卷积神经网络(CNN)的基础介绍见http://blog.csdn.net/fengbingchun/article/details/50529500，这里主要以代码实现为主。

CNN是一个多层的神经网络，每层由多个二维平面组成，而每个平面由多个独立神经元组成。

以MNIST作为数据库，仿照LeNet-5和tiny-cnn( http://blog.csdn.net/fengbingchun/article/details/50573841 ) 设计一个简单的7层CNN结构如下：

输入层Input：神经元数量32*32=1024；

C1层：卷积窗大小5*5，输出特征图数量6，卷积窗种类6，输出特征图大小28*28，可训练参数(权值+阈值(偏置))5*5*6+6=150+6，神经元数量28*28*6=4704；

S2层：卷积窗大小2*2，输出下采样图数量6，卷积窗种类6，输出下采样图大小14*14，可训练参数1*6+6=6+6，神经元数量14*14*6=1176；

C3层：卷积窗大小5*5，输出特征图数量16，卷积窗种类16，输出特征图大小10*10，可训练参数5*5*(6*16)+16=2400+16，神经元数量10*10*16=1600；

S4层：卷积窗大小2*2，输出下采样图数量16，卷积窗种类16，输出下采样图大小5*5，可训练参数1*16+16=16+16，神经元数量5*5*16=400；

C5层：卷积窗大小5*5，输出特征图数量120，卷积窗种类16*120=1920，输出特征图大小1*1，可训练参数5*5*(16*120)+120=48000+120，神经元数量1*1*120=120；

输出层Output：卷积窗大小1*1，输出特征图数量10，卷积窗种类120*10=1200，输出特征图大小1*1，可训练参数1*(120*10)+10=1200+10，神经元数量1*1*10=10。

下面对实现执行过程进行描述说明：

1.      从MNIST数据库中分别获取训练样本和测试样本数据：

(1)、原有MNIST库中图像大小为28*28，这里缩放为32*32，数据值范围为[-1,1]，扩充值均取-1；总共60000个32*32训练样本，10000个32*32测试样本；

(2)、输出层有10个输出节点，在训练阶段，对应位置的节点值设为0.8，其它节点设为-0.8.

2.        初始化权值和阈值(偏置)：权值就是卷积图像，每一个特征图上的神经元共享相同的权值和阈值，特征图的数量等于阈值的个数

(1)、权值采用uniform rand的方法初始化；

(2)、阈值均初始化为0.

3.      前向传播：根据权值和阈值，主要计算每层神经元的值

(1)、输入层：每次输入一个32*32数据。

(2)、C1层：分别用每一个5*5的卷积图像去乘以32*32的图像，获得一个28*28的图像，即对应位置相加再求和，stride长度为1；一共6个5*5的卷积图像，然后对每一个神经元加上一个阈值，最后再通过tanh激活函数对每一神经元进行运算得到最终每一个神经元的结果。

(3)、S2层：对C1中6个28*28的特征图生成6个14*14的下采样图，相邻四个神经元分别进行相加求和，然后乘以一个权值，再求均值即除以4，然后再加上一个阈值，最后再通过tanh激活函数对每一神经元进行运算得到最终每一个神经元的结果。

(4)、C3层：由S2中的6个14*14下采样图生成16个10*10特征图，对于生成的每一个10*10的特征图，是由6个5*5的卷积图像去乘以6个14*14的下采样图，然后对应位置相加求和，然后对每一个神经元加上一个阈值，最后再通过tanh激活函数对每一神经元进行运算得到最终每一个神经元的结果。

(5)、S4层：由C3中16个10*10的特征图生成16个5*5下采样图，相邻四个神经元分别进行相加求和，然后乘以一个权值，再求均值即除以4，然后再加上一个阈值，最后再通过tanh激活函数对每一神经元进行运算得到最终每一个神经元的结果。

(6)、C5层：由S4中16个5*5下采样图生成120个1*1特征图，对于生成的每一个1*1的特征图，是由16个5*5的卷积图像去乘以16个5*5的下采用图，然后相加求和，然后对每一个神经元加上一个阈值，最后再通过tanh激活函数对每一神经元进行运算得到最终每一个神经元的结果。

(7)、输出层：即全连接层，输出层中的每一个神经元均是由C5层中的120个神经元乘以相对应的权值，然后相加求和；然后对每一个神经元加上一个阈值，最后再通过tanh激活函数对每一神经元进行运算得到最终每一个神经元的结果。

4.      反向传播：主要计算每层神经元、权值和阈值的误差，以用来更新权值和阈值

(1)、输出层：计算输出层神经元误差；通过mse损失函数的导数函数和tanh激活函数的导数函数来计算输出层神经元误差。

(2)、C5层：计算C5层神经元误差、输出层权值误差、输出层阈值误差；通过输出层神经元误差乘以输出层权值，求和，结果再乘以C5层神经元的tanh激活函数的导数，获得C5层每一个神经元误差；通过输出层神经元误差乘以C5层神经元获得输出层权值误差；输出层误差即为输出层阈值误差。

(3)、S4层：计算S4层神经元误差、C5层权值误差、C5层阈值误差；通过C5层权值乘以C5层神经元误差，求和，结果再乘以S4层神经元的tanh激活函数的导数，获得S4层每一个神经元误差；通过S4层神经元乘以C5层神经元误差，求和，获得C5层权值误差；C5层神经元误差即为C5层阈值误差。

(4)、C3层：计算C3层神经元误差、S4层权值误差、S4层阈值误差；

(5)、S2层：计算S2层神经元误差、C3层权值误差、C3层阈值误差；

(6)、C1层：计算C1层神经元误差、S2层权值误差、S2层阈值误差；

(7)、输入层：计算C1层权值误差、C1层阈值误差.

