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563 lines
21 KiB
C++
563 lines
21 KiB
C++
// 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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#ifndef SVD_STATIC_OPTIONS
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#error a macro SVD_STATIC_OPTIONS(MatrixType, Options) must be defined prior to including svd_common.h
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#endif
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#include "svd_fill.h"
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#include "solverbase.h"
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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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typedef typename MatrixType::RealScalar RealScalar;
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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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RealScalar scaling = m.cwiseAbs().maxCoeff();
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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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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 MatrixType, typename SvdType, int Options>
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void svd_compare_to_full(const MatrixType& m,
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const SvdType& referenceSvd)
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{
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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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Index diagSize = (std::min)(rows, cols);
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RealScalar prec = test_precision<RealScalar>();
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SVD_STATIC_OPTIONS(MatrixType, Options) svd(m);
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VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
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if(Options & (ComputeFullV|ComputeThinV))
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{
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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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}
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if(Options & (ComputeFullU|ComputeThinU))
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{
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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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}
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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 computed 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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if(Options & ComputeFullU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
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if(Options & ComputeThinU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
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if(Options & ComputeFullV) VERIFY_IS_APPROX(svd.matrixV().cwiseAbs(), referenceSvd.matrixV().cwiseAbs());
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if(Options & ComputeThinV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
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--g_test_level;
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}
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template<typename SvdType, typename MatrixType>
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void svd_least_square(const MatrixType& m)
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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);
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if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
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else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(2e-4);
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SolutionType x = svd.solve(rhs);
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RealScalar residual = (m*x-rhs).norm();
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RealScalar rhs_norm = rhs.norm();
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if(!test_isMuchSmallerThan(residual,rhs.norm()))
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{
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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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// 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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for(Index k=0;k<x.rows();++k)
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{
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using std::abs;
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SolutionType y(x);
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y.row(k) = (RealScalar(1)+2*NumTraits<RealScalar>::epsilon())*x.row(k);
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RealScalar residual_y = (m*y-rhs).norm();
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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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VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
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if(internal::is_same<RealScalar,float>::value) --g_test_level;
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y.row(k) = (RealScalar(1)-2*NumTraits<RealScalar>::epsilon())*x.row(k);
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residual_y = (m*y-rhs).norm();
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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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VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
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if(internal::is_same<RealScalar,float>::value) --g_test_level;
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}
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}
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}
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// check minimal norm solutions, the input matrix m is only used to recover problem size
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template<typename MatrixType, int Options>
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void svd_min_norm(const MatrixType& m)
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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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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_STATIC_OPTIONS(MatrixType2, Options) svd2(m2);
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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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// 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_STATIC_OPTIONS(MatrixType3, Options) svd3(m3);
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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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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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// work around stupid msvc error when constructing at compile time an expression that involves
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// a division by zero, even if the numeric type has floating point
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template<typename Scalar>
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EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
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// workaround aggressive optimization in ICC
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template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
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// This function verifies we don't iterate infinitely on nan/inf values,
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// and that info() returns InvalidInput.
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template<typename MatrixType>
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void svd_inf_nan()
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{
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SVD_STATIC_OPTIONS(MatrixType, ComputeFullU | ComputeFullV) svd;
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typedef typename MatrixType::Scalar Scalar;
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Scalar some_inf = Scalar(1) / zero<Scalar>();
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VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
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svd.compute(MatrixType::Constant(10,10,some_inf));
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VERIFY(svd.info() == InvalidInput);
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Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
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VERIFY(nan != nan);
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svd.compute(MatrixType::Constant(10,10,nan));
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VERIFY(svd.info() == InvalidInput);
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MatrixType m = MatrixType::Zero(10,10);
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m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
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svd.compute(m);
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VERIFY(svd.info() == InvalidInput);
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m = MatrixType::Zero(10,10);
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m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;
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svd.compute(m);
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VERIFY(svd.info() == InvalidInput);
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// regression test for bug 791
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m.resize(3,3);
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m << 0, 2*NumTraits<Scalar>::epsilon(), 0.5,
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0, -0.5, 0,
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nan, 0, 0;
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svd.compute(m);
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VERIFY(svd.info() == InvalidInput);
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m.resize(4,4);
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m << 1, 0, 0, 0,
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0, 3, 1, 2e-308,
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1, 0, 1, nan,
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0, nan, nan, 0;
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svd.compute(m);
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VERIFY(svd.info() == InvalidInput);
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}
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// Regression test for bug 286: JacobiSVD loops indefinitely with some
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// matrices containing denormal numbers.
