import torch
import torch.nn as nn
import numpy as np


class APLoss (nn.Module):
    """ differentiable AP loss, through quantization.
        
        Input: (N, M)   values in [min, max]
        label: (N, M)   values in {0, 1}
        
        Returns: list of query AP (for each n in {1..N})
                 Note: typically, you want to minimize 1 - mean(AP)
    """
    def __init__(self, nq=25, min=0, max=1, euc=False):
        nn.Module.__init__(self)
        assert isinstance(nq, int) and 2 <= nq <= 100
        self.nq = nq
        self.min = min
        self.max = max
        self.euc = euc
        gap = max - min
        assert gap > 0
        
        # init quantizer = non-learnable (fixed) convolution
        self.quantizer = q = nn.Conv1d(1, 2*nq, kernel_size=1, bias=True)
        a = (nq-1) / gap
        #1st half = lines passing to (min+x,1) and (min+x+1/a,0) with x = {nq-1..0}*gap/(nq-1)
        q.weight.data[:nq] = -a
        q.bias.data[:nq] = torch.from_numpy(a*min + np.arange(nq, 0, -1)) # b = 1 + a*(min+x)
        #2nd half = lines passing to (min+x,1) and (min+x-1/a,0) with x = {nq-1..0}*gap/(nq-1)
        q.weight.data[nq:] = a
        q.bias.data[nq:] = torch.from_numpy(np.arange(2-nq, 2, 1) - a*min) # b = 1 - a*(min+x)
        # first and last one are special: just horizontal straight line
        q.weight.data[0] = q.weight.data[-1] = 0
        q.bias.data[0] = q.bias.data[-1] = 1

    def compute_AP(self, x, label):
        N, M = x.shape
        # print(x.shape, label.shape)
        if self.euc:  # euclidean distance in same range than similarities
            x = 1 - torch.sqrt(2.001 - 2*x)

        # quantize all predictions
        q = self.quantizer(x.unsqueeze(1))
        q = torch.min(q[:,:self.nq], q[:,self.nq:]).clamp(min=0) # N x Q x M [1600, 20, 1681]

        nbs = q.sum(dim=-1) # number of samples  N x Q = c
        rec = (q * label.view(N,1,M).float()).sum(dim=-1) # nb of correct samples = c+ N x Q
        prec = rec.cumsum(dim=-1) / (1e-16 + nbs.cumsum(dim=-1)) # precision
        rec /= rec.sum(dim=-1).unsqueeze(1) # norm in [0,1]

        ap = (prec * rec).sum(dim=-1) # per-image AP
        return ap

    def forward(self, x, label):
        assert x.shape == label.shape # N x M
        return self.compute_AP(x, label)


class PixelAPLoss (nn.Module):
    """ Computes the pixel-wise AP loss:
        Given two images and ground-truth optical flow, computes the AP per pixel.
        
        feat1:  (B, C, H, W)   pixel-wise features extracted from img1
        feat2:  (B, C, H, W)   pixel-wise features extracted from img2
        aflow:  (B, 2, H, W)   absolute flow: aflow[...,y1,x1] = x2,y2
    """
    def __init__(self, sampler, nq=20):
        nn.Module.__init__(self)
        self.aploss = APLoss(nq, min=0, max=1, euc=False)
        self.name = 'pixAP'
        self.sampler = sampler

    def loss_from_ap(self, ap, rel):
        return 1 - ap

    def forward(self, feat0, feat1, conf0, conf1, pos0, pos1, B, H, W, N=1200):
        # subsample things
        scores, gt, msk, qconf = self.sampler(feat0, feat1, conf0, conf1, pos0, pos1, B, H, W, N=1200)
        
        # compute pixel-wise AP
        n = qconf.numel()
        if n == 0: return 0
        scores, gt = scores.view(n,-1), gt.view(n,-1)
        ap = self.aploss(scores, gt).view(msk.shape)

        pixel_loss = self.loss_from_ap(ap, qconf)
        
        loss = pixel_loss[msk].mean()
        return loss


class ReliabilityLoss (PixelAPLoss):
    """ same than PixelAPLoss, but also train a pixel-wise confidence
        that this pixel is going to have a good AP.
    """
    def __init__(self, sampler, base=0.5, **kw):
        PixelAPLoss.__init__(self, sampler, **kw)
        assert 0 <= base < 1
        self.base = base

    def loss_from_ap(self, ap, rel):
        return 1 - ap*rel - (1-rel)*self.base