代码文件：

CNN.hpp：

#ifndef _CNN_HPP_
#define _CNN_HPP_#include <vector>
#include <unordered_map> namespace ANN {#define width_image_input_CNN     32 //归一化图像宽
#define height_image_input_CNN      32 //归一化图像高
#define width_image_C1_CNN      28
#define height_image_C1_CNN     28
#define width_image_S2_CNN      14
#define height_image_S2_CNN     14
#define width_image_C3_CNN      10
#define height_image_C3_CNN     10
#define width_image_S4_CNN      5
#define height_image_S4_CNN     5
#define width_image_C5_CNN      1
#define height_image_C5_CNN     1
#define width_image_output_CNN      1
#define height_image_output_CNN     1#define width_kernel_conv_CNN      5 //卷积核大小
#define height_kernel_conv_CNN      5
#define width_kernel_pooling_CNN    2
#define height_kernel_pooling_CNN   2
#define size_pooling_CNN        2#define num_map_input_CNN      1 //输入层map个数
#define num_map_C1_CNN          6 //C1层map个数
#define num_map_S2_CNN          6 //S2层map个数
#define num_map_C3_CNN          16 //C3层map个数
#define num_map_S4_CNN          16 //S4层map个数
#define num_map_C5_CNN          120 //C5层map个数
#define num_map_output_CNN      10 //输出层map个数#define num_patterns_train_CNN     60000 //训练模式对数(总数)
#define num_patterns_test_CNN       10000 //测试模式对数(总数)
#define num_epochs_CNN          100 //最大迭代次数
#define accuracy_rate_CNN       0.985 //要求达到的准确率
#define learning_rate_CNN       0.01 //学习率
#define eps_CNN             1e-8#define len_weight_C1_CNN       150 //C1层权值数，5*5*6*1=150
#define len_bias_C1_CNN         6 //C1层阈值数，6
#define len_weight_S2_CNN       6 //S2层权值数,1*6=6
#define len_bias_S2_CNN         6 //S2层阈值数,6
#define len_weight_C3_CNN       2400 //C3层权值数，5*5*16*6=2400
#define len_bias_C3_CNN         16 //C3层阈值数,16
#define len_weight_S4_CNN       16 //S4层权值数，1*16=16
#define len_bias_S4_CNN         16 //S4层阈值数，16
#define len_weight_C5_CNN       48000 //C5层权值数，5*5*16*120=48000
#define len_bias_C5_CNN         120 //C5层阈值数，120
#define len_weight_output_CNN       1200 //输出层权值数，120*10=1200
#define len_bias_output_CNN     10 //输出层阈值数，10#define num_neuron_input_CNN       1024 //输入层神经元数，32*32=1024
#define num_neuron_C1_CNN       4704 //C1层神经元数，28*28*6=4704
#define num_neuron_S2_CNN       1176 //S2层神经元数，14*14*6=1176
#define num_neuron_C3_CNN       1600 //C3层神经元数，10*10*16=1600
#define num_neuron_S4_CNN       400 //S4层神经元数，5*5*16=400
#define num_neuron_C5_CNN       120 //C5层神经元数，1*120=120
#define num_neuron_output_CNN       10 //输出层神经元数，1*10=10class CNN {
public:CNN();~CNN();void init(); //初始化，分配空间bool train(); //训练int predict(const unsigned char* data, int width, int height); //预测bool readModelFile(const char* name); //读取已训练好的BP modelprotected:typedef std::vector<std::pair<int, int> > wi_connections;typedef std::vector<std::pair<int, int> > wo_connections;typedef std::vector<std::pair<int, int> > io_connections;void release(); //释放申请的空间bool saveModelFile(const char* name); //将训练好的model保存起来，包括各层的节点数，权值和阈值bool initWeightThreshold(); //初始化，产生[-1, 1]之间的随机小数bool getSrcData(); //读取MNIST数据double test(); //训练完一次计算一次准确率double activation_function_tanh(double x); //激活函数:tanhdouble activation_function_tanh_derivative(double x); //激活函数tanh的导数double activation_function_identity(double x);double activation_function_identity_derivative(double x);double loss_function_mse(double y, double t); //损失函数:mean squared errordouble loss_function_mse_derivative(double y, double t);void loss_function_gradient(const double* y, const double* t, double* dst, int len);double dot_product(const double* s1, const double* s2, int len); //点乘bool muladd(const double* src, double c, int len, double* dst); //dst[i] += c * src[i]void init_variable(double* val, double c, int len);bool uniform_rand(double* src, int len, double min, double max);double uniform_rand(double min, double max);int get_index(int x, int y, int channel, int width, int height, int depth);void calc_out2wi(int width_in, int height_in, int width_out, int height_out, int depth_out, std::vector<wi_connections>& out2wi);void calc_out2bias(int width, int height, int depth, std::vector<int>& out2bias);void calc_in2wo(int width_in, int height_in, int width_out, int height_out, int depth_in, int depth_out, std::vector<wo_connections>& in2wo);void calc_weight2io(int width_in, int height_in, int width_out, int height_out, int depth_in, int depth_out, std::vector<io_connections>& weight2io);void calc_bias2out(int width_in, int height_in, int width_out, int height_out, int depth_in, int depth_out, std::vector<std::vector<int> >& bias2out);bool Forward_C1(); //前向传播bool Forward_S2();bool Forward_C3();bool Forward_S4();bool Forward_C5();bool Forward_output();bool Backward_output();bool Backward_C5(); //反向传播bool Backward_S4();bool Backward_C3();bool Backward_S2();bool Backward_C1();bool Backward_input();bool UpdateWeights(); //更新权值、阈值void update_weights_bias(const double* delta, double* e_weight, double* weight, int len);private:double* data_input_train; //原始标准输入数据，训练,范围：[-1, 1]double* data_output_train; //原始标准期望结果，训练,取值：-0.8/0.8double* data_input_test; //原始标准输入数据，测试,范围：[-1, 1]double* data_output_test; //原始标准期望结果，测试,取值：-0.8/0.8double* data_single_image;double* data_single_label;double weight_C1[len_weight_C1_CNN];double bias_C1[len_bias_C1_CNN];double weight_S2[len_weight_S2_CNN];double bias_S2[len_bias_S2_CNN];double weight_C3[len_weight_C3_CNN];double bias_C3[len_bias_C3_CNN];double weight_S4[len_weight_S4_CNN];double bias_S4[len_bias_S4_CNN];double weight_C5[len_weight_C5_CNN];double bias_C5[len_bias_C5_CNN];double weight_output[len_weight_output_CNN];double bias_output[len_bias_output_CNN];double E_weight_C1[len_weight_C1_CNN];double E_bias_C1[len_bias_C1_CNN];double E_weight_S2[len_weight_S2_CNN];double E_bias_S2[len_bias_S2_CNN];double E_weight_C3[len_weight_C3_CNN];double E_bias_C3[len_bias_C3_CNN];double E_weight_S4[len_weight_S4_CNN];double E_bias_S4[len_bias_S4_CNN];double* E_weight_C5;double* E_bias_C5;double* E_weight_output;double* E_bias_output;double neuron_input[num_neuron_input_CNN]; //data_single_imagedouble neuron_C1[num_neuron_C1_CNN];double neuron_S2[num_neuron_S2_CNN];double neuron_C3[num_neuron_C3_CNN];double neuron_S4[num_neuron_S4_CNN];double neuron_C5[num_neuron_C5_CNN];double neuron_output[num_neuron_output_CNN];double delta_neuron_output[num_neuron_output_CNN]; //神经元误差double delta_neuron_C5[num_neuron_C5_CNN];double delta_neuron_S4[num_neuron_S4_CNN];double delta_neuron_C3[num_neuron_C3_CNN];double delta_neuron_S2[num_neuron_S2_CNN];double delta_neuron_C1[num_neuron_C1_CNN];double delta_neuron_input[num_neuron_input_CNN];double delta_weight_C1[len_weight_C1_CNN]; //权值、阈值误差double delta_bias_C1[len_bias_C1_CNN];double delta_weight_S2[len_weight_S2_CNN];double delta_bias_S2[len_bias_S2_CNN];double delta_weight_C3[len_weight_C3_CNN];double delta_bias_C3[len_bias_C3_CNN];double delta_weight_S4[len_weight_S4_CNN];double delta_bias_S4[len_bias_S4_CNN];double delta_weight_C5[len_weight_C5_CNN];double delta_bias_C5[len_bias_C5_CNN];double delta_weight_output[len_weight_output_CNN];double delta_bias_output[len_bias_output_CNN];std::vector<wi_connections> out2wi_S2; // out_id -> [(weight_id, in_id)]std::vector<int> out2bias_S2;std::vector<wi_connections> out2wi_S4;std::vector<int> out2bias_S4;std::vector<wo_connections> in2wo_C3; // in_id -> [(weight_id, out_id)]std::vector<io_connections> weight2io_C3; // weight_id -> [(in_id, out_id)]std::vector<std::vector<int> > bias2out_C3;std::vector<wo_connections> in2wo_C1;std::vector<io_connections> weight2io_C1;std::vector<std::vector<int> > bias2out_C1;
};}#endif //_CNN_HPP_

