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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>
//
// 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/SVD>
#include <Eigen/LU>
template<typename MatrixType> void svd(const MatrixType& m)
{
/* this test covers the following files:
SVD.h
*/
int rows = m.rows();
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
MatrixType a = MatrixType::Random(rows,cols);
Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> b =
Matrix<Scalar, MatrixType::RowsAtCompileTime, 1>::Random(rows,1);
Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> x(cols,1), x2(cols,1);
{
SVD<MatrixType> svd(a);
MatrixType sigma = MatrixType::Zero(rows,cols);
MatrixType matU = MatrixType::Zero(rows,rows);
sigma.diagonal() = svd.singularValues();
matU = svd.matrixU();
VERIFY_IS_APPROX(a, matU * sigma * svd.matrixV().transpose());
}
if (rows==cols)
{
if (ei_is_same_type<RealScalar,float>::ret)
{
MatrixType a1 = MatrixType::Random(rows,cols);
a += a * a.adjoint() + a1 * a1.adjoint();
}
SVD<MatrixType> svd(a);
svd.solve(b, &x);
VERIFY_IS_APPROX(a * x,b);
}
if(rows==cols)
{
SVD<MatrixType> svd(a);
MatrixType unitary, positive;
svd.computeUnitaryPositive(&unitary, &positive);
VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
VERIFY_IS_APPROX(positive, positive.adjoint());
for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
VERIFY_IS_APPROX(unitary*positive, a);
svd.computePositiveUnitary(&positive, &unitary);
VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
VERIFY_IS_APPROX(positive, positive.adjoint());
for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
VERIFY_IS_APPROX(positive*unitary, a);
}
}
template<typename MatrixType> void svd_verify_assert()
{
MatrixType tmp;
SVD<MatrixType> svd;
VERIFY_RAISES_ASSERT(svd.solve(tmp, &tmp))
VERIFY_RAISES_ASSERT(svd.matrixU())
VERIFY_RAISES_ASSERT(svd.singularValues())
VERIFY_RAISES_ASSERT(svd.matrixV())
VERIFY_RAISES_ASSERT(svd.computeUnitaryPositive(&tmp,&tmp))
VERIFY_RAISES_ASSERT(svd.computePositiveUnitary(&tmp,&tmp))
VERIFY_RAISES_ASSERT(svd.computeRotationScaling(&tmp,&tmp))
VERIFY_RAISES_ASSERT(svd.computeScalingRotation(&tmp,&tmp))
}
void test_svd()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( svd(Matrix3f()) );
CALL_SUBTEST( svd(Matrix4d()) );
CALL_SUBTEST( svd(MatrixXf(7,7)) );
CALL_SUBTEST( svd(MatrixXd(14,7)) );
// complex are not implemented yet
// CALL_SUBTEST( svd(MatrixXcd(6,6)) );
// CALL_SUBTEST( svd(MatrixXcf(3,3)) );
}
CALL_SUBTEST( svd_verify_assert<Matrix3f>() );
CALL_SUBTEST( svd_verify_assert<Matrix3d>() );
CALL_SUBTEST( svd_verify_assert<MatrixXf>() );
CALL_SUBTEST( svd_verify_assert<MatrixXd>() );
}
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