test_mathlib.cpp

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/**
 * @file test_mathlib.cpp
 * Tests for the PX4 math library.
 */

#include <unit_test.h>

#include <errno.h>
#include <fcntl.h>
#include <float.h>
#include <math.h>
#include <px4_platform_common/px4_config.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/types.h>
#include <unistd.h>

#include <px4_platform_common/log.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <string.h>
#include <time.h>
#include <mathlib/mathlib.h>
#include <systemlib/err.h>
#include <drivers/drv_hrt.h>
#include <matrix/math.hpp>

#include "tests_main.h"

class MathlibTest : public UnitTest
{
public:
    virtual bool run_tests();

private:
    bool testVector2();
    bool testVector3();
    bool testVector10();
    bool testMatrix3x3();
    bool testMatrix10x10();
    bool testMatrixNonsymmetric();
    bool testRotationMatrixQuaternion();
    bool testQuaternionfrom_dcm();
    bool testQuaternionfrom_euler();
    bool testQuaternionRotate();
    bool testFinite();
};

#define TEST_OP(_title, _op) { unsigned int n = 30000; hrt_abstime t0, t1; t0 = hrt_absolute_time(); for (unsigned int j = 0; j < n; j++) { _op; }; t1 = hrt_absolute_time(); PX4_INFO(_title ": %.6fus", (double)(t1 - t0) / n); }

using namespace math;

bool MathlibTest::testVector2()
{
    {
        matrix::Vector2f v;
        matrix::Vector2f v1(1.0f, 2.0f);
        matrix::Vector2f v2(1.0f, -1.0f);
        float data[2] = {1.0f, 2.0f};
        TEST_OP("Constructor matrix::Vector2f()", matrix::Vector2f v3);
        TEST_OP("Constructor matrix::Vector2f(matrix::Vector2f)", matrix::Vector2f v3(v1); ut_assert_true(v3 == v1); v3.zero());
        TEST_OP("Constructor matrix::Vector2f(float[])", matrix::Vector2f v3(data));
        TEST_OP("Constructor matrix::Vector2f(float, float)", matrix::Vector2f v3(1.0f, 2.0f));
        TEST_OP("matrix::Vector2f = matrix::Vector2f", v = v1);
        TEST_OP("matrix::Vector2f + matrix::Vector2f", v + v1);
        TEST_OP("matrix::Vector2f - matrix::Vector2f", v - v1);
        TEST_OP("matrix::Vector2f += matrix::Vector2f", v += v1);
        TEST_OP("matrix::Vector2f -= matrix::Vector2f", v -= v1);
        TEST_OP("matrix::Vector2f * matrix::Vector2f", v * v1);
        TEST_OP("matrix::Vector2f %% matrix::Vector2f", v1 % v2);
    }
    return true;
}

bool MathlibTest::testVector3()
{

    {
        matrix::Vector3f v;
        matrix::Vector3f v1(1.0f, 2.0f, 0.0f);
        matrix::Vector3f v2(1.0f, -1.0f, 2.0f);
        float data[3] = {1.0f, 2.0f, 3.0f};
        TEST_OP("Constructor matrix::Vector3f()", matrix::Vector3f v3);
        TEST_OP("Constructor matrix::Vector3f(matrix::Vector3f)", matrix::Vector3f v3(v1); ut_assert_true(v3 == v1); v3.zero());
        TEST_OP("Constructor matrix::Vector3f(float[])", matrix::Vector3f v3(data));
        TEST_OP("Constructor matrix::Vector3f(float, float, float)", matrix::Vector3f v3(1.0f, 2.0f, 3.0f));
        TEST_OP("matrix::Vector3f = matrix::Vector3f", v = v1);
        TEST_OP("matrix::Vector3f + matrix::Vector3f", v + v1);
        TEST_OP("matrix::Vector3f - matrix::Vector3f", v - v1);
        TEST_OP("matrix::Vector3f += matrix::Vector3f", v += v1);
        TEST_OP("matrix::Vector3f -= matrix::Vector3f", v -= v1);
        TEST_OP("matrix::Vector3f * float", v1 * 2.0f);
        TEST_OP("matrix::Vector3f / float", v1 / 2.0f);
        TEST_OP("matrix::Vector3f *= float", v1 *= 2.0f);
        TEST_OP("matrix::Vector3f /= float", v1 /= 2.0f);
        TEST_OP("matrix::Vector3f * matrix::Vector3f", v * v1);
        TEST_OP("matrix::Vector3f %% matrix::Vector3f", v1 % v2);
        TEST_OP("matrix::Vector3f length", v1.length());
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-variable"
        // Need pragma here instead of moving variable out of TEST_OP and just reference because
        // TEST_OP measures performance of vector operations.
        TEST_OP("matrix::Vector3f element read", volatile float a = v1(0));
#pragma GCC diagnostic pop
        TEST_OP("matrix::Vector3f element write", v1(0) = 1.0f);
    }
    return true;
}

