用C实现单隐层神经网络的训练和预测（手写BP算法）

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>
//归一化二维数组
void normalization(float num[1000][2]){
    float max1 = 0.0,max2 = 0.0;
    float min1 = 0.0,min2 = 0.0;
    for(int i = 0;i<1000;i++){
        if(num[i][0]>max1||num[i][0]<min1){
            if(num[i][0]>max1){
                max1 = num[i][0];
            }
            if(num[i][0]<min1){
                min1 = num[i][0];
            }
        }
        if(num[i][1]>max2||num[i][1]<min2){
            if(num[i][1]>max2){
                max2 = num[i][1];
            }
            if(num[i][1]<min2){
                min2 = num[i][1];
            }
        }
    }
    for(int i = 0;i<1000;i++){
        num[i][0] = (num[i][0]-min1+1)/(max1-min1+1);
        num[i][1] = (num[i][1]-min2+1)/(max2-min1+1);
    }
    printf("a[][0]的最大值和最小值分别为：%f\t%f",max1,min1);
    printf("\na[][1]的最大值和最小值分别为：%f\t%f",max2,min2);
    printf("\n");
}
//归一化一维数组
void normalization_b(float num[1000]){
    float max = 0.0,min = 0.0;
    for(int i = 0;i<1000;i++){
        if(num[i]>max||num[i]<min){
            if(num[i]>max){
                max = num[i];
            }else{
                min = num[i];
            }
        }
    }
    for(int i = 0;i<1000;i++){
        num[i] = (num[i]-min+1)/(max-min+1);
    }
    printf("b数组归一化的最大值和最小值为:%f,%f",max,min);
}
//后向隐藏层公式计算
float compute_hidden(float a,float b,float *w_a,float *w_b,float *bias_c){
    float value = 0.0;
    value = a*(*w_a)+b*(*w_b)+(*bias_c);
    value = 1/(1+exp(-value));
    return value;
}
//后向输出层公式计算
float compute_output(float c,float *w_c,float *bias_d){
    float value = 0.0;
    value = c*(*w_c)+(*bias_d);
    value = 1/(1+exp(-value));
    return value;
}
//前向输出层公式计算
float pro_output(float predict_num,float real_num){
    float error = 0.0;
    error = predict_num*(1-predict_num)*(real_num-predict_num);
    return error;
}
//bp算法
void bp(float a,float b,float real_num,float *w_a,float *w_b,float *v,float *bias_c,float *bias_d){
    //前向计算
    //隐藏层
    float output = compute_hidden(a,b,w_a,w_b,bias_c);
    //输出层
    float output_final = compute_output(output,v,bias_d);
    //反向计算
    float error_output = 0.0;
    //输出层
    error_output = pro_output(output_final,real_num);
    //更新权重和偏向！
    //定义学习率
    double learning_rate = 0.01;
    *v = *v + learning_rate*error_output*output;
    *bias_d = *bias_d + learning_rate*error_output;
    //前向隐藏层
    float error_hidden = 0.0;
    error_hidden = output*(1-output)*(error_output*(*v));
    //更新权重和偏向
    *w_a = *w_a + learning_rate*(error_hidden*a);
    *w_b = *w_b + learning_rate*(error_hidden*b);
    *bias_c = *bias_c + learning_rate*error_hidden;
}
int main(int argc, const char * argv[]) {
    //随机初始化1000对数值在0-10之间的双精度浮点数，保存在二维数组a[1000][2]中
    srand((unsigned) (time(NULL)));
    float a[1000][2],b[1000];
    for(int i = 0;i<1000;i++){
        for(int j = 0;j<2;j++){
            int rd = rand()%1001;
            a[i][j] = rd/100.0;
        }
    }
    for(int i = 0;i<1000;i++){
        b[i] = a[i][0] +a[i][1];
    }
    //归一化处理
    normalization(a);
    normalization_b(b);
    //定义浮点数组w,v分别存放隐层和输出层的权值数据，并随机初始化w,v为（-1，1）之间的浮点数
    int w_a_rand = rand()%200001;
    int w_b_rand = rand()%200001;
    float w_a = w_a_rand/100000.0-1;
    float w_b = w_b_rand/100000.0-1;
    int v_rand = rand()%200001;
    float v = v_rand/100000.0-1;
    int bias_c_rand = rand()%200001;
    float bias_c = bias_c_rand/100000.0-1;
    int bias_d_rand = rand()%200001;
    float bias_d = bias_d_rand/100000.0-1;
    printf("w_a,w_b,v初始随机值分别是:%f    %f    %f\n",w_a,w_b,v);
    //将1000组输入（a[1000][2]）逐个进行前馈计算，并根据计算的输出结果与b[1000]中对应标签值的差值进行反馈权值更新，调整w、v中各元素的数值。
    //对于每一个训练实例：执行bp算法
    float max1 ,max2 ,min1 ,min2,max,min;
    printf("x0的归一化参数（最大最小值):");
    scanf("%f,%f",&max1,&min1);
    printf("x1的归一化参数（最大最小值):");
    scanf("%f,%f",&max2,&min2);
    printf("b的归一化参数（最大最小值):");
    scanf("%f,%f",&max,&min);
    int mark = 0;
    float trainnig_data_a[800][2],trainnig_data_b[800],test_data_a[200][2],test_data_b[200];
    int i = 0;
    while (i<1000) {
        if(i == mark){
            //设置测试集
        for(int k = i;k<(i+200);k++){
                test_data_a[k][0] = a[k][0];
                test_data_a[k][1] = a[k][1];
                test_data_b[k] = b[k];
            }
            i +=200;
        }
        //设置训练集
        if(i<mark){
        trainnig_data_a[i][0] = a[i][0];
        trainnig_data_a[i][1] = a[i][1];
        trainnig_data_b[i] = b[i];
        i++;
        }
        if(i>mark){
            trainnig_data_a[i-200][0] = a[i][0];
            trainnig_data_a[i-200][1] = a[i][1];
            trainnig_data_b[i-200] = b[i];
            i++;
        }
    }
    for(int i = 0;i<800;i++){
        //迭代600次
        int times = 0;
        for(int i= 0;i<600;i++){
            bp(trainnig_data_a[i][0],trainnig_data_a[i][1],trainnig_data_b[i],&w_a,&w_b,&v,&bias_c,&bias_d);
            times++;
        }
    }
    //进行预测
    float pre_1,pre_2,predict_value,true_value;
    
    float MSE[200];
    for(int i = 0;i<200;i++){
        pre_1 = test_data_a[i][0];
        pre_2 = test_data_a[i][1];
        true_value = test_data_b[i];
        //进行计算
        float pre_hidden = compute_hidden(pre_1, pre_2, &w_a, &w_b, &bias_c);
        predict_value = compute_output(pre_hidden, &v, &bias_d);
        //求均方误差
        MSE[i] = (predict_value - true_value)*(predict_value-true_value);
        predict_value = (predict_value*(max-min+1))-1+min;
        true_value = (true_value*(max-min+1))-1+min;
        printf("预测值为:%f   真实值为:%f\n",predict_value,true_value);
    }
    float mean_square_error = 0;
    for(int i = 0;i<200;i++){
        mean_square_error += MSE[i];
    }
    mean_square_error = mean_square_error/200;
    printf("均方误差为:%lf",mean_square_error);
}