.dedent(text.__doc__) % martist.kwdocd
def annotate(self, *args, **kwargs):
"""
call signature::
annotate(s, xy, xytext=None, xycoords='data',
textcoords='data', arrowprops=None, **kwargs)
Keyword arguments:
%(Annotation)s
.. plot:: mpl_examples/pylab_examples/annotation_demo2.py
"""
a = mtext.Annotation(*args, **kwargs)
a.set_transform(mtransforms.IdentityTransform())
self._set_artist_props(a)
if kwargs.has_key('clip_on'): a.set_clip_path(self.patch)
self.texts.append(a)
return a
annotate.__doc__ = cbook.dedent(annotate.__doc__) % martist.kwdocd
#### Lines and spans
def axhline(self, y=0, xmin=0, xmax=1, **kwargs):
"""
call signature::
axhline(y=0, xmin=0, xmax=1, **kwargs)
Axis Horizontal Line
Draw a horizontal line at *y* from *xmin* to *xmax*. With the
default values of *xmin* = 0 and *xmax* = 1, this line will
always span the horizontal extent of the axes, regardless of
the xlim settings, even if you change them, eg. with the
:meth:`set_xlim` command. That is, the horizontal extent is
in axes coords: 0=left, 0.5=middle, 1.0=right but the *y*
location is in data coordinates.
Return value is the :class:`~matplotlib.lines.Line2D`
instance. kwargs are the same as kwargs to plot, and can be
used to control the line properties. Eg.,
* draw a thick red hline at *y* = 0 that spans the xrange
>>> axhline(linewidth=4, color='r')
* draw a default hline at *y* = 1 that spans the xrange
>>> axhline(y=1)
* draw a default hline at *y* = .5 that spans the the middle half of
the xrange
>>> axhline(y=.5, xmin=0.25, xmax=0.75)
Valid kwargs are :class:`~matplotlib.lines.Line2D` properties:
%(Line2D)s
.. seealso::
:meth:`axhspan`:
for example plot and source code
"""
ymin, ymax = self.get_ybound()
# We need to strip away the units for comparison with
# non-unitized bounds
yy = self.convert_yunits( y )
scaley = (yy<ymin) or (yy>ymax)
trans = mtransforms.blended_transform_factory(
self.transAxes, self.transData)
l = mlines.Line2D([xmin,xmax], [y,y], transform=trans, **kwargs)
l.x_isdata = False
self.add_line(l)
self.autoscale_view(scalex=False, scaley=scaley)
return l
axhline.__doc__ = cbook.dedent(axhline.__doc__) % martist.kwdocd
def axvline(self, x=0, ymin=0, ymax=1, **kwargs):
"""
call signature::
axvline(x=0, ymin=0, ymax=1, **kwargs)
Axis Vertical Line
Draw a vertical line at *x* from *ymin* to *ymax*. With the
default values of *ymin* = 0 and *ymax* = 1, this line will
always span the vertical extent of the axes, regardless of the
xlim settings, even if you change them, eg. with the
:meth:`set_xlim` command. That is, the vertical extent is in
axes coords: 0=bottom, 0.5=middle, 1.0=top but the *x* location
is in data coordinates.
Return value is the :class:`~matplotlib.lines.Line2D`
instance. kwargs are the same as kwargs to plot, and can be
used to control the line properties. Eg.,
* draw a thick red vline at *x* = 0 that spans the yrange
>>> axvline(linewidth=4, color='r')
* draw a default vline at *x* = 1 that spans the yrange
>>> axvline(x=1)
* draw a default vline at *x* = .5 that spans the the middle half of
the yrange
>>> axvline(x=.5, ymin=0.25, ymax=0.75)
Valid kwargs are :class:`~matplotlib.lines.Line2D` properties:
%(Line2D)s
.. seealso::
:meth:`axhspan`:
for example plot and source code
"""
xmin, xmax = self.get_xbound()
# We need to strip away the units for comparison with
# non-unitized bounds
xx = self.convert_xunits( x )
scalex = (xx<xmin) or (xx>xmax)
trans = mtransforms.blended_transform_factory(
self.transData, self.transAxes)
l = mlines.Line2D([x,x], [ymin,ymax] , transform=trans, **kwargs)
l.y_isdata = False
self.add_line(l)
self.autoscale_view(scalex=scalex, scaley=False)
return l
axvline.__doc__ = cbook.dedent(axvline.__doc__) % martist.kwdocd
def axhspan(self, ymin, ymax, xmin=0, xmax=1, **kwargs):
"""
call signature::
axhspan(ymin, ymax, xmin=0, xmax=1, **kwargs)
Axis Horizontal Span.
*y* coords are in data units and *x* coords are in axes (relative
0-1) units.
Draw a horizontal span (rectangle) from *ymin* to *ymax*.
With the default values of *xmin* = 0 and *xmax* = 1, this
always spans the xrange, regardless of the xlim settings, even
if you change them, eg. with the :meth:`set_xlim` command.
That is, the horizontal extent is in axes coords: 0=left,
0.5=middle, 1.0=right but the *y* location is in data
coordinates.
Return value is a :class:`matplotlib.patches.Polygon`
instance.
Examples:
* draw a gray rectangle from *y* = 0.25-0.75 that spans the
horizontal extent of the axes
>>> axhspan(0.25, 0.75, facecolor='0.5', alpha=0.5)
Valid kwargs are :class:`~matplotlib.patches.Polygon` properties:
%(Polygon)s
**Example:**
.. plot:: mpl_examples/pylab_examples/axhspan_demo.py
"""
trans = mtransforms.blended_transform_factory(
self.transAxes, self.transData)
# process the unit information
self._process_unit_info( [xmin, xmax], [ymin, ymax], kwargs=kwargs )
# first we need to strip away the units
xmin, xmax = self.convert_xunits( [xmin, xmax] )
ymin, ymax = self.convert_yunits( [ymin, ymax] )
verts = (xmin, ymin), (xmin, ymax), (xmax, ymax), (xmax, ymin)
p = mpatches.Polygon(verts, **kwargs)
p.set_transform(trans)
p.x_isdata = False
self.add_patch(p)
return p
axhspan.__doc__ = cbook.dedent(axhspan.__doc__) % martist.kwdocd
def axvspan(self, xmin, xmax, ymin=0, ymax=1, **kwargs):
"""
call signature::
axvspan(xmin, xmax, ymin=0, ymax=1, **kwargs)
Axis Vertical Span.
*x* coords are in data units and *y* coords are in axes (relative
0-1) units.
Draw a vertical span (rectangle) from *xmin* to *xmax*. With
the default values of *ymin* = 0 and *ymax* = 1, this always
spans the yrange, regardless of the ylim settings, even if you
change them, eg. with the :meth:`set_ylim` command. That is,
the vertical extent is in axes coords: 0=bottom, 0.5=middle,
1.0=top but the *y* location is in data coordinates.
Return value is the :class:`matplotlib.patches.Polygon`
instance.
Examples:
* draw a vertical green translucent rectangle from x=1.25 to 1.55 that
spans the yrange of the axes
>>> axvspan(1.25, 1.55, facecolor='g', alpha=0.5)
Valid kwargs are :class:`~matplotlib.patches.Polygon`
properties:
%(Polygon)s
.. seealso::
:meth:`axhspan`:
for example plot and source code
"""
trans = mtransforms.blended_transform_factory(
self.transData, self.transAxes)
# process the unit information
self._process_unit_info( [xmin, xmax], [ymin, ymax], kwargs=kwargs )
# first we need to strip away the units
xmin, xmax = self.convert_xunits( [xmin, xmax] )
ymin, ymax = self.convert_yunits( [ymin, ymax] )
verts = [(xmin, ymin), (xmin, ymax), (xmax, ymax), (xmax, ymin)]
p = mpatches.Polygon(verts, **kwargs)
p.set_transform(trans)
p.y_isdata = False
self.add_patch(p)
return p
axvspan.__doc__ = cbook.dedent(axvspan.__doc__) % martist.kwdocd
def hlines(self, y, xmin, xmax, colors='k', linestyles='solid',
label='', **kwargs):
"""
call signature::
hlines(y, xmin, xmax, colors='k', linestyles='solid', **kwargs)
Plot horizontal lines at each *y* from *xmin* to *xmax*.
Returns the :class:`~matplotlib.collections.LineCollection`
that was added.
Required arguments:
*y*:
a 1-D numpy array or iterable.
*xmin* and *xmax*:
can be scalars or ``len(x)`` numpy arrays. If they are
scalars, then the respective values are constant, else the
widths of the lines are determined by *xmin* and *xmax*.
Optional keyword arguments:
*colors*:
a line collections color argument, either a single color
or a ``len(y)`` list of colors
*linestyles*:
[ 'solid' | 'dashed' | 'dashdot' | 'dotted' ]
**Example:**
.. plot:: mpl_examples/pylab_examples/hline_demo.py
"""
if kwargs.get('fmt') is not None:
raise DeprecationWarning('hlines now uses a '
'collections.LineCollection and not a '
'list of Line2D to draw; see API_CHANGES')
# We do the conversion first since not all unitized data is uniform
y = self.convert_yunits( y )
xmin = self.convert_xunits( xmin )
xmax = self.convert_xunits( xmax )
if not iterable(y): y = [y]
if not iterable(xmin): xmin = [xmin]
if not iterable(xmax): xmax = [xmax]
y = np.asarray(y)
xmin = np.asarray(xmin)
xmax = np.asarray(xmax)
if len(xmin)==1:
xmin = np.resize( xmin, y.shape )
if len(xmax)==1:
xmax = np.resize( xmax, y.shape )
if len(xmin)!=len(y):
raise ValueError, 'xmin and y are unequal sized sequences'
if len(xmax)!=len(y):
raise ValueError, 'xmax and y are unequal sized sequences'
verts = [ ((thisxmin, thisy), (thisxmax, thisy))
for thisxmin, thisxmax, thisy in zip(xmin, xmax, y)]
coll = mcoll.LineCollection(verts, colors=colors,
linestyles=linestyles, label=label)
self.add_collection(coll)
coll.update(kwargs)
minx = min(xmin.min(), xmax.min())
maxx = max(xmin.max(), xmax.max())
miny = y.min()
maxy = y.max()
corners = (minx, miny), (maxx, maxy)
self.update_datalim(corners)
self.autoscale_view()
return coll
hlines.__doc__ = cbook.dedent(hlines.__doc__)
def vlines(self, x, ymin, ymax, colors='k', linestyles='solid',
label='', **kwargs):
"""
call signature::
vlines(x, ymin, ymax, color='k', linestyles='solid')
Plot vertical lines at each *x* from *ymin* to *ymax*. *ymin*
or *ymax* can be scalars or len(*x*) numpy arrays. If they are
scalars, then the respective values are constant, else the
heights of the lines are determined by *ymin* and *ymax*.
*colors*
a line collections color args, either a single color
or a len(*x*) list of colors
*linestyles*
one of [ 'solid' | 'dashed' | 'dashdot' | 'dotted' ]
Returns the :class:`matplotlib.collections.LineCollection`
that was added.
kwargs are :class:`~matplotlib.collections.LineCollection` properties:
%(LineCollection)s
"""
if kwargs.get('fmt') is not None:
raise DeprecationWarning('vlines now uses a '
'collections.LineCollection and not a '
'list of Line2D to draw; see API_CHANGES')
self._process_unit_info(xdata=x, ydata=ymin, kwargs=kwargs)
# We do the conversion first since not all unitized data is uniform
x = self.convert_xunits( x )
ymin = self.convert_yunits( ymin )
ymax = self.convert_yunits( ymax )
if not iterable(x): x = [x]
if not iterable(ymin): ymin = [ymin]
if not iterable(ymax): ymax = [ymax]
x = np.asarray(x)
ymin = np.asarray(ymin)
ymax = np.asarray(ymax)
if len(ymin)==1:
ymin = np.resize( ymin, x.shape )
if len(ymax)==1:
ymax = np.resize( ymax, x.shape )
if len(ymin)!=len(x):
raise ValueError, 'ymin and x are unequal sized sequences'
if len(ymax)!=len(x):
raise ValueError, 'ymax and x are unequal sized sequences'
Y = np.array([ymin, ymax]).T
verts = [ ((thisx, thisymin), (thisx, thisymax))
for thisx, (thisymin, thisymax) in zip(x,Y)]
#print 'creating line collection'
coll = mcoll.LineCollection(verts, colors=colors,
linestyles=linestyles, label=label)
self.add_collection(coll)
coll.update(kwargs)
minx = min( x )
maxx = max( x )
miny = min( min(ymin), min(ymax) )
maxy = max( max(ymin), max(ymax) )
corners = (minx, miny), (maxx, maxy)
self.update_datalim(corners)
self.autoscale_view()
return coll
vlines.__doc__ = cbook.dedent(vlines.__doc__) % martist.kwdocd
#### Basic plotting
def plot(self, *args, **kwargs):
"""
Plot lines and/or markers to the
:class:`~matplotlib.axes.Axes`. *args* is a variable length
argument, allowing for multiple *x*, *y* pairs with an
optional format string. For example, each of the following is
legal::
plot(x, y) # plot x and y using default line style and color
plot(x, y, 'bo') # plot x and y using blue circle markers
plot(y) # plot y using x as index array 0..N-1
plot(y, 'r+') # ditto, but with red plusses
If *x* and/or *y* is 2-dimensional, then the corresponding columns
will be plotted.
An arbitrary number of *x*, *y*, *fmt* groups can be
specified, as in::
a.plot(x1, y1, 'g^', x2, y2, 'g-')
Return value is a list of lines that were added.
The following format string characters are accepted to control
the line style or marker:
================ ===============================
character description
================ ===============================
'-' solid line style
'--' dashed line style
'-.' dash-dot line style
':' dotted line style
'.' point marker
',' pixel marker
'o' circle marker
'v' triangle_down marker
'^' triangle_up marker
'<' triangle_left marker
'>' triangle_right marker
'1' tri_down marker
'2' tri_up marker
'3' tri_left marker
'4' tri_right marker
's' square marker
'p' pentagon marker
'*' star marker
'h' hexagon1 marker
'H' hexagon2 marker
'+' plus marker
'x' x marker
'D' diamond marker
'd' thin_diamond marker
'|' vline marker
'_' hline marker
================ ===============================
The following color abbreviations are supported:
========== ========
character color
========== ========
'b' blue
'g' green
'r' red
'c' cyan
'm' magenta
'y' yellow
'k' black
'w' white
========== ========
In addition, you can specify colors in many weird and
wonderful ways, including full names (``'green'``), hex
strings (``'#008000'``), RGB or RGBA tuples (``(0,1,0,1)``) or
grayscale intensities as a string (``'0.8'``). Of these, the
string specifications can be used in place of a ``fmt`` group,
but the tuple forms can be used only as ``kwargs``.
Line styles and colors are combined in a single format string, as in
``'bo'`` for blue circles.
The *kwargs* can be used to set line properties (any property that has
a ``set_*`` method). You can use this to set a line label (for auto
legends), linewidth, anitialising, marker face color, etc. Here is an
example::
plot([1,2,3], [1,2,3], 'go-', label='line 1', linewidth=2)
plot([1,2,3], [1,4,9], 'rs', label='line 2')
axis([0, 4, 0, 10])
legend()
If you make multiple lines with one plot command, the kwargs
apply to all those lines, e.g.::
plot(x1, y1, x2, y2, antialised=False)
Neither line will be antialiased.
You do not need to use format strings, which are just
abbreviations. All of the line properties can be controlled
by keyword arguments. For example, you can set the color,
marker, linestyle, and markercolor with::
plot(x, y, color='green', linestyle='dashed', marker='o',
markerfacecolor='blue', markersize=12). See
:class:`~matplotlib.lines.Line2D` for details.
The kwargs are :class:`~matplotlib.lines.Line2D` properties:
%(Line2D)s
kwargs *scalex* and *scaley*, if defined, are passed on to
:meth:`~matplotlib.axes.Axes.autoscale_view` to determine
whether the *x* and *y* axes are autoscaled; the default is
*True*.
"""
scalex = kwargs.pop( 'scalex', True)
scaley = kwargs.pop( 'scaley', True)
if not self._hold: self.cla()
lines = []
for line in self._get_lines(*args, **kwargs):
self.add_line(line)
lines.append(line)
self.autoscale_view(scalex=scalex, scaley=scaley)
return lines
plot.__doc__ = cbook.dedent(plot.__doc__) % martist.kwdocd
def plot_date(self, x, y, fmt='bo', tz=None, xdate=True, ydate=False,
**kwargs):
"""
call signature::
plot_date(x, y, fmt='bo', tz=None, xdate=True, ydate=False, **kwargs)
Similar to the :func:`~matplotlib.pyplot.plot` command, except
the *x* or *y* (or both) data is considered to be dates, and the
axis is labeled accordingly.
*x* and/or *y* can be a sequence of dates represented as float
days since 0001-01-01 UTC.
Keyword arguments:
*fmt*: string
The plot format string.
*tz*: [ None | timezone string ]
The time zone to use in labeling dates. If *None*, defaults to rc
value.
*xdate*: [ True | False ]
If *True*, the *x*-axis will be labeled with dates.
*ydate*: [ False | True ]
If *True*, the *y*-axis will be labeled with dates.
Note if you are using custom date tickers and formatters, it
may be necessary to set the formatters/locators after the call
to :meth:`plot_date` since :meth:`plot_date` will set the
default tick locator to
:class:`matplotlib.ticker.AutoDateLocator` (if the tick
locator is not already set to a
:class:`matplotlib.ticker.DateLocator` instance) and the
default tick formatter to
:class:`matplotlib.ticker.AutoDateFormatter` (if the tick
formatter is not already set to a
:class:`matplotlib.ticker.DateFormatter` instance).
Valid kwargs are :class:`~matplotlib.lines.Line2D` properties:
%(Line2D)s
.. seealso::
:mod:`~matplotlib.dates`:
for helper functions
:func:`~matplotlib.dates.date2num`,
:func:`~matplotlib.dates.num2date` and
:func:`~matplotlib.dates.drange`:
for help on creating the required floating point
dates.
"""
if not self._hold: self.cla()
ret = self.plot(x, y, fmt, **kwargs)
if xdate:
self.xaxis_date(tz)
if ydate:
self.yaxis_date(tz)
self.autoscale_view()
return ret
plot_date.__doc__ = cbook.dedent(plot_date.__doc__) % martist.kwdocd
def loglog(self, *args, **kwargs):
"""
call signature::
loglog(*args, **kwargs)
Make a plot with log scaling on the *x* and *y* axis.
:func:`~matplotlib.pyplot.loglog` supports all the keyword
arguments of :func:`~matplotlib.pyplot.plot` and
:meth:`matplotlib.axes.Axes.set_xscale` /
:meth:`matplotlib.axes.Axes.set_yscale`.
Notable keyword arguments:
*basex*/*basey*: scalar > 1
base of the *x*/*y* logarithm
*subsx*/*subsy*: [ None | sequence ]
the location of the minor *x*/*y* ticks; *None* defaults
to autosubs, which depend on the number of decades in the
plot; see :meth:`matplotlib.axes.Axes.set_xscale` /
:meth:`matplotlib.axes.Axes.set_yscale` for details
The remaining valid kwargs are
:class:`~matplotlib.lines.Line2D` properties:
%(Line2D)s
**Example:**
.. plot:: mpl_examples/pylab_examples/log_demo.py
"""
if not self._hold: self.cla()
dx = {'basex': kwargs.pop('basex', 10),
'subsx': kwargs.pop('subsx', None),
}
dy = {'basey': kwargs.pop('basey', 10),
'subsy': kwargs.pop('subsy', None),
}
self.set_xscale('log', **dx)
self.set_yscale('log', **dy)
b = self._hold
self._hold = True # we've already processed the hold
l = self.plot(*args, **kwargs)
self._hold = b # restore the hold
return l
loglog.__doc__ = cbook.dedent(loglog.__doc__) % martist.kwdocd
def semilogx(self, *args, **kwargs):
"""
call signature::
semilogx(*args, **kwargs)
Make a plot with log scaling on the *x* axis.
:func:`semilogx` supports all the keyword arguments of
:func:`~matplotlib.pyplot.plot` and
:meth:`matplotlib.axes.Axes.set_xscale`.
Notable keyword arguments:
*basex*: scalar > 1
base of the *x* logarithm
*subsx*: [ None | sequence ]
The location of the minor xticks; *None* defaults to
autosubs, which depend on the number of decades in the
plot; see :meth:`~matplotlib.axes.Axes.set_xscale` for
details.
The remaining valid kwargs are
:class:`~matplotlib.lines.Line2D` properties:
%(Line2D)s
.. seealso::
:meth:`loglog`:
For example code and figure
"""
if not self._hold: self.cla()
d = {'basex': kwargs.pop( 'basex', 10),
'subsx': kwargs.pop( 'subsx', None),
}
self.set_xscale('log', **d)
b = self._hold
self._hold = True # we've already processed the hold
l = self.plot(*args, **kwargs)
self._hold = b # restore the hold
return l
semilogx.__doc__ = cbook.dedent(semilogx.__doc__) % martist.kwdocd
def semilogy(self, *args, **kwargs):
"""
call signature::
semilogy(*args, **kwargs)
Make a plot with log scaling on the *y* axis.
:func:`semilogy` supports all the keyword arguments of
:func:`~matplotlib.pylab.plot` and
:meth:`matplotlib.axes.Axes.set_yscale`.
Notable keyword arguments:
*basey*: scalar > 1
Base of the *y* logarithm
*subsy*: [ None | sequence ]
The location of the minor yticks; *None* defaults to
autosubs, which depend on the number of decades in the
plot; see :meth:`~matplotlib.axes.Axes.set_yscale` for
details.
The remaining valid kwargs are
:class:`~matplotlib.lines.Line2D` properties:
%(Line2D)s
.. seealso::
:meth:`loglog`:
For example code and figure
"""
if not self._hold: self.cla()
d = {'basey': kwargs.pop('basey', 10),
'subsy': kwargs.pop('subsy', None),
}
self.set_yscale('log', **d)
b = self._hold
self._hold = True # we've already processed the hold
l = self.plot(*args, **kwargs)
self._hold = b # restore the hold
return l
semilogy.__doc__ = cbook.dedent(semilogy.__doc__) % martist.kwdocd
def acorr(self, x, **kwargs):
"""
call signature::
acorr(x, normed=False, detrend=mlab.detrend_none, usevlines=False,
maxlags=None, **kwargs)
Plot the autocorrelation of *x*. If *normed* = *True*,
normalize the data by the autocorrelation at 0-th lag. *x* is
detrended by the *detrend* callable (default no normalization).
Data are plotted as ``plot(lags, c, **kwargs)``
Return value is a tuple (*lags*, *c*, *line*) where:
- *lags* are a length 2*maxlags+1 lag vector
- *c* is the 2*maxlags+1 auto correlation vector
- *line* is a :class:`~matplotlib.lines.Line2D` instance
returned by :meth:`plot`
The default *linestyle* is None and the default *marker* is
``'o'``, though these can be overridden with keyword args.
The cross correlation is performed with
:func:`numpy.correlate` with *mode* = 2.
If *usevlines* is *True*, :meth:`~matplotlib.axes.Axes.vlines`
rather than :meth:`~matplotlib.axes.Axes.plot` is used to draw
vertical lines from the origin to the acorr. Otherwise, the
plot style is determined by the kwargs, which are
:class:`~matplotlib.lines.Line2D` properties.
*maxlags* is a positive integer detailing the number of lags
to show. The default value of *None* will return all
:math:`2 \mathrm{len}(x) - 1` lags.
The return value is a tuple (*lags*, *c*, *linecol*, *b*)
where
- *linecol* is the
:class:`~matplotlib.collections.LineCollection`
- *b* is the *x*-axis.
.. seealso::
:meth:`~matplotlib.axes.Axes.plot` or
:meth:`~matplotlib.axes.Axes.vlines`: For documentation on
valid kwargs.
**Example:**
:func:`~matplotlib.pyplot.xcorr` above, and
:func:`~matplotlib.pyplot.acorr` below.
**Example:**
.. plot:: mpl_examples/pylab_examples/xcorr_demo.py
"""
return self.xcorr(x, x, **kwargs)
acorr.__doc__ = cbook.dedent(acorr.__doc__) % martist.kwdocd
def xcorr(self, x, y, normed=False, detrend=mlab.detrend_none,
usevlines=False, maxlags=None, **kwargs):
"""
call signature::
xcorr(x, y, normed=False, detrend=mlab.detrend_none,
usevlines=False, **kwargs):
Plot the cross correlation between *x* and *y*. If *normed* =
*True*, normalize the data by the cross correlation at 0-th
lag. *x* and y are detrended by the *detrend* callable
(default no normalization). *x* and *y* must be equal length.
Data are plotted as ``plot(lags, c, **kwargs)``
Return value is a tuple (*lags*, *c*, *line*) where:
- *lags* are a length ``2*maxlags+1`` lag vector
- *c* is the ``2*maxlags+1`` auto correlation vector
- *line* is a :class:`~matplotlib.lines.Line2D` instance
returned by :func:`~matplotlib.pyplot.plot`.
The default *linestyle* is *None* and the default *marker* is
'o', though these can be overridden with keyword args. The
cross correlation is performed with :func:`numpy.correlate`
with *mode* = 2.
If *usevlines* is *True*:
:func:`~matplotlib.pyplot.vlines`
rather than :func:`~matplotlib.pyplot.plot` is used to draw
vertical lines from the origin to the xcorr. Otherwise the
plotstyle is determined by the kwargs, which are
:class:`~matplotlib.lines.Line2D` properties.
The return value is a tuple (*lags*, *c*, *linecol*, *b*)
where *linecol* is the
:class:`matplotlib.collections.LineCollection` instance and
*b* is the *x*-axis.
*maxlags* is a positive integer detailing the number of lags to show.
The default value of *None* will return all ``(2*len(x)-1)`` lags.
**Example:**
:func:`~matplotlib.pyplot.xcorr` above, and
:func:`~matplotlib.pyplot.acorr` below.
**Example:**
.. plot:: mpl_examples/pylab_examples/xcorr_demo.py
"""
Nx = len(x)
if Nx!=len(y):
raise ValueError('x and y must be equal length')
x = detrend(np.asarray(x))
y = detrend(np.asarray(y))
c = np.correlate(x, y, mode=2)
if normed: c/= np.sqrt(np.dot(x,x) * np.dot(y,y))
if maxlags is None: maxlags = Nx - 1
if maxlags >= Nx or maxlags < 1:
raise ValueError('maglags must be None or strictly '
'positive < %d'%Nx)
lags = np.arange(-maxlags,maxlags+1)
c = c[Nx-1-maxlags:Nx+maxlags]
if usevlines:
a = self.vlines(lags, [0], c, **kwargs)
b = self.axhline(**kwargs)
else:
kwargs.setdefault('marker', 'o')
kwargs.setdefault('linestyle', 'None')
a, = self.plot(lags, c, **kwargs)
b = None
return lags, c, a, b
xcorr.__doc__ = cbook.dedent(xcorr.__doc__) % martist.kwdocd
def legend(self, *args, **kwargs):
"""
call signature::
legend(*args, **kwargs)
Place a legend on the current axes at location *loc*. Labels are a
sequence of strings and *loc* can be a string or an integer specifying
the legend location.
To make a legend with existing lines::
legend()
:meth:`legend` by itself will try and build a legend using the label
property of the lines/patches/collections. You can set the label of
a line by doing::
plot(x, y, label='my data')
or::
line.set_label('my data').
If label is set to '_nolegend_', the item will not be shown in
legend.
To automatically generate the legend from labels::
legend( ('label1', 'label2', 'label3') )
To make a legend for a list of lines and labels::
legend( (line1, line2, line3), ('label1', 'label2', 'label3') )
To make a legend at a given location, using a location argument::
legend( ('label1', 'label2', 'label3'), loc='upper left')
or::
legend( (line1, line2, line3), ('label1', 'label2', 'label3'), loc=2)
The location codes are
=============== =============
Location String Location Code
=============== =============
'best' 0
'upper right' 1
'upper left' 2
'lower left' 3
'lower right' 4
'right' 5
'center left' 6
'center right' 7
'lower center' 8
'upper center' 9
'center' 10
=============== =============
If none of these are locations are suitable, loc can be a 2-tuple
giving x,y in axes coords, ie::
loc = 0, 1 # left top
loc = 0.5, 0.5 # center
Keyword arguments:
*isaxes*: [ True | False ]
Indicates that this is an axes legend
*numpoints*: integer
The number of points in the legend line, default is 4
*prop*: [ None | FontProperties ]
A :class:`matplotlib.font_manager.FontProperties`
instance, or *None* to use rc settings.
*pad*: [ None | scalar ]
The fractional whitespace inside the legend border, between 0 and 1.
If *None*, use rc settings.
*markerscale*: [ None | scalar ]
The relative size of legend markers vs. original. If *None*, use rc
settings.
*shadow*: [ None | False | True ]
If *True*, draw a shadow behind legend. If *None*, use rc settings.
*labelsep*: [ None | scalar ]
The vertical space between the legend entries. If *None*, use rc
settings.
*handlelen*: [ None | scalar ]
The length of the legend lines. If *None*, use rc settings.
*handletextsep*: [ None | scalar ]
The space between the legend line and legend text. If *None*, use rc
settings.
*axespad*: [ None | scalar ]
The border between the axes and legend edge. If *None*, use rc
settings.
**Example:**
.. plot:: mpl_examples/api/legend_demo.py
"""
def get_handles():
handles = self.lines[:]
handles.extend(self.patches)
handles.extend([c for c in self.collections
if isinstance(c, mcoll.LineCollection)])
handles.extend([c for c in self.collections
if isinstance(c, mcoll.RegularPolyCollection)])
return handles
if len(args)==0:
handles = []
labels = []
for handle in get_handles():
label = handle.get_label()
if (label is not None and
label != '' and not label.startswith('_')):
handles.append(handle)
labels.append(label)
if len(handles) == 0:
warnings.warn("No labeled objects found. "
"Use label='...' kwarg on individual plots.")
return None
elif len(args)==1:
# LABELS
labels = args[0]
handles = [h for h, label in zip(get_handles(), labels)]
elif len(args)==2:
if is_string_like(args[1]) or isinstance(args[1], int):
# LABELS, LOC
labels, loc = args
handles = [h for h, label in zip(get_handles(), labels)]
kwargs['loc'] = loc
else:
# LINES, LABELS
handles, labels = args
elif len(args)==3:
# LINES, LABELS, LOC
handles, labels, loc = args
kwargs['loc'] = loc
else:
raise TypeError('Invalid arguments to legend')
handles = cbook.flatten(handles)
self.legend_ = mlegend.Legend(self, handles, labels, **kwargs)
return self.legend_
#### Specialized plotting
def step(self, x, y, *args, **kwargs):
'''
call signature::
step(x, y, *args, **kwargs)
Make a step plot. Additional keyword args to :func:`step` are the same
as those for :func:`~matplotlib.pyplot.plot`.
*x* and *y* must be 1-D sequences, and it is assumed, but not checked,
that *x* is uniformly increasing.
Keyword arguments:
*where*: [ 'pre' | 'post' | 'mid' ]
If 'pre', the interval from x[i] to x[i+1] has level y[i]
If 'post', that interval has level y[i+1]
If 'mid', the jumps in *y* occur half-way between the
*x*-values.
'''
where = kwargs.pop('where', 'pre')
if where not in ('pre', 'post', 'mid'):
raise ValueError("'where' argument to step must be "
"'pre', 'post' or 'mid'")
kwargs['linestyle'] = 'steps-' + where
return self.plot(x, y, *args, **kwargs)
def bar(self, left, height, width=0.8, bottom=None,
color=None, edgecolor=None, linewidth=None,
yerr=None, xerr=None, ecolor=None, capsize=3,
align='edge', orientation='vertical', log=False,
**kwargs
):
"""
call signature::
bar(left, height, width=0.8, bottom=0,
color=None, edgecolor=None, linewidth=None,
yerr=None, xerr=None, ecolor=None, capsize=3,
align='edge', orientation='vertical', log=False)
Make a bar plot with rectangles bounded by:
*left*, *left* + *width*, *bottom*, *bottom* + *height*
(left, right, bottom and top edges)
*left*, *height*, *width*, and *bottom* can be either scalars
or sequences
Return value is a list of
:class:`matplotlib.patches.Rectangle` instances.
Required arguments:
======== ===============================================
Argument Description
======== ===============================================
*left* the x coordinates of the left sides of the bars
*height* the heights of the bars
======== ===============================================
Optional keyword arguments:
=============== ==========================================
Keyword Description
=============== ==========================================
*width* the widths of the bars
*bottom* the y coordinates of the bottom edges of
the bars
*color* the colors of the bars
*edgecolor* the colors of the bar edges
*linewidth* width of bar edges; None means use default
linewidth; 0 means don't draw edges.
*xerr* if not None, will be used to generate
errorbars on the bar chart
*yerr* if not None, will be used to generate
errorbars on the bar chart
*ecolor* specifies the color of any errorbar
*capsize* (default 3) determines the length in
points of the error bar caps
*align* 'edge' (default) | 'center'
*orientation* 'vertical' | 'horizontal'
*log* [False|True] False (default) leaves the
orientation axis as-is; True sets it to
log scale
=============== ==========================================
For vertical bars, *align* = 'edge' aligns bars by their left
edges in left, while *align* = 'center' interprets these
values as the *x* coordinates of the bar centers. For
horizontal bars, *align* = 'edge' aligns bars by their bottom
edges in bottom, while *align* = 'center' interprets these
values as the *y* coordinates of the bar centers.
The optional arguments *color*, *edgecolor*, *linewidth*,
*xerr*, and *yerr* can be either scalars or sequences of
length equal to the number of bars. This enables you to use
bar as the basis for stacked bar charts, or candlestick plots.
Other optional kwargs:
%(Rectangle)s
**Example:** A stacked bar chart.
.. plot:: mpl_examples/pylab_examples/bar_stacked.py
"""
if not self._hold: self.cla()
label = kwargs.pop('label', '')
def make_iterable(x):
if not iterable(x):
return [x]
else:
return x
# make them safe to take len() of
_left = left
left = make_iterable(left)
height = make_iterable(height)
width = make_iterable(width)
_bottom = bottom
bottom = make_iterable(bottom)
linewidth = make_iterable(linewidth)
adjust_ylim = False
adjust_xlim = False
if orientation == 'vertical':
self._process_unit_info(xdata=left, ydata=height, kwargs=kwargs)
if log:
self.set_yscale('log')
# size width and bottom according to length of left
if _bottom is None:
if self.get_yscale() == 'log':
bottom = [1e-100]
adjust_ylim = True
else:
bottom = [0]
nbars = len(left)
if len(width) == 1:
width *= nbars
if len(bottom) == 1:
bottom *= nbars
elif orientation == 'horizontal':
self._process_unit_info(xdata=width, ydata=bottom, kwargs=kwargs)
if log:
self.set_xscale('log')
# size left and height according to length of bottom
if _left is None:
if self.get_xscale() == 'log':
left = [1e-100]
adjust_xlim = True
else:
left = [0]
nbars = len(bottom)
if len(left) == 1:
left *= nbars
if len(height) == 1:
height *= nbars
else:
raise ValueError, 'invalid orientation: %s' % orientation
# do not convert to array here as unit info is lost
#left = np.asarray(left)
#height = np.asarray(height)
#width = np.asarray(width)
#bottom = np.asarray(bottom)
if len(linewidth) < nbars:
linewidth *= nbars
if color is None:
color = [None] * nbars
else:
color = list(mcolors.colorConverter.to_rgba_array(color))
if len(color) < nbars:
color *= nbars
if edgecolor is None:
edgecolor = [None] * nbars
else:
edgecolor = list(mcolors.colorConverter.to_rgba_array(edgecolor))
if len(edgecolor) < nbars:
edgecolor *= nbars
if yerr is not None:
if not iterable(yerr):
yerr = [yerr]*nbars
if xerr is not None:
if not iterable(xerr):
xerr = [xerr]*nbars
# FIXME: convert the following to proper input validation
# raising ValueError; don't use assert for this.
assert len(left)==nbars, "argument 'left' must be %d or scalar" % nbars
assert len(height)==nbars, ("argument 'height' must be %d or scalar" %
nbars)
assert len(width)==nbars, ("argument 'width' must be %d or scalar" %
nbars)
assert len(bottom)==nbars, ("argument 'bottom' must be %d or scalar" %
nbars)
if yerr is not None and len(yerr)!=nbars:
raise ValueError(
"bar() argument 'yerr' must be len(%s) or scalar" % nbars)
if xerr is not None and len(xerr)!=nbars:
raise ValueError(
"bar() argument 'xerr' must be len(%s) or scalar" % nbars)
patches = []
# lets do some conversions now since some types cannot be
# subtracted uniformly
if self.xaxis is not None:
xconv = self.xaxis.converter
if xconv is not None:
units = self.xaxis.get_units()
left = xconv.convert( left, units )
width = xconv.convert( width, units )
if self.yaxis is not None:
yconv = self.yaxis.converter
if yconv is not None :
units = self.yaxis.get_units()
bottom = yconv.convert( bottom, units )
height = yconv.convert( height, units )
if align == 'edge':
pass
elif align == 'center':
if orientation == 'vertical':
left = [left[i] - width[i]/2. for i in xrange(len(left))]
elif orientation == 'horizontal':
bottom = [bottom[i] - height[i]/2. for i in xrange(len(bottom))]
else:
raise ValueError, 'invalid alignment: %s' % align
args = zip(left, bottom, width, height, color, edgecolor, linewidth)
for l, b, w, h, c, e, lw in args:
if h<0:
b += h
h = abs(h)
if w<0:
l += w
w = abs(w)
r = mpatches.Rectangle(
xy=(l, b), width=w, height=h,
facecolor=c,
edgecolor=e,
linewidth=lw,
label=label
)
label = '_nolegend_'
r.update(kwargs)
#print r.get_label(), label, 'label' in kwargs
self.add_patch(r)
patches.append(r)
holdstate = self._hold
self.hold(True) # ensure hold is on before plotting errorbars
if xerr is not None or yerr is not None:
if orientation == 'vertical':
# using list comps rather than arrays to preserve unit info
x = [l+0.5*w for l, w in zip(left, width)]
y = [b+h for b,h in zip(bottom, height)]
elif orientation == 'horizontal':
# using list comps rather than arrays to preserve unit info
x = [l+w for l,w in zip(left, width)]
y = [b+0.5*h for b,h in zip(bottom, height)]
self.errorbar(
x, y,
yerr=yerr, xerr=xerr,
fmt=None, ecolor=ecolor, capsize=capsize)
self.hold(holdstate) # restore previous hold state
if adjust_xlim:
xmin, xmax = self.dataLim.intervalx
xmin = np.amin(width[width!=0]) # filter out the 0 width rects
if xerr is not None:
xmin = xmin - np.amax(xerr)
xmin = max(xmin*0.9, 1e-100)
self.dataLim.intervalx = (xmin, xmax)
if adjust_ylim:
ymin, ymax = self.dataLim.intervaly
ymin = np.amin(height[height!=0]) # filter out the 0 height rects
if yerr is not None:
ymin = ymin - np.amax(yerr)
ymin = max(ymin*0.9, 1e-100)
self.dataLim.intervaly = (ymin, ymax)
self.autoscale_view()
return patches
bar.__doc__ = cbook.dedent(bar.__doc__) % martist.kwdocd
def barh(self, bottom, width, height=0.8, left=None, **kwargs):
"""
call signature::
barh(bottom, width, height=0.8, left=0, **kwargs)
Make a horizontal bar plot with rectangles bounded by:
*left*, *left* + *width*, *bottom*, *bottom* + *height*
(left, right, bottom and top edges)
*bottom*, *width*, *height*, and *left* can be either scalars
or sequences
Return value is a list of
:class:`matplotlib.patches.Rectangle` instances.
Required arguments:
======== ======================================================
Argument Description
======== ======================================================
*bottom* the vertical positions of the bottom edges of the bars
*width* the lengths of the bars
======== ======================================================
Optional keyword arguments:
=============== ==========================================
Keyword Description
=============== ==========================================
*height* the heights (thicknesses) of the bars
*left* the x coordinates of the left edges of the
bars
*color* the colors of the bars
*edgecolor* the colors of the bar edges
*linewidth* width of bar edges; None means use default
linewidth; 0 means don't draw edges.
*xerr* if not None, will be used to generate
errorbars on the bar chart
*yerr* if not None, will be used to generate
errorbars on the bar chart
*ecolor* specifies the color of any errorbar
*capsize* (default 3) determines the length in
points of the error bar caps
*align* 'edge' (default) | 'center'
*log* [False|True] False (default) leaves the
horizontal axis as-is; True sets it to log
scale
=============== ==========================================
Setting *align* = 'edge' aligns bars by their bottom edges in
bottom, while *align* = 'center' interprets these values as
the *y* coordinates of the bar centers.
The optional arguments *color*, *edgecolor*, *linewidth*,
*xerr*, and *yerr* can be either scalars or sequences of
length equal to the number of bars. This enables you to use
barh as the basis for stacked bar charts, or candlestick
plots.
other optional kwargs:
%(Rectangle)s
"""
patches = self.bar(left=left, height=height, width=width, bottom=bottom,
orientation='horizontal', **kwargs)
return patches
barh.__doc__ = cbook.dedent(barh.__doc__) % martist.kwdocd
def broken_barh(self, xranges, yrange, **kwargs):
"""
call signature::
broken_barh(self, xranges, yrange, **kwargs)
A collection of horizontal bars spanning *yrange* with a sequence of
*xranges*.
Required arguments:
========= ==============================
Argument Description
========= ==============================
*xranges* sequence of (*xmin*, *xwidth*)
*yrange* sequence of (*ymin*, *ywidth*)
========= ==============================
kwargs are
:class:`matplotlib.collections.BrokenBarHCollection`
properties:
%(BrokenBarHCollection)s
these can either be a single argument, ie::
facecolors = 'black'
or a sequence of arguments for the various bars, ie::
facecolors = ('black', 'red', 'green')
**Example:**
.. plot:: mpl_examples/pylab_examples/broken_barh.py
"""
col = mcoll.BrokenBarHCollection(xranges, yrange, **kwargs)
self.add_collection(col, autolim=True)
self.autoscale_view()
return col
broken_barh.__doc__ = cbook.dedent(broken_barh.__doc__) % martist.kwdocd
def stem(self, x, y, linefmt='b-', markerfmt='bo', basefmt='r-'):
"""
call signature::
stem(x, y, linefmt='b-', markerfmt='bo', basefmt='r-')
A stem plot plots vertical lines (using *linefmt*) at each *x*
location from the baseline to *y*, and places a marker there
using *markerfmt*. A horizontal line at 0 is is plotted using
*basefmt*.
Return value is a tuple (*markerline*, *stemlines*,
*baseline*).
.. seealso::
`this document`__ for details
:file:`examples/pylab_examples/stem_plot.py`:
for a demo
__ http://www.mathworks.com/access/helpdesk/help/techdoc/ref/stem.html
"""
remember_hold=self._hold
if not self._hold: self.cla()
self.hold(True)
markerline, = self.plot(x, y, markerfmt)
stemlines = []
for thisx, thisy in zip(x, y):
l, = self.plot([thisx,thisx], [0, thisy], linefmt)
stemlines.append(l)
baseline, = self.plot([np.amin(x), np.amax(x)], [0,0], basefmt)
self.hold(remember_hold)
return markerline, stemlines, baseline
def pie(self, x, explode=None, labels=None, colors=None,
autopct=None, pctdistance=0.6, shadow=False,
labeldistance=1.1):
r"""
call signature::
pie(x, explode=None, labels=None,
colors=('b', 'g', 'r', 'c', 'm', 'y', 'k', 'w'),
autopct=None, pctdistance=0.6, labeldistance=1.1, shadow=False)
Make a pie chart of array *x*. The fractional area of each
wedge is given by x/sum(x). If sum(x) <= 1, then the values
of x give the fractional area directly and the array will not
be normalized.
Keyword arguments:
*explode*: [ None | len(x) sequence ]
If not *None*, is a len(*x*) array which specifies the
fraction of the radius with which to offset each wedge.
*colors*: [ None | color sequence ]
A sequence of matplotlib color args through which the pie chart
will cycle.
*labels*: [ None | len(x) sequence of strings ]
A sequence of strings providing the labels for each wedge
*autopct*: [ None | format string | format function ]
If not *None*, is a string or function used to label the
wedges with their numeric value. The label will be placed inside
the wedge. If it is a format string, the label will be ``fmt%pct``.
If it is a function, it will be called.
*pctdistance*: scalar
The ratio between the center of each pie slice and the
start of the text generated by *autopct*. Ignored if
*autopct* is *None*; default is 0.6.
*labeldistance*: scalar
The radial distance at which the pie labels are drawn
*shadow*: [ False | True ]
Draw a shadow beneath the pie.
The pie chart will probably look best if the figure and axes are
square. Eg.::
figure(figsize=(8,8))
ax = axes([0.1, 0.1, 0.8, 0.8])
Return value:
If *autopct* is None, return the tuple (*patches*, *texts*):
- *patches* is a sequence of
:class:`matplotlib.patches.Wedge` instances
- *texts* is a list of the label
:class:`matplotlib.text.Text` instances.
If *autopct* is not *None*, return the tuple (*patches*,
*texts*, *autotexts*), where *patches* and *texts* are as
above, and *autotexts* is a list of
:class:`~matplotlib.text.Text` instances for the numeric
labels.
"""
self.set_frame_on(False)
x = np.asarray(x).astype(np.float32)
sx = float(x.sum())
if sx>1: x = np.divide(x,sx)
if labels is None: labels = ['']*len(x)
if explode is None: explode = [0]*len(x)
assert(len(x)==len(labels))
assert(len(x)==len(explode))
if colors is None: colors = ('b', 'g', 'r', 'c', 'm', 'y', 'k', 'w')
center = 0,0
radius = 1
theta1 = 0
i = 0
texts = []
slices = []
autotexts = []
for frac, label, expl in cbook.safezip(x,labels, explode):
x, y = center
theta2 = theta1 + frac
thetam = 2*math.pi*0.5*(theta1+theta2)
x += expl*math.cos(thetam)
y += expl*math.sin(thetam)
w = mpatches.Wedge((x,y), radius, 360.*theta1, 360.*theta2,
facecolor=colors[i%len(colors)])
slices.append(w)
self.add_patch(w)
w.set_label(label)
if shadow:
# make sure to add a shadow after the call to
# add_patch so the figure and transform props will be
# set
shad = mpatches.Shadow(w, -0.02, -0.02,
#props={'facecolor':w.get_facecolor()}
)
shad.set_zorder(0.9*w.get_zorder())
self.add_patch(shad)
xt = x + labeldistance*radius*math.cos(thetam)
yt = y + labeldistance*radius*math.sin(thetam)
label_alignment = xt > 0 and 'left' or 'right'
t = self.text(xt, yt, label,
size=rcParams['xtick.labelsize'],
horizontalalignment=label_alignment,
verticalalignment='center')
texts.append(t)
if autopct is not None:
xt = x + pctdistance*radius*math.cos(thetam)
yt = y + pctdistance*radius*math.sin(thetam)
if is_string_like(autopct):
s = autopct%(100.*frac)
elif callable(autopct):
s = autopct(100.*frac)
else:
raise TypeError(
'autopct must be callable or a format string')
t = self.text(xt, yt, s,
horizontalalignment='center',
verticalalignment='center')
autotexts.append(t)
theta1 = theta2
i += 1
self.set_xlim((-1.25, 1.25))
self.set_ylim((-1.25, 1.25))
self.set_xticks([])
self.set_yticks([])
if autopct is None: return slices, texts
else: return slices, texts, autotexts
def errorbar(self, x, y, yerr=None, xerr=None,
fmt='-', ecolor=None, elinewidth=None, capsize=3,
barsabove=False, lolims=False, uplims=False,
xlolims=False, xuplims=False, **kwargs):
"""
call signature::
errorbar(x, y, yerr=None, xerr=None,
fmt='-', ecolor=None, elinewidth=None, capsize=3,
barsabove=False, lolims=False, uplims=False,
xlolims=False, xuplims=False)
Plot *x* versus *y* with error deltas in *yerr* and *xerr*.
Vertical errorbars are plotted if *yerr* is not *None*.
Horizontal errorbars are plotted if *xerr* is not *None*.
*x*, *y*, *xerr*, and *yerr* can all be scalars, which plots a
single error bar at *x*, *y*.
Optional keyword arguments:
*xerr*/*yerr*: [ scalar | N, Nx1, Nx2 array-like ]
If a scalar number, len(N) array-like object, or an Nx1 array-like
object, errorbars are drawn +/- value.
If a rank-1, Nx2 Numpy array, errorbars are drawn at -column1 and
+column2
*fmt*: '-'
The plot format symbol for *y*. If *fmt* is *None*, just plot the
errorbars with no line symbols. This can be useful for creating a
bar plot with errorbars.
*ecolor*: [ None | mpl color ]
a matplotlib color arg which gives the color the errorbar lines; if
*None*, use the marker color.
*elinewidth*: scalar
the linewidth of the errorbar lines. If *None*, use the linewidth.
*capsize*: scalar
the size of the error bar caps in points
*barsabove*: [ True | False ]
if *True*, will plot the errorbars above the plot
symbols. Default is below.
*lolims*/*uplims*/*xlolims*/*xuplims*: [ False | True ]
These arguments can be used to indicate that a value gives
only upper/lower limits. In that case a caret symbol is
used to indicate this. lims-arguments may be of the same
type as *xerr* and *yerr*.
All other keyword arguments are passed on to the plot command for the
markers, so you can add additional key=value pairs to control the
errorbar markers. For example, this code makes big red squares with
thick green edges::
x,y,yerr = rand(3,10)
errorbar(x, y, yerr, marker='s',
mfc='red', mec='green', ms=20, mew=4)
where *mfc*, *mec*, *ms* and *mew* are aliases for the longer
property names, *markerfacecolor*, *markeredgecolor*, *markersize*
and *markeredgewith*.
valid kwargs for the marker properties are
%(Line2D)s
Return value is a length 3 tuple. The first element is the
:class:`~matplotlib.lines.Line2D` instance for the *y* symbol
lines. The second element is a list of error bar cap lines,
the third element is a list of
:class:`~matplotlib.collections.LineCollection` instances for
the horizontal and vertical error ranges.
