2014-09-19 21:25:48 +08:00
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef SVD_DEFAULT
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#error a macro SVD_DEFAULT(MatrixType) must be defined prior to including svd_common.h
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#endif
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#ifndef SVD_FOR_MIN_NORM
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#error a macro SVD_FOR_MIN_NORM(MatrixType) must be defined prior to including svd_common.h
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#endif
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2015-05-07 21:54:07 +08:00
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#include "svd_fill.h"
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2019-01-17 08:17:39 +08:00
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#include "solverbase.h"
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2015-05-07 21:54:07 +08:00
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2014-09-19 21:25:48 +08:00
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// Check that the matrix m is properly reconstructed and that the U and V factors are unitary
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// The SVD must have already been computed.
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template<typename SvdType, typename MatrixType>
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void svd_check_full(const MatrixType& m, const SvdType& svd)
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{
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Index rows = m.rows();
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Index cols = m.cols();
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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = MatrixType::ColsAtCompileTime
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};
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typedef typename MatrixType::Scalar Scalar;
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2015-06-23 21:05:20 +08:00
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typedef typename MatrixType::RealScalar RealScalar;
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2014-09-19 21:25:48 +08:00
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typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
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typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
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MatrixType sigma = MatrixType::Zero(rows,cols);
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sigma.diagonal() = svd.singularValues().template cast<Scalar>();
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MatrixUType u = svd.matrixU();
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MatrixVType v = svd.matrixV();
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2015-06-23 21:05:20 +08:00
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RealScalar scaling = m.cwiseAbs().maxCoeff();
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2016-07-12 23:19:26 +08:00
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if(scaling<(std::numeric_limits<RealScalar>::min)())
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{
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VERIFY(sigma.cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
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}
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else
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{
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VERIFY_IS_APPROX(m/scaling, u * (sigma/scaling) * v.adjoint());
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}
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2014-09-19 21:25:48 +08:00
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VERIFY_IS_UNITARY(u);
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VERIFY_IS_UNITARY(v);
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}
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// Compare partial SVD defined by computationOptions to a full SVD referenceSvd
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template<typename SvdType, typename MatrixType>
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void svd_compare_to_full(const MatrixType& m,
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unsigned int computationOptions,
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const SvdType& referenceSvd)
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{
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2015-03-27 17:55:53 +08:00
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typedef typename MatrixType::RealScalar RealScalar;
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2014-09-19 21:25:48 +08:00
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Index rows = m.rows();
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Index cols = m.cols();
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Index diagSize = (std::min)(rows, cols);
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2015-03-27 17:55:53 +08:00
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RealScalar prec = test_precision<RealScalar>();
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2014-09-19 21:25:48 +08:00
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SvdType svd(m, computationOptions);
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VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
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2015-03-27 17:55:53 +08:00
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if(computationOptions & (ComputeFullV|ComputeThinV))
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{
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2015-03-27 19:07:14 +08:00
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VERIFY( (svd.matrixV().adjoint()*svd.matrixV()).isIdentity(prec) );
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VERIFY_IS_APPROX( svd.matrixV().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint(),
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referenceSvd.matrixV().leftCols(diagSize) * referenceSvd.singularValues().asDiagonal() * referenceSvd.matrixV().leftCols(diagSize).adjoint());
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2015-03-27 17:55:53 +08:00
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}
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if(computationOptions & (ComputeFullU|ComputeThinU))
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{
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2015-03-27 19:07:14 +08:00
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VERIFY( (svd.matrixU().adjoint()*svd.matrixU()).isIdentity(prec) );
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VERIFY_IS_APPROX( svd.matrixU().leftCols(diagSize) * svd.singularValues().cwiseAbs2().asDiagonal() * svd.matrixU().leftCols(diagSize).adjoint(),
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referenceSvd.matrixU().leftCols(diagSize) * referenceSvd.singularValues().cwiseAbs2().asDiagonal() * referenceSvd.matrixU().leftCols(diagSize).adjoint());
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2015-03-27 17:55:53 +08:00
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}
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// The following checks are not critical.
