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from functools import reduce | |
from itertools import cycle | |
from math import factorial | |
import numpy as np | |
import scipy.sparse as sp | |
def difference(derivative, accuracy=1): | |
# Central differences implemented based on the article here: | |
# http://web.media.mit.edu/~crtaylor/calculator.html | |
derivative += 1 | |
radius = accuracy + derivative // 2 - 1 | |
points = range(-radius, radius + 1) | |
coefficients = np.linalg.inv(np.vander(points)) | |
return coefficients[-derivative] * factorial(derivative - 1), points | |
def operator(shape, *differences): | |
# Credit to Philip Zucker for figuring out | |
# that kronsum's argument order is reversed. | |
# Without that bit of wisdom I'd have lost it. | |
differences = zip(shape, cycle(differences)) | |
factors = (sp.diags(*diff, shape=(dim,) * 2) for dim, diff in differences) | |
return reduce(lambda a, f: sp.kronsum(f, a, format='csc'), factors) |