**Example:**
.. plot:: mpl_examples/pylab_examples/errorbar_demo.py
"""
self._process_unit_info(xdata=x, ydata=y, kwargs=kwargs)
if not self._hold: self.cla()
# make sure all the args are iterable; use lists not arrays to
# preserve units
if not iterable(x):
x = [x]
if not iterable(y):
y = [y]
if xerr is not None:
if not iterable(xerr):
xerr = [xerr]*len(x)
if yerr is not None:
if not iterable(yerr):
yerr = [yerr]*len(y)
l0 = None
if barsabove and fmt is not None:
l0, = self.plot(x,y,fmt,**kwargs)
barcols = []
caplines = []
lines_kw = {'label':'_nolegend_'}
if elinewidth:
lines_kw['linewidth'] = elinewidth
else:
if 'linewidth' in kwargs:
lines_kw['linewidth']=kwargs['linewidth']
if 'lw' in kwargs:
lines_kw['lw']=kwargs['lw']
if 'transform' in kwargs:
lines_kw['transform'] = kwargs['transform']
# arrays fine here, they are booleans and hence not units
if not iterable(lolims):
lolims = np.asarray([lolims]*len(x), bool)
else: lolims = np.asarray(lolims, bool)
if not iterable(uplims): uplims = np.array([uplims]*len(x), bool)
else: uplims = np.asarray(uplims, bool)
if not iterable(xlolims): xlolims = np.array([xlolims]*len(x), bool)
else: xlolims = np.asarray(xlolims, bool)
if not iterable(xuplims): xuplims = np.array([xuplims]*len(x), bool)
else: xuplims = np.asarray(xuplims, bool)
def xywhere(xs, ys, mask):
"""
return xs[mask], ys[mask] where mask is True but xs and
ys are not arrays
"""
assert len(xs)==len(ys)
assert len(xs)==len(mask)
xs = [thisx for thisx, b in zip(xs, mask) if b]
ys = [thisy for thisy, b in zip(ys, mask) if b]
return xs, ys
if capsize > 0:
plot_kw = {
'ms':2*capsize,
'label':'_nolegend_'}
if 'markeredgewidth' in kwargs:
plot_kw['markeredgewidth']=kwargs['markeredgewidth']
if 'mew' in kwargs:
plot_kw['mew']=kwargs['mew']
if 'transform' in kwargs:
plot_kw['transform'] = kwargs['transform']
if xerr is not None:
if (iterable(xerr) and len(xerr)==2 and
iterable(xerr[0]) and iterable(xerr[1])):
# using list comps rather than arrays to preserve units
left = [thisx-thiserr for (thisx, thiserr)
in cbook.safezip(x,xerr[0])]
right = [thisx+thiserr for (thisx, thiserr)
in cbook.safezip(x,xerr[1])]
else:
# using list comps rather than arrays to preserve units
left = [thisx-thiserr for (thisx, thiserr)
in cbook.safezip(x,xerr)]
right = [thisx+thiserr for (thisx, thiserr)
in cbook.safezip(x,xerr)]
barcols.append( self.hlines(y, left, right, **lines_kw ) )
if capsize > 0:
if xlolims.any():
# can't use numpy logical indexing since left and
# y are lists
leftlo, ylo = xywhere(left, y, xlolims)
caplines.extend(
self.plot(leftlo, ylo, ls='None',
marker=mlines.CARETLEFT, **plot_kw) )
xlolims = ~xlolims
leftlo, ylo = xywhere(left, y, xlolims)
caplines.extend( self.plot(leftlo, ylo, 'k|', **plot_kw) )
else:
caplines.extend( self.plot(left, y, 'k|', **plot_kw) )
if xuplims.any():
rightup, yup = xywhere(right, y, xuplims)
caplines.extend(
self.plot(rightup, yup, ls='None',
marker=mlines.CARETRIGHT, **plot_kw) )
xuplims = ~xuplims
rightup, yup = xywhere(right, y, xuplims)
caplines.extend( self.plot(rightup, yup, 'k|', **plot_kw) )
else:
caplines.extend( self.plot(right, y, 'k|', **plot_kw) )
if yerr is not None:
if (iterable(yerr) and len(yerr)==2 and
iterable(yerr[0]) and iterable(yerr[1])):
# using list comps rather than arrays to preserve units
lower = [thisy-thiserr for (thisy, thiserr)
in cbook.safezip(y,yerr[0])]
upper = [thisy+thiserr for (thisy, thiserr)
in cbook.safezip(y,yerr[1])]
else:
# using list comps rather than arrays to preserve units
lower = [thisy-thiserr for (thisy, thiserr)
in cbook.safezip(y,yerr)]
upper = [thisy+thiserr for (thisy, thiserr)
in cbook.safezip(y,yerr)]
barcols.append( self.vlines(x, lower, upper, **lines_kw) )
if capsize > 0:
if lolims.any():
xlo, lowerlo = xywhere(x, lower, lolims)
caplines.extend(
self.plot(xlo, lowerlo, ls='None',
marker=mlines.CARETDOWN, **plot_kw) )
lolims = ~lolims
xlo, lowerlo = xywhere(x, lower, lolims)
caplines.extend( self.plot(xlo, lowerlo, 'k_', **plot_kw) )
else:
caplines.extend( self.plot(x, lower, 'k_', **plot_kw) )
if uplims.any():
xup, upperup = xywhere(x, upper, uplims)
caplines.extend(
self.plot(xup, upperup, ls='None',
marker=mlines.CARETUP, **plot_kw) )
uplims = ~uplims
xup, upperup = xywhere(x, upper, uplims)
caplines.extend( self.plot(xup, upperup, 'k_', **plot_kw) )
else:
caplines.extend( self.plot(x, upper, 'k_', **plot_kw) )
if not barsabove and fmt is not None:
l0, = self.plot(x,y,fmt,**kwargs)
if ecolor is None:
if l0 is None:
ecolor = self._get_lines._get_next_cycle_color()
else:
ecolor = l0.get_color()
for l in barcols:
l.set_color(ecolor)
for l in caplines:
l.set_color(ecolor)
self.autoscale_view()
return (l0, caplines, barcols)
errorbar.__doc__ = cbook.dedent(errorbar.__doc__) % martist.kwdocd
def boxplot(self, x, notch=0, sym='b+', vert=1, whis=1.5,
positions=None, widths=None):
"""
call signature::
boxplot(x, notch=0, sym='+', vert=1, whis=1.5,
positions=None, widths=None)
Make a box and whisker plot for each column of *x* or each
vector in sequence *x*. The box extends from the lower to
upper quartile values of the data, with a line at the median.
The whiskers extend from the box to show the range of the
data. Flier points are those past the end of the whiskers.
- *notch* = 0 (default) produces a rectangular box plot.
- *notch* = 1 will produce a notched box plot
*sym* (default 'b+') is the default symbol for flier points.
Enter an empty string ('') if you don't want to show fliers.
- *vert* = 1 (default) makes the boxes vertical.
- *vert* = 0 makes horizontal boxes. This seems goofy, but
that's how Matlab did it.
*whis* (default 1.5) defines the length of the whiskers as
a function of the inner quartile range. They extend to the
most extreme data point within ( ``whis*(75%-25%)`` ) data range.
*positions* (default 1,2,...,n) sets the horizontal positions of
the boxes. The ticks and limits are automatically set to match
the positions.
*widths* is either a scalar or a vector and sets the width of
each box. The default is 0.5, or ``0.15*(distance between extreme
positions)`` if that is smaller.
*x* is an array or a sequence of vectors.
Returns a dictionary mapping each component of the boxplot
to a list of the :class:`matplotlib.lines.Line2D`
instances created.
**Example:**
.. plot:: pyplots/boxplot_demo.py
"""
if not self._hold: self.cla()
holdStatus = self._hold
whiskers, caps, boxes, medians, fliers = [], [], [], [], []
# convert x to a list of vectors
if hasattr(x, 'shape'):
if len(x.shape) == 1:
if hasattr(x[0], 'shape'):
x = list(x)
else:
x = [x,]
elif len(x.shape) == 2:
nr, nc = x.shape
if nr == 1:
x = [x]
elif nc == 1:
x = [x.ravel()]
else:
x = [x[:,i] for i in xrange(nc)]
else:
raise ValueError, "input x can have no more than 2 dimensions"
if not hasattr(x[0], '__len__'):
x = [x]
col = len(x)
# get some plot info
if positions is None:
positions = range(1, col + 1)
if widths is None:
distance = max(positions) - min(positions)
widths = min(0.15*max(distance,1.0), 0.5)
if isinstance(widths, float) or isinstance(widths, int):
widths = np.ones((col,), float) * widths
# loop through columns, adding each to plot
self.hold(True)
for i,pos in enumerate(positions):
d = np.ravel(x[i])
row = len(d)
# get median and quartiles
q1, med, q3 = mlab.prctile(d,[25,50,75])
# get high extreme
iq = q3 - q1
hi_val = q3 + whis*iq
wisk_hi = np.compress( d <= hi_val , d )
if len(wisk_hi) == 0:
wisk_hi = q3
else:
wisk_hi = max(wisk_hi)
# get low extreme
lo_val = q1 - whis*iq
wisk_lo = np.compress( d >= lo_val, d )
if len(wisk_lo) == 0:
wisk_lo = q1
else:
wisk_lo = min(wisk_lo)
# get fliers - if we are showing them
flier_hi = []
flier_lo = []
flier_hi_x = []
flier_lo_x = []
if len(sym) != 0:
flier_hi = np.compress( d > wisk_hi, d )
flier_lo = np.compress( d < wisk_lo, d )
flier_hi_x = np.ones(flier_hi.shape[0]) * pos
flier_lo_x = np.ones(flier_lo.shape[0]) * pos
# get x locations for fliers, whisker, whisker cap and box sides
box_x_min = pos - widths[i] * 0.5
box_x_max = pos + widths[i] * 0.5
wisk_x = np.ones(2) * pos
cap_x_min = pos - widths[i] * 0.25
cap_x_max = pos + widths[i] * 0.25
cap_x = [cap_x_min, cap_x_max]
# get y location for median
med_y = [med, med]
# calculate 'regular' plot
if notch == 0:
# make our box vectors
box_x = [box_x_min, box_x_max, box_x_max, box_x_min, box_x_min ]
box_y = [q1, q1, q3, q3, q1 ]
# make our median line vectors
med_x = [box_x_min, box_x_max]
# calculate 'notch' plot
else:
notch_max = med + 1.57*iq/np.sqrt(row)
notch_min = med - 1.57*iq/np.sqrt(row)
if notch_max > q3:
notch_max = q3
if notch_min < q1:
notch_min = q1
# make our notched box vectors
box_x = [box_x_min, box_x_max, box_x_max, cap_x_max, box_x_max,
box_x_max, box_x_min, box_x_min, cap_x_min, box_x_min,
box_x_min ]
box_y = [q1, q1, notch_min, med, notch_max, q3, q3, notch_max,
med, notch_min, q1]
# make our median line vectors
med_x = [cap_x_min, cap_x_max]
med_y = [med, med]
# vertical or horizontal plot?
if vert:
def doplot(*args):
return self.plot(*args)
else:
def doplot(*args):
shuffled = []
for i in xrange(0, len(args), 3):
shuffled.extend([args[i+1], args[i], args[i+2]])
return self.plot(*shuffled)
whiskers.extend(doplot(wisk_x, [q1, wisk_lo], 'b--',
wisk_x, [q3, wisk_hi], 'b--'))
caps.extend(doplot(cap_x, [wisk_hi, wisk_hi], 'k-',
cap_x, [wisk_lo, wisk_lo], 'k-'))
boxes.extend(doplot(box_x, box_y, 'b-'))
medians.extend(doplot(med_x, med_y, 'r-'))
fliers.extend(doplot(flier_hi_x, flier_hi, sym,
flier_lo_x, flier_lo, sym))
# fix our axes/ticks up a little
if 1 == vert:
setticks, setlim = self.set_xticks, self.set_xlim
else:
setticks, setlim = self.set_yticks, self.set_ylim
newlimits = min(positions)-0.5, max(positions)+0.5
setlim(newlimits)
setticks(positions)
# reset hold status
self.hold(holdStatus)
return dict(whiskers=whiskers, caps=caps, boxes=boxes,
medians=medians, fliers=fliers)
def scatter(self, x, y, s=20, c='b', marker='o', cmap=None, norm=None,
vmin=None, vmax=None, alpha=1.0, linewidths=None,
faceted=True, verts=None,
**kwargs):
"""
call signatures::
scatter(x, y, s=20, c='b', marker='o', cmap=None, norm=None,
vmin=None, vmax=None, alpha=1.0, linewidths=None,
verts=None, **kwargs)
Make a scatter plot of *x* versus *y*, where *x*, *y* are 1-D
sequences of the same length, *N*.
Keyword arguments:
*s*:
size in points^2. It is a scalar or an array of the same
length as *x* and *y*.
*c*:
a color. *c* can be a single color format string, or a
sequence of color specifications of length *N*, or a
sequence of *N* numbers to be mapped to colors using the
*cmap* and *norm* specified via kwargs (see below). Note
that *c* should not be a single numeric RGB or RGBA
sequence because that is indistinguishable from an array
of values to be colormapped. *c* can be a 2-D array in
which the rows are RGB or RGBA, however.
*marker*:
can be one of:
===== ==============
Value Description
===== ==============
's' square
'o' circle
'^' triangle up
'>' triangle right
'v' triangle down
'<' triangle left
'd' diamond
'p' pentagram
'h' hexagon
'8' octagon
'+' plus
'x' cross
===== ==============
The marker can also be a tuple (*numsides*, *style*,
*angle*), which will create a custom, regular symbol.
*numsides*:
the number of sides
*style*:
the style of the regular symbol:
===== =============================================
Value Description
===== =============================================
0 a regular polygon
1 a star-like symbol
2 an asterisk
3 a circle (*numsides* and *angle* is ignored)
===== =============================================
*angle*:
the angle of rotation of the symbol
Finally, *marker* can be (*verts*, 0): *verts* is a
sequence of (*x*, *y*) vertices for a custom scatter
symbol. Alternatively, use the kwarg combination
*marker* = *None*, *verts* = *verts*.
Any or all of *x*, *y*, *s*, and *c* may be masked arrays, in
which case all masks will be combined and only unmasked points
will be plotted.
Other keyword arguments: the color mapping and normalization
arguments will be used only if *c* is an array of floats.
*cmap*: [ None | Colormap ]
A :class:`matplotlib.colors.Colormap` instance. If *None*,
defaults to rc ``image.cmap``. *cmap* is only used if *c*
is an array of floats.
*norm*: [ None | Normalize ]
A :class:`matplotlib.colors.Normalize` instance is used to
scale luminance data to 0, 1. If *None*, use the default
:func:`normalize`. *norm* is only used if *c* is an array
of floats.
*vmin*/*vmax*:
*vmin* and *vmax* are used in conjunction with norm to
normalize luminance data. If either are None, the min and
max of the color array *C* is used. Note if you pass a
*norm* instance, your settings for *vmin* and *vmax* will
be ignored.
*alpha*: 0 <= scalar <= 1
The alpha value for the patches
*linewidths*: [ None | scalar | sequence ]
If *None*, defaults to (lines.linewidth,). Note that this
is a tuple, and if you set the linewidths argument you
must set it as a sequence of floats, as required by
:class:`~matplotlib.collections.RegularPolyCollection`.
Optional kwargs control the
:class:`~matplotlib.collections.Collection` properties; in
particular:
*edgecolors*:
'none' to plot faces with no outlines
*facecolors*:
'none' to plot unfilled outlines
Here are the standard descriptions of all the
:class:`~matplotlib.collections.Collection` kwargs:
%(Collection)s
A :class:`~matplotlib.collections.Collection` instance is
returned.
"""
if not self._hold: self.cla()
syms = { # a dict from symbol to (numsides, angle)
's' : (4,math.pi/4.0,0), # square
'o' : (20,3,0), # circle
'^' : (3,0,0), # triangle up
'>' : (3,math.pi/2.0,0), # triangle right
'v' : (3,math.pi,0), # triangle down
'<' : (3,3*math.pi/2.0,0), # triangle left
'd' : (4,0,0), # diamond
'p' : (5,0,0), # pentagram
'h' : (6,0,0), # hexagon
'8' : (8,0,0), # octagon
'+' : (4,0,2), # plus
'x' : (4,math.pi/4.0,2) # cross
}
self._process_unit_info(xdata=x, ydata=y, kwargs=kwargs)
x, y, s, c = cbook.delete_masked_points(x, y, s, c)
if is_string_like(c) or cbook.is_sequence_of_strings(c):
colors = mcolors.colorConverter.to_rgba_array(c, alpha)
else:
sh = np.shape(c)
# The inherent ambiguity is resolved in favor of color
# mapping, not interpretation as rgb or rgba:
if len(sh) == 1 and sh[0] == len(x):
colors = None # use cmap, norm after collection is created
else:
colors = mcolors.colorConverter.to_rgba_array(c, alpha)
if not iterable(s):
scales = (s,)
else:
scales = s
if faceted:
edgecolors = None
else:
edgecolors = 'none'
warnings.warn(
'''replace "faceted=False" with "edgecolors='none'"''',
DeprecationWarning) #2008/04/18
sym = None
symstyle = 0
# to be API compatible
if marker is None and not (verts is None):
marker = (verts, 0)
verts = None
if is_string_like(marker):
# the standard way to define symbols using a string character
sym = syms.get(marker)
if sym is None and verts is None:
raise ValueError('Unknown marker symbol to scatter')
numsides, rotation, symstyle = syms[marker]
elif iterable(marker):
# accept marker to be:
# (numsides, style, [angle])
# or
# (verts[], style, [angle])
if len(marker)<2 or len(marker)>3:
raise ValueError('Cannot create markersymbol from marker')
if cbook.is_numlike(marker[0]):
# (numsides, style, [angle])
if len(marker)==2:
numsides, rotation = marker[0], 0.
elif len(marker)==3:
numsides, rotation = marker[0], marker[2]
sym = True
if marker[1] in (1,2):
symstyle = marker[1]
else:
verts = np.asarray(marker[0])
if sym is not None:
if symstyle==0:
collection = mcoll.RegularPolyCollection(
numsides, rotation, scales,
facecolors = colors,
edgecolors = edgecolors,
linewidths = linewidths,
offsets = zip(x,y),
transOffset = self.transData,
)
elif symstyle==1:
collection = mcoll.StarPolygonCollection(
numsides, rotation, scales,
facecolors = colors,
edgecolors = edgecolors,
linewidths = linewidths,
offsets = zip(x,y),
transOffset = self.transData,
)
elif symstyle==2:
collection = mcoll.AsteriskPolygonCollection(
numsides, rotation, scales,
facecolors = colors,
edgecolors = edgecolors,
linewidths = linewidths,
offsets = zip(x,y),
transOffset = self.transData,
)
elif symstyle==3:
collection = mcoll.CircleCollection(
scales,
facecolors = colors,
edgecolors = edgecolors,
linewidths = linewidths,
offsets = zip(x,y),
transOffset = self.transData,
)
else:
rescale = np.sqrt(max(verts[:,0]**2+verts[:,1]**2))
verts /= rescale
collection = mcoll.PolyCollection(
(verts,), scales,
facecolors = colors,
edgecolors = edgecolors,
linewidths = linewidths,
offsets = zip(x,y),
transOffset = self.transData,
)
collection.set_transform(mtransforms.IdentityTransform())
collection.set_alpha(alpha)
collection.update(kwargs)
if colors is None:
if norm is not None: assert(isinstance(norm, mcolors.Normalize))
if cmap is not None: assert(isinstance(cmap, mcolors.Colormap))
collection.set_array(np.asarray(c))
collection.set_cmap(cmap)
collection.set_norm(norm)
if vmin is not None or vmax is not None:
collection.set_clim(vmin, vmax)
else:
collection.autoscale_None()
temp_x = x
temp_y = y
minx = np.amin(temp_x)
maxx = np.amax(temp_x)
miny = np.amin(temp_y)
maxy = np.amax(temp_y)
w = maxx-minx
h = maxy-miny
# the pad is a little hack to deal with the fact that we don't
# want to transform all the symbols whose scales are in points
# to data coords to get the exact bounding box for efficiency
# reasons. It can be done right if this is deemed important
padx, pady = 0.05*w, 0.05*h
corners = (minx-padx, miny-pady), (maxx+padx, maxy+pady)
self.update_datalim( corners)
self.autoscale_view()
# add the collection last
self.add_collection(collection)
return collection
scatter.__doc__ = cbook.dedent(scatter.__doc__) % martist.kwdocd
def hexbin(self, x, y, C = None, gridsize = 100, bins = None,
xscale = 'linear', yscale = 'linear',
cmap=None, norm=None, vmin=None, vmax=None,
alpha=1.0, linewidths=None, edgecolors='none',
reduce_C_function = np.mean,
**kwargs):
"""
call signature::
hexbin(x, y, C = None, gridsize = 100, bins = None,
xscale = 'linear', yscale = 'linear',
cmap=None, norm=None, vmin=None, vmax=None,
alpha=1.0, linewidths=None, edgecolors='none'
reduce_C_function = np.mean,
**kwargs)
Make a hexagonal binning plot of *x* versus *y*, where *x*,
*y* are 1-D sequences of the same length, *N*. If *C* is None
(the default), this is a histogram of the number of occurences
of the observations at (x[i],y[i]).
If *C* is specified, it specifies values at the coordinate
(x[i],y[i]). These values are accumulated for each hexagonal
bin and then reduced according to *reduce_C_function*, which
defaults to numpy's mean function (np.mean). (If *C* is
specified, it must also be a 1-D sequence of the same length
as *x* and *y*.)
*x*, *y* and/or *C* may be masked arrays, in which case only
unmasked points will be plotted.
Optional keyword arguments:
*gridsize*: [ 100 | integer ]
The number of hexagons in the *x*-direction, default is
100. The corresponding number of hexagons in the
*y*-direction is chosen such that the hexagons are
approximately regular. Alternatively, gridsize can be a
tuple with two elements specifying the number of hexagons
in the *x*-direction and the *y*-direction.
*bins*: [ None | 'log' | integer | sequence ]
If *None*, no binning is applied; the color of each hexagon
directly corresponds to its count value.
If 'log', use a logarithmic scale for the color
map. Internally, :math:`log_{10}(i+1)` is used to
determine the hexagon color.
If an integer, divide the counts in the specified number
of bins, and color the hexagons accordingly.
If a sequence of values, the values of the lower bound of
the bins to be used.
*xscale*: [ 'linear' | 'log' ]
Use a linear or log10 scale on the horizontal axis.
*scale*: [ 'linear' | 'log' ]
Use a linear or log10 scale on the vertical axis.
Other keyword arguments controlling color mapping and normalization
arguments:
*cmap*: [ None | Colormap ]
a :class:`matplotlib.cm.Colormap` instance. If *None*,
defaults to rc ``image.cmap``.
*norm*: [ None | Normalize ]
:class:`matplotlib.colors.Normalize` instance is used to
scale luminance data to 0,1.
*vmin*/*vmax*: scalar
*vmin* and *vmax* are used in conjunction with *norm* to normalize
luminance data. If either are *None*, the min and max of the color
array *C* is used. Note if you pass a norm instance, your settings
for *vmin* and *vmax* will be ignored.
*alpha*: scalar
the alpha value for the patches
*linewidths*: [ None | scalar ]
If *None*, defaults to rc lines.linewidth. Note that this
is a tuple, and if you set the linewidths argument you
must set it as a sequence of floats, as required by
:class:`~matplotlib.collections.RegularPolyCollection`.
Other keyword arguments controlling the Collection properties:
*edgecolors*: [ None | mpl color | color sequence ]
If 'none', draws the edges in the same color as the fill color.
This is the default, as it avoids unsightly unpainted pixels
between the hexagons.
If *None*, draws the outlines in the default color.
If a matplotlib color arg or sequence of rgba tuples, draws the
outlines in the specified color.
Here are the standard descriptions of all the
:class:`~matplotlib.collections.Collection` kwargs:
%(Collection)s
The return value is a
:class:`~matplotlib.collections.PolyCollection` instance; use
:meth:`~matplotlib.collection.PolyCollection.get_array` on
this :class:`~matplotlib.collections.PolyCollection` to get
the counts in each hexagon.
**Example:**
.. plot:: mpl_examples/pylab_examples/hexbin_demo.py
"""
if not self._hold: self.cla()
self._process_unit_info(xdata=x, ydata=y, kwargs=kwargs)
x, y, C = cbook.delete_masked_points(x, y, C)
# Set the size of the hexagon grid
if iterable(gridsize):
nx, ny = gridsize
else:
nx = gridsize
ny = int(nx/math.sqrt(3))
# Count the number of data in each hexagon
x = np.array(x, float)
y = np.array(y, float)
if xscale=='log':
x = np.log10(x)
if yscale=='log':
y = np.log10(y)
xmin = np.amin(x)
xmax = np.amax(x)
ymin = np.amin(y)
ymax = np.amax(y)
# In the x-direction, the hexagons exactly cover the region from
# xmin to xmax. Need some padding to avoid roundoff errors.
padding = 1.e-9 * (xmax - xmin)
xmin -= padding
xmax += padding
sx = (xmax-xmin) / nx
sy = (ymax-ymin) / ny
x = (x-xmin)/sx
y = (y-ymin)/sy
ix1 = np.round(x).astype(int)
iy1 = np.round(y).astype(int)
ix2 = np.floor(x).astype(int)
iy2 = np.floor(y).astype(int)
nx1 = nx + 1
ny1 = ny + 1
nx2 = nx
ny2 = ny
n = nx1*ny1+nx2*ny2
d1 = (x-ix1)**2 + 3.0 * (y-iy1)**2
d2 = (x-ix2-0.5)**2 + 3.0 * (y-iy2-0.5)**2
bdist = (d1<d2)
if C is None:
accum = np.zeros(n)
# Create appropriate views into "accum" array.
lattice1 = accum[:nx1*ny1]
lattice2 = accum[nx1*ny1:]
lattice1.shape = (nx1,ny1)
lattice2.shape = (nx2,ny2)
for i in xrange(len(x)):
if bdist[i]:
lattice1[ix1[i], iy1[i]]+=1
else:
lattice2[ix2[i], iy2[i]]+=1
else:
# create accumulation arrays
lattice1 = np.empty((nx1,ny1),dtype=object)
for i in xrange(nx1):
for j in xrange(ny1):
lattice1[i,j] = []
lattice2 = np.empty((nx2,ny2),dtype=object)
for i in xrange(nx2):
for j in xrange(ny2):
lattice2[i,j] = []
for i in xrange(len(x)):
if bdist[i]:
lattice1[ix1[i], iy1[i]].append( C[i] )
else:
lattice2[ix2[i], iy2[i]].append( C[i] )
for i in xrange(nx1):
for j in xrange(ny1):
vals = lattice1[i,j]
if len(vals):
lattice1[i,j] = reduce_C_function( vals )
else:
lattice1[i,j] = np.nan
for i in xrange(nx2):
for j in xrange(ny2):
vals = lattice2[i,j]
if len(vals):
lattice2[i,j] = reduce_C_function( vals )
else:
lattice2[i,j] = np.nan
accum = np.hstack((
lattice1.astype(float).ravel(), lattice2.astype(float).ravel()))
good_idxs = ~np.isnan(accum)
px = xmin + sx * np.array([ 0.5, 0.5, 0.0, -0.5, -0.5, 0.0])
py = ymin + sy * np.array([-0.5, 0.5, 1.0, 0.5, -0.5, -1.0]) / 3.0
polygons = np.zeros((6, n, 2), float)
polygons[:,:nx1*ny1,0] = np.repeat(np.arange(nx1), ny1)
polygons[:,:nx1*ny1,1] = np.tile(np.arange(ny1), nx1)
polygons[:,nx1*ny1:,0] = np.repeat(np.arange(nx2) + 0.5, ny2)
polygons[:,nx1*ny1:,1] = np.tile(np.arange(ny2), nx2) + 0.5
if C is not None:
# remove accumulation bins with no data
polygons = polygons[:,good_idxs,:]
accum = accum[good_idxs]
polygons = np.transpose(polygons, axes=[1,0,2])
polygons[:,:,0] *= sx
polygons[:,:,1] *= sy
polygons[:,:,0] += px
polygons[:,:,1] += py
if xscale=='log':
polygons[:,:,0] = 10**(polygons[:,:,0])
xmin = 10**xmin
xmax = 10**xmax
self.set_xscale('log')
if yscale=='log':
polygons[:,:,1] = 10**(polygons[:,:,1])
ymin = 10**ymin
ymax = 10**ymax
self.set_yscale('log')
if edgecolors=='none':
edgecolors = 'face'
collection = mcoll.PolyCollection(
polygons,
edgecolors = edgecolors,
linewidths = linewidths,
transOffset = self.transData,
)
# Transform accum if needed
if bins=='log':
accum = np.log10(accum+1)
elif bins!=None:
if not iterable(bins):
minimum, maximum = min(accum), max(accum)
bins-=1 # one less edge than bins
bins = minimum + (maximum-minimum)*np.arange(bins)/bins
bins = np.sort(bins)
accum = bins.searchsorted(accum)
if norm is not None: assert(isinstance(norm, mcolors.Normalize))
if cmap is not None: assert(isinstance(cmap, mcolors.Colormap))
collection.set_array(accum)
collection.set_cmap(cmap)
collection.set_norm(norm)
collection.set_alpha(alpha)
collection.update(kwargs)
if vmin is not None or vmax is not None:
collection.set_clim(vmin, vmax)
else:
collection.autoscale_None()
corners = ((xmin, ymin), (xmax, ymax))
self.update_datalim( corners)
self.autoscale_view()
# add the collection last
self.add_collection(collection)
return collection
hexbin.__doc__ = cbook.dedent(hexbin.__doc__) % martist.kwdocd
def arrow(self, x, y, dx, dy, **kwargs):
"""
call signature::
arrow(x, y, dx, dy, **kwargs)
Draws arrow on specified axis from (*x*, *y*) to (*x* + *dx*,
*y* + *dy*).
Optional kwargs control the arrow properties:
%(FancyArrow)s
**Example:**
.. plot:: mpl_examples/pylab_examples/arrow_demo.py
"""
a = mpatches.FancyArrow(x, y, dx, dy, **kwargs)
self.add_artist(a)
return a
arrow.__doc__ = cbook.dedent(arrow.__doc__) % martist.kwdocd
def quiverkey(self, *args, **kw):
qk = mquiver.QuiverKey(*args, **kw)
self.add_artist(qk)
return qk
quiverkey.__doc__ = mquiver.QuiverKey.quiverkey_doc
def quiver(self, *args, **kw):
if not self._hold: self.cla()
q = mquiver.Quiver(self, *args, **kw)
self.add_collection(q, False)
self.update_datalim(q.XY)
self.autoscale_view()
return q
quiver.__doc__ = mquiver.Quiver.quiver_doc
def barbs(self, *args, **kw):
"""
%(barbs_doc)s
**Example:**
.. plot:: mpl_examples/pylab_examples/barb_demo.py
"""
if not self._hold: self.cla()
b = mquiver.Barbs(self, *args, **kw)
self.add_collection(b)
self.update_datalim(b.get_offsets())
self.autoscale_view()
return b
barbs.__doc__ = cbook.dedent(barbs.__doc__) % {
'barbs_doc': mquiver.Barbs.barbs_doc}
def fill(self, *args, **kwargs):
"""
call signature::
fill(*args, **kwargs)
Plot filled polygons. *args* is a variable length argument,
allowing for multiple *x*, *y* pairs with an optional color
format string; see :func:`~matplotlib.pyplot.plot` for details
on the argument parsing. For example, to plot a polygon with
vertices at *x*, *y* in blue.::
ax.fill(x,y, 'b' )
An arbitrary number of *x*, *y*, *color* groups can be specified::
ax.fill(x1, y1, 'g', x2, y2, 'r')
Return value is a list of :class:`~matplotlib.patches.Patch`
instances that were added.
The same color strings that :func:`~matplotlib.pyplot.plot`
supports are supported by the fill format string.
If you would like to fill below a curve, eg. shade a region
between 0 and *y* along *x*, use :meth:`fill_between`
The *closed* kwarg will close the polygon when *True* (default).
kwargs control the Polygon properties:
%(Polygon)s
**Example:**
.. plot:: mpl_examples/pylab_examples/fill_demo.py
"""
if not self._hold: self.cla()
patches = []
for poly in self._get_patches_for_fill(*args, **kwargs):
self.add_patch( poly )
patches.append( poly )
self.autoscale_view()
return patches
fill.__doc__ = cbook.dedent(fill.__doc__) % martist.kwdocd
def fill_between(self, x, y1, y2=0, where=None, **kwargs):
"""
call signature::
fill_between(x, y1, y2=0, where=None, **kwargs)
Create a :class:`~matplotlib.collections.PolyCollection`
filling the regions between *y1* and *y2* where
``where==True``
*x*
an N length np array of the x data
*y1*
an N length scalar or np array of the x data
*y2*
an N length scalar or np array of the x data
*where*
if None, default to fill between everywhere. If not None,
it is a a N length numpy boolean array and the fill will
only happen over the regions where ``where==True``
*kwargs*
keyword args passed on to the :class:`PolyCollection`
kwargs control the Polygon properties:
%(PolyCollection)s
.. plot:: mpl_examples/pylab_examples/fill_between.py
"""
# Handle united data, such as dates
self._process_unit_info(xdata=x, ydata=y1, kwargs=kwargs)
self._process_unit_info(ydata=y2)
# Convert the arrays so we can work with them
x = np.asarray(self.convert_xunits(x))
y1 = np.asarray(self.convert_yunits(y1))
y2 = np.asarray(self.convert_yunits(y2))
if not cbook.iterable(y1):
y1 = np.ones_like(x)*y1
if not cbook.iterable(y2):
y2 = np.ones_like(x)*y2
if where is None:
where = np.ones(len(x), np.bool)
where = np.asarray(where)
assert( (len(x)==len(y1)) and (len(x)==len(y2)) and len(x)==len(where))
polys = []
for ind0, ind1 in mlab.contiguous_regions(where):
theseverts = []
xslice = x[ind0:ind1]
y1slice = y1[ind0:ind1]
y2slice = y2[ind0:ind1]
if not len(xslice):
continue
N = len(xslice)
X = np.zeros((2*N+2, 2), np.float)
# the purpose of the next two lines is for when y2 is a
# scalar like 0 and we want the fill to go all the way
# down to 0 even if none of the y1 sample points do
X[0] = xslice[0], y2slice[0]
X[N+1] = xslice[-1], y2slice[-1]
X[1:N+1,0] = xslice
X[1:N+1,1] = y1slice
X[N+2:,0] = xslice[::-1]
X[N+2:,1] = y2slice[::-1]
polys.append(X)
collection = mcoll.PolyCollection(polys, **kwargs)
# now update the datalim and autoscale
XY1 = np.array([x[where], y1[where]]).T
XY2 = np.array([x[where], y2[where]]).T
self.dataLim.update_from_data_xy(XY1, self.ignore_existing_data_limits,
updatex=True, updatey=True)
self.dataLim.update_from_data_xy(XY2, self.ignore_existing_data_limits,
updatex=False, updatey=True)
self.add_collection(collection)
self.autoscale_view()
return collection
fill_between.__doc__ = cbook.dedent(fill_between.__doc__) % martist.kwdocd
#### plotting z(x,y): imshow, pcolor and relatives, contour
def imshow(self, X, cmap=None, norm=None, aspect=None,
interpolation=None, alpha=1.0, vmin=None, vmax=None,
origin=None, extent=None, shape=None, filternorm=1,
filterrad=4.0, imlim=None, resample=None, url=None, **kwargs):
"""
call signature::
imshow(X, cmap=None, norm=None, aspect=None, interpolation=None,
alpha=1.0, vmin=None, vmax=None, origin=None, extent=None,
**kwargs)
Display the image in *X* to current axes. *X* may be a float
array, a uint8 array or a PIL image. If *X* is an array, *X*
can have the following shapes:
* MxN -- luminance (grayscale, float array only)
* MxNx3 -- RGB (float or uint8 array)
* MxNx4 -- RGBA (float or uint8 array)
The value for each component of MxNx3 and MxNx4 float arrays should be
in the range 0.0 to 1.0; MxN float arrays may be normalised.
An :class:`matplotlib.image.AxesImage` instance is returned.
Keyword arguments:
*cmap*: [ None | Colormap ]
A :class:`matplotlib.cm.Colormap` instance, eg. cm.jet.
If *None*, default to rc ``image.cmap`` value.
*cmap* is ignored when *X* has RGB(A) information
*aspect*: [ None | 'auto' | 'equal' | scalar ]
If 'auto', changes the image aspect ratio to match that of the axes
If 'equal', and *extent* is *None*, changes the axes
aspect ratio to match that of the image. If *extent* is
not *None*, the axes aspect ratio is changed to match that
of the extent.
If *None*, default to rc ``image.aspect`` value.
*interpolation*:
Acceptable values are *None*, 'nearest', 'bilinear',
'bicubic', 'spline16', 'spline36', 'hanning', 'hamming',
'hermite', 'kaiser', 'quadric', 'catrom', 'gaussian',
'bessel', 'mitchell', 'sinc', 'lanczos',
If *interpolation* is *None*, default to rc
``image.interpolation``. See also the *filternorm* and
*filterrad* parameters
*norm*: [ None | Normalize ]
An :class:`matplotlib.colors.Normalize` instance; if
*None*, default is ``normalization()``. This scales
luminance -> 0-1
*norm* is only used for an MxN float array.
*vmin*/*vmax*: [ None | scalar ]
Used to scale a luminance image to 0-1. If either is
*None*, the min and max of the luminance values will be
used. Note if *norm* is not *None*, the settings for
*vmin* and *vmax* will be ignored.
*alpha*: scalar
The alpha blending value, between 0 (transparent) and 1 (opaque)
*origin*: [ None | 'upper' | 'lower' ]
Place the [0,0] index of the array in the upper left or lower left
corner of the axes. If *None*, default to rc ``image.origin``.
*extent*: [ None | scalars (left, right, bottom, top) ]
Eata values of the axes. The default assigns zero-based row,
column indices to the *x*, *y* centers of the pixels.
*shape*: [ None | scalars (columns, rows) ]
For raw buffer images
*filternorm*:
A parameter for the antigrain image resize filter. From the
antigrain documentation, if *filternorm* = 1, the filter normalizes
integer values and corrects the rounding errors. It doesn't do
anything with the source floating point values, it corrects only
integers according to the rule of 1.0 which means that any sum of
pixel weights must be equal to 1.0. So, the filter function must
produce a graph of the proper shape.
*filterrad*:
The filter radius for filters that have a radius
parameter, i.e. when interpolation is one of: 'sinc',
'lanczos' or 'blackman'
Additional kwargs are :class:`~matplotlib.artist.Artist` properties:
%(Artist)s
**Example:**
.. plot:: mpl_examples/pylab_examples/image_demo.py
"""
if not self._hold: self.cla()
if norm is not None: assert(isinstance(norm, mcolors.Normalize))
if cmap is not None: assert(isinstance(cmap, mcolors.Colormap))
if aspect is None: aspect = rcParams['image.aspect']
self.set_aspect(aspect)
im = mimage.AxesImage(self, cmap, norm, interpolation, origin, extent,
filternorm=filternorm,
filterrad=filterrad, resample=resample, **kwargs)
im.set_data(X)
im.set_alpha(alpha)
self._set_artist_props(im)
im.set_clip_path(self.patch)
#if norm is None and shape is None:
# im.set_clim(vmin, vmax)
if vmin is not None or vmax is not None:
im.set_clim(vmin, vmax)
else:
im.autoscale_None()
im.set_url(url)
xmin, xmax, ymin, ymax = im.get_extent()
corners = (xmin, ymin), (xmax, ymax)
self.update_datalim(corners)
if self._autoscaleon:
self.set_xlim((xmin, xmax))
self.set_ylim((ymin, ymax))
self.images.append(im)
return im
imshow.__doc__ = cbook.dedent(imshow.__doc__) % martist.kwdocd
def _pcolorargs(self, funcname, *args):
if len(args)==1:
C = args[0]
numRows, numCols = C.shape
X, Y = np.meshgrid(np.arange(numCols+1), np.arange(numRows+1) )
elif len(args)==3:
X, Y, C = args
else:
raise TypeError(
'Illegal arguments to %s; see help(%s)' % (funcname, funcname))
Nx = X.shape[-1]
Ny = Y.shape[0]
if len(X.shape) <> 2 or X.shape[0] == 1:
x = X.reshape(1,Nx)
X = x.repeat(Ny, axis=0)
if len(Y.shape) <> 2 or Y.shape[1] == 1:
y = Y.reshape(Ny, 1)
Y = y.repeat(Nx, axis=1)
if X.shape != Y.shape:
raise TypeError(
'Incompatible X, Y inputs to %s; see help(%s)' % (
funcname, funcname))
return X, Y, C
def pcolor(self, *args, **kwargs):
"""
call signatures::
pcolor(C, **kwargs)
pcolor(X, Y, C, **kwargs)
Create a pseudocolor plot of a 2-D array.
*C* is the array of color values.
*X* and *Y*, if given, specify the (*x*, *y*) coordinates of
the colored quadrilaterals; the quadrilateral for C[i,j] has
corners at::
(X[i, j], Y[i, j]),
(X[i, j+1], Y[i, j+1]),
(X[i+1, j], Y[i+1, j]),
(X[i+1, j+1], Y[i+1, j+1]).
Ideally the dimensions of *X* and *Y* should be one greater
than those of *C*; if the dimensions are the same, then the
last row and column of *C* will be ignored.
Note that the the column index corresponds to the
*x*-coordinate, and the row index corresponds to *y*; for
details, see the :ref:`Grid Orientation
<axes-pcolor-grid-orientation>` section below.
If either or both of *X* and *Y* are 1-D arrays or column vectors,
they will be expanded as needed into the appropriate 2-D arrays,
making a rectangular grid.
*X*, *Y* and *C* may be masked arrays. If either C[i, j], or one
of the vertices surrounding C[i,j] (*X* or *Y* at [i, j], [i+1, j],
[i, j+1],[i+1, j+1]) is masked, nothing is plotted.
Keyword arguments:
*cmap*: [ None | Colormap ]
A :class:`matplotlib.cm.Colormap` instance. If *None*, use
rc settings.
norm: [ None | Normalize ]
An :class:`matplotlib.colors.Normalize` instance is used
to scale luminance data to 0,1. If *None*, defaults to
:func:`normalize`.
*vmin*/*vmax*: [ None | scalar ]
*vmin* and *vmax* are used in conjunction with *norm* to
normalize luminance data. If either are *None*, the min
and max of the color array *C* is used. If you pass a
*norm* instance, *vmin* and *vmax* will be ignored.
*shading*: [ 'flat' | 'faceted' ]
If 'faceted', a black grid is drawn around each rectangle; if
'flat', edges are not drawn. Default is 'flat', contrary to
Matlab(TM).
This kwarg is deprecated; please use 'edgecolors' instead:
* shading='flat' -- edgecolors='None'
* shading='faceted -- edgecolors='k'
*edgecolors*: [ None | 'None' | color | color sequence]
If *None*, the rc setting is used by default.
If 'None', edges will not be visible.
An mpl color or sequence of colors will set the edge color
*alpha*: 0 <= scalar <= 1
the alpha blending value
Return value is a :class:`matplotlib.collection.Collection`
instance.
.. _axes-pcolor-grid-orientation:
The grid orientation follows the Matlab(TM) convention: an
array *C* with shape (*nrows*, *ncolumns*) is plotted with
the column number as *X* and the row number as *Y*, increasing
up; hence it is plotted the way the array would be printed,
except that the *Y* axis is reversed. That is, *C* is taken
as *C*(*y*, *x*).
Similarly for :func:`~matplotlib.pyplot.meshgrid`::
x = np.arange(5)
y = np.arange(3)
X, Y = meshgrid(x,y)
is equivalent to:
X = array([[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4]])
Y = array([[0, 0, 0, 0, 0],
[1, 1, 1, 1, 1],
[2, 2, 2, 2, 2]])
so if you have::
C = rand( len(x), len(y))
then you need::
pcolor(X, Y, C.T)
or::
pcolor(C.T)
Matlab :func:`pcolor` always discards the last row and column
of *C*, but matplotlib displays the last row and column if *X* and
*Y* are not specified, or if *X* and *Y* have one more row and
column than *C*.
kwargs can be used to control the
:class:`~matplotlib.collection.PolyCollection` properties:
%(PolyCollection)s
"""
if not self._hold: self.cla()
alpha = kwargs.pop('alpha', 1.0)
norm = kwargs.pop('norm', None)
cmap = kwargs.pop('cmap', None)
vmin = kwargs.pop('vmin', None)
vmax = kwargs.pop('vmax', None)
shading = kwargs.pop('shading', 'flat')
X, Y, C = self._pcolorargs('pcolor', *args)
Ny, Nx = X.shape
# convert to MA, if necessary.
C = ma.asarray(C)
X = ma.asarray(X)
Y = ma.asarray(Y)
mask = ma.getmaskarray(X)+ma.getmaskarray(Y)
xymask = mask[0:-1,0:-1]+mask[1:,1:]+mask[0:-1,1:]+mask[1:,0:-1]
# don't plot if C or any of the surrounding vertices are masked.
mask = ma.getmaskarray(C)[0:Ny-1,0:Nx-1]+xymask
newaxis = np.newaxis
compress = np.compress
ravelmask = (mask==0).ravel()
X1 = compress(ravelmask, ma.filled(X[0:-1,0:-1]).ravel())
Y1 = compress(ravelmask, ma.filled(Y[0:-1,0:-1]).ravel())
X2 = compress(ravelmask, ma.filled(X[1:,0:-1]).ravel())
Y2 = compress(ravelmask, ma.filled(Y[1:,0:-1]).ravel())
X3 = compress(ravelmask, ma.filled(X[1:,1:]).ravel())
Y3 = compress(ravelmask, ma.filled(Y[1:,1:]).ravel())
X4 = compress(ravelmask, ma.filled(X[0:-1,1:]).ravel())
Y4 = compress(ravelmask, ma.filled(Y[0:-1,1:]).ravel())
npoly = len(X1)
xy = np.concatenate((X1[:,newaxis], Y1[:,newaxis],
X2[:,newaxis], Y2[:,newaxis],
X3[:,newaxis], Y3[:,newaxis],
X4[:,newaxis], Y4[:,newaxis],
X1[:,newaxis], Y1[:,newaxis]),
axis=1)
verts = xy.reshape((npoly, 5, 2))
#verts = zip(zip(X1,Y1),zip(X2,Y2),zip(X3,Y3),zip(X4,Y4))
C = compress(ravelmask, ma.filled(C[0:Ny-1,0:Nx-1]).ravel())
if shading == 'faceted':
edgecolors = (0,0,0,1),
linewidths = (0.25,)
else:
edgecolors = 'face'
linewidths = (1.0,)
kwargs.setdefault('edgecolors', edgecolors)
kwargs.setdefault('antialiaseds', (0,))
kwargs.setdefault('linewidths', linewidths)
collection = mcoll.PolyCollection(verts, **kwargs)
collection.set_alpha(alpha)
collection.set_array(C)
if norm is not None: assert(isinstance(norm, mcolors.Normalize))
if cmap is not None: assert(isinstance(cmap, mcolors.Colormap))
collection.set_cmap(cmap)
collection.set_norm(norm)
if vmin is not None or vmax is not None:
collection.set_clim(vmin, vmax)
else:
collection.autoscale_None()
self.grid(False)
x = X.compressed()
y = Y.compressed()
minx = np.amin(x)
maxx = np.amax(x)
miny = np.amin(y)
maxy = np.amax(y)
corners = (minx, miny), (maxx, maxy)
self.update_datalim( corners)
self.autoscale_view()
self.add_collection(collection)
return collection
pcolor.__doc__ = cbook.dedent(pcolor.__doc__) % martist.kwdocd
def pcolormesh(self, *args, **kwargs):
"""
call signatures::
pcolormesh(C)
pcolormesh(X, Y, C)
pcolormesh(C, **kwargs)
*C* may be a masked array, but *X* and *Y* may not. Masked
array support is implemented via *cmap* and *norm*; in
contrast, :func:`~matplotlib.pyplot.pcolor` simply does not
draw quadrilaterals with masked colors or vertices.
Keyword arguments:
*cmap*: [ None | Colormap ]
A :class:`matplotlib.cm.Colormap` instance. If None, use
rc settings.
*norm*: [ None | Normalize ]
A :class:`matplotlib.colors.Normalize` instance is used to
scale luminance data to 0,1. If None, defaults to
:func:`normalize`.
*vmin*/*vmax*: [ None | scalar ]
*vmin* and *vmax* are used in conjunction with *norm* to
normalize luminance data. If either are *None*, the min
and max of the color array *C* is used. If you pass a
*norm* instance, *vmin* and *vmax* will be ignored.
*shading*: [ 'flat' | 'faceted' ]
If 'faceted', a black grid is drawn around each rectangle; if
'flat', edges are not drawn. Default is 'flat', contrary to
Matlab(TM).
This kwarg is deprecated; please use 'edgecolors' instead:
* shading='flat' -- edgecolors='None'
* shading='faceted -- edgecolors='k'
*edgecolors*: [ None | 'None' | color | color sequence]
If None, the rc setting is used by default.
If 'None', edges will not be visible.
An mpl color or sequence of colors will set the edge color
*alpha*: 0 <= scalar <= 1
the alpha blending value
Return value is a :class:`matplotlib.collection.QuadMesh`
object.
kwargs can be used to control the
:class:`matplotlib.collections.QuadMesh`
properties:
%(QuadMesh)s
.. seealso::
:func:`~matplotlib.pyplot.pcolor`:
For an explanation of the grid orientation and the
expansion of 1-D *X* and/or *Y* to 2-D arrays.
