C/C++ Python MATLAB Sample source code of using SVD for each software library

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Sample source codes of SVD (singular value decomposition) are shown here. Note that these codes simply calls the function defined in each software library. SVD programming codes witten by MATLAB, and Python&numpy are shown. SVD program written in C/C++ is also available. SVD codes of Eigen library and SVD codes of OpenCV are shown.

Sample source code of SVD (singular value decomposition) using MATLAB

ROW = randi([2 10]);
COL = randi([2 10]);
A = 99.9*rand(ROW, COL);
[U,W,V] = svd(A,'econ');
VT = V.';
disp("SVD result")
disp("A =")
disp(A)
disp("U =")
disp(U)
disp("W =")
disp(W)
disp("V^T =")
disp(VT)
check = U * W * VT;
disp("Check")
disp("U W V^T =")
disp(check)
disp("Coincide with A")

Sample source code of SVD (singular value decomposition) using Python and numpy

import numpy as np

def main():
    ROW = np.random.randint(2, 10)
    COL = np.random.randint(2, 10)
    A = np.random.uniform(0.0, 99.9, (ROW, COL))
    U,W,VT = np.linalg.svd(A, full_matrices=False)
    print("SVD result")
    print("A=", A)
    print("U=", U)
    print("W=", W)
    print("V^T=", VT)
    matw = np.diag(W)
    check = np.dot(np.dot(U, matw), VT)
    print("Check")
    print("U W V^T=", check)
    print("Coincide with A")

if __name__ == '__main__':
    main()

Sample source code of SVD (singular value decomposition) using Python and OpenCV

import numpy as np
import cv2

def main():
    ROW = np.random.randint(2, 10)
    COL = np.random.randint(2, 10)
    A = np.random.uniform(0.0, 99.9, (ROW, COL))
    W,U,VT = cv2.SVDecomp(A)
    print("SVD result")
    print("A=", A)
    print("U=", U)
    print("W=", W)
    print("V^T=", VT)
    matw = np.diagflat(W)
    check = np.dot(np.dot(U, matw), VT)
    print("Check")
    print("U W V^T=", check)
    print("Coincide with A")

if __name__ == '__main__':
    main()

Sample source code of SVD (singular value decomposition) using C/C++ and Eigen library

#include <stdlib.h>
#include <time.h>

#include <iostream>
using namespace std;

#include "Eigen/Core"
#include "Eigen/SVD"
using namespace Eigen;

int main()
{
    srand((unsigned)time(NULL));
    int ROW = rand() % 8 + 2;
    int COL = rand() % 8 + 2;
    MatrixXd A = (MatrixXd::Random(ROW, COL) + MatrixXd::Ones(ROW, COL)) / 2.0 * 99.9;
    JacobiSVD<MatrixXd> svd(A, ComputeThinU | ComputeThinV);
    MatrixXd VT = svd.matrixV().transpose();
    cout << "SVD result" << endl << endl;
    cout << "A=" << endl << A << endl << endl;
    cout << "U=" << endl << svd.matrixU() << endl << endl;
    cout << "W=" << endl << svd.singularValues() << endl << endl;
    cout << "V^T=" << endl << VT << endl << endl;
    cout << endl;
    MatrixXd W = svd.singularValues().asDiagonal();
    MatrixXd check = svd.matrixU() * W * VT;
    cout << "Check" << endl << endl;
    cout << "U W V^T=" << endl << kenzan << endl << endl;
    cout << "Coincide with A" << endl << endl;
    cout << "Push enter" << endl;
    cin.get();
    return 0;
}

Sample source code of SVD (singular value decomposition) using C/C++ and Eigen library

#include <stdlib.h>
#include <time.h>

#include <iostream>
using namespace std;

