matrix_ops3_unittest.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2020, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */

// Note: Matrices unit tests have been split in different files since
// building them with eigen3 eats a lot of RAM and may be a problem while
// compiling in small systems.

#include <gtest/gtest.h>
#include <mrpt/math/CMatrixDynamic.h>
#include <mrpt/math/CMatrixFixed.h>
#include <mrpt/math/ops_matrices.h>
#include <mrpt/math/utils.h>
#include <mrpt/random.h>
#include <Eigen/Dense>

using namespace mrpt;
using namespace mrpt::math;
using namespace mrpt::random;
using namespace std;

#define CHECK_AND_RET_ERROR(_COND_, _MSG_) EXPECT_FALSE(_COND_) << _MSG_;

TEST(Matrices, HCHt_3x2_2x2_2x3)
{
    const double dat_H[] = {0.2, -0.3, 0.1, 0.9, -0.07, 1.2};
    const CMatrixFixed<double, 3, 2> H(dat_H);

    const double dat_C[] = {0.8, -0.1, -0.1, 0.8};
    const CMatrixFixed<double, 2, 2> C(dat_C);

    const double dat_R[] = {0.11600, -0.21500, -0.32530, -0.21500, 0.63800,
                            0.85270, -0.32530, 0.85270,  1.17272};
    const CMatrixFixed<double, 3, 3> R_REAL(dat_R);

    const auto R = mrpt::math::multiply_HCHt(H, C);

    EXPECT_NEAR((R_REAL - R).sum_abs(), 0, 1e-4) << "R:\n"
                                                 << R << "\nR_REAL:\n"
                                                 << R_REAL << "\n";
}

TEST(Matrices, HCHt_scalar_1x2_2x2_2x1)
{
    const double dat_H[] = {0.2, -0.3};
    CMatrixDouble H(1, 2, dat_H);

    const double dat_C[] = {0.8, -0.1, -0.1, 0.8};
    CMatrixDouble C(2, 2, dat_C);

    const double r = mrpt::math::multiply_HCHt_scalar(H, C);

    const double r2 =
        (H.asEigen() * C.asEigen() * H.asEigen().transpose()).eval()(0, 0);
    CHECK_AND_RET_ERROR(
        fabs(r - r2) > 1e-4, "Error in HCHt_scalar: 1x2 * 2x2 * 2x1")
}

TEST(Matrices, det_2x2_dyn)
{
    const double dat_A[] = {0.8, -0.3, -0.7, 0.1};
    CMatrixDouble A(2, 2, dat_A);

    const double d = A.det();
    const double d_R = -0.13;

    CHECK_AND_RET_ERROR(fabs(d - d_R) > 1e-4, "Error in Determinant: 2x2 dyn")
}

TEST(Matrices, det_2x2_fix)
{
    const double dat_A[] = {0.8, -0.3, -0.7, 0.1};
    CMatrixDouble22 A(dat_A);

    const double d = A.det();
    const double d_R = -0.13;

    CHECK_AND_RET_ERROR(fabs(d - d_R) > 1e-4, "Error in Determinant: 2x2 fix")
}

TEST(Matrices, det_3x3_dyn)
{
    const double dat_A[] = {-3.3304e-01, -2.0585e-01, 6.2026e-05,
                            1.4631e+00,  6.0985e-01,  2.3746e+00,
                            -3.6451e-01, 4.8169e-01,  -8.4419e-01};
    CMatrixDouble A(3, 3, dat_A);
    const double d = A.det();
    const double d_R = 0.476380435871666;
    // cout << "d: " << d << endl;
    CHECK_AND_RET_ERROR(fabs(d - d_R) > 1e-4, "Error in Determinant: 3x3 dyn")
}

