Incorrect gradient

[leinxx]

The gradient computation is incorrect. Test code:

import numpy as np
import torch
import time

from emd import EMDLoss

dist =  EMDLoss()

xs = np.linspace(10, 50, 41)
ys = np.linspace(10, 50, 41)

l1 = np.stack((xs, np.ones(41)*10)).transpose()
l2 = np.stack((xs, np.ones(41)*50)).transpose()
l3 = np.stack((np.ones(41)*10, ys)).transpose()
l4 = np.stack((np.ones(41)*50, ys)).transpose()

p1 = np.concatenate((l1,l2,l3,l4))
npts = len(p1)
p1 = torch.from_numpy(p1).cuda().unsqueeze_(0)
for i in range(-3, 3):
    print('offset: ', i)
    p2 = p1 + i
    p1.requires_grad = True
    cost1 = dist(p1, p2)
    print('\tdistance: ', cost1.data.cpu().numpy()[0])
    loss = torch.sum(cost1)/npts
    loss.backward()
    print('\tgradient: ', p1.grad.data.cpu().numpy()[0][0])

Run script, the output looks like this:

offset:  -3
    distance:  489.7591609045162
    gradient:  [0.48759389 0.48759389]
offset:  -2
    distance:  323.4196924319101
    gradient:  [8124.4279909  6355.79031227]
offset:  -1
    distance:  162.74898605187073
    gradient:  [14667.35957541 11995.79261712]
offset:  0
    distance:  0.0
    gradient:  [6.25019588e+08 6.25016916e+08]
offset:  1
    distance:  162.7489860518707
    gradient:  [6.25026458e+08 6.25022920e+08]
offset:  2
    distance:  323.41969243191016
    gradient:  [6.25035163e+08 6.25029917e+08]

The gradient is always positive when offset is both positive and negative, gradient is none zero when offset = 0.