"""
if not self._hold: self.cla()
alpha = kwargs.pop('alpha', 1.0)
norm = kwargs.pop('norm', None)
cmap = kwargs.pop('cmap', None)
vmin = kwargs.pop('vmin', None)
vmax = kwargs.pop('vmax', None)
shading = kwargs.pop('shading', 'flat')
edgecolors = kwargs.pop('edgecolors', 'None')
antialiased = kwargs.pop('antialiased', False)
X, Y, C = self._pcolorargs('pcolormesh', *args)
Ny, Nx = X.shape
# convert to one dimensional arrays
C = ma.ravel(C[0:Ny-1, 0:Nx-1]) # data point in each cell is value at
# lower left corner
X = X.ravel()
Y = Y.ravel()
coords = np.zeros(((Nx * Ny), 2), dtype=float)
coords[:, 0] = X
coords[:, 1] = Y
if shading == 'faceted' or edgecolors != 'None':
showedges = 1
else:
showedges = 0
collection = mcoll.QuadMesh(
Nx - 1, Ny - 1, coords, showedges,
antialiased=antialiased) # kwargs are not used
collection.set_alpha(alpha)
collection.set_array(C)
if norm is not None: assert(isinstance(norm, mcolors.Normalize))
if cmap is not None: assert(isinstance(cmap, mcolors.Colormap))
collection.set_cmap(cmap)
collection.set_norm(norm)
if vmin is not None or vmax is not None:
collection.set_clim(vmin, vmax)
else:
collection.autoscale_None()
self.grid(False)
minx = np.amin(X)
maxx = np.amax(X)
miny = np.amin(Y)
maxy = np.amax(Y)
corners = (minx, miny), (maxx, maxy)
self.update_datalim( corners)
self.autoscale_view()
self.add_collection(collection)
return collection
pcolormesh.__doc__ = cbook.dedent(pcolormesh.__doc__) % martist.kwdocd
def pcolorfast(self, *args, **kwargs):
"""
pseudocolor plot of a 2-D array
Experimental; this is a version of pcolor that
does not draw lines, that provides the fastest
possible rendering with the Agg backend, and that
can handle any quadrilateral grid.
Call signatures::
pcolor(C, **kwargs)
pcolor(xr, yr, C, **kwargs)
pcolor(x, y, C, **kwargs)
pcolor(X, Y, C, **kwargs)
C is the 2D array of color values corresponding to quadrilateral
cells. Let (nr, nc) be its shape. C may be a masked array.
``pcolor(C, **kwargs)`` is equivalent to
``pcolor([0,nc], [0,nr], C, **kwargs)``
*xr*, *yr* specify the ranges of *x* and *y* corresponding to the
rectangular region bounding *C*. If::
xr = [x0, x1]
and::
yr = [y0,y1]
then *x* goes from *x0* to *x1* as the second index of *C* goes
from 0 to *nc*, etc. (*x0*, *y0*) is the outermost corner of
cell (0,0), and (*x1*, *y1*) is the outermost corner of cell
(*nr*-1, *nc*-1). All cells are rectangles of the same size.
This is the fastest version.
*x*, *y* are 1D arrays of length *nc* +1 and *nr* +1, respectively,
giving the x and y boundaries of the cells. Hence the cells are
rectangular but the grid may be nonuniform. The speed is
intermediate. (The grid is checked, and if found to be
uniform the fast version is used.)
*X* and *Y* are 2D arrays with shape (*nr* +1, *nc* +1) that specify
the (x,y) coordinates of the corners of the colored
quadrilaterals; the quadrilateral for C[i,j] has corners at
(X[i,j],Y[i,j]), (X[i,j+1],Y[i,j+1]), (X[i+1,j],Y[i+1,j]),
(X[i+1,j+1],Y[i+1,j+1]). The cells need not be rectangular.
This is the most general, but the slowest to render. It may
produce faster and more compact output using ps, pdf, and
svg backends, however.
Note that the the column index corresponds to the x-coordinate,
and the row index corresponds to y; for details, see
the "Grid Orientation" section below.
Optional keyword arguments:
*cmap*: [ None | Colormap ]
A cm Colormap instance from cm. If None, use rc settings.
*norm*: [ None | Normalize ]
An mcolors.Normalize instance is used to scale luminance data to
0,1. If None, defaults to normalize()
*vmin*/*vmax*: [ None | scalar ]
*vmin* and *vmax* are used in conjunction with norm to normalize
luminance data. If either are *None*, the min and max of the color
array *C* is used. If you pass a norm instance, *vmin* and *vmax*
will be *None*.
*alpha*: 0 <= scalar <= 1
the alpha blending value
Return value is an image if a regular or rectangular grid
is specified, and a QuadMesh collection in the general
quadrilateral case.
"""
if not self._hold: self.cla()
alpha = kwargs.pop('alpha', 1.0)
norm = kwargs.pop('norm', None)
cmap = kwargs.pop('cmap', None)
vmin = kwargs.pop('vmin', None)
vmax = kwargs.pop('vmax', None)
if norm is not None: assert(isinstance(norm, mcolors.Normalize))
if cmap is not None: assert(isinstance(cmap, mcolors.Colormap))
C = args[-1]
nr, nc = C.shape
if len(args) == 1:
style = "image"
x = [0, nc]
y = [0, nr]
elif len(args) == 3:
x, y = args[:2]
x = np.asarray(x)
y = np.asarray(y)
if x.ndim == 1 and y.ndim == 1:
if x.size == 2 and y.size == 2:
style = "image"
else:
dx = np.diff(x)
dy = np.diff(y)
if (np.ptp(dx) < 0.01*np.abs(dx.mean()) and
np.ptp(dy) < 0.01*np.abs(dy.mean())):
style = "image"
else:
style = "pcolorimage"
elif x.ndim == 2 and y.ndim == 2:
style = "quadmesh"
else:
raise TypeError("arguments do not match valid signatures")
else:
raise TypeError("need 1 argument or 3 arguments")
if style == "quadmesh":
# convert to one dimensional arrays
# This should also be moved to the QuadMesh class
C = ma.ravel(C) # data point in each cell is value
# at lower left corner
X = x.ravel()
Y = y.ravel()
Nx = nc+1
Ny = nr+1
# The following needs to be cleaned up; the renderer
# requires separate contiguous arrays for X and Y,
# but the QuadMesh class requires the 2D array.
coords = np.empty(((Nx * Ny), 2), np.float64)
coords[:, 0] = X
coords[:, 1] = Y
# The QuadMesh class can also be changed to
# handle relevant superclass kwargs; the initializer
# should do much more than it does now.
collection = mcoll.QuadMesh(nc, nr, coords, 0)
collection.set_alpha(alpha)
collection.set_array(C)
collection.set_cmap(cmap)
collection.set_norm(norm)
self.add_collection(collection)
xl, xr, yb, yt = X.min(), X.max(), Y.min(), Y.max()
ret = collection
else:
# One of the image styles:
xl, xr, yb, yt = x[0], x[-1], y[0], y[-1]
if style == "image":
im = mimage.AxesImage(self, cmap, norm,
interpolation='nearest',
origin='lower',
extent=(xl, xr, yb, yt),
**kwargs)
im.set_data(C)
im.set_alpha(alpha)
self.images.append(im)
ret = im
if style == "pcolorimage":
im = mimage.PcolorImage(self, x, y, C,
cmap=cmap,
norm=norm,
alpha=alpha,
**kwargs)
self.images.append(im)
ret = im
self._set_artist_props(ret)
if vmin is not None or vmax is not None:
ret.set_clim(vmin, vmax)
else:
ret.autoscale_None()
self.update_datalim(np.array([[xl, yb], [xr, yt]]))
self.autoscale_view(tight=True)
return ret
def contour(self, *args, **kwargs):
if not self._hold: self.cla()
kwargs['filled'] = False
return mcontour.ContourSet(self, *args, **kwargs)
contour.__doc__ = mcontour.ContourSet.contour_doc
def contourf(self, *args, **kwargs):
if not self._hold: self.cla()
kwargs['filled'] = True
return mcontour.ContourSet(self, *args, **kwargs)
contourf.__doc__ = mcontour.ContourSet.contour_doc
def clabel(self, CS, *args, **kwargs):
return CS.clabel(*args, **kwargs)
clabel.__doc__ = mcontour.ContourSet.clabel.__doc__
def table(self, **kwargs):
"""
call signature::
table(cellText=None, cellColours=None,
cellLoc='right', colWidths=None,
rowLabels=None, rowColours=None, rowLoc='left',
colLabels=None, colColours=None, colLoc='center',
loc='bottom', bbox=None):
Add a table to the current axes. Returns a
:class:`matplotlib.table.Table` instance. For finer grained
control over tables, use the :class:`~matplotlib.table.Table`
class and add it to the axes with
:meth:`~matplotlib.axes.Axes.add_table`.
Thanks to John Gill for providing the class and table.
kwargs control the :class:`~matplotlib.table.Table`
properties:
%(Table)s
"""
return mtable.table(self, **kwargs)
table.__doc__ = cbook.dedent(table.__doc__) % martist.kwdocd
def twinx(self):
"""
call signature::
ax = twinx()
create a twin of Axes for generating a plot with a sharex
x-axis but independent y axis. The y-axis of self will have
ticks on left and the returned axes will have ticks on the
right
"""
ax2 = self.figure.add_axes(self.get_position(True), sharex=self,
frameon=False)
ax2.yaxis.tick_right()
ax2.yaxis.set_label_position('right')
self.yaxis.tick_left()
return ax2
def twiny(self):
"""
call signature::
ax = twiny()
create a twin of Axes for generating a plot with a shared
y-axis but independent x axis. The x-axis of self will have
ticks on bottom and the returned axes will have ticks on the
top
"""
ax2 = self.figure.add_axes(self.get_position(True), sharey=self,
frameon=False)
ax2.xaxis.tick_top()
ax2.xaxis.set_label_position('top')
self.xaxis.tick_bottom()
return ax2
def get_shared_x_axes(self):
'Return a copy of the shared axes Grouper object for x axes'
return self._shared_x_axes
def get_shared_y_axes(self):
'Return a copy of the shared axes Grouper object for y axes'
return self._shared_y_axes
#### Data analysis
def hist(self, x, bins=10, range=None, normed=False, cumulative=False,
bottom=None, histtype='bar', align='mid',
orientation='vertical', rwidth=None, log=False, **kwargs):
"""
call signature::
hist(x, bins=10, range=None, normed=False, cumulative=False,
bottom=None, histtype='bar', align='mid',
orientation='vertical', rwidth=None, log=False, **kwargs)
Compute and draw the histogram of *x*. The return value is a
tuple (*n*, *bins*, *patches*) or ([*n0*, *n1*, ...], *bins*,
[*patches0*, *patches1*,...]) if the input contains multiple
data.
Keyword arguments:
*bins*:
Either an integer number of bins or a sequence giving the
bins. *x* are the data to be binned. *x* can be an array,
a 2D array with multiple data in its columns, or a list of
arrays with data of different length. Note, if *bins*
is an integer input argument=numbins, *bins* + 1 bin edges
will be returned, compatible with the semantics of
:func:`numpy.histogram` with the *new* = True argument.
Unequally spaced bins are supported if *bins* is a sequence.
*range*:
The lower and upper range of the bins. Lower and upper outliers
are ignored. If not provided, *range* is (x.min(), x.max()).
Range has no effect if *bins* is a sequence.
If *bins* is a sequence or *range* is specified, autoscaling is
set off (*autoscale_on* is set to *False*) and the xaxis limits
are set to encompass the full specified bin range.
*normed*:
If *True*, the first element of the return tuple will
be the counts normalized to form a probability density, i.e.,
``n/(len(x)*dbin)``. In a probability density, the integral of
the histogram should be 1; you can verify that with a
trapezoidal integration of the probability density function::
pdf, bins, patches = ax.hist(...)
print np.sum(pdf * np.diff(bins))
*cumulative*:
If *True*, then a histogram is computed where each bin
gives the counts in that bin plus all bins for smaller values.
The last bin gives the total number of datapoints. If *normed*
is also *True* then the histogram is normalized such that the
last bin equals 1. If *cumulative* evaluates to less than 0
(e.g. -1), the direction of accumulation is reversed. In this
case, if *normed* is also *True*, then the histogram is normalized
such that the first bin equals 1.
*histtype*: [ 'bar' | 'barstacked' | 'step' | 'stepfilled' ]
The type of histogram to draw.
- 'bar' is a traditional bar-type histogram. If multiple data
are given the bars are aranged side by side.
- 'barstacked' is a bar-type histogram where multiple
data are stacked on top of each other.
- 'step' generates a lineplot that is by default
unfilled.
- 'stepfilled' generates a lineplot that is by default
filled.
*align*: ['left' | 'mid' | 'right' ]
Controls how the histogram is plotted.
- 'left': bars are centered on the left bin edges.
- 'mid': bars are centered between the bin edges.
- 'right': bars are centered on the right bin edges.
*orientation*: [ 'horizontal' | 'vertical' ]
If 'horizontal', :func:`~matplotlib.pyplot.barh` will be
used for bar-type histograms and the *bottom* kwarg will be
the left edges.
*rwidth*:
The relative width of the bars as a fraction of the bin
width. If *None*, automatically compute the width. Ignored
if *histtype* = 'step' or 'stepfilled'.
*log*:
If *True*, the histogram axis will be set to a log scale.
If *log* is *True* and *x* is a 1D array, empty bins will
be filtered out and only the non-empty (*n*, *bins*,
*patches*) will be returned.
kwargs are used to update the properties of the hist
:class:`~matplotlib.patches.Rectangle` instances:
%(Rectangle)s
You can use labels for your histogram, and only the first
:class:`~matplotlib.patches.Rectangle` gets the label (the
others get the magic string '_nolegend_'. This will make the
histograms work in the intuitive way for bar charts::
ax.hist(10+2*np.random.randn(1000), label='men')
ax.hist(12+3*np.random.randn(1000), label='women', alpha=0.5)
ax.legend()
**Example:**
.. plot:: mpl_examples/pylab_examples/histogram_demo.py
"""
if not self._hold: self.cla()
# NOTE: the range keyword overwrites the built-in func range !!!
# needs to be fixed in with numpy !!!
if kwargs.get('width') is not None:
raise DeprecationWarning(
'hist now uses the rwidth to give relative width '
'and not absolute width')
try:
# make sure a copy is created: don't use asarray
x = np.transpose(np.array(x))
if len(x.shape)==1:
x.shape = (1,x.shape[0])
elif len(x.shape)==2 and x.shape[1]<x.shape[0]:
warnings.warn('2D hist should be nsamples x nvariables; '
'this looks transposed')
except ValueError:
# multiple hist with data of different length
if iterable(x[0]) and not is_string_like(x[0]):
tx = []
for i in xrange(len(x)):
tx.append( np.array(x[i]) )
x = tx
else:
raise ValueError, 'Can not use providet data to create a histogram'
# Check whether bins or range are given explicitly. In that
# case do not autoscale axes.
binsgiven = (cbook.iterable(bins) or range != None)
# check the version of the numpy
if np.__version__ < "1.3": # version 1.1 and 1.2
hist_kwargs = dict(range=range,
normed=bool(normed), new=True)
else: # version 1.3 and later, drop new=True
hist_kwargs = dict(range=range,
normed=bool(normed))
n = []
for i in xrange(len(x)):
# this will automatically overwrite bins,
# so that each histogram uses the same bins
m, bins = np.histogram(x[i], bins, **hist_kwargs)
n.append(m)
if cumulative:
slc = slice(None)
if cbook.is_numlike(cumulative) and cumulative < 0:
slc = slice(None,None,-1)
if normed:
n = [(m * np.diff(bins))[slc].cumsum()[slc] for m in n]
else:
n = [m[slc].cumsum()[slc] for m in n]
patches = []
if histtype.startswith('bar'):
totwidth = np.diff(bins)
stacked = False
if rwidth is not None: dr = min(1., max(0., rwidth))
elif len(n)>1: dr = 0.8
else: dr = 1.0
if histtype=='bar':
width = dr*totwidth/len(n)
dw = width
if len(n)>1:
boffset = -0.5*dr*totwidth*(1.-1./len(n))
else:
boffset = 0.0
elif histtype=='barstacked':
width = dr*totwidth
boffset, dw = 0.0, 0.0
stacked = True
else:
raise ValueError, 'invalid histtype: %s' % histtype
if align == 'mid' or align == 'edge':
boffset += 0.5*totwidth
elif align == 'right':
boffset += totwidth
elif align != 'left' and align != 'center':
raise ValueError, 'invalid align: %s' % align
if orientation == 'horizontal':
for m in n:
color = self._get_lines._get_next_cycle_color()
patch = self.barh(bins[:-1]+boffset, m, height=width,
left=bottom, align='center', log=log,
color=color)
patches.append(patch)
if stacked:
if bottom is None: bottom = 0.0
bottom += m
boffset += dw
elif orientation == 'vertical':
for m in n:
color = self._get_lines._get_next_cycle_color()
patch = self.bar(bins[:-1]+boffset, m, width=width,
bottom=bottom, align='center', log=log,
color=color)
patches.append(patch)
if stacked:
if bottom is None: bottom = 0.0
bottom += m
boffset += dw
else:
raise ValueError, 'invalid orientation: %s' % orientation
elif histtype.startswith('step'):
x = np.zeros( 2*len(bins), np.float )
y = np.zeros( 2*len(bins), np.float )
x[0::2], x[1::2] = bins, bins
if align == 'left' or align == 'center':
x -= 0.5*(bins[1]-bins[0])
elif align == 'right':
x += 0.5*(bins[1]-bins[0])
elif align != 'mid' and align != 'edge':
raise ValueError, 'invalid align: %s' % align
if log:
y[0],y[-1] = 1e-100, 1e-100
if orientation == 'horizontal':
self.set_xscale('log')
elif orientation == 'vertical':
self.set_yscale('log')
fill = False
if histtype == 'stepfilled':
fill = True
elif histtype != 'step':
raise ValueError, 'invalid histtype: %s' % histtype
for m in n:
y[1:-1:2], y[2::2] = m, m
if orientation == 'horizontal':
x,y = y,x
elif orientation != 'vertical':
raise ValueError, 'invalid orientation: %s' % orientation
color = self._get_lines._get_next_cycle_color()
if fill:
patches.append( self.fill(x, y,
closed=False, facecolor=color) )
else:
patches.append( self.fill(x, y,
closed=False, edgecolor=color, fill=False) )
# adopted from adjust_x/ylim part of the bar method
if orientation == 'horizontal':
xmin, xmax = 0, self.dataLim.intervalx[1]
for m in n:
xmin = np.amin(m[m!=0]) # filter out the 0 height bins
xmin = max(xmin*0.9, 1e-100)
self.dataLim.intervalx = (xmin, xmax)
elif orientation == 'vertical':
ymin, ymax = 0, self.dataLim.intervaly[1]
for m in n:
ymin = np.amin(m[m!=0]) # filter out the 0 height bins
ymin = max(ymin*0.9, 1e-100)
self.dataLim.intervaly = (ymin, ymax)
self.autoscale_view()
else:
raise ValueError, 'invalid histtype: %s' % histtype
label = kwargs.pop('label', '')
for patch in patches:
for p in patch:
p.update(kwargs)
p.set_label(label)
label = '_nolegend_'
if binsgiven:
self.set_autoscale_on(False)
if orientation == 'vertical':
self.autoscale_view(scalex=False, scaley=True)
XL = self.xaxis.get_major_locator().view_limits(bins[0], bins[-1])
self.set_xbound(XL)
else:
self.autoscale_view(scalex=True, scaley=False)
YL = self.yaxis.get_major_locator().view_limits(bins[0], bins[-1])
self.set_ybound(YL)
if len(n)==1:
return n[0], bins, cbook.silent_list('Patch', patches[0])
else:
return n, bins, cbook.silent_list('Lists of Patches', patches)
hist.__doc__ = cbook.dedent(hist.__doc__) % martist.kwdocd
def psd(self, x, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
window=mlab.window_hanning, noverlap=0, pad_to=None,
sides='default', scale_by_freq=None, **kwargs):
"""
call signature::
psd(x, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
window=mlab.window_hanning, noverlap=0, pad_to=None,
sides='default', scale_by_freq=None, **kwargs)
The power spectral density by Welch's average periodogram
method. The vector *x* is divided into *NFFT* length
segments. Each segment is detrended by function *detrend* and
windowed by function *window*. *noverlap* gives the length of
the overlap between segments. The :math:`|\mathrm{fft}(i)|^2`
of each segment :math:`i` are averaged to compute *Pxx*, with a
scaling to correct for power loss due to windowing. *Fs* is the
sampling frequency.
%(PSD)s
*Fc*: integer
The center frequency of *x* (defaults to 0), which offsets
the x extents of the plot to reflect the frequency range used
when a signal is acquired and then filtered and downsampled to
baseband.
Returns the tuple (*Pxx*, *freqs*).
For plotting, the power is plotted as
:math:`10\log_{10}(P_{xx})` for decibels, though *Pxx* itself
is returned.
References:
Bendat & Piersol -- Random Data: Analysis and Measurement
Procedures, John Wiley & Sons (1986)
kwargs control the :class:`~matplotlib.lines.Line2D` properties:
%(Line2D)s
**Example:**
.. plot:: mpl_examples/pylab_examples/psd_demo.py
"""
if not self._hold: self.cla()
pxx, freqs = mlab.psd(x, NFFT, Fs, detrend, window, noverlap, pad_to,
sides, scale_by_freq)
pxx.shape = len(freqs),
freqs += Fc
if scale_by_freq in (None, True):
psd_units = 'dB/Hz'
else:
psd_units = 'dB'
self.plot(freqs, 10*np.log10(pxx), **kwargs)
self.set_xlabel('Frequency')
self.set_ylabel('Power Spectral Density (%s)' % psd_units)
self.grid(True)
vmin, vmax = self.viewLim.intervaly
intv = vmax-vmin
logi = int(np.log10(intv))
if logi==0: logi=.1
step = 10*logi
#print vmin, vmax, step, intv, math.floor(vmin), math.ceil(vmax)+1
ticks = np.arange(math.floor(vmin), math.ceil(vmax)+1, step)
self.set_yticks(ticks)
return pxx, freqs
psd_doc_dict = dict()
psd_doc_dict.update(martist.kwdocd)
psd_doc_dict.update(mlab.kwdocd)
psd_doc_dict['PSD'] = cbook.dedent(psd_doc_dict['PSD'])
psd.__doc__ = cbook.dedent(psd.__doc__) % psd_doc_dict
def csd(self, x, y, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
window=mlab.window_hanning, noverlap=0, pad_to=None,
sides='default', scale_by_freq=None, **kwargs):
"""
call signature::
csd(x, y, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
window=mlab.window_hanning, noverlap=0, pad_to=None,
sides='default', scale_by_freq=None, **kwargs)
The cross spectral density :math:`P_{xy}` by Welch's average
periodogram method. The vectors *x* and *y* are divided into
*NFFT* length segments. Each segment is detrended by function
*detrend* and windowed by function *window*. The product of
the direct FFTs of *x* and *y* are averaged over each segment
to compute :math:`P_{xy}`, with a scaling to correct for power
loss due to windowing.
Returns the tuple (*Pxy*, *freqs*). *P* is the cross spectrum
(complex valued), and :math:`10\log_{10}|P_{xy}|` is
plotted.
%(PSD)s
*Fc*: integer
The center frequency of *x* (defaults to 0), which offsets
the x extents of the plot to reflect the frequency range used
when a signal is acquired and then filtered and downsampled to
baseband.
References:
Bendat & Piersol -- Random Data: Analysis and Measurement
Procedures, John Wiley & Sons (1986)
kwargs control the Line2D properties:
%(Line2D)s
**Example:**
.. plot:: mpl_examples/pylab_examples/csd_demo.py
.. seealso:
:meth:`psd`
For a description of the optional parameters.
"""
if not self._hold: self.cla()
pxy, freqs = mlab.csd(x, y, NFFT, Fs, detrend, window, noverlap,
pad_to, sides, scale_by_freq)
pxy.shape = len(freqs),
# pxy is complex
freqs += Fc
self.plot(freqs, 10*np.log10(np.absolute(pxy)), **kwargs)
self.set_xlabel('Frequency')
self.set_ylabel('Cross Spectrum Magnitude (dB)')
self.grid(True)
vmin, vmax = self.viewLim.intervaly
intv = vmax-vmin
step = 10*int(np.log10(intv))
ticks = np.arange(math.floor(vmin), math.ceil(vmax)+1, step)
self.set_yticks(ticks)
return pxy, freqs
csd.__doc__ = cbook.dedent(csd.__doc__) % psd_doc_dict
def cohere(self, x, y, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
window=mlab.window_hanning, noverlap=0, pad_to=None,
sides='default', scale_by_freq=None, **kwargs):
"""
call signature::
cohere(x, y, NFFT=256, Fs=2, Fc=0, detrend = mlab.detrend_none,
window = mlab.window_hanning, noverlap=0, pad_to=None,
sides='default', scale_by_freq=None, **kwargs)
cohere the coherence between *x* and *y*. Coherence is the normalized
cross spectral density:
.. math::
C_{xy} = \\frac{|P_{xy}|^2}{P_{xx}P_{yy}}
%(PSD)s
*Fc*: integer
The center frequency of *x* (defaults to 0), which offsets
the x extents of the plot to reflect the frequency range used
when a signal is acquired and then filtered and downsampled to
baseband.
The return value is a tuple (*Cxy*, *f*), where *f* are the
frequencies of the coherence vector.
kwargs are applied to the lines.
References:
* Bendat & Piersol -- Random Data: Analysis and Measurement
Procedures, John Wiley & Sons (1986)
kwargs control the :class:`~matplotlib.lines.Line2D`
properties of the coherence plot:
%(Line2D)s
**Example:**
.. plot:: mpl_examples/pylab_examples/cohere_demo.py
"""
if not self._hold: self.cla()
cxy, freqs = mlab.cohere(x, y, NFFT, Fs, detrend, window, noverlap,
scale_by_freq)
freqs += Fc
self.plot(freqs, cxy, **kwargs)
self.set_xlabel('Frequency')
self.set_ylabel('Coherence')
self.grid(True)
return cxy, freqs
cohere.__doc__ = cbook.dedent(cohere.__doc__) % psd_doc_dict
def specgram(self, x, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
window=mlab.window_hanning, noverlap=128,
cmap=None, xextent=None, pad_to=None, sides='default',
scale_by_freq=None):
"""
call signature::
specgram(x, NFFT=256, Fs=2, Fc=0, detrend=mlab.detrend_none,
window=mlab.window_hanning, noverlap=128,
cmap=None, xextent=None, pad_to=None, sides='default',
scale_by_freq=None)
Compute a spectrogram of data in *x*. Data are split into
*NFFT* length segments and the PSD of each section is
computed. The windowing function *window* is applied to each
segment, and the amount of overlap of each segment is
specified with *noverlap*.
%(PSD)s
*Fc*: integer
The center frequency of *x* (defaults to 0), which offsets
the y extents of the plot to reflect the frequency range used
when a signal is acquired and then filtered and downsampled to
baseband.
*cmap*:
A :class:`matplotlib.cm.Colormap` instance; if *None* use
default determined by rc
*xextent*:
The image extent along the x-axis. xextent = (xmin,xmax)
The default is (0,max(bins)), where bins is the return
value from :func:`mlab.specgram`
Return value is (*Pxx*, *freqs*, *bins*, *im*):
- *bins* are the time points the spectrogram is calculated over
- *freqs* is an array of frequencies
- *Pxx* is a len(times) x len(freqs) array of power
- *im* is a :class:`matplotlib.image.AxesImage` instance
Note: If *x* is real (i.e. non-complex), only the positive
spectrum is shown. If *x* is complex, both positive and
negative parts of the spectrum are shown. This can be
overridden using the *sides* keyword argument.
**Example:**
.. plot:: mpl_examples/pylab_examples/specgram_demo.py
"""
if not self._hold: self.cla()
Pxx, freqs, bins = mlab.specgram(x, NFFT, Fs, detrend,
window, noverlap, pad_to, sides, scale_by_freq)
Z = 10. * np.log10(Pxx)
Z = np.flipud(Z)
if xextent is None: xextent = 0, np.amax(bins)
xmin, xmax = xextent
freqs += Fc
extent = xmin, xmax, freqs[0], freqs[-1]
im = self.imshow(Z, cmap, extent=extent)
self.axis('auto')
return Pxx, freqs, bins, im
specgram.__doc__ = cbook.dedent(specgram.__doc__) % psd_doc_dict
del psd_doc_dict #So that this does not become an Axes attribute
def spy(self, Z, precision=0, marker=None, markersize=None,
aspect='equal', **kwargs):
"""
call signature::
spy(Z, precision=0, marker=None, markersize=None,
aspect='equal', **kwargs)
``spy(Z)`` plots the sparsity pattern of the 2-D array *Z*.
If *precision* is 0, any non-zero value will be plotted;
else, values of :math:`|Z| > precision` will be plotted.
For :class:`scipy.sparse.spmatrix` instances, there is a
special case: if *precision* is 'present', any value present in
the array will be plotted, even if it is identically zero.
The array will be plotted as it would be printed, with
the first index (row) increasing down and the second
index (column) increasing to the right.
By default aspect is 'equal', so that each array element
occupies a square space; set the aspect kwarg to 'auto'
to allow the plot to fill the plot box, or to any scalar
number to specify the aspect ratio of an array element
directly.
Two plotting styles are available: image or marker. Both
are available for full arrays, but only the marker style
works for :class:`scipy.sparse.spmatrix` instances.
If *marker* and *markersize* are *None*, an image will be
returned and any remaining kwargs are passed to
:func:`~matplotlib.pyplot.imshow`; else, a
:class:`~matplotlib.lines.Line2D` object will be returned with
the value of marker determining the marker type, and any
remaining kwargs passed to the
:meth:`~matplotlib.axes.Axes.plot` method.
If *marker* and *markersize* are *None*, useful kwargs include:
* *cmap*
* *alpha*
.. seealso::
:func:`~matplotlib.pyplot.imshow`
For controlling colors, e.g. cyan background and red marks,
use::
cmap = mcolors.ListedColormap(['c','r'])
If *marker* or *markersize* is not *None*, useful kwargs include:
* *marker*
* *markersize*
* *color*
Useful values for *marker* include:
* 's' square (default)
* 'o' circle
* '.' point
* ',' pixel
.. seealso::
:func:`~matplotlib.pyplot.plot`
"""
if precision is None:
precision = 0
warnings.DeprecationWarning("Use precision=0 instead of None")
# 2008/10/03
if marker is None and markersize is None and hasattr(Z, 'tocoo'):
marker = 's'
if marker is None and markersize is None:
Z = np.asarray(Z)
mask = np.absolute(Z)>precision
if 'cmap' not in kwargs:
kwargs['cmap'] = mcolors.ListedColormap(['w', 'k'],
name='binary')
nr, nc = Z.shape
extent = [-0.5, nc-0.5, nr-0.5, -0.5]
ret = self.imshow(mask, interpolation='nearest', aspect=aspect,
extent=extent, origin='upper', **kwargs)
else:
if hasattr(Z, 'tocoo'):
c = Z.tocoo()
if precision == 'present':
y = c.row
x = c.col
else:
nonzero = np.absolute(c.data) > precision
y = c.row[nonzero]
x = c.col[nonzero]
else:
Z = np.asarray(Z)
nonzero = np.absolute(Z)>precision
y, x = np.nonzero(nonzero)
if marker is None: marker = 's'
if markersize is None: markersize = 10
marks = mlines.Line2D(x, y, linestyle='None',
marker=marker, markersize=markersize, **kwargs)
self.add_line(marks)
nr, nc = Z.shape
self.set_xlim(xmin=-0.5, xmax=nc-0.5)
self.set_ylim(ymin=nr-0.5, ymax=-0.5)
self.set_aspect(aspect)
ret = marks
self.title.set_y(1.05)
self.xaxis.tick_top()
self.xaxis.set_ticks_position('both')
self.xaxis.set_major_locator(mticker.MaxNLocator(nbins=9,
steps=[1, 2, 5, 10],
integer=True))
self.yaxis.set_major_locator(mticker.MaxNLocator(nbins=9,
steps=[1, 2, 5, 10],
integer=True))
return ret
def matshow(self, Z, **kwargs):
'''
Plot a matrix or array as an image.
The matrix will be shown the way it would be printed,
with the first row at the top. Row and column numbering
is zero-based.
Argument:
*Z* anything that can be interpreted as a 2-D array
kwargs all are passed to :meth:`~matplotlib.axes.Axes.imshow`.
:meth:`matshow` sets defaults for *extent*, *origin*,
*interpolation*, and *aspect*; use care in overriding the
*extent* and *origin* kwargs, because they interact. (Also,
if you want to change them, you probably should be using
imshow directly in your own version of matshow.)
Returns: an :class:`matplotlib.image.AxesImage` instance.
'''
Z = np.asarray(Z)
nr, nc = Z.shape
extent = [-0.5, nc-0.5, nr-0.5, -0.5]
kw = {'extent': extent,
'origin': 'upper',
'interpolation': 'nearest',
'aspect': 'equal'} # (already the imshow default)
kw.update(kwargs)
im = self.imshow(Z, **kw)
self.title.set_y(1.05)
self.xaxis.tick_top()
self.xaxis.set_ticks_position('both')
self.xaxis.set_major_locator(mticker.MaxNLocator(nbins=9,
steps=[1, 2, 5, 10],
integer=True))
self.yaxis.set_major_locator(mticker.MaxNLocator(nbins=9,
steps=[1, 2, 5, 10],
integer=True))
return im
class SubplotBase:
"""
Base class for subplots, which are :class:`Axes` instances with
additional methods to facilitate generating and manipulating a set
of :class:`Axes` within a figure.
"""
def __init__(self, fig, *args, **kwargs):
"""
*fig* is a :class:`matplotlib.figure.Figure` instance.
*args* is the tuple (*numRows*, *numCols*, *plotNum*), where
the array of subplots in the figure has dimensions *numRows*,
*numCols*, and where *plotNum* is the number of the subplot
being created. *plotNum* starts at 1 in the upper left
corner and increases to the right.
If *numRows* <= *numCols* <= *plotNum* < 10, *args* can be the
decimal integer *numRows* * 100 + *numCols* * 10 + *plotNum*.
"""
self.figure = fig
if len(args)==1:
s = str(args[0])
if len(s) != 3:
raise ValueError('Argument to subplot must be a 3 digits long')
rows, cols, num = map(int, s)
elif len(args)==3:
rows, cols, num = args
else:
raise ValueError( 'Illegal argument to subplot')
total = rows*cols
num -= 1 # convert from matlab to python indexing
# ie num in range(0,total)
if num >= total:
raise ValueError( 'Subplot number exceeds total subplots')
self._rows = rows
self._cols = cols
self._num = num
self.update_params()
# _axes_class is set in the subplot_class_factory
self._axes_class.__init__(self, fig, self.figbox, **kwargs)
def get_geometry(self):
'get the subplot geometry, eg 2,2,3'
return self._rows, self._cols, self._num+1
# COVERAGE NOTE: Never used internally or from examples
def change_geometry(self, numrows, numcols, num):
'change subplot geometry, eg. from 1,1,1 to 2,2,3'
self._rows = numrows
self._cols = numcols
self._num = num-1
self.update_params()
self.set_position(self.figbox)
def update_params(self):
'update the subplot position from fig.subplotpars'
rows = self._rows
cols = self._cols
num = self._num
pars = self.figure.subplotpars
left = pars.left
right = pars.right
bottom = pars.bottom
top = pars.top
wspace = pars.wspace
hspace = pars.hspace
totWidth = right-left
totHeight = top-bottom
figH = totHeight/(rows + hspace*(rows-1))
sepH = hspace*figH
figW = totWidth/(cols + wspace*(cols-1))
sepW = wspace*figW
rowNum, colNum = divmod(num, cols)
figBottom = top - (rowNum+1)*figH - rowNum*sepH
figLeft = left + colNum*(figW + sepW)
self.figbox = mtransforms.Bbox.from_bounds(figLeft, figBottom,
figW, figH)
self.rowNum = rowNum
self.colNum = colNum
self.numRows = rows
self.numCols = cols
if 0:
print 'rcn', rows, cols, num
print 'lbrt', left, bottom, right, top
print 'self.figBottom', self.figBottom
print 'self.figLeft', self.figLeft
print 'self.figW', self.figW
print 'self.figH', self.figH
print 'self.rowNum', self.rowNum
print 'self.colNum', self.colNum
print 'self.numRows', self.numRows
print 'self.numCols', self.numCols
def is_first_col(self):
return self.colNum==0
def is_first_row(self):
return self.rowNum==0
def is_last_row(self):
return self.rowNum==self.numRows-1
def is_last_col(self):
return self.colNum==self.numCols-1
# COVERAGE NOTE: Never used internally or from examples
def label_outer(self):
"""
set the visible property on ticklabels so xticklabels are
visible only if the subplot is in the last row and yticklabels
are visible only if the subplot is in the first column
"""
lastrow = self.is_last_row()
firstcol = self.is_first_col()
for label in self.get_xticklabels():
label.set_visible(lastrow)
for label in self.get_yticklabels():
label.set_visible(firstcol)
_subplot_classes = {}
def subplot_class_factory(axes_class=None):
# This makes a new class that inherits from SubclassBase and the
# given axes_class (which is assumed to be a subclass of Axes).
# This is perhaps a little bit roundabout to make a new class on
# the fly like this, but it means that a new Subplot class does
# not have to be created for every type of Axes.
if axes_class is None:
axes_class = Axes
new_class = _subplot_classes.get(axes_class)
if new_class is None:
new_class = new.classobj("%sSubplot" % (axes_class.__name__),
(SubplotBase, axes_class),
{'_axes_class': axes_class})
_subplot_classes[axes_class] = new_class
return new_class
# This is provided for backward compatibility
Subplot = subplot_class_factory()
martist.kwdocd['Axes'] = martist.kwdocd['Subplot'] = martist.kwdoc(Axes)
"""
# this is some discarded code I was using to find the minimum positive
# data point for some log scaling fixes. I realized there was a
# cleaner way to do it, but am keeping this around as an example for
# how to get the data out of the axes. Might want to make something
# like this a method one day, or better yet make get_verts an Artist
# method
minx, maxx = self.get_xlim()
if minx<=0 or maxx<=0:
# find the min pos value in the data
xs = []
for line in self.lines:
xs.extend(line.get_xdata(orig=False))
for patch in self.patches:
xs.extend([x for x,y in patch.get_verts()])
for collection in self.collections:
xs.extend([x for x,y in collection.get_verts()])
posx = [x for x in xs if x>0]
if len(posx):
minx = min(posx)
maxx = max(posx)
# warning, probably breaks inverted axis
self.set_xlim((0.1*minx, maxx))
"""
| gpl-3.0 |
fabioticconi/scikit-learn | benchmarks/bench_plot_lasso_path.py | 301 | 4003 | """Benchmarks of Lasso regularization path computation using Lars and CD
The input data is mostly low rank but is a fat infinite tail.
"""
from __future__ import print_function
from collections import defaultdict
import gc
import sys
from time import time
import numpy as np
from sklearn.linear_model import lars_path
from sklearn.linear_model import lasso_path
from sklearn.datasets.samples_generator import make_regression
def compute_bench(samples_range, features_range):
it = 0
results = defaultdict(lambda: [])
max_it = len(samples_range) * len(features_range)
for n_samples in samples_range:
for n_features in features_range:
it += 1
print('====================')
print('Iteration %03d of %03d' % (it, max_it))
print('====================')
dataset_kwargs = {
'n_samples': n_samples,
'n_features': n_features,
'n_informative': n_features / 10,
'effective_rank': min(n_samples, n_features) / 10,
#'effective_rank': None,
'bias': 0.0,
}
print("n_samples: %d" % n_samples)
print("n_features: %d" % n_features)
X, y = make_regression(**dataset_kwargs)
gc.collect()
print("benchmarking lars_path (with Gram):", end='')
sys.stdout.flush()
tstart = time()
G = np.dot(X.T, X) # precomputed Gram matrix
Xy = np.dot(X.T, y)
lars_path(X, y, Xy=Xy, Gram=G, method='lasso')
delta = time() - tstart
print("%0.3fs" % delta)
results['lars_path (with Gram)'].append(delta)
gc.collect()
print("benchmarking lars_path (without Gram):", end='')
sys.stdout.flush()
tstart = time()
lars_path(X, y, method='lasso')
delta = time() - tstart
print("%0.3fs" % delta)
results['lars_path (without Gram)'].append(delta)
gc.collect()
print("benchmarking lasso_path (with Gram):", end='')
sys.stdout.flush()
tstart = time()
lasso_path(X, y, precompute=True)
delta = time() - tstart
print("%0.3fs" % delta)
results['lasso_path (with Gram)'].append(delta)
gc.collect()
print("benchmarking lasso_path (without Gram):", end='')
sys.stdout.flush()
tstart = time()
lasso_path(X, y, precompute=False)
delta = time() - tstart
print("%0.3fs" % delta)
results['lasso_path (without Gram)'].append(delta)
return results
if __name__ == '__main__':
from mpl_toolkits.mplot3d import axes3d # register the 3d projection
import matplotlib.pyplot as plt
samples_range = np.linspace(10, 2000, 5).astype(np.int)
features_range = np.linspace(10, 2000, 5).astype(np.int)
results = compute_bench(samples_range, features_range)
max_time = max(max(t) for t in results.values())
fig = plt.figure('scikit-learn Lasso path benchmark results')
i = 1
for c, (label, timings) in zip('bcry', sorted(results.items())):
ax = fig.add_subplot(2, 2, i, projection='3d')
X, Y = np.meshgrid(samples_range, features_range)
Z = np.asarray(timings).reshape(samples_range.shape[0],
features_range.shape[0])
# plot the actual surface
ax.plot_surface(X, Y, Z.T, cstride=1, rstride=1, color=c, alpha=0.8)
# dummy point plot to stick the legend to since surface plot do not
# support legends (yet?)
#ax.plot([1], [1], [1], color=c, label=label)
ax.set_xlabel('n_samples')
ax.set_ylabel('n_features')
ax.set_zlabel('Time (s)')
ax.set_zlim3d(0.0, max_time * 1.1)
ax.set_title(label)
#ax.legend()
i += 1
plt.show()
| bsd-3-clause |
FluidityProject/multifluids | tests/sloshing_tank/plot_freesurface.py | 5 | 2631 | #!/usr/bin/env python
import settings
import ana_sol
import sys
import math
import commands
import matplotlib.pyplot as plt
import getopt
from scipy.special import erf
from numpy import poly1d
from matplotlib.pyplot import figure, show
from numpy import pi, sin, linspace
from matplotlib.mlab import stineman_interp
from numpy import exp, cos
from fluidity_tools import stat_parser as stat
# Usage
def usage():
print "plt_freesurface.py --file=detectorfile"
print "All the other options are read from settings.py"
################# Main ###########################
def main(argv=None):
a_0 = settings.a0 # initial maximum perturbation
g = settings.g # gravity
eta= settings.eta # viscosity
L= settings.L # wavelength
timestep= settings.timestep # timestep
filename=''
global debug
debug=False
#debug=True
try:
opts, args = getopt.getopt(sys.argv[1:], "h:", ['file='])
except getopt.GetoptError:
usage()
sys.exit(2)
for opt, arg in opts:
if opt == '--file':
filename=arg
elif opt == '-h' or opt == '--help':
usage()
sys.exit(2)
if filename=='':
usage()
sys.exit(2)
print 'Using:\n\ta_0 =', a_0 # initial maximum perturbation
print '\tg =', g # gravity
print '\teta=', eta # viscosity
print '\tL=', L # wavelength
print '\ttimestep=', timestep # timestep
####################### Print time plot ###########################
print 'Generating time plot'
x_time= stat(filename)["ElapsedTime"]["value"]
fs_simu= stat(filename)["water"]["FreeSurface"]["left"]
# fs_simu= stat(filename)["water"]["FreeSurface"]["middle"]
fs_ana = stat(filename)["water"]["FreeSurface_Analytical"]["left"]
# fs_ana = stat(filename)["water"]["FreeSurface_Analytical"]["middle"]
plt.ion() # swith on interactive mode
fig = figure()
ax = fig.add_subplot(111)
ax.plot(x_time,fs_simu,'ro')
ax.plot(x_time,fs_ana,'-')
plt.title('Free Surface timeplot at x=0')
plt.xlabel('Time [s]')
plt.ylabel('Free surface [m]')
plt.draw()
raw_input("Please press Enter")
#plt.cla()
if __name__ == "__main__":
main()
| lgpl-2.1 |
mupif/mupif | mupif/Field.py | 1 | 42683 | #
# MuPIF: Multi-Physics Integration Framework
# Copyright (C) 2010-2015 Borek Patzak
#
# Czech Technical University, Faculty of Civil Engineering,
# Department of Structural Mechanics, 166 29 Prague, Czech Republic
#
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License as published by the Free Software Foundation; either
# version 2.1 of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with this library; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor,
# Boston, MA 02110-1301 USA
#
from builtins import range
from builtins import object
from . import Cell
from . import FieldID
from . import ValueType
from . import BBox
from . import APIError
from . import MupifObject
from . import Mesh
from .Physics import PhysicalQuantities
from .Physics.PhysicalQuantities import PhysicalQuantity
from numpy import array, arange, random, zeros
import numpy
import copy
import Pyro4
from enum import IntEnum
import logging
log = logging.getLogger()
try:
import cPickle as pickle # faster serialization if available
except:
import pickle
# import logging - never use it here, it causes cPickle.PicklingError: Can't pickle <type 'thread.lock'>: attribute
# lookup thread.lock failed
# debug flag
debug = 0
class FieldType(IntEnum):
"""
Represent the supported values of FieldType, i.e. FT_vertexBased or FT_cellBased.
"""
FT_vertexBased = 1
FT_cellBased = 2
@Pyro4.expose
class Field(MupifObject.MupifObject, PhysicalQuantity):
"""
Representation of field. Field is a scalar, vector, or tensorial
quantity defined on a spatial domain. The field, however is assumed
to be fixed at certain time. The field can be evaluated in any spatial point
belonging to underlying domain.
Derived classes will implement fields defined on common discretizations,
like fields defined on structured/unstructured FE meshes, FD grids, etc.
.. automethod:: __init__
.. automethod:: _evaluate
"""
def __init__(self, mesh, fieldID, valueType, units, time, values=None, fieldType=FieldType.FT_vertexBased, objectID=0, metaData={}):
"""
Initializes the field instance.
:param Mesh.Mesh mesh: Instance of a Mesh class representing the underlying discretization
:param FieldID fieldID: Field type (displacement, strain, temperature ...)
:param ValueType valueType: Type of field values (scalar, vector, tensor). Tensor is a tuple of 9 values. It is changed to 3x3 for VTK output automatically.
:param Physics.PhysicalUnits units: Field value units
:param Physics.PhysicalQuantity time: Time associated with field values
:param values: Field values (format dependent on a particular field type, however each individual value should be stored as tuple, even scalar value)
:type values: list of tuples representing individual values
:param FieldType fieldType: Optional, determines field type (values specified as vertex or cell values), default is FT_vertexBased
:param int objectID: Optional ID of problem object/subdomain to which field is related, default = 0
:param dict metaData: Optionally pass metadata for merging
"""
super(Field, self).__init__()
self.mesh = mesh
self.fieldID = fieldID
self.valueType = valueType
self.time = time
self.uri = None # pyro uri; used in distributed setting
# self.log = logging.getLogger()
self.fieldType = fieldType
self.objectID = objectID
if values is None:
if self.fieldType == FieldType.FT_vertexBased:
ncomponents = mesh.getNumberOfVertices()
else:
ncomponents = mesh.getNumberOfCells()
self.value = zeros((ncomponents, self.getRecordSize()))
else:
self.value = values
if PhysicalQuantities.isPhysicalUnit(units):
self.unit = units
else:
self.unit = PhysicalQuantities.findUnit(units)
self.setMetadata('Units', self.unit.name())
self.setMetadata('Type', 'mupif.Field.Field')
self.setMetadata('Type_ID', str(self.fieldID))
self.setMetadata('FieldType', str(fieldType))
self.setMetadata('ValueType', str(self.valueType))
self.updateMetadata(metaData)
@classmethod
def loadFromLocalFile(cls, fileName):
"""
Alternative constructor which loads instance directly from a Pickle module.
:param str fileName: File name
:return: Returns Field instance
:rtype: Field
"""
return pickle.load(open(fileName, 'rb'))
def getRecordSize(self):
"""
Return the number of scalars per value, depending on :obj:`valueType` passed when constructing the instance.
:return: number of scalars (1,3,9 respectively for scalar, vector, tensor)
:rtype: int
"""
if self.valueType == ValueType.Scalar:
return 1
elif self.valueType == ValueType.Vector:
return 3
elif self.valueType == ValueType.Tensor:
return 9
else:
raise ValueError("Invalid value of Field.valueType (%d)." % self.valueType)
def getMesh(self):
"""
Obtain mesh.
:return: Returns a mesh of underlying discretization
:rtype: Mesh.Mesh
"""
return self.mesh
def getValueType(self):
"""
Returns ValueType of the field, e.g. scalar, vector, tensor.
:return: Returns value type of the receiver
:rtype: ValueType
"""
return self.valueType
def getFieldID(self):
"""
Returns FieldID, e.g. FID_Displacement, FID_Temperature.
:return: Returns field ID
:rtype: FieldID
"""
return self.fieldID
def getFieldIDName(self):
"""
Returns name of the field.
:return: Returns fieldID name
:rtype: string
"""
return self.fieldID.name
def getFieldType(self):
"""
Returns receiver field type (values specified as vertex or cell values)
:return: Returns fieldType id
:rtype: FieldType
"""
return self.fieldType
def getTime(self):
"""
Get time of the field.
:return: Time of field data
:rtype: Physics.PhysicalQuantity
"""
return self.time
def evaluate(self, positions, eps=0.0):
"""
Evaluates the receiver at given spatial position(s).