TEST(Matrices, det_3x3_fix)
{
    const double dat_A[] = {-3.3304e-01, -2.0585e-01, 6.2026e-05,
                            1.4631e+00,  6.0985e-01,  2.3746e+00,
                            -3.6451e-01, 4.8169e-01,  -8.4419e-01};
    CMatrixDouble33 A(dat_A);
    const double d = A.det();
    const double d_R = 0.476380435871666;
    CHECK_AND_RET_ERROR(fabs(d - d_R) > 1e-4, "Error in Determinant: 3x3 fix")
}

TEST(Matrices, det_4x4_dyn)
{
    const double dat_A[] = {0.773931,  -0.336130, 1.131764,  0.385890,
                            1.374906,  -0.540629, -0.952902, 0.659769,
                            -0.387254, -1.557355, 0.139683,  -2.056635,
                            -0.750078, -0.653811, 0.872027,  0.217554};
    CMatrixDouble A(4, 4, dat_A);
    const double d = A.det();
    const double d_R = -6.29527837425056;
    CHECK_AND_RET_ERROR(fabs(d - d_R) > 1e-4, "Error in Determinant: 4x4 dyn")
}

TEST(Matrices, det_4x4_fix)
{
    const double dat_A[] = {0.773931,  -0.336130, 1.131764,  0.385890,
                            1.374906,  -0.540629, -0.952902, 0.659769,
                            -0.387254, -1.557355, 0.139683,  -2.056635,
                            -0.750078, -0.653811, 0.872027,  0.217554};
    CMatrixDouble44 A(dat_A);
    const double d = A.det();
    const double d_R = -6.29527837425056;
    CHECK_AND_RET_ERROR(fabs(d - d_R) > 1e-4, "Error in Determinant: 4x4 fix")
}

TEST(Matrices, det_10x10_dyn)
{
    const double dat_A[] = {
        1.2305462976,  -0.2944257811, 0.8176140437,  -0.0487601371,
        0.4418235581,  -0.0088466980, -1.4100223408, -0.6219629815,
        1.1089237266,  -0.6450262619, -2.0862614547, 0.2699762709,
        -0.0705918517, 1.1763963161,  -0.3461819597, -1.3013222580,
        -0.3310621595, -0.2595069675, -0.5188213591, 1.2261476224,
        -1.1334297957, 2.1452881319,  1.7856021357,  0.5406722888,
        0.5497545623,  0.4282217402,  -1.6175210256, -0.3522824764,
        0.2773929603,  0.8507134453,  0.4046854117,  -2.1638696195,
        1.0044939778,  0.9755939720,  0.9640788301,  0.5641138097,
        0.7382236207,  -0.4422212587, 0.8507041571,  1.3764399072,
        0.3446492224,  1.1681336612,  -1.3440052449, 1.0120691406,
        -0.0430604384, 0.4823901171,  0.0881769800,  0.3984805283,
        -1.9988153178, 0.9509748328,  0.3202853059,  1.9688559025,
        0.4020581289,  -1.5558616735, -0.8753527614, 0.1207830427,
        0.0457715031,  -0.1557123759, -0.3161307172, -0.0759276933,
        -0.0417386037, 1.2079564736,  -2.5839030155, -0.7648863647,
        1.1541464803,  0.2127569446,  -1.4882083860, -0.7630836781,
        0.8550884427,  -0.8440402465, -0.4903597050, -0.1457982930,
        0.5893448560,  -0.2353784687, 0.3474655757,  2.5874616045,
        0.6608448038,  -1.0105315509, -1.5276853710, -0.1400026815,
        -1.7630264416, 2.4048579514,  -0.3111046623, 0.7463774799,
        -0.2800404492, -1.4175124130, -0.5708536580, -1.2085107661,
        0.8169107561,  -1.1659481510, -0.1406355512, 2.3507381980,
        2.6346742737,  -1.1028788167, -0.0533115044, 0.3752684649,
        -1.3799576309, -0.7274190037, 1.1188847602,  -0.6624231096};
    CMatrixDouble A(10, 10, dat_A);
    const double d = A.det();
    const double d_R = 330.498518199239;
    CHECK_AND_RET_ERROR(fabs(d - d_R) > 1e-4, "Error in Determinant: 10x10 dyn")
}