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// For instance, with Dived&Conquer SVD, if only the factor 'V' is computedt then different matrix-matrix product implementation will be used
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// and the resulting 'V' factor might be significantly different when the SVD decomposition is not unique, especially with single precision float.
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++g_test_level;
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2014-09-19 21:25:48 +08:00
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if(computationOptions & ComputeFullU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
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if(computationOptions & ComputeThinU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
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2015-03-27 17:55:53 +08:00
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if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(svd.matrixV().cwiseAbs(), referenceSvd.matrixV().cwiseAbs());
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2014-09-19 21:25:48 +08:00
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if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
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2015-03-27 17:55:53 +08:00
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--g_test_level;
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2014-09-19 21:25:48 +08:00
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}
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//
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template<typename SvdType, typename MatrixType>
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void svd_least_square(const MatrixType& m, unsigned int computationOptions)
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{
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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Index rows = m.rows();
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Index cols = m.cols();
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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = MatrixType::ColsAtCompileTime
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};
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typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
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typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
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RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
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SvdType svd(m, computationOptions);
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if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
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2015-03-27 17:55:53 +08:00
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else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(2e-4);
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2014-09-19 21:25:48 +08:00
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SolutionType x = svd.solve(rhs);
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2015-03-27 17:55:53 +08:00
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2014-09-19 21:25:48 +08:00
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RealScalar residual = (m*x-rhs).norm();
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2015-03-27 17:55:53 +08:00
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RealScalar rhs_norm = rhs.norm();
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2014-09-19 21:25:48 +08:00
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if(!test_isMuchSmallerThan(residual,rhs.norm()))
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{
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2014-10-15 22:32:16 +08:00
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// ^^^ If the residual is very small, then we have an exact solution, so we are already good.
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2015-03-27 17:55:53 +08:00
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// evaluate normal equation which works also for least-squares solutions
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if(internal::is_same<RealScalar,double>::value || svd.rank()==m.diagonal().size())
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{
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using std::sqrt;
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// This test is not stable with single precision.
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// This is probably because squaring m signicantly affects the precision.
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if(internal::is_same<RealScalar,float>::value) ++g_test_level;
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VERIFY_IS_APPROX(m.adjoint()*(m*x),m.adjoint()*rhs);
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if(internal::is_same<RealScalar,float>::value) --g_test_level;
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}
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// Check that there is no significantly better solution in the neighborhood of x
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2014-10-15 22:32:16 +08:00
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for(Index k=0;k<x.rows();++k)
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2014-09-19 21:25:48 +08:00
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{
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2015-03-27 17:55:53 +08:00
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using std::abs;
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2014-09-19 21:25:48 +08:00
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SolutionType y(x);
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2016-05-05 19:35:45 +08:00
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y.row(k) = (RealScalar(1)+2*NumTraits<RealScalar>::epsilon())*x.row(k);
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2014-09-19 21:25:48 +08:00
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RealScalar residual_y = (m*y-rhs).norm();
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2015-03-27 17:55:53 +08:00
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VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );
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if(internal::is_same<RealScalar,float>::value) ++g_test_level;
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2014-09-19 21:25:48 +08:00
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VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
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2015-03-27 17:55:53 +08:00
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if(internal::is_same<RealScalar,float>::value) --g_test_level;