:param positions: 1D/2D/3D position vectors
:type positions: tuple, a list of tuples
:param float eps: Optional tolerance for probing whether the point belongs to a cell (should really not be used)
:return: field value(s)
:rtype: Physics.PhysicalQuantity with given value or tuple of values
"""
# test if positions is a list of positions
if isinstance(positions, list):
ans = []
for pos in positions:
ans.append(self._evaluate(pos, eps))
return PhysicalQuantity(ans, self.unit)
else:
# single position passed
return PhysicalQuantity(self._evaluate(positions, eps), self.unit)
def _evaluate(self, position, eps):
"""
Evaluates the receiver at a single spatial position.
:param tuple position: 1D/2D/3D position vector
:param float eps: Optional tolerance
:return: field value
:rtype: tuple of doubles
.. note:: This method has some issues related to https://sourceforge.net/p/mupif/tickets/22/ .
"""
cells = self.mesh.giveCellLocalizer().giveItemsInBBox(BBox.BBox([c-eps for c in position], [c+eps for c in position]))
# answer=None
if len(cells):
if self.fieldType == FieldType.FT_vertexBased:
for icell in cells:
try:
if icell.containsPoint(position):
if debug:
log.debug(icell.getVertices())
try:
answer = icell.interpolate(position, [self.value[i.number] for i in icell.getVertices()])
except IndexError:
log.error('Field::evaluate failed, inconsistent data at cell %d' % icell.label)
raise
return answer
except ZeroDivisionError:
print('ZeroDivisionError?')
log.debug(icell.number)
log.debug(position)
icell.debug = 1
log.debug(icell.containsPoint(position), icell.glob2loc(position))
log.error('Field::evaluate - no source cell found for position %s' % str(position))
for icell in cells:
log.debug(icell.number)
log.debug(icell.containsPoint(position))
log.debug(icell.glob2loc(position))
else: # if (self.fieldType == FieldType.FT_vertexBased):
# in case of cell based fields do compute average of cell values containing point
# this typically happens when point is on the shared edge or vertex
count = 0
for icell in cells:
if icell.containsPoint(position):
if debug:
log.debug(icell.getVertices())
try:
tmp = self.value[icell.number]
if count == 0:
answer = list(tmp)
else:
for i in answer:
answer = [x+y for x in answer for y in tmp]
count += 1
except IndexError:
log.error('Field::evaluate failed, inconsistent data at cell %d' % icell.label)
log.error(icell.getVertices())
raise
# end loop over icells
if count == 0:
log.error('Field::evaluate - no source cell found for position %s', str(position))
# for icell in cells:
# log.debug(icell.number, icell.containsPoint(position), icell.glob2loc(position))
else:
answer = [x/count for x in answer]
return answer
else:
# no source cell found
log.error('Field::evaluate - no source cell found for position ' + str(position))
raise ValueError('Field::evaluate - no source cell found for position ' + str(position))
def getVertexValue(self, vertexID):
"""
Returns the value associated with a given vertex.
:param int vertexID: Vertex identifier
:return: The value
:rtype: Physics.PhysicalQuantity
"""
if self.fieldType == FieldType.FT_vertexBased:
return PhysicalQuantity(self.value[vertexID], self.unit)
else:
raise TypeError('Attempt to acces vertex value of cell based field, use evaluate instead')
def getCellValue(self, cellID):
"""
Returns the value associated with a given cell.
:param int cellID: Cell identifier
:return: The value
:rtype: Physics.PhysicalQuantity
"""
if self.fieldType == FieldType.FT_cellBased:
return PhysicalQuantity(self.value[cellID], self.unit)
else:
raise TypeError('Attempt to acces cell value of vertex based field, use evaluate instead')
def _giveValue(self, componentID):
"""
Returns the value associated with a given component (vertex or cell).
Depreceated, use getVertexValue() or getCellValue()
:param int componentID: An identifier of a component: vertexID or cellID
:return: The value
:rtype: Physics.PhysicalQuantity
"""
return PhysicalQuantity(self.value[componentID], self.unit)
def giveValue(self, componentID):
"""
Returns the value associated with a given component (vertex or cell).
:param int componentID: An identifier of a component: vertexID or cellID
:return: The value
:rtype: tuple
"""
return self.value[componentID]
def setValue(self, componentID, value):
"""
Sets the value associated with a given component (vertex or cell).
:param int componentID: An identifier of a component: vertexID or cellID
:param tuple value: Value to be set for a given component, should have the same units as receiver
.. Note:: If a mesh has mapping attached (a mesh view) then we have to remember value locally and record change. The source field values are updated after commit() method is invoked.
"""
self.value[componentID] = value
def commit(self):
"""
Commits the recorded changes (via setValue method) to a primary field.
"""
def getObjectID(self):
"""
Returns field objectID.
:return: Object's ID
:rtype: int
"""
return self.objectID
def getUnits(self):
"""
:return: Returns units of the receiver
:rtype: Physics.PhysicalUnits
"""
return self.unit
def merge(self, field):
"""
Merges the receiver with given field together. Both fields should be on different parts of the domain (can also overlap), but should refer to same underlying discretization, otherwise unpredictable results can occur.
:param Field field: given field to merge with.
"""
# first merge meshes
mesh = copy.deepcopy(self.mesh)
mesh.merge(field.mesh)
log.debug(mesh)
# merge the field values
# some type checking first
if self.fieldType != field.fieldType:
raise TypeError("Field::merge: fieldType of receiver and parameter is different")
if self.fieldType == FieldType.FT_vertexBased:
values = [0]*mesh.getNumberOfVertices()
for v in range(self.mesh.getNumberOfVertices()):
values[mesh.vertexLabel2Number(self.mesh.getVertex(v).label)] = self.value[v]
for v in range(field.mesh.getNumberOfVertices()):
values[mesh.vertexLabel2Number(field.mesh.getVertex(v).label)] = field.value[v]
else:
values = [0]*mesh.getNumberOfCells()
for v in range(self.mesh.getNumberOfCells()):
values[mesh.cellLabel2Number(self.mesh.giveCell(v).label)] = self.value[v]
for v in range(field.mesh.getNumberOfCells()):
values[mesh.cellLabel2Number(field.mesh.giveCell(v).label)] = field.value[v]
self.mesh = mesh
self.value = values
def field2VTKData (self, name=None, lookupTable=None):
"""
Creates VTK representation of the receiver. Useful for visualization. Requires pyvtk module.
:param str name: human-readable name of the field
:param pyvtk.LookupTable lookupTable: color lookup table
:return: Instance of pyvtk
:rtype: pyvtk.VtkData
"""
import pyvtk
if name is None:
name = self.getFieldIDName()
if lookupTable and not isinstance(lookupTable, pyvtk.LookupTable):
log.info('ignoring lookupTable which is not a pyvtk.LookupTable instance.')
lookupTable = None
if lookupTable is None:
lookupTable=pyvtk.LookupTable([(0, .231, .298, 1.0), (.4, .865, .865, 1.0), (.8, .706, .016, 1.0)], name='coolwarm')
# Scalars use different name than 'coolwarm'. Then Paraview uses its own color mapping instead of taking
# 'coolwarm' from *.vtk file. This prevents setting Paraview's color mapping.
scalarsKw = dict(name=name, lookup_table='default')
else:
scalarsKw = dict(name=name, lookup_table=lookupTable.name)
# see http://cens.ioc.ee/cgi-bin/cvsweb/python/pyvtk/examples/example1.py?rev=1.3 for an example
vectorsKw = dict(name=name) # vectors don't have a lookup_table
if self.fieldType == FieldType.FT_vertexBased:
if self.getValueType() == ValueType.Scalar:
return pyvtk.VtkData(self.mesh.getVTKRepresentation(), pyvtk.PointData(pyvtk.Scalars([val[0] for val in self.value], **scalarsKw), lookupTable), 'Unstructured Grid Example')
elif self.getValueType() == ValueType.Vector:
return pyvtk.VtkData(self.mesh.getVTKRepresentation(), pyvtk.PointData(pyvtk.Vectors(self.value, **vectorsKw), lookupTable), 'Unstructured Grid Example')
elif self.getValueType() == ValueType.Tensor:
return pyvtk.VtkData(self.mesh.getVTKRepresentation(), pyvtk.PointData(pyvtk.Tensors(self.getMartixForTensor(self.value), **vectorsKw), lookupTable), 'Unstructured Grid Example')
else:
if self.getValueType() == ValueType.Scalar:
return pyvtk.VtkData(self.mesh.getVTKRepresentation(), pyvtk.CellData(pyvtk.Scalars([val[0] for val in self.value], **scalarsKw), lookupTable), 'Unstructured Grid Example')
elif self.getValueType() == ValueType.Vector:
return pyvtk.VtkData(self.mesh.getVTKRepresentation(), pyvtk.CellData(pyvtk.Vectors(self.value, **vectorsKw),lookupTable), 'Unstructured Grid Example')
elif self.getValueType() == ValueType.Tensor:
return pyvtk.VtkData(self.mesh.getVTKRepresentation(), pyvtk.CellData(pyvtk.Tensors(self.getMartixForTensor(self.value), **vectorsKw), lookupTable), 'Unstructured Grid Example')
def getMartixForTensor(self, values):
"""
Reshape values to a list with 3x3 arrays. Usable for VTK export.
:param list values: List containing tuples of 9 values, e.g. [(1,2,3,4,5,6,7,8,9), (1,2,3,4,5,6,7,8,9), ...]
:return: List containing 3x3 matrices for each tensor
:rtype: list
"""
tensor = []
for i in values:
tensor.append(numpy.reshape(i, (3, 3)))
return tensor
def dumpToLocalFile(self, fileName, protocol=pickle.HIGHEST_PROTOCOL):
"""
Dump Field to a file using a Pickle serialization module.
:param str fileName: File name
:param int protocol: Used protocol - 0=ASCII, 1=old binary, 2=new binary
"""
pickle.dump(self, open(fileName, 'wb'), protocol)
def field2Image2D(self, plane='xy', elevation=(-1.e-6, 1.e-6), numX=10, numY=20, interp='linear', fieldComponent=0, vertex=True, colorBar='horizontal', colorBarLegend='', barRange=(None, None), barFormatNum='%.3g', title='', xlabel='', ylabel='', fileName='', show=True, figsize=(8, 4), matPlotFig=None):
"""
Plots and/or saves 2D image using a matplotlib library. Works for structured and unstructured 2D/3D fields. 2D/3D fields need to define plane. This method gives only basic viewing options, for aesthetic and more elaborated output use e.g. VTK field export with
postprocessors such as ParaView or Mayavi. Idea from https://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html#id1
:param str plane: what plane to extract from field, valid values are 'xy', 'xz', 'yz'
:param tuple elevation: range of third coordinate. For example, in plane='xy' is grabs z coordinates in the range
:param int numX: number of divisions on x graph axis
:param int numY: number of divisions on y graph axis
:param str interp: interpolation type when transferring to a grid. Valid values 'linear', 'nearest' or 'cubic'
:param int fieldComponent: component of the field
:param bool vertex: if vertices shoud be plot as points
:param str colorBar: color bar details. Valid values '' for no colorbar, 'vertical' or 'horizontal'
:param str colorBarLegend: Legend for color bar. If '', current field name and units are printed. None prints nothing.
:param tuple barRange: min and max bar range. If barRange=('NaN','NaN'), it is adjusted automatically
:param str barFormatNum: format of color bar numbers
:param str title: title
:param str xlabel: x axis label
:param str ylabel: y axis label
:param str fileName: if nonempty, a filename is written to the disk, usually png, pdf, ps, eps and svg are supported
:param bool show: if the plot should be showed
:param tuple figsize: size of canvas in inches. Affects only showing a figure. Image to a file adjust one side automatically.
:param obj matPlotFig: False means plot window remains in separate thread, True waits until a plot window becomes closed
:return: handle to matPlotFig
:rtype: matPlotFig
"""
try:
import numpy as np
import math
from scipy.interpolate import griddata
import matplotlib
matplotlib.use('TkAgg') # Qt4Agg gives an empty, black window
import matplotlib.pyplot as plt
except ImportError as e:
log.error('Skipping field2Image2D due to missing modules: %s' % e)
return None
# raise
if self.fieldType != FieldType.FT_vertexBased:
raise APIError.APIError('Only FieldType.FT_vertexBased is now supported')
mesh = self.getMesh()
numVertices = mesh.getNumberOfVertices()
indX = 0
indY = 0
elev = 0
if plane == 'xy':
indX = 0
indY = 1
elev = 2
elif plane == 'xz':
indX = 0
indY = 2
elev = 1
elif plane == 'yz':
indX = 1
indY = 2
elev = 0
# find eligible vertex points and values
vertexPoints = []
vertexValue = []
for i in range(0, numVertices):
coords = mesh.getVertex(i).getCoordinates()
# print(coords)
value = self.giveValue(i)[fieldComponent]
if elevation[1] > coords[elev] > elevation[0]:
vertexPoints.append((coords[indX], coords[indY]))
vertexValue.append(value)
if len(vertexPoints) == 0:
log.info('No valid vertex points found, putting zeros on domain 1 x 1')
for i in range(5):
vertexPoints.append((i % 2, i/4.))
vertexValue.append(0)
# for i in range (0, len(vertexPoints)):
# print (vertexPoints[i], vertexValue[i])
vertexPointsArr = np.array(vertexPoints)
vertexValueArr = np.array(vertexValue)
xMin = vertexPointsArr[:, 0].min()
xMax = vertexPointsArr[:, 0].max()
yMin = vertexPointsArr[:, 1].min()
yMax = vertexPointsArr[:, 1].max()
# print(xMin, xMax, yMin, yMax)
grid_x, grid_y = np.mgrid[xMin:xMax:complex(0, numX), yMin:yMax:complex(0, numY)]
grid_z1 = griddata(vertexPointsArr, vertexValueArr, (grid_x, grid_y), interp)
# print (grid_z1.T)
plt.ion() # ineractive mode
if matPlotFig is None:
matPlotFig = plt.figure(figsize=figsize)
# plt.xlim(xMin, xMax)
# plt.ylim(yMin, yMax)
plt.clf()
plt.axis((xMin, xMax, yMin, yMax))
image = plt.imshow(grid_z1.T, extent=(xMin, xMax, yMin, yMax), origin='lower', aspect='equal')
# plt.margins(tight=True)
# plt.tight_layout()
# plt.margins(x=-0.3, y=-0.3)
if colorBar:
cbar = plt.colorbar(orientation=colorBar, format=barFormatNum)
if colorBarLegend is not None:
if colorBarLegend == '':
colorBarLegend = self.getFieldIDName() + '_' + str(fieldComponent)
if self.unit is not None:
colorBarLegend = colorBarLegend + ' (' + self.unit.name() + ')'
cbar.set_label(colorBarLegend, rotation=0 if colorBar == 'horizontal' else 90)
if title:
plt.title(title)
if xlabel:
plt.xlabel(xlabel)
if ylabel:
plt.ylabel(ylabel)
if vertex == 1:
plt.scatter(vertexPointsArr[:, 0], vertexPointsArr[:, 1], marker='o', c='b', s=5, zorder=10)
# plt.axis('equal')
# plt.gca().set_aspect('equal', adjustable='box-forced')
if isinstance(barRange[0], float) or isinstance(barRange[0], int):
image.set_clim(vmin=barRange[0], vmax=barRange[1])
if fileName:
plt.savefig(fileName, bbox_inches='tight')
if show:
matPlotFig.canvas.draw()
# plt.ioff()
# plt.show(block=True)
return matPlotFig
def field2Image2DBlock(self):
"""
Block an open window from matPlotLib. Waits until closed.
"""
import matplotlib.pyplot as plt
plt.ioff()
plt.show(block=True)
def toHdf5(self, fileName, group='component1/part1'):
"""
Dump field to HDF5, in a simple format suitable for interoperability (TODO: document).
:param str fileName: HDF5 file
:param str group: HDF5 group the data will be saved under.
The HDF hierarchy is like this::
group
|
+--- mesh_01 {hash=25aa0aa04457}
| +--- [vertex_coords]
| +--- [cell_types]
| \--- [cell_vertices]
+--- mesh_02 {hash=17809e2b86ea}
| +--- [vertex_coords]
| +--- [cell_types]
| \--- [cell_vertices]
+--- ...
+--- field_01
| +--- -> mesh_01
| \--- [vertex_values]
+--- field_02
| +--- -> mesh_01
| \--- [vertex_values]
+--- field_03
| +--- -> mesh_02
| \--- [cell_values]
\--- ...
where ``plain`` names are HDF (sub)groups, ``[bracketed]`` names are datasets, ``{name=value}`` are HDF attributes, ``->`` prefix indicated HDF5 hardlink (transparent to the user); numerical suffixes (``_01``, ...) are auto-allocated. Mesh objects are hardlinked using HDF5 hardlinks if an identical mesh is already stored in the group, based on hexdigest of its full data.
.. note:: This method has not been tested yet. The format is subject to future changes.
"""
import h5py
hdf = h5py.File(fileName, 'a', libver='latest')
if group not in hdf:
gg = hdf.create_group(group)
else:
gg = hdf[group]
# raise IOError('Path "%s" is already used in "%s".'%(path,fileName))
def lowestUnused(trsf, predicate, start=1):
"""
Find the lowest unused index, where *predicate* is used to test for existence, and *trsf* transforms
integer (starting at *start* and incremented until unused value is found) to whatever predicate accepts
as argument. Lowest transformed value is returned.
"""
import itertools
for i in itertools.count(start=start):
t = trsf(i)
if not predicate(t):
return t
# save mesh (not saved if there already)
newgrp = lowestUnused(trsf=lambda i: 'mesh_%02d' % i, predicate=lambda t: t in gg)
mh5 = self.getMesh().asHdf5Object(parentgroup=gg, newgroup=newgrp)
if self.value:
fieldGrp = hdf.create_group(lowestUnused(trsf=lambda i, group=group: group+'/field_%02d' % i, predicate=lambda t: t in hdf))
fieldGrp['mesh'] = mh5
fieldGrp.attrs['fieldID'] = self.fieldID
fieldGrp.attrs['valueType'] = self.valueType
# string/bytes may not contain NULL when stored as string in HDF5
# see http://docs.h5py.org/en/2.3/strings.html
# that's why we cast to opaque type "void" and uncast using tostring before unpickling
fieldGrp.attrs['units'] = numpy.void(pickle.dumps(self.unit))
fieldGrp.attrs['time'] = numpy.void(pickle.dumps(self.time))
# fieldGrp.attrs['time']=self.time.getValue()
if self.fieldType == FieldType.FT_vertexBased:
val = numpy.empty(shape=(self.getMesh().getNumberOfVertices(), self.getRecordSize()), dtype=numpy.float)
for vert in range(self.getMesh().getNumberOfVertices()):
val[vert] = self.getVertexValue(vert).getValue()
fieldGrp['vertex_values'] = val
elif self.fieldType == FieldType.FT_cellBased:
# raise NotImplementedError("Saving cell-based fields to HDF5 is not yet implemented.")
val = numpy.empty(shape=(self.getMesh().getNumberOfCells(), self.getRecordSize()), dtype=numpy.float)
for cell in range(self.getMesh().getNumberOfCells()):
val[cell] = self.getCellValue(cell)
fieldGrp['cell_values'] = val
else:
raise RuntimeError("Unknown fieldType %d." % self.fieldType)
@staticmethod
def makeFromHdf5(fileName, group='component1/part1'):
"""
Restore Fields from HDF5 file.
:param str fileName: HDF5 file
:param str group: HDF5 group the data will be read from (IOError is raised if the group does not exist).
:return: list of new :obj:`Field` instances
:rtype: [Field,Field,...]
.. note:: This method has not been tested yet.
"""
import h5py
hdf = h5py.File(fileName, 'r', libver='latest')
grp = hdf[group]
# load mesh and field data from HDF5
meshObjs = [obj for name, obj in grp.items() if name.startswith('mesh_')]
fieldObjs = [obj for name, obj in grp.items() if name.startswith('field_')]
# construct all meshes as mupif objects
meshes = [Mesh.Mesh.makeFromHdf5Object(meshObj) for meshObj in meshObjs]
# construct all fields as mupif objects
ret = []
for f in fieldObjs:
if 'vertex_values' in f:
fieldType, values = FieldType.FT_vertexBased, f['vertex_values']
elif 'cell_values' in f:
fieldType, values = FieldType.FT_cellBased, f['cell_values']
else:
ValueError("HDF5/mupif format error: unable to determine field type.")
fieldID, valueType, units, time = FieldID(f.attrs['fieldID']), f.attrs['valueType'], f.attrs['units'].tostring(), f.attrs['time'].tostring()
if units == '':
units = None # special case, handled at saving time
else:
units = pickle.loads(units)
if time == '':
time = None # special case, handled at saving time
else:
time = pickle.loads(time)
meshIndex = meshObjs.index(f['mesh']) # find which mesh object this field refers to
ret.append(Field(mesh=meshes[meshIndex], fieldID=fieldID, units=units, time=time, valueType=valueType, values=values, fieldType=fieldType))
return ret
def toVTK2(self, fileName, format='ascii'):
"""
Save the instance as Unstructured Grid in VTK2 format (``.vtk``).
:param str fileName: where to save
:param str format: one of ``ascii`` or ``binary``
"""
self.field2VTKData().tofile(filename=fileName, format=format)
@staticmethod
def makeFromVTK2(fileName, unit, time=0, skip=['coolwarm']):
"""
Return fields stored in *fileName* in the VTK2 (``.vtk``) format.
:param str fileName: filename to load from
:param PhysicalUnit unit: physical unit of filed values
:param float time: time value for created fields (time is not saved in VTK2, thus cannot be recovered)
:param [string,] skip: file names to be skipped when reading the input file; the default value skips the default coolwarm colormap.
:returns: one field from VTK
:rtype: Field
"""
import pyvtk
from .dataID import FieldID
if not fileName.endswith('.vtk'):
log.warning('Field.makeFromVTK2: fileName should end with .vtk, you may get in trouble (proceeding).')
ret = []
try:
data = pyvtk.VtkData(fileName) # this is where reading the file happens (inside pyvtk)
except NotImplementedError:
log.info('pyvtk fails to open (binary?) file "%s", trying through vtk.vtkGenericDataReader.' % fileName)
return Field.makeFromVTK3(fileName, time=time, units=unit, forceVersion2=True)
ugr = data.structure
if not isinstance(ugr, pyvtk.UnstructuredGrid):
raise NotImplementedError(
"grid type %s is not handled by mupif (only UnstructuredGrid is)." % ugr.__class__.__name__)
mesh = Mesh.UnstructuredMesh.makeFromPyvtkUnstructuredGrid(ugr)
# get cell and point data
pd, cd = data.point_data.data, data.cell_data.data
for dd, fieldType in (pd, FieldType.FT_vertexBased), (cd, FieldType.FT_cellBased):
for d in dd:
# will raise KeyError if fieldID with that name is not defined
if d.name in skip:
continue
fid = FieldID[d.name]
# determine the number of components using the expected number of values from the mesh
expectedNumVal = (mesh.getNumberOfVertices() if fieldType == FieldType.FT_vertexBased else mesh.getNumberOfCells())
nc = len(d.scalars)//expectedNumVal
valueType = ValueType.fromNumberOfComponents(nc)
values = [d.scalars[i*nc:i*nc+nc] for i in range(len(d.scalars))]
ret.append(Field(
mesh=mesh,
fieldID=fid,
units=unit, # not stored at all
time=time, # not stored either, set by caller
valueType=valueType,
values=values,
fieldType=fieldType
))
return ret
def toVTK3(self, fileName, **kw):
"""
Save the instance as Unstructured Grid in VTK3 format (``.vtu``). This is a simple proxy for calling :obj:`manyToVTK3` with the instance as the only field to be saved. If multiple fields with identical mesh are to be saved in VTK3, use :obj:`manyToVTK3` directly.
:param fileName: output file name
:param ``**kw``: passed to :obj:`manyToVTK3`
"""
return self.manyToVTK3([self], fileName, **kw)
@staticmethod
def manyToVTK3(fields, fileName, ascii=False, compress=True):
"""
Save all fields passed as argument into VTK3 Unstructured Grid file (``*.vtu``).
All *fields* must be defined on the same mesh object; exception will be raised if this is not the case.
:param list of Field fields:
:param fileName: output file name
:param bool ascii: write numbers are ASCII in the XML-based VTU file (rather than base64-encoded binary in XML)
:param bool compress: apply compression to the data
"""
import vtk
if not fields:
raise ValueError('At least one field must be passed.')
# check if all fields are defined on the same mesh
if len(set([f.mesh for f in fields])) != 1:
raise RuntimeError(
'Not all fields are sharing the same Mesh object (and could not be saved to a single .vtu file')
# convert mesh to VTK UnstructuredGrid
mesh = fields[0].getMesh()
vtkgrid = mesh.asVtkUnstructuredGrid()
# add fields as arrays
for f in fields:
arr = vtk.vtkDoubleArray()
arr.SetNumberOfComponents(f.getRecordSize())
arr.SetName(f.getFieldIDName())
assert f.getFieldType() in (FieldType.FT_vertexBased, FieldType.FT_cellBased) # other future types not handled
if f.getFieldType() == FieldType.FT_vertexBased:
nn = mesh.getNumberOfVertices()
else:
nn = mesh.getNumberOfCells()
arr.SetNumberOfValues(nn)
for i in range(nn):
arr.SetTuple(i, f.giveValue(i))
if f.getFieldType() == FieldType.FT_vertexBased:
vtkgrid.GetPointData().AddArray(arr)
else:
vtkgrid.GetCellData().AddArray(arr)
# write the unstructured grid to file
writer = vtk.vtkXMLUnstructuredGridWriter()
if compress:
writer.SetCompressor(vtk.vtkZLibDataCompressor())
if ascii:
writer.SetDataModeToAscii()
writer.SetFileName(fileName)
# change between VTK5 and VTK6
if vtk.vtkVersion().GetVTKMajorVersion() == 6:
writer.SetInputData(vtkgrid)
else:
writer.SetInputData(vtkgrid)
writer.Write()
# finito
@staticmethod
def makeFromVTK3(fileName, units, time=0, forceVersion2=False):
"""
Create fields from a VTK unstructured grid file (``.vtu``, format version 3, or ``.vtp`` with *forceVersion2*); the mesh is shared between fields.
``vtk.vtkXMLGenericDataObjectReader`` is used to open the file (unless *forceVersion2* is set), but it is checked that contained dataset is a ``vtk.vtkUnstructuredGrid`` and an error is raised if not.
.. note:: Units are not supported when loading from VTK, all fields will have ``None`` unit assigned.
:param str fileName: VTK (``*.vtu``) file
:param PhysicalUnit units: units of read values
:param float time: time value for created fields (time is not saved in VTK3, thus cannot be recovered)
:param bool forceVersion2: if ``True``, ``vtk.vtkGenericDataObjectReader`` (for VTK version 2) will be used to open the file, isntead of ``vtk.vtkXMLGenericDataObjectReader``; this also supposes *fileName* ends with ``.vtk`` (not checked, but may cause an error).
:return: list of new :obj:`Field` instances
:rtype: [Field,Field,...]
"""
import vtk
from .dataID import FieldID
# rr=vtk.vtkXMLUnstructuredGridReader()
if forceVersion2 or fileName.endswith('.vtk'):
rr = vtk.vtkGenericDataObjectReader()
else:
rr = vtk.vtkXMLGenericDataObjectReader()
rr.SetFileName(fileName)
rr.Update()
ugrid = rr.GetOutput()
if not isinstance(ugrid, vtk.vtkUnstructuredGrid):
raise RuntimeError("vtkDataObject read from '%s' must be a vtkUnstructuredGrid (not a %s)" % (
fileName, ugrid.__class__.__name__))
# import sys
# sys.stderr.write(str((ugrid,ugrid.__class__,vtk.vtkUnstructuredGrid)))
# make mesh -- implemented separately
mesh = Mesh.UnstructuredMesh.makeFromVtkUnstructuredGrid(ugrid)
# fields which will be returned
ret = []
# get cell and point data
cd, pd = ugrid.GetCellData(), ugrid.GetPointData()
for data, fieldType in (pd, FieldType.FT_vertexBased), (cd, FieldType.FT_cellBased):
for idata in range(data.GetNumberOfArrays()):
aname, arr = pd.GetArrayName(idata), pd.GetArray(idata)
nt = arr.GetNumberOfTuples()
if nt == 0:
raise RuntimeError("Zero values in field '%s', unable to determine value type." % aname)
t0 = arr.GetTuple(0)
valueType = ValueType.fromNumberOfComponents(len(arr.GetTuple(0)))
# this will raise KeyError if fieldID with that name not defined
fid = FieldID[aname]
# get actual values as tuples
values = [arr.GetTuple(t) for t in range(nt)]
ret.append(Field(
mesh=mesh,
fieldID=fid,
units=units, # not stored at all
time=time, # not stored either, set by caller
valueType=valueType,
values=values,
fieldType=fieldType
))
return ret
def _sum(self, other, sign1, sign2):
"""
Should return a new instance. As deep copy is expensive,
this operation should be avoided. Better to modify the field values.
"""
raise TypeError('Not supported')
def inUnitsOf(self, *units):
"""
Should return a new instance. As deep copy is expensive,
this operation should be avoided. Better to use convertToUnits method
performing in place conversion.
"""
raise TypeError('Not supported')
# def __deepcopy__(self, memo):
# """ Deepcopy operatin modified not to include attributes starting with underscore.
# These are supposed to be the ones valid only to s specific copy of the receiver.
# An example of these attributes are _PyroURI (injected by Application),
# where _PyroURI contains the URI of specific object, the copy should receive
# its own URI
# """
# cls = self.__class__
# dpcpy = cls.__new__(cls)
#
# memo[id(self)] = dpcpy
# for attr in dir(self):
# if not attr.startswith('_'):
# value = getattr(self, attr)
# setattr(dpcpy, attr, copy.deepcopy(value, memo))
# return dpcpy
| lgpl-3.0 |
miloharper/neural-network-animation | matplotlib/tests/test_ticker.py | 9 | 4261 | from __future__ import (absolute_import, division, print_function,
unicode_literals)
import six
import nose.tools
from nose.tools import assert_raises
from numpy.testing import assert_almost_equal
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import matplotlib.ticker as mticker
from matplotlib.testing.decorators import cleanup
def test_MaxNLocator():
loc = mticker.MaxNLocator(nbins=5)
test_value = np.array([20., 40., 60., 80., 100.])
assert_almost_equal(loc.tick_values(20, 100), test_value)
test_value = np.array([0., 0.0002, 0.0004, 0.0006, 0.0008, 0.001])
assert_almost_equal(loc.tick_values(0.001, 0.0001), test_value)
test_value = np.array([-1.0e+15, -5.0e+14, 0e+00, 5e+14, 1.0e+15])
assert_almost_equal(loc.tick_values(-1e15, 1e15), test_value)
def test_LinearLocator():
loc = mticker.LinearLocator(numticks=3)
test_value = np.array([-0.8, -0.3, 0.2])
assert_almost_equal(loc.tick_values(-0.8, 0.2), test_value)
def test_MultipleLocator():
loc = mticker.MultipleLocator(base=3.147)
test_value = np.array([-9.441, -6.294, -3.147, 0., 3.147, 6.294,
9.441, 12.588])
assert_almost_equal(loc.tick_values(-7, 10), test_value)
@cleanup
def test_AutoMinorLocator():
fig, ax = plt.subplots()
ax.set_xlim(0, 1.39)
ax.minorticks_on()
test_value = np.array([0.05, 0.1, 0.15, 0.25, 0.3, 0.35, 0.45,
0.5, 0.55, 0.65, 0.7, 0.75, 0.85, 0.9,
0.95, 1, 1.05, 1.1, 1.15, 1.25, 1.3, 1.35])
assert_almost_equal(ax.xaxis.get_ticklocs(minor=True), test_value)
def test_LogLocator():
loc = mticker.LogLocator(numticks=5)
assert_raises(ValueError, loc.tick_values, 0, 1000)
test_value = np.array([1.00000000e-05, 1.00000000e-03, 1.00000000e-01,
1.00000000e+01, 1.00000000e+03, 1.00000000e+05,
1.00000000e+07, 1.000000000e+09])
assert_almost_equal(loc.tick_values(0.001, 1.1e5), test_value)
loc = mticker.LogLocator(base=2)
test_value = np.array([0.5, 1., 2., 4., 8., 16., 32., 64., 128., 256.])
assert_almost_equal(loc.tick_values(1, 100), test_value)
def test_LogFormatterExponent():
class FakeAxis(object):
"""Allow Formatter to be called without having a "full" plot set up."""
def get_view_interval(self):
return 1, 10
i = np.arange(-3, 4, dtype=float)
expected_result = ['-3', '-2', '-1', '0', '1', '2', '3']
for base in [2, 5, 10, np.pi, np.e]:
formatter = mticker.LogFormatterExponent(base=base)
formatter.axis = FakeAxis()
vals = base**i
labels = [formatter(x, pos) for (x, pos) in zip(vals, i)]
nose.tools.assert_equal(labels, expected_result)
# Should be a blank string for non-integer powers if labelOnlyBase=True
formatter = mticker.LogFormatterExponent(base=10, labelOnlyBase=True)
formatter.axis = FakeAxis()
nose.tools.assert_equal(formatter(10**0.1), '')
# Otherwise, non-integer powers should be nicely formatted
locs = np.array([0.1, 0.00001, np.pi, 0.2, -0.2, -0.00001])
i = range(len(locs))
expected_result = ['0.1', '1e-05', '3.14', '0.2', '-0.2', '-1e-05']
for base in [2, 5, 10, np.pi, np.e]:
formatter = mticker.LogFormatterExponent(base, labelOnlyBase=False)
formatter.axis = FakeAxis()
vals = base**locs
labels = [formatter(x, pos) for (x, pos) in zip(vals, i)]
nose.tools.assert_equal(labels, expected_result)
def test_use_offset():
for use_offset in [True, False]:
with matplotlib.rc_context({'axes.formatter.useoffset': use_offset}):
tmp_form = mticker.ScalarFormatter()
nose.tools.assert_equal(use_offset, tmp_form.get_useOffset())
def test_formatstrformatter():
# test % style formatter
tmp_form = mticker.FormatStrFormatter('%05d')
nose.tools.assert_equal('00002', tmp_form(2))
# test str.format() style formatter
tmp_form = mticker.StrMethodFormatter('{x:05d}')
nose.tools.assert_equal('00002', tmp_form(2))
if __name__ == '__main__':
import nose
nose.runmodule(argv=['-s', '--with-doctest'], exit=False)
| mit |
marionleborgne/nupic | external/linux32/lib/python2.6/site-packages/matplotlib/contour.py | 69 | 42063 | """
These are classes to support contour plotting and
labelling for the axes class
"""
from __future__ import division
import warnings
import matplotlib as mpl
import numpy as np
from numpy import ma
import matplotlib._cntr as _cntr
import matplotlib.path as path
import matplotlib.ticker as ticker
import matplotlib.cm as cm
import matplotlib.colors as colors
import matplotlib.collections as collections
import matplotlib.font_manager as font_manager
import matplotlib.text as text
import matplotlib.cbook as cbook
import matplotlib.mlab as mlab
# Import needed for adding manual selection capability to clabel
from matplotlib.blocking_input import BlockingContourLabeler
# We can't use a single line collection for contour because a line
# collection can have only a single line style, and we want to be able to have
# dashed negative contours, for example, and solid positive contours.
# We could use a single polygon collection for filled contours, but it
# seems better to keep line and filled contours similar, with one collection
# per level.
class ContourLabeler:
'''Mixin to provide labelling capability to ContourSet'''
def clabel(self, *args, **kwargs):
"""
call signature::
clabel(cs, **kwargs)
adds labels to line contours in *cs*, where *cs* is a
:class:`~matplotlib.contour.ContourSet` object returned by
contour.
::
clabel(cs, v, **kwargs)
only labels contours listed in *v*.
Optional keyword arguments:
*fontsize*:
See http://matplotlib.sf.net/fonts.html
*colors*:
- if *None*, the color of each label matches the color of
the corresponding contour
- if one string color, e.g. *colors* = 'r' or *colors* =
'red', all labels will be plotted in this color
- if a tuple of matplotlib color args (string, float, rgb, etc),
different labels will be plotted in different colors in the order
specified
*inline*:
controls whether the underlying contour is removed or
not. Default is *True*.
*inline_spacing*:
space in pixels to leave on each side of label when
placing inline. Defaults to 5. This spacing will be
exact for labels at locations where the contour is
straight, less so for labels on curved contours.
*fmt*:
a format string for the label. Default is '%1.3f'
Alternatively, this can be a dictionary matching contour
levels with arbitrary strings to use for each contour level
(i.e., fmt[level]=string)
*manual*:
if *True*, contour labels will be placed manually using
mouse clicks. Click the first button near a contour to
add a label, click the second button (or potentially both
mouse buttons at once) to finish adding labels. The third
button can be used to remove the last label added, but
only if labels are not inline. Alternatively, the keyboard
can be used to select label locations (enter to end label
placement, delete or backspace act like the third mouse button,
and any other key will select a label location).
.. plot:: mpl_examples/pylab_examples/contour_demo.py
"""
"""
NOTES on how this all works:
clabel basically takes the input arguments and uses them to
add a list of "label specific" attributes to the ContourSet
object. These attributes are all of the form label* and names
should be fairly self explanatory.
Once these attributes are set, clabel passes control to the
labels method (case of automatic label placement) or
BlockingContourLabeler (case of manual label placement).
"""
fontsize = kwargs.get('fontsize', None)
inline = kwargs.get('inline', 1)
inline_spacing = kwargs.get('inline_spacing', 5)
self.labelFmt = kwargs.get('fmt', '%1.3f')
_colors = kwargs.get('colors', None)
# Detect if manual selection is desired and remove from argument list
self.labelManual=kwargs.get('manual',False)
if len(args) == 0:
levels = self.levels
indices = range(len(self.levels))
elif len(args) == 1:
levlabs = list(args[0])
indices, levels = [], []
for i, lev in enumerate(self.levels):
if lev in levlabs:
indices.append(i)
levels.append(lev)
if len(levels) < len(levlabs):
msg = "Specified levels " + str(levlabs)
msg += "\n don't match available levels "
msg += str(self.levels)
raise ValueError(msg)
else:
raise TypeError("Illegal arguments to clabel, see help(clabel)")
self.labelLevelList = levels
self.labelIndiceList = indices
self.labelFontProps = font_manager.FontProperties()
if fontsize == None:
font_size = int(self.labelFontProps.get_size_in_points())
else:
if type(fontsize) not in [int, float, str]:
raise TypeError("Font size must be an integer number.")
# Can't it be floating point, as indicated in line above?
else:
if type(fontsize) == str:
font_size = int(self.labelFontProps.get_size_in_points())
else:
self.labelFontProps.set_size(fontsize)
font_size = fontsize
self.labelFontSizeList = [font_size] * len(levels)
if _colors == None:
self.labelMappable = self
self.labelCValueList = np.take(self.cvalues, self.labelIndiceList)
else:
cmap = colors.ListedColormap(_colors, N=len(self.labelLevelList))
self.labelCValueList = range(len(self.labelLevelList))
self.labelMappable = cm.ScalarMappable(cmap = cmap,
norm = colors.NoNorm())
#self.labelTexts = [] # Initialized in ContourSet.__init__
#self.labelCValues = [] # same
self.labelXYs = []
if self.labelManual:
print 'Select label locations manually using first mouse button.'
print 'End manual selection with second mouse button.'
if not inline:
print 'Remove last label by clicking third mouse button.'
blocking_contour_labeler = BlockingContourLabeler(self)
blocking_contour_labeler(inline,inline_spacing)
else:
self.labels(inline,inline_spacing)
# Hold on to some old attribute names. These are depricated and will
# be removed in the near future (sometime after 2008-08-01), but keeping
# for now for backwards compatibility
self.cl = self.labelTexts
self.cl_xy = self.labelXYs
self.cl_cvalues = self.labelCValues
self.labelTextsList = cbook.silent_list('text.Text', self.labelTexts)
return self.labelTextsList
def print_label(self, linecontour,labelwidth):
"if contours are too short, don't plot a label"
lcsize = len(linecontour)
if lcsize > 10 * labelwidth:
return 1
xmax = np.amax(linecontour[:,0])
xmin = np.amin(linecontour[:,0])
ymax = np.amax(linecontour[:,1])
ymin = np.amin(linecontour[:,1])
lw = labelwidth
if (xmax - xmin) > 1.2* lw or (ymax - ymin) > 1.2 * lw:
return 1
else:
return 0
def too_close(self, x,y, lw):
"if there's a label already nearby, find a better place"
if self.labelXYs != []:
dist = [np.sqrt((x-loc[0]) ** 2 + (y-loc[1]) ** 2)
for loc in self.labelXYs]
for d in dist:
if d < 1.2*lw:
return 1
else: return 0
else: return 0
def get_label_coords(self, distances, XX, YY, ysize, lw):
""" labels are ploted at a location with the smallest
dispersion of the contour from a straight line
unless there's another label nearby, in which case
the second best place on the contour is picked up
if there's no good place a label isplotted at the
beginning of the contour
"""
hysize = int(ysize/2)
adist = np.argsort(distances)
for ind in adist:
x, y = XX[ind][hysize], YY[ind][hysize]
if self.too_close(x,y, lw):
continue
else:
return x,y, ind
ind = adist[0]
x, y = XX[ind][hysize], YY[ind][hysize]
return x,y, ind
def get_label_width(self, lev, fmt, fsize):
"get the width of the label in points"
if cbook.is_string_like(lev):
lw = (len(lev)) * fsize
else:
lw = (len(self.get_text(lev,fmt))) * fsize
return lw
def get_real_label_width( self, lev, fmt, fsize ):
"""
This computes actual onscreen label width.
This uses some black magic to determine onscreen extent of non-drawn
label. This magic may not be very robust.
"""
# Find middle of axes
xx = np.mean( np.asarray(self.ax.axis()).reshape(2,2), axis=1 )
# Temporarily create text object
t = text.Text( xx[0], xx[1] )
self.set_label_props( t, self.get_text(lev,fmt), 'k' )
# Some black magic to get onscreen extent
# NOTE: This will only work for already drawn figures, as the canvas
# does not have a renderer otherwise. This is the reason this function
# can't be integrated into the rest of the code.
bbox = t.get_window_extent(renderer=self.ax.figure.canvas.renderer)
# difference in pixel extent of image
lw = np.diff(bbox.corners()[0::2,0])[0]
return lw
def set_label_props(self, label, text, color):
"set the label properties - color, fontsize, text"
label.set_text(text)
label.set_color(color)
label.set_fontproperties(self.labelFontProps)
label.set_clip_box(self.ax.bbox)
def get_text(self, lev, fmt):
"get the text of the label"
if cbook.is_string_like(lev):
return lev
else:
if isinstance(fmt,dict):
return fmt[lev]
else:
return fmt%lev
def locate_label(self, linecontour, labelwidth):
"""find a good place to plot a label (relatively flat
part of the contour) and the angle of rotation for the
text object
"""
nsize= len(linecontour)
if labelwidth > 1:
xsize = int(np.ceil(nsize/labelwidth))
else:
xsize = 1
if xsize == 1:
ysize = nsize
else:
ysize = labelwidth
XX = np.resize(linecontour[:,0],(xsize, ysize))
YY = np.resize(linecontour[:,1],(xsize, ysize))
#I might have fouled up the following:
yfirst = YY[:,0].reshape(xsize, 1)
ylast = YY[:,-1].reshape(xsize, 1)
xfirst = XX[:,0].reshape(xsize, 1)
xlast = XX[:,-1].reshape(xsize, 1)
s = (yfirst-YY) * (xlast-xfirst) - (xfirst-XX) * (ylast-yfirst)
L = np.sqrt((xlast-xfirst)**2+(ylast-yfirst)**2).ravel()
dist = np.add.reduce(([(abs(s)[i]/L[i]) for i in range(xsize)]),-1)
x,y,ind = self.get_label_coords(dist, XX, YY, ysize, labelwidth)
#print 'ind, x, y', ind, x, y
# There must be a more efficient way...
lc = [tuple(l) for l in linecontour]
dind = lc.index((x,y))
#print 'dind', dind
#dind = list(linecontour).index((x,y))
return x, y, dind
def calc_label_rot_and_inline( self, slc, ind, lw, lc=None, spacing=5 ):
"""
This function calculates the appropriate label rotation given
the linecontour coordinates in screen units, the index of the
label location and the label width.
It will also break contour and calculate inlining if *lc* is
not empty (lc defaults to the empty list if None). *spacing*
is the space around the label in pixels to leave empty.
Do both of these tasks at once to avoid calling mlab.path_length
multiple times, which is relatively costly.
The method used here involves calculating the path length
along the contour in pixel coordinates and then looking
approximately label width / 2 away from central point to
determine rotation and then to break contour if desired.
"""
if lc is None: lc = []
# Half the label width
hlw = lw/2.0
# Check if closed and, if so, rotate contour so label is at edge
closed = mlab.is_closed_polygon(slc)
if closed:
slc = np.r_[ slc[ind:-1], slc[:ind+1] ]
if len(lc): # Rotate lc also if not empty
lc = np.r_[ lc[ind:-1], lc[:ind+1] ]
ind = 0
# Path length in pixel space
pl = mlab.path_length(slc)
pl = pl-pl[ind]
# Use linear interpolation to get points around label
xi = np.array( [ -hlw, hlw ] )
if closed: # Look at end also for closed contours
dp = np.array([pl[-1],0])
else:
dp = np.zeros_like(xi)
ll = mlab.less_simple_linear_interpolation( pl, slc, dp+xi,
extrap=True )
# get vector in pixel space coordinates from one point to other
dd = np.diff( ll, axis=0 ).ravel()
# Get angle of vector - must be calculated in pixel space for
# text rotation to work correctly
if np.all(dd==0): # Must deal with case of zero length label
rotation = 0.0
else:
rotation = np.arctan2(dd[1], dd[0]) * 180.0 / np.pi
# Fix angle so text is never upside-down
if rotation > 90:
rotation = rotation - 180.0
if rotation < -90:
rotation = 180.0 + rotation
# Break contour if desired
nlc = []
if len(lc):
# Expand range by spacing
xi = dp + xi + np.array([-spacing,spacing])
# Get indices near points of interest
I = mlab.less_simple_linear_interpolation(
pl, np.arange(len(pl)), xi, extrap=False )
# If those indices aren't beyond contour edge, find x,y
if (not np.isnan(I[0])) and int(I[0])<>I[0]:
xy1 = mlab.less_simple_linear_interpolation(
pl, lc, [ xi[0] ] )
if (not np.isnan(I[1])) and int(I[1])<>I[1]:
xy2 = mlab.less_simple_linear_interpolation(
pl, lc, [ xi[1] ] )
# Make integer
I = [ np.floor(I[0]), np.ceil(I[1]) ]
# Actually break contours
if closed:
# This will remove contour if shorter than label
if np.all(~np.isnan(I)):
nlc.append( np.r_[ xy2, lc[I[1]:I[0]+1], xy1 ] )
else:
# These will remove pieces of contour if they have length zero
if not np.isnan(I[0]):
nlc.append( np.r_[ lc[:I[0]+1], xy1 ] )
if not np.isnan(I[1]):
nlc.append( np.r_[ xy2, lc[I[1]:] ] )
# The current implementation removes contours completely
# covered by labels. Uncomment line below to keep
# original contour if this is the preferred behavoir.
#if not len(nlc): nlc = [ lc ]
return (rotation,nlc)
def add_label(self,x,y,rotation,lev,cvalue):
dx,dy = self.ax.transData.inverted().transform_point((x,y))
t = text.Text(dx, dy, rotation = rotation,
horizontalalignment='center',
verticalalignment='center')
color = self.labelMappable.to_rgba(cvalue,alpha=self.alpha)
_text = self.get_text(lev,self.labelFmt)
self.set_label_props(t, _text, color)
self.labelTexts.append(t)
self.labelCValues.append(cvalue)
self.labelXYs.append((x,y))
# Add label to plot here - useful for manual mode label selection
self.ax.add_artist(t)
def pop_label(self,index=-1):
'''Defaults to removing last label, but any index can be supplied'''
self.labelCValues.pop(index)
t = self.labelTexts.pop(index)
t.remove()
def labels(self, inline, inline_spacing):
trans = self.ax.transData # A bit of shorthand
for icon, lev, fsize, cvalue in zip(
self.labelIndiceList, self.labelLevelList, self.labelFontSizeList,
self.labelCValueList ):
con = self.collections[icon]
lw = self.get_label_width(lev, self.labelFmt, fsize)
additions = []
paths = con.get_paths()
for segNum, linepath in enumerate(paths):
lc = linepath.vertices # Line contour
slc0 = trans.transform(lc) # Line contour in screen coords
# For closed polygons, add extra point to avoid division by
# zero in print_label and locate_label. Other than these
# functions, this is not necessary and should probably be
# eventually removed.
if mlab.is_closed_polygon( lc ):
slc = np.r_[ slc0, slc0[1:2,:] ]
else:
slc = slc0
if self.print_label(slc,lw): # Check if long enough for a label
x,y,ind = self.locate_label(slc, lw)
if inline: lcarg = lc
else: lcarg = None
rotation,new=self.calc_label_rot_and_inline(
slc0, ind, lw, lcarg,
inline_spacing )
# Actually add the label
self.add_label(x,y,rotation,lev,cvalue)
# If inline, add new contours
if inline:
for n in new:
# Add path if not empty or single point
if len(n)>1: additions.append( path.Path(n) )
else: # If not adding label, keep old path
additions.append(linepath)
# After looping over all segments on a contour, remove old
# paths and add new ones if inlining
if inline:
del paths[:]
paths.extend(additions)
class ContourSet(cm.ScalarMappable, ContourLabeler):
"""
Create and store a set of contour lines or filled regions.
User-callable method: clabel
Useful attributes:
ax:
the axes object in which the contours are drawn
collections:
a silent_list of LineCollections or PolyCollections
levels:
contour levels
layers:
same as levels for line contours; half-way between
levels for filled contours. See _process_colors method.
"""
def __init__(self, ax, *args, **kwargs):
"""
Draw contour lines or filled regions, depending on
whether keyword arg 'filled' is False (default) or True.
