代码：基于pytorch的验证

#%%
import torch
from torch import nn

#%% 产生数据
N = 2
Cin =2
Cout = 3
H = 4
W = 4
arry = torch.arange(N*Cin*4*4,dtype=torch.float32).view([N,Cin,H,W])
print('原始数据：',arry)

#%% 2d卷积(pytorch)
conv1 = nn.Conv2d(in_channels=Cin,out_channels=Cout,kernel_size=3,stride=1,padding=0)
print('2d卷积(pytorch)：',conv1(arry))

#%% 获取pytorch 2d卷积的变量
it = conv1.parameters() #迭代器
kernel = next(it)
bias   = next(it)
print('卷积核：',kernel)
print('卷积偏置：',bias)

#%% 2d卷积(公式)
arr = arry.detach().numpy()
ker = kernel.detach().numpy()
bia = bias.detach().numpy()

import numpy as np
rr = 0                      #卷积用
cc = 0                      #卷积用
con = np.zeros((N,Cout,2,2)) #卷积输出
#依次遍历Batch中每张图像
for n in range(N):
    for kernel in range(Cout):          #第i个kernel
        for channel in range(Cin):      #第i个kernel中第j个channel
            
            #图像卷积，Batch中每张图像，第i个kernel中第j个channel
            rr = 0;cc = 0;conTemp=np.zeros((2,2))
            for r in [1,2]:             #图像行
                for c in [1,2]:         #图像列
                    conTemp[rr,cc] = np.sum(arr[n,channel,(r-1):(r+2),(c-1):(c+2)]*ker[kernel,channel,:,:])
                    cc+=1
                cc=0
                rr+=1
            
            con[n,kernel,:,:] += conTemp    #多个channel相加
        con[n,kernel,:,:] += bia[kernel]    #加上bias
print('2d卷积(公式)',con)

结果：pytorch函数和自己写的函数结果一致。证明了我上面的解释正确。

2d卷积(pytorch)： tensor([[[[ -0.8406,  -0.8379],
          [ -0.8299,  -0.8272]],

         [[-16.8945, -17.8185],
          [-20.5904, -21.5144]],

         [[  6.9472,   7.4892],
          [  9.1152,   9.6572]]],


        [[[ -0.7549,  -0.7523],
          [ -0.7442,  -0.7415]],

         [[-46.4619, -47.3859],
          [-50.1579, -51.0818]],

         [[ 24.2914,  24.8334],
          [ 26.4594,  27.0014]]]], grad_fn=<ThnnConv2DBackward>)


2d卷积(公式) [[[[ -0.84061861  -0.83794105]
   [ -0.82990921  -0.82723093]]

  [[-16.89449914 -17.81848235]
   [-20.59042831 -21.51441355]]

  [[  6.94720098   7.48920748]
   [  9.11522838   9.65723416]]]


 [[[ -0.75493801  -0.75225866]
   [ -0.74422729  -0.7415489 ]]

  [[-46.46194191 -47.38591881]
   [-50.15787096 -51.08184786]]

  [[ 24.29141471  24.83342215]
   [ 26.45944354  27.00144812]]]]

tensorflow的二维卷积

import tensorflow as tf
import numpy as np
 
#%% 产生数据
N = 2
Cin =2
Cout = 3
H = 4
W = 4

arry = np.arange(N*Cin*H*W).reshape([N,H,W,Cin])
#%%
input = tf.placeholder(dtype=tf.float32,shape=[N,H,W,Cin])
filter = tf.Variable(tf.random_normal([3,3,Cin,Cout]))
conv2 = tf.nn.conv2d(input,filter,strides=[1,1,1,1],padding='VALID',use_cudnn_on_gpu=False)

with tf.Session() as sess:
    tf.global_variables_initializer().run()
    print(sess.run(conv2,feed_dict={input:arry}))

注意事项：

nn.Conv2d中的padding操作，pytorch同tensorflow不同，padding没有“SAME”和“VALID”选项，根据熟人padding=（X,Y）来决定在哪里进行padding。**则第一个参数表示高度（上下）上面的padding，第2个参数表示宽度（左右）上面的。**如下图