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2014-09-19 21:25:48 +08:00
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2016-05-05 19:35:45 +08:00
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y.row(k) = (RealScalar(1)-2*NumTraits<RealScalar>::epsilon())*x.row(k);
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2014-09-19 21:25:48 +08:00
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residual_y = (m*y-rhs).norm();
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2015-03-27 17:55:53 +08:00
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VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );
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if(internal::is_same<RealScalar,float>::value) ++g_test_level;
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2014-09-19 21:25:48 +08:00
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VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
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2015-03-27 17:55:53 +08:00
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if(internal::is_same<RealScalar,float>::value) --g_test_level;
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2014-09-19 21:25:48 +08:00
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}
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}
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}
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// check minimal norm solutions, the inoput matrix m is only used to recover problem size
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template<typename MatrixType>
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void svd_min_norm(const MatrixType& m, unsigned int computationOptions)
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{
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typedef typename MatrixType::Scalar Scalar;
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Index cols = m.cols();
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enum {
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ColsAtCompileTime = MatrixType::ColsAtCompileTime
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};
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typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
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// generate a full-rank m x n problem with m<n
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enum {
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RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,
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RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1
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};
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typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;
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typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;
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typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;
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Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);
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MatrixType2 m2(rank,cols);
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int guard = 0;
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do {
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m2.setRandom();
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} while(SVD_FOR_MIN_NORM(MatrixType2)(m2).setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);
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VERIFY(guard<10);
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2014-10-10 05:29:01 +08:00
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2014-09-19 21:25:48 +08:00
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RhsType2 rhs2 = RhsType2::Random(rank);
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// use QR to find a reference minimal norm solution
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HouseholderQR<MatrixType2T> qr(m2.adjoint());
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Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);
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tmp.conservativeResize(cols);
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tmp.tail(cols-rank).setZero();
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SolutionType x21 = qr.householderQ() * tmp;
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// now check with SVD
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SVD_FOR_MIN_NORM(MatrixType2) svd2(m2, computationOptions);
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SolutionType x22 = svd2.solve(rhs2);
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VERIFY_IS_APPROX(m2*x21, rhs2);
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VERIFY_IS_APPROX(m2*x22, rhs2);
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VERIFY_IS_APPROX(x21, x22);
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2014-10-10 05:29:01 +08:00
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2014-09-19 21:25:48 +08:00
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// Now check with a rank deficient matrix
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typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;
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typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;
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Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);
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Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);
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MatrixType3 m3 = C * m2;
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RhsType3 rhs3 = C * rhs2;
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SVD_FOR_MIN_NORM(MatrixType3) svd3(m3, computationOptions);
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SolutionType x3 = svd3.solve(rhs3);
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VERIFY_IS_APPROX(m3*x3, rhs3);
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VERIFY_IS_APPROX(m3*x21, rhs3);
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VERIFY_IS_APPROX(m2*x3, rhs2);
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VERIFY_IS_APPROX(x21, x3);
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}
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2019-01-17 08:17:39 +08:00
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template<typename MatrixType, typename SolverType>
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void svd_test_solvers(const MatrixType& m, const SolverType& solver) {
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Index rows, cols, cols2;
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rows = m.rows();