CNN.cpp：

#include <CNN.hpp>
#include <assert.h>
#include <time.h>
#include <iostream>
#include <fstream>
#include <numeric>
#include <windows.h>
#include <random>
#include <algorithm>
#include <string>namespace ANN {CNN::CNN()
{data_input_train = NULL;data_output_train = NULL;data_input_test = NULL;data_output_test = NULL;data_single_image = NULL;data_single_label = NULL;E_weight_C5 = NULL;E_bias_C5 = NULL;E_weight_output = NULL;E_bias_output = NULL;
}CNN::~CNN()
{release();
}void CNN::release()
{if (data_input_train) {delete[] data_input_train;data_input_train = NULL;}if (data_output_train) {delete[] data_output_train;data_output_train = NULL;}if (data_input_test) {delete[] data_input_test;data_input_test = NULL;}if (data_output_test) {delete[] data_output_test;data_output_test = NULL;}if (E_weight_C5) {delete[] E_weight_C5;E_weight_C5 = NULL;}if (E_bias_C5) {delete[] E_bias_C5;E_bias_C5 = NULL;}if (E_weight_output) {delete[] E_weight_output;E_weight_output = NULL;}if (E_bias_output) {delete[] E_bias_output;E_bias_output = NULL;}
}// connection table [Y.Lecun, 1998 Table.1]
#define O true
#define X false
static const bool tbl[6][16] = {O, X, X, X, O, O, O, X, X, O, O, O, O, X, O, O,O, O, X, X, X, O, O, O, X, X, O, O, O, O, X, O,O, O, O, X, X, X, O, O, O, X, X, O, X, O, O, O,X, O, O, O, X, X, O, O, O, O, X, X, O, X, O, O,X, X, O, O, O, X, X, O, O, O, O, X, O, O, X, O,X, X, X, O, O, O, X, X, O, O, O, O, X, O, O, O
};
#undef O
#undef Xvoid CNN::init_variable(double* val, double c, int len)
{for (int i = 0; i < len; i++) {val[i] = c;}
}void CNN::init()
{int len1 = width_image_input_CNN * height_image_input_CNN * num_patterns_train_CNN;data_input_train = new double[len1];init_variable(data_input_train, -1.0, len1);int len2 = num_map_output_CNN * num_patterns_train_CNN;data_output_train = new double[len2];init_variable(data_output_train, -0.8, len2);int len3 = width_image_input_CNN * height_image_input_CNN * num_patterns_test_CNN;data_input_test = new double[len3];init_variable(data_input_test, -1.0, len3);int len4 = num_map_output_CNN * num_patterns_test_CNN;data_output_test = new double[len4];init_variable(data_output_test, -0.8, len4);std::fill(E_weight_C1, E_weight_C1 + len_weight_C1_CNN, 0.0);std::fill(E_bias_C1, E_bias_C1 + len_bias_C1_CNN, 0.0);std::fill(E_weight_S2, E_weight_S2 + len_weight_S2_CNN, 0.0);std::fill(E_bias_S2, E_bias_S2 + len_bias_S2_CNN, 0.0);std::fill(E_weight_C3, E_weight_C3 + len_weight_C3_CNN, 0.0);std::fill(E_bias_C3, E_bias_C3 + len_bias_C3_CNN, 0.0);std::fill(E_weight_S4, E_weight_S4 + len_weight_S4_CNN, 0.0);std::fill(E_bias_S4, E_bias_S4 + len_bias_S4_CNN, 0.0);E_weight_C5 = new double[len_weight_C5_CNN];std::fill(E_weight_C5, E_weight_C5 + len_weight_C5_CNN, 0.0);E_bias_C5 = new double[len_bias_C5_CNN];std::fill(E_bias_C5, E_bias_C5 + len_bias_C5_CNN, 0.0);E_weight_output = new double[len_weight_output_CNN];std::fill(E_weight_output, E_weight_output + len_weight_output_CNN, 0.0);E_bias_output = new double[len_bias_output_CNN];std::fill(E_bias_output, E_bias_output + len_bias_output_CNN, 0.0);initWeightThreshold();getSrcData();
}double CNN::uniform_rand(double min, double max)
{static std::mt19937 gen(1);std::uniform_real_distribution<double> dst(min, max);return dst(gen);
}bool CNN::uniform_rand(double* src, int len, double min, double max)
{for (int i = 0; i < len; i++) {src[i] = uniform_rand(min, max);}return true;
}bool CNN::initWeightThreshold()
{srand(time(0) + rand());const double scale = 6.0;double min_ = -std::sqrt(scale / (25.0 + 150.0));double max_ = std::sqrt(scale / (25.0 + 150.0));uniform_rand(weight_C1, len_weight_C1_CNN, min_, max_);for (int i = 0; i < len_bias_C1_CNN; i++) {bias_C1[i] = 0.0;}min_ = -std::sqrt(scale / (4.0 + 1.0));max_ = std::sqrt(scale / (4.0 + 1.0));uniform_rand(weight_S2, len_weight_S2_CNN, min_, max_);for (int i = 0; i < len_bias_S2_CNN; i++) {bias_S2[i] = 0.0;}min_ = -std::sqrt(scale / (150.0 + 400.0));max_ = std::sqrt(scale / (150.0 + 400.0));uniform_rand(weight_C3, len_weight_C3_CNN, min_, max_);for (int i = 0; i < len_bias_C3_CNN; i++) {bias_C3[i] = 0.0;}min_ = -std::sqrt(scale / (4.0 + 1.0));max_ = std::sqrt(scale / (4.0 + 1.0));uniform_rand(weight_S4, len_weight_S4_CNN, min_, max_);for (int i = 0; i < len_bias_S4_CNN; i++) {bias_S4[i] = 0.0;}min_ = -std::sqrt(scale / (400.0 + 3000.0));max_ = std::sqrt(scale / (400.0 + 3000.0));uniform_rand(weight_C5, len_weight_C5_CNN, min_, max_);for (int i = 0; i < len_bias_C5_CNN; i++) {bias_C5[i] = 0.0;}min_ = -std::sqrt(scale / (120.0 + 10.0));max_ = std::sqrt(scale / (120.0 + 10.0));uniform_rand(weight_output, len_weight_output_CNN, min_, max_);for (int i = 0; i < len_bias_output_CNN; i++) {bias_output[i] = 0.0;}return true;
}static int reverseInt(int i)
{unsigned char ch1, ch2, ch3, ch4;ch1 = i & 255;ch2 = (i >> 8) & 255;ch3 = (i >> 16) & 255;ch4 = (i >> 24) & 255;return((int)ch1 << 24) + ((int)ch2 << 16) + ((int)ch3 << 8) + ch4;
}static void readMnistImages(std::string filename, double* data_dst, int num_image)
{const int width_src_image = 28;const int height_src_image = 28;const int x_padding = 2;const int y_padding = 2;const double scale_min = -1;const double scale_max = 1;std::ifstream file(filename, std::ios::binary);assert(file.is_open());int magic_number = 0;int number_of_images = 0;int n_rows = 0;int n_cols = 0;file.read((char*)&magic_number, sizeof(magic_number));magic_number = reverseInt(magic_number);file.read((char*)&number_of_images, sizeof(number_of_images));number_of_images = reverseInt(number_of_images);assert(number_of_images == num_image);file.read((char*)&n_rows, sizeof(n_rows));n_rows = reverseInt(n_rows);file.read((char*)&n_cols, sizeof(n_cols));n_cols = reverseInt(n_cols);assert(n_rows == height_src_image && n_cols == width_src_image);int size_single_image = width_image_input_CNN * height_image_input_CNN;for (int i = 0; i < number_of_images; ++i) {int addr = size_single_image * i;for (int r = 0; r < n_rows; ++r) {for (int c = 0; c < n_cols; ++c) {unsigned char temp = 0;file.read((char*)&temp, sizeof(temp));data_dst[addr + width_image_input_CNN * (r + y_padding) + c + x_padding] = (temp / 255.0) * (scale_max - scale_min) + scale_min;}}}
}static void readMnistLabels(std::string filename, double* data_dst, int num_image)
{const double scale_max = 0.8;std::ifstream file(filename, std::ios::binary);assert(file.is_open());int magic_number = 0;int number_of_images = 0;file.read((char*)&magic_number, sizeof(magic_number));magic_number = reverseInt(magic_number);file.read((char*)&number_of_images, sizeof(number_of_images));number_of_images = reverseInt(number_of_images);assert(number_of_images == num_image);for (int i = 0; i < number_of_images; ++i) {unsigned char temp = 0;file.read((char*)&temp, sizeof(temp));data_dst[i * num_map_output_CNN + temp] = scale_max;}
}bool CNN::getSrcData()
{assert(data_input_train && data_output_train && data_input_test && data_output_test);std::string filename_train_images = "E:/GitCode/NN_Test/data/train-images.idx3-ubyte";std::string filename_train_labels = "E:/GitCode/NN_Test/data/train-labels.idx1-ubyte";readMnistImages(filename_train_images, data_input_train, num_patterns_train_CNN);readMnistLabels(filename_train_labels, data_output_train, num_patterns_train_CNN);std::string filename_test_images = "E:/GitCode/NN_Test/data/t10k-images.idx3-ubyte";std::string filename_test_labels = "E:/GitCode/NN_Test/data/t10k-labels.idx1-ubyte";readMnistImages(filename_test_images, data_input_test, num_patterns_test_CNN);readMnistLabels(filename_test_labels, data_output_test, num_patterns_test_CNN);return true;
}bool CNN::train()