bool MathlibTest::testMatrix3x3()
{
    {
        matrix::Matrix3f m1;
        m1.identity();
        matrix::Matrix3f m2;
        m2.identity();
        matrix::Vector3f v1(1.0f, 2.0f, 0.0f);
        TEST_OP("matrix::Matrix3f * matrix::Vector3f", m1 * v1);
        TEST_OP("matrix::Matrix3f + matrix::Matrix3f", m1 + m2);
        TEST_OP("matrix::Matrix3f * matrix::Matrix3f", m1 * m2);
    }
    return true;
}

bool MathlibTest::testMatrixNonsymmetric()
{
    int rc = true;
    {
        //PX4_INFO("Nonsymmetric matrix operations test");
        // test nonsymmetric +, -, +=, -=

        float data1[2][3] = {{1, 2, 3}, {4, 5, 6}};
        float data2[2][3] = {{2, 4, 6}, {8, 10, 12}};
        float data3[2][3] = {{3, 6, 9}, {12, 15, 18}};

        matrix::Matrix<float, 2, 3> m1(data1);
        matrix::Matrix<float, 2, 3> m2(data2);
        matrix::Matrix<float, 2, 3> m3(data3);

        if (m1 + m2 != m3) {
            PX4_ERR("matrix::Matrix<float, 2, 3> + matrix::Matrix<float, 2, 3> failed!");
            (m1 + m2).print();
            printf("!=\n");
            m3.print();
            rc = false;
        }

        ut_assert("m1 + m2 == m3", m1 + m2 == m3);

        if (m3 - m2 != m1) {
            PX4_ERR("matrix::Matrix<float, 2, 3> - matrix::Matrix<float, 2, 3> failed!");
            (m3 - m2).print();
            printf("!=\n");
            m1.print();
            rc = false;
        }

        ut_assert("m3 - m2 == m1", m3 - m2 == m1);

        m1 += m2;

        if (m1 != m3) {
            PX4_ERR("matrix::Matrix<float, 2, 3> += matrix::Matrix<float, 2, 3> failed!");
            m1.print();
            printf("!=\n");
            m3.print();
            rc = false;
        }

        ut_assert("m1 == m3", m1 == m3);

        m1 -= m2;
        matrix::Matrix<float, 2, 3> m1_orig(data1);

        if (m1 != m1_orig) {
            PX4_ERR("matrix::Matrix<float, 2, 3> -= matrix::Matrix<float, 2, 3> failed!");
            m1.print();
            printf("!=\n");
            m1_orig.print();
            rc = false;
        }

        ut_assert("m1 == m1_orig", m1 == m1_orig);

    }
    return rc;
}

bool MathlibTest::testRotationMatrixQuaternion()
{
    // test conversion rotation matrix to quaternion and back
    matrix::Dcmf R_orig;
    matrix::Dcmf R;
    matrix::Quatf q;
    float diff = 0.2f;
    float tol = 0.00001f;

