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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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)
{
typedef typename MatrixType::Index Index;
/* this test covers the following files:
Inverse.h
*/
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType m1(rows, cols),
m2(rows, cols),
mzero = MatrixType::Zero(rows, cols),
identity = MatrixType::Identity(rows, rows);
createRandomPIMatrixOfRank(rows,rows,rows,m1);
m2 = m1.inverse();
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(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose()));
#if !defined(EIGEN_TEST_PART_5) && !defined(EIGEN_TEST_PART_6)
//computeInverseAndDetWithCheck tests
//First: an invertible matrix
bool invertible;
RealScalar det;
m2.setZero();
m1.computeInverseAndDetWithCheck(m2, det, invertible);
VERIFY(invertible);
VERIFY_IS_APPROX(identity, m1*m2);
VERIFY_IS_APPROX(det, m1.determinant());
m2.setZero();
m1.computeInverseWithCheck(m2, invertible);
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);
m3.computeInverseAndDetWithCheck(m4, det, invertible);
VERIFY( rows==1 ? invertible : !invertible );
VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(det-m3.determinant()), RealScalar(1));
m3.computeInverseWithCheck(m4, invertible);
VERIFY( rows==1 ? invertible : !invertible );
#endif
// check in-place inversion
if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4)
{
// in-place is forbidden
VERIFY_RAISES_ASSERT(m1 = m1.inverse());
}
else
{
m2 = m1.inverse();
m1 = m1.inverse();
VERIFY_IS_APPROX(m1,m2);
}
}
void test_inverse()
{
int s;
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( inverse(Matrix<double,1,1>()) );
CALL_SUBTEST_2( inverse(Matrix2d()) );
CALL_SUBTEST_3( inverse(Matrix3f()) );
CALL_SUBTEST_4( inverse(Matrix4f()) );
CALL_SUBTEST_4( inverse(Matrix<float,4,4,DontAlign>()) );
s = internal::random<int>(50,320);
CALL_SUBTEST_5( inverse(MatrixXf(s,s)) );
s = internal::random<int>(25,100);
CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) );
CALL_SUBTEST_7( inverse(Matrix4d()) );
CALL_SUBTEST_7( inverse(Matrix<double,4,4,DontAlign>()) );
}
}
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