The first argument of the initializer must be an axes
object. The remaining arguments and keyword arguments
are described in ContourSet.contour_doc.
"""
self.ax = ax
self.levels = kwargs.get('levels', None)
self.filled = kwargs.get('filled', False)
self.linewidths = kwargs.get('linewidths', None)
self.linestyles = kwargs.get('linestyles', 'solid')
self.alpha = kwargs.get('alpha', 1.0)
self.origin = kwargs.get('origin', None)
self.extent = kwargs.get('extent', None)
cmap = kwargs.get('cmap', None)
self.colors = kwargs.get('colors', None)
norm = kwargs.get('norm', None)
self.extend = kwargs.get('extend', 'neither')
self.antialiased = kwargs.get('antialiased', True)
self.nchunk = kwargs.get('nchunk', 0)
self.locator = kwargs.get('locator', None)
if (isinstance(norm, colors.LogNorm)
or isinstance(self.locator, ticker.LogLocator)):
self.logscale = True
if norm is None:
norm = colors.LogNorm()
if self.extend is not 'neither':
raise ValueError('extend kwarg does not work yet with log scale')
else:
self.logscale = False
if self.origin is not None: assert(self.origin in
['lower', 'upper', 'image'])
if self.extent is not None: assert(len(self.extent) == 4)
if cmap is not None: assert(isinstance(cmap, colors.Colormap))
if self.colors is not None and cmap is not None:
raise ValueError('Either colors or cmap must be None')
if self.origin == 'image': self.origin = mpl.rcParams['image.origin']
x, y, z = self._contour_args(*args) # also sets self.levels,
# self.layers
if self.colors is not None:
cmap = colors.ListedColormap(self.colors, N=len(self.layers))
if self.filled:
self.collections = cbook.silent_list('collections.PolyCollection')
else:
self.collections = cbook.silent_list('collections.LineCollection')
# label lists must be initialized here
self.labelTexts = []
self.labelCValues = []
kw = {'cmap': cmap}
if norm is not None:
kw['norm'] = norm
cm.ScalarMappable.__init__(self, **kw) # sets self.cmap;
self._process_colors()
_mask = ma.getmask(z)
if _mask is ma.nomask:
_mask = None
if self.filled:
if self.linewidths is not None:
warnings.warn('linewidths is ignored by contourf')
C = _cntr.Cntr(x, y, z.filled(), _mask)
lowers = self._levels[:-1]
uppers = self._levels[1:]
for level, level_upper in zip(lowers, uppers):
nlist = C.trace(level, level_upper, points = 0,
nchunk = self.nchunk)
col = collections.PolyCollection(nlist,
antialiaseds = (self.antialiased,),
edgecolors= 'none',
alpha=self.alpha)
self.ax.add_collection(col)
self.collections.append(col)
else:
tlinewidths = self._process_linewidths()
self.tlinewidths = tlinewidths
tlinestyles = self._process_linestyles()
C = _cntr.Cntr(x, y, z.filled(), _mask)
for level, width, lstyle in zip(self.levels, tlinewidths, tlinestyles):
nlist = C.trace(level, points = 0)
col = collections.LineCollection(nlist,
linewidths = width,
linestyle = lstyle,
alpha=self.alpha)
if level < 0.0 and self.monochrome:
ls = mpl.rcParams['contour.negative_linestyle']
col.set_linestyle(ls)
col.set_label('_nolegend_')
self.ax.add_collection(col, False)
self.collections.append(col)
self.changed() # set the colors
x0 = ma.minimum(x)
x1 = ma.maximum(x)
y0 = ma.minimum(y)
y1 = ma.maximum(y)
self.ax.update_datalim([(x0,y0), (x1,y1)])
self.ax.autoscale_view()
def changed(self):
tcolors = [ (tuple(rgba),) for rgba in
self.to_rgba(self.cvalues, alpha=self.alpha)]
self.tcolors = tcolors
for color, collection in zip(tcolors, self.collections):
collection.set_alpha(self.alpha)
collection.set_color(color)
for label, cv in zip(self.labelTexts, self.labelCValues):
label.set_alpha(self.alpha)
label.set_color(self.labelMappable.to_rgba(cv))
# add label colors
cm.ScalarMappable.changed(self)
def _autolev(self, z, N):
'''
Select contour levels to span the data.
We need two more levels for filled contours than for
line contours, because for the latter we need to specify
the lower and upper boundary of each range. For example,
a single contour boundary, say at z = 0, requires only
one contour line, but two filled regions, and therefore
three levels to provide boundaries for both regions.
'''
if self.locator is None:
if self.logscale:
self.locator = ticker.LogLocator()
else:
self.locator = ticker.MaxNLocator(N+1)
self.locator.create_dummy_axis()
zmax = self.zmax
zmin = self.zmin
self.locator.set_bounds(zmin, zmax)
lev = self.locator()
zmargin = (zmax - zmin) * 0.000001 # so z < (zmax + zmargin)
if zmax >= lev[-1]:
lev[-1] += zmargin
if zmin <= lev[0]:
if self.logscale:
lev[0] = 0.99 * zmin
else:
lev[0] -= zmargin
self._auto = True
if self.filled:
return lev
return lev[1:-1]
def _initialize_x_y(self, z):
'''
Return X, Y arrays such that contour(Z) will match imshow(Z)
if origin is not None.
The center of pixel Z[i,j] depends on origin:
if origin is None, x = j, y = i;
if origin is 'lower', x = j + 0.5, y = i + 0.5;
if origin is 'upper', x = j + 0.5, y = Nrows - i - 0.5
If extent is not None, x and y will be scaled to match,
as in imshow.
If origin is None and extent is not None, then extent
will give the minimum and maximum values of x and y.
'''
if z.ndim != 2:
raise TypeError("Input must be a 2D array.")
else:
Ny, Nx = z.shape
if self.origin is None: # Not for image-matching.
if self.extent is None:
return np.meshgrid(np.arange(Nx), np.arange(Ny))
else:
x0,x1,y0,y1 = self.extent
x = np.linspace(x0, x1, Nx)
y = np.linspace(y0, y1, Ny)
return np.meshgrid(x, y)
# Match image behavior:
if self.extent is None:
x0,x1,y0,y1 = (0, Nx, 0, Ny)
else:
x0,x1,y0,y1 = self.extent
dx = float(x1 - x0)/Nx
dy = float(y1 - y0)/Ny
x = x0 + (np.arange(Nx) + 0.5) * dx
y = y0 + (np.arange(Ny) + 0.5) * dy
if self.origin == 'upper':
y = y[::-1]
return np.meshgrid(x,y)
def _check_xyz(self, args):
'''
For functions like contour, check that the dimensions
of the input arrays match; if x and y are 1D, convert
them to 2D using meshgrid.
Possible change: I think we should make and use an ArgumentError
Exception class (here and elsewhere).
'''
# We can strip away the x and y units
x = self.ax.convert_xunits( args[0] )
y = self.ax.convert_yunits( args[1] )
x = np.asarray(x, dtype=np.float64)
y = np.asarray(y, dtype=np.float64)
z = ma.asarray(args[2], dtype=np.float64)
if z.ndim != 2:
raise TypeError("Input z must be a 2D array.")
else: Ny, Nx = z.shape
if x.shape == z.shape and y.shape == z.shape:
return x,y,z
if x.ndim != 1 or y.ndim != 1:
raise TypeError("Inputs x and y must be 1D or 2D.")
nx, = x.shape
ny, = y.shape
if nx != Nx or ny != Ny:
raise TypeError("Length of x must be number of columns in z,\n" +
"and length of y must be number of rows.")
x,y = np.meshgrid(x,y)
return x,y,z
def _contour_args(self, *args):
if self.filled: fn = 'contourf'
else: fn = 'contour'
Nargs = len(args)
if Nargs <= 2:
z = ma.asarray(args[0], dtype=np.float64)
x, y = self._initialize_x_y(z)
elif Nargs <=4:
x,y,z = self._check_xyz(args[:3])
else:
raise TypeError("Too many arguments to %s; see help(%s)" % (fn,fn))
self.zmax = ma.maximum(z)
self.zmin = ma.minimum(z)
if self.logscale and self.zmin <= 0:
z = ma.masked_where(z <= 0, z)
warnings.warn('Log scale: values of z <=0 have been masked')
self.zmin = z.min()
self._auto = False
if self.levels is None:
if Nargs == 1 or Nargs == 3:
lev = self._autolev(z, 7)
else: # 2 or 4 args
level_arg = args[-1]
try:
if type(level_arg) == int:
lev = self._autolev(z, level_arg)
else:
lev = np.asarray(level_arg).astype(np.float64)
except:
raise TypeError(
"Last %s arg must give levels; see help(%s)" % (fn,fn))
if self.filled and len(lev) < 2:
raise ValueError("Filled contours require at least 2 levels.")
# Workaround for cntr.c bug wrt masked interior regions:
#if filled:
# z = ma.masked_array(z.filled(-1e38))
# It's not clear this is any better than the original bug.
self.levels = lev
#if self._auto and self.extend in ('both', 'min', 'max'):
# raise TypeError("Auto level selection is inconsistent "
# + "with use of 'extend' kwarg")
self._levels = list(self.levels)
if self.extend in ('both', 'min'):
self._levels.insert(0, min(self.levels[0],self.zmin) - 1)
if self.extend in ('both', 'max'):
self._levels.append(max(self.levels[-1],self.zmax) + 1)
self._levels = np.asarray(self._levels)
self.vmin = np.amin(self.levels) # alternative would be self.layers
self.vmax = np.amax(self.levels)
if self.extend in ('both', 'min'):
self.vmin = 2 * self.levels[0] - self.levels[1]
if self.extend in ('both', 'max'):
self.vmax = 2 * self.levels[-1] - self.levels[-2]
self.layers = self._levels # contour: a line is a thin layer
if self.filled:
self.layers = 0.5 * (self._levels[:-1] + self._levels[1:])
if self.extend in ('both', 'min'):
self.layers[0] = 0.5 * (self.vmin + self._levels[1])
if self.extend in ('both', 'max'):
self.layers[-1] = 0.5 * (self.vmax + self._levels[-2])
return (x, y, z)
def _process_colors(self):
"""
Color argument processing for contouring.
Note that we base the color mapping on the contour levels,
not on the actual range of the Z values. This means we
don't have to worry about bad values in Z, and we always have
the full dynamic range available for the selected levels.
The color is based on the midpoint of the layer, except for
an extended end layers.
"""
self.monochrome = self.cmap.monochrome
if self.colors is not None:
i0, i1 = 0, len(self.layers)
if self.extend in ('both', 'min'):
i0 = -1
if self.extend in ('both', 'max'):
i1 = i1 + 1
self.cvalues = range(i0, i1)
self.set_norm(colors.NoNorm())
else:
self.cvalues = self.layers
if not self.norm.scaled():
self.set_clim(self.vmin, self.vmax)
if self.extend in ('both', 'max', 'min'):
self.norm.clip = False
self.set_array(self.layers)
# self.tcolors are set by the "changed" method
def _process_linewidths(self):
linewidths = self.linewidths
Nlev = len(self.levels)
if linewidths is None:
tlinewidths = [(mpl.rcParams['lines.linewidth'],)] *Nlev
else:
if cbook.iterable(linewidths) and len(linewidths) < Nlev:
linewidths = list(linewidths) * int(np.ceil(Nlev/len(linewidths)))
elif not cbook.iterable(linewidths) and type(linewidths) in [int, float]:
linewidths = [linewidths] * Nlev
tlinewidths = [(w,) for w in linewidths]
return tlinewidths
def _process_linestyles(self):
linestyles = self.linestyles
Nlev = len(self.levels)
if linestyles is None:
tlinestyles = ['solid'] * Nlev
else:
if cbook.is_string_like(linestyles):
tlinestyles = [linestyles] * Nlev
elif cbook.iterable(linestyles) and len(linestyles) <= Nlev:
tlinestyles = list(linestyles) * int(np.ceil(Nlev/len(linestyles)))
return tlinestyles
def get_alpha(self):
'''returns alpha to be applied to all ContourSet artists'''
return self.alpha
def set_alpha(self, alpha):
'''sets alpha for all ContourSet artists'''
self.alpha = alpha
self.changed()
contour_doc = """
:func:`~matplotlib.pyplot.contour` and
:func:`~matplotlib.pyplot.contourf` draw contour lines and
filled contours, respectively. Except as noted, function
signatures and return values are the same for both versions.
:func:`~matplotlib.pyplot.contourf` differs from the Matlab
(TM) version in that it does not draw the polygon edges,
because the contouring engine yields simply connected regions
with branch cuts. To draw the edges, add line contours with
calls to :func:`~matplotlib.pyplot.contour`.
call signatures::
contour(Z)
make a contour plot of an array *Z*. The level values are chosen
automatically.
::
contour(X,Y,Z)
*X*, *Y* specify the (*x*, *y*) coordinates of the surface
::
contour(Z,N)
contour(X,Y,Z,N)
contour *N* automatically-chosen levels.
::
contour(Z,V)
contour(X,Y,Z,V)
draw contour lines at the values specified in sequence *V*
::
contourf(..., V)
fill the (len(*V*)-1) regions between the values in *V*
::
contour(Z, **kwargs)
Use keyword args to control colors, linewidth, origin, cmap ... see
below for more details.
*X*, *Y*, and *Z* must be arrays with the same dimensions.
*Z* may be a masked array, but filled contouring may not
handle internal masked regions correctly.
``C = contour(...)`` returns a
:class:`~matplotlib.contour.ContourSet` object.
Optional keyword arguments:
*colors*: [ None | string | (mpl_colors) ]
If *None*, the colormap specified by cmap will be used.
If a string, like 'r' or 'red', all levels will be plotted in this
color.
If a tuple of matplotlib color args (string, float, rgb, etc),
different levels will be plotted in different colors in the order
specified.
*alpha*: float
The alpha blending value
*cmap*: [ None | Colormap ]
A cm :class:`~matplotlib.cm.Colormap` instance or
*None*. If *cmap* is *None* and *colors* is *None*, a
default Colormap is used.
*norm*: [ None | Normalize ]
A :class:`matplotlib.colors.Normalize` instance for
scaling data values to colors. If *norm* is *None* and
*colors* is *None*, the default linear scaling is used.
*origin*: [ None | 'upper' | 'lower' | 'image' ]
If *None*, the first value of *Z* will correspond to the
lower left corner, location (0,0). If 'image', the rc
value for ``image.origin`` will be used.
This keyword is not active if *X* and *Y* are specified in
the call to contour.
*extent*: [ None | (x0,x1,y0,y1) ]
If *origin* is not *None*, then *extent* is interpreted as
in :func:`matplotlib.pyplot.imshow`: it gives the outer
pixel boundaries. In this case, the position of Z[0,0]
is the center of the pixel, not a corner. If *origin* is
*None*, then (*x0*, *y0*) is the position of Z[0,0], and
(*x1*, *y1*) is the position of Z[-1,-1].
This keyword is not active if *X* and *Y* are specified in
the call to contour.
*locator*: [ None | ticker.Locator subclass ]
If *locator* is None, the default
:class:`~matplotlib.ticker.MaxNLocator` is used. The
locator is used to determine the contour levels if they
are not given explicitly via the *V* argument.
*extend*: [ 'neither' | 'both' | 'min' | 'max' ]
Unless this is 'neither', contour levels are automatically
added to one or both ends of the range so that all data
are included. These added ranges are then mapped to the
special colormap values which default to the ends of the
colormap range, but can be set via
:meth:`matplotlib.cm.Colormap.set_under` and
:meth:`matplotlib.cm.Colormap.set_over` methods.
contour-only keyword arguments:
*linewidths*: [ None | number | tuple of numbers ]
If *linewidths* is *None*, the default width in
``lines.linewidth`` in ``matplotlibrc`` is used.
If a number, all levels will be plotted with this linewidth.
If a tuple, different levels will be plotted with different
linewidths in the order specified
*linestyles*: [None | 'solid' | 'dashed' | 'dashdot' | 'dotted' ]
If *linestyles* is *None*, the 'solid' is used.
*linestyles* can also be an iterable of the above strings
specifying a set of linestyles to be used. If this
iterable is shorter than the number of contour levels
it will be repeated as necessary.
If contour is using a monochrome colormap and the contour
level is less than 0, then the linestyle specified
in ``contour.negative_linestyle`` in ``matplotlibrc``
will be used.
contourf-only keyword arguments:
*antialiased*: [ True | False ]
enable antialiasing
*nchunk*: [ 0 | integer ]
If 0, no subdivision of the domain. Specify a positive integer to
divide the domain into subdomains of roughly *nchunk* by *nchunk*
points. This may never actually be advantageous, so this option may
be removed. Chunking introduces artifacts at the chunk boundaries
unless *antialiased* is *False*.
**Example:**
.. plot:: mpl_examples/pylab_examples/contour_demo.py
"""
def find_nearest_contour( self, x, y, indices=None, pixel=True ):
"""
Finds contour that is closest to a point. Defaults to
measuring distance in pixels (screen space - useful for manual
contour labeling), but this can be controlled via a keyword
argument.
Returns a tuple containing the contour, segment, index of
segment, x & y of segment point and distance to minimum point.
Call signature::
conmin,segmin,imin,xmin,ymin,dmin = find_nearest_contour(
self, x, y, indices=None, pixel=True )
Optional keyword arguments::
*indices*:
Indexes of contour levels to consider when looking for
nearest point. Defaults to using all levels.
*pixel*:
If *True*, measure distance in pixel space, if not, measure
distance in axes space. Defaults to *True*.
"""
# This function uses a method that is probably quite
# inefficient based on converting each contour segment to
# pixel coordinates and then comparing the given point to
# those coordinates for each contour. This will probably be
# quite slow for complex contours, but for normal use it works
# sufficiently well that the time is not noticeable.
# Nonetheless, improvements could probably be made.
if indices==None:
indices = range(len(self.levels))
dmin = 1e10
conmin = None
segmin = None
xmin = None
ymin = None
for icon in indices:
con = self.collections[icon]
paths = con.get_paths()
for segNum, linepath in enumerate(paths):
lc = linepath.vertices
# transfer all data points to screen coordinates if desired
if pixel:
lc = self.ax.transData.transform(lc)
ds = (lc[:,0]-x)**2 + (lc[:,1]-y)**2
d = min( ds )
if d < dmin:
dmin = d
conmin = icon
segmin = segNum
imin = mpl.mlab.find( ds == d )[0]
xmin = lc[imin,0]
ymin = lc[imin,1]
return (conmin,segmin,imin,xmin,ymin,dmin)
| agpl-3.0 |
numenta/nupic | external/linux32/lib/python2.6/site-packages/matplotlib/colorbar.py | 69 | 27260 | '''
Colorbar toolkit with two classes and a function:
:class:`ColorbarBase`
the base class with full colorbar drawing functionality.
It can be used as-is to make a colorbar for a given colormap;
a mappable object (e.g., image) is not needed.
:class:`Colorbar`
the derived class for use with images or contour plots.
:func:`make_axes`
a function for resizing an axes and adding a second axes
suitable for a colorbar
The :meth:`~matplotlib.figure.Figure.colorbar` method uses :func:`make_axes`
and :class:`Colorbar`; the :func:`~matplotlib.pyplot.colorbar` function
is a thin wrapper over :meth:`~matplotlib.figure.Figure.colorbar`.
'''
import numpy as np
import matplotlib as mpl
import matplotlib.colors as colors
import matplotlib.cm as cm
import matplotlib.ticker as ticker
import matplotlib.cbook as cbook
import matplotlib.lines as lines
import matplotlib.patches as patches
import matplotlib.collections as collections
import matplotlib.contour as contour
make_axes_kw_doc = '''
========== ====================================================
Property Description
========== ====================================================
*fraction* 0.15; fraction of original axes to use for colorbar
*pad* 0.05 if vertical, 0.15 if horizontal; fraction
of original axes between colorbar and new image axes
*shrink* 1.0; fraction by which to shrink the colorbar
*aspect* 20; ratio of long to short dimensions
========== ====================================================
'''
colormap_kw_doc = '''
=========== ====================================================
Property Description
=========== ====================================================
*extend* [ 'neither' | 'both' | 'min' | 'max' ]
If not 'neither', make pointed end(s) for out-of-
range values. These are set for a given colormap
using the colormap set_under and set_over methods.
*spacing* [ 'uniform' | 'proportional' ]
Uniform spacing gives each discrete color the same
space; proportional makes the space proportional to
the data interval.
*ticks* [ None | list of ticks | Locator object ]
If None, ticks are determined automatically from the
input.
*format* [ None | format string | Formatter object ]
If None, the
:class:`~matplotlib.ticker.ScalarFormatter` is used.
If a format string is given, e.g. '%.3f', that is
used. An alternative
:class:`~matplotlib.ticker.Formatter` object may be
given instead.
*drawedges* [ False | True ] If true, draw lines at color
boundaries.
=========== ====================================================
The following will probably be useful only in the context of
indexed colors (that is, when the mappable has norm=NoNorm()),
or other unusual circumstances.
============ ===================================================
Property Description
============ ===================================================
*boundaries* None or a sequence
*values* None or a sequence which must be of length 1 less
than the sequence of *boundaries*. For each region
delimited by adjacent entries in *boundaries*, the
color mapped to the corresponding value in values
will be used.
============ ===================================================
'''
colorbar_doc = '''
Add a colorbar to a plot.
Function signatures for the :mod:`~matplotlib.pyplot` interface; all
but the first are also method signatures for the
:meth:`~matplotlib.figure.Figure.colorbar` method::
colorbar(**kwargs)
colorbar(mappable, **kwargs)
colorbar(mappable, cax=cax, **kwargs)
colorbar(mappable, ax=ax, **kwargs)
arguments:
*mappable*
the :class:`~matplotlib.image.Image`,
:class:`~matplotlib.contour.ContourSet`, etc. to
which the colorbar applies; this argument is mandatory for the
:meth:`~matplotlib.figure.Figure.colorbar` method but optional for the
:func:`~matplotlib.pyplot.colorbar` function, which sets the
default to the current image.
keyword arguments:
*cax*
None | axes object into which the colorbar will be drawn
*ax*
None | parent axes object from which space for a new
colorbar axes will be stolen
Additional keyword arguments are of two kinds:
axes properties:
%s
colorbar properties:
%s
If *mappable* is a :class:`~matplotlib.contours.ContourSet`, its *extend*
kwarg is included automatically.
Note that the *shrink* kwarg provides a simple way to keep a vertical
colorbar, for example, from being taller than the axes of the mappable
to which the colorbar is attached; but it is a manual method requiring
some trial and error. If the colorbar is too tall (or a horizontal
colorbar is too wide) use a smaller value of *shrink*.
For more precise control, you can manually specify the positions of
the axes objects in which the mappable and the colorbar are drawn. In
this case, do not use any of the axes properties kwargs.
returns:
:class:`~matplotlib.colorbar.Colorbar` instance; see also its base class,
:class:`~matplotlib.colorbar.ColorbarBase`. Call the
:meth:`~matplotlib.colorbar.ColorbarBase.set_label` method
to label the colorbar.
''' % (make_axes_kw_doc, colormap_kw_doc)
class ColorbarBase(cm.ScalarMappable):
'''
Draw a colorbar in an existing axes.
This is a base class for the :class:`Colorbar` class, which is the
basis for the :func:`~matplotlib.pyplot.colorbar` method and pylab
function.
It is also useful by itself for showing a colormap. If the *cmap*
kwarg is given but *boundaries* and *values* are left as None,
then the colormap will be displayed on a 0-1 scale. To show the
under- and over-value colors, specify the *norm* as::
colors.Normalize(clip=False)
To show the colors versus index instead of on the 0-1 scale,
use::
norm=colors.NoNorm.
Useful attributes:
:attr:`ax`
the Axes instance in which the colorbar is drawn
:attr:`lines`
a LineCollection if lines were drawn, otherwise None
:attr:`dividers`
a LineCollection if *drawedges* is True, otherwise None
Useful public methods are :meth:`set_label` and :meth:`add_lines`.
'''
_slice_dict = {'neither': slice(0,1000000),
'both': slice(1,-1),
'min': slice(1,1000000),
'max': slice(0,-1)}
def __init__(self, ax, cmap=None,
norm=None,
alpha=1.0,
values=None,
boundaries=None,
orientation='vertical',
extend='neither',
spacing='uniform', # uniform or proportional
ticks=None,
format=None,
drawedges=False,
filled=True,
):
self.ax = ax
if cmap is None: cmap = cm.get_cmap()
if norm is None: norm = colors.Normalize()
self.alpha = alpha
cm.ScalarMappable.__init__(self, cmap=cmap, norm=norm)
self.values = values
self.boundaries = boundaries
self.extend = extend
self._inside = self._slice_dict[extend]
self.spacing = spacing
self.orientation = orientation
self.drawedges = drawedges
self.filled = filled
self.solids = None
self.lines = None
self.dividers = None
self.set_label('')
if cbook.iterable(ticks):
self.locator = ticker.FixedLocator(ticks, nbins=len(ticks))
else:
self.locator = ticks # Handle default in _ticker()
if format is None:
if isinstance(self.norm, colors.LogNorm):
self.formatter = ticker.LogFormatter()
else:
self.formatter = ticker.ScalarFormatter()
elif cbook.is_string_like(format):
self.formatter = ticker.FormatStrFormatter(format)
else:
self.formatter = format # Assume it is a Formatter
# The rest is in a method so we can recalculate when clim changes.
self.draw_all()
def draw_all(self):
'''
Calculate any free parameters based on the current cmap and norm,
and do all the drawing.
'''
self._process_values()
self._find_range()
X, Y = self._mesh()
C = self._values[:,np.newaxis]
self._config_axes(X, Y)
if self.filled:
self._add_solids(X, Y, C)
self._set_label()
def _config_axes(self, X, Y):
'''
Make an axes patch and outline.
'''
ax = self.ax
ax.set_frame_on(False)
ax.set_navigate(False)
xy = self._outline(X, Y)
ax.update_datalim(xy)
ax.set_xlim(*ax.dataLim.intervalx)
ax.set_ylim(*ax.dataLim.intervaly)
self.outline = lines.Line2D(xy[:, 0], xy[:, 1], color=mpl.rcParams['axes.edgecolor'],
linewidth=mpl.rcParams['axes.linewidth'])
ax.add_artist(self.outline)
self.outline.set_clip_box(None)
self.outline.set_clip_path(None)
c = mpl.rcParams['axes.facecolor']
self.patch = patches.Polygon(xy, edgecolor=c,
facecolor=c,
linewidth=0.01,
zorder=-1)
ax.add_artist(self.patch)
ticks, ticklabels, offset_string = self._ticker()
if self.orientation == 'vertical':
ax.set_xticks([])
ax.yaxis.set_label_position('right')
ax.yaxis.set_ticks_position('right')
ax.set_yticks(ticks)
ax.set_yticklabels(ticklabels)
ax.yaxis.get_major_formatter().set_offset_string(offset_string)
else:
ax.set_yticks([])
ax.xaxis.set_label_position('bottom')
ax.set_xticks(ticks)
ax.set_xticklabels(ticklabels)
ax.xaxis.get_major_formatter().set_offset_string(offset_string)
def _set_label(self):
if self.orientation == 'vertical':
self.ax.set_ylabel(self._label, **self._labelkw)
else:
self.ax.set_xlabel(self._label, **self._labelkw)
def set_label(self, label, **kw):
'''
Label the long axis of the colorbar
'''
self._label = label
self._labelkw = kw
self._set_label()
def _outline(self, X, Y):
'''
Return *x*, *y* arrays of colorbar bounding polygon,
taking orientation into account.
'''
N = X.shape[0]
ii = [0, 1, N-2, N-1, 2*N-1, 2*N-2, N+1, N, 0]
x = np.take(np.ravel(np.transpose(X)), ii)
y = np.take(np.ravel(np.transpose(Y)), ii)
x = x.reshape((len(x), 1))
y = y.reshape((len(y), 1))
if self.orientation == 'horizontal':
return np.hstack((y, x))
return np.hstack((x, y))
def _edges(self, X, Y):
'''
Return the separator line segments; helper for _add_solids.
'''
N = X.shape[0]
# Using the non-array form of these line segments is much
# simpler than making them into arrays.
if self.orientation == 'vertical':
return [zip(X[i], Y[i]) for i in range(1, N-1)]
else:
return [zip(Y[i], X[i]) for i in range(1, N-1)]
def _add_solids(self, X, Y, C):
'''
Draw the colors using :meth:`~matplotlib.axes.Axes.pcolor`;
optionally add separators.
'''
## Change to pcolorfast after fixing bugs in some backends...
if self.orientation == 'vertical':
args = (X, Y, C)
else:
args = (np.transpose(Y), np.transpose(X), np.transpose(C))
kw = {'cmap':self.cmap, 'norm':self.norm,
'shading':'flat', 'alpha':self.alpha}
# Save, set, and restore hold state to keep pcolor from
# clearing the axes. Ordinarily this will not be needed,
# since the axes object should already have hold set.
_hold = self.ax.ishold()
self.ax.hold(True)
col = self.ax.pcolor(*args, **kw)
self.ax.hold(_hold)
#self.add_observer(col) # We should observe, not be observed...
self.solids = col
if self.drawedges:
self.dividers = collections.LineCollection(self._edges(X,Y),
colors=(mpl.rcParams['axes.edgecolor'],),
linewidths=(0.5*mpl.rcParams['axes.linewidth'],)
)
self.ax.add_collection(self.dividers)
def add_lines(self, levels, colors, linewidths):
'''
Draw lines on the colorbar.
'''
N = len(levels)
dummy, y = self._locate(levels)
if len(y) <> N:
raise ValueError("levels are outside colorbar range")
x = np.array([0.0, 1.0])
X, Y = np.meshgrid(x,y)
if self.orientation == 'vertical':
xy = [zip(X[i], Y[i]) for i in range(N)]
else:
xy = [zip(Y[i], X[i]) for i in range(N)]
col = collections.LineCollection(xy, linewidths=linewidths)
self.lines = col
col.set_color(colors)
self.ax.add_collection(col)
def _ticker(self):
'''
Return two sequences: ticks (colorbar data locations)
and ticklabels (strings).
'''
locator = self.locator
formatter = self.formatter
if locator is None:
if self.boundaries is None:
if isinstance(self.norm, colors.NoNorm):
nv = len(self._values)
base = 1 + int(nv/10)
locator = ticker.IndexLocator(base=base, offset=0)
elif isinstance(self.norm, colors.BoundaryNorm):
b = self.norm.boundaries
locator = ticker.FixedLocator(b, nbins=10)
elif isinstance(self.norm, colors.LogNorm):
locator = ticker.LogLocator()
else:
locator = ticker.MaxNLocator()
else:
b = self._boundaries[self._inside]
locator = ticker.FixedLocator(b, nbins=10)
if isinstance(self.norm, colors.NoNorm):
intv = self._values[0], self._values[-1]
else:
intv = self.vmin, self.vmax
locator.create_dummy_axis()
formatter.create_dummy_axis()
locator.set_view_interval(*intv)
locator.set_data_interval(*intv)
formatter.set_view_interval(*intv)
formatter.set_data_interval(*intv)
b = np.array(locator())
b, ticks = self._locate(b)
formatter.set_locs(b)
ticklabels = [formatter(t, i) for i, t in enumerate(b)]
offset_string = formatter.get_offset()
return ticks, ticklabels, offset_string
def _process_values(self, b=None):
'''
Set the :attr:`_boundaries` and :attr:`_values` attributes
based on the input boundaries and values. Input boundaries
can be *self.boundaries* or the argument *b*.
'''
if b is None:
b = self.boundaries
if b is not None:
self._boundaries = np.asarray(b, dtype=float)
if self.values is None:
self._values = 0.5*(self._boundaries[:-1]
+ self._boundaries[1:])
if isinstance(self.norm, colors.NoNorm):
self._values = (self._values + 0.00001).astype(np.int16)
return
self._values = np.array(self.values)
return
if self.values is not None:
self._values = np.array(self.values)
if self.boundaries is None:
b = np.zeros(len(self.values)+1, 'd')
b[1:-1] = 0.5*(self._values[:-1] - self._values[1:])
b[0] = 2.0*b[1] - b[2]
b[-1] = 2.0*b[-2] - b[-3]
self._boundaries = b
return
self._boundaries = np.array(self.boundaries)
return
# Neither boundaries nor values are specified;
# make reasonable ones based on cmap and norm.
if isinstance(self.norm, colors.NoNorm):
b = self._uniform_y(self.cmap.N+1) * self.cmap.N - 0.5
v = np.zeros((len(b)-1,), dtype=np.int16)
v[self._inside] = np.arange(self.cmap.N, dtype=np.int16)
if self.extend in ('both', 'min'):
v[0] = -1
if self.extend in ('both', 'max'):
v[-1] = self.cmap.N
self._boundaries = b
self._values = v
return
elif isinstance(self.norm, colors.BoundaryNorm):
b = list(self.norm.boundaries)
if self.extend in ('both', 'min'):
b = [b[0]-1] + b
if self.extend in ('both', 'max'):
b = b + [b[-1] + 1]
b = np.array(b)
v = np.zeros((len(b)-1,), dtype=float)
bi = self.norm.boundaries
v[self._inside] = 0.5*(bi[:-1] + bi[1:])
if self.extend in ('both', 'min'):
v[0] = b[0] - 1
if self.extend in ('both', 'max'):
v[-1] = b[-1] + 1
self._boundaries = b
self._values = v
return
else:
if not self.norm.scaled():
self.norm.vmin = 0
self.norm.vmax = 1
b = self.norm.inverse(self._uniform_y(self.cmap.N+1))
if self.extend in ('both', 'min'):
b[0] = b[0] - 1
if self.extend in ('both', 'max'):
b[-1] = b[-1] + 1
self._process_values(b)
def _find_range(self):
'''
Set :attr:`vmin` and :attr:`vmax` attributes to the first and
last boundary excluding extended end boundaries.
'''
b = self._boundaries[self._inside]
self.vmin = b[0]
self.vmax = b[-1]
def _central_N(self):
'''number of boundaries **before** extension of ends'''
nb = len(self._boundaries)
if self.extend == 'both':
nb -= 2
elif self.extend in ('min', 'max'):
nb -= 1
return nb
def _extended_N(self):
'''
Based on the colormap and extend variable, return the
number of boundaries.
'''
N = self.cmap.N + 1
if self.extend == 'both':
N += 2
elif self.extend in ('min', 'max'):
N += 1
return N
def _uniform_y(self, N):
'''
Return colorbar data coordinates for *N* uniformly
spaced boundaries, plus ends if required.
'''
if self.extend == 'neither':
y = np.linspace(0, 1, N)
else:
if self.extend == 'both':
y = np.zeros(N + 2, 'd')
y[0] = -0.05
y[-1] = 1.05
elif self.extend == 'min':
y = np.zeros(N + 1, 'd')
y[0] = -0.05
else:
y = np.zeros(N + 1, 'd')
y[-1] = 1.05
y[self._inside] = np.linspace(0, 1, N)
return y
def _proportional_y(self):
'''
Return colorbar data coordinates for the boundaries of
a proportional colorbar.
'''
if isinstance(self.norm, colors.BoundaryNorm):
b = self._boundaries[self._inside]
y = (self._boundaries - self._boundaries[0])
y = y / (self._boundaries[-1] - self._boundaries[0])
else:
y = self.norm(self._boundaries.copy())
if self.extend in ('both', 'min'):
y[0] = -0.05
if self.extend in ('both', 'max'):
y[-1] = 1.05
yi = y[self._inside]
norm = colors.Normalize(yi[0], yi[-1])
y[self._inside] = norm(yi)
return y
def _mesh(self):
'''
Return X,Y, the coordinate arrays for the colorbar pcolormesh.
These are suitable for a vertical colorbar; swapping and
transposition for a horizontal colorbar are done outside
this function.
'''
x = np.array([0.0, 1.0])
if self.spacing == 'uniform':
y = self._uniform_y(self._central_N())
else:
y = self._proportional_y()
self._y = y
X, Y = np.meshgrid(x,y)
if self.extend in ('min', 'both'):
X[0,:] = 0.5
if self.extend in ('max', 'both'):
X[-1,:] = 0.5
return X, Y
def _locate(self, x):
'''
Given a possible set of color data values, return the ones
within range, together with their corresponding colorbar
data coordinates.
'''
if isinstance(self.norm, (colors.NoNorm, colors.BoundaryNorm)):
b = self._boundaries
xn = x
xout = x
else:
# Do calculations using normalized coordinates so
# as to make the interpolation more accurate.
b = self.norm(self._boundaries, clip=False).filled()
# We do our own clipping so that we can allow a tiny
# bit of slop in the end point ticks to allow for
# floating point errors.
xn = self.norm(x, clip=False).filled()
in_cond = (xn > -0.001) & (xn < 1.001)
xn = np.compress(in_cond, xn)
xout = np.compress(in_cond, x)
# The rest is linear interpolation with clipping.
y = self._y
N = len(b)
ii = np.minimum(np.searchsorted(b, xn), N-1)
i0 = np.maximum(ii - 1, 0)
#db = b[ii] - b[i0]
db = np.take(b, ii) - np.take(b, i0)
db = np.where(i0==ii, 1.0, db)
#dy = y[ii] - y[i0]
dy = np.take(y, ii) - np.take(y, i0)
z = np.take(y, i0) + (xn-np.take(b,i0))*dy/db
return xout, z
def set_alpha(self, alpha):
self.alpha = alpha
class Colorbar(ColorbarBase):
def __init__(self, ax, mappable, **kw):
mappable.autoscale_None() # Ensure mappable.norm.vmin, vmax
# are set when colorbar is called,
# even if mappable.draw has not yet
# been called. This will not change
# vmin, vmax if they are already set.
self.mappable = mappable
kw['cmap'] = mappable.cmap
kw['norm'] = mappable.norm
kw['alpha'] = mappable.get_alpha()
if isinstance(mappable, contour.ContourSet):
CS = mappable
kw['boundaries'] = CS._levels
kw['values'] = CS.cvalues
kw['extend'] = CS.extend
#kw['ticks'] = CS._levels
kw.setdefault('ticks', ticker.FixedLocator(CS.levels, nbins=10))
kw['filled'] = CS.filled
ColorbarBase.__init__(self, ax, **kw)
if not CS.filled:
self.add_lines(CS)
else:
ColorbarBase.__init__(self, ax, **kw)
def add_lines(self, CS):
'''
Add the lines from a non-filled
:class:`~matplotlib.contour.ContourSet` to the colorbar.
'''
if not isinstance(CS, contour.ContourSet) or CS.filled:
raise ValueError('add_lines is only for a ContourSet of lines')
tcolors = [c[0] for c in CS.tcolors]
tlinewidths = [t[0] for t in CS.tlinewidths]
# The following was an attempt to get the colorbar lines
# to follow subsequent changes in the contour lines,
# but more work is needed: specifically, a careful
# look at event sequences, and at how
# to make one object track another automatically.
#tcolors = [col.get_colors()[0] for col in CS.collections]
#tlinewidths = [col.get_linewidth()[0] for lw in CS.collections]
#print 'tlinewidths:', tlinewidths
ColorbarBase.add_lines(self, CS.levels, tcolors, tlinewidths)
def update_bruteforce(self, mappable):
'''
Manually change any contour line colors. This is called
when the image or contour plot to which this colorbar belongs
is changed.
'''
# We are using an ugly brute-force method: clearing and
# redrawing the whole thing. The problem is that if any
# properties have been changed by methods other than the
# colorbar methods, those changes will be lost.
self.ax.cla()
self.draw_all()
#if self.vmin != self.norm.vmin or self.vmax != self.norm.vmax:
# self.ax.cla()
# self.draw_all()
if isinstance(self.mappable, contour.ContourSet):
CS = self.mappable
if not CS.filled:
self.add_lines(CS)
#if self.lines is not None:
# tcolors = [c[0] for c in CS.tcolors]
# self.lines.set_color(tcolors)
#Fixme? Recalculate boundaries, ticks if vmin, vmax have changed.
#Fixme: Some refactoring may be needed; we should not
# be recalculating everything if there was a simple alpha
# change.
def make_axes(parent, **kw):
orientation = kw.setdefault('orientation', 'vertical')
fraction = kw.pop('fraction', 0.15)
shrink = kw.pop('shrink', 1.0)
aspect = kw.pop('aspect', 20)
#pb = transforms.PBox(parent.get_position())
pb = parent.get_position(original=True).frozen()
if orientation == 'vertical':
pad = kw.pop('pad', 0.05)
x1 = 1.0-fraction
pb1, pbx, pbcb = pb.splitx(x1-pad, x1)
pbcb = pbcb.shrunk(1.0, shrink).anchored('C', pbcb)
anchor = (0.0, 0.5)
panchor = (1.0, 0.5)
else:
pad = kw.pop('pad', 0.15)
pbcb, pbx, pb1 = pb.splity(fraction, fraction+pad)
pbcb = pbcb.shrunk(shrink, 1.0).anchored('C', pbcb)
aspect = 1.0/aspect
anchor = (0.5, 1.0)
panchor = (0.5, 0.0)
parent.set_position(pb1)
parent.set_anchor(panchor)
fig = parent.get_figure()
cax = fig.add_axes(pbcb)
cax.set_aspect(aspect, anchor=anchor, adjustable='box')
return cax, kw
make_axes.__doc__ ='''
Resize and reposition a parent axes, and return a child
axes suitable for a colorbar::
cax, kw = make_axes(parent, **kw)
Keyword arguments may include the following (with defaults):
*orientation*
'vertical' or 'horizontal'
%s
All but the first of these are stripped from the input kw set.
Returns (cax, kw), the child axes and the reduced kw dictionary.
''' % make_axes_kw_doc
| agpl-3.0 |
NDManh/numbbo | code-postprocessing/bbob_pproc/comp2/pptable2.py | 3 | 20251 | #! /usr/bin/env python
# -*- coding: utf-8 -*-
"""Rank-sum tests table on "Final Data Points".
That is, for example, using 1/#fevals(ftarget) if ftarget was reached
and -f_final otherwise as input for the rank-sum test, where obviously
the larger the better.
One table per function and dimension.
"""
from __future__ import absolute_import
import os, warnings
import numpy
import matplotlib.pyplot as plt
from .. import genericsettings, bestalg, toolsstats, pproc
from ..pptex import tableLaTeX, tableLaTeXStar, writeFEvals2, writeFEvalsMaxPrec, writeLabels
from ..toolsstats import significancetest
from pdb import set_trace
targetsOfInterest = pproc.TargetValues((1e+1, 1e-1, 1e-3, 1e-5, 1e-7))
targetf = 1e-8 # value for determining the success ratio
samplesize = genericsettings.simulated_runlength_bootstrap_sample_size
table_caption_one = r"""%
Expected running time (ERT in number of function
evaluations) divided by the respective best ERT measured during BBOB-2009 in
dimensions 5 (left) and 20 (right).
The ERT and in braces, as dispersion measure, the half difference between 90 and
10\%-tile of bootstrapped run lengths appear for each algorithm and
"""
table_caption_two1 = r"""%
target, the corresponding best ERT
in the first row. The different target \Df-values are shown in the top row.
\#succ is the number of trials that reached the (final) target $\fopt + 10^{-8}$.
"""
table_caption_two2 = r"""%
run-length based target, the corresponding best ERT
(preceded by the target \Df-value in \textit{italics}) in the first row.
\#succ is the number of trials that reached the target value of the last column.
"""
table_caption_rest = r"""%
The median number of conducted function evaluations is additionally given in
\textit{italics}, if the target in the last column was never reached.
1:\algorithmAshort\ is \algorithmA\ and 2:\algorithmBshort\ is \algorithmB.
Bold entries are statistically significantly better compared to the other algorithm,
with $p=0.05$ or $p=10^{-k}$ where $k\in\{2,3,4,\dots\}$ is the number
following the $\star$ symbol, with Bonferroni correction of #1.
A $\downarrow$ indicates the same tested against the best algorithm of BBOB-2009.
"""
table_caption = table_caption_one + table_caption_two1 + table_caption_rest
table_caption_expensive = table_caption_one + table_caption_two2 + table_caption_rest
def main(dsList0, dsList1, dimsOfInterest, outputdir, info='', verbose=True):
"""One table per dimension, modified to fit in 1 page per table."""