{out2wi_S2.clear();out2bias_S2.clear();out2wi_S4.clear();out2bias_S4.clear();in2wo_C3.clear();weight2io_C3.clear();bias2out_C3.clear();in2wo_C1.clear();weight2io_C1.clear();bias2out_C1.clear();calc_out2wi(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN, out2wi_S2);calc_out2bias(width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN, out2bias_S2);calc_out2wi(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN, out2wi_S4);calc_out2bias(width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN, out2bias_S4);calc_in2wo(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_C3_CNN, num_map_S4_CNN, in2wo_C3);calc_weight2io(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_C3_CNN, num_map_S4_CNN, weight2io_C3);calc_bias2out(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_C3_CNN, num_map_S4_CNN, bias2out_C3);calc_in2wo(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_C1_CNN, num_map_C3_CNN, in2wo_C1);calc_weight2io(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_C1_CNN, num_map_C3_CNN, weight2io_C1);calc_bias2out(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_C1_CNN, num_map_C3_CNN, bias2out_C1);int iter = 0;for (iter = 0; iter < num_epochs_CNN; iter++) {std::cout << "epoch: " << iter + 1;for (int i = 0; i < num_patterns_train_CNN; i++) {data_single_image = data_input_train + i * num_neuron_input_CNN;data_single_label = data_output_train + i * num_neuron_output_CNN;Forward_C1();Forward_S2();Forward_C3();Forward_S4();Forward_C5();Forward_output();Backward_output();Backward_C5();Backward_S4();Backward_C3();Backward_S2();Backward_C1();Backward_input();UpdateWeights();}double accuracyRate = test();std::cout << ",    accuray rate: " << accuracyRate << std::endl;if (accuracyRate > accuracy_rate_CNN) {saveModelFile("E:/GitCode/NN_Test/data/cnn.model");std::cout << "generate cnn model" << std::endl;break;}}if (iter == num_epochs_CNN) {saveModelFile("E:/GitCode/NN_Test/data/cnn.model");std::cout << "generate cnn model" << std::endl;}return true;
}double CNN::activation_function_tanh(double x)
{double ep = std::exp(x);double em = std::exp(-x);return (ep - em) / (ep + em);
}double CNN::activation_function_tanh_derivative(double x)
{return (1.0 - x * x);
}double CNN::activation_function_identity(double x)
{return x;
}double CNN::activation_function_identity_derivative(double x)
{return 1;
}double CNN::loss_function_mse(double y, double t)
{return (y - t) * (y - t) / 2;
}double CNN::loss_function_mse_derivative(double y, double t)
{return (y - t);
}void CNN::loss_function_gradient(const double* y, const double* t, double* dst, int len)
{for (int i = 0; i < len; i++) {dst[i] = loss_function_mse_derivative(y[i], t[i]);}
}double CNN::dot_product(const double* s1, const double* s2, int len)
{double result = 0.0;for (int i = 0; i < len; i++) {result += s1[i] * s2[i];}return result;
}bool CNN::muladd(const double* src, double c, int len, double* dst)
{for (int i = 0; i < len; i++) {dst[i] += (src[i] * c);}return true;
}int CNN::get_index(int x, int y, int channel, int width, int height, int depth)
{assert(x >= 0 && x < width);assert(y >= 0 && y < height);assert(channel >= 0 && channel < depth);return (height * channel + y) * width + x;
}void CNN::calc_out2wi(int width_in, int height_in, int width_out, int height_out, int depth_out, std::vector<wi_connections>& out2wi)
{for (int i = 0; i < depth_out; i++) {int block = width_in * height_in * i;for (int y = 0; y < height_out; y++) {for (int x = 0; x < width_out; x++) {int rows = y * width_kernel_pooling_CNN;int cols = x * height_kernel_pooling_CNN;wi_connections wi_connections_;std::pair<int, int> pair_;for (int m = 0; m < width_kernel_pooling_CNN; m++) {for (int n = 0; n < height_kernel_pooling_CNN; n++) {pair_.first = i;pair_.second = (rows + m) * width_in + cols + n + block;wi_connections_.push_back(pair_);}}out2wi.push_back(wi_connections_);}}}
}void CNN::calc_out2bias(int width, int height, int depth, std::vector<int>& out2bias)
{for (int i = 0; i < depth; i++) {for (int y = 0; y < height; y++) {for (int x = 0; x < width; x++) {out2bias.push_back(i);}}}
}void CNN::calc_in2wo(int width_in, int height_in, int width_out, int height_out, int depth_in, int depth_out, std::vector<wo_connections>& in2wo)
{int len = width_in * height_in * depth_in;in2wo.resize(len);for (int c = 0; c < depth_in; c++) {for (int y = 0; y < height_in; y += height_kernel_pooling_CNN) {for (int x = 0; x < width_in; x += width_kernel_pooling_CNN) {int dymax = min(size_pooling_CNN, height_in - y);int dxmax = min(size_pooling_CNN, width_in - x);int dstx = x / width_kernel_pooling_CNN;int dsty = y / height_kernel_pooling_CNN;for (int dy = 0; dy < dymax; dy++) {for (int dx = 0; dx < dxmax; dx++) {int index_in = get_index(x + dx, y + dy, c, width_in, height_in, depth_in);int index_out = get_index(dstx, dsty, c, width_out, height_out, depth_out);wo_connections wo_connections_;std::pair<int, int> pair_;pair_.first = c;pair_.second = index_out;wo_connections_.push_back(pair_);in2wo[index_in] = wo_connections_;}}}}}
}void CNN::calc_weight2io(int width_in, int height_in, int width_out, int height_out, int depth_in, int depth_out, std::vector<io_connections>& weight2io)
{int len = depth_in;weight2io.resize(len);for (int c = 0; c < depth_in; c++) {for (int y = 0; y < height_in; y += height_kernel_pooling_CNN) {for (int x = 0; x < width_in; x += width_kernel_pooling_CNN) {int dymax = min(size_pooling_CNN, height_in - y);int dxmax = min(size_pooling_CNN, width_in - x);int dstx = x / width_kernel_pooling_CNN;int dsty = y / height_kernel_pooling_CNN;for (int dy = 0; dy < dymax; dy++) {for (int dx = 0; dx < dxmax; dx++) {int index_in = get_index(x + dx, y + dy, c, width_in, height_in, depth_in);int index_out = get_index(dstx, dsty, c, width_out, height_out, depth_out);std::pair<int, int> pair_;pair_.first = index_in;pair_.second = index_out;weight2io[c].push_back(pair_);}}}}}
}void CNN::calc_bias2out(int width_in, int height_in, int width_out, int height_out, int depth_in, int depth_out, std::vector<std::vector<int> >& bias2out)
{int len = depth_in;bias2out.resize(len);for (int c = 0; c < depth_in; c++) {for (int y = 0; y < height_out; y++) {for (int x = 0; x < width_out; x++) {int index_out = get_index(x, y, c, width_out, height_out, depth_out);bias2out[c].push_back(index_out);}}}
}bool CNN::Forward_C1()
{init_variable(neuron_C1, 0.0, num_neuron_C1_CNN);for (int o = 0; o < num_map_C1_CNN; o++) {for (int inc = 0; inc < num_map_input_CNN; inc++) {int addr1 = get_index(0, 0, num_map_input_CNN * o + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C1_CNN * num_map_input_CNN);int addr2 = get_index(0, 0, inc, width_image_input_CNN, height_image_input_CNN, num_map_input_CNN);int addr3 = get_index(0, 0, o, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);const double* pw = &weight_C1[0] + addr1;const double* pi = data_single_image + addr2;double* pa = &neuron_C1[0] + addr3;for (int y = 0; y < height_image_C1_CNN; y++) {for (int x = 0; x < width_image_C1_CNN; x++) {const double* ppw = pw;const double* ppi = pi + y * width_image_input_CNN + x;double sum = 0.0;for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {sum += *ppw++ * ppi[wy * width_image_input_CNN + wx];}}pa[y * width_image_C1_CNN + x] += sum;}}}int addr3 = get_index(0, 0, o, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);double* pa = &neuron_C1[0] + addr3;double b = bias_C1[o];for (int y = 0; y < height_image_C1_CNN; y++) {for (int x = 0; x < width_image_C1_CNN; x++) {pa[y * width_image_C1_CNN + x] += b;}}}for (int i = 0; i < num_neuron_C1_CNN; i++) {neuron_C1[i] = activation_function_tanh(neuron_C1[i]);}return true;
}bool CNN::Forward_S2()
{init_variable(neuron_S2, 0.0, num_neuron_S2_CNN);double scale_factor = 1.0 / (width_kernel_pooling_CNN * height_kernel_pooling_CNN);assert(out2wi_S2.size() == num_neuron_S2_CNN);assert(out2bias_S2.size() == num_neuron_S2_CNN);for (int i = 0; i < num_neuron_S2_CNN; i++) {const wi_connections& connections = out2wi_S2[i];neuron_S2[i] = 0;for (int index = 0; index < connections.size(); index++) {neuron_S2[i] += weight_S2[connections[index].first] * neuron_C1[connections[index].second];}neuron_S2[i] *= scale_factor;neuron_S2[i] += bias_S2[out2bias_S2[i]];}for (int i = 0; i < num_neuron_S2_CNN; i++) {neuron_S2[i] = activation_function_tanh(neuron_S2[i]);}return true;
}bool CNN::Forward_C3()
{init_variable(neuron_C3, 0.0, num_neuron_C3_CNN);for (int o = 0; o < num_map_C3_CNN; o++) {for (int inc = 0; inc < num_map_S2_CNN; inc++) {if (!tbl[inc][o]) continue;int addr1 = get_index(0, 0, num_map_S2_CNN * o + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C3_CNN * num_map_S2_CNN);int addr2 = get_index(0, 0, inc, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN);int addr3 = get_index(0, 0, o, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);const double* pw = &weight_C3[0] + addr1;const double* pi = &neuron_S2[0] + addr2;double* pa = &neuron_C3[0] + addr3;for (int y = 0; y < height_image_C3_CNN; y++) {for (int x = 0; x < width_image_C3_CNN; x++) {const double* ppw = pw;const double* ppi = pi + y * width_image_S2_CNN + x;double sum = 0.0;for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {sum += *ppw++ * ppi[wy * width_image_S2_CNN + wx];}}pa[y * width_image_C3_CNN + x] += sum;}}}int addr3 = get_index(0, 0, o, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);double* pa = &neuron_C3[0] + addr3;double b = bias_C3[o];for (int y = 0; y < height_image_C3_CNN; y++) {for (int x = 0; x < width_image_C3_CNN; x++) {pa[y * width_image_C3_CNN + x] += b;}}}for (int i = 0; i < num_neuron_C3_CNN; i++) {neuron_C3[i] = activation_function_tanh(neuron_C3[i]);}return true;
