Example: math_matrix_example

C++ example source code:

/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2024, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */

#include <mrpt/math/CMatrixF.h>
#include <mrpt/math/CMatrixFixed.h>
#include <mrpt/math/ops_matrices.h>
#include <mrpt/math/ops_vectors.h>
#include <mrpt/math/utils.h>
#include <mrpt/system/CTicTac.h>

#include <Eigen/Dense>
#include <iostream>

using namespace mrpt;
using namespace mrpt::math;
using namespace mrpt::system;
using namespace std;

#include <mrpt/examples_config.h>
string myDataDir(MRPT_EXAMPLES_BASE_DIRECTORY + string("math_matrix_example/"));

// ------------------------------------------------------
//              TestChol
// ------------------------------------------------------
void TestChol()
{
    CMatrixFloat A, B;
    A.loadFromTextFile(myDataDir + string("in_for_cholesky.txt"));
    A.chol(B);

    cout << "Cholesky decomposition result:" << endl << B;
}

void TestInitMatrix()
{
    // Initialize a matrix from a C array:
    const double numbers[] = {1, 2, 3, 4, 5, 6};
    CMatrixDouble M(2, 3, numbers);
    cout << "Initialized matrix (I): " << endl << M << endl;

    const double numbers2[] = {0.5, 4.5, 6.7, 8.9, 15.2};
    CVectorDouble v1;
    loadVector(v1, numbers2);
    cout << "Initialized double vector: " << v1 << endl;

    std::vector<int> v2;
    loadVector(v2, numbers2);
    cout << "Initialized int vector: " << v2 << endl;

    /*  // I/O Test
        CMatrixD  B(M);
        CFileOutputStream("mat.bin") << B;
        CMatrixD  A;
        CFileInputStream("mat.bin") >> A;
        cout << "B:" << endl << B;
        cout << "A:" << endl << A;
    */
}

void TestHCH()
{
    CMatrixFloat H, C, RES;

    cout << "reading H.txt...";
    H.loadFromTextFile(myDataDir + string("H.txt"));
    cout << "ok" << endl;

    cout << "reading C.txt...";
    C.loadFromTextFile(myDataDir + string("C.txt"));
    cout << "ok" << endl;

    // RES = H * C * H'
    mrpt::math::multiply_HCHt(H, C, RES);
    cout << "Saving RES.txt ...";
    RES.saveToTextFile("RES.txt");
    cout << "ok" << endl;

    // The same for a column vector:
    H.loadFromTextFile(myDataDir + string("H_col.txt"));
    cout << "H*C*(H') = " << mrpt::math::multiply_HCHt_scalar(H, C) << endl;
    cout << "Should be= 31.434 " << endl;

    // The same for a row vector:
    H.loadFromTextFile(myDataDir + string("H_row.txt"));
    cout << "Loaded H: " << endl << H;
    cout << "H*C*(H') = " << mrpt::math::multiply_HCHt_scalar(H, C) << endl;
    cout << "Should be= 31.434" << endl;
}

void TestMatrixTemplate()
{
    CTicTac tictac;
    CMatrixDouble M;

    // --------------------------------------
    M.loadFromTextFile(myDataDir + string("matrixA.txt"));
    cout << M << "\n";

    CMatrixDouble eigenVectors;
    std::vector<double> eigenValues;
    M.eig(eigenVectors, eigenValues);
    cout << "eigenVectors:\n"
         << eigenVectors << "\n Eigenvalues:\n"
         << eigenValues;

    CMatrixDouble D;
    D.setDiagonal(eigenValues);

    CMatrixDouble RES;
    RES = M.asEigen() * D.asEigen() * M.transpose();
    cout << "RES:\n" << RES;
}

void TestMatrices()
{
    CMatrixFloat m, l;
    CTicTac tictac;
    double t;

    m.setSize(4, 4);
    m(0, 0) = 4;
    m(0, 1) = -2;
    m(0, 2) = -1;
    m(0, 3) = 0;
    m(1, 0) = -2;
    m(1, 1) = 4;
    m(1, 2) = 0;
    m(1, 3) = -1;
    m(2, 0) = -1;
    m(2, 1) = 0;
    m(2, 2) = 4;
    m(2, 3) = -2;
    m(3, 0) = 0;
    m(3, 1) = -1;
    m(3, 2) = -2;
    m(3, 3) = 4;

    cout << "Matrix:\n" << m << endl;

    // I/O test through a text file:
    m.saveToTextFile("matrix1.txt");
    tictac.Tic();
    l.loadFromTextFile(myDataDir + string("matrix1.txt"));
    t = tictac.Tac();
    cout << "Read (text file) in " << 1e6 * t << "us:\n" << l << endl;
    mrpt::math::laplacian(m, l);

    cout << "Laplacian:\n" << l << endl;
}

void TestCov()
{
    // Initialize a matrix from a C array:
    const double numbers[] = {1, 2, 3, 10, 4, 5, 6, 14, 10, -5, -3, 1};
    CMatrixDouble Mdyn(4, 3, numbers);
    CMatrixFixed<double, 4, 3> Mfix(numbers);

    vector<CVectorDouble> samples(4);
    for (size_t i = 0; i < 4; i++)
    {
        samples[i].resize(3);
        for (size_t j = 0; j < 3; j++)
            samples[i][j] = Mdyn(i, j);
    }

    cout << "COV (vector of vectors): " << endl
         << mrpt::math::covVector<vector<CVectorDouble>, Eigen::MatrixXd>(
                samples)
         << endl;
    cout << "COV (mat fix): " << endl << mrpt::math::cov(Mfix) << endl;
    cout << "COV (mat dyn): " << endl << mrpt::math::cov(Mdyn) << endl;
}

// ------------------------------------------------------
//                      MAIN
// ------------------------------------------------------
int main()
{
    try
    {
        TestInitMatrix();
        TestMatrixTemplate();
        TestMatrices();
        TestHCH();
        TestChol();
        TestCov();

        return 0;
    }
    catch (exception& e)
    {
        cout << "MRPT exception caught: " << e.what() << endl;
        return -1;
    }
}