#include "Eigen/Core"
#include "Eigen/SVD"
using namespace Eigen;

int main()
{
    srand((unsigned)time(NULL));
    int ROW = rand() % 8 + 2;
    int COL = rand() % 8 + 2;
    MatrixXd A = (MatrixXd::Random(ROW, COL) + MatrixXd::Ones(ROW, COL)) / 2.0 * 99.9;
    BDCSVD<MatrixXd> svd(A, ComputeThinU | ComputeThinV);
    MatrixXd VT = svd.matrixV().transpose();
    cout << "SVD result" << endl << endl;
    cout << "A=" << endl << A << endl << endl;
    cout << "U=" << endl << svd.matrixU() << endl << endl;
    cout << "W=" << endl << svd.singularValues() << endl << endl;
    cout << "V^T=" << endl << VT << endl << endl;
    cout << endl;
    MatrixXd W = svd.singularValues().asDiagonal();
    MatrixXd check = svd.matrixU() * W * VT;
    cout << "Check" << endl << endl;
    cout << "U W V^T=" << endl << kenzan << endl << endl;
    cout << "Coincide with A" << endl << endl;
    cout << "Push enter" << endl;
    cin.get();
    return 0;
}

Sample source code of SVD (singular value decomposition) using C/C++ and OpenCV

// Include directory C:\OpenCV3.1\build\include
// Library directory (x64) C:\OpenCV3.1\build\x64\vc14\lib
// PATH (x64) C:\OpenCV3.1\build\x64\vc14\bin
#if _DEBUG
#pragma comment(lib, "opencv_world310d.lib")
#else
#pragma comment(lib, "opencv_world310.lib")
#endif

#include <time.h>
#include <iostream>
using namespace std;

#include <opencv2/opencv.hpp>
using namespace cv;

int main()
{
    RNG gen(getTickCount());
    int ROW = gen.uniform(2, 10);
    int COL = gen.uniform(2, 10);
    Mat A(ROW, COL, CV_64F);
    gen.fill(A, RNG::UNIFORM, 0.0, 99.9);
    SVD svd(A);
    cout << "SVD result" << endl << endl;
    cout << "A=" << A << endl << endl;
    cout << "U=" << svd.u << endl << endl;
    cout << "W=" << svd.w << endl << endl;
    cout << "V^T=" << svd.vt << endl << endl;
    cout << endl;
    Mat matw = Mat::diag(svd.w);
    Mat check = svd.u * matw * svd.vt;
    cout << "Check" << endl << endl;
    cout << "U W V^T=" << check << endl << endl;
    cout << "Coincide with A" << endl << endl;
    cout << "Push enter" << endl;
    cin.get();
    return 0;
}

Sample source code of SVD (singular value decomposition) using C/C++ and OpenCV

// Include directory C:\OpenCV2.4.11\build\include
// Library directory (x86) C:\OpenCV2.4.11\build\x86\vc12\lib
// Library directory (x64) C:\OpenCV2.4.11\build\x64\vc12\lib
// PATH (x86) C:\OpenCV2.4.11\build\x86\vc12\bin
// PATH (x64) C:\OpenCV2.4.11\build\x64\vc12\bin
#if _DEBUG
#pragma comment(lib, "opencv_core2411d.lib")
#pragma comment(lib, "opencv_highgui2411d.lib")
#pragma comment(lib, "opencv_imgproc2411d.lib")
#else
#pragma comment(lib, "opencv_core2411.lib")
#pragma comment(lib, "opencv_highgui2411.lib")
#pragma comment(lib, "opencv_imgproc2411.lib")
#endif

#include <opencv2/opencv.hpp>
using namespace cv;

