C++卷积计算实现

张一极

如果是全连接的nerual network，输入是img（100*100），其参数，100 x 100 x 3，每个通道含有100x100的参数量，三个通道，第一层的nerual network假设为1000个nerual，第一层的参数量为30000 x 1000，所以引入了卷积，有目的地放弃一些权重，卷积其实可以看作，放弃了一部分权重的dnn，那么它对应的反向传播，只需要在最终的upload的结果上，不更新某一些参数即可，具体的后续实现会进行记录。

卷积作为一种拟合，把图像矩阵每一部分都变换成一个新的值，其核心就是权重的封装：

filter的四个数据，通过不断刷新去获取最合适的四个值：

运算的具体过程是这样的：（stride = 1）

每一次卷积都是使用等同于卷积核大小的尺寸数据进行计算，也就是黄色区域每一个像素乘以卷积核对应位置的每一个参数：

output：

cnn中的卷积方式不止有这一种，另外两种方式分别是：

1.（mode = full）从卷积核的第一个卷积接触到的element进行直接卷积：

2.（mode = same）

第三种就是最普遍的情况：

代码实现，mode = 0:

x
1
Matrix conv_element(Matrix mid1,Matrix kernel,int kernel_size = 2,int stride = 1)
2
{
3
  Matrix conv_result = CreateMatrix(((mid1.row-kernel_size)/stride)+1,((mid1.col-kernel_size)/stride)+1);
4
    for(int x_ = 0;x_<=(mid1.row-kernel_size)/stride;x_+=stride)
5
    {
6
      for(int y_ = 0;y_<=(mid1.col-kernel_size)/stride;y_+=stride)
7
      {
8
      Matrix crop_pic = iloc(mid1,x_,x_+kernel.col,y_,y_+kernel.row);
9
      change_va(conv_result,x_,y_,matrix_sum(mul_simple(crop_pic,kernel)));
10
      }
11
    }
12
    // cout<<"row: "<<conv_result.row<<" , "<<"col: "<<conv_result.col<<endl;
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    // cout_mat(conv_result);
14
    return conv_result;
15
    }
16
  /*
17
  parameter: 
18
    Matrix mid1,
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    int input_dim = 3
20
    int output_channels = 3
21
    int stride = 1
22
    int kernel_size = 2
23
    int mode = 0
24
    int padding = 0
25
  */
26
double conv_test(Matrix mid1,int input_dim = 3,int output_channels = 3,int stride = 1,int kernel_size = 2,int mode = 0,int padding = 0)
27
{
28
  // cout_mat(mid1);
29
  Matrix mid_rgb[input_dim];
30
  for(int rgb_idx = 0;rgb_idx<input_dim;rgb_idx++)
31
  {
32
    mid_rgb[rgb_idx] = CreateRandMat(mid1.row,mid1.col);
33
    cout<<"---------rgb: "<<rgb_idx<<"---------"<<endl;
34
    cout_mat(mid_rgb[rgb_idx]);
35
  }
36
  Matrix filters[output_channels][input_dim];
37
  for(int channel_index = 0;channel_index<input_dim;channel_index++)
38
  {
39
    for(int filter_index = 0;filter_index<output_channels;filter_index++)
40
      {
41
        Matrix kernel = ones(kernel_size,kernel_size);
42
        filters[channel_index][filter_index] = kernel;    
43
        // cout<<"---------"<<endl;
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        // cout<<"channel: "<<channel_index<<", index: "<<filter_index<<endl;
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        // cout_mat(filters[channel_index][filter_index]);
46
      }
47
  }
48
  if(mode == 0)
49
  {
50
    cout<<"input_img:"<<endl;
51
    cout_mat(mid1);
52
    Matrix conv_result = CreateMatrix(((mid1.row-kernel_size)/stride)+1,((mid1.col-kernel_size)/stride)+1);
53
    Matrix kernel = ones(kernel_size,kernel_size);
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    cout<<"--------- kernels: 3x3--------"<<endl;
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    cout_mat(kernel);
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    cout<<"--------- mid1 ---------"<<endl;
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    cout<<"row: "<<mid1.row<<" , "<<"col: "<<mid1.col<<endl;
58
    cout_mat(mid1);
59
    cout<<"--------- output: ---------"<<endl;  
60
    Matrix feature_maps[output_channels];
61
    for(int filter_idx = 0;filter_idx<output_channels;filter_idx++)
62
    { 
63
      Matrix sum_rgb = CreateMatrix(((mid1.row-kernel_size)/stride)+1,((mid1.col-kernel_size)/stride)+1);
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    for(int channel_idx=0;channel_idx<input_dim;channel_idx++)
65
    {
66
      sum_rgb = add(sum_rgb,conv_element(mid_rgb[channel_idx],filters[filter_idx][channel_idx],kernel_size,stride),0);
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      cout<<"sum_rgb"<<"filters_index: "<<filter_idx<<" "<<endl;
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      cout_mat(sum_rgb);
69
    }
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    feature_maps[filter_idx]=sum_rgb;
71
  }
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  for(int i = 0;i < output_channels;i++)
73
  {
74
    cout<<"==========filter: "<<i<<"========="<<endl;
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    cout_mat(feature_maps[i]);
76
​
77
  }
78
  return 0.0;
79
}
80
}