}bool CNN::Forward_S4()
{double scale_factor = 1.0 / (width_kernel_pooling_CNN * height_kernel_pooling_CNN);init_variable(neuron_S4, 0.0, num_neuron_S4_CNN);assert(out2wi_S4.size() == num_neuron_S4_CNN);assert(out2bias_S4.size() == num_neuron_S4_CNN);for (int i = 0; i < num_neuron_S4_CNN; i++) {const wi_connections& connections = out2wi_S4[i];neuron_S4[i] = 0.0;for (int index = 0; index < connections.size(); index++) {neuron_S4[i] += weight_S4[connections[index].first] * neuron_C3[connections[index].second];}neuron_S4[i] *= scale_factor;neuron_S4[i] += bias_S4[out2bias_S4[i]];}for (int i = 0; i < num_neuron_S4_CNN; i++) {neuron_S4[i] = activation_function_tanh(neuron_S4[i]);}return true;
}bool CNN::Forward_C5()
{init_variable(neuron_C5, 0.0, num_neuron_C5_CNN);for (int o = 0; o < num_map_C5_CNN; o++) {for (int inc = 0; inc < num_map_S4_CNN; inc++) {int addr1 = get_index(0, 0, num_map_S4_CNN * o + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C5_CNN * num_map_S4_CNN);int addr2 = get_index(0, 0, inc, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN);int addr3 = get_index(0, 0, o, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);const double *pw = &weight_C5[0] + addr1;const double *pi = &neuron_S4[0] + addr2;double *pa = &neuron_C5[0] + addr3;for (int y = 0; y < height_image_C5_CNN; y++) {for (int x = 0; x < width_image_C5_CNN; x++) {const double *ppw = pw;const double *ppi = pi + y * width_image_S4_CNN + x;double sum = 0.0;for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {sum += *ppw++ * ppi[wy * width_image_S4_CNN + wx];}}pa[y * width_image_C5_CNN + x] += sum;}}}int addr3 = get_index(0, 0, o, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);double *pa = &neuron_C5[0] + addr3;double b = bias_C5[o];for (int y = 0; y < height_image_C5_CNN; y++) {for (int x = 0; x < width_image_C5_CNN; x++) {pa[y * width_image_C5_CNN + x] += b;}}}for (int i = 0; i < num_neuron_C5_CNN; i++) {neuron_C5[i] = activation_function_tanh(neuron_C5[i]);}return true;
}bool CNN::Forward_output()
{init_variable(neuron_output, 0.0, num_neuron_output_CNN);for (int i = 0; i < num_neuron_output_CNN; i++) {neuron_output[i] = 0.0;for (int c = 0; c < num_neuron_C5_CNN; c++) {neuron_output[i] += weight_output[c * num_neuron_output_CNN + i] * neuron_C5[c];}neuron_output[i] += bias_output[i];}for (int i = 0; i < num_neuron_output_CNN; i++) {neuron_output[i] = activation_function_tanh(neuron_output[i]);}return true;
}bool CNN::Backward_output()
{init_variable(delta_neuron_output, 0.0, num_neuron_output_CNN);double dE_dy[num_neuron_output_CNN];init_variable(dE_dy, 0.0, num_neuron_output_CNN);loss_function_gradient(neuron_output, data_single_label, dE_dy, num_neuron_output_CNN); // 损失函数: mean squared error(均方差)// delta = dE/da = (dE/dy) * (dy/da)for (int i = 0; i < num_neuron_output_CNN; i++) {double dy_da[num_neuron_output_CNN];init_variable(dy_da, 0.0, num_neuron_output_CNN);dy_da[i] = activation_function_tanh_derivative(neuron_output[i]);delta_neuron_output[i] = dot_product(dE_dy, dy_da, num_neuron_output_CNN);}return true;
}bool CNN::Backward_C5()
{init_variable(delta_neuron_C5, 0.0, num_neuron_C5_CNN);init_variable(delta_weight_output, 0.0, len_weight_output_CNN);init_variable(delta_bias_output, 0.0, len_bias_output_CNN);for (int c = 0; c < num_neuron_C5_CNN; c++) {// propagate delta to previous layer// prev_delta[c] += current_delta[r] * W_[c * out_size_ + r]delta_neuron_C5[c] = dot_product(&delta_neuron_output[0], &weight_output[c * num_neuron_output_CNN], num_neuron_output_CNN);delta_neuron_C5[c] *= activation_function_tanh_derivative(neuron_C5[c]);}// accumulate weight-step using delta// dW[c * out_size + i] += current_delta[i] * prev_out[c]for (int c = 0; c < num_neuron_C5_CNN; c++) {muladd(&delta_neuron_output[0], neuron_C5[c], num_neuron_output_CNN, &delta_weight_output[0] + c * num_neuron_output_CNN);}for (int i = 0; i < len_bias_output_CNN; i++) {delta_bias_output[i] += delta_neuron_output[i];}return true;
}bool CNN::Backward_S4()
{init_variable(delta_neuron_S4, 0.0, num_neuron_S4_CNN);init_variable(delta_weight_C5, 0.0, len_weight_C5_CNN);init_variable(delta_bias_C5, 0.0, len_bias_C5_CNN);// propagate delta to previous layerfor (int inc = 0; inc < num_map_S4_CNN; inc++) {for (int outc = 0; outc < num_map_C5_CNN; outc++) {int addr1 = get_index(0, 0, num_map_S4_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_S4_CNN * num_map_C5_CNN);int addr2 = get_index(0, 0, outc, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);int addr3 = get_index(0, 0, inc, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN);const double* pw = &weight_C5[0] + addr1;const double* pdelta_src = &delta_neuron_C5[0] + addr2;double* pdelta_dst = &delta_neuron_S4[0] + addr3;for (int y = 0; y < height_image_C5_CNN; y++) {for (int x = 0; x < width_image_C5_CNN; x++) {const double* ppw = pw;const double ppdelta_src = pdelta_src[y * width_image_C5_CNN + x];double* ppdelta_dst = pdelta_dst + y * width_image_S4_CNN + x;for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {ppdelta_dst[wy * width_image_S4_CNN + wx] += *ppw++ * ppdelta_src;}}}}}}for (int i = 0; i < num_neuron_S4_CNN; i++) {delta_neuron_S4[i] *= activation_function_tanh_derivative(neuron_S4[i]);}// accumulate dwfor (int inc = 0; inc < num_map_S4_CNN; inc++) {for (int outc = 0; outc < num_map_C5_CNN; outc++) {for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {int addr1 = get_index(wx, wy, inc, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN);int addr2 = get_index(0, 0, outc, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);int addr3 = get_index(wx, wy, num_map_S4_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_S4_CNN * num_map_C5_CNN);double dst = 0.0;const double* prevo = &neuron_S4[0] + addr1;const double* delta = &delta_neuron_C5[0] + addr2;for (int y = 0; y < height_image_C5_CNN; y++) {dst += dot_product(prevo + y * width_image_S4_CNN, delta + y * width_image_C5_CNN, width_image_C5_CNN);}delta_weight_C5[addr3] += dst;}}}}// accumulate dbfor (int outc = 0; outc < num_map_C5_CNN; outc++) {int addr2 = get_index(0, 0, outc, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);const double* delta = &delta_neuron_C5[0] + addr2;for (int y = 0; y < height_image_C5_CNN; y++) {for (int x = 0; x < width_image_C5_CNN; x++) {delta_bias_C5[outc] += delta[y * width_image_C5_CNN + x];}}}return true;
}bool CNN::Backward_C3()
{init_variable(delta_neuron_C3, 0.0, num_neuron_C3_CNN);init_variable(delta_weight_S4, 0.0, len_weight_S4_CNN);init_variable(delta_bias_S4, 0.0, len_bias_S4_CNN);double scale_factor = 1.0 / (width_kernel_pooling_CNN * height_kernel_pooling_CNN);assert(in2wo_C3.size() == num_neuron_C3_CNN);assert(weight2io_C3.size() == len_weight_S4_CNN);assert(bias2out_C3.size() == len_bias_S4_CNN);for (int i = 0; i < num_neuron_C3_CNN; i++) {const wo_connections& connections = in2wo_C3[i];double delta = 0.0;for (int j = 0; j < connections.size(); j++) {delta += weight_S4[connections[j].first] * delta_neuron_S4[connections[j].second];}delta_neuron_C3[i] = delta * scale_factor * activation_function_tanh_derivative(neuron_C3[i]);}for (int i = 0; i < len_weight_S4_CNN; i++) {const io_connections& connections = weight2io_C3[i];double diff = 0;for (int j = 0; j < connections.size(); j++) {diff += neuron_C3[connections[j].first] * delta_neuron_S4[connections[j].second];}delta_weight_S4[i] += diff * scale_factor;}for (int i = 0; i < len_bias_S4_CNN; i++) {const std::vector<int>& outs = bias2out_C3[i];double diff = 0;for (int o = 0; o < outs.size(); o++) {diff += delta_neuron_S4[outs[o]];}delta_bias_S4[i] += diff;}return true;
}bool CNN::Backward_S2()