#include <stdio.h>
#include <conio.h>
#include <time.h>

int main()
{
    srand((unsigned)time(NULL));
    int ROW = rand() % 8 + 2;
    int COL = rand() % 8 + 2;
    Mat A(ROW, COL, CV_64F);
    for (int i = 0; i < A.rows; i++) {
        for (int j = 0; j < A.cols; j++) {
            A.at<double>(i, j) = 99.9 * (double)rand() / (double)RAND_MAX;
        }
    }
    SVD svd(A);
    printf("SVD result\n");
    printf("\n");
    printf("A=\n");
    for (int i = 0; i < A.rows; i++) {
        for (int j = 0; j < A.cols; j++) {
            printf("%1.2f ", A.at<double>(i, j));
        }
        printf("\n");
    }
    printf("U=\n");
    for (int i = 0; i < svd.u.rows; i++) {
        for (int j = 0; j < svd.u.cols; j++) {
            printf("%1.2f ", svd.u.at<double>(i, j));
        }
        printf("\n");
    }
    printf("W=\n");
    for (int i = 0; i < svd.w.rows; i++) {
        for (int j = 0; j < svd.w.cols; j++) {
            printf("%1.2f ", svd.w.at<double>(i, j));
        }
        printf("\n");
    }
    printf("V^T=\n");
    for (int i = 0; i < svd.vt.rows; i++) {
        for (int j = 0; j < svd.vt.cols; j++) {
            printf("%1.2f ", svd.vt.at<double>(i, j));
        }
        printf("\n");
    }
    printf("\n");
    Mat matw = Mat::zeros(svd.w.rows, svd.w.rows, CV_64F);
    for (int i = 0; i < svd.w.rows; i++) {
        matw.at<double>(i, i) = svd.w.at<double>(i, 0);
    }
    Mat check = svd.u * matw * svd.vt;
    printf("Check\n");
    printf("U W V^T=\n");
    for (int i = 0; i < check.rows; i++) {
        for (int j = 0; j < check.cols; j++) {
            printf("%1.2f ", check.at<double>(i, j));
        }
        printf("\n");
    }
    printf("Coincide with A\n");
    _getch();
    return 0;
}

Sample source code of SVD (singular value decomposition) using C/C++ and Numerical Recipes in C 3rd edition

#include <stdio.h>
#include <conio.h>
#include <time.h>

#include "nr3/nr3.h"
#include "nr3/svd.h"

int main()
{
    srand((unsigned)time(NULL));
    int ROW = rand() % 8 + 2;
    int COL = rand() % 8 + 2;
    MatDoub A(ROW, COL);
    for (int i = 0; i < ROW; i++) {
        for (int j = 0;j < COL;j++) {
            A[i][j] = 99.9 * (double)rand() / (double)RAND_MAX;
        }
    }
    SVD svd(A);
    printf("SVD result\n");
    printf("\n");
    printf("A=\n");
    for (int i = 0; i < ROW; i++) {
        for (int j = 0; j < COL; j++) {
            printf("%1.2f ", A[i][j]);
        }
        printf("\n");
    }
    printf("U=\n");
    for (int i = 0; i < svd.u.nrows(); i++) {
        for (int j = 0; j < svd.u.ncols(); j++) {
            printf("%1.2f ", svd.u[i][j]);
        }
        printf("\n");
    }
    printf("W=\n");
    for (int i = 0; i < svd.w.size(); i++) {
        printf("%1.2f\n", svd.w[i]);
    }
    printf("V^T=\n");
    for (int i = 0; i < svd.v.ncols(); i++) {
        for (int j = 0; j < svd.v.nrows(); j++) {
            printf("%1.2f ", svd.v[j][i]);
        }
        printf("\n");
    }
    printf("\n");
    MatDoub check(ROW, COL);
    for (int i = 0; i < ROW; i++) {
        for (int j = 0; j < COL; j++) {
            double val = 0.0;
            for (int k = 0; k < svd.u.ncols(); k++) {
                val += svd.u[i][k] * svd.w[k] * svd.v[j][k];
            }
            check[i][j] = val;
        }
    }
    printf("Check\n");
    printf("U W V^T=\n");
    for (int i = 0; i < check.nrows(); i++) {
        for (int j = 0; j < check.ncols(); j++) {
            printf("%1.2f ", check[i][j]);
        }
        printf("\n");
    }
    printf("Coincide with A\n");
    printf("Push any key\n");
    _getch();
    return 0;
}

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