Given a matrix with the shape (1,3, H, W), I wish to obtain its difference in x-direction by channels.  I use the function F.conv2d as follows.
import torch
import torch.nn as nn
import numpy as np
import torch.nn.functional as F

# the shape of bdx3 is 1X3X3X3
bdx3 = torch.Tensor([[[[0.0,  0.0,  0.0], [0.0, 1.0, -1.0], [0.0, 0.0,  0.0]], 
					[[0.0,  0.0,  0.0], [0.0, 0.0, 0.0], [0.0, 0.0,  0.0]],
					[[0.0,  0.0,  0.0], [0.0, 0.0, 0.0], [0.0, 0.0,  0.0]]
					],
					[[[0.0,  0.0,  0.0], [0.0, 0.0, 0.0], [0.0, 0.0,  0.0]], 
					[[0.0,  0.0,  0.0], [0.0, 1.0, -1.0], [0.0, 0.0,  0.0]],
					[[0.0,  0.0,  0.0], [0.0, 0.0, 0.0], [0.0, 0.0,  0.0]]
					],
					[[[0.0,  0.0,  0.0], [0.0, 0.0, 0.0], [0.0, 0.0,  0.0]], 
					[[0.0,  0.0,  0.0], [0.0, 0.0, 0.0], [0.0, 0.0,  0.0]],
					[[0.0,  0.0,  0.0], [0.0, 1.0, -1.0], [0.0, 0.0,  0.0]]
					]
					])
class MyGradientx(nn.Module):
    def __init__(self):
        super(MyGradientx, self).__init__()

    def forward(self, input):
        output = F.conv2d(input, bdx30, padding=1)
        return output

H = 4
W = 5
u = np.arange(0, 3*H*W).astype(np.float32).reshape(1, 3, 4,5)
u = torch.from_numpy(u)
print("this is u: \n", u)

net1 = MyGradientx()
u1 = net1(u)

print("this is u1: \n", u1, "\n u1 shape", u1.shape)

I get the results:
this is u:
 tensor([[[[ 0.,  1.,  2.,  3.,  4.],
          [ 5.,  6.,  7.,  8.,  9.],
          [10., 11., 12., 13., 14.],
          [15., 16., 17., 18., 19.]],

         [[20., 21., 22., 23., 24.],
          [25., 26., 27., 28., 29.],
          [30., 31., 32., 33., 34.],
          [35., 36., 37., 38., 39.]],

         [[40., 41., 42., 43., 44.],
          [45., 46., 47., 48., 49.],
          [50., 51., 52., 53., 54.],
          [55., 56., 57., 58., 59.]]]])
this is u1:
 tensor([[[[-1., -1., -1., -1., 4.],
          [-1., -1., -1., -1., 9.],
          [-1., -1., -1., -1., 14.],
          [-1., -1., -1., -1., 19.]],

         [[-1., -1., -1., -1., 24.],
          [-1., -1., -1., -1., 29.],
          [-1., -1., -1., -1., 34.],
          [-1., -1., -1., -1., 39.]],

         [[-1., -1., -1., -1., 44.],
          [-1., -1., -1., -1., 49.],
          [-1., -1., -1., -1., 54.],
          [-1., -1., -1., -1., 59.]]]])
 u1 shape torch.Size([1, 3, 4, 5])

The first problem is if there are some functions in pytorch for the difference to a matrix give the same results?
Thank you!