{init_variable(delta_neuron_S2, 0.0, num_neuron_S2_CNN);init_variable(delta_weight_C3, 0.0, len_weight_C3_CNN);init_variable(delta_bias_C3, 0.0, len_bias_C3_CNN);// propagate delta to previous layerfor (int inc = 0; inc < num_map_S2_CNN; inc++) {for (int outc = 0; outc < num_map_C3_CNN; outc++) {if (!tbl[inc][outc]) continue;int addr1 = get_index(0, 0, num_map_S2_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_S2_CNN * num_map_C3_CNN);int addr2 = get_index(0, 0, outc, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);int addr3 = get_index(0, 0, inc, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN);const double *pw = &weight_C3[0] + addr1;const double *pdelta_src = &delta_neuron_C3[0] + addr2;;double* pdelta_dst = &delta_neuron_S2[0] + addr3;for (int y = 0; y < height_image_C3_CNN; y++) {for (int x = 0; x < width_image_C3_CNN; x++) {const double* ppw = pw;const double ppdelta_src = pdelta_src[y * width_image_C3_CNN + x];double* ppdelta_dst = pdelta_dst + y * width_image_S2_CNN + x;for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {ppdelta_dst[wy * width_image_S2_CNN + wx] += *ppw++ * ppdelta_src;}}}}}}for (int i = 0; i < num_neuron_S2_CNN; i++) {delta_neuron_S2[i] *= activation_function_tanh_derivative(neuron_S2[i]);}// accumulate dwfor (int inc = 0; inc < num_map_S2_CNN; inc++) {for (int outc = 0; outc < num_map_C3_CNN; outc++) {if (!tbl[inc][outc]) continue;for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {int addr1 = get_index(wx, wy, inc, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN);int addr2 = get_index(0, 0, outc, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);int addr3 = get_index(wx, wy, num_map_S2_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_S2_CNN * num_map_C3_CNN);double dst = 0.0;const double* prevo = &neuron_S2[0] + addr1;const double* delta = &delta_neuron_C3[0] + addr2;for (int y = 0; y < height_image_C3_CNN; y++) {dst += dot_product(prevo + y * width_image_S2_CNN, delta + y * width_image_C3_CNN, width_image_C3_CNN);}delta_weight_C3[addr3] += dst;}}}}// accumulate dbfor (int outc = 0; outc < len_bias_C3_CNN; outc++) {int addr1 = get_index(0, 0, outc, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);const double* delta = &delta_neuron_C3[0] + addr1;for (int y = 0; y < height_image_C3_CNN; y++) {for (int x = 0; x < width_image_C3_CNN; x++) {delta_bias_C3[outc] += delta[y * width_image_C3_CNN + x];}}}return true;
}bool CNN::Backward_C1()
{init_variable(delta_neuron_C1, 0.0, num_neuron_C1_CNN);init_variable(delta_weight_S2, 0.0, len_weight_S2_CNN);init_variable(delta_bias_S2, 0.0, len_bias_S2_CNN);double scale_factor = 1.0 / (width_kernel_pooling_CNN * height_kernel_pooling_CNN);assert(in2wo_C1.size() == num_neuron_C1_CNN);assert(weight2io_C1.size() == len_weight_S2_CNN);assert(bias2out_C1.size() == len_bias_S2_CNN);for (int i = 0; i < num_neuron_C1_CNN; i++) {const wo_connections& connections = in2wo_C1[i];double delta = 0.0;for (int j = 0; j < connections.size(); j++) {delta += weight_S2[connections[j].first] * delta_neuron_S2[connections[j].second];}delta_neuron_C1[i] = delta * scale_factor * activation_function_tanh_derivative(neuron_C1[i]);}for (int i = 0; i < len_weight_S2_CNN; i++) {const io_connections& connections = weight2io_C1[i];double diff = 0.0;for (int j = 0; j < connections.size(); j++) {diff += neuron_C1[connections[j].first] * delta_neuron_S2[connections[j].second];}delta_weight_S2[i] += diff * scale_factor;}for (int i = 0; i < len_bias_S2_CNN; i++) {const std::vector<int>& outs = bias2out_C1[i];double diff = 0;for (int o = 0; o < outs.size(); o++) {diff += delta_neuron_S2[outs[o]];}delta_bias_S2[i] += diff;}return true;
}bool CNN::Backward_input()
{init_variable(delta_neuron_input, 0.0, num_neuron_input_CNN);init_variable(delta_weight_C1, 0.0, len_weight_C1_CNN);init_variable(delta_bias_C1, 0.0, len_bias_C1_CNN);// propagate delta to previous layerfor (int inc = 0; inc < num_map_input_CNN; inc++) {for (int outc = 0; outc < num_map_C1_CNN; outc++) {int addr1 = get_index(0, 0, num_map_input_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C1_CNN);int addr2 = get_index(0, 0, outc, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);int addr3 = get_index(0, 0, inc, width_image_input_CNN, height_image_input_CNN, num_map_input_CNN);const double* pw = &weight_C1[0] + addr1;const double* pdelta_src = &delta_neuron_C1[0] + addr2;double* pdelta_dst = &delta_neuron_input[0] + addr3;for (int y = 0; y < height_image_C1_CNN; y++) {for (int x = 0; x < width_image_C1_CNN; x++) {const double* ppw = pw;const double ppdelta_src = pdelta_src[y * width_image_C1_CNN + x];double* ppdelta_dst = pdelta_dst + y * width_image_input_CNN + x;for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {ppdelta_dst[wy * width_image_input_CNN + wx] += *ppw++ * ppdelta_src;}}}}}}for (int i = 0; i < num_neuron_input_CNN; i++) {delta_neuron_input[i] *= activation_function_identity_derivative(data_single_image[i]/*neuron_input[i]*/);}// accumulate dwfor (int inc = 0; inc < num_map_input_CNN; inc++) {for (int outc = 0; outc < num_map_C1_CNN; outc++) {for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {int addr1 = get_index(wx, wy, inc, width_image_input_CNN, height_image_input_CNN, num_map_input_CNN);int addr2 = get_index(0, 0, outc, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);int addr3 = get_index(wx, wy, num_map_input_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C1_CNN);double dst = 0.0;const double* prevo = data_single_image + addr1;//&neuron_input[0]const double* delta = &delta_neuron_C1[0] + addr2;for (int y = 0; y < height_image_C1_CNN; y++) {dst += dot_product(prevo + y * width_image_input_CNN, delta + y * width_image_C1_CNN, width_image_C1_CNN);}delta_weight_C1[addr3] += dst;}}}}// accumulate dbfor (int outc = 0; outc < len_bias_C1_CNN; outc++) {int addr1 = get_index(0, 0, outc, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);const double* delta = &delta_neuron_C1[0] + addr1;for (int y = 0; y < height_image_C1_CNN; y++) {for (int x = 0; x < width_image_C1_CNN; x++) {delta_bias_C1[outc] += delta[y * width_image_C1_CNN + x];}}}return true;
}void CNN::update_weights_bias(const double* delta, double* e_weight, double* weight, int len)
{for (int i = 0; i < len; i++) {e_weight[i] += delta[i] * delta[i];weight[i] -= learning_rate_CNN * delta[i] / (std::sqrt(e_weight[i]) + eps_CNN);}
}bool CNN::UpdateWeights()
{update_weights_bias(delta_weight_C1, E_weight_C1, weight_C1, len_weight_C1_CNN);update_weights_bias(delta_bias_C1, E_bias_C1, bias_C1, len_bias_C1_CNN);update_weights_bias(delta_weight_S2, E_weight_S2, weight_S2, len_weight_S2_CNN);update_weights_bias(delta_bias_S2, E_bias_S2, bias_S2, len_bias_S2_CNN);update_weights_bias(delta_weight_C3, E_weight_C3, weight_C3, len_weight_C3_CNN);update_weights_bias(delta_bias_C3, E_bias_C3, bias_C3, len_bias_C3_CNN);update_weights_bias(delta_weight_S4, E_weight_S4, weight_S4, len_weight_S4_CNN);update_weights_bias(delta_bias_S4, E_bias_S4, bias_S4, len_bias_S4_CNN);update_weights_bias(delta_weight_C5, E_weight_C5, weight_C5, len_weight_C5_CNN);update_weights_bias(delta_bias_C5, E_bias_C5, bias_C5, len_bias_C5_CNN);update_weights_bias(delta_weight_output, E_weight_output, weight_output, len_weight_output_CNN);update_weights_bias(delta_bias_output, E_bias_output, bias_output, len_bias_output_CNN);return true;
}int CNN::predict(const unsigned char* data, int width, int height)
{assert(data && width == width_image_input_CNN && height == height_image_input_CNN);const double scale_min = -1;const double scale_max = 1;double tmp[width_image_input_CNN * height_image_input_CNN];for (int y = 0; y < height; y++) {for (int x = 0; x < width; x++) {tmp[y * width + x] = (data[y * width + x] / 255.0) * (scale_max - scale_min) + scale_min;}}data_single_image = &tmp[0];Forward_C1();Forward_S2();Forward_C3();Forward_S4();Forward_C5();Forward_output();int pos = -1;double max_value = -9999.0;for (int i = 0; i < num_neuron_output_CNN; i++) {if (neuron_output[i] > max_value) {max_value = neuron_output[i];pos = i;}}return pos;
}bool CNN::readModelFile(const char* name)