TEST(Matrices, chol_2x2_dyn)
{
    const double dat_A[] = {1.0727710178, 0.6393375593, 0.6393375593,
                            0.8262219720};
    CMatrixDouble A(2, 2, dat_A);
    CMatrixDouble C;
    A.chol(C);
    const double dat_CHOL[] = {1.0357465992, 0.6172721781, 0.0000000000,
                               0.6672308672};
    CMatrixDouble CHOL(2, 2, dat_CHOL);
    CHECK_AND_RET_ERROR(
        (CHOL - C).sum_abs() > 1e-4, "Error in Choleski, 2x2 dyn")
}

TEST(Matrices, chol_2x2_fix)
{
    const double dat_A[] = {1.0727710178, 0.6393375593, 0.6393375593,
                            0.8262219720};
    CMatrixDouble22 A(dat_A);
    CMatrixDouble22 C;
    A.chol(C);
    const double dat_CHOL[] = {1.0357465992, 0.6172721781, 0.0000000000,
                               0.6672308672};
    CMatrixDouble CHOL(2, 2, dat_CHOL);
    CHECK_AND_RET_ERROR(
        (CHOL - CMatrixDouble(C)).sum_abs() > 1e-4,
        "Error in Choleski, 2x2 fix")
}

TEST(Matrices, chol_3x3_dyn)
{
    const double dat_A[] = {
        0.515479426556448, 0.832723636299236, 0.249691538245735,
        0.832723636299236, 1.401081397506934, 0.385539356127255,
        0.249691538245735, 0.385539356127255, 0.128633962591437};
    CMatrixDouble A(3, 3, dat_A);
    CMatrixDouble C;
    A.chol(C);

    const double dat_CHOL[] = {
        0.717968959326549, 1.159832365288224, 0.347774837619643,
        0.000000000000000, 0.236368952988455, -0.075395504153773,
        0.000000000000000, 0.000000000000000, 0.044745311077990};
    CMatrixDouble CHOL(3, 3, dat_CHOL);
    CHECK_AND_RET_ERROR(
        (CHOL - C).sum_abs() > 1e-4, "Error in Choleski, 3x3 dyn")
}

TEST(Matrices, chol_3x3_fix)
{
    const double dat_A[] = {
        0.515479426556448, 0.832723636299236, 0.249691538245735,
        0.832723636299236, 1.401081397506934, 0.385539356127255,
        0.249691538245735, 0.385539356127255, 0.128633962591437};
    CMatrixDouble33 A(dat_A);
    CMatrixDouble33 C;
    A.chol(C);

    const double dat_CHOL[] = {
        0.717968959326549, 1.159832365288224, 0.347774837619643,
        0.000000000000000, 0.236368952988455, -0.075395504153773,
        0.000000000000000, 0.000000000000000, 0.044745311077990};
    CMatrixDouble33 CHOL(dat_CHOL);
    CHECK_AND_RET_ERROR(
        (CHOL - C).sum_abs() > 1e-4, "Error in Choleski, 3x3 fix")
}