#TODO: method is long, split if possible
dictDim0 = dsList0.dictByDim()
dictDim1 = dsList1.dictByDim()
alg0 = set(i[0] for i in dsList0.dictByAlg().keys()).pop().replace(genericsettings.extraction_folder_prefix, '')[0:3]
alg1 = set(i[0] for i in dsList1.dictByAlg().keys()).pop().replace(genericsettings.extraction_folder_prefix, '')[0:3]
open(os.path.join(outputdir, 'bbob_pproc_commands.tex'), 'a'
).write(r'\providecommand{\algorithmAshort}{%s}' % writeLabels(alg0) + '\n' +
r'\providecommand{\algorithmBshort}{%s}' % writeLabels(alg1) + '\n')
if info:
info = '_' + info
dims = set.intersection(set(dictDim0.keys()), set(dictDim1.keys()))
bestalgentries = bestalg.loadBestAlgorithm(dsList0.isBiobjective())
header = []
if isinstance(targetsOfInterest, pproc.RunlengthBasedTargetValues):
header = [r'\#FEs/D']
headerHtml = ['<thead>\n<tr>\n<th>#FEs/D</th>\n']
for label in targetsOfInterest.labels():
header.append(r'\multicolumn{2}{@{}c@{}}{%s}' % label)
headerHtml.append('<td>%s</td>\n' % label)
else:
header = [r'$\Delta f_\mathrm{opt}$']
headerHtml = ['<thead>\n<tr>\n<th>Δ f</th>\n']
for label in targetsOfInterest.labels():
header.append(r'\multicolumn{2}{@{\,}c@{\,}}{%s}' % label)
headerHtml.append('<td>%s</td>\n' % label)
header.append(r'\multicolumn{2}{@{}l@{}}{\#succ}')
headerHtml.append('<td>#succ</td>\n</tr>\n</thead>\n')
for d in dimsOfInterest: # TODO set as input arguments
table = [header]
tableHtml = headerHtml
extraeol = [r'\hline']
try:
dictFunc0 = dictDim0[d].dictByFunc()
dictFunc1 = dictDim1[d].dictByFunc()
except KeyError:
continue
funcs = set.union(set(dictFunc0.keys()), set(dictFunc1.keys()))
nbtests = len(funcs) * 2. #len(dimsOfInterest)
tableHtml.append('<tbody>\n')
for f in sorted(funcs):
tableHtml.append('<tr>\n')
targets = targetsOfInterest((f, d))
targetf = targets[-1]
bestalgentry = bestalgentries[(d, f)]
curline = [r'${\bf f_{%d}}$' % f]
curlineHtml = ['<th><b>f<sub>%d</sub></b></th>\n' % f]
bestalgdata = bestalgentry.detERT(targets)
bestalgevals, bestalgalgs = bestalgentry.detEvals(targets)
if isinstance(targetsOfInterest, pproc.RunlengthBasedTargetValues):
# write ftarget:fevals
for i in xrange(len(bestalgdata[:-1])):
temp = "%.1e" % targetsOfInterest((f, d))[i]
if temp[-2]=="0":
temp = temp[:-2]+temp[-1]
curline.append(r'\multicolumn{2}{@{}c@{}}{\textit{%s}:%s \quad}'
% (temp,writeFEvalsMaxPrec(bestalgdata[i], 2)))
curlineHtml.append('<td><i>%s</i>:%s</td>\n'
% (temp, writeFEvalsMaxPrec(bestalgdata[i], 2)))
temp = "%.1e" % targetsOfInterest((f, d))[-1]
if temp[-2]=="0":
temp = temp[:-2]+temp[-1]
curline.append(r'\multicolumn{2}{@{}c@{}|}{\textit{%s}:%s }'
% (temp,writeFEvalsMaxPrec(bestalgdata[-1], 2)))
curlineHtml.append('<td><i>%s</i>:%s</td>\n'
% (temp, writeFEvalsMaxPrec(bestalgdata[-1], 2)))
else:
# write #fevals of the reference alg
for i in bestalgdata[:-1]:
curline.append(r'\multicolumn{2}{@{}c@{}}{%s \quad}'
% writeFEvalsMaxPrec(i, 2))
curlineHtml.append('<td>%s</td>\n' % writeFEvalsMaxPrec(i, 2))
curline.append(r'\multicolumn{2}{@{}c@{}|}{%s}'
% writeFEvalsMaxPrec(bestalgdata[-1], 2))
curlineHtml.append('<td>%s</td>\n' % writeFEvalsMaxPrec(bestalgdata[-1], 2))
tmp = bestalgentry.detEvals([targetf])[0][0]
tmp2 = numpy.sum(numpy.isnan(tmp) == False)
curline.append('%d' % (tmp2))
if tmp2 > 0:
curline.append('/%d' % len(tmp))
curlineHtml.append('<td>%d/%d</td>\n' % (tmp2, len(tmp)))
else:
curlineHtml.append('<td>%d</td>\n' % (tmp2))
table.append(curline[:])
tableHtml.extend(curlineHtml[:])
tableHtml.append('</tr>\n')
extraeol.append('')
rankdata0 = [] # never used
# generate all data from ranksum test
entries = []
ertdata = {}
for nb, dsList in enumerate((dictFunc0, dictFunc1)):
try:
entry = dsList[f][0] # take the first DataSet, there should be only one?
except KeyError:
warnings.warn('data missing for data set ' + str(nb) + ' and function ' + str(f))
print('*** Warning: data missing for data set ' + str(nb) + ' and function ' + str(f) + '***')
continue # TODO: problem here!
ertdata[nb] = entry.detERT(targets)
entries.append(entry)
for _t in ertdata.values():
for _tt in _t:
if _tt is None:
raise ValueError
if len(entries) < 2: # funcion not available for *both* algorithms
continue # TODO: check which one is missing and make sure that what is there is displayed properly in the following
testres0vs1 = significancetest(entries[0], entries[1], targets)
testresbestvs1 = significancetest(bestalgentry, entries[1], targets)
testresbestvs0 = significancetest(bestalgentry, entries[0], targets)
for nb, entry in enumerate(entries):
tableHtml.append('<tr>\n')
if nb == 0:
curline = [r'1:\:\algorithmAshort\hspace*{\fill}']
curlineHtml = ['<th>1: %s</th>\n' % alg0]
else:
curline = [r'2:\:\algorithmBshort\hspace*{\fill}']
curlineHtml = ['<th>2: %s</th>\n' % alg1]
#data = entry.detERT(targetsOfInterest)
dispersion = []
data = []
evals = entry.detEvals(targets)
for i in evals:
succ = (numpy.isnan(i) == False)
tmp = i.copy()
tmp[succ==False] = entry.maxevals[numpy.isnan(i)]
#set_trace()
data.append(toolsstats.sp(tmp, issuccessful=succ)[0])
#if not any(succ):
#set_trace()
if any(succ):
tmp2 = toolsstats.drawSP(tmp[succ], tmp[succ==False],
(10, 50, 90), samplesize)[0]
dispersion.append((tmp2[-1]-tmp2[0])/2.)
else:
dispersion.append(None)
if nb == 0:
assert not isinstance(data, numpy.ndarray)
data0 = data[:] # TODO: check if it is not an array, it's never used anyway?
for i, dati in enumerate(data):
z, p = testres0vs1[i] # TODO: there is something with the sign that I don't get
# assign significance flag, which is the -log10(p)
significance0vs1 = 0
if nb != 0:
z = -z # the test is symmetric
if nbtests * p < 0.05 and z > 0:
significance0vs1 = -int(numpy.ceil(numpy.log10(min([1.0, nbtests * p])))) # this is the larger the more significant
isBold = significance0vs1 > 0
alignment = 'c'
if i == len(data) - 1: # last element
alignment = 'c|'
if numpy.isinf(bestalgdata[i]): # if the 2009 best did not solve the problem
tmp = writeFEvalsMaxPrec(float(dati), 2)
if not numpy.isinf(dati):
tmpHtml = '<i>%s</i>' % (tmp)
tmp = r'\textit{%s}' % (tmp)
if isBold:
tmp = r'\textbf{%s}' % tmp
tmpHtml = '<b>%s</b>' % tmpHtml
if dispersion[i] and numpy.isfinite(dispersion[i]):
tmp += r'${\scriptscriptstyle (%s)}$' % writeFEvalsMaxPrec(dispersion[i], 1)
tableentry = (r'\multicolumn{2}{@{}%s@{}}{%s}'
% (alignment, tmp))
tableentryHtml = (' (%s)' % tmp)
else:
# Formatting
tmp = float(dati)/bestalgdata[i]
assert not numpy.isnan(tmp)
isscientific = False
if tmp >= 1000:
isscientific = True
tableentry = writeFEvals2(tmp, 2, isscientific=isscientific)
tableentry = writeFEvalsMaxPrec(tmp, 2)
tableentryHtml = writeFEvalsMaxPrec(tmp, 2)
if numpy.isinf(tmp) and i == len(data)-1:
tableentry = (tableentry
+ r'\textit{%s}' % writeFEvals2(numpy.median(entry.maxevals), 2))
tableentryHtml = (tableentryHtml
+ ' <i>%s</i>' % writeFEvals2(numpy.median(entry.maxevals), 2))
if isBold:
tableentry = r'\textbf{%s}' % tableentry
tableentryHtml = '<b>%s</b>' % tableentryHtml
elif 11 < 3 and significance0vs1 < 0: # cave: negative significance has no meaning anymore
tableentry = r'\textit{%s}' % tableentry
tableentryHtml = '<i>%s</i>' % tableentryHtml
if dispersion[i] and numpy.isfinite(dispersion[i]/bestalgdata[i]):
tableentry += r'${\scriptscriptstyle (%s)}$' % writeFEvalsMaxPrec(dispersion[i]/bestalgdata[i], 1)
tableentryHtml += ' (%s)' % writeFEvalsMaxPrec(dispersion[i]/bestalgdata[i], 1)
tableentry = (r'\multicolumn{2}{@{}%s@{}}{%s}'
% (alignment, tableentry))
elif tableentry.find('e') > -1 or (numpy.isinf(tmp) and i != len(data) - 1):
if isBold:
tableentry = r'\textbf{%s}' % tableentry
tableentryHtml = '<b>%s</b>' % tableentryHtml
elif 11 < 3 and significance0vs1 < 0:
tableentry = r'\textit{%s}' % tableentry
tableentryHtml = '<i>%s</i>' % tableentryHtml
if dispersion[i] and numpy.isfinite(dispersion[i]/bestalgdata[i]):
tableentry += r'${\scriptscriptstyle (%s)}$' % writeFEvalsMaxPrec(dispersion[i]/bestalgdata[i], 1)
tableentryHtml += ' (%s)' % writeFEvalsMaxPrec(dispersion[i]/bestalgdata[i], 1)
tableentry = (r'\multicolumn{2}{@{}%s@{}}{%s}'
% (alignment, tableentry))
else:
tmp = tableentry.split('.', 1)
tmpHtml = tableentryHtml.split('.', 1)
if isBold:
tmp = list(r'\textbf{%s}' % i for i in tmp)
tmpHtml = list('<b>%s</b>' % i for i in tmpHtml)
elif 11 < 3 and significance0vs1 < 0:
tmp = list(r'\textit{%s}' % i for i in tmp)
tmpHtml = list('<i>%s</i>' % i for i in tmpHtml)
tableentry = ' & .'.join(tmp)
tableentryHtml = '.'.join(tmpHtml)
if len(tmp) == 1:
tableentry += '&'
if dispersion[i] and numpy.isfinite(dispersion[i]/bestalgdata[i]):
tableentry += r'${\scriptscriptstyle (%s)}$' % writeFEvalsMaxPrec(dispersion[i]/bestalgdata[i], 1)
tableentryHtml += ' (%s)' % writeFEvalsMaxPrec(dispersion[i]/bestalgdata[i], 1)
superscript = ''
superscriptHtml = ''
if nb == 0:
z, p = testresbestvs0[i]
else:
z, p = testresbestvs1[i]
#The conditions are now that ERT < ERT_best
if ((nbtests * p) < 0.05 and dati - bestalgdata[i] < 0.
and z < 0.):
nbstars = -numpy.ceil(numpy.log10(nbtests * p))
#tmp = '\hspace{-.5ex}'.join(nbstars * [r'\star'])
if z > 0:
superscript = r'\uparrow' #* nbstars
superscriptHtml = '↑'
else:
superscript = r'\downarrow' #* nbstars
superscriptHtml = '↓'
# print z, linebest[i], line1
if nbstars > 1:
superscript += str(int(nbstars))
superscriptHtml += str(int(nbstars))
if superscript or significance0vs1:
s = ''
shtml = ''
if significance0vs1 > 0:
s = '\star'
shtml = '★'
if significance0vs1 > 1:
s += str(significance0vs1)
shtml += str(significance0vs1)
s = r'$^{' + s + superscript + r'}$'
shtml = '<sup>' + shtml + superscriptHtml + '</sup>'
if tableentry.endswith('}'):
tableentry = tableentry[:-1] + s + r'}'
else:
tableentry += s
tableentryHtml += shtml
tableentryHtml = tableentryHtml.replace('$\infty$', '∞')
curlineHtml.append('<td>%s</td>\n' % tableentryHtml)
curline.append(tableentry)
#curline.append(tableentry)
#if dispersion[i] is None or numpy.isinf(bestalgdata[i]):
#curline.append('')
#else:
#tmp = writeFEvalsMaxPrec(dispersion[i]/bestalgdata[i], 2)
#curline.append('(%s)' % tmp)
tmp = entry.evals[entry.evals[:, 0] <= targetf, 1:]
try:
tmp = tmp[0]
curline.append('%d' % numpy.sum(numpy.isnan(tmp) == False))
curlineHtml.append('<td>%d' % numpy.sum(numpy.isnan(tmp) == False))
except IndexError:
curline.append('%d' % 0)
curlineHtml.append('<td>%d' % 0)
curline.append('/%d' % entry.nbRuns())
curlineHtml.append('/%d</td>\n' % entry.nbRuns())
table.append(curline[:])
tableHtml.extend(curlineHtml[:])
tableHtml.append('</tr>\n')
extraeol.append('')
extraeol[-1] = r'\hline'
extraeol[-1] = ''
outputfile = os.path.join(outputdir, 'pptable2_%02dD%s.tex' % (d, info))
spec = r'@{}c@{}|' + '*{%d}{@{}r@{}@{}l@{}}' % len(targetsOfInterest) + '|@{}r@{}@{}l@{}'
res = r'\providecommand{\algorithmAshort}{%s}' % writeLabels(alg0) + '\n'
res += r'\providecommand{\algorithmBshort}{%s}' % writeLabels(alg1) + '\n'
# open(os.path.join(outputdir, 'bbob_pproc_commands.tex'), 'a').write(res)
#res += tableLaTeXStar(table, width=r'0.45\textwidth', spec=spec,
#extraeol=extraeol)
res += tableLaTeX(table, spec=spec, extraeol=extraeol)
f = open(outputfile, 'w')
f.write(res)
f.close()
res = ("").join(str(item) for item in tableHtml)
res = '<p><b>%d-D</b></p>\n<table>\n%s</table>\n' % (d, res)
filename = os.path.join(outputdir, genericsettings.two_algorithm_file_name + '.html')
lines = []
with open(filename) as infile:
for line in infile:
if '<!--pptable2Html-->' in line:
lines.append(res)
lines.append(line)
with open(filename, 'w') as outfile:
for line in lines:
outfile.write(line)
if verbose:
print "Table written in %s" % outputfile
| bsd-3-clause |
mattpitkin/GraWIToNStatisticsLectures | figures/scripts/pvalue.py | 1 | 1242 | #!/usr/bin/env python
"""
Make plots showing how to calculate the p-value
"""
import matplotlib.pyplot as pl
from scipy.stats import norm
from scipy.special import erf
import numpy as np
mu = 0. # the mean, mu
sigma = 1. # standard deviation
x = np.linspace(-4, 4, 1000) # x
# set plot to render labels using latex
pl.rc('text', usetex=True)
pl.rc('font', family='serif')
pl.rc('font', size=14)
fig = pl.figure(figsize=(7,4), dpi=100)
# value of x for calculating p-value
Z = 1.233
y = norm.pdf(x, mu, sigma)
# plot pdfs
pl.plot(x, y, 'r')
pl.plot([-Z, -Z], [0., np.max(y)], 'k--')
pl.plot([Z, Z], [0., np.max(y)], 'k--')
pl.fill_between(x, np.zeros(len(x)), y, where=x<=-Z, facecolor='green', interpolate=True, alpha=0.6)
pl.fill_between(x, np.zeros(len(x)), y, where=x>=Z, facecolor='green', interpolate=True, alpha=0.6)
pvalue = 1.-erf(Z/np.sqrt(2.))
ax = pl.gca()
ax.set_xlabel('$Z$', fontsize=14)
ax.set_ylabel('$p(Z)$', fontsize=14)
ax.set_xlim(-4, 4)
ax.grid(True)
ax.text(Z+0.1, 0.3, '$Z_{\\textrm{obs}} = 1.233$', fontsize=16)
ax.text(-3.6, 0.31, '$p$-value$= %.2f$' % pvalue, fontsize=18,
bbox={'facecolor': 'none', 'pad':12, 'ec': 'r'})
fig.subplots_adjust(bottom=0.15)
pl.savefig('../pvalue.pdf')
pl.show()
| mit |
gwpy/gwpy.github.io | docs/0.8.0/plotter/colors-1.py | 7 | 1123 | from __future__ import division
import numpy
from matplotlib import (pyplot, rcParams)
from matplotlib.colors import to_hex
from gwpy.plotter import colors
rcParams.update({
'text.usetex': False,
'font.size': 15
})
th = numpy.linspace(0, 2*numpy.pi, 512)
names = [
'gwpy:geo600',
'gwpy:kagra',
'gwpy:ligo-hanford',
'gwpy:ligo-india',
'gwpy:ligo-livingston',
'gwpy:virgo',
]
fig = pyplot.figure(figsize=(5, 2))
ax = fig.gca()
ax.axis('off')
for j, name in enumerate(sorted(names)):
c = str(to_hex(name))
v_offset = -(j / len(names))
ax.plot(th, .1*numpy.sin(th) + v_offset, color=c)
ax.annotate("{!r}".format(name), (0, v_offset), xytext=(-1.5, 0),
ha='right', va='center', color=c,
textcoords='offset points', family='monospace')
ax.annotate("{!r}".format(c), (2*numpy.pi, v_offset), xytext=(1.5, 0),
ha='left', va='center', color=c,
textcoords='offset points', family='monospace')
fig.subplots_adjust(**{'bottom': 0.0, 'left': 0.54,
'right': 0.78, 'top': 1})
pyplot.show() | gpl-3.0 |
karpeev/libmesh | doc/statistics/libmesh_citations.py | 1 | 2340 | #!/usr/bin/env python
import matplotlib.pyplot as plt
import numpy as np
# Number of "papers using libmesh" by year.
#
# Note 1: this does not count citations "only," the authors must have actually
# used libmesh in part of their work. Therefore, these counts do not include
# things like Wolfgang citing us in his papers to show how Deal.II is
# superior...
#
# Note 2: I typically update this data after regenerating the web page,
# since bibtex2html renumbers the references starting from "1" each year.
#
# Note 3: These citations include anything that is not a dissertation/thesis.
# So, some are conference papers, some are journal articles, etc.
#
# Note 4: The libmesh paper came out in 2006, but there are some citations
# prior to that date, obviously. These counts include citations of the
# website libmesh.sf.net as well...
#
# Note 5: Preprints are listed as the "current year + 1" and are constantly
# being moved to their respective years after being published.
data = [
'2004', 5,
'\'05', 2,
'\'06', 13,
'\'07', 8,
'\'08', 23,
'\'09', 30,
'\'10', 24,
'\'11', 37,
'\'12', 50,
'\'13', 78,
'\'14', 62,
'\'15', 24,
'P', 5, # Preprints
'T', 38 # Theses
]
# Extract the x-axis labels from the data array
xlabels = data[0::2]
# Extract the publication counts from the data array
n_papers = data[1::2]
# The number of data points
N = len(xlabels);
# Get a reference to the figure
fig = plt.figure()
# 111 is equivalent to Matlab's subplot(1,1,1) command
ax = fig.add_subplot(111)
# Create an x-axis for plotting
x = np.linspace(1, N, N)
# Width of the bars
width = 0.8
# Make the bar chart. Plot years in blue, preprints and theses in green.
ax.bar(x[0:N-2], n_papers[0:N-2], width, color='b')
ax.bar(x[N-2:N], n_papers[N-2:N], width, color='g')
# Label the x-axis
plt.xlabel('P=Preprints, T=Theses')
# Set up the xtick locations and labels. Note that you have to offset
# the position of the ticks by width/2, where width is the width of
# the bars.
ax.set_xticks(np.linspace(1,N,N) + width/2)
ax.set_xticklabels(xlabels)
# Create a title string
title_string = 'LibMesh Citations, (' + str(sum(n_papers)) + ' Total)'
fig.suptitle(title_string)
# Save as PDF
plt.savefig('libmesh_citations.pdf')
# Local Variables:
# python-indent: 2
# End:
| lgpl-2.1 |
numenta/nupic | external/linux32/lib/python2.6/site-packages/matplotlib/mlab.py | 69 | 104273 | """
Numerical python functions written for compatability with matlab(TM)
commands with the same names.
Matlab(TM) compatible functions
-------------------------------
:func:`cohere`
Coherence (normalized cross spectral density)
:func:`csd`
Cross spectral density uing Welch's average periodogram
:func:`detrend`
Remove the mean or best fit line from an array
:func:`find`
Return the indices where some condition is true;
numpy.nonzero is similar but more general.
:func:`griddata`
interpolate irregularly distributed data to a
regular grid.
:func:`prctile`
find the percentiles of a sequence
:func:`prepca`
Principal Component Analysis
:func:`psd`
Power spectral density uing Welch's average periodogram
:func:`rk4`
A 4th order runge kutta integrator for 1D or ND systems
:func:`specgram`
Spectrogram (power spectral density over segments of time)
Miscellaneous functions
-------------------------
Functions that don't exist in matlab(TM), but are useful anyway:
:meth:`cohere_pairs`
Coherence over all pairs. This is not a matlab function, but we
compute coherence a lot in my lab, and we compute it for a lot of
pairs. This function is optimized to do this efficiently by
caching the direct FFTs.
:meth:`rk4`
A 4th order Runge-Kutta ODE integrator in case you ever find
yourself stranded without scipy (and the far superior
scipy.integrate tools)
record array helper functions
-------------------------------
A collection of helper methods for numpyrecord arrays
.. _htmlonly::
See :ref:`misc-examples-index`
:meth:`rec2txt`
pretty print a record array
:meth:`rec2csv`
store record array in CSV file
:meth:`csv2rec`
import record array from CSV file with type inspection
:meth:`rec_append_fields`
adds field(s)/array(s) to record array
:meth:`rec_drop_fields`
drop fields from record array
:meth:`rec_join`
join two record arrays on sequence of fields
:meth:`rec_groupby`
summarize data by groups (similar to SQL GROUP BY)
:meth:`rec_summarize`
helper code to filter rec array fields into new fields
For the rec viewer functions(e rec2csv), there are a bunch of Format
objects you can pass into the functions that will do things like color
negative values red, set percent formatting and scaling, etc.
Example usage::
r = csv2rec('somefile.csv', checkrows=0)
formatd = dict(
weight = FormatFloat(2),
change = FormatPercent(2),
cost = FormatThousands(2),
)
rec2excel(r, 'test.xls', formatd=formatd)
rec2csv(r, 'test.csv', formatd=formatd)
scroll = rec2gtk(r, formatd=formatd)
win = gtk.Window()
win.set_size_request(600,800)
win.add(scroll)
win.show_all()
gtk.main()
Deprecated functions
---------------------
The following are deprecated; please import directly from numpy (with
care--function signatures may differ):
:meth:`conv`
convolution (numpy.convolve)
:meth:`corrcoef`
The matrix of correlation coefficients
:meth:`hist`
Histogram (numpy.histogram)
:meth:`linspace`
Linear spaced array from min to max
:meth:`load`
load ASCII file - use numpy.loadtxt
:meth:`meshgrid`
Make a 2D grid from 2 1 arrays (numpy.meshgrid)
:meth:`polyfit`
least squares best polynomial fit of x to y (numpy.polyfit)
:meth:`polyval`
evaluate a vector for a vector of polynomial coeffs (numpy.polyval)
:meth:`save`
save ASCII file - use numpy.savetxt
:meth:`trapz`
trapeziodal integration (trapz(x,y) -> numpy.trapz(y,x))
:meth:`vander`
the Vandermonde matrix (numpy.vander)
"""
from __future__ import division
import csv, warnings, copy, os
import numpy as np
ma = np.ma
from matplotlib import verbose
import matplotlib.nxutils as nxutils
import matplotlib.cbook as cbook
# set is a new builtin function in 2.4; delete the following when
# support for 2.3 is dropped.
try:
set
except NameError:
from sets import Set as set
def linspace(*args, **kw):
warnings.warn("use numpy.linspace", DeprecationWarning)
return np.linspace(*args, **kw)
def meshgrid(x,y):
warnings.warn("use numpy.meshgrid", DeprecationWarning)
return np.meshgrid(x,y)
def mean(x, dim=None):
warnings.warn("Use numpy.mean(x) or x.mean()", DeprecationWarning)
if len(x)==0: return None
return np.mean(x, axis=dim)
def logspace(xmin,xmax,N):
return np.exp(np.linspace(np.log(xmin), np.log(xmax), N))
def _norm(x):
"return sqrt(x dot x)"
return np.sqrt(np.dot(x,x))
def window_hanning(x):
"return x times the hanning window of len(x)"
return np.hanning(len(x))*x
def window_none(x):
"No window function; simply return x"
return x
#from numpy import convolve as conv
def conv(x, y, mode=2):
'convolve x with y'
warnings.warn("Use numpy.convolve(x, y, mode='full')", DeprecationWarning)
return np.convolve(x,y,mode)
def detrend(x, key=None):
if key is None or key=='constant':
return detrend_mean(x)
elif key=='linear':
return detrend_linear(x)
def demean(x, axis=0):
"Return x minus its mean along the specified axis"
x = np.asarray(x)
if axis:
ind = [slice(None)] * axis
ind.append(np.newaxis)
return x - x.mean(axis)[ind]
return x - x.mean(axis)
def detrend_mean(x):
"Return x minus the mean(x)"
return x - x.mean()
def detrend_none(x):
"Return x: no detrending"
return x
def detrend_linear(y):
"Return y minus best fit line; 'linear' detrending "
# This is faster than an algorithm based on linalg.lstsq.
x = np.arange(len(y), dtype=np.float_)
C = np.cov(x, y, bias=1)
b = C[0,1]/C[0,0]
a = y.mean() - b*x.mean()
return y - (b*x + a)
#This is a helper function that implements the commonality between the
#psd, csd, and spectrogram. It is *NOT* meant to be used outside of mlab
def _spectral_helper(x, y, NFFT=256, Fs=2, detrend=detrend_none,
window=window_hanning, noverlap=0, pad_to=None, sides='default',
scale_by_freq=None):
#The checks for if y is x are so that we can use the same function to
#implement the core of psd(), csd(), and spectrogram() without doing
#extra calculations. We return the unaveraged Pxy, freqs, and t.
same_data = y is x
#Make sure we're dealing with a numpy array. If y and x were the same
#object to start with, keep them that way
x = np.asarray(x)
if not same_data:
y = np.asarray(y)
# zero pad x and y up to NFFT if they are shorter than NFFT
if len(x)<NFFT:
n = len(x)
x = np.resize(x, (NFFT,))
x[n:] = 0
if not same_data and len(y)<NFFT:
n = len(y)
y = np.resize(y, (NFFT,))
y[n:] = 0
if pad_to is None:
pad_to = NFFT
if scale_by_freq is None:
warnings.warn("psd, csd, and specgram have changed to scale their "
"densities by the sampling frequency for better MatLab "
"compatibility. You can pass scale_by_freq=False to disable "
"this behavior. Also, one-sided densities are scaled by a "
"factor of 2.")
scale_by_freq = True
# For real x, ignore the negative frequencies unless told otherwise
if (sides == 'default' and np.iscomplexobj(x)) or sides == 'twosided':
numFreqs = pad_to
scaling_factor = 1.
elif sides in ('default', 'onesided'):
numFreqs = pad_to//2 + 1
scaling_factor = 2.
else:
raise ValueError("sides must be one of: 'default', 'onesided', or "
"'twosided'")
# Matlab divides by the sampling frequency so that density function
# has units of dB/Hz and can be integrated by the plotted frequency
# values. Perform the same scaling here.
if scale_by_freq:
scaling_factor /= Fs
if cbook.iterable(window):
assert(len(window) == NFFT)
windowVals = window
else:
windowVals = window(np.ones((NFFT,), x.dtype))
step = NFFT - noverlap
ind = np.arange(0, len(x) - NFFT + 1, step)
n = len(ind)
Pxy = np.zeros((numFreqs,n), np.complex_)
# do the ffts of the slices
for i in range(n):
thisX = x[ind[i]:ind[i]+NFFT]
thisX = windowVals * detrend(thisX)
fx = np.fft.fft(thisX, n=pad_to)
if same_data:
fy = fx
else:
thisY = y[ind[i]:ind[i]+NFFT]
thisY = windowVals * detrend(thisY)
fy = np.fft.fft(thisY, n=pad_to)
Pxy[:,i] = np.conjugate(fx[:numFreqs]) * fy[:numFreqs]
# Scale the spectrum by the norm of the window to compensate for
# windowing loss; see Bendat & Piersol Sec 11.5.2. Also include
# scaling factors for one-sided densities and dividing by the sampling
# frequency, if desired.
Pxy *= scaling_factor / (np.abs(windowVals)**2).sum()
t = 1./Fs * (ind + NFFT / 2.)
freqs = float(Fs) / pad_to * np.arange(numFreqs)
return Pxy, freqs, t
#Split out these keyword docs so that they can be used elsewhere
kwdocd = dict()
kwdocd['PSD'] ="""
Keyword arguments:
*NFFT*: integer
The number of data points used in each block for the FFT.
Must be even; a power 2 is most efficient. The default value is 256.
*Fs*: scalar
The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.
*detrend*: callable
The function applied to each segment before fft-ing,
designed to remove the mean or linear trend. Unlike in
matlab, where the *detrend* parameter is a vector, in
matplotlib is it a function. The :mod:`~matplotlib.pylab`
module defines :func:`~matplotlib.pylab.detrend_none`,
:func:`~matplotlib.pylab.detrend_mean`, and
:func:`~matplotlib.pylab.detrend_linear`, but you can use
a custom function as well.
*window*: callable or ndarray
A function or a vector of length *NFFT*. To create window
vectors see :func:`window_hanning`, :func:`window_none`,
:func:`numpy.blackman`, :func:`numpy.hamming`,
:func:`numpy.bartlett`, :func:`scipy.signal`,
:func:`scipy.signal.get_window`, etc. The default is
:func:`window_hanning`. If a function is passed as the
argument, it must take a data segment as an argument and
return the windowed version of the segment.
*noverlap*: integer
The number of points of overlap between blocks. The default value
is 0 (no overlap).
*pad_to*: integer
The number of points to which the data segment is padded when
performing the FFT. This can be different from *NFFT*, which
specifies the number of data points used. While not increasing
the actual resolution of the psd (the minimum distance between
resolvable peaks), this can give more points in the plot,
allowing for more detail. This corresponds to the *n* parameter
in the call to fft(). The default is None, which sets *pad_to*
equal to *NFFT*
*sides*: [ 'default' | 'onesided' | 'twosided' ]
Specifies which sides of the PSD to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. 'onesided' forces the return of a one-sided PSD,
while 'twosided' forces two-sided.
*scale_by_freq*: boolean
Specifies whether the resulting density values should be scaled
by the scaling frequency, which gives density in units of Hz^-1.
This allows for integration over the returned frequency values.
The default is True for MatLab compatibility.
"""
def psd(x, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning,
noverlap=0, pad_to=None, sides='default', scale_by_freq=None):
"""
The power spectral density by Welch's average periodogram method.
The vector *x* is divided into *NFFT* length blocks. Each block
is detrended by the function *detrend* and windowed by the function
*window*. *noverlap* gives the length of the overlap between blocks.
The absolute(fft(block))**2 of each segment are averaged to compute
*Pxx*, with a scaling to correct for power loss due to windowing.
If len(*x*) < *NFFT*, it will be zero padded to *NFFT*.
*x*
Array or sequence containing the data
%(PSD)s
Returns the tuple (*Pxx*, *freqs*).
Refs:
Bendat & Piersol -- Random Data: Analysis and Measurement
Procedures, John Wiley & Sons (1986)
"""
Pxx,freqs = csd(x, x, NFFT, Fs, detrend, window, noverlap, pad_to, sides,
scale_by_freq)
return Pxx.real,freqs
psd.__doc__ = psd.__doc__ % kwdocd
def csd(x, y, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning,
noverlap=0, pad_to=None, sides='default', scale_by_freq=None):
"""
The cross power spectral density by Welch's average periodogram
method. The vectors *x* and *y* are divided into *NFFT* length
blocks. Each block is detrended by the function *detrend* and
windowed by the function *window*. *noverlap* gives the length
of the overlap between blocks. The product of the direct FFTs
of *x* and *y* are averaged over each segment to compute *Pxy*,
with a scaling to correct for power loss due to windowing.
If len(*x*) < *NFFT* or len(*y*) < *NFFT*, they will be zero
padded to *NFFT*.
*x*, *y*
Array or sequence containing the data
%(PSD)s
Returns the tuple (*Pxy*, *freqs*).
Refs:
Bendat & Piersol -- Random Data: Analysis and Measurement
Procedures, John Wiley & Sons (1986)
"""
Pxy, freqs, t = _spectral_helper(x, y, NFFT, Fs, detrend, window,
noverlap, pad_to, sides, scale_by_freq)
if len(Pxy.shape) == 2 and Pxy.shape[1]>1:
Pxy = Pxy.mean(axis=1)
return Pxy, freqs
csd.__doc__ = csd.__doc__ % kwdocd
def specgram(x, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning,
noverlap=128, pad_to=None, sides='default', scale_by_freq=None):
"""
Compute a spectrogram of data in *x*. Data are split into *NFFT*
length segements and the PSD of each section is computed. The
windowing function *window* is applied to each segment, and the
amount of overlap of each segment is specified with *noverlap*.
If *x* is real (i.e. non-complex) only the spectrum of the positive
frequencie is returned. If *x* is complex then the complete
spectrum is returned.
%(PSD)s
Returns a tuple (*Pxx*, *freqs*, *t*):
- *Pxx*: 2-D array, columns are the periodograms of
successive segments
- *freqs*: 1-D array of frequencies corresponding to the rows
in Pxx
- *t*: 1-D array of times corresponding to midpoints of
segments.
.. seealso::
:func:`psd`:
:func:`psd` differs in the default overlap; in returning
the mean of the segment periodograms; and in not returning
times.
"""
assert(NFFT > noverlap)
Pxx, freqs, t = _spectral_helper(x, x, NFFT, Fs, detrend, window,
noverlap, pad_to, sides, scale_by_freq)
Pxx = Pxx.real #Needed since helper implements generically
if (np.iscomplexobj(x) and sides == 'default') or sides == 'twosided':
# center the frequency range at zero
freqs = np.concatenate((freqs[NFFT/2:]-Fs,freqs[:NFFT/2]))
Pxx = np.concatenate((Pxx[NFFT/2:,:],Pxx[:NFFT/2,:]),0)
return Pxx, freqs, t
specgram.__doc__ = specgram.__doc__ % kwdocd
_coh_error = """Coherence is calculated by averaging over *NFFT*
length segments. Your signal is too short for your choice of *NFFT*.
"""
def cohere(x, y, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning,
noverlap=0, pad_to=None, sides='default', scale_by_freq=None):
"""
The coherence between *x* and *y*. Coherence is the normalized
cross spectral density:
.. math::
C_{xy} = \\frac{|P_{xy}|^2}{P_{xx}P_{yy}}
*x*, *y*
Array or sequence containing the data
%(PSD)s
The return value is the tuple (*Cxy*, *f*), where *f* are the
frequencies of the coherence vector. For cohere, scaling the
individual densities by the sampling frequency has no effect, since
the factors cancel out.
.. seealso::
:func:`psd` and :func:`csd`:
For information about the methods used to compute
:math:`P_{xy}`, :math:`P_{xx}` and :math:`P_{yy}`.
"""
if len(x)<2*NFFT:
raise ValueError(_coh_error)
Pxx, f = psd(x, NFFT, Fs, detrend, window, noverlap, pad_to, sides,
scale_by_freq)
Pyy, f = psd(y, NFFT, Fs, detrend, window, noverlap, pad_to, sides,
scale_by_freq)
Pxy, f = csd(x, y, NFFT, Fs, detrend, window, noverlap, pad_to, sides,
scale_by_freq)
Cxy = np.divide(np.absolute(Pxy)**2, Pxx*Pyy)
Cxy.shape = (len(f),)
return Cxy, f
cohere.__doc__ = cohere.__doc__ % kwdocd
def corrcoef(*args):
"""
corrcoef(*X*) where *X* is a matrix returns a matrix of correlation
coefficients for the columns of *X*
corrcoef(*x*, *y*) where *x* and *y* are vectors returns the matrix of
correlation coefficients for *x* and *y*.
Numpy arrays can be real or complex.
The correlation matrix is defined from the covariance matrix *C*
as
.. math::
r_{ij} = \\frac{C_{ij}}{\\sqrt{C_{ii}C_{jj}}}
"""
warnings.warn("Use numpy.corrcoef", DeprecationWarning)
kw = dict(rowvar=False)
return np.corrcoef(*args, **kw)
def polyfit(*args, **kwargs):
u"""
polyfit(*x*, *y*, *N*)
Do a best fit polynomial of order *N* of *y* to *x*. Return value
is a vector of polynomial coefficients [pk ... p1 p0]. Eg, for
*N*=2::
p2*x0^2 + p1*x0 + p0 = y1
p2*x1^2 + p1*x1 + p0 = y1
p2*x2^2 + p1*x2 + p0 = y2
.....
p2*xk^2 + p1*xk + p0 = yk
Method: if *X* is a the Vandermonde Matrix computed from *x* (see
`vandermonds
<http://mathworld.wolfram.com/VandermondeMatrix.html>`_), then the
polynomial least squares solution is given by the '*p*' in
X*p = y
where *X* is a (len(*x*) \N{MULTIPLICATION SIGN} *N* + 1) matrix,
*p* is a *N*+1 length vector, and *y* is a (len(*x*)
\N{MULTIPLICATION SIGN} 1) vector.
This equation can be solved as
.. math::
p = (X_t X)^-1 X_t y
where :math:`X_t` is the transpose of *X* and -1 denotes the
inverse. Numerically, however, this is not a good method, so we
use :func:`numpy.linalg.lstsq`.
For more info, see `least squares fitting
<http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html>`_,
but note that the *k*'s and *n*'s in the superscripts and
subscripts on that page. The linear algebra is correct, however.
.. seealso::
:func:`polyval`
"""
warnings.warn("use numpy.poyfit", DeprecationWarning)
return np.polyfit(*args, **kwargs)
def polyval(*args, **kwargs):
"""
*y* = polyval(*p*, *x*)
*p* is a vector of polynomial coeffients and *y* is the polynomial
evaluated at *x*.
Example code to remove a polynomial (quadratic) trend from y::
p = polyfit(x, y, 2)
trend = polyval(p, x)
resid = y - trend
.. seealso::
:func:`polyfit`
"""
warnings.warn("use numpy.polyval", DeprecationWarning)
return np.polyval(*args, **kwargs)
def vander(*args, **kwargs):
"""
*X* = vander(*x*, *N* = *None*)
The Vandermonde matrix of vector *x*. The *i*-th column of *X* is the
the *i*-th power of *x*. *N* is the maximum power to compute; if *N* is
*None* it defaults to len(*x*).
"""
warnings.warn("Use numpy.vander()", DeprecationWarning)
return np.vander(*args, **kwargs)
def donothing_callback(*args):
pass
def cohere_pairs( X, ij, NFFT=256, Fs=2, detrend=detrend_none,
window=window_hanning, noverlap=0,
preferSpeedOverMemory=True,
progressCallback=donothing_callback,
returnPxx=False):
u"""
Cxy, Phase, freqs = cohere_pairs(X, ij, ...)
Compute the coherence for all pairs in *ij*. *X* is a
(*numSamples*, *numCols*) numpy array. *ij* is a list of tuples
(*i*, *j*). Each tuple is a pair of indexes into the columns of *X*
for which you want to compute coherence. For example, if *X* has 64
columns, and you want to compute all nonredundant pairs, define *ij*
as::
ij = []
for i in range(64):
for j in range(i+1,64):
ij.append( (i, j) )
The other function arguments, except for *preferSpeedOverMemory*
(see below), are explained in the help string of :func:`psd`.
Return value is a tuple (*Cxy*, *Phase*, *freqs*).
- *Cxy*: a dictionary of (*i*, *j*) tuples -> coherence vector for that
pair. I.e., ``Cxy[(i,j)] = cohere(X[:,i], X[:,j])``. Number of
dictionary keys is ``len(ij)``.
- *Phase*: a dictionary of phases of the cross spectral density at
each frequency for each pair. The keys are ``(i,j)``.
- *freqs*: a vector of frequencies, equal in length to either
the coherence or phase vectors for any (*i*, *j*) key.. Eg,
to make a coherence Bode plot::
subplot(211)
plot( freqs, Cxy[(12,19)])
subplot(212)
plot( freqs, Phase[(12,19)])
For a large number of pairs, :func:`cohere_pairs` can be much more
efficient than just calling :func:`cohere` for each pair, because
it caches most of the intensive computations. If *N* is the
number of pairs, this function is O(N) for most of the heavy
lifting, whereas calling cohere for each pair is
O(N\N{SUPERSCRIPT TWO}). However, because of the caching, it is
also more memory intensive, making 2 additional complex arrays
with approximately the same number of elements as *X*.
The parameter *preferSpeedOverMemory*, if *False*, limits the
caching by only making one, rather than two, complex cache arrays.
This is useful if memory becomes critical. Even when
*preferSpeedOverMemory* is *False*, :func:`cohere_pairs` will
still give significant performace gains over calling
:func:`cohere` for each pair, and will use subtantially less
memory than if *preferSpeedOverMemory* is *True*. In my tests
with a (43000, 64) array over all non-redundant pairs,
*preferSpeedOverMemory* = *True* delivered a 33% performace boost
on a 1.7GHZ Athlon with 512MB RAM compared with
*preferSpeedOverMemory* = *False*. But both solutions were more
than 10x faster than naievly crunching all possible pairs through
cohere.
.. seealso::
:file:`test/cohere_pairs_test.py` in the src tree:
For an example script that shows that this
:func:`cohere_pairs` and :func:`cohere` give the same
results for a given pair.
"""
numRows, numCols = X.shape
# zero pad if X is too short
if numRows < NFFT:
tmp = X
X = np.zeros( (NFFT, numCols), X.dtype)
X[:numRows,:] = tmp
del tmp
numRows, numCols = X.shape
# get all the columns of X that we are interested in by checking
# the ij tuples
seen = {}
for i,j in ij:
seen[i]=1; seen[j] = 1
allColumns = seen.keys()
Ncols = len(allColumns)
del seen
# for real X, ignore the negative frequencies
if np.iscomplexobj(X): numFreqs = NFFT
else: numFreqs = NFFT//2+1
# cache the FFT of every windowed, detrended NFFT length segement
# of every channel. If preferSpeedOverMemory, cache the conjugate
# as well
if cbook.iterable(window):
assert(len(window) == NFFT)
windowVals = window
else:
windowVals = window(np.ones((NFFT,), typecode(X)))
ind = range(0, numRows-NFFT+1, NFFT-noverlap)
numSlices = len(ind)
FFTSlices = {}
FFTConjSlices = {}
Pxx = {}
slices = range(numSlices)
normVal = norm(windowVals)**2
for iCol in allColumns:
progressCallback(i/Ncols, 'Cacheing FFTs')
Slices = np.zeros( (numSlices,numFreqs), dtype=np.complex_)
for iSlice in slices:
thisSlice = X[ind[iSlice]:ind[iSlice]+NFFT, iCol]
thisSlice = windowVals*detrend(thisSlice)
Slices[iSlice,:] = fft(thisSlice)[:numFreqs]
FFTSlices[iCol] = Slices
if preferSpeedOverMemory:
FFTConjSlices[iCol] = conjugate(Slices)
Pxx[iCol] = np.divide(np.mean(absolute(Slices)**2), normVal)
del Slices, ind, windowVals
# compute the coherences and phases for all pairs using the
# cached FFTs
Cxy = {}
Phase = {}
count = 0
N = len(ij)
for i,j in ij:
count +=1
if count%10==0:
progressCallback(count/N, 'Computing coherences')
if preferSpeedOverMemory:
Pxy = FFTSlices[i] * FFTConjSlices[j]
else:
Pxy = FFTSlices[i] * np.conjugate(FFTSlices[j])
if numSlices>1: Pxy = np.mean(Pxy)
Pxy = np.divide(Pxy, normVal)
Cxy[(i,j)] = np.divide(np.absolute(Pxy)**2, Pxx[i]*Pxx[j])
Phase[(i,j)] = np.arctan2(Pxy.imag, Pxy.real)
freqs = Fs/NFFT*np.arange(numFreqs)
if returnPxx:
return Cxy, Phase, freqs, Pxx
else:
return Cxy, Phase, freqs
def entropy(y, bins):
r"""
Return the entropy of the data in *y*.
.. math::
\sum p_i \log_2(p_i)
where :math:`p_i` is the probability of observing *y* in the
:math:`i^{th}` bin of *bins*. *bins* can be a number of bins or a
range of bins; see :func:`numpy.histogram`.
Compare *S* with analytic calculation for a Gaussian::
x = mu + sigma * randn(200000)
Sanalytic = 0.5 * ( 1.0 + log(2*pi*sigma**2.0) )
"""
n,bins = np.histogram(y, bins)
n = n.astype(np.float_)
n = np.take(n, np.nonzero(n)[0]) # get the positive
p = np.divide(n, len(y))
delta = bins[1]-bins[0]
S = -1.0*np.sum(p*log(p)) + log(delta)
#S = -1.0*np.sum(p*log(p))
return S
def hist(y, bins=10, normed=0):
"""
Return the histogram of *y* with *bins* equally sized bins. If
bins is an array, use those bins. Return value is (*n*, *x*)
where *n* is the count for each bin in *x*.
If *normed* is *False*, return the counts in the first element of
the returned tuple. If *normed* is *True*, return the probability
density :math:`\\frac{n}{(len(y)\mathrm{dbin}}`.
If *y* has rank > 1, it will be raveled. If *y* is masked, only the
unmasked values will be used.
Credits: the Numeric 22 documentation
"""
warnings.warn("Use numpy.histogram()", DeprecationWarning)
return np.histogram(y, bins=bins, range=None, normed=normed)
def normpdf(x, *args):
"Return the normal pdf evaluated at *x*; args provides *mu*, *sigma*"
mu, sigma = args
return 1./(np.sqrt(2*np.pi)*sigma)*np.exp(-0.5 * (1./sigma*(x - mu))**2)
def levypdf(x, gamma, alpha):
"Returm the levy pdf evaluated at *x* for params *gamma*, *alpha*"
N = len(x)
if N%2 != 0:
raise ValueError, 'x must be an event length array; try\n' + \
'x = np.linspace(minx, maxx, N), where N is even'
dx = x[1]-x[0]
f = 1/(N*dx)*np.arange(-N/2, N/2, np.float_)
ind = np.concatenate([np.arange(N/2, N, int),
np.arange(0, N/2, int)])
df = f[1]-f[0]
cfl = exp(-gamma*np.absolute(2*pi*f)**alpha)
px = np.fft.fft(np.take(cfl,ind)*df).astype(np.float_)
return np.take(px, ind)
def find(condition):
"Return the indices where ravel(condition) is true"
res, = np.nonzero(np.ravel(condition))
return res
def trapz(x, y):
"""
Trapezoidal integral of *y*(*x*).
"""
warnings.warn("Use numpy.trapz(y,x) instead of trapz(x,y)", DeprecationWarning)
return np.trapz(y, x)
#if len(x)!=len(y):
# raise ValueError, 'x and y must have the same length'
#if len(x)<2:
# raise ValueError, 'x and y must have > 1 element'
#return np.sum(0.5*np.diff(x)*(y[1:]+y[:-1]))
def longest_contiguous_ones(x):
"""
Return the indices of the longest stretch of contiguous ones in *x*,
assuming *x* is a vector of zeros and ones. If there are two
equally long stretches, pick the first.
"""
x = np.ravel(x)
if len(x)==0:
return np.array([])
ind = (x==0).nonzero()[0]
if len(ind)==0:
return np.arange(len(x))
if len(ind)==len(x):
return np.array([])
y = np.zeros( (len(x)+2,), x.dtype)
y[1:-1] = x
dif = np.diff(y)
up = (dif == 1).nonzero()[0];
dn = (dif == -1).nonzero()[0];
i = (dn-up == max(dn - up)).nonzero()[0][0]
ind = np.arange(up[i], dn[i])
return ind
def longest_ones(x):
'''alias for longest_contiguous_ones'''
return longest_contiguous_ones(x)
def prepca(P, frac=0):
"""
Compute the principal components of *P*. *P* is a (*numVars*,
*numObs*) array. *frac* is the minimum fraction of variance that a
component must contain to be included.
Return value is a tuple of the form (*Pcomponents*, *Trans*,
*fracVar*) where:
- *Pcomponents* : a (numVars, numObs) array
- *Trans* : the weights matrix, ie, *Pcomponents* = *Trans* *
*P*
- *fracVar* : the fraction of the variance accounted for by each
component returned
A similar function of the same name was in the Matlab (TM)
R13 Neural Network Toolbox but is not found in later versions;
its successor seems to be called "processpcs".
"""
U,s,v = np.linalg.svd(P)
varEach = s**2/P.shape[1]
totVar = varEach.sum()
fracVar = varEach/totVar
ind = slice((fracVar>=frac).sum())
# select the components that are greater
Trans = U[:,ind].transpose()
# The transformed data
Pcomponents = np.dot(Trans,P)
return Pcomponents, Trans, fracVar[ind]
def prctile(x, p = (0.0, 25.0, 50.0, 75.0, 100.0)):
"""
Return the percentiles of *x*. *p* can either be a sequence of
percentile values or a scalar. If *p* is a sequence, the ith
element of the return sequence is the *p*(i)-th percentile of *x*.
If *p* is a scalar, the largest value of *x* less than or equal to
the *p* percentage point in the sequence is returned.
"""
x = np.array(x).ravel() # we need a copy
x.sort()
Nx = len(x)
if not cbook.iterable(p):
return x[int(p*Nx/100.0)]
p = np.asarray(p)* Nx/100.0
ind = p.astype(int)
ind = np.where(ind>=Nx, Nx-1, ind)
return x.take(ind)
def prctile_rank(x, p):
"""
Return the rank for each element in *x*, return the rank
0..len(*p*). Eg if *p* = (25, 50, 75), the return value will be a
len(*x*) array with values in [0,1,2,3] where 0 indicates the
value is less than the 25th percentile, 1 indicates the value is
>= the 25th and < 50th percentile, ... and 3 indicates the value
is above the 75th percentile cutoff.
*p* is either an array of percentiles in [0..100] or a scalar which
indicates how many quantiles of data you want ranked.
"""
if not cbook.iterable(p):
p = np.arange(100.0/p, 100.0, 100.0/p)
else:
p = np.asarray(p)
if p.max()<=1 or p.min()<0 or p.max()>100:
raise ValueError('percentiles should be in range 0..100, not 0..1')
ptiles = prctile(x, p)
return np.searchsorted(ptiles, x)
def center_matrix(M, dim=0):
"""
Return the matrix *M* with each row having zero mean and unit std.
If *dim* = 1 operate on columns instead of rows. (*dim* is
opposite to the numpy axis kwarg.)
"""
M = np.asarray(M, np.float_)
if dim:
M = (M - M.mean(axis=0)) / M.std(axis=0)
else:
M = (M - M.mean(axis=1)[:,np.newaxis])
M = M / M.std(axis=1)[:,np.newaxis]
return M
def rk4(derivs, y0, t):
"""
Integrate 1D or ND system of ODEs using 4-th order Runge-Kutta.
This is a toy implementation which may be useful if you find
yourself stranded on a system w/o scipy. Otherwise use
:func:`scipy.integrate`.
*y0*
initial state vector
*t*
sample times
*derivs*
returns the derivative of the system and has the
signature ``dy = derivs(yi, ti)``
Example 1 ::
## 2D system
def derivs6(x,t):
d1 = x[0] + 2*x[1]
d2 = -3*x[0] + 4*x[1]
return (d1, d2)
dt = 0.0005
t = arange(0.0, 2.0, dt)
y0 = (1,2)
yout = rk4(derivs6, y0, t)
Example 2::
## 1D system
alpha = 2
def derivs(x,t):
return -alpha*x + exp(-t)
y0 = 1
yout = rk4(derivs, y0, t)
If you have access to scipy, you should probably be using the
scipy.integrate tools rather than this function.
"""
try: Ny = len(y0)
except TypeError:
yout = np.zeros( (len(t),), np.float_)
else:
yout = np.zeros( (len(t), Ny), np.float_)
yout[0] = y0
i = 0
for i in np.arange(len(t)-1):
thist = t[i]
dt = t[i+1] - thist
dt2 = dt/2.0
y0 = yout[i]
k1 = np.asarray(derivs(y0, thist))
k2 = np.asarray(derivs(y0 + dt2*k1, thist+dt2))
k3 = np.asarray(derivs(y0 + dt2*k2, thist+dt2))
k4 = np.asarray(derivs(y0 + dt*k3, thist+dt))
yout[i+1] = y0 + dt/6.0*(k1 + 2*k2 + 2*k3 + k4)
return yout
def bivariate_normal(X, Y, sigmax=1.0, sigmay=1.0,
mux=0.0, muy=0.0, sigmaxy=0.0):
"""
Bivariate Gaussian distribution for equal shape *X*, *Y*.
See `bivariate normal
<http://mathworld.wolfram.com/BivariateNormalDistribution.html>`_
at mathworld.
"""
Xmu = X-mux
Ymu = Y-muy
rho = sigmaxy/(sigmax*sigmay)
z = Xmu**2/sigmax**2 + Ymu**2/sigmay**2 - 2*rho*Xmu*Ymu/(sigmax*sigmay)
denom = 2*np.pi*sigmax*sigmay*np.sqrt(1-rho**2)
return np.exp( -z/(2*(1-rho**2))) / denom
def get_xyz_where(Z, Cond):
"""
*Z* and *Cond* are *M* x *N* matrices. *Z* are data and *Cond* is
a boolean matrix where some condition is satisfied. Return value
is (*x*, *y*, *z*) where *x* and *y* are the indices into *Z* and
*z* are the values of *Z* at those indices. *x*, *y*, and *z* are
1D arrays.
"""
X,Y = np.indices(Z.shape)
return X[Cond], Y[Cond], Z[Cond]
def get_sparse_matrix(M,N,frac=0.1):
"""
Return a *M* x *N* sparse matrix with *frac* elements randomly
filled.
"""
data = np.zeros((M,N))*0.
for i in range(int(M*N*frac)):
x = np.random.randint(0,M-1)
y = np.random.randint(0,N-1)
data[x,y] = np.random.rand()
return data
def dist(x,y):
"""
Return the distance between two points.
"""
d = x-y
return np.sqrt(np.dot(d,d))
def dist_point_to_segment(p, s0, s1):
"""
Get the distance of a point to a segment.
