C++实现矩阵对称正交化的示例代码

1.python代码

import numpy as np
import pandas as pd
df=pd.dataframe()
df['fac_01']=(34, 45, 65)
df['fac_02']=(56, 25, 94)
print(df)
print('------------------矩阵的特征跟d、和特征向量u-----------------------')
d,u=np.linalg.eig(np.dot(df.t, df)) # 求矩阵的特征跟d、和特征向量u
print(d,u,sep='\n')
print('\n------------------对角矩阵-----------------------')
print(np.diag(d**(-0.5)))
print('\n------------------对称正交后的矩阵-----------------------')
s = np.dot(np.dot(u, np.diag(d**(-0.5))), u.t) # 求过渡矩阵s = u* dex *u'
f_hat = np.dot(df, s) # 求对称正交后的矩阵
print(f_hat)

2.c++的eigen库实现

#include "eigen/dense"
using namespace eigen;
int main()
{
    //初始化
    matrixxf a(3, 2);
    a(0,0) = 34;a(0,1) = 56;
    a(1,0) = 45;a(1,1) = 25;
    a(2,0) = 65;a(2,1) = 94;
    //生成正交矩阵
    matrixxf aex = a.transpose() * a;
    int nrowsize = aex.rows();
    int ncolsize = aex.cols();
    //求特征根、特征向量
    selfadjointeigensolver<matrix2f> eigensolver(aex);
    matrixxf d = eigensolver.eigenvalues();
    matrixxf u = eigensolver.eigenvectors();
    std::cout<<"特征根如下：" <<std::endl;
    nrowsize = d.rows();
    ncolsize = d.cols();
    for(size_t i=0; i<nrowsize; i++)
    {
        for(size_t j=0; j<ncolsize; j++)
        {
            std::cout<<d(i,j)<<"    ";
        }
        std::cout<<std::endl;
    }
    std::cout<<"特征向量如下：" <<std::endl;
    nrowsize = u.rows();
    ncolsize = u.cols();
    for(size_t i=0; i<nrowsize; i++)
    {
        for(size_t j=0; j<ncolsize; j++)
        {
            std::cout<<u(i,j)<<"    ";
        }
        std::cout<<std::endl;
    }
    //生成np.diag(d**(-0.5)))对角线矩阵
    matrixxf dex(2,2);
    for(size_t i=0; i<2; i++)
    {
        for(size_t j=0; j<2; j++)
        {
            if(i == j)
            {
                dex(i,j) = pow(d(i,0),-0.5);
            }
            else
            {
                dex(i,j) = 0;
            }
        }
    }
    nrowsize = dex.rows();
    ncolsize = dex.cols();
    std::cout<<"对角线矩阵如下：" <<std::endl;
    for(size_t i=0; i<nrowsize; i++)
    {
        for(size_t j=0; j<ncolsize; j++)
        {
            std::cout<<dex(i,j)<<"    ";
        }
        std::cout<<std::endl;
    }
    //生成过度矩阵s
    matrixxf s = u * dex * u.transpose();
    //生成正交化矩阵
    matrixxf r = a * s;
    nrowsize = r.rows();
    ncolsize = r.cols();
    std::cout<<"正交化结果如下：" <<std::endl;
    for(size_t i=0; i<nrowsize; i++)
    {
        for(size_t j=0; j<ncolsize; j++)
        {
            std::cout<<r(i,j)<<"    ";
        }
        std::cout<<std::endl;
    }
	return 0;
}

3.结果对比

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