    //PX4_INFO("Quaternion transformation methods test.");

    for (float roll = -M_PI_F; roll <= M_PI_F; roll += diff) {
        for (float pitch = -M_PI_2_F; pitch <= M_PI_2_F; pitch += diff) {
            for (float yaw = -M_PI_F; yaw <= M_PI_F; yaw += diff) {
                R_orig = matrix::Eulerf(roll, pitch, yaw);
                q = R_orig;
                R = q;

                for (int i = 0; i < 3; i++) {
                    for (int j = 0; j < 3; j++) {
                        ut_assert("matrix::Quatf method 'from_dcm' or 'to_dcm' outside tolerance!", fabsf(R_orig(i, j) - R(i, j)) < tol);
                    }
                }
            }
        }
    }

    return true;
}


bool MathlibTest::testQuaternionfrom_dcm()
{
    // test against some known values
    float tol = 0.0001f;
    matrix::Quatf q_true = {1.0f, 0.0f, 0.0f, 0.0f};

    matrix::Matrix3f R_orig;
    R_orig.identity();

    matrix::Quatf q;
    q.from_dcm(R_orig);

    for (unsigned i = 0; i < 4; i++) {
        ut_assert("matrix::Quatf method 'from_dcm()' outside tolerance!", fabsf(q(i) - q_true(i)) < tol);
    }

    return true;
}

bool MathlibTest::testQuaternionfrom_euler()
{
    float tol = 0.0001f;
    matrix::Quatf q_true = {1.0f, 0.0f, 0.0f, 0.0f};

    matrix::Matrix3f R_orig;
    R_orig.identity();

    matrix::Quatf q;
    q.from_dcm(R_orig);

    q_true = matrix::Eulerf(0.3f, 0.2f, 0.1f);
    q = {0.9833f, 0.1436f, 0.1060f, 0.0343f};

    for (unsigned i = 0; i < 4; i++) {
        ut_assert("matrix::Quatf method 'from_euler()' outside tolerance!", fabsf(q(i) - q_true(i)) < tol);
    }

    q_true = matrix::Eulerf(-1.5f, -0.2f, 0.5f);
    q = {0.7222f, -0.6391f, -0.2386f, 0.1142f};

    for (unsigned i = 0; i < 4; i++) {
        ut_assert("matrix::Quatf method 'from_euler()' outside tolerance!", fabsf(q(i) - q_true(i)) < tol);
    }

    q_true = matrix::Eulerf(M_PI_2_F, -M_PI_2_F, -M_PI_F / 3);
    q = {0.6830f, 0.1830f, -0.6830f, 0.1830f};

    for (unsigned i = 0; i < 4; i++) {
        ut_assert("matrix::Quatf method 'from_euler()' outside tolerance!", fabsf(q(i) - q_true(i)) < tol);
    }

    return true;
}

bool MathlibTest::testQuaternionRotate()
{
    // test quaternion method "rotate" (rotate vector by quaternion)
    matrix::Vector3f vector = {1.0f, 1.0f, 1.0f};
    matrix::Vector3f vector_q;
    matrix::Vector3f vector_r;
    matrix::Quatf q;
    matrix::Dcmf R;
    float diff = 0.2f;
    float tol = 0.00001f;

    //PX4_INFO("matrix::Quatf vector rotation method test.");

    for (float roll = -M_PI_F; roll <= M_PI_F; roll += diff) {
        for (float pitch = -M_PI_2_F; pitch <= M_PI_2_F; pitch += diff) {
            for (float yaw = -M_PI_F; yaw <= M_PI_F; yaw += diff) {
                R = matrix::Eulerf(roll, pitch, yaw);
                q = matrix::Eulerf(roll, pitch, yaw);
                vector_r = R * vector;
                vector_q = q.conjugate(vector);

                for (int i = 0; i < 3; i++) {
                    ut_assert("matrix::Quatf method 'rotate' outside tolerance", fabsf(vector_r(i) - vector_q(i)) < tol);
                }
            }
        }
    }