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cols = m.cols();
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if(MatrixType::ColsAtCompileTime==Dynamic)
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{
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cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
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}
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else
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{
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cols2 = cols;
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}
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typedef Matrix<typename MatrixType::Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> CMatrixType;
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check_solverbase<CMatrixType, MatrixType>(m, solver, rows, cols, cols2);
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}
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2014-09-19 21:25:48 +08:00
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// Check full, compare_to_full, least_square, and min_norm for all possible compute-options
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template<typename SvdType, typename MatrixType>
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void svd_test_all_computation_options(const MatrixType& m, bool full_only)
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{
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// if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
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// return;
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2019-01-17 08:17:39 +08:00
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STATIC_CHECK(( internal::is_same<typename SvdType::StorageIndex,int>::value ));
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2014-09-19 21:25:48 +08:00
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SvdType fullSvd(m, ComputeFullU|ComputeFullV);
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CALL_SUBTEST(( svd_check_full(m, fullSvd) ));
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CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeFullV) ));
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CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeFullV) ));
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#if defined __INTEL_COMPILER
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// remark #111: statement is unreachable
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#pragma warning disable 111
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#endif
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2019-01-17 08:17:39 +08:00
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svd_test_solvers(m, fullSvd);
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2014-09-19 21:25:48 +08:00
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if(full_only)
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return;
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CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU, fullSvd) ));
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CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullV, fullSvd) ));
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CALL_SUBTEST(( svd_compare_to_full(m, 0, fullSvd) ));
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if (MatrixType::ColsAtCompileTime == Dynamic) {
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// thin U/V are only available with dynamic number of columns
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CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));
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CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinV, fullSvd) ));
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CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));
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CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU , fullSvd) ));
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CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));
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CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeThinV) ));
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CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeFullV) ));
|
|
|
|
CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeThinV) ));
|
2014-10-10 05:29:01 +08:00
|
|
|
|
2014-09-19 21:25:48 +08:00
|
|
|
CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeThinV) ));
|
|
|
|
CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeFullV) ));
|
|
|
|
CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeThinV) ));
|
|
|
|
|
|
|
|
// test reconstruction
|
|
|
|
Index diagSize = (std::min)(m.rows(), m.cols());
|
|
|
|
SvdType svd(m, ComputeThinU | ComputeThinV);
|
|
|
|
VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
// work around stupid msvc error when constructing at compile time an expression that involves
|
|
|
|
// a division by zero, even if the numeric type has floating point
|
|
|
|
template<typename Scalar>
|
|
|
|
EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
|
|
|
|
|
|
|
|
// workaround aggressive optimization in ICC
|
|
|
|
template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
|
|
|
|
|
|
|
|
// all this function does is verify we don't iterate infinitely on nan/inf values
|
|
|
|
template<typename SvdType, typename MatrixType>
|
|
|
|
void svd_inf_nan()
|
|
|
|
{
|
|
|
|
SvdType svd;
|
|
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
|
|
Scalar some_inf = Scalar(1) / zero<Scalar>();
|
|
|
|
VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
|
|
|
|
svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
|
|
|
|
|
|
|
|
Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
|
|
|
|
VERIFY(nan != nan);
|
|
|
|
svd.compute(MatrixType::Constant(10,10,nan), ComputeFullU | ComputeFullV);
|
|
|
|
|
|
|
|
MatrixType m = MatrixType::Zero(10,10);
|
|
|
|
m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
|
|
|
|
svd.compute(m, ComputeFullU | ComputeFullV);
|
|
|
|
|
|
|
|
m = MatrixType::Zero(10,10);
|
|
|
|
m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;
|
|
|
|
svd.compute(m, ComputeFullU | ComputeFullV);
|
|
|
|
|
|
|
|
// regression test for bug 791
|
|
|
|
m.resize(3,3);
|
|
|
|
m << 0, 2*NumTraits<Scalar>::epsilon(), 0.5,
|
|
|
|
0, -0.5, 0,
|
|
|
|
nan, 0, 0;
|
|
|
|
svd.compute(m, ComputeFullU | ComputeFullV);
|
|
|
|
|
|
|
|
m.resize(4,4);
|
|
|
|
m << 1, 0, 0, 0,
|
|
|
|
0, 3, 1, 2e-308,
|
|
|
|
1, 0, 1, nan,
|
|
|
|
0, nan, nan, 0;
|
|
|
|
svd.compute(m, ComputeFullU | ComputeFullV);
|
|
|
|
}
|
|
|
|
|
|
|
|
// Regression test for bug 286: JacobiSVD loops indefinitely with some
|
|
|
|
// matrices containing denormal numbers.