*p*, *s0*, *s1* are *xy* sequences
This algorithm from
http://softsurfer.com/Archive/algorithm_0102/algorithm_0102.htm#Distance%20to%20Ray%20or%20Segment
"""
p = np.asarray(p, np.float_)
s0 = np.asarray(s0, np.float_)
s1 = np.asarray(s1, np.float_)
v = s1 - s0
w = p - s0
c1 = np.dot(w,v);
if ( c1 <= 0 ):
return dist(p, s0);
c2 = np.dot(v,v)
if ( c2 <= c1 ):
return dist(p, s1);
b = c1 / c2
pb = s0 + b * v;
return dist(p, pb)
def segments_intersect(s1, s2):
"""
Return *True* if *s1* and *s2* intersect.
*s1* and *s2* are defined as::
s1: (x1, y1), (x2, y2)
s2: (x3, y3), (x4, y4)
"""
(x1, y1), (x2, y2) = s1
(x3, y3), (x4, y4) = s2
den = ((y4-y3) * (x2-x1)) - ((x4-x3)*(y2-y1))
n1 = ((x4-x3) * (y1-y3)) - ((y4-y3)*(x1-x3))
n2 = ((x2-x1) * (y1-y3)) - ((y2-y1)*(x1-x3))
if den == 0:
# lines parallel
return False
u1 = n1/den
u2 = n2/den
return 0.0 <= u1 <= 1.0 and 0.0 <= u2 <= 1.0
def fftsurr(x, detrend=detrend_none, window=window_none):
"""
Compute an FFT phase randomized surrogate of *x*.
"""
if cbook.iterable(window):
x=window*detrend(x)
else:
x = window(detrend(x))
z = np.fft.fft(x)
a = 2.*np.pi*1j
phase = a * np.random.rand(len(x))
z = z*np.exp(phase)
return np.fft.ifft(z).real
def liaupunov(x, fprime):
"""
*x* is a very long trajectory from a map, and *fprime* returns the
derivative of *x*.
Returns :
.. math::
\lambda = \\frac{1}{n}\\sum \\ln|f^'(x_i)|
.. seealso::
Sec 10.5 Strogatz (1994) "Nonlinear Dynamics and Chaos".
`Wikipedia article on Lyapunov Exponent
<http://en.wikipedia.org/wiki/Lyapunov_exponent>`_.
.. note::
What the function here calculates may not be what you really want;
*caveat emptor*.
It also seems that this function's name is badly misspelled.
"""
return np.mean(np.log(np.absolute(fprime(x))))
class FIFOBuffer:
"""
A FIFO queue to hold incoming *x*, *y* data in a rotating buffer
using numpy arrays under the hood. It is assumed that you will
call asarrays much less frequently than you add data to the queue
-- otherwise another data structure will be faster.
This can be used to support plots where data is added from a real
time feed and the plot object wants to grab data from the buffer
and plot it to screen less freqeuently than the incoming.
If you set the *dataLim* attr to
:class:`~matplotlib.transforms.BBox` (eg
:attr:`matplotlib.Axes.dataLim`), the *dataLim* will be updated as
new data come in.
TODO: add a grow method that will extend nmax
.. note::
mlab seems like the wrong place for this class.
"""
def __init__(self, nmax):
"""
Buffer up to *nmax* points.
"""
self._xa = np.zeros((nmax,), np.float_)
self._ya = np.zeros((nmax,), np.float_)
self._xs = np.zeros((nmax,), np.float_)
self._ys = np.zeros((nmax,), np.float_)
self._ind = 0
self._nmax = nmax
self.dataLim = None
self.callbackd = {}
def register(self, func, N):
"""
Call *func* every time *N* events are passed; *func* signature
is ``func(fifo)``.
"""
self.callbackd.setdefault(N, []).append(func)
def add(self, x, y):
"""
Add scalar *x* and *y* to the queue.
"""
if self.dataLim is not None:
xys = ((x,y),)
self.dataLim.update(xys, -1) #-1 means use the default ignore setting
ind = self._ind % self._nmax
#print 'adding to fifo:', ind, x, y
self._xs[ind] = x
self._ys[ind] = y
for N,funcs in self.callbackd.items():
if (self._ind%N)==0:
for func in funcs:
func(self)
self._ind += 1
def last(self):
"""
Get the last *x*, *y* or *None*. *None* if no data set.
"""
if self._ind==0: return None, None
ind = (self._ind-1) % self._nmax
return self._xs[ind], self._ys[ind]
def asarrays(self):
"""
Return *x* and *y* as arrays; their length will be the len of
data added or *nmax*.
"""
if self._ind<self._nmax:
return self._xs[:self._ind], self._ys[:self._ind]
ind = self._ind % self._nmax
self._xa[:self._nmax-ind] = self._xs[ind:]
self._xa[self._nmax-ind:] = self._xs[:ind]
self._ya[:self._nmax-ind] = self._ys[ind:]
self._ya[self._nmax-ind:] = self._ys[:ind]
return self._xa, self._ya
def update_datalim_to_current(self):
"""
Update the *datalim* in the current data in the fifo.
"""
if self.dataLim is None:
raise ValueError('You must first set the dataLim attr')
x, y = self.asarrays()
self.dataLim.update_numerix(x, y, True)
def movavg(x,n):
"""
Compute the len(*n*) moving average of *x*.
"""
w = np.empty((n,), dtype=np.float_)
w[:] = 1.0/n
return np.convolve(x, w, mode='valid')
def save(fname, X, fmt='%.18e',delimiter=' '):
"""
Save the data in *X* to file *fname* using *fmt* string to convert the
data to strings.
*fname* can be a filename or a file handle. If the filename ends
in '.gz', the file is automatically saved in compressed gzip
format. The :func:`load` function understands gzipped files
transparently.
Example usage::
save('test.out', X) # X is an array
save('test1.out', (x,y,z)) # x,y,z equal sized 1D arrays
save('test2.out', x) # x is 1D
save('test3.out', x, fmt='%1.4e') # use exponential notation
*delimiter* is used to separate the fields, eg. *delimiter* ','
for comma-separated values.
"""
if cbook.is_string_like(fname):
if fname.endswith('.gz'):
import gzip
fh = gzip.open(fname,'wb')
else:
fh = file(fname,'w')
elif hasattr(fname, 'seek'):
fh = fname
else:
raise ValueError('fname must be a string or file handle')
X = np.asarray(X)
origShape = None
if X.ndim == 1:
origShape = X.shape
X.shape = len(X), 1
for row in X:
fh.write(delimiter.join([fmt%val for val in row]) + '\n')
if origShape is not None:
X.shape = origShape
def load(fname,comments='#',delimiter=None, converters=None,skiprows=0,
usecols=None, unpack=False, dtype=np.float_):
"""
Load ASCII data from *fname* into an array and return the array.
The data must be regular, same number of values in every row
*fname* can be a filename or a file handle. Support for gzipped
files is automatic, if the filename ends in '.gz'.
matfile data is not supported; for that, use :mod:`scipy.io.mio`
module.
Example usage::
X = load('test.dat') # data in two columns
t = X[:,0]
y = X[:,1]
Alternatively, you can do the same with "unpack"; see below::
X = load('test.dat') # a matrix of data
x = load('test.dat') # a single column of data
- *comments*: the character used to indicate the start of a comment
in the file
- *delimiter* is a string-like character used to seperate values
in the file. If *delimiter* is unspecified or *None*, any
whitespace string is a separator.
- *converters*, if not *None*, is a dictionary mapping column number to
a function that will convert that column to a float (or the optional
*dtype* if specified). Eg, if column 0 is a date string::
converters = {0:datestr2num}
- *skiprows* is the number of rows from the top to skip.
- *usecols*, if not *None*, is a sequence of integer column indexes to
extract where 0 is the first column, eg ``usecols=[1,4,5]`` to extract
just the 2nd, 5th and 6th columns
- *unpack*, if *True*, will transpose the matrix allowing you to unpack
into named arguments on the left hand side::
t,y = load('test.dat', unpack=True) # for two column data
x,y,z = load('somefile.dat', usecols=[3,5,7], unpack=True)
- *dtype*: the array will have this dtype. default: ``numpy.float_``
.. seealso::
See :file:`examples/pylab_examples/load_converter.py` in the source tree:
Exercises many of these options.
"""
if converters is None: converters = {}
fh = cbook.to_filehandle(fname)
X = []
if delimiter==' ':
# space splitting is a special case since x.split() is what
# you want, not x.split(' ')
def splitfunc(x):
return x.split()
else:
def splitfunc(x):
return x.split(delimiter)
converterseq = None
for i,line in enumerate(fh):
if i<skiprows: continue
line = line.split(comments, 1)[0].strip()
if not len(line): continue
if converterseq is None:
converterseq = [converters.get(j,float)
for j,val in enumerate(splitfunc(line))]
if usecols is not None:
vals = splitfunc(line)
row = [converterseq[j](vals[j]) for j in usecols]
else:
row = [converterseq[j](val)
for j,val in enumerate(splitfunc(line))]
thisLen = len(row)
X.append(row)
X = np.array(X, dtype)
r,c = X.shape
if r==1 or c==1:
X.shape = max(r,c),
if unpack: return X.transpose()
else: return X
def slopes(x,y):
"""
SLOPES calculate the slope y'(x) Given data vectors X and Y SLOPES
calculates Y'(X), i.e the slope of a curve Y(X). The slope is
estimated using the slope obtained from that of a parabola through
any three consecutive points.
This method should be superior to that described in the appendix
of A CONSISTENTLY WELL BEHAVED METHOD OF INTERPOLATION by Russel
W. Stineman (Creative Computing July 1980) in at least one aspect:
Circles for interpolation demand a known aspect ratio between x-
and y-values. For many functions, however, the abscissa are given
in different dimensions, so an aspect ratio is completely
arbitrary.
The parabola method gives very similar results to the circle
method for most regular cases but behaves much better in special
cases
Norbert Nemec, Institute of Theoretical Physics, University or
Regensburg, April 2006 Norbert.Nemec at physik.uni-regensburg.de
(inspired by a original implementation by Halldor Bjornsson,
Icelandic Meteorological Office, March 2006 halldor at vedur.is)
"""
# Cast key variables as float.
x=np.asarray(x, np.float_)
y=np.asarray(y, np.float_)
yp=np.zeros(y.shape, np.float_)
dx=x[1:] - x[:-1]
dy=y[1:] - y[:-1]
dydx = dy/dx
yp[1:-1] = (dydx[:-1] * dx[1:] + dydx[1:] * dx[:-1])/(dx[1:] + dx[:-1])
yp[0] = 2.0 * dy[0]/dx[0] - yp[1]
yp[-1] = 2.0 * dy[-1]/dx[-1] - yp[-2]
return yp
def stineman_interp(xi,x,y,yp=None):
"""
STINEMAN_INTERP Well behaved data interpolation. Given data
vectors X and Y, the slope vector YP and a new abscissa vector XI
the function stineman_interp(xi,x,y,yp) uses Stineman
interpolation to calculate a vector YI corresponding to XI.
Here's an example that generates a coarse sine curve, then
interpolates over a finer abscissa:
x = linspace(0,2*pi,20); y = sin(x); yp = cos(x)
xi = linspace(0,2*pi,40);
yi = stineman_interp(xi,x,y,yp);
plot(x,y,'o',xi,yi)
The interpolation method is described in the article A
CONSISTENTLY WELL BEHAVED METHOD OF INTERPOLATION by Russell
W. Stineman. The article appeared in the July 1980 issue of
Creative Computing with a note from the editor stating that while
they were
not an academic journal but once in a while something serious
and original comes in adding that this was
"apparently a real solution" to a well known problem.
For yp=None, the routine automatically determines the slopes using
the "slopes" routine.
X is assumed to be sorted in increasing order
For values xi[j] < x[0] or xi[j] > x[-1], the routine tries a
extrapolation. The relevance of the data obtained from this, of
course, questionable...
original implementation by Halldor Bjornsson, Icelandic
Meteorolocial Office, March 2006 halldor at vedur.is
completely reworked and optimized for Python by Norbert Nemec,
Institute of Theoretical Physics, University or Regensburg, April
2006 Norbert.Nemec at physik.uni-regensburg.de
"""
# Cast key variables as float.
x=np.asarray(x, np.float_)
y=np.asarray(y, np.float_)
assert x.shape == y.shape
N=len(y)
if yp is None:
yp = slopes(x,y)
else:
yp=np.asarray(yp, np.float_)
xi=np.asarray(xi, np.float_)
yi=np.zeros(xi.shape, np.float_)
# calculate linear slopes
dx = x[1:] - x[:-1]
dy = y[1:] - y[:-1]
s = dy/dx #note length of s is N-1 so last element is #N-2
# find the segment each xi is in
# this line actually is the key to the efficiency of this implementation
idx = np.searchsorted(x[1:-1], xi)
# now we have generally: x[idx[j]] <= xi[j] <= x[idx[j]+1]
# except at the boundaries, where it may be that xi[j] < x[0] or xi[j] > x[-1]
# the y-values that would come out from a linear interpolation:
sidx = s.take(idx)
xidx = x.take(idx)
yidx = y.take(idx)
xidxp1 = x.take(idx+1)
yo = yidx + sidx * (xi - xidx)
# the difference that comes when using the slopes given in yp
dy1 = (yp.take(idx)- sidx) * (xi - xidx) # using the yp slope of the left point
dy2 = (yp.take(idx+1)-sidx) * (xi - xidxp1) # using the yp slope of the right point
dy1dy2 = dy1*dy2
# The following is optimized for Python. The solution actually
# does more calculations than necessary but exploiting the power
# of numpy, this is far more efficient than coding a loop by hand
# in Python
yi = yo + dy1dy2 * np.choose(np.array(np.sign(dy1dy2), np.int32)+1,
((2*xi-xidx-xidxp1)/((dy1-dy2)*(xidxp1-xidx)),
0.0,
1/(dy1+dy2),))
return yi
def inside_poly(points, verts):
"""
points is a sequence of x,y points
verts is a sequence of x,y vertices of a poygon
return value is a sequence of indices into points for the points
that are inside the polygon
"""
res, = np.nonzero(nxutils.points_inside_poly(points, verts))
return res
def poly_below(ymin, xs, ys):
"""
given a arrays *xs* and *ys*, return the vertices of a polygon
that has a scalar lower bound *ymin* and an upper bound at the *ys*.
intended for use with Axes.fill, eg::
xv, yv = poly_below(0, x, y)
ax.fill(xv, yv)
"""
return poly_between(xs, ys, xmin)
def poly_between(x, ylower, yupper):
"""
given a sequence of x, ylower and yupper, return the polygon that
fills the regions between them. ylower or yupper can be scalar or
iterable. If they are iterable, they must be equal in length to x
return value is x, y arrays for use with Axes.fill
"""
Nx = len(x)
if not cbook.iterable(ylower):
ylower = ylower*np.ones(Nx)
if not cbook.iterable(yupper):
yupper = yupper*np.ones(Nx)
x = np.concatenate( (x, x[::-1]) )
y = np.concatenate( (yupper, ylower[::-1]) )
return x,y
### the following code was written and submitted by Fernando Perez
### from the ipython numutils package under a BSD license
# begin fperez functions
"""
A set of convenient utilities for numerical work.
Most of this module requires numpy or is meant to be used with it.
Copyright (c) 2001-2004, Fernando Perez. <Fernando.Perez@colorado.edu>
All rights reserved.
This license was generated from the BSD license template as found in:
http://www.opensource.org/licenses/bsd-license.php
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of the IPython project nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
"""
import operator
import math
#*****************************************************************************
# Globals
#****************************************************************************
# function definitions
exp_safe_MIN = math.log(2.2250738585072014e-308)
exp_safe_MAX = 1.7976931348623157e+308
def exp_safe(x):
"""
Compute exponentials which safely underflow to zero.
Slow, but convenient to use. Note that numpy provides proper
floating point exception handling with access to the underlying
hardware.
"""
if type(x) is np.ndarray:
return exp(np.clip(x,exp_safe_MIN,exp_safe_MAX))
else:
return math.exp(x)
def amap(fn,*args):
"""
amap(function, sequence[, sequence, ...]) -> array.
Works like :func:`map`, but it returns an array. This is just a
convenient shorthand for ``numpy.array(map(...))``.
"""
return np.array(map(fn,*args))
#from numpy import zeros_like
def zeros_like(a):
"""
Return an array of zeros of the shape and typecode of *a*.
"""
warnings.warn("Use numpy.zeros_like(a)", DeprecationWarning)
return np.zeros_like(a)
#from numpy import sum as sum_flat
def sum_flat(a):
"""
Return the sum of all the elements of *a*, flattened out.
It uses ``a.flat``, and if *a* is not contiguous, a call to
``ravel(a)`` is made.
"""
warnings.warn("Use numpy.sum(a) or a.sum()", DeprecationWarning)
return np.sum(a)
#from numpy import mean as mean_flat
def mean_flat(a):
"""
Return the mean of all the elements of *a*, flattened out.
"""
warnings.warn("Use numpy.mean(a) or a.mean()", DeprecationWarning)
return np.mean(a)
def rms_flat(a):
"""
Return the root mean square of all the elements of *a*, flattened out.
"""
return np.sqrt(np.mean(np.absolute(a)**2))
def l1norm(a):
"""
Return the *l1* norm of *a*, flattened out.
Implemented as a separate function (not a call to :func:`norm` for speed).
"""
return np.sum(np.absolute(a))
def l2norm(a):
"""
Return the *l2* norm of *a*, flattened out.
Implemented as a separate function (not a call to :func:`norm` for speed).
"""
return np.sqrt(np.sum(np.absolute(a)**2))
def norm_flat(a,p=2):
"""
norm(a,p=2) -> l-p norm of a.flat
Return the l-p norm of *a*, considered as a flat array. This is NOT a true
matrix norm, since arrays of arbitrary rank are always flattened.
*p* can be a number or the string 'Infinity' to get the L-infinity norm.
"""
# This function was being masked by a more general norm later in
# the file. We may want to simply delete it.
if p=='Infinity':
return np.amax(np.absolute(a))
else:
return (np.sum(np.absolute(a)**p))**(1.0/p)
def frange(xini,xfin=None,delta=None,**kw):
"""
frange([start,] stop[, step, keywords]) -> array of floats
Return a numpy ndarray containing a progression of floats. Similar to
:func:`numpy.arange`, but defaults to a closed interval.
``frange(x0, x1)`` returns ``[x0, x0+1, x0+2, ..., x1]``; *start*
defaults to 0, and the endpoint *is included*. This behavior is
different from that of :func:`range` and
:func:`numpy.arange`. This is deliberate, since :func:`frange`
will probably be more useful for generating lists of points for
function evaluation, and endpoints are often desired in this
use. The usual behavior of :func:`range` can be obtained by
setting the keyword *closed* = 0, in this case, :func:`frange`
basically becomes :func:numpy.arange`.
When *step* is given, it specifies the increment (or
decrement). All arguments can be floating point numbers.
``frange(x0,x1,d)`` returns ``[x0,x0+d,x0+2d,...,xfin]`` where
*xfin* <= *x1*.
:func:`frange` can also be called with the keyword *npts*. This
sets the number of points the list should contain (and overrides
the value *step* might have been given). :func:`numpy.arange`
doesn't offer this option.
Examples::
>>> frange(3)
array([ 0., 1., 2., 3.])
>>> frange(3,closed=0)
array([ 0., 1., 2.])
>>> frange(1,6,2)
array([1, 3, 5]) or 1,3,5,7, depending on floating point vagueries
>>> frange(1,6.5,npts=5)
array([ 1. , 2.375, 3.75 , 5.125, 6.5 ])
"""
#defaults
kw.setdefault('closed',1)
endpoint = kw['closed'] != 0
# funny logic to allow the *first* argument to be optional (like range())
# This was modified with a simpler version from a similar frange() found
# at http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66472
if xfin == None:
xfin = xini + 0.0
xini = 0.0
if delta == None:
delta = 1.0
# compute # of points, spacing and return final list
try:
npts=kw['npts']
delta=(xfin-xini)/float(npts-endpoint)
except KeyError:
npts = int(round((xfin-xini)/delta)) + endpoint
#npts = int(floor((xfin-xini)/delta)*(1.0+1e-10)) + endpoint
# round finds the nearest, so the endpoint can be up to
# delta/2 larger than xfin.
return np.arange(npts)*delta+xini
# end frange()
#import numpy.diag as diagonal_matrix
def diagonal_matrix(diag):
"""
Return square diagonal matrix whose non-zero elements are given by the
input array.
"""
warnings.warn("Use numpy.diag(d)", DeprecationWarning)
return np.diag(diag)
def identity(n, rank=2, dtype='l', typecode=None):
"""
Returns the identity matrix of shape (*n*, *n*, ..., *n*) (rank *r*).
For ranks higher than 2, this object is simply a multi-index Kronecker
delta::
/ 1 if i0=i1=...=iR,
id[i0,i1,...,iR] = -|
\ 0 otherwise.
Optionally a *dtype* (or typecode) may be given (it defaults to 'l').
Since rank defaults to 2, this function behaves in the default case (when
only *n* is given) like ``numpy.identity(n)`` -- but surprisingly, it is
much faster.
"""
if typecode is not None:
warnings.warn("Use dtype kwarg instead of typecode",
DeprecationWarning)
dtype = typecode
iden = np.zeros((n,)*rank, dtype)
for i in range(n):
idx = (i,)*rank
iden[idx] = 1
return iden
def base_repr (number, base = 2, padding = 0):
"""
Return the representation of a *number* in any given *base*.
"""
chars = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'
if number < base: \
return (padding - 1) * chars [0] + chars [int (number)]
max_exponent = int (math.log (number)/math.log (base))
max_power = long (base) ** max_exponent
lead_digit = int (number/max_power)
return chars [lead_digit] + \
base_repr (number - max_power * lead_digit, base, \
max (padding - 1, max_exponent))
def binary_repr(number, max_length = 1025):
"""
Return the binary representation of the input *number* as a
string.
This is more efficient than using :func:`base_repr` with base 2.
Increase the value of max_length for very large numbers. Note that
on 32-bit machines, 2**1023 is the largest integer power of 2
which can be converted to a Python float.
"""
#assert number < 2L << max_length
shifts = map (operator.rshift, max_length * [number], \
range (max_length - 1, -1, -1))
digits = map (operator.mod, shifts, max_length * [2])
if not digits.count (1): return 0
digits = digits [digits.index (1):]
return ''.join (map (repr, digits)).replace('L','')
def log2(x,ln2 = math.log(2.0)):
"""
Return the log(*x*) in base 2.
This is a _slow_ function but which is guaranteed to return the correct
integer value if the input is an integer exact power of 2.
"""
try:
bin_n = binary_repr(x)[1:]
except (AssertionError,TypeError):
return math.log(x)/ln2
else:
if '1' in bin_n:
return math.log(x)/ln2
else:
return len(bin_n)
def ispower2(n):
"""
Returns the log base 2 of *n* if *n* is a power of 2, zero otherwise.
Note the potential ambiguity if *n* == 1: 2**0 == 1, interpret accordingly.
"""
bin_n = binary_repr(n)[1:]
if '1' in bin_n:
return 0
else:
return len(bin_n)
def isvector(X):
"""
Like the Matlab (TM) function with the same name, returns *True*
if the supplied numpy array or matrix *X* looks like a vector,
meaning it has a one non-singleton axis (i.e., it can have
multiple axes, but all must have length 1, except for one of
them).
If you just want to see if the array has 1 axis, use X.ndim == 1.
"""
return np.prod(X.shape)==np.max(X.shape)
#from numpy import fromfunction as fromfunction_kw
def fromfunction_kw(function, dimensions, **kwargs):
"""
Drop-in replacement for :func:`numpy.fromfunction`.
Allows passing keyword arguments to the desired function.
Call it as (keywords are optional)::
fromfunction_kw(MyFunction, dimensions, keywords)
The function ``MyFunction`` is responsible for handling the
dictionary of keywords it will receive.
"""
warnings.warn("Use numpy.fromfunction()", DeprecationWarning)
return np.fromfunction(function, dimensions, **kwargs)
### end fperez numutils code
def rem(x,y):
"""
Deprecated - see :func:`numpy.remainder`
"""
raise NotImplementedError('Deprecated - see numpy.remainder')
def norm(x,y=2):
"""
Deprecated - see :func:`numpy.linalg.norm`
"""
raise NotImplementedError('Deprecated - see numpy.linalg.norm')
def orth(A):
"""
Deprecated - needs clean room implementation
"""
raise NotImplementedError('Deprecated - needs clean room implementation')
def rank(x):
"""
Deprecated - see :func:`numpy.rank`
"""
raise NotImplementedError('Deprecated - see numpy.rank')
def sqrtm(x):
"""
Deprecated - needs clean room implementation
"""
raise NotImplementedError('Deprecated - see scipy.linalg.sqrtm')
def mfuncC(f, x):
"""
Deprecated
"""
raise NotImplementedError('Deprecated - needs clean room implementation')
def approx_real(x):
"""
Deprecated - needs clean room implementation
"""
raise NotImplementedError('Deprecated - needs clean room implementation')
#helpers for loading, saving, manipulating and viewing numpy record arrays
def safe_isnan(x):
':func:`numpy.isnan` for arbitrary types'
if cbook.is_string_like(x):
return False
try: b = np.isnan(x)
except NotImplementedError: return False
except TypeError: return False
else: return b
def safe_isinf(x):
':func:`numpy.isinf` for arbitrary types'
if cbook.is_string_like(x):
return False
try: b = np.isinf(x)
except NotImplementedError: return False
except TypeError: return False
else: return b
def rec_view(rec):
"""
Return a view of an ndarray as a recarray
.. seealso::
http://projects.scipy.org/pipermail/numpy-discussion/2008-August/036429.html
"""
return rec.view(np.recarray)
#return rec.view(dtype=(np.record, rec.dtype), type=np.recarray)
def rec_append_field(rec, name, arr, dtype=None):
"""
Return a new record array with field name populated with data from
array *arr*. This function is Deprecated. Please use
:func:`rec_append_fields`.
"""
warnings.warn("use rec_append_fields", DeprecationWarning)
return rec_append_fields(rec, name, arr, dtype)
def rec_append_fields(rec, names, arrs, dtypes=None):
"""
Return a new record array with field names populated with data
from arrays in *arrs*. If appending a single field, then *names*,
*arrs* and *dtypes* do not have to be lists. They can just be the
values themselves.
"""
if (not cbook.is_string_like(names) and cbook.iterable(names) \
and len(names) and cbook.is_string_like(names[0])):
if len(names) != len(arrs):
raise ValueError, "number of arrays do not match number of names"
else: # we have only 1 name and 1 array
names = [names]
arrs = [arrs]
arrs = map(np.asarray, arrs)
if dtypes is None:
dtypes = [a.dtype for a in arrs]
elif not cbook.iterable(dtypes):
dtypes = [dtypes]
if len(arrs) != len(dtypes):
if len(dtypes) == 1:
dtypes = dtypes * len(arrs)
else:
raise ValueError, "dtypes must be None, a single dtype or a list"
newdtype = np.dtype(rec.dtype.descr + zip(names, dtypes))
newrec = np.empty(rec.shape, dtype=newdtype)
for field in rec.dtype.fields:
newrec[field] = rec[field]
for name, arr in zip(names, arrs):
newrec[name] = arr
return rec_view(newrec)
def rec_drop_fields(rec, names):
"""
Return a new numpy record array with fields in *names* dropped.
"""
names = set(names)
Nr = len(rec)
newdtype = np.dtype([(name, rec.dtype[name]) for name in rec.dtype.names
if name not in names])
newrec = np.empty(Nr, dtype=newdtype)
for field in newdtype.names:
newrec[field] = rec[field]
return rec_view(newrec)
def rec_groupby(r, groupby, stats):
"""
*r* is a numpy record array
*groupby* is a sequence of record array attribute names that
together form the grouping key. eg ('date', 'productcode')
*stats* is a sequence of (*attr*, *func*, *outname*) tuples which
will call ``x = func(attr)`` and assign *x* to the record array
output with attribute *outname*. For example::
stats = ( ('sales', len, 'numsales'), ('sales', np.mean, 'avgsale') )
Return record array has *dtype* names for each attribute name in
the the *groupby* argument, with the associated group values, and
for each outname name in the *stats* argument, with the associated
stat summary output.
"""
# build a dictionary from groupby keys-> list of indices into r with
# those keys
rowd = dict()
for i, row in enumerate(r):
key = tuple([row[attr] for attr in groupby])
rowd.setdefault(key, []).append(i)
# sort the output by groupby keys
keys = rowd.keys()
keys.sort()
rows = []
for key in keys:
row = list(key)
# get the indices for this groupby key
ind = rowd[key]
thisr = r[ind]
# call each stat function for this groupby slice
row.extend([func(thisr[attr]) for attr, func, outname in stats])
rows.append(row)
# build the output record array with groupby and outname attributes
attrs, funcs, outnames = zip(*stats)
names = list(groupby)
names.extend(outnames)
return np.rec.fromrecords(rows, names=names)
def rec_summarize(r, summaryfuncs):
"""
*r* is a numpy record array
*summaryfuncs* is a list of (*attr*, *func*, *outname*) tuples
which will apply *func* to the the array *r*[attr] and assign the
output to a new attribute name *outname*. The returned record
array is identical to *r*, with extra arrays for each element in
*summaryfuncs*.
"""
names = list(r.dtype.names)
arrays = [r[name] for name in names]
for attr, func, outname in summaryfuncs:
names.append(outname)
arrays.append(np.asarray(func(r[attr])))
return np.rec.fromarrays(arrays, names=names)
def rec_join(key, r1, r2, jointype='inner', defaults=None, r1postfix='1', r2postfix='2'):
"""
Join record arrays *r1* and *r2* on *key*; *key* is a tuple of
field names -- if *key* is a string it is assumed to be a single
attribute name. If *r1* and *r2* have equal values on all the keys
in the *key* tuple, then their fields will be merged into a new
record array containing the intersection of the fields of *r1* and
*r2*.
*r1* (also *r2*) must not have any duplicate keys.
The *jointype* keyword can be 'inner', 'outer', 'leftouter'. To
do a rightouter join just reverse *r1* and *r2*.
The *defaults* keyword is a dictionary filled with
``{column_name:default_value}`` pairs.
The keywords *r1postfix* and *r2postfix* are postfixed to column names
(other than keys) that are both in *r1* and *r2*.
"""
if cbook.is_string_like(key):
key = (key, )
for name in key:
if name not in r1.dtype.names:
raise ValueError('r1 does not have key field %s'%name)
if name not in r2.dtype.names:
raise ValueError('r2 does not have key field %s'%name)
def makekey(row):
return tuple([row[name] for name in key])
r1d = dict([(makekey(row),i) for i,row in enumerate(r1)])
r2d = dict([(makekey(row),i) for i,row in enumerate(r2)])
r1keys = set(r1d.keys())
r2keys = set(r2d.keys())
common_keys = r1keys & r2keys
r1ind = np.array([r1d[k] for k in common_keys])
r2ind = np.array([r2d[k] for k in common_keys])
common_len = len(common_keys)
left_len = right_len = 0
if jointype == "outer" or jointype == "leftouter":
left_keys = r1keys.difference(r2keys)
left_ind = np.array([r1d[k] for k in left_keys])
left_len = len(left_ind)
if jointype == "outer":
right_keys = r2keys.difference(r1keys)
right_ind = np.array([r2d[k] for k in right_keys])
right_len = len(right_ind)
def key_desc(name):
'if name is a string key, use the larger size of r1 or r2 before merging'
dt1 = r1.dtype[name]
if dt1.type != np.string_:
return (name, dt1.descr[0][1])
dt2 = r1.dtype[name]
assert dt2==dt1
if dt1.num>dt2.num:
return (name, dt1.descr[0][1])
else:
return (name, dt2.descr[0][1])
keydesc = [key_desc(name) for name in key]
def mapped_r1field(name):
"""
The column name in *newrec* that corresponds to the column in *r1*.
"""
if name in key or name not in r2.dtype.names: return name
else: return name + r1postfix
def mapped_r2field(name):
"""
The column name in *newrec* that corresponds to the column in *r2*.
"""
if name in key or name not in r1.dtype.names: return name
else: return name + r2postfix
r1desc = [(mapped_r1field(desc[0]), desc[1]) for desc in r1.dtype.descr if desc[0] not in key]
r2desc = [(mapped_r2field(desc[0]), desc[1]) for desc in r2.dtype.descr if desc[0] not in key]
newdtype = np.dtype(keydesc + r1desc + r2desc)
newrec = np.empty(common_len + left_len + right_len, dtype=newdtype)
if jointype != 'inner' and defaults is not None: # fill in the defaults enmasse
newrec_fields = newrec.dtype.fields.keys()
for k, v in defaults.items():
if k in newrec_fields:
newrec[k] = v
for field in r1.dtype.names:
newfield = mapped_r1field(field)
if common_len:
newrec[newfield][:common_len] = r1[field][r1ind]
if (jointype == "outer" or jointype == "leftouter") and left_len:
newrec[newfield][common_len:(common_len+left_len)] = r1[field][left_ind]
for field in r2.dtype.names:
newfield = mapped_r2field(field)
if field not in key and common_len:
newrec[newfield][:common_len] = r2[field][r2ind]
if jointype == "outer" and right_len:
newrec[newfield][-right_len:] = r2[field][right_ind]
newrec.sort(order=key)
return rec_view(newrec)
def csv2rec(fname, comments='#', skiprows=0, checkrows=0, delimiter=',',
converterd=None, names=None, missing='', missingd=None,
use_mrecords=True):
"""
Load data from comma/space/tab delimited file in *fname* into a
numpy record array and return the record array.
If *names* is *None*, a header row is required to automatically
assign the recarray names. The headers will be lower cased,
spaces will be converted to underscores, and illegal attribute
name characters removed. If *names* is not *None*, it is a
sequence of names to use for the column names. In this case, it
is assumed there is no header row.
- *fname*: can be a filename or a file handle. Support for gzipped
files is automatic, if the filename ends in '.gz'
- *comments*: the character used to indicate the start of a comment
in the file
- *skiprows*: is the number of rows from the top to skip
- *checkrows*: is the number of rows to check to validate the column
data type. When set to zero all rows are validated.
- *converted*: if not *None*, is a dictionary mapping column number or
munged column name to a converter function.
- *names*: if not None, is a list of header names. In this case, no
header will be read from the file
- *missingd* is a dictionary mapping munged column names to field values
which signify that the field does not contain actual data and should
be masked, e.g. '0000-00-00' or 'unused'
- *missing*: a string whose value signals a missing field regardless of
the column it appears in
- *use_mrecords*: if True, return an mrecords.fromrecords record array if any of the data are missing
If no rows are found, *None* is returned -- see :file:`examples/loadrec.py`
"""
if converterd is None:
converterd = dict()
if missingd is None:
missingd = {}
import dateutil.parser
import datetime
parsedate = dateutil.parser.parse
fh = cbook.to_filehandle(fname)
class FH:
"""
For space-delimited files, we want different behavior than
comma or tab. Generally, we want multiple spaces to be
treated as a single separator, whereas with comma and tab we
want multiple commas to return multiple (empty) fields. The
join/strip trick below effects this.
"""
def __init__(self, fh):
self.fh = fh
def close(self):
self.fh.close()
def seek(self, arg):
self.fh.seek(arg)
def fix(self, s):
return ' '.join(s.split())
def next(self):
return self.fix(self.fh.next())
def __iter__(self):
for line in self.fh:
yield self.fix(line)
if delimiter==' ':
fh = FH(fh)
reader = csv.reader(fh, delimiter=delimiter)
def process_skiprows(reader):
if skiprows:
for i, row in enumerate(reader):
if i>=(skiprows-1): break
return fh, reader
process_skiprows(reader)
def ismissing(name, val):
"Should the value val in column name be masked?"
if val == missing or val == missingd.get(name) or val == '':
return True
else:
return False
def with_default_value(func, default):
def newfunc(name, val):
if ismissing(name, val):
return default
else:
return func(val)
return newfunc
def mybool(x):
if x=='True': return True
elif x=='False': return False
else: raise ValueError('invalid bool')
dateparser = dateutil.parser.parse
mydateparser = with_default_value(dateparser, datetime.date(1,1,1))
myfloat = with_default_value(float, np.nan)
myint = with_default_value(int, -1)
mystr = with_default_value(str, '')
mybool = with_default_value(mybool, None)
def mydate(x):
# try and return a date object
d = dateparser(x)
if d.hour>0 or d.minute>0 or d.second>0:
raise ValueError('not a date')
return d.date()
mydate = with_default_value(mydate, datetime.date(1,1,1))
def get_func(name, item, func):
# promote functions in this order
funcmap = {mybool:myint,myint:myfloat, myfloat:mydate, mydate:mydateparser, mydateparser:mystr}
try: func(name, item)
except:
if func==mystr:
raise ValueError('Could not find a working conversion function')
else: return get_func(name, item, funcmap[func]) # recurse
else: return func
# map column names that clash with builtins -- TODO - extend this list
itemd = {
'return' : 'return_',
'file' : 'file_',
'print' : 'print_',
}
def get_converters(reader):
converters = None
for i, row in enumerate(reader):
if i==0:
converters = [mybool]*len(row)
if checkrows and i>checkrows:
break
#print i, len(names), len(row)
#print 'converters', zip(converters, row)
for j, (name, item) in enumerate(zip(names, row)):
func = converterd.get(j)
if func is None:
func = converterd.get(name)
if func is None:
#if not item.strip(): continue
func = converters[j]
if len(item.strip()):
func = get_func(name, item, func)
else:
# how should we handle custom converters and defaults?
func = with_default_value(func, None)
converters[j] = func
return converters
# Get header and remove invalid characters
needheader = names is None
if needheader:
for row in reader:
#print 'csv2rec', row
if len(row) and row[0].startswith(comments):
continue
headers = row
break
# remove these chars
delete = set("""~!@#$%^&*()-=+~\|]}[{';: /?.>,<""")
delete.add('"')
names = []
seen = dict()
for i, item in enumerate(headers):
item = item.strip().lower().replace(' ', '_')
item = ''.join([c for c in item if c not in delete])
if not len(item):
item = 'column%d'%i
item = itemd.get(item, item)
cnt = seen.get(item, 0)
if cnt>0:
names.append(item + '_%d'%cnt)
else:
names.append(item)
seen[item] = cnt+1
else:
if cbook.is_string_like(names):
names = [n.strip() for n in names.split(',')]
# get the converter functions by inspecting checkrows
converters = get_converters(reader)
if converters is None:
raise ValueError('Could not find any valid data in CSV file')
# reset the reader and start over
fh.seek(0)
reader = csv.reader(fh, delimiter=delimiter)
process_skiprows(reader)
if needheader:
skipheader = reader.next()
# iterate over the remaining rows and convert the data to date
# objects, ints, or floats as approriate
rows = []
rowmasks = []
for i, row in enumerate(reader):
if not len(row): continue
if row[0].startswith(comments): continue
rows.append([func(name, val) for func, name, val in zip(converters, names, row)])
rowmasks.append([ismissing(name, val) for name, val in zip(names, row)])
fh.close()
if not len(rows):
return None
if use_mrecords and np.any(rowmasks):
try: from numpy.ma import mrecords
except ImportError:
raise RuntimeError('numpy 1.05 or later is required for masked array support')
else:
r = mrecords.fromrecords(rows, names=names, mask=rowmasks)
else:
r = np.rec.fromrecords(rows, names=names)
return r
# a series of classes for describing the format intentions of various rec views
class FormatObj:
def tostr(self, x):
return self.toval(x)
def toval(self, x):
return str(x)
def fromstr(self, s):
return s
class FormatString(FormatObj):
def tostr(self, x):
val = repr(x)
return val[1:-1]
#class FormatString(FormatObj):
# def tostr(self, x):
# return '"%r"'%self.toval(x)
class FormatFormatStr(FormatObj):
def __init__(self, fmt):
self.fmt = fmt
def tostr(self, x):
if x is None: return 'None'
return self.fmt%self.toval(x)
class FormatFloat(FormatFormatStr):
def __init__(self, precision=4, scale=1.):
FormatFormatStr.__init__(self, '%%1.%df'%precision)
self.precision = precision
self.scale = scale
def toval(self, x):
if x is not None:
x = x * self.scale
return x
def fromstr(self, s):
return float(s)/self.scale
class FormatInt(FormatObj):
def tostr(self, x):
return '%d'%int(x)
def toval(self, x):
return int(x)
def fromstr(self, s):
return int(s)
class FormatBool(FormatObj):
def toval(self, x):
return str(x)
def fromstr(self, s):
return bool(s)
class FormatPercent(FormatFloat):
def __init__(self, precision=4):
FormatFloat.__init__(self, precision, scale=100.)
class FormatThousands(FormatFloat):
def __init__(self, precision=4):
FormatFloat.__init__(self, precision, scale=1e-3)
class FormatMillions(FormatFloat):
def __init__(self, precision=4):
FormatFloat.__init__(self, precision, scale=1e-6)
class FormatDate(FormatObj):
def __init__(self, fmt):
self.fmt = fmt
def toval(self, x):
if x is None: return 'None'
return x.strftime(self.fmt)
def fromstr(self, x):
import dateutil.parser
return dateutil.parser.parse(x).date()
class FormatDatetime(FormatDate):
def __init__(self, fmt='%Y-%m-%d %H:%M:%S'):
FormatDate.__init__(self, fmt)
def fromstr(self, x):
import dateutil.parser
return dateutil.parser.parse(x)
defaultformatd = {
np.bool_ : FormatBool(),
np.int16 : FormatInt(),
np.int32 : FormatInt(),
np.int64 : FormatInt(),
np.float32 : FormatFloat(),
np.float64 : FormatFloat(),
np.object_ : FormatObj(),
np.string_ : FormatString(),
}
def get_formatd(r, formatd=None):
'build a formatd guaranteed to have a key for every dtype name'
if formatd is None:
formatd = dict()
for i, name in enumerate(r.dtype.names):
dt = r.dtype[name]
format = formatd.get(name)
if format is None:
format = defaultformatd.get(dt.type, FormatObj())
formatd[name] = format
return formatd
def csvformat_factory(format):
format = copy.deepcopy(format)
if isinstance(format, FormatFloat):
format.scale = 1. # override scaling for storage
format.fmt = '%r'
return format
def rec2txt(r, header=None, padding=3, precision=3):
"""
Returns a textual representation of a record array.
*r*: numpy recarray
*header*: list of column headers
*padding*: space between each column
*precision*: number of decimal places to use for floats.
Set to an integer to apply to all floats. Set to a
list of integers to apply precision individually.
Precision for non-floats is simply ignored.
Example::
precision=[0,2,3]
Output::
ID Price Return
ABC 12.54 0.234
XYZ 6.32 -0.076
"""
if cbook.is_numlike(precision):
precision = [precision]*len(r.dtype)
def get_type(item,atype=int):
tdict = {None:int, int:float, float:str}
try: atype(str(item))
except: return get_type(item,tdict[atype])
return atype
def get_justify(colname, column, precision):
ntype = type(column[0])
if ntype==np.str or ntype==np.str_ or ntype==np.string0 or ntype==np.string_:
length = max(len(colname),column.itemsize)
return 0, length+padding, "%s" # left justify
if ntype==np.int or ntype==np.int16 or ntype==np.int32 or ntype==np.int64 or ntype==np.int8 or ntype==np.int_:
length = max(len(colname),np.max(map(len,map(str,column))))
return 1, length+padding, "%d" # right justify
# JDH: my powerbook does not have np.float96 using np 1.3.0
"""
In [2]: np.__version__
Out[2]: '1.3.0.dev5948'
In [3]: !uname -a
Darwin Macintosh-5.local 9.4.0 Darwin Kernel Version 9.4.0: Mon Jun 9 19:30:53 PDT 2008; root:xnu-1228.5.20~1/RELEASE_I386 i386 i386
In [4]: np.float96
---------------------------------------------------------------------------
AttributeError Traceback (most recent call la
"""
if ntype==np.float or ntype==np.float32 or ntype==np.float64 or (hasattr(np, 'float96') and (ntype==np.float96)) or ntype==np.float_:
fmt = "%." + str(precision) + "f"
length = max(len(colname),np.max(map(len,map(lambda x:fmt%x,column))))
return 1, length+padding, fmt # right justify
return 0, max(len(colname),np.max(map(len,map(str,column))))+padding, "%s"
if header is None:
header = r.dtype.names
justify_pad_prec = [get_justify(header[i],r.__getitem__(colname),precision[i]) for i, colname in enumerate(r.dtype.names)]
justify_pad_prec_spacer = []
for i in range(len(justify_pad_prec)):
just,pad,prec = justify_pad_prec[i]
if i == 0:
justify_pad_prec_spacer.append((just,pad,prec,0))
else:
pjust,ppad,pprec = justify_pad_prec[i-1]
if pjust == 0 and just == 1:
justify_pad_prec_spacer.append((just,pad-padding,prec,0))
elif pjust == 1 and just == 0:
justify_pad_prec_spacer.append((just,pad,prec,padding))
else:
justify_pad_prec_spacer.append((just,pad,prec,0))
def format(item, just_pad_prec_spacer):
just, pad, prec, spacer = just_pad_prec_spacer
if just == 0:
return spacer*' ' + str(item).ljust(pad)
else:
if get_type(item) == float:
item = (prec%float(item))
elif get_type(item) == int:
item = (prec%int(item))
return item.rjust(pad)
textl = []
textl.append(''.join([format(colitem,justify_pad_prec_spacer[j]) for j, colitem in enumerate(header)]))
for i, row in enumerate(r):
textl.append(''.join([format(colitem,justify_pad_prec_spacer[j]) for j, colitem in enumerate(row)]))
if i==0:
textl[0] = textl[0].rstrip()
text = os.linesep.join(textl)
return text
def rec2csv(r, fname, delimiter=',', formatd=None, missing='',
missingd=None):
"""
Save the data from numpy recarray *r* into a
comma-/space-/tab-delimited file. The record array dtype names
will be used for column headers.
*fname*: can be a filename or a file handle. Support for gzipped
files is automatic, if the filename ends in '.gz'
.. seealso::
:func:`csv2rec`:
For information about *missing* and *missingd*, which can
be used to fill in masked values into your CSV file.
"""
if missingd is None:
missingd = dict()
def with_mask(func):
def newfunc(val, mask, mval):
if mask:
return mval
else:
return func(val)
return newfunc
formatd = get_formatd(r, formatd)
funcs = []
for i, name in enumerate(r.dtype.names):
funcs.append(with_mask(csvformat_factory(formatd[name]).tostr))
fh, opened = cbook.to_filehandle(fname, 'w', return_opened=True)
writer = csv.writer(fh, delimiter=delimiter)
header = r.dtype.names
writer.writerow(header)
# Our list of specials for missing values
mvals = []
for name in header:
mvals.append(missingd.get(name, missing))
ismasked = False
if len(r):
row = r[0]
ismasked = hasattr(row, '_fieldmask')
for row in r:
if ismasked:
row, rowmask = row.item(), row._fieldmask.item()
else:
rowmask = [False] * len(row)
writer.writerow([func(val, mask, mval) for func, val, mask, mval
in zip(funcs, row, rowmask, mvals)])
if opened:
fh.close()
def griddata(x,y,z,xi,yi):
"""
``zi = griddata(x,y,z,xi,yi)`` fits a surface of the form *z* =
*f*(*x*, *y*) to the data in the (usually) nonuniformly spaced
vectors (*x*, *y*, *z*). :func:`griddata` interpolates this
surface at the points specified by (*xi*, *yi*) to produce
*zi*. *xi* and *yi* must describe a regular grid, can be either 1D
or 2D, but must be monotonically increasing.
A masked array is returned if any grid points are outside convex
hull defined by input data (no extrapolation is done).
Uses natural neighbor interpolation based on Delaunay
triangulation. By default, this algorithm is provided by the
:mod:`matplotlib.delaunay` package, written by Robert Kern. The
triangulation algorithm in this package is known to fail on some
nearly pathological cases. For this reason, a separate toolkit
(:mod:`mpl_tookits.natgrid`) has been created that provides a more
robust algorithm fof triangulation and interpolation. This
toolkit is based on the NCAR natgrid library, which contains code
that is not redistributable under a BSD-compatible license. When
installed, this function will use the :mod:`mpl_toolkits.natgrid`
algorithm, otherwise it will use the built-in
:mod:`matplotlib.delaunay` package.
The natgrid matplotlib toolkit can be downloaded from
http://sourceforge.net/project/showfiles.php?group_id=80706&package_id=142792
"""
try:
from mpl_toolkits.natgrid import _natgrid, __version__
_use_natgrid = True
except ImportError:
import matplotlib.delaunay as delaunay
from matplotlib.delaunay import __version__
_use_natgrid = False
if not griddata._reported:
if _use_natgrid:
verbose.report('using natgrid version %s' % __version__)
else:
verbose.report('using delaunay version %s' % __version__)
griddata._reported = True
if xi.ndim != yi.ndim:
raise TypeError("inputs xi and yi must have same number of dimensions (1 or 2)")
if xi.ndim != 1 and xi.ndim != 2:
raise TypeError("inputs xi and yi must be 1D or 2D.")
if not len(x)==len(y)==len(z):
raise TypeError("inputs x,y,z must all be 1D arrays of the same length")
# remove masked points.
if hasattr(z,'mask'):
x = x.compress(z.mask == False)
y = y.compress(z.mask == False)
z = z.compressed()
if _use_natgrid: # use natgrid toolkit if available.
if xi.ndim == 2:
xi = xi[0,:]
yi = yi[:,0]
# override default natgrid internal parameters.
_natgrid.seti('ext',0)
_natgrid.setr('nul',np.nan)
# cast input arrays to doubles (this makes a copy)
x = x.astype(np.float)
y = y.astype(np.float)
z = z.astype(np.float)
xo = xi.astype(np.float)
yo = yi.astype(np.float)
if min(xo[1:]-xo[0:-1]) < 0 or min(yo[1:]-yo[0:-1]) < 0:
raise ValueError, 'output grid defined by xi,yi must be monotone increasing'
# allocate array for output (buffer will be overwritten by nagridd)
zo = np.empty((yo.shape[0],xo.shape[0]), np.float)
_natgrid.natgridd(x,y,z,xo,yo,zo)
else: # use Robert Kern's delaunay package from scikits (default)
if xi.ndim != yi.ndim:
raise TypeError("inputs xi and yi must have same number of dimensions (1 or 2)")
if xi.ndim != 1 and xi.ndim != 2:
raise TypeError("inputs xi and yi must be 1D or 2D.")
if xi.ndim == 1:
xi,yi = np.meshgrid(xi,yi)
# triangulate data
tri = delaunay.Triangulation(x,y)
# interpolate data
interp = tri.nn_interpolator(z)
zo = interp(xi,yi)
# mask points on grid outside convex hull of input data.
if np.any(np.isnan(zo)):
zo = np.ma.masked_where(np.isnan(zo),zo)
return zo
griddata._reported = False
##################################################
# Linear interpolation algorithms
##################################################
def less_simple_linear_interpolation( x, y, xi, extrap=False ):
"""
This function provides simple (but somewhat less so than
:func:`cbook.simple_linear_interpolation`) linear interpolation.