    // test some values calculated with matlab
    tol = 0.0001f;
    q = matrix::Eulerf(M_PI_2_F, 0.0f, 0.0f);
    vector_q = q.conjugate(vector);
    matrix::Vector3f vector_true = {1.00f, -1.00f, 1.00f};

    for (unsigned i = 0; i < 3; i++) {
        ut_assert("matrix::Quatf method 'rotate' outside tolerance", fabsf(vector_true(i) - vector_q(i)) < tol);
    }

    q = matrix::Eulerf(0.3f, 0.2f, 0.1f);
    vector_q = q.conjugate(vector);
    vector_true = {1.1566, 0.7792, 1.0273};

    for (unsigned i = 0; i < 3; i++) {
        ut_assert("matrix::Quatf method 'rotate' outside tolerance", fabsf(vector_true(i) - vector_q(i)) < tol);
    }

    q = matrix::Eulerf(-1.5f, -0.2f, 0.5f);
    vector_q = q.conjugate(vector);
    vector_true = {0.5095, 1.4956, -0.7096};

    for (unsigned i = 0; i < 3; i++) {
        ut_assert("matrix::Quatf method 'rotate' outside tolerance", fabsf(vector_true(i) - vector_q(i)) < tol);
    }

    q = matrix::Eulerf(M_PI_2_F, -M_PI_2_F, -M_PI_F / 3.0f);
    vector_q = q.conjugate(vector);
    vector_true = { -1.3660, 0.3660, 1.0000};

    for (unsigned i = 0; i < 3; i++) {
        ut_assert("matrix::Quatf method 'rotate' outside tolerance", fabsf(vector_true(i) - vector_q(i)) < tol);
    }

    return true;
}

bool MathlibTest::testFinite()
{
    ut_assert("PX4_ISFINITE(0.0f)", PX4_ISFINITE(0.0f) == true);
    ut_assert("PX4_ISFINITE(-0.0f)", PX4_ISFINITE(-0.0f) == true);
    ut_assert("PX4_ISFINITE(1.0f)", PX4_ISFINITE(1.0f) == true);
    ut_assert("PX4_ISFINITE(-1.0f)", PX4_ISFINITE(-1.0f) == true);

    ut_assert("PX4_ISFINITE(NAN)", PX4_ISFINITE(NAN) == false);
    ut_assert("PX4_ISFINITE(1/0)", PX4_ISFINITE(1.0f / 0.0f) == false);
    ut_assert("PX4_ISFINITE(0/0)", PX4_ISFINITE(0.0f / 0.0f) == false);
    ut_assert("PX4_ISFINITE(INFINITY)", PX4_ISFINITE(INFINITY) == false);
    ut_assert("PX4_ISFINITE(NAN * INFINITY)", PX4_ISFINITE(NAN * INFINITY) == false);
    ut_assert("PX4_ISFINITE(NAN * 1.0f)", PX4_ISFINITE(NAN * 1.0f) == false);
    ut_assert("PX4_ISFINITE(INFINITY * 2.0f)", PX4_ISFINITE(INFINITY * 2.0f) == false);

    return true;
}

bool MathlibTest::run_tests()
{
    ut_run_test(testVector2);
    ut_run_test(testVector3);
    ut_run_test(testMatrix3x3);
    ut_run_test(testMatrixNonsymmetric);
    ut_run_test(testRotationMatrixQuaternion);
    ut_run_test(testQuaternionfrom_dcm);
    ut_run_test(testQuaternionfrom_euler);
    ut_run_test(testQuaternionRotate);
    ut_run_test(testFinite);

    return (_tests_failed == 0);
}

ut_declare_test_c(test_mathlib, MathlibTest)