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103 lines
3.6 KiB
C++
103 lines
3.6 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#include "main.h"
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#include <Eigen/SVD>
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template<typename MatrixType> void svd(const MatrixType& m)
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{
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/* this test covers the following files:
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SVD.h
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*/
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int rows = m.rows();
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int cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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MatrixType a = MatrixType::Random(rows,cols);
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Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> b =
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Matrix<Scalar, MatrixType::RowsAtCompileTime, 1>::Random(rows,1);
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Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> x(cols,1), x2(cols,1);
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RealScalar largerEps = test_precision<RealScalar>();
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if (ei_is_same_type<RealScalar,float>::ret)
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largerEps = 1e-3f;
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{
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SVD<MatrixType> svd(a);
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MatrixType sigma = MatrixType::Zero(rows,cols);
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MatrixType matU = MatrixType::Zero(rows,rows);
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sigma.block(0,0,cols,cols) = svd.singularValues().asDiagonal();
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matU.block(0,0,rows,cols) = svd.matrixU();
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VERIFY_IS_APPROX(a, matU * sigma * svd.matrixV().transpose());
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}
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if (rows==cols)
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{
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if (ei_is_same_type<RealScalar,float>::ret)
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{
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MatrixType a1 = MatrixType::Random(rows,cols);
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a += a * a.adjoint() + a1 * a1.adjoint();
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}
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SVD<MatrixType> svd(a);
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svd.solve(b, &x);
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VERIFY_IS_APPROX(a * x,b);
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}
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if(rows==cols)
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{
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SVD<MatrixType> svd(a);
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MatrixType unitary, positive;
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svd.computeUnitaryPositive(&unitary, &positive);
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VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
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VERIFY_IS_APPROX(positive, positive.adjoint());
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for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
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VERIFY_IS_APPROX(unitary*positive, a);
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svd.computePositiveUnitary(&positive, &unitary);
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VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
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VERIFY_IS_APPROX(positive, positive.adjoint());
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for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
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VERIFY_IS_APPROX(positive*unitary, a);
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}
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}
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void test_eigen2_svd()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( svd(Matrix3f()) );
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CALL_SUBTEST_2( svd(Matrix4d()) );
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CALL_SUBTEST_3( svd(MatrixXf(7,7)) );
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CALL_SUBTEST_4( svd(MatrixXd(14,7)) );
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// complex are not implemented yet
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// CALL_SUBTEST( svd(MatrixXcd(6,6)) );
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// CALL_SUBTEST( svd(MatrixXcf(3,3)) );
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SVD<MatrixXf> s;
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MatrixXf m = MatrixXf::Random(10,1);
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s.compute(m);
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}
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}
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