:func:`simple_linear_interpolation` will give a list of point
between a start and an end, while this does true linear
interpolation at an arbitrary set of points.
This is very inefficient linear interpolation meant to be used
only for a small number of points in relatively non-intensive use
cases. For real linear interpolation, use scipy.
"""
if cbook.is_scalar(xi): xi = [xi]
x = np.asarray(x)
y = np.asarray(y)
xi = np.asarray(xi)
s = list(y.shape)
s[0] = len(xi)
yi = np.tile( np.nan, s )
for ii,xx in enumerate(xi):
bb = x == xx
if np.any(bb):
jj, = np.nonzero(bb)
yi[ii] = y[jj[0]]
elif xx<x[0]:
if extrap:
yi[ii] = y[0]
elif xx>x[-1]:
if extrap:
yi[ii] = y[-1]
else:
jj, = np.nonzero(x<xx)
jj = max(jj)
yi[ii] = y[jj] + (xx-x[jj])/(x[jj+1]-x[jj]) * (y[jj+1]-y[jj])
return yi
def slopes(x,y):
"""
:func:`slopes` calculates the slope *y*'(*x*)
The slope is estimated using the slope obtained from that of a
parabola through any three consecutive points.
This method should be superior to that described in the appendix
of A CONSISTENTLY WELL BEHAVED METHOD OF INTERPOLATION by Russel
W. Stineman (Creative Computing July 1980) in at least one aspect:
Circles for interpolation demand a known aspect ratio between
*x*- and *y*-values. For many functions, however, the abscissa
are given in different dimensions, so an aspect ratio is
completely arbitrary.
The parabola method gives very similar results to the circle
method for most regular cases but behaves much better in special
cases.
Norbert Nemec, Institute of Theoretical Physics, University or
Regensburg, April 2006 Norbert.Nemec at physik.uni-regensburg.de
(inspired by a original implementation by Halldor Bjornsson,
Icelandic Meteorological Office, March 2006 halldor at vedur.is)
"""
# Cast key variables as float.
x=np.asarray(x, np.float_)
y=np.asarray(y, np.float_)
yp=np.zeros(y.shape, np.float_)
dx=x[1:] - x[:-1]
dy=y[1:] - y[:-1]
dydx = dy/dx
yp[1:-1] = (dydx[:-1] * dx[1:] + dydx[1:] * dx[:-1])/(dx[1:] + dx[:-1])
yp[0] = 2.0 * dy[0]/dx[0] - yp[1]
yp[-1] = 2.0 * dy[-1]/dx[-1] - yp[-2]
return yp
def stineman_interp(xi,x,y,yp=None):
"""
Given data vectors *x* and *y*, the slope vector *yp* and a new
abscissa vector *xi*, the function :func:`stineman_interp` uses
Stineman interpolation to calculate a vector *yi* corresponding to
*xi*.
Here's an example that generates a coarse sine curve, then
interpolates over a finer abscissa::
x = linspace(0,2*pi,20); y = sin(x); yp = cos(x)
xi = linspace(0,2*pi,40);
yi = stineman_interp(xi,x,y,yp);
plot(x,y,'o',xi,yi)
The interpolation method is described in the article A
CONSISTENTLY WELL BEHAVED METHOD OF INTERPOLATION by Russell
W. Stineman. The article appeared in the July 1980 issue of
Creative Computing with a note from the editor stating that while
they were:
not an academic journal but once in a while something serious
and original comes in adding that this was
"apparently a real solution" to a well known problem.
For *yp* = *None*, the routine automatically determines the slopes
using the :func:`slopes` routine.
*x* is assumed to be sorted in increasing order.
For values ``xi[j] < x[0]`` or ``xi[j] > x[-1]``, the routine
tries an extrapolation. The relevance of the data obtained from
this, of course, is questionable...
Original implementation by Halldor Bjornsson, Icelandic
Meteorolocial Office, March 2006 halldor at vedur.is
Completely reworked and optimized for Python by Norbert Nemec,
Institute of Theoretical Physics, University or Regensburg, April
2006 Norbert.Nemec at physik.uni-regensburg.de
"""
# Cast key variables as float.
x=np.asarray(x, np.float_)
y=np.asarray(y, np.float_)
assert x.shape == y.shape
N=len(y)
if yp is None:
yp = slopes(x,y)
else:
yp=np.asarray(yp, np.float_)
xi=np.asarray(xi, np.float_)
yi=np.zeros(xi.shape, np.float_)
# calculate linear slopes
dx = x[1:] - x[:-1]
dy = y[1:] - y[:-1]
s = dy/dx #note length of s is N-1 so last element is #N-2
# find the segment each xi is in
# this line actually is the key to the efficiency of this implementation
idx = np.searchsorted(x[1:-1], xi)
# now we have generally: x[idx[j]] <= xi[j] <= x[idx[j]+1]
# except at the boundaries, where it may be that xi[j] < x[0] or xi[j] > x[-1]
# the y-values that would come out from a linear interpolation:
sidx = s.take(idx)
xidx = x.take(idx)
yidx = y.take(idx)
xidxp1 = x.take(idx+1)
yo = yidx + sidx * (xi - xidx)
# the difference that comes when using the slopes given in yp
dy1 = (yp.take(idx)- sidx) * (xi - xidx) # using the yp slope of the left point
dy2 = (yp.take(idx+1)-sidx) * (xi - xidxp1) # using the yp slope of the right point
dy1dy2 = dy1*dy2
# The following is optimized for Python. The solution actually
# does more calculations than necessary but exploiting the power
# of numpy, this is far more efficient than coding a loop by hand
# in Python
yi = yo + dy1dy2 * np.choose(np.array(np.sign(dy1dy2), np.int32)+1,
((2*xi-xidx-xidxp1)/((dy1-dy2)*(xidxp1-xidx)),
0.0,
1/(dy1+dy2),))
return yi
##################################################
# Code related to things in and around polygons
##################################################
def inside_poly(points, verts):
"""
*points* is a sequence of *x*, *y* points.
*verts* is a sequence of *x*, *y* vertices of a polygon.
Return value is a sequence of indices into points for the points
that are inside the polygon.
"""
res, = np.nonzero(nxutils.points_inside_poly(points, verts))
return res
def poly_below(xmin, xs, ys):
"""
Given a sequence of *xs* and *ys*, return the vertices of a
polygon that has a horizontal base at *xmin* and an upper bound at
the *ys*. *xmin* is a scalar.
Intended for use with :meth:`matplotlib.axes.Axes.fill`, eg::
xv, yv = poly_below(0, x, y)
ax.fill(xv, yv)
"""
if ma.isMaskedArray(xs) or ma.isMaskedArray(ys):
nx = ma
else:
nx = np
xs = nx.asarray(xs)
ys = nx.asarray(ys)
Nx = len(xs)
Ny = len(ys)
assert(Nx==Ny)
x = xmin*nx.ones(2*Nx)
y = nx.ones(2*Nx)
x[:Nx] = xs
y[:Nx] = ys
y[Nx:] = ys[::-1]
return x, y
def poly_between(x, ylower, yupper):
"""
Given a sequence of *x*, *ylower* and *yupper*, return the polygon
that fills the regions between them. *ylower* or *yupper* can be
scalar or iterable. If they are iterable, they must be equal in
length to *x*.
Return value is *x*, *y* arrays for use with
:meth:`matplotlib.axes.Axes.fill`.
"""
if ma.isMaskedArray(ylower) or ma.isMaskedArray(yupper) or ma.isMaskedArray(x):
nx = ma
else:
nx = np
Nx = len(x)
if not cbook.iterable(ylower):
ylower = ylower*nx.ones(Nx)
if not cbook.iterable(yupper):
yupper = yupper*nx.ones(Nx)
x = nx.concatenate( (x, x[::-1]) )
y = nx.concatenate( (yupper, ylower[::-1]) )
return x,y
def is_closed_polygon(X):
"""
Tests whether first and last object in a sequence are the same. These are
presumably coordinates on a polygonal curve, in which case this function
tests if that curve is closed.
"""
return np.all(X[0] == X[-1])
def contiguous_regions(mask):
"""
return a list of (ind0, ind1) such that mask[ind0:ind1].all() is
True and we cover all such regions
TODO: this is a pure python implementation which probably has a much faster numpy impl
"""
in_region = None
boundaries = []
for i, val in enumerate(mask):
if in_region is None and val:
in_region = i
elif in_region is not None and not val:
boundaries.append((in_region, i))
in_region = None
if in_region is not None:
boundaries.append((in_region, i+1))
return boundaries
##################################################
# Vector and path length geometry calculations
##################################################
def vector_lengths( X, P=2., axis=None ):
"""
Finds the length of a set of vectors in *n* dimensions. This is
like the :func:`numpy.norm` function for vectors, but has the ability to
work over a particular axis of the supplied array or matrix.
Computes ``(sum((x_i)^P))^(1/P)`` for each ``{x_i}`` being the
elements of *X* along the given axis. If *axis* is *None*,
compute over all elements of *X*.
"""
X = np.asarray(X)
return (np.sum(X**(P),axis=axis))**(1./P)
def distances_along_curve( X ):
"""
Computes the distance between a set of successive points in *N* dimensions.
Where *X* is an *M* x *N* array or matrix. The distances between
successive rows is computed. Distance is the standard Euclidean
distance.
"""
X = np.diff( X, axis=0 )
return vector_lengths(X,axis=1)
def path_length(X):
"""
Computes the distance travelled along a polygonal curve in *N* dimensions.
Where *X* is an *M* x *N* array or matrix. Returns an array of
length *M* consisting of the distance along the curve at each point
(i.e., the rows of *X*).
"""
X = distances_along_curve(X)
return np.concatenate( (np.zeros(1), np.cumsum(X)) )
def quad2cubic(q0x, q0y, q1x, q1y, q2x, q2y):
"""
Converts a quadratic Bezier curve to a cubic approximation.
The inputs are the *x* and *y* coordinates of the three control
points of a quadratic curve, and the output is a tuple of *x* and
*y* coordinates of the four control points of the cubic curve.
"""
# c0x, c0y = q0x, q0y
c1x, c1y = q0x + 2./3. * (q1x - q0x), q0y + 2./3. * (q1y - q0y)
c2x, c2y = c1x + 1./3. * (q2x - q0x), c1y + 1./3. * (q2y - q0y)
# c3x, c3y = q2x, q2y
return q0x, q0y, c1x, c1y, c2x, c2y, q2x, q2y
| agpl-3.0 |
RomainBrault/scikit-learn | examples/decomposition/plot_kernel_pca.py | 353 | 2011 | """
==========
Kernel PCA
==========
This example shows that Kernel PCA is able to find a projection of the data
that makes data linearly separable.
"""
print(__doc__)
# Authors: Mathieu Blondel
# Andreas Mueller
# License: BSD 3 clause
import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA, KernelPCA
from sklearn.datasets import make_circles
np.random.seed(0)
X, y = make_circles(n_samples=400, factor=.3, noise=.05)
kpca = KernelPCA(kernel="rbf", fit_inverse_transform=True, gamma=10)
X_kpca = kpca.fit_transform(X)
X_back = kpca.inverse_transform(X_kpca)
pca = PCA()
X_pca = pca.fit_transform(X)
# Plot results
plt.figure()
plt.subplot(2, 2, 1, aspect='equal')
plt.title("Original space")
reds = y == 0
blues = y == 1
plt.plot(X[reds, 0], X[reds, 1], "ro")
plt.plot(X[blues, 0], X[blues, 1], "bo")
plt.xlabel("$x_1$")
plt.ylabel("$x_2$")
X1, X2 = np.meshgrid(np.linspace(-1.5, 1.5, 50), np.linspace(-1.5, 1.5, 50))
X_grid = np.array([np.ravel(X1), np.ravel(X2)]).T
# projection on the first principal component (in the phi space)
Z_grid = kpca.transform(X_grid)[:, 0].reshape(X1.shape)
plt.contour(X1, X2, Z_grid, colors='grey', linewidths=1, origin='lower')
plt.subplot(2, 2, 2, aspect='equal')
plt.plot(X_pca[reds, 0], X_pca[reds, 1], "ro")
plt.plot(X_pca[blues, 0], X_pca[blues, 1], "bo")
plt.title("Projection by PCA")
plt.xlabel("1st principal component")
plt.ylabel("2nd component")
plt.subplot(2, 2, 3, aspect='equal')
plt.plot(X_kpca[reds, 0], X_kpca[reds, 1], "ro")
plt.plot(X_kpca[blues, 0], X_kpca[blues, 1], "bo")
plt.title("Projection by KPCA")
plt.xlabel("1st principal component in space induced by $\phi$")
plt.ylabel("2nd component")
plt.subplot(2, 2, 4, aspect='equal')
plt.plot(X_back[reds, 0], X_back[reds, 1], "ro")
plt.plot(X_back[blues, 0], X_back[blues, 1], "bo")
plt.title("Original space after inverse transform")
plt.xlabel("$x_1$")
plt.ylabel("$x_2$")
plt.subplots_adjust(0.02, 0.10, 0.98, 0.94, 0.04, 0.35)
plt.show()
| bsd-3-clause |
notkarol/banjin | experiment/python_word_matching_speed.py | 1 | 4650 | #!/usr/bin/python
# Takes in a dictionary of words
# Verifies that all functions return the same answers
# Generates random hands from the probability of getting tiles from the bunch
# Then prints out how long each function takes to find all matching words
# Generates various hand sizes to see if there's any scaling
import matplotlib.pyplot as plt
import numpy as np
import pickle
import os
import sys
import timeit
# Naive list way of matching wordbank
def f0_list(hand, wordbank):
results = []
for w_i in range(len(wordbank)):
match = True
for i in range(26):
if hand[i] < wordbank[w_i][i]:
match = False
break
if match:
results.append(w_i)
return results
# A for loop and some numpy
def f1_list(hand, wordbank):
results = []
for w_i in range(len(wordbank)):
if min(list(map(lambda x: x[1] - x[0], zip(wordbank[w_i], hand)))) >= 0:
results.append(w_i)
return results
# Naive way using numpy
def f0_np(hand, wordbank):
results = []
for w_i in range(len(wordbank)):
match = True
for i in range(26):
if hand[i] < wordbank[w_i,i]:
match = False
break
if match:
results.append(w_i)
return results
# A for loop and some numpy
def f1_np(hand, wordbank):
results = []
for w_i in range(len(wordbank)):
if not np.any((hand - wordbank[w_i]) < 0):
results.append(w_i)
return results
# A for loop and some numpy
def f2_np(hand, wordbank):
results = []
for w_i in range(len(wordbank)):
if np.min(hand - wordbank[w_i]) >= 0:
results.append(w_i)
return results
# Vectorized sum and difference
def f3_np(hand, wordbank):
return np.where(np.sum((wordbank - hand) > 0, axis=1) == 0)[0]
# vectorized just using any
def f4_np(hand, wordbank):
return np.where(np.any(wordbank > hand, axis=1) == 0)[0]
# Prepare a 2D list and a 2D np array of letter frequencies
with open(sys.argv[1]) as f:
words = [x.split()[0] for x in f.readlines()]
wordbank_list = [[0] * 26 for _ in range(len(words))]
wordbank_np = np.zeros((len(words), 26))
for w_i in range(len(words)):
for letter in sorted(words[w_i]):
pos = ord(letter) - 65
wordbank_list[w_i][pos] += 1
wordbank_np[w_i][pos] += 1
# Arrays for keeping track of functions and data-specific wordbanks
hand_sizes = list(range(2, 9))
functions = {'list' : [f0_list, f1_list],
'numpy': [f0_np, f1_np, f2_np, f3_np, f4_np]}
wordbanks = {'list' : wordbank_list,
'numpy': wordbank_np}
n_iter = 10 if len(sys.argv) < 3 else int(sys.argv[2])
timings = {}
for datatype in functions:
timings[datatype] = np.zeros((max(hand_sizes) + 1, n_iter, len(functions[datatype])))
# Verify that our functions give the same answers
for datatype in functions:
for func in functions[datatype]:
print(datatype, func(wordbanks[datatype][len(wordbank_list) // 2], wordbanks[datatype]))
# Time each word
imports = 'from __main__ import functions, wordbanks'
for counter in range(n_iter):
for hand_size in hand_sizes:
# Get a specific hand size
hand = [13,3,3,6,18,3,4,3,12,2,2,5,3,8,11,3,2,9,6,9,6,3,3,2,3,2]
while sum(hand) > hand_size:
pos = np.random.randint(sum(hand))
for i in range(len(hand)):
pos -= hand[i]
if pos < 0:
hand[i] -= 1
break
hand = str(hand)
# For this hand go wild
for datatype in functions:
for f_i in range(len(functions[datatype])):
cmd = 'functions["%s"][%i](%s, wordbanks["%s"])' % (datatype, f_i, hand, datatype)
timings[datatype][hand_size, counter, f_i] += timeit.timeit(cmd, imports, number=8)
print("\rCompleted %.1f%%" % (100 * (counter + 1) / n_iter), end='')
print()
# Save words and timings in case we're doing a long-lasting operation
filename = 'word_matching_timings_%s.pkl' % os.path.basename(sys.argv[1])
with open(filename, 'wb') as f:
print("Saving", filename)
pickle.dump((words, wordbanks, timings), f)
# Show Results
for datatype in functions:
means = np.mean(timings[datatype], axis=1)
for f_i in range(means.shape[1]):
plt.semilogy(hand_sizes, means[:, f_i][min(hand_sizes):], label='%s F%i' % (datatype, f_i))
plt.legend(loc='center left', bbox_to_anchor=(0.85, 0.5))
plt.xlabel("Hand Size")
plt.ylabel("Execution Time")
plt.title("Word Matching")
plt.show()
| mit |
PatrickOReilly/scikit-learn | examples/model_selection/plot_validation_curve.py | 141 | 1931 | """
==========================
Plotting Validation Curves
==========================
In this plot you can see the training scores and validation scores of an SVM
for different values of the kernel parameter gamma. For very low values of
gamma, you can see that both the training score and the validation score are
low. This is called underfitting. Medium values of gamma will result in high
values for both scores, i.e. the classifier is performing fairly well. If gamma
is too high, the classifier will overfit, which means that the training score
is good but the validation score is poor.
"""
print(__doc__)
import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import load_digits
from sklearn.svm import SVC
from sklearn.model_selection import validation_curve
digits = load_digits()
X, y = digits.data, digits.target
param_range = np.logspace(-6, -1, 5)
train_scores, test_scores = validation_curve(
SVC(), X, y, param_name="gamma", param_range=param_range,
cv=10, scoring="accuracy", n_jobs=1)
train_scores_mean = np.mean(train_scores, axis=1)
train_scores_std = np.std(train_scores, axis=1)
test_scores_mean = np.mean(test_scores, axis=1)
test_scores_std = np.std(test_scores, axis=1)
plt.title("Validation Curve with SVM")
plt.xlabel("$\gamma$")
plt.ylabel("Score")
plt.ylim(0.0, 1.1)
lw = 2
plt.semilogx(param_range, train_scores_mean, label="Training score",
color="darkorange", lw=lw)
plt.fill_between(param_range, train_scores_mean - train_scores_std,
train_scores_mean + train_scores_std, alpha=0.2,
color="darkorange", lw=lw)
plt.semilogx(param_range, test_scores_mean, label="Cross-validation score",
color="navy", lw=lw)
plt.fill_between(param_range, test_scores_mean - test_scores_std,
test_scores_mean + test_scores_std, alpha=0.2,
color="navy", lw=lw)
plt.legend(loc="best")
plt.show()
| bsd-3-clause |
mortonjt/scipy | scipy/signal/wavelets.py | 23 | 10483 | from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.dual import eig
from scipy.special import comb
from scipy import linspace, pi, exp
from scipy.signal import convolve
__all__ = ['daub', 'qmf', 'cascade', 'morlet', 'ricker', 'cwt']
def daub(p):
"""
The coefficients for the FIR low-pass filter producing Daubechies wavelets.
p>=1 gives the order of the zero at f=1/2.
There are 2p filter coefficients.
Parameters
----------
p : int
Order of the zero at f=1/2, can have values from 1 to 34.
Returns
-------
daub : ndarray
Return
"""
sqrt = np.sqrt
if p < 1:
raise ValueError("p must be at least 1.")
if p == 1:
c = 1 / sqrt(2)
return np.array([c, c])
elif p == 2:
f = sqrt(2) / 8
c = sqrt(3)
return f * np.array([1 + c, 3 + c, 3 - c, 1 - c])
elif p == 3:
tmp = 12 * sqrt(10)
z1 = 1.5 + sqrt(15 + tmp) / 6 - 1j * (sqrt(15) + sqrt(tmp - 15)) / 6
z1c = np.conj(z1)
f = sqrt(2) / 8
d0 = np.real((1 - z1) * (1 - z1c))
a0 = np.real(z1 * z1c)
a1 = 2 * np.real(z1)
return f / d0 * np.array([a0, 3 * a0 - a1, 3 * a0 - 3 * a1 + 1,
a0 - 3 * a1 + 3, 3 - a1, 1])
elif p < 35:
# construct polynomial and factor it
if p < 35:
P = [comb(p - 1 + k, k, exact=1) for k in range(p)][::-1]
yj = np.roots(P)
else: # try different polynomial --- needs work
P = [comb(p - 1 + k, k, exact=1) / 4.0**k
for k in range(p)][::-1]
yj = np.roots(P) / 4
# for each root, compute two z roots, select the one with |z|>1
# Build up final polynomial
c = np.poly1d([1, 1])**p
q = np.poly1d([1])
for k in range(p - 1):
yval = yj[k]
part = 2 * sqrt(yval * (yval - 1))
const = 1 - 2 * yval
z1 = const + part
if (abs(z1)) < 1:
z1 = const - part
q = q * [1, -z1]
q = c * np.real(q)
# Normalize result
q = q / np.sum(q) * sqrt(2)
return q.c[::-1]
else:
raise ValueError("Polynomial factorization does not work "
"well for p too large.")
def qmf(hk):
"""
Return high-pass qmf filter from low-pass
Parameters
----------
hk : array_like
Coefficients of high-pass filter.
"""
N = len(hk) - 1
asgn = [{0: 1, 1: -1}[k % 2] for k in range(N + 1)]
return hk[::-1] * np.array(asgn)
def cascade(hk, J=7):
"""
Return (x, phi, psi) at dyadic points ``K/2**J`` from filter coefficients.
Parameters
----------
hk : array_like
Coefficients of low-pass filter.
J : int, optional
Values will be computed at grid points ``K/2**J``. Default is 7.
Returns
-------
x : ndarray
The dyadic points ``K/2**J`` for ``K=0...N * (2**J)-1`` where
``len(hk) = len(gk) = N+1``.
phi : ndarray
The scaling function ``phi(x)`` at `x`:
``phi(x) = sum(hk * phi(2x-k))``, where k is from 0 to N.
psi : ndarray, optional
The wavelet function ``psi(x)`` at `x`:
``phi(x) = sum(gk * phi(2x-k))``, where k is from 0 to N.
`psi` is only returned if `gk` is not None.
Notes
-----
The algorithm uses the vector cascade algorithm described by Strang and
Nguyen in "Wavelets and Filter Banks". It builds a dictionary of values
and slices for quick reuse. Then inserts vectors into final vector at the
end.
"""
N = len(hk) - 1
if (J > 30 - np.log2(N + 1)):
raise ValueError("Too many levels.")
if (J < 1):
raise ValueError("Too few levels.")
# construct matrices needed
nn, kk = np.ogrid[:N, :N]
s2 = np.sqrt(2)
# append a zero so that take works
thk = np.r_[hk, 0]
gk = qmf(hk)
tgk = np.r_[gk, 0]
indx1 = np.clip(2 * nn - kk, -1, N + 1)
indx2 = np.clip(2 * nn - kk + 1, -1, N + 1)
m = np.zeros((2, 2, N, N), 'd')
m[0, 0] = np.take(thk, indx1, 0)
m[0, 1] = np.take(thk, indx2, 0)
m[1, 0] = np.take(tgk, indx1, 0)
m[1, 1] = np.take(tgk, indx2, 0)
m *= s2
# construct the grid of points
x = np.arange(0, N * (1 << J), dtype=np.float) / (1 << J)
phi = 0 * x
psi = 0 * x
# find phi0, and phi1
lam, v = eig(m[0, 0])
ind = np.argmin(np.absolute(lam - 1))
# a dictionary with a binary representation of the
# evaluation points x < 1 -- i.e. position is 0.xxxx
v = np.real(v[:, ind])
# need scaling function to integrate to 1 so find
# eigenvector normalized to sum(v,axis=0)=1
sm = np.sum(v)
if sm < 0: # need scaling function to integrate to 1
v = -v
sm = -sm
bitdic = {}
bitdic['0'] = v / sm
bitdic['1'] = np.dot(m[0, 1], bitdic['0'])
step = 1 << J
phi[::step] = bitdic['0']
phi[(1 << (J - 1))::step] = bitdic['1']
psi[::step] = np.dot(m[1, 0], bitdic['0'])
psi[(1 << (J - 1))::step] = np.dot(m[1, 1], bitdic['0'])
# descend down the levels inserting more and more values
# into bitdic -- store the values in the correct location once we
# have computed them -- stored in the dictionary
# for quicker use later.
prevkeys = ['1']
for level in range(2, J + 1):
newkeys = ['%d%s' % (xx, yy) for xx in [0, 1] for yy in prevkeys]
fac = 1 << (J - level)
for key in newkeys:
# convert key to number
num = 0
for pos in range(level):
if key[pos] == '1':
num += (1 << (level - 1 - pos))
pastphi = bitdic[key[1:]]
ii = int(key[0])
temp = np.dot(m[0, ii], pastphi)
bitdic[key] = temp
phi[num * fac::step] = temp
psi[num * fac::step] = np.dot(m[1, ii], pastphi)
prevkeys = newkeys
return x, phi, psi
def morlet(M, w=5.0, s=1.0, complete=True):
"""
Complex Morlet wavelet.
Parameters
----------
M : int
Length of the wavelet.
w : float, optional
Omega0. Default is 5
s : float, optional
Scaling factor, windowed from ``-s*2*pi`` to ``+s*2*pi``. Default is 1.
complete : bool, optional
Whether to use the complete or the standard version.
Returns
-------
morlet : (M,) ndarray
See Also
--------
scipy.signal.gausspulse
Notes
-----
The standard version::
pi**-0.25 * exp(1j*w*x) * exp(-0.5*(x**2))
This commonly used wavelet is often referred to simply as the
Morlet wavelet. Note that this simplified version can cause
admissibility problems at low values of w.
The complete version::
pi**-0.25 * (exp(1j*w*x) - exp(-0.5*(w**2))) * exp(-0.5*(x**2))
The complete version of the Morlet wavelet, with a correction
term to improve admissibility. For w greater than 5, the
correction term is negligible.
Note that the energy of the return wavelet is not normalised
according to s.
The fundamental frequency of this wavelet in Hz is given
by ``f = 2*s*w*r / M`` where r is the sampling rate.
"""
x = linspace(-s * 2 * pi, s * 2 * pi, M)
output = exp(1j * w * x)
if complete:
output -= exp(-0.5 * (w**2))
output *= exp(-0.5 * (x**2)) * pi**(-0.25)
return output
def ricker(points, a):
"""
Return a Ricker wavelet, also known as the "Mexican hat wavelet".
It models the function:
``A (1 - x^2/a^2) exp(-x^2/2 a^2)``,
where ``A = 2/sqrt(3a)pi^1/4``.
Parameters
----------
points : int
Number of points in `vector`.
Will be centered around 0.
a : scalar
Width parameter of the wavelet.
Returns
-------
vector : (N,) ndarray
Array of length `points` in shape of ricker curve.
Examples
--------
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> points = 100
>>> a = 4.0
>>> vec2 = signal.ricker(points, a)
>>> print(len(vec2))
100
>>> plt.plot(vec2)
>>> plt.show()
"""
A = 2 / (np.sqrt(3 * a) * (np.pi**0.25))
wsq = a**2
vec = np.arange(0, points) - (points - 1.0) / 2
xsq = vec**2
mod = (1 - xsq / wsq)
gauss = np.exp(-xsq / (2 * wsq))
total = A * mod * gauss
return total
def cwt(data, wavelet, widths):
"""
Continuous wavelet transform.
Performs a continuous wavelet transform on `data`,
using the `wavelet` function. A CWT performs a convolution
with `data` using the `wavelet` function, which is characterized
by a width parameter and length parameter.
Parameters
----------
data : (N,) ndarray
data on which to perform the transform.
wavelet : function
Wavelet function, which should take 2 arguments.
The first argument is the number of points that the returned vector
will have (len(wavelet(width,length)) == length).
The second is a width parameter, defining the size of the wavelet
(e.g. standard deviation of a gaussian). See `ricker`, which
satisfies these requirements.
widths : (M,) sequence
Widths to use for transform.
Returns
-------
cwt: (M, N) ndarray
Will have shape of (len(widths), len(data)).
Notes
-----
>>> length = min(10 * width[ii], len(data))
>>> cwt[ii,:] = scipy.signal.convolve(data, wavelet(length,
... width[ii]), mode='same')
Examples
--------
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> t = np.linspace(-1, 1, 200, endpoint=False)
>>> sig = np.cos(2 * np.pi * 7 * t) + signal.gausspulse(t - 0.4, fc=2)
>>> widths = np.arange(1, 31)
>>> cwtmatr = signal.cwt(sig, signal.ricker, widths)
>>> plt.imshow(cwtmatr, extent=[-1, 1, 1, 31], cmap='PRGn', aspect='auto',
... vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max())
>>> plt.show()
"""
output = np.zeros([len(widths), len(data)])
for ind, width in enumerate(widths):
wavelet_data = wavelet(min(10 * width, len(data)), width)
output[ind, :] = convolve(data, wavelet_data,
mode='same')
return output
| bsd-3-clause |
broadinstitute/cms | cms/power/power_func.py | 1 | 8625 | ## functions for analyzing empirical/simulated CMS output
## last updated 09.14.2017 vitti@broadinstitute.org
import matplotlib as mp
mp.use('agg')
import matplotlib.pyplot as plt
import numpy as np
import math
from scipy.stats import percentileofscore
###################
## DEFINE SCORES ##
###################
def write_master_likesfile(writefilename, model, selpop, freq,basedir, miss = "neut",):
'''adapted from run_likes_func.py'''
writefile = open(writefilename, 'w')
for score in ['ihs', 'nsl', 'delihh']:
hitlikesfilename = basedir + model + "/" + score + "/likes_sel" + str(selpop) + "_" + str(freq) + "_causal.txt"#_smoothed.txt"
misslikesfilename = basedir + model + "/" + score + "/likes_sel" + str(selpop) + "_" + str(freq) + "_" + miss + ".txt"#"_smoothed.txt"
#assert(os.path.isfile(hitlikesfilename) and os.path.isfile(misslikesfilename))
writefile.write(hitlikesfilename + "\n" + misslikesfilename + "\n")
for score in ['xpehh', 'fst', 'deldaf']:
hitlikesfilename = basedir + model + "/" + score + "/likes_sel" + str(selpop) + "_choose_" + str(freq) + "_causal.txt"#_smoothed.txt"
misslikesfilename = basedir + model + "/" + score + "/likes_sel" + str(selpop) + "_choose_" + str(freq) + "_" + miss + ".txt"#"_smoothed.txt"
#assert(os.path.isfile(hitlikesfilename) and os.path.isfile(misslikesfilename))
writefile.write(hitlikesfilename + "\n" + misslikesfilename + "\n")
writefile.close()
print("wrote to: " + writefilename)
return
###############
## REGION ID ##
###############
def get_window(istart, physpos, scores, windowlen = 100000):
window_scores = [scores[istart]]
startpos = physpos[istart]
pos = startpos
iscore = istart
while pos < (startpos + windowlen):
iscore += 1
if iscore >= len(scores):
break
window_scores.append(scores[iscore])
pos = physpos[iscore]
#print(str(pos) + " " + str(startpos))
return window_scores
def check_outliers(scorelist, cutoff = 3):
numscores = len(scorelist)
outliers = [item for item in scorelist if item > cutoff]
numoutliers = len(outliers)
percentage = (float(numoutliers) / float(numscores)) * 100.
return percentage
def check_rep_windows(physpos, scores, windowlen = 100000, cutoff = 3, totalchrlen=1000000):
'''
previous implementation: !!!! this is going to result in false positives whenever I have a small uptick right near the edge of the replicate
'''
#check window defined by each snp as starting point
rep_percentages = []
numSnps = len(physpos)
numWindows = 0
#get exhaustive windows and stop at chrom edge
for isnp in range(numSnps):
if physpos[isnp] + windowlen < totalchrlen:
numWindows +=1
else:
#print(str(physpos[isnp]) + "\t")
break
for iPos in range(numWindows):
window_scores = get_window(iPos, physpos, scores, windowlen)
percentage = check_outliers(window_scores, cutoff)
rep_percentages.append(percentage)
return rep_percentages
def merge_windows(chrom_signif, windowlen, maxGap = 100000):
print('should implement this using bedtools')
starts, ends = [], []
contig = False
this_windowlen = 0
starting_pos = 0
if len(chrom_signif) > 0:
for i_start in range(len(chrom_signif) - 1):
if not contig:
starts.append(chrom_signif[i_start])
this_windowlen = windowlen #unmerged, default
starting_pos = chrom_signif[i_start]
if ((chrom_signif[i_start] + this_windowlen) > chrom_signif[i_start + 1]): #contiguous
contig = True
this_windowlen = chrom_signif[i_start +1] + windowlen - starting_pos
#or, could also be contiguous in the situation where the next snp is not within this window because there doesn't exist such a snp
elif chrom_signif[i_start +1] >=(chrom_signif[i_start] + this_windowlen) and chrom_signif[i_start +1] < (chrom_signif[i_start] + maxGap):
contig = True
this_windowlen = chrom_signif[i_start +1] + windowlen - starting_pos
else:
contig = False
if not contig:
windowend = chrom_signif[i_start] + windowlen
ends.append(windowend)
if contig: #last region is overlapped by its predecssor
ends.append(chrom_signif[-1] + windowlen)
else:
starts.append(chrom_signif[-1])
ends.append(chrom_signif[-1] + windowlen)
assert len(starts) == len(ends)
return starts, ends
##########################
## POWER & SIGNIFICANCE ##
##########################
def calc_pr(all_percentages, threshhold):
numNeutReps_exceedThresh = 0
totalnumNeutReps = len(all_percentages)
for irep in range(totalnumNeutReps):
if len(all_percentages[irep]) != 0:
if max(all_percentages[irep]) > threshhold:
numNeutReps_exceedThresh +=1
numNeutReps_exceedThresh, totalnumNeutReps = float(numNeutReps_exceedThresh), float(totalnumNeutReps)
if totalnumNeutReps != 0:
pr = numNeutReps_exceedThresh / totalnumNeutReps
else:
pr = 0
print('ERROR; empty set')
return pr
def get_causal_rank(values, causal_val):
if np.isnan(causal_val):
return(float('nan'))
assert(causal_val in values)
cleanvals = []
for item in values:
if not np.isnan(item) and not np.isinf(item):
cleanvals.append(item)
values = cleanvals
values.sort()
values.reverse()
causal_rank = values.index(causal_val)
return causal_rank
def get_cdf_from_causal_ranks(causal_ranks):
numbins = max(causal_ranks) #? heuristic
counts, bins = np.histogram(causal_ranks, bins=numbins, normed = True) #doublecheck
cdf = np.cumsum(counts)
return bins, cdf
def get_pval(all_simscores, thisScore):
r = np.searchsorted(all_simscores,thisScore)
n = len(all_simscores)
pval = 1. - ((r + 1.) / (n + 1.))
if pval > 0:
#pval *= nSnps #Bonferroni
return pval
else:
#print("r: " +str(r) + " , n: " + str(n))
pval = 1. - (r/(n+1))
#pval *= nSnps #Bonferroni
return pval
###############
## VISUALIZE ##
###############
def quick_plot(ax, pos, val, ylabel,causal_index=-1):
ax.scatter(pos, val, s=.8)
if causal_index != -1:
ax.scatter(pos[causal_index], val[causal_index], color='r', s=4)
for tick in ax.yaxis.get_major_ticks():
tick.label.set_fontsize('6')
ax.set_ylabel(ylabel, fontsize='6')
#ax.set_xlim([0, 1500000]) #make flexible?
ax.yaxis.set_label_position('right')
#ax.set_ylim([min(val), max(val)])
return ax
def plot_dist(allvals, savefilename= "/web/personal/vitti/test.png", numBins=1000):
#print(allvals)
#get rid of nans and infs
#cleanvals = [item for item in allvals if not np.isnan(item)]
#allvals = cleanvals
allvals = np.array(allvals)
allvals = allvals[~np.isnan(allvals)]
allvals = allvals[~np.isinf(allvals)]
#allvals = list(allvals)
#print(allvals)
print("percentile for score = 10: " + str(percentileofscore(allvals, 10)))
print("percentile for score = 15: " + str(percentileofscore(allvals, 15)))
if len(allvals) > 0:
f, ax = plt.subplots(1)
ax.hist(allvals, bins=numBins)
plt.savefig(savefilename)
print('plotted to ' + savefilename)
return
def plotManhattan(ax, neut_rep_scores, emp_scores, chrom_pos, nSnps, maxSkipVal = 0, zscores = True):
#neut_rep_scores.sort()
#print('sorted neutral scores...')
lastpos = 0
for chrom in range(1,23):
ichrom = chrom-1
if ichrom%2 == 0:
plotcolor = "darkblue"
else:
plotcolor = "lightblue"
if zscores == True:
#http://stackoverflow.com/questions/3496656/convert-z-score-z-value-standard-score-to-p-value-for-normal-distribution-in?rq=1
#Z SCORE cf SG email 103116
#pvals = [get_pval(neut_rep_scores, item) for item in emp_scores[ichrom]]
pvalues = []
for item in emp_scores[ichrom]:
if item < maxSkipVal: #speed up this process by ignoring anything obviously insignificant
pval = 1
else:
#print('scipy')
#sys.exit()
pval = scipy.stats.norm.sf(abs(item))
pvalues.append(pval)
#else:
# pval = get_pval(neut_rep_scores, item)
#pvalues.append(pval)
print("calculated pvalues for chrom " + str(chrom))
chrom_pos = range(lastpos, lastpos + len(pvalues))
logtenpvals = [(-1. * math.log10(pval)) for pval in pvalues]
ax.scatter(chrom_pos, logtenpvals, color =plotcolor, s=.5)
lastpos = chrom_pos[-1]
else:
chrom_pos = range(lastpos, lastpos + len(emp_scores[ichrom]))
ax.scatter(chrom_pos, emp_scores[ichrom], color=plotcolor, s=.5)
lastpos = chrom_pos[-1]
return ax
def plotManhattan_extended(ax, emp_scores, chrom_pos, chrom):
''' makes a figure more like in Karlsson 2013 instead of Grossman 2013'''
ax.plot(chrom_pos, emp_scores, linestyle='None', marker=".", markersize=.3, color="black")
ax.set_ylabel('chr' + str(chrom), fontsize=6, rotation='horizontal')
labels = ax.get_yticklabels()
ax.set_yticklabels(labels, fontsize=6)
ax.set_axis_bgcolor('LightGray')
return ax
| bsd-2-clause |
vshtanko/scikit-learn | examples/applications/plot_prediction_latency.py | 234 | 11277 | """
==================
Prediction Latency
==================
This is an example showing the prediction latency of various scikit-learn
estimators.
The goal is to measure the latency one can expect when doing predictions
either in bulk or atomic (i.e. one by one) mode.
The plots represent the distribution of the prediction latency as a boxplot.
"""
# Authors: Eustache Diemert <eustache@diemert.fr>
# License: BSD 3 clause
from __future__ import print_function
from collections import defaultdict
import time
import gc
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import scoreatpercentile
from sklearn.datasets.samples_generator import make_regression
from sklearn.ensemble.forest import RandomForestRegressor
from sklearn.linear_model.ridge import Ridge
from sklearn.linear_model.stochastic_gradient import SGDRegressor
from sklearn.svm.classes import SVR
def _not_in_sphinx():
# Hack to detect whether we are running by the sphinx builder
return '__file__' in globals()
def atomic_benchmark_estimator(estimator, X_test, verbose=False):
"""Measure runtime prediction of each instance."""
n_instances = X_test.shape[0]
runtimes = np.zeros(n_instances, dtype=np.float)
for i in range(n_instances):
instance = X_test[i, :]
start = time.time()
estimator.predict(instance)
runtimes[i] = time.time() - start
if verbose:
print("atomic_benchmark runtimes:", min(runtimes), scoreatpercentile(
runtimes, 50), max(runtimes))
return runtimes
def bulk_benchmark_estimator(estimator, X_test, n_bulk_repeats, verbose):
"""Measure runtime prediction of the whole input."""
n_instances = X_test.shape[0]
runtimes = np.zeros(n_bulk_repeats, dtype=np.float)
for i in range(n_bulk_repeats):
start = time.time()
estimator.predict(X_test)
runtimes[i] = time.time() - start
runtimes = np.array(list(map(lambda x: x / float(n_instances), runtimes)))
if verbose:
print("bulk_benchmark runtimes:", min(runtimes), scoreatpercentile(
runtimes, 50), max(runtimes))
return runtimes
def benchmark_estimator(estimator, X_test, n_bulk_repeats=30, verbose=False):
"""
Measure runtimes of prediction in both atomic and bulk mode.
Parameters
----------
estimator : already trained estimator supporting `predict()`
X_test : test input
n_bulk_repeats : how many times to repeat when evaluating bulk mode
Returns
-------
atomic_runtimes, bulk_runtimes : a pair of `np.array` which contain the
runtimes in seconds.
"""
atomic_runtimes = atomic_benchmark_estimator(estimator, X_test, verbose)
bulk_runtimes = bulk_benchmark_estimator(estimator, X_test, n_bulk_repeats,
verbose)
return atomic_runtimes, bulk_runtimes
def generate_dataset(n_train, n_test, n_features, noise=0.1, verbose=False):
"""Generate a regression dataset with the given parameters."""
if verbose:
print("generating dataset...")
X, y, coef = make_regression(n_samples=n_train + n_test,
n_features=n_features, noise=noise, coef=True)
X_train = X[:n_train]
y_train = y[:n_train]
X_test = X[n_train:]
y_test = y[n_train:]
idx = np.arange(n_train)
np.random.seed(13)
np.random.shuffle(idx)
X_train = X_train[idx]
y_train = y_train[idx]
std = X_train.std(axis=0)
mean = X_train.mean(axis=0)
X_train = (X_train - mean) / std
X_test = (X_test - mean) / std
std = y_train.std(axis=0)
mean = y_train.mean(axis=0)
y_train = (y_train - mean) / std
y_test = (y_test - mean) / std
gc.collect()
if verbose:
print("ok")
return X_train, y_train, X_test, y_test
def boxplot_runtimes(runtimes, pred_type, configuration):
"""
Plot a new `Figure` with boxplots of prediction runtimes.
Parameters
----------
runtimes : list of `np.array` of latencies in micro-seconds
cls_names : list of estimator class names that generated the runtimes
pred_type : 'bulk' or 'atomic'
"""
fig, ax1 = plt.subplots(figsize=(10, 6))
bp = plt.boxplot(runtimes, )
cls_infos = ['%s\n(%d %s)' % (estimator_conf['name'],
estimator_conf['complexity_computer'](
estimator_conf['instance']),
estimator_conf['complexity_label']) for
estimator_conf in configuration['estimators']]
plt.setp(ax1, xticklabels=cls_infos)
plt.setp(bp['boxes'], color='black')
plt.setp(bp['whiskers'], color='black')
plt.setp(bp['fliers'], color='red', marker='+')
ax1.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',
alpha=0.5)
ax1.set_axisbelow(True)
ax1.set_title('Prediction Time per Instance - %s, %d feats.' % (
pred_type.capitalize(),
configuration['n_features']))
ax1.set_ylabel('Prediction Time (us)')
plt.show()
def benchmark(configuration):
"""Run the whole benchmark."""
X_train, y_train, X_test, y_test = generate_dataset(
configuration['n_train'], configuration['n_test'],
configuration['n_features'])
stats = {}
for estimator_conf in configuration['estimators']:
print("Benchmarking", estimator_conf['instance'])
estimator_conf['instance'].fit(X_train, y_train)
gc.collect()
a, b = benchmark_estimator(estimator_conf['instance'], X_test)
stats[estimator_conf['name']] = {'atomic': a, 'bulk': b}
cls_names = [estimator_conf['name'] for estimator_conf in configuration[
'estimators']]
runtimes = [1e6 * stats[clf_name]['atomic'] for clf_name in cls_names]
boxplot_runtimes(runtimes, 'atomic', configuration)
runtimes = [1e6 * stats[clf_name]['bulk'] for clf_name in cls_names]
boxplot_runtimes(runtimes, 'bulk (%d)' % configuration['n_test'],
configuration)
def n_feature_influence(estimators, n_train, n_test, n_features, percentile):
"""
Estimate influence of the number of features on prediction time.
Parameters
----------
estimators : dict of (name (str), estimator) to benchmark
n_train : nber of training instances (int)
n_test : nber of testing instances (int)
n_features : list of feature-space dimensionality to test (int)
percentile : percentile at which to measure the speed (int [0-100])
Returns:
--------
percentiles : dict(estimator_name,
dict(n_features, percentile_perf_in_us))
"""
percentiles = defaultdict(defaultdict)
for n in n_features:
print("benchmarking with %d features" % n)
X_train, y_train, X_test, y_test = generate_dataset(n_train, n_test, n)
for cls_name, estimator in estimators.items():
estimator.fit(X_train, y_train)
gc.collect()
runtimes = bulk_benchmark_estimator(estimator, X_test, 30, False)
percentiles[cls_name][n] = 1e6 * scoreatpercentile(runtimes,
percentile)
return percentiles
def plot_n_features_influence(percentiles, percentile):
fig, ax1 = plt.subplots(figsize=(10, 6))
colors = ['r', 'g', 'b']
for i, cls_name in enumerate(percentiles.keys()):
x = np.array(sorted([n for n in percentiles[cls_name].keys()]))
y = np.array([percentiles[cls_name][n] for n in x])
plt.plot(x, y, color=colors[i], )
ax1.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',
alpha=0.5)
ax1.set_axisbelow(True)
ax1.set_title('Evolution of Prediction Time with #Features')
ax1.set_xlabel('#Features')
ax1.set_ylabel('Prediction Time at %d%%-ile (us)' % percentile)
plt.show()
def benchmark_throughputs(configuration, duration_secs=0.1):
"""benchmark throughput for different estimators."""
X_train, y_train, X_test, y_test = generate_dataset(
configuration['n_train'], configuration['n_test'],
configuration['n_features'])
throughputs = dict()
for estimator_config in configuration['estimators']:
estimator_config['instance'].fit(X_train, y_train)
start_time = time.time()
n_predictions = 0
while (time.time() - start_time) < duration_secs:
estimator_config['instance'].predict(X_test[0])
n_predictions += 1
throughputs[estimator_config['name']] = n_predictions / duration_secs
return throughputs
def plot_benchmark_throughput(throughputs, configuration):
fig, ax = plt.subplots(figsize=(10, 6))
colors = ['r', 'g', 'b']
cls_infos = ['%s\n(%d %s)' % (estimator_conf['name'],
estimator_conf['complexity_computer'](
estimator_conf['instance']),
estimator_conf['complexity_label']) for
estimator_conf in configuration['estimators']]
cls_values = [throughputs[estimator_conf['name']] for estimator_conf in
configuration['estimators']]
plt.bar(range(len(throughputs)), cls_values, width=0.5, color=colors)
ax.set_xticks(np.linspace(0.25, len(throughputs) - 0.75, len(throughputs)))
ax.set_xticklabels(cls_infos, fontsize=10)
ymax = max(cls_values) * 1.2
ax.set_ylim((0, ymax))
ax.set_ylabel('Throughput (predictions/sec)')
ax.set_title('Prediction Throughput for different estimators (%d '
'features)' % configuration['n_features'])
plt.show()
###############################################################################
# main code
start_time = time.time()
# benchmark bulk/atomic prediction speed for various regressors
configuration = {
'n_train': int(1e3),
'n_test': int(1e2),
'n_features': int(1e2),
'estimators': [
{'name': 'Linear Model',
'instance': SGDRegressor(penalty='elasticnet', alpha=0.01,
l1_ratio=0.25, fit_intercept=True),
'complexity_label': 'non-zero coefficients',
'complexity_computer': lambda clf: np.count_nonzero(clf.coef_)},
{'name': 'RandomForest',
'instance': RandomForestRegressor(),
'complexity_label': 'estimators',
'complexity_computer': lambda clf: clf.n_estimators},
{'name': 'SVR',
'instance': SVR(kernel='rbf'),
'complexity_label': 'support vectors',
'complexity_computer': lambda clf: len(clf.support_vectors_)},
]
}
benchmark(configuration)
# benchmark n_features influence on prediction speed
percentile = 90
percentiles = n_feature_influence({'ridge': Ridge()},
configuration['n_train'],
configuration['n_test'],
[100, 250, 500], percentile)
plot_n_features_influence(percentiles, percentile)
# benchmark throughput
throughputs = benchmark_throughputs(configuration)
plot_benchmark_throughput(throughputs, configuration)
stop_time = time.time()
print("example run in %.2fs" % (stop_time - start_time))
| bsd-3-clause |