{FILE* fp = fopen(name, "rb");if (fp == NULL) {return false;}int width_image_input =0;int height_image_input = 0;int width_image_C1 = 0;int height_image_C1 = 0;int width_image_S2 = 0;int height_image_S2 = 0;int width_image_C3 = 0;int height_image_C3 = 0;int width_image_S4 = 0;int height_image_S4 = 0;int width_image_C5 = 0;int height_image_C5 = 0;int width_image_output = 0;int height_image_output = 0;int width_kernel_conv = 0;int height_kernel_conv = 0;int width_kernel_pooling = 0;int height_kernel_pooling = 0;int num_map_input = 0;int num_map_C1 = 0;int num_map_S2 = 0;int num_map_C3 = 0;int num_map_S4 = 0;int num_map_C5 = 0;int num_map_output = 0;int len_weight_C1 = 0;int len_bias_C1 = 0;int len_weight_S2 = 0;int len_bias_S2 = 0;int len_weight_C3 = 0;int len_bias_C3 = 0;int len_weight_S4 = 0;int len_bias_S4 = 0;int len_weight_C5 = 0;int len_bias_C5 = 0;int len_weight_output = 0;int len_bias_output = 0;int num_neuron_input = 0;int num_neuron_C1 = 0;int num_neuron_S2 = 0;int num_neuron_C3 = 0;int num_neuron_S4 = 0;int num_neuron_C5 = 0;int num_neuron_output = 0;fread(&width_image_input, sizeof(int), 1, fp);fread(&height_image_input, sizeof(int), 1, fp);fread(&width_image_C1, sizeof(int), 1, fp);fread(&height_image_C1, sizeof(int), 1, fp);fread(&width_image_S2, sizeof(int), 1, fp);fread(&height_image_S2, sizeof(int), 1, fp);fread(&width_image_C3, sizeof(int), 1, fp);fread(&height_image_C3, sizeof(int), 1, fp);fread(&width_image_S4, sizeof(int), 1, fp);fread(&height_image_S4, sizeof(int), 1, fp);fread(&width_image_C5, sizeof(int), 1, fp);fread(&height_image_C5, sizeof(int), 1, fp);fread(&width_image_output, sizeof(int), 1, fp);fread(&height_image_output, sizeof(int), 1, fp);fread(&width_kernel_conv, sizeof(int), 1, fp);fread(&height_kernel_conv, sizeof(int), 1, fp);fread(&width_kernel_pooling, sizeof(int), 1, fp);fread(&height_kernel_pooling, sizeof(int), 1, fp);fread(&num_map_input, sizeof(int), 1, fp);fread(&num_map_C1, sizeof(int), 1, fp);fread(&num_map_S2, sizeof(int), 1, fp);fread(&num_map_C3, sizeof(int), 1, fp);fread(&num_map_S4, sizeof(int), 1, fp);fread(&num_map_C5, sizeof(int), 1, fp);fread(&num_map_output, sizeof(int), 1, fp);fread(&len_weight_C1, sizeof(int), 1, fp);fread(&len_bias_C1, sizeof(int), 1, fp);fread(&len_weight_S2, sizeof(int), 1, fp);fread(&len_bias_S2, sizeof(int), 1, fp);fread(&len_weight_C3, sizeof(int), 1, fp);fread(&len_bias_C3, sizeof(int), 1, fp);fread(&len_weight_S4, sizeof(int), 1, fp);fread(&len_bias_S4, sizeof(int), 1, fp);fread(&len_weight_C5, sizeof(int), 1, fp);fread(&len_bias_C5, sizeof(int), 1, fp);fread(&len_weight_output, sizeof(int), 1, fp);fread(&len_bias_output, sizeof(int), 1, fp);fread(&num_neuron_input, sizeof(int), 1, fp);fread(&num_neuron_C1, sizeof(int), 1, fp);fread(&num_neuron_S2, sizeof(int), 1, fp);fread(&num_neuron_C3, sizeof(int), 1, fp);fread(&num_neuron_S4, sizeof(int), 1, fp);fread(&num_neuron_C5, sizeof(int), 1, fp);fread(&num_neuron_output, sizeof(int), 1, fp);fread(weight_C1, sizeof(weight_C1), 1, fp);fread(bias_C1, sizeof(bias_C1), 1, fp);fread(weight_S2, sizeof(weight_S2), 1, fp);fread(bias_S2, sizeof(bias_S2), 1, fp);fread(weight_C3, sizeof(weight_C3), 1, fp);fread(bias_C3, sizeof(bias_C3), 1, fp);fread(weight_S4, sizeof(weight_S4), 1, fp);fread(bias_S4, sizeof(bias_S4), 1, fp);fread(weight_C5, sizeof(weight_C5), 1, fp);fread(bias_C5, sizeof(bias_C5), 1, fp);fread(weight_output, sizeof(weight_output), 1, fp);fread(bias_output, sizeof(bias_output), 1, fp);fflush(fp);fclose(fp);out2wi_S2.clear();out2bias_S2.clear();out2wi_S4.clear();out2bias_S4.clear();calc_out2wi(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN, out2wi_S2);calc_out2bias(width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN, out2bias_S2);calc_out2wi(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN, out2wi_S4);calc_out2bias(width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN, out2bias_S4);return true;
}bool CNN::saveModelFile(const char* name)
{FILE* fp = fopen(name, "wb");if (fp == NULL) {return false;}int width_image_input = width_image_input_CNN;int height_image_input = height_image_input_CNN;int width_image_C1 = width_image_C1_CNN;int height_image_C1 = height_image_C1_CNN;int width_image_S2 = width_image_S2_CNN;int height_image_S2 = height_image_S2_CNN;int width_image_C3 = width_image_C3_CNN;int height_image_C3 = height_image_C3_CNN;int width_image_S4 = width_image_S4_CNN;int height_image_S4 = height_image_S4_CNN;int width_image_C5 = width_image_C5_CNN;int height_image_C5 = height_image_C5_CNN;int width_image_output = width_image_output_CNN;int height_image_output = height_image_output_CNN;int width_kernel_conv = width_kernel_conv_CNN;int height_kernel_conv = height_kernel_conv_CNN;int width_kernel_pooling = width_kernel_pooling_CNN;int height_kernel_pooling = height_kernel_pooling_CNN;int num_map_input = num_map_input_CNN;int num_map_C1 = num_map_C1_CNN;int num_map_S2 = num_map_S2_CNN;int num_map_C3 = num_map_C3_CNN;int num_map_S4 = num_map_S4_CNN;int num_map_C5 = num_map_C5_CNN;int num_map_output = num_map_output_CNN;int len_weight_C1 = len_weight_C1_CNN;int len_bias_C1 = len_bias_C1_CNN;int len_weight_S2 = len_weight_S2_CNN;int len_bias_S2 = len_bias_S2_CNN;int len_weight_C3 = len_weight_C3_CNN;int len_bias_C3 = len_bias_C3_CNN;int len_weight_S4 = len_weight_S4_CNN;int len_bias_S4 = len_bias_S4_CNN;int len_weight_C5 = len_weight_C5_CNN;int len_bias_C5 = len_bias_C5_CNN;int len_weight_output = len_weight_output_CNN;int len_bias_output = len_bias_output_CNN;int num_neuron_input = num_neuron_input_CNN;int num_neuron_C1 = num_neuron_C1_CNN;int num_neuron_S2 = num_neuron_S2_CNN;int num_neuron_C3 = num_neuron_C3_CNN;int num_neuron_S4 = num_neuron_S4_CNN;int num_neuron_C5 = num_neuron_C5_CNN;int num_neuron_output = num_neuron_output_CNN;fwrite(&width_image_input, sizeof(int), 1, fp);fwrite(&height_image_input, sizeof(int), 1, fp);fwrite(&width_image_C1, sizeof(int), 1, fp);fwrite(&height_image_C1, sizeof(int), 1, fp);fwrite(&width_image_S2, sizeof(int), 1, fp);fwrite(&height_image_S2, sizeof(int), 1, fp);fwrite(&width_image_C3, sizeof(int), 1, fp);fwrite(&height_image_C3, sizeof(int), 1, fp);fwrite(&width_image_S4, sizeof(int), 1, fp);fwrite(&height_image_S4, sizeof(int), 1, fp);fwrite(&width_image_C5, sizeof(int), 1, fp);fwrite(&height_image_C5, sizeof(int), 1, fp);fwrite(&width_image_output, sizeof(int), 1, fp);fwrite(&height_image_output, sizeof(int), 1, fp);fwrite(&width_kernel_conv, sizeof(int), 1, fp);fwrite(&height_kernel_conv, sizeof(int), 1, fp);fwrite(&width_kernel_pooling, sizeof(int), 1, fp);fwrite(&height_kernel_pooling, sizeof(int), 1, fp);fwrite(&num_map_input, sizeof(int), 1, fp);fwrite(&num_map_C1, sizeof(int), 1, fp);fwrite(&num_map_S2, sizeof(int), 1, fp);fwrite(&num_map_C3, sizeof(int), 1, fp);fwrite(&num_map_S4, sizeof(int), 1, fp);fwrite(&num_map_C5, sizeof(int), 1, fp);fwrite(&num_map_output, sizeof(int), 1, fp);fwrite(&len_weight_C1, sizeof(int), 1, fp);fwrite(&len_bias_C1, sizeof(int), 1, fp);fwrite(&len_weight_S2, sizeof(int), 1, fp);fwrite(&len_bias_S2, sizeof(int), 1, fp);fwrite(&len_weight_C3, sizeof(int), 1, fp);fwrite(&len_bias_C3, sizeof(int), 1, fp);fwrite(&len_weight_S4, sizeof(int), 1, fp);fwrite(&len_bias_S4, sizeof(int), 1, fp);fwrite(&len_weight_C5, sizeof(int), 1, fp);fwrite(&len_bias_C5, sizeof(int), 1, fp);fwrite(&len_weight_output, sizeof(int), 1, fp);fwrite(&len_bias_output, sizeof(int), 1, fp);fwrite(&num_neuron_input, sizeof(int), 1, fp);fwrite(&num_neuron_C1, sizeof(int), 1, fp);fwrite(&num_neuron_S2, sizeof(int), 1, fp);fwrite(&num_neuron_C3, sizeof(int), 1, fp);fwrite(&num_neuron_S4, sizeof(int), 1, fp);fwrite(&num_neuron_C5, sizeof(int), 1, fp);fwrite(&num_neuron_output, sizeof(int), 1, fp);fwrite(weight_C1, sizeof(weight_C1), 1, fp);fwrite(bias_C1, sizeof(bias_C1), 1, fp);fwrite(weight_S2, sizeof(weight_S2), 1, fp);fwrite(bias_S2, sizeof(bias_S2), 1, fp);fwrite(weight_C3, sizeof(weight_C3), 1, fp);fwrite(bias_C3, sizeof(bias_C3), 1, fp);fwrite(weight_S4, sizeof(weight_S4), 1, fp);fwrite(bias_S4, sizeof(bias_S4), 1, fp);fwrite(weight_C5, sizeof(weight_C5), 1, fp);fwrite(bias_C5, sizeof(bias_C5), 1, fp);fwrite(weight_output, sizeof(weight_output), 1, fp);fwrite(bias_output, sizeof(bias_output), 1, fp);fflush(fp);fclose(fp);return true;
}double CNN::test()
{int count_accuracy = 0;for (int num = 0; num < num_patterns_test_CNN; num++) {data_single_image = data_input_test + num * num_neuron_input_CNN;data_single_label = data_output_test + num * num_neuron_output_CNN;Forward_C1();Forward_S2();Forward_C3();Forward_S4();Forward_C5();Forward_output();int pos_t = -1;int pos_y = -2;double max_value_t = -9999.0;double max_value_y = -9999.0;for (int i = 0; i < num_neuron_output_CNN; i++) {if (neuron_output[i] > max_value_y) {max_value_y = neuron_output[i];pos_y = i;}if (data_single_label[i] > max_value_t) {max_value_t = data_single_label[i];pos_t = i;}}if (pos_y == pos_t) {++count_accuracy;}Sleep(1);}return (count_accuracy * 1.0 / num_patterns_test_CNN);
}}