TEST(Matrices, chol_10x10_dyn)
{
    const double dat_A[] = {
        2.8955668335, 2.3041932983, 1.9002381085, 1.7993158652, 1.8456197228,
        2.9632296740, 1.9368565578, 2.1988923358, 2.0547605617, 2.5655678993,
        2.3041932983, 3.8406914364, 2.1811218706, 3.2312564555, 2.4736403918,
        3.4703311380, 1.4874417483, 3.1073538218, 2.1353324397, 2.9541115932,
        1.9002381085, 2.1811218706, 2.4942067597, 1.6851007198, 1.4585872052,
        2.3015952197, 1.0955231591, 2.2979627790, 1.3918738834, 2.1854562572,
        1.7993158652, 3.2312564555, 1.6851007198, 3.1226161015, 1.6779632687,
        2.7195826381, 1.2397348013, 2.3757864319, 1.6291224768, 2.4463194915,
        1.8456197228, 2.4736403918, 1.4585872052, 1.6779632687, 2.8123267839,
        2.5860688816, 1.4131630919, 2.1914803135, 1.5542420639, 2.7170092067,
        2.9632296740, 3.4703311380, 2.3015952197, 2.7195826381, 2.5860688816,
        4.1669180394, 2.1145239023, 3.3214801332, 2.6694845663, 3.0742063088,
        1.9368565578, 1.4874417483, 1.0955231591, 1.2397348013, 1.4131630919,
        2.1145239023, 1.8928811570, 1.7097998455, 1.7205860530, 1.8710847505,
        2.1988923358, 3.1073538218, 2.2979627790, 2.3757864319, 2.1914803135,
        3.3214801332, 1.7097998455, 3.4592638415, 2.1518695071, 2.8907499694,
        2.0547605617, 2.1353324397, 1.3918738834, 1.6291224768, 1.5542420639,
        2.6694845663, 1.7205860530, 2.1518695071, 2.1110960664, 1.6731209980,
        2.5655678993, 2.9541115932, 2.1854562572, 2.4463194915, 2.7170092067,
        3.0742063088, 1.8710847505, 2.8907499694, 1.6731209980, 3.9093678727};
    CMatrixDouble A(10, 10, dat_A);
    CMatrixDouble C;
    A.chol(C);

    const double dat_CHOL[] = {
        1.7016365163,  1.3541042851,  1.1167121124,  1.0574031810,
        1.0846145491,  1.7413999087,  1.1382316607,  1.2922221137,
        1.2075202560,  1.5077061845,  0.0000000000,  1.4167191047,
        0.4722017314,  1.2701334167,  0.7093566960,  0.7851196867,
        -0.0380051491, 0.9582353452,  0.3530862859,  0.6441080558,
        0.0000000000,  0.0000000000,  1.0120209201,  -0.0943393725,
        -0.0865342379, -0.0136183214, -0.1557357390, 0.3976620401,
        -0.1218419159, 0.1952860421,  0.0000000000,  0.0000000000,
        0.0000000000,  0.6183654266,  -0.6113744707, -0.1944977093,
        0.1127886805,  -0.2752173394, -0.1741275611, 0.0847171764,
        0.0000000000,  0.0000000000,  0.0000000000,  0.0000000000,
        0.8668818973,  0.0234194680,  0.3011475111,  -0.0272963639,
        -0.1417917925, 0.8000162775,  0.0000000000,  0.0000000000,
        0.0000000000,  0.0000000000,  0.0000000000,  0.6924364129,
        0.2527445784,  0.3919505633,  0.3715689962,  -0.0817608778,
        0.0000000000,  0.0000000000,  0.0000000000,  0.0000000000,
        0.0000000000,  0.0000000000,  0.6358623279,  0.4364121485,
        0.4859857603,  -0.0313828244, 0.0000000000,  0.0000000000,
        0.0000000000,  0.0000000000,  0.0000000000,  0.0000000000,
        0.0000000000,  0.5408375843,  -0.1995475524, 0.6258606925,
        0.0000000000,  0.0000000000,  0.0000000000,  0.0000000000,
        0.0000000000,  0.0000000000,  0.0000000000,  0.0000000000,
        0.2213262214,  -0.2367037013, 0.0000000000,  0.0000000000,
        0.0000000000,  0.0000000000,  0.0000000000,  0.0000000000,
        0.0000000000,  0.0000000000,  0.0000000000,  0.2838575216};
    CMatrixDouble CHOL(10, 10, dat_CHOL);
    CHECK_AND_RET_ERROR(
        (CHOL - C).sum_abs() > 1e-4, "Error in Choleski, 10x10 dyn")
}