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291 lines
10 KiB
C++
291 lines
10 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 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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// 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, int QRPreconditioner>
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void jacobisvd_check_full(const MatrixType& m, const JacobiSVD<MatrixType, QRPreconditioner>& svd)
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{
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typedef typename MatrixType::Index Index;
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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 NumTraits<Scalar>::Real 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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typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
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typedef Matrix<Scalar, ColsAtCompileTime, 1> InputVectorType;
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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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VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
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VERIFY_IS_UNITARY(u);
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VERIFY_IS_UNITARY(v);
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}
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template<typename MatrixType, int QRPreconditioner>
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void jacobisvd_compare_to_full(const MatrixType& m,
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unsigned int computationOptions,
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const JacobiSVD<MatrixType, QRPreconditioner>& referenceSvd)
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{
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typedef typename MatrixType::Index Index;
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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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JacobiSVD<MatrixType, QRPreconditioner> svd(m, computationOptions);
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VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
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if(computationOptions & ComputeFullU)
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VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
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if(computationOptions & ComputeThinU)
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VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
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if(computationOptions & ComputeFullV)
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VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
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if(computationOptions & ComputeThinV)
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VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
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}
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template<typename MatrixType, int QRPreconditioner>
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void jacobisvd_solve(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::Index Index;
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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, ei_random<Index>(1, cols));
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JacobiSVD<MatrixType, QRPreconditioner> svd(m, computationOptions);
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SolutionType x = svd.solve(rhs);
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// evaluate normal equation which works also for least-squares solutions
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VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
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}
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template<typename MatrixType, int QRPreconditioner>
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void jacobisvd_test_all_computation_options(const MatrixType& m)
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{
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if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
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return;
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JacobiSVD<MatrixType, QRPreconditioner> fullSvd(m, ComputeFullU|ComputeFullV);
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jacobisvd_check_full(m, fullSvd);
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jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeFullV);
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if(QRPreconditioner == FullPivHouseholderQRPreconditioner)
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return;
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jacobisvd_compare_to_full(m, ComputeFullU, fullSvd);
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jacobisvd_compare_to_full(m, ComputeFullV, fullSvd);
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jacobisvd_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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jacobisvd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd);
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jacobisvd_compare_to_full(m, ComputeThinV, fullSvd);
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jacobisvd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd);
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jacobisvd_compare_to_full(m, ComputeThinU , fullSvd);
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jacobisvd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd);
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jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeThinV);
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jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeFullV);
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jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeThinV);
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}
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}
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template<typename MatrixType>
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void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
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{
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MatrixType m = pickrandom ? MatrixType::Random(a.rows(), a.cols()) : a;
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jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m);
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jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m);
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jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m);
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jacobisvd_test_all_computation_options<MatrixType, NoQRPreconditioner>(m);
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}
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template<typename MatrixType> void jacobisvd_verify_assert(const MatrixType& m)
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{
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::Index Index;
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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, 1> RhsType;
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RhsType rhs(rows);
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JacobiSVD<MatrixType> svd;
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VERIFY_RAISES_ASSERT(svd.matrixU())
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VERIFY_RAISES_ASSERT(svd.singularValues())
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VERIFY_RAISES_ASSERT(svd.matrixV())
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VERIFY_RAISES_ASSERT(svd.solve(rhs))
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MatrixType a = MatrixType::Zero(rows, cols);
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a.setZero();
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svd.compute(a, 0);
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VERIFY_RAISES_ASSERT(svd.matrixU())
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VERIFY_RAISES_ASSERT(svd.matrixV())
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svd.singularValues();
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VERIFY_RAISES_ASSERT(svd.solve(rhs))
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if (ColsAtCompileTime == Dynamic)
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{
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svd.compute(a, ComputeThinU);
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svd.matrixU();
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VERIFY_RAISES_ASSERT(svd.matrixV())
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VERIFY_RAISES_ASSERT(svd.solve(rhs))
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svd.compute(a, ComputeThinV);
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svd.matrixV();
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VERIFY_RAISES_ASSERT(svd.matrixU())
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VERIFY_RAISES_ASSERT(svd.solve(rhs))
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JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> svd_fullqr;
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VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV))
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VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV))
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VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV))
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}
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else
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{
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VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
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VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
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}
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}
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template<typename MatrixType>
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void jacobisvd_method()
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{
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enum { Size = MatrixType::RowsAtCompileTime };
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typedef typename MatrixType::RealScalar RealScalar;
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typedef Matrix<RealScalar, Size, 1> RealVecType;
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MatrixType m = MatrixType::Identity();
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VERIFY_IS_APPROX(m.jacobiSvd().singularValues(), RealVecType::Ones());
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VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixU());
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VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixV());
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VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m);
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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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template<typename MatrixType>
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void jacobisvd_inf_nan()
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{
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// all this function does is verify we don't iterate infinitely on nan/inf values
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JacobiSVD<MatrixType> 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((some_inf - some_inf) != (some_inf - some_inf));
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svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
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Scalar some_nan = zero<Scalar>() / zero<Scalar>();
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VERIFY(some_nan != some_nan);
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svd.compute(MatrixType::Constant(10,10,some_nan), ComputeFullU | ComputeFullV);
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MatrixType m = MatrixType::Zero(10,10);
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m(ei_random<int>(0,9), ei_random<int>(0,9)) = some_inf;
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svd.compute(m, ComputeFullU | ComputeFullV);
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m = MatrixType::Zero(10,10);
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m(ei_random<int>(0,9), ei_random<int>(0,9)) = some_nan;
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svd.compute(m, ComputeFullU | ComputeFullV);
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}
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void test_jacobisvd()
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{
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CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) ));
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CALL_SUBTEST_4(( jacobisvd_verify_assert(Matrix4d()) ));
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CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) ));
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CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) ));
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for(int i = 0; i < g_repeat; i++) {
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Matrix2cd m;
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m << 0, 1,
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0, 1;
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CALL_SUBTEST_1(( jacobisvd(m, false) ));
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m << 1, 0,
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1, 0;
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CALL_SUBTEST_1(( jacobisvd(m, false) ));
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Matrix2d n;
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n << 0, 0,
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0, 0;
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CALL_SUBTEST_2(( jacobisvd(n, false) ));
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n << 0, 0,
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0, 1;
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CALL_SUBTEST_2(( jacobisvd(n, false) ));
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CALL_SUBTEST_3(( jacobisvd<Matrix3f>() ));
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CALL_SUBTEST_4(( jacobisvd<Matrix4d>() ));
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CALL_SUBTEST_5(( jacobisvd<Matrix<float,3,5> >() ));
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CALL_SUBTEST_6(( jacobisvd<Matrix<double,Dynamic,2> >(Matrix<double,Dynamic,2>(10,2)) ));
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int r = ei_random<int>(1, 30),
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c = ei_random<int>(1, 30);
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CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(r,c)) ));
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CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(r,c)) ));
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(void) r;
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(void) c;
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// Test on inf/nan matrix
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CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() );
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}
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CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(ei_random<int>(100, 150), ei_random<int>(100, 150))) ));
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CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(ei_random<int>(80, 100), ei_random<int>(80, 100))) ));
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// test matrixbase method
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CALL_SUBTEST_1(( jacobisvd_method<Matrix2cd>() ));
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CALL_SUBTEST_3(( jacobisvd_method<Matrix3f>() ));
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// Test problem size constructors
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CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) );
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}
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