magnum/src/Magnum/Math/Test/MatrixTest.cpp

/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013 Vladimír Vondruš <mosra@centrum.cz>

    Permission is hereby granted, free of charge, to any person obtaining a
    copy of this software and associated documentation files (the "Software"),
    to deal in the Software without restriction, including without limitation
    the rights to use, copy, modify, merge, publish, distribute, sublicense,
    and/or sell copies of the Software, and to permit persons to whom the
    Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included
    in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
    DEALINGS IN THE SOFTWARE.
*/

#include <sstream>
#include <TestSuite/Tester.h>
#include <Utility/Configuration.h>

#include "Math/Matrix.h"

struct Mat3 {
    float a[9];
};

namespace Magnum { namespace Math {

namespace Implementation {

template<> struct RectangularMatrixConverter<3, 3, float, Mat3> {
    constexpr static RectangularMatrix<3, 3, Float> from(const Mat3& other) {
        return RectangularMatrix<3, 3, Float>(
            Vector<3, Float>(other.a[0], other.a[1], other.a[2]),
            Vector<3, Float>(other.a[3], other.a[4], other.a[5]),
            Vector<3, Float>(other.a[6], other.a[7], other.a[8]));
    }

    constexpr static Mat3 to(const RectangularMatrix<3, 3, Float>& other) {
        return Mat3{{other[0][0], other[0][1], other[0][2],
                     other[1][0], other[1][1], other[1][2],
                     other[2][0], other[2][1], other[2][2]}};
    }
};

}

namespace Test {

class MatrixTest: public Corrade::TestSuite::Tester {
    public:
        MatrixTest();

        void construct();
        void constructIdentity();
        void constructZero();
        void constructConversion();
        void constructCopy();

        void convert();

        void isOrthogonal();

        void trace();
        void ij();
        void determinant();
        void inverted();
        void invertedOrthogonal();

        void subclassTypes();
        void subclass();

        void debug();
        void configuration();
};

typedef Matrix<4, Float> Matrix4x4;
typedef Matrix<4, Int> Matrix4x4i;
typedef Matrix<3, Float> Matrix3x3;
typedef Vector<4, Float> Vector4;
typedef Vector<4, Int> Vector4i;
typedef Vector<3, Float> Vector3;
typedef Math::Constants<Float> Constants;

MatrixTest::MatrixTest() {
    addTests({&MatrixTest::construct,
              &MatrixTest::constructIdentity,
              &MatrixTest::constructZero,
              &MatrixTest::constructConversion,
              &MatrixTest::constructCopy,

              &MatrixTest::convert,

              &MatrixTest::isOrthogonal,

              &MatrixTest::trace,
              &MatrixTest::ij,
              &MatrixTest::determinant,
              &MatrixTest::inverted,
              &MatrixTest::invertedOrthogonal,

              &MatrixTest::subclassTypes,
              &MatrixTest::subclass,

              &MatrixTest::debug,
              &MatrixTest::configuration});
}

void MatrixTest::construct() {
    constexpr Matrix4x4 a = {Vector4(3.0f,  5.0f, 8.0f, -3.0f),
                             Vector4(4.5f,  4.0f, 7.0f,  2.0f),
                             Vector4(1.0f,  2.0f, 3.0f, -1.0f),
                             Vector4(7.9f, -1.0f, 8.0f, -1.5f)};
    CORRADE_COMPARE(a, Matrix4x4(Vector4(3.0f,  5.0f, 8.0f, -3.0f),
                                 Vector4(4.5f,  4.0f, 7.0f,  2.0f),
                                 Vector4(1.0f,  2.0f, 3.0f, -1.0f),
                                 Vector4(7.9f, -1.0f, 8.0f, -1.5f)));
}

void MatrixTest::constructIdentity() {
    constexpr Matrix4x4 identity;
    constexpr Matrix4x4 identity2(Matrix4x4::Identity);
    constexpr Matrix4x4 identity3(Matrix4x4::Identity, 4.0f);

    Matrix4x4 identityExpected(Vector4(1.0f, 0.0f, 0.0f, 0.0f),
                               Vector4(0.0f, 1.0f, 0.0f, 0.0f),
                               Vector4(0.0f, 0.0f, 1.0f, 0.0f),
                               Vector4(0.0f, 0.0f, 0.0f, 1.0f));

    Matrix4x4 identity3Expected(Vector4(4.0f, 0.0f, 0.0f, 0.0f),
                                Vector4(0.0f, 4.0f, 0.0f, 0.0f),
                                Vector4(0.0f, 0.0f, 4.0f, 0.0f),
                                Vector4(0.0f, 0.0f, 0.0f, 4.0f));

    CORRADE_COMPARE(identity, identityExpected);
    CORRADE_COMPARE(identity2, identityExpected);
    CORRADE_COMPARE(identity3, identity3Expected);
}

void MatrixTest::constructZero() {
    constexpr Matrix4x4 a(Matrix4x4::Zero);
    CORRADE_COMPARE(a, Matrix4x4(Vector4(0.0f, 0.0f, 0.0f, 0.0f),
                                 Vector4(0.0f, 0.0f, 0.0f, 0.0f),
                                 Vector4(0.0f, 0.0f, 0.0f, 0.0f),
                                 Vector4(0.0f, 0.0f, 0.0f, 0.0f)));
}

void MatrixTest::constructConversion() {
    constexpr Matrix4x4 a(Vector4(3.0f,  5.0f, 8.0f, -3.0f),
                          Vector4(4.5f,  4.0f, 7.0f,  2.0f),
                          Vector4(1.0f,  2.0f, 3.0f, -1.0f),
                          Vector4(7.9f, -1.0f, 8.0f, -1.5f));
    #ifndef CORRADE_GCC46_COMPATIBILITY
    constexpr /* Not constexpr under GCC < 4.7 */
    #endif
    Matrix4x4i b(a);
    CORRADE_COMPARE(b, Matrix4x4i(Vector4i(3,  5, 8, -3),
                                  Vector4i(4,  4, 7,  2),
                                  Vector4i(1,  2, 3, -1),
                                  Vector4i(7, -1, 8, -1)));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Matrix4x4, Matrix4x4i>::value));
}

void MatrixTest::constructCopy() {
    constexpr RectangularMatrix<4, 4, Float> a(Vector4(3.0f,  5.0f, 8.0f, -3.0f),
                                               Vector4(4.5f,  4.0f, 7.0f,  2.0f),
                                               Vector4(1.0f,  2.0f, 3.0f, -1.0f),
                                               Vector4(7.9f, -1.0f, 8.0f, -1.5f));
    constexpr Matrix4x4 b(a);
    CORRADE_COMPARE(b, Matrix4x4(Vector4(3.0f,  5.0f, 8.0f, -3.0f),
                                 Vector4(4.5f,  4.0f, 7.0f,  2.0f),
                                 Vector4(1.0f,  2.0f, 3.0f, -1.0f),
                                 Vector4(7.9f, -1.0f, 8.0f, -1.5f)));
}

void MatrixTest::convert() {
    constexpr Mat3 a{{1.5f,  2.0f, -3.5f,
                      2.0f, -3.1f,  0.4f,
                      9.5f, -1.5f,  0.1f}};
    constexpr Matrix3x3 b(Vector3(1.5f, 2.0f, -3.5f),
                          Vector3(2.0f, -3.1f,  0.4f),
                          Vector3(9.5f, -1.5f,  0.1f));

    constexpr Matrix3x3 c(b);
    CORRADE_COMPARE(c, b);

    #ifndef CORRADE_GCC46_COMPATIBILITY
    constexpr /* Not constexpr under GCC < 4.7 */
    #endif
    Mat3 d(b);
    for(std::size_t i = 0; i != 9; ++i)
        CORRADE_COMPARE(d.a[i], a.a[i]);

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Mat3, Matrix3x3>::value));
    CORRADE_VERIFY(!(std::is_convertible<Matrix3x3, Mat3>::value));
}

void MatrixTest::isOrthogonal() {
    CORRADE_VERIFY(!Matrix3x3(Vector3(1.0f, 0.0f, 0.0f),
                              Vector3(0.0f, 1.0f, 0.0f),
                              Vector3(0.0f, 0.1f, 1.0f)).isOrthogonal());
    CORRADE_VERIFY(!Matrix3x3(Vector3(1.0f, 0.0f, 0.0f),
                              Vector3(0.0f, 1.0f, 0.0f),
                              Vector3(0.0f, 1.0f, 0.0f)).isOrthogonal());
    CORRADE_VERIFY(Matrix3x3(Vector3(1.0f, 0.0f, 0.0f),
                             Vector3(0.0f, 1.0f, 0.0f),
                             Vector3(0.0f, 0.0f, 1.0f)).isOrthogonal());
}

void MatrixTest::trace() {
    Matrix<5, Int> m(
        Vector<5, Int>(1, 2,   3,  0,  0),
        Vector<5, Int>(2, 3,   2,  1, -2),
        Vector<5, Int>(1, 1, -20,  1,  0),
        Vector<5, Int>(2, 0,   0, 10,  2),
        Vector<5, Int>(3, 1,   0,  1, -2)
    );

    CORRADE_COMPARE(m.trace(), -8);
}

void MatrixTest::ij() {
    Matrix4x4 original(Vector4( 0.0f,  1.0f,  2.0f,  3.0f),
                       Vector4( 4.0f,  5.0f,  6.0f,  7.0f),
                       Vector4( 8.0f,  9.0f, 10.0f, 11.0f),
                       Vector4(12.0f, 13.0f, 14.0f, 15.0f));

    Matrix3x3 skipped(Vector3( 0.0f,  1.0f,  3.0f),
                      Vector3( 8.0f,  9.0f, 11.0f),
                      Vector3(12.0f, 13.0f, 15.0f));

    CORRADE_COMPARE(original.ij(1, 2), skipped);
}

void MatrixTest::determinant() {
    Matrix<5, Int> m(
        Vector<5, Int>(1, 2, 2, 1,  0),
        Vector<5, Int>(2, 3, 2, 1, -2),
        Vector<5, Int>(1, 1, 1, 1,  0),
        Vector<5, Int>(2, 0, 0, 1,  2),
        Vector<5, Int>(3, 1, 0, 1, -2)
    );

    CORRADE_COMPARE(m.determinant(), -2);
}

void MatrixTest::inverted() {
    Matrix4x4 m(Vector4(3.0f,  5.0f, 8.0f, 4.0f),
                Vector4(4.0f,  4.0f, 7.0f, 3.0f),
                Vector4(7.0f, -1.0f, 8.0f, 0.0f),
                Vector4(9.0f,  4.0f, 5.0f, 9.0f));

    Matrix4x4 inverse(Vector4(-60/103.0f,   71/103.0f,  -4/103.0f,  3/103.0f),
                      Vector4(-66/103.0f,  109/103.0f, -25/103.0f, -7/103.0f),
                      Vector4(177/412.0f,  -97/206.0f,  53/412.0f, -7/206.0f),
                      Vector4(259/412.0f, -185/206.0f,  31/412.0f, 27/206.0f));

    Matrix4x4 _inverse = m.inverted();

    CORRADE_COMPARE(_inverse, inverse);
    CORRADE_COMPARE(_inverse*m, Matrix4x4());
}

void MatrixTest::invertedOrthogonal() {
    std::ostringstream o;
    Error::setOutput(&o);

    Matrix3x3 a(Vector3(Constants::sqrt3()/2.0f, 0.5f, 0.0f),
                Vector3(-0.5f, Constants::sqrt3()/2.0f, 0.0f),
                Vector3(0.0f, 0.0f, 1.0f));
    (a*2).invertedOrthogonal();
    CORRADE_COMPARE(o.str(), "Math::Matrix::invertedOrthogonal(): the matrix is not orthogonal\n");

    CORRADE_COMPARE(a.invertedOrthogonal()*a, Matrix3x3());
    CORRADE_COMPARE(a.invertedOrthogonal(), a.inverted());
}

template<class T> class BasicVec2: public Math::Vector<2, T> {
    public:
        template<class ...U> BasicVec2(U&&... args): Math::Vector<2, T>{std::forward<U>(args)...} {}
};

template<class T> class BasicMat2: public Math::Matrix<2, T> {
    public:
        template<class ...U> BasicMat2(U&&... args): Math::Matrix<2, T>{std::forward<U>(args)...} {}

        MAGNUM_MATRIX_SUBCLASS_IMPLEMENTATION(2, BasicMat2, BasicVec2)
};

typedef BasicVec2<Float> Vec2;
typedef BasicMat2<Float> Mat2;

void MatrixTest::subclassTypes() {
    const Mat2 c;
    Mat2 a;
    CORRADE_VERIFY((std::is_same<decltype(c[1]), const Vec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(a[1]), Vec2&>::value));
    CORRADE_VERIFY((std::is_same<decltype(c.row(1)), Vec2>::value));

    const Mat2 c2;
    const Vec2 cv;
    CORRADE_VERIFY((std::is_same<decltype(c*c2), Mat2>::value));
    CORRADE_VERIFY((std::is_same<decltype(c*cv), Vec2>::value));

    CORRADE_VERIFY((std::is_same<decltype(c.transposed()), Mat2>::value));
    CORRADE_VERIFY((std::is_same<decltype(c.diagonal()), Vec2>::value));
    CORRADE_VERIFY((std::is_same<decltype(c.inverted()), Mat2>::value));
    CORRADE_VERIFY((std::is_same<decltype(c.invertedOrthogonal()), Mat2>::value));
}

void MatrixTest::subclass() {
    const Mat2 a(Vec2(2.0f, 3.5f),
                 Vec2(3.0f, 1.0f));
    Mat2 b(Vec2(2.0f, 3.5f),
           Vec2(3.0f, 1.0f));
    CORRADE_COMPARE(a[1], Vec2(3.0f, 1.0f));
    CORRADE_COMPARE(b[1], Vec2(3.0f, 1.0f));
    CORRADE_COMPARE(a.row(1), Vec2(3.5f, 1.0f));

    CORRADE_COMPARE(a*b, Mat2(Vec2(14.5f, 10.5f),
                              Vec2(9.0f, 11.5f)));
    CORRADE_COMPARE(a*Vec2(1.0f, 0.5f), Vec2(3.5f, 4.0f));

    CORRADE_COMPARE(a.transposed(), Mat2(Vec2(2.0f, 3.0f),
                                         Vec2(3.5f, 1.0f)));
    CORRADE_COMPARE(a.diagonal(), Vec2(2.0f, 1.0f));

    Mat2 c(Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f),
           Vec2(-Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f));
    CORRADE_COMPARE(c.inverted(), Mat2(Vec2(Constants::sqrt2()/2.0f, -Constants::sqrt2()/2.0f),
                                       Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f)));
    CORRADE_COMPARE(c.invertedOrthogonal(), Mat2(Vec2(Constants::sqrt2()/2.0f, -Constants::sqrt2()/2.0f),
                                                 Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f)));
}

void MatrixTest::debug() {
    Matrix4x4 m(Vector4(3.0f,  5.0f, 8.0f, 4.0f),
                Vector4(4.0f,  4.0f, 7.0f, 3.0f),
                Vector4(7.0f, -1.0f, 8.0f, 0.0f),
                Vector4(9.0f,  4.0f, 5.0f, 9.0f));

    std::ostringstream o;
    Debug(&o) << m;
    CORRADE_COMPARE(o.str(), "Matrix(3, 4, 7, 9,\n"
                             "       5, 4, -1, 4,\n"
                             "       8, 7, 8, 5,\n"
                             "       4, 3, 0, 9)\n");

    o.str({});
    Debug(&o) << "a" << Matrix4x4() << "b" << Matrix4x4();
    CORRADE_COMPARE(o.str(), "a Matrix(1, 0, 0, 0,\n"
                             "       0, 1, 0, 0,\n"
                             "       0, 0, 1, 0,\n"
                             "       0, 0, 0, 1) b Matrix(1, 0, 0, 0,\n"
                             "       0, 1, 0, 0,\n"
                             "       0, 0, 1, 0,\n"
                             "       0, 0, 0, 1)\n");
}

void MatrixTest::configuration() {
    Corrade::Utility::Configuration c;

    Matrix4x4 m(Vector4(3.0f,  5.0f, 8.0f,   4.0f),
                Vector4(4.0f,  4.0f, 7.0f, 3.125f),
                Vector4(7.0f, -1.0f, 8.0f,   0.0f),
                Vector4(9.0f,  4.0f, 5.0f,  9.55f));
    std::string value("3 4 7 9 5 4 -1 4 8 7 8 5 4 3.125 0 9.55");

    c.setValue("matrix", m);
    CORRADE_COMPARE(c.value("matrix"), value);
    CORRADE_COMPARE(c.value<Matrix4x4>("matrix"), m);
}

}}}

CORRADE_TEST_MAIN(Magnum::Math::Test::MatrixTest)