线性回归-批量梯度下降

void lir_BGD()
{
    //在x中添加一列1,对应w0
    std::vector<std::vector<double>> x={
        {1,1.1,1.5},
        {1,1.3,1.9},
        {1,1.5,2.3},
        {1,1.7,2.7},
        {1,1.9,3.1},
        {1,2.1,3.5},
        {1,2.3,3.9},
        {1,2.5,4.3},
        {1,2.7,4.7},
        {1,2.9,5.1}
    };

    std::vector<double> y={
        2.5,
        3.2,
        3.9,
        4.6,
        5.3,
        6,
        6.7,
        7.4,
        8.1,
        8.8
    };

    //学习速率
    double alpha=0.01;
    std::vector<double> w=std::vector<double>(x[0].size(),0);
    //每个w的导数
    std::vector<double> deri=std::vector<double>(x[0].size(),0);

    int loop=1;
    while(loop++<10000) {
        for(auto &iter:deri) iter=0;

        for(int i=0;i<x.size();i++) {
            //计算w*x值
            double wx=0;
            for(int j=0;j<w.size();j++) {
                wx+=w[j]*x[i][j];
            }

            //计算w*x 和y 之间的误差
            double wx_y=wx-y[i];

            //计算每个w的导数,每个w对应-个x中的每个位置
            for(int j=0;j<w.size();j++) {
                deri[j]+=wx_y*x[i][j];
            }
        }

        //更新每个的w值
        for(int j=0;j<w.size();j++) {
            w[j]-=alpha*deri[j];
        }
    }

    std::cout<<"loop:"<<loop-1<<" alpha:"<<alpha<<std::endl;
    //输出每个w的值
    for(int i=0;i<w.size();i++) {
       std::cout<<"w["<<i<<"]:"<<w[i]<<" ";
       if(i==w.size()-1) std::cout<<std::endl;
    }

    //验证结果
    std::cout<<"res:3.2 5.5 9.50:"<<w[0]+w[1]*3.2+w[2]*5.5<<std::endl;
    std::cout<<"res:3.3 5.9 10.2:"<<w[0]+w[1]*3.3+w[2]*5.9<<std::endl;
    std::cout<<"res:3.5 6.3 10.9:"<<w[0]+w[1]*3.5+w[2]*6.3<<std::endl;
    std::cout<<"res:3.7 6.7 11.6:"<<w[0]+w[1]*3.7+w[2]*6.7<<std::endl;
    std::cout<<"res:3.9 7.1 12.3:"<<w[0]+w[1]*3.9+w[2]*7.1<<std::endl;
}