|
2015-06-22 15:58:06 +08:00
|
|
|
template<typename>
|
2014-09-19 21:25:48 +08:00
|
|
|
void svd_underoverflow()
|
|
|
|
{
|
|
|
|
#if defined __INTEL_COMPILER
|
|
|
|
// shut up warning #239: floating point underflow
|
|
|
|
#pragma warning push
|
|
|
|
#pragma warning disable 239
|
|
|
|
#endif
|
|
|
|
Matrix2d M;
|
|
|
|
M << -7.90884e-313, -4.94e-324,
|
|
|
|
0, 5.60844e-313;
|
|
|
|
SVD_DEFAULT(Matrix2d) svd;
|
|
|
|
svd.compute(M,ComputeFullU|ComputeFullV);
|
2014-10-07 01:35:57 +08:00
|
|
|
CALL_SUBTEST( svd_check_full(M,svd) );
|
2014-09-19 21:25:48 +08:00
|
|
|
|
|
|
|
// Check all 2x2 matrices made with the following coefficients:
|
|
|
|
VectorXd value_set(9);
|
|
|
|
value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
|
|
|
|
Array4i id(0,0,0,0);
|
|
|
|
int k = 0;
|
|
|
|
do
|
|
|
|
{
|
|
|
|
M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
|
|
|
|
svd.compute(M,ComputeFullU|ComputeFullV);
|
2014-10-07 01:35:57 +08:00
|
|
|
CALL_SUBTEST( svd_check_full(M,svd) );
|
2016-07-12 23:19:26 +08:00
|
|
|
|
2014-09-19 21:25:48 +08:00
|
|
|
id(k)++;
|
|
|
|
if(id(k)>=value_set.size())
|
|
|
|
{
|
|
|
|
while(k<3 && id(k)>=value_set.size()) id(++k)++;
|
|
|
|
id.head(k).setZero();
|
|
|
|
k=0;
|
|
|
|
}
|
2016-07-12 23:19:26 +08:00
|
|
|
|
2014-09-19 21:25:48 +08:00
|
|
|
} while((id<int(value_set.size())).all());
|
|
|
|
|
|
|
|
#if defined __INTEL_COMPILER
|
|
|
|
#pragma warning pop
|
|
|
|
#endif
|
|
|
|
|
|
|
|
// Check for overflow:
|
|
|
|
Matrix3d M3;
|
|
|
|
M3 << 4.4331978442502944e+307, -5.8585363752028680e+307, 6.4527017443412964e+307,
|
|
|
|
3.7841695601406358e+307, 2.4331702789740617e+306, -3.5235707140272905e+307,
|
|
|
|
-8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
|
|
|
|
|
|
|
|
SVD_DEFAULT(Matrix3d) svd3;
|
|
|
|
svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
|
2014-10-07 01:35:57 +08:00
|
|
|
CALL_SUBTEST( svd_check_full(M3,svd3) );
|
2014-09-19 21:25:48 +08:00
|
|
|
}
|
|
|
|
|
|
|
|
// void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
|
|
|
|
|
|
|
|
template<typename MatrixType>
|
|
|
|
void svd_all_trivial_2x2( void (*cb)(const MatrixType&,bool) )
|
|
|
|
{
|
|
|
|
MatrixType M;
|
|
|
|
VectorXd value_set(3);
|
|
|
|
value_set << 0, 1, -1;
|
|
|
|
Array4i id(0,0,0,0);
|
|
|
|
int k = 0;
|
|
|
|
do
|
|
|
|
{
|
|
|
|
M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
|
|
|
|
|
|
|
|
cb(M,false);
|
|
|
|
|
|
|
|
id(k)++;
|
|
|
|
if(id(k)>=value_set.size())
|
|
|
|
{
|
|
|
|
while(k<3 && id(k)>=value_set.size()) id(++k)++;
|
|
|
|
id.head(k).setZero();
|
|
|
|
k=0;
|
|
|
|
}
|
|
|
|
|
|
|
|
} while((id<int(value_set.size())).all());
|
|
|
|
}
|
|
|
|
|
2015-06-22 15:58:06 +08:00
|
|
|
template<typename>
|
2014-09-19 21:25:48 +08:00
|
|
|
void svd_preallocate()
|
|
|
|
{
|
|
|
|
Vector3f v(3.f, 2.f, 1.f);
|
|
|
|
MatrixXf m = v.asDiagonal();
|
|
|
|
|
|
|
|
internal::set_is_malloc_allowed(false);
|
|
|
|
VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
|
|
|
|
SVD_DEFAULT(MatrixXf) svd;
|
|
|
|
internal::set_is_malloc_allowed(true);
|
|
|
|
svd.compute(m);
|
|
|
|
VERIFY_IS_APPROX(svd.singularValues(), v);
|
|
|
|
|
|
|
|
SVD_DEFAULT(MatrixXf) svd2(3,3);
|
|
|
|
internal::set_is_malloc_allowed(false);
|
|
|
|
svd2.compute(m);
|
|
|
|
internal::set_is_malloc_allowed(true);
|
|
|
|
VERIFY_IS_APPROX(svd2.singularValues(), v);
|
|
|
|
VERIFY_RAISES_ASSERT(svd2.matrixU());
|
|
|
|
VERIFY_RAISES_ASSERT(svd2.matrixV());
|
|
|
|
svd2.compute(m, ComputeFullU | ComputeFullV);
|
|
|
|
VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
|
|
|
|
VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
|
|
|
|
internal::set_is_malloc_allowed(false);
|
|
|
|
svd2.compute(m);
|
|
|
|
internal::set_is_malloc_allowed(true);
|
|
|
|
|
|
|
|
SVD_DEFAULT(MatrixXf) svd3(3,3,ComputeFullU|ComputeFullV);
|
|
|
|
internal::set_is_malloc_allowed(false);
|
|
|
|
svd2.compute(m);
|
|
|
|
internal::set_is_malloc_allowed(true);
|
|
|
|
VERIFY_IS_APPROX(svd2.singularValues(), v);
|
|
|
|
VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
|
|
|
|
VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
|
|
|
|
internal::set_is_malloc_allowed(false);
|
|
|
|
svd2.compute(m, ComputeFullU|ComputeFullV);
|
|
|
|
internal::set_is_malloc_allowed(true);
|
|
|
|
}
|
|
|
|
|
|
|
|
template<typename SvdType,typename MatrixType>
|
|
|
|
void svd_verify_assert(const MatrixType& m)
|
|
|
|
{
|
|
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
|
|
Index rows = m.rows();
|
|
|
|
Index cols = m.cols();
|
|
|
|
|
|
|
|
enum {
|
|
|
|
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
|
|
|
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
|
|
|
};
|
|
|
|
|
|
|
|
typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
|
|
|
|
RhsType rhs(rows);
|
|
|
|
SvdType svd;
|
|
|
|
VERIFY_RAISES_ASSERT(svd.matrixU())
|
|
|
|
VERIFY_RAISES_ASSERT(svd.singularValues())
|
|
|
|
VERIFY_RAISES_ASSERT(svd.matrixV())
|
|
|
|
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
2019-01-17 08:17:39 +08:00
|
|
|
VERIFY_RAISES_ASSERT(svd.transpose().solve(rhs))
|
|
|
|
VERIFY_RAISES_ASSERT(svd.adjoint().solve(rhs))
|
2014-09-19 21:25:48 +08:00
|
|
|
MatrixType a = MatrixType::Zero(rows, cols);
|
|
|
|
a.setZero();
|
|
|
|
svd.compute(a, 0);
|
|
|
|
VERIFY_RAISES_ASSERT(svd.matrixU())
|
|
|
|
VERIFY_RAISES_ASSERT(svd.matrixV())
|
|
|
|
svd.singularValues();
|
|
|
|
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
|
|
|
|
|
|
|
if (ColsAtCompileTime == Dynamic)
|
|
|
|
{
|
|
|
|
svd.compute(a, ComputeThinU);
|
|
|
|
svd.matrixU();
|
|
|
|
VERIFY_RAISES_ASSERT(svd.matrixV())
|
|
|
|
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
|
|
|
svd.compute(a, ComputeThinV);
|
|
|
|
svd.matrixV();
|
|
|
|
VERIFY_RAISES_ASSERT(svd.matrixU())
|
|
|
|
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
|
|
|
|
VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
#undef SVD_DEFAULT
|
|
|
|
#undef SVD_FOR_MIN_NORM
|