测试代码如下：

int test_CNN_train()
{ANN::CNN cnn1;cnn1.init();cnn1.train();return 0;
}int test_CNN_predict()
{ANN::CNN cnn2;bool flag = cnn2.readModelFile("E:/GitCode/NN_Test/data/cnn.model");if (!flag) {std::cout << "read cnn model error" << std::endl;return -1;}int width{ 32 }, height{ 32 };std::vector<int> target{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };std::string image_path{ "E:/GitCode/NN_Test/data/images/" };for (auto i : target) {std::string str = std::to_string(i);str += ".png";str = image_path + str;cv::Mat src = cv::imread(str, 0);if (src.data == nullptr) {fprintf(stderr, "read image error: %s\n", str.c_str());return -1;}cv::Mat tmp(src.rows, src.cols, CV_8UC1, cv::Scalar::all(255));cv::subtract(tmp, src, tmp);cv::resize(tmp, tmp, cv::Size(width, height));auto ret = cnn2.predict(tmp.data, width, height);fprintf(stdout, "the actual digit is: %d, correct digit is: %d\n", ret, i);}return 0;
}

通过执行test_CNN_train()函数可生成cnn model文件，执行结果如下：

通过执行test_CNN_predict()函数来测试CNN的准确率，通过画图工具，每个数字生成一张图像，共10幅，如下图：

测试结果如下：

代码实现解析见：http://blog.csdn.net/fengbingchun/article/details/53445209

GitHub：https://github.com/fengbingchun/NN

卷积神经网络(CNN)的简单实现(MNIST)相关推荐

1. 卷积神经网络（三）：卷积神经网络CNN的简单实现（部分Python源码）

   转载自: 卷积神经网络(三):卷积神经网络CNN的简单实现(部分Python源码) - xuanyuansen的专栏 - 博客频道 - CSDN.NET http://blog.csdn.net/xu ...

2. 机器学习|卷积神经网络(CNN) 手写体识别 (MNIST)入门

   人工智能,机器学习,监督学习,神经网络,无论哪一个都是非常大的话题,都覆盖到可能就成一本书了,所以这篇文档只会包含在 RT-Thread 物联网操作系统,上面加载 MNIST 手写体识别模型相关的部分 ...

3. 卷积神经网络(CNN,ConvNet)

   卷积神经网络(CNN,ConvNet) 卷积神经网络(CNN,有时被称为 ConvNet)是很吸引人的.在短时间内,变成了一种颠覆性的技术,打破了从文本.视频到语音等多个领域所有最先进的算法,远远超出 ...

4. 深度学习(DL)与卷积神经网络(CNN)学习笔记随笔-04-基于Python的LeNet之MLP

   原文地址可以查看更多信息 本文主要参考于:Multilayer Perceptron  python源代码(github下载 CSDN免费下载) 本文主要介绍含有单隐层的MLP的建模及实现.建议在阅读 ...

5. 深度学习(DL)与卷积神经网络(CNN)学习笔记随笔-03-基于Python的LeNet之LR

   原地址可以查看更多信息 本文主要参考于:Classifying MNIST digits using Logistic Regression  python源代码(GitHub下载 CSDN免费下载) ...

6. DL之CNN优化技术：学习卷积神经网络CNN的优化、实践经验(练习调参)、从代码深刻认知CNN架构之练习技巧

   DL之CNN优化技术:学习卷积神经网络CNN的优化.调参实践.从代码深刻认知CNN架构之练习技巧 目录 卷积神经网络CNN调参学习实践 练习技巧 1.练习攻略一 2.VGG16练习攻略二 卷积神经网络 ...

7. 卷积神经网络(CNN)介绍与实践

   七月 上海 | 高性能计算之GPU CUDA培训 7月27-29日三天密集式学习  快速带你入门阅读全文> 正文共4499个字,26张图,预计阅读时间18分钟. CNN的前世今世 1.1.大脑 ...

8. c语言实现图片卷积_卷积神经网络(CNN)Python的底层实现——以LeNet为例

   本文介绍了如何使用Python从底层实现一个简单但经典的卷积神经网络结构--LeNet,并用它完成MNIST手写数字识别任务. 具体的完整代码以及代码的使用方法,可以光顾我的Github Profes ...

9. 卷积神经网络 CNN 简述

   文章目录 所解决的问题 需要处理的数据量太大 很难保留图像特征 基本原理 卷积层 -- 提取图像特征 池化层 -- 数据降维(避免过拟合) 全连接层 -- 输出结果 实际应用 图像分类.检索 目标检测 ...

最新文章

1. django_2.0_请求处理
2. 【线上分享】超分辨技术在RTC领域面临的机遇与挑战
3. viewController详解
4. jQuery框架学习第五天：事件与事件对象
5. VS2010与.NET4系列 16.ASP.NET 4 Web Forms 更加干净的HTML标记
6. 上海找python工作容易吗_Python 在上海什么程度才能找到工作？
7. java ordered list_Java - JSON对象和ListOrderedMap问题
8. HDU2050 折线分割平面【组合】
9. Atitit 规范标准化的艺术 -----java jsr的实现 目录 1. Atitit jsr规范有多少个 407个。Jsr规范大全 1 2. Atitit jsr规范化分类 attilax总
10. chrome插件Adblock Plus拓展程序
11. excel 2003 VBA编程入门教程
12. python批量处理1000+的excel文件
13. C语言求一元二次方程根
14. Ubuntu快捷键——终端
15. 中国最好的职业TOP10
16. 揭秘家用路由器0day漏洞挖掘技术读书笔记 D-Link DIR-645 authentication.cgi溢出漏洞分析
17. 微型计算机原理-期末
18. 【python爬虫】爬取Bing词典的单词存到SQLite数据库（加了pyqt5界面显示）
19. 一种基于快速GeoHash实现海量商品与商圈高效匹配的算法
20. 端口号是访问服务器的标识

热门文章

1. LabVIEW设置应用程序显示标签透明
2. 和12岁小同志搞创客开发：手撕代码，做一款火焰报警器
3. Opencv中的FaceRecognizer类
4. LeetCode刷题记录7——824. Goat Latin（easy）
5. mysql libs 冲突_mysql-libs的冲突
6. java从入门到精通_想要开始学java？你要的java从入门到精通布列如下！
7. 剑指offer：面试题32 - I. 从上到下打印二叉树
8. the different between Const and Static in C++
9. ubuntu常用翻译工具stardict
10. nvidia-jetson系列硬件平台上安装Qt