假设rgb：

xxxxxxxxxx
1
21
1
———rgb: 0———
2
0.6868,1.358,-0.0419,0.3864,-0.87,0.7874,0.1393,
3
0.7593,0.1114,-0.7965,-0.7005,1.5068,-0.3997,1.1945,
4
-0.6814,-0.6164,1.7819,0.933,1.0805,0.2337,-0.7265,
5
1.6941,0.5209,-0.9397,-0.3,0.9019,-0.5348,-0.9147,
6
0.257,1.2136,1.9702,0.996,-0.394,-0.0892,-0.6112,
7
0.9649,0.2556,-0.6445,-0.3106,1.3732,-0.4526,1.5519,
8
———rgb: 1———
9
0.5726,-0.2106,-0.6804,-0.6533,-0.7418,1.4237,-0.0423,
10
0.3982,1.0687,-0.2758,-0.7519,0.9336,-0.4004,0.7577,
11
1.0035,1.8065,0.7624,1.0708,0.0301,-0.0468,-0.3465,
12
1.5645,-0.397,1.6417,1.148,-0.1405,-0.3185,-0.7553,
13
1.5715,1.2818,-0.9162,0.0648,1.2894,0.8675,1.2892,
14
1.9186,1.0597,-0.7541,1.4489,-0.5107,1.0148,0.0982,
15
———rgb: 2———
16
1.3683,0.3772,1.4713,1.8638,1.019,-0.9855,0.2794,
17
-0.1709,0.7684,1.7359,1.7779,1.4403,0.0131,1.4975,
18
0.2598,1.6541,1.6398,0.9777,-0.0517,0.0652,-0.0643,
19
1.0337,0.4624,1.9443,1.9263,0.4125,-0.9113,0.2605,
20
-0.656,-0.7297,-0.398,0.2574,-0.157,1.5341,0.8177,
21
-0.7898,1.1526,0.2964,0.1901,1.4331,-0.9055,-0.8993,

卷积核是1x1的3x3，输出如下：

xxxxxxxxxx
1
61
1
--------- output: ---------
2
sum_rgbfilters_index: 0
3
2.5612,2.4154,3.2797,2.9576,2.946,
4
1.8336,-0.00589997,3.4674,2.7209,2.3417,
5
5.2002,5.5595,6.0298,2.8271,-1.0543,
6
5.2921,2.7615,2.6525,1.1899,0.8305,
7
sum_rgbfilters_index: 0
8
7.0063,4.5518,2.9734,3.8216,4.5133,
9
9.4063,6.0675,7.8858,4.2453,2.0551,
10
13.5189,12.0223,10.9803,6.7919,0.8143,
11
12.2626,7.3391,5.9238,6.0536,3.6646,
12
sum_rgbfilters_index: 0
13
16.1102,16.8179,14.8474,9.9414,7.7263,
14
18.7338,18.9543,19.6888,9.8953,4.7169,
15
18.7293,19.7566,17.5316,10.8451,2.72,
16
14.5785,12.4409,11.8289,9.8333,5.2494,
17
sum_rgbfilters_index: 1
18
2.5612,2.4154,3.2797,2.9576,2.946,
19
1.8336,-0.00589997,3.4674,2.7209,2.3417,
20
5.2002,5.5595,6.0298,2.8271,-1.0543,
21
5.2921,2.7615,2.6525,1.1899,0.8305,
22
sum_rgbfilters_index: 1
23
7.0063,4.5518,2.9734,3.8216,4.5133,
24
9.4063,6.0675,7.8858,4.2453,2.0551,
25
13.5189,12.0223,10.9803,6.7919,0.8143,
26
12.2626,7.3391,5.9238,6.0536,3.6646,
27
sum_rgbfilters_index: 1
28
16.1102,16.8179,14.8474,9.9414,7.7263,
29
18.7338,18.9543,19.6888,9.8953,4.7169,
30
18.7293,19.7566,17.5316,10.8451,2.72,
31
14.5785,12.4409,11.8289,9.8333,5.2494,
32
sum_rgbfilters_index: 2
33
2.5612,2.4154,3.2797,2.9576,2.946,
34
1.8336,-0.00589997,3.4674,2.7209,2.3417,
35
5.2002,5.5595,6.0298,2.8271,-1.0543,
36
5.2921,2.7615,2.6525,1.1899,0.8305,
37
sum_rgbfilters_index: 2
38
7.0063,4.5518,2.9734,3.8216,4.5133,
39
9.4063,6.0675,7.8858,4.2453,2.0551,
40
13.5189,12.0223,10.9803,6.7919,0.8143,
41
12.2626,7.3391,5.9238,6.0536,3.6646,
42
sum_rgbfilters_index: 2
43
16.1102,16.8179,14.8474,9.9414,7.7263,
44
18.7338,18.9543,19.6888,9.8953,4.7169,
45
18.7293,19.7566,17.5316,10.8451,2.72,
46
14.5785,12.4409,11.8289,9.8333,5.2494,
47
==========filter: 0=========
48
16.1102,16.8179,14.8474,9.9414,7.7263,
49
18.7338,18.9543,19.6888,9.8953,4.7169,
50
18.7293,19.7566,17.5316,10.8451,2.72,
51
14.5785,12.4409,11.8289,9.8333,5.2494,
52
==========filter: 1=========
53
16.1102,16.8179,14.8474,9.9414,7.7263,
54
18.7338,18.9543,19.6888,9.8953,4.7169,
55
18.7293,19.7566,17.5316,10.8451,2.72,
56
14.5785,12.4409,11.8289,9.8333,5.2494,
57
==========filter: 2=========
58
16.1102,16.8179,14.8474,9.9414,7.7263,
59
18.7338,18.9543,19.6888,9.8953,4.7169,
60
18.7293,19.7566,17.5316,10.8451,2.72,
61
14.5785,12.4409,11.8289,9.8333,5.2494,