SVD分解 Eigen库 opencv库[通俗易懂]

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如题，使用库函数进行svd分解，形如 A = U * S * VT.

Eigen 库：

#include <iostream> #include <Eigen/SVD> #include <Eigen/Dense> //using Eigen::MatrixXf; using namespace Eigen; using namespace Eigen::internal; using namespace Eigen::Architecture; int main() { //-------------------------------svd测试 eigen Matrix3f A; A(0,0)=1,A(0,1)=0,A(0,2)=1; A(1,0)=0,A(1,1)=1,A(1,2)=1; A(2,0)=0,A(2,1)=0,A(2,2)=0; JacobiSVD<Eigen::MatrixXf> svd(A, ComputeThinU | ComputeThinV ); Matrix3f V = svd.matrixV(), U = svd.matrixU(); Matrix3f S = U.inverse() * A * V.transpose().inverse(); // S = U^-1 * A * VT * -1 std::cout<<"A :\n"<<A<<std::endl; std::cout<<"U :\n"<<U<<std::endl; std::cout<<"S :\n"<<S<<std::endl; std::cout<<"V :\n"<<V<<std::endl; std::cout<<"U * S * VT :\n"<<U * S * V.transpose()<<std::endl; system("pause"); //-------------------------------svd测试 eigen return 0; }

OpenCV库：

#include <opencv2/core/core.hpp> #include <opencv2/highgui/highgui.hpp> #include"opencv2/imgproc/imgproc.hpp" #include <iostream> using namespace std; using namespace cv; void print(CvMat& m){ for (int row = 0; row < m.rows; row++){ float* ptr = (float*)(m.data.ptr + row * m.step);//第row行数据的起始指针 for (int col = 0; col < m.cols; col++) cout<<*(ptr+3*col)<<" "; std::cout<<std::endl; } } int main () { float abt[3 * 3] = { 1,0,1, 0,1,1, 0,0,0 }; float abt_d[3 * 3]={0}, abt_u[3 * 3]={0}, abt_v[3 * 3]={0}; CvMat ABt = cvMat(3, 3, CV_64F, abt);//CvMat 取对数组的引用而不是拷贝 CvMat ABt_D = cvMat(3, 3, CV_64F, abt_d); CvMat ABt_U = cvMat(3, 3, CV_64F, abt_u); CvMat ABt_VT = cvMat(3, 3, CV_64F, abt_v); cvSVD(&ABt, &ABt_D, &ABt_U, &ABt_VT, CV_SVD_V_T);//最后一个参数用于控制返回 UT或U  VT或V std::cout<<"A : "<<std::endl; print(ABt); std::cout<<"U : "<<std::endl; print(ABt_U); std::cout<<"S : "<<std::endl; print(ABt_D); std::cout<<"V : "<<std::endl; print(ABt_VT); system("pause"); return 0; }