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496 lines
18 KiB
C++
496 lines
18 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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// 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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// discard stack allocation as that too bypasses malloc
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#define EIGEN_STACK_ALLOCATION_LIMIT 0
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#define EIGEN_RUNTIME_NO_MALLOC
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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 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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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::RealScalar RealScalar;
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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, internal::random<Index>(1, cols));
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JacobiSVD<MatrixType, QRPreconditioner> svd(m, computationOptions);
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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(1e-4);
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SolutionType x = svd.solve(rhs);
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RealScalar residual = (m*x-rhs).norm();
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// Check that there is no significantly better solution in the neighborhood of x
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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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for(int k=0;k<x.rows();++k)
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{
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SolutionType y(x);
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y.row(k).array() += 2*NumTraits<RealScalar>::epsilon();
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RealScalar residual_y = (m*y-rhs).norm();
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VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
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y.row(k) = x.row(k).array() - 2*NumTraits<RealScalar>::epsilon();
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residual_y = (m*y-rhs).norm();
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VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
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}
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}
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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)
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{
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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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VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
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}
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// check minimal norm solutions
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{
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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(m2.jacobiSvd().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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JacobiSVD<MatrixType2, ColPivHouseholderQRPreconditioner> 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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// 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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JacobiSVD<MatrixType3, ColPivHouseholderQRPreconditioner> 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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}
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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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CALL_SUBTEST(( jacobisvd_check_full(m, fullSvd) ));
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CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(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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if(QRPreconditioner == FullPivHouseholderQRPreconditioner)
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return;
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CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullU, fullSvd) ));
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CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullV, fullSvd) ));
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CALL_SUBTEST(( 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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CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));
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CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinV, fullSvd) ));
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CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));
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CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU , fullSvd) ));
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CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));
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CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeThinV) ));
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CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeFullV) ));
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CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeThinV) ));
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// test reconstruction
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typedef typename MatrixType::Index Index;
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Index diagSize = (std::min)(m.rows(), m.cols());
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JacobiSVD<MatrixType, QRPreconditioner> svd(m, ComputeThinU | ