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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <Eigen/LU>
template<typename MatrixType> void inverse(const MatrixType& m)
{
/* this test covers the following files:
Inverse.h
*/
int rows = m.rows();
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType m1 = MatrixType::Random(rows, cols),
m2(rows, cols),
mzero = MatrixType::Zero(rows, cols),
identity = MatrixType::Identity(rows, rows);
if (ei_is_same_type<RealScalar,float>::ret)
{
// let's build a more stable to inverse matrix
MatrixType a = MatrixType::Random(rows,cols);
m1 += m1 * m1.adjoint() + a * a.adjoint();
}
m2 = m1.inverse();
VERIFY_IS_APPROX(m1, m2.inverse() );
m1.computeInverse(&m2);
VERIFY_IS_APPROX(m1, m2.inverse() );
VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5));
VERIFY_IS_APPROX(identity, m1.inverse() * m1 );
VERIFY_IS_APPROX(identity, m1 * m1.inverse() );
VERIFY_IS_APPROX(m1, m1.inverse().inverse() );
// since for the general case we implement separately row-major and col-major, test that
VERIFY_IS_APPROX(m1.transpose().inverse(), m1.inverse().transpose());
//computeInverseWithCheck tests
//First: an invertible matrix
bool invertible = m1.computeInverseWithCheck(&m2);
VERIFY(invertible);
VERIFY_IS_APPROX(identity, m1*m2);
//Second: a rank one matrix (not invertible, except for 1x1 matrices)
VectorType v3 = VectorType::Random(rows);
MatrixType m3 = v3*v3.transpose(), m4(rows,cols);
invertible = m3.computeInverseWithCheck( &m4 );
VERIFY( rows==1 ? invertible : !invertible );
}
void test_inverse()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( inverse(Matrix<double,1,1>()) );
CALL_SUBTEST( inverse(Matrix2d()) );
CALL_SUBTEST( inverse(Matrix3f()) );
CALL_SUBTEST( inverse(Matrix4f()) );
CALL_SUBTEST( inverse(MatrixXf(8,8)) );
CALL_SUBTEST( inverse(MatrixXcd(7,7)) );
}
// test some tricky cases for 4x4 matrices
VERIFY_IS_APPROX((Matrix4f() << 0,0,1,0, 1,0,0,0, 0,1,0,0, 0,0,0,1).finished().inverse(),
(Matrix4f() << 0,1,0,0, 0,0,1,0, 1,0,0,0, 0,0,0,1).finished());
VERIFY_IS_APPROX((Matrix4f() << 1,0,0,0, 0,0,1,0, 0,0,0,1, 0,1,0,0).finished().inverse(),
(Matrix4f() << 1,0,0,0, 0,0,0,1, 0,1,0,0, 0,0,1,0).finished());
}
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