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template<typename>
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void svd_underoverflow()
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{
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#if defined __INTEL_COMPILER
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// shut up warning #239: floating point underflow
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#pragma warning push
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#pragma warning disable 239
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#endif
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Matrix2d M;
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M << -7.90884e-313, -4.94e-324,
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0, 5.60844e-313;
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SVD_STATIC_OPTIONS(Matrix2d, ComputeFullU | ComputeFullV) svd;
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svd.compute(M);
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CALL_SUBTEST( svd_check_full(M,svd) );
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// Check all 2x2 matrices made with the following coefficients:
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VectorXd value_set(9);
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value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
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Array4i id(0,0,0,0);
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int k = 0;
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do
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{
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M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
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svd.compute(M);
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CALL_SUBTEST( svd_check_full(M,svd) );
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id(k)++;
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if(id(k)>=value_set.size())
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{
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while(k<3 && id(k)>=value_set.size()) id(++k)++;
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id.head(k).setZero();
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k=0;
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}
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} while((id<int(value_set.size())).all());
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#if defined __INTEL_COMPILER
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#pragma warning pop
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#endif
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// Check for overflow:
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Matrix3d M3;
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M3 << 4.4331978442502944e+307, -5.8585363752028680e+307, 6.4527017443412964e+307,
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3.7841695601406358e+307, 2.4331702789740617e+306, -3.5235707140272905e+307,
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-8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
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SVD_STATIC_OPTIONS(Matrix3d, ComputeFullU|ComputeFullV) svd3;
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svd3.compute(M3); // just check we don't loop indefinitely
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CALL_SUBTEST( svd_check_full(M3,svd3) );
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}
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template<typename MatrixType>
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void svd_all_trivial_2x2( void (*cb)(const MatrixType&) )
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{
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MatrixType M;
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VectorXd value_set(3);
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value_set << 0, 1, -1;
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Array4i id(0,0,0,0);
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int k = 0;
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do
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{
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M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
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cb(M);
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id(k)++;
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if(id(k)>=value_set.size())
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{
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while(k<3 && id(k)>=value_set.size()) id(++k)++;
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id.head(k).setZero();
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k=0;
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}
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} while((id<int(value_set.size())).all());
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}
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template<typename>
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void svd_preallocate()
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{
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Vector3f v(3.f, 2.f, 1.f);
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MatrixXf m = v.asDiagonal();
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internal::set_is_malloc_allowed(false);
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VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
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SVD_DEFAULT(MatrixXf) svd;
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internal::set_is_malloc_allowed(true);
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svd.compute(m);
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VERIFY_IS_APPROX(svd.singularValues(), v);
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VERIFY_RAISES_ASSERT(svd.matrixU());
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VERIFY_RAISES_ASSERT(svd.matrixV());
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SVD_STATIC_OPTIONS(MatrixXf, ComputeFullU | ComputeFullV) svd2(3,3);
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internal::set_is_malloc_allowed(false);
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svd2.compute(m);
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internal::set_is_malloc_allowed(true);
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VERIFY_IS_APPROX(svd2.singularValues(), v);
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VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
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VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
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internal::set_is_malloc_allowed(false);
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svd2.compute(m);
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internal::set_is_malloc_allowed(true);
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}
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template<typename MatrixType, int QRPreconditioner = 0>
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void svd_verify_assert_full_only(const MatrixType& m = MatrixType())
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{
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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime
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};
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typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, 1> RhsType;
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RhsType rhs = RhsType::Zero(m.rows());
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SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner) svd0;
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VERIFY_RAISES_ASSERT(( svd0.matrixU() ));
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VERIFY_RAISES_ASSERT(( svd0.singularValues() ));
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VERIFY_RAISES_ASSERT(( svd0.matrixV() ));
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VERIFY_RAISES_ASSERT(( svd0.solve(rhs) ));
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VERIFY_RAISES_ASSERT(( svd0.transpose().solve(rhs) ));
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VERIFY_RAISES_ASSERT(( svd0.adjoint().solve(rhs) ));
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SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner) svd1(m);
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VERIFY_RAISES_ASSERT(( svd1.matrixU() ));
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VERIFY_RAISES_ASSERT(( svd1.matrixV() ));
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VERIFY_RAISES_ASSERT(( svd1.solve(rhs)));
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SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU) svdFullU(m);
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VERIFY_RAISES_ASSERT(( svdFullU.matrixV() ));
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|
VERIFY_RAISES_ASSERT(( svdFullU.solve(rhs)));
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SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullV) svdFullV(m);
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VERIFY_RAISES_ASSERT(( svdFullV.matrixU() ));
|
|
VERIFY_RAISES_ASSERT(( svdFullV.solve(rhs)));
|
|
}
|
|
|
|
template<typename MatrixType, int QRPreconditioner = 0>
|
|
void svd_verify_assert(const MatrixType& m = MatrixType())
|
|
{
|
|
enum {
|
|
RowsAtCompileTime = MatrixType::RowsAtCompileTime
|
|
};
|
|
|
|
typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, 1> RhsType;
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RhsType rhs = RhsType::Zero(m.rows());
|
|
|
|
SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeThinU) svdThinU(m);
|
|
VERIFY_RAISES_ASSERT(( svdThinU.matrixV() ));
|
|
VERIFY_RAISES_ASSERT(( svdThinU.solve(rhs)));
|
|
SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeThinV) svdThinV(m);
|
|
VERIFY_RAISES_ASSERT(( svdThinV.matrixU() ));
|
|
VERIFY_RAISES_ASSERT(( svdThinV.solve(rhs)));
|
|
|
|
svd_verify_assert_full_only<MatrixType, QRPreconditioner>(m);
|
|
}
|
|
|
|
template<typename MatrixType, int Options>
|
|
void svd_compute_checks(const MatrixType& m)
|
|
{
|
|
typedef SVD_STATIC_OPTIONS(MatrixType, Options) SVDType;
|
|
|
|
enum {
|
|
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
|
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
|
DiagAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime),
|
|
MatrixURowsAtCompileTime = SVDType::MatrixUType::RowsAtCompileTime,
|
|
MatrixUColsAtCompileTime = SVDType::MatrixUType::ColsAtCompileTime,
|
|
MatrixVRowsAtCompileTime = SVDType::MatrixVType::RowsAtCompileTime,
|
|
MatrixVColsAtCompileTime = SVDType::MatrixVType::ColsAtCompileTime
|
|
};
|
|
|
|
SVDType staticSvd(m);
|
|
|
|
VERIFY(MatrixURowsAtCompileTime == RowsAtCompileTime);
|
|
VERIFY(MatrixVRowsAtCompileTime == ColsAtCompileTime);
|
|
if (Options & ComputeThinU) VERIFY(MatrixUColsAtCompileTime == DiagAtCompileTime);
|
|
if (Options & ComputeFullU) VERIFY(MatrixUColsAtCompileTime == RowsAtCompileTime);
|
|
if (Options & ComputeThinV) VERIFY(MatrixVColsAtCompileTime == DiagAtCompileTime);
|
|
if (Options & ComputeFullV) VERIFY(MatrixVColsAtCompileTime == ColsAtCompileTime);
|
|
|
|
if (Options & (ComputeThinU|ComputeFullU)) VERIFY(staticSvd.computeU());
|
|
else VERIFY(!staticSvd.computeU());
|
|
if (Options & (ComputeThinV|ComputeFullV)) VERIFY(staticSvd.computeV());
|
|
else VERIFY(!staticSvd.computeV());
|
|
|
|
if (staticSvd.computeU()) VERIFY(staticSvd.matrixU().isUnitary());
|
|
if (staticSvd.computeV()) VERIFY(staticSvd.matrixV().isUnitary());
|
|
|
|
if (staticSvd.computeU() && staticSvd.computeV())
|
|
{
|
|
svd_test_solvers(m, staticSvd);
|
|
svd_least_square<SVDType, MatrixType>(m);
|
|
// svd_min_norm generates non-square matrices so it can't be used with NoQRPreconditioner
|
|
if ((Options & internal::QRPreconditionerBits) != NoQRPreconditioner)
|
|
svd_min_norm<MatrixType, Options>(m);
|
|
}
|
|
}
|
|
|
|
template<typename MatrixType, int QRPreconditioner = 0>
|
|
void svd_option_checks(const MatrixType& m)
|
|
{
|
|
// singular values only
|
|
svd_compute_checks<MatrixType, QRPreconditioner>(m);
|
|
// Thin only
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeThinU >(m);
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeThinV >(m);
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeThinU | ComputeThinV>(m);
|
|
// Full only
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU >(m);
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullV >(m);
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV>(m);
|
|
// Mixed
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeThinU | ComputeFullV>(m);
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU | ComputeThinV>(m);
|
|
|
|
typedef SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV) FullSvdType;
|
|
FullSvdType fullSvd(m);
|
|
svd_check_full(m, fullSvd);
|
|
svd_compare_to_full<MatrixType, FullSvdType, QRPreconditioner | ComputeFullU | ComputeFullV>(m, fullSvd);
|
|
}
|
|
|
|
template<typename MatrixType, int QRPreconditioner = 0>
|
|
void svd_option_checks_full_only(const MatrixType& m)
|
|
{
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU>(m);
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullV>(m);
|
|
svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV>(m);
|
|
|
|
SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV) fullSvd(m);
|
|
svd_check_full(m, fullSvd);
|
|
}
|
|
|
|
template<typename MatrixType, int QRPreconditioner = 0>
|
|
void svd_check_max_size_matrix(int initialRows, int initialCols)
|
|
{
|
|
enum {
|
|
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
|
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
|
};
|
|
|
|
int rows = MaxRowsAtCompileTime == Dynamic ? initialRows : (std::min)(initialRows, (int)MaxRowsAtCompileTime);
|
|
int cols = MaxColsAtCompileTime == Dynamic ? initialCols : (std::min)(initialCols, (int)MaxColsAtCompileTime);
|
|
|
|
MatrixType m(rows, cols);
|
|
SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeThinU | ComputeThinV) thinSvd(m);
|
|
SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeThinU | ComputeFullV) mixedSvd1(m);
|
|
SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU | ComputeThinV) mixedSvd2(m);
|
|
SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV) fullSvd(m);
|
|
|
|
MatrixType n(MaxRowsAtCompileTime, MaxColsAtCompileTime);
|
|
thinSvd.compute(n);
|
|
mixedSvd1.compute(n);
|
|
mixedSvd2.compute(n);
|
|
fullSvd.compute(n);
|
|
|
|
MatrixX<typename MatrixType::Scalar> dynamicMatrix(MaxRowsAtCompileTime + 1, MaxColsAtCompileTime + 1);
|
|
|
|
VERIFY_RAISES_ASSERT(thinSvd.compute(dynamicMatrix));
|
|
VERIFY_RAISES_ASSERT(mixedSvd1.compute(dynamicMatrix));
|
|
VERIFY_RAISES_ASSERT(mixedSvd2.compute(dynamicMatrix));
|
|
VERIFY_RAISES_ASSERT(fullSvd.compute(dynamicMatrix));
|
|
}
|
|
|
|
#undef SVD_DEFAULT
|
|
#undef SVD_FOR_MIN_NORM
|
|
#undef SVD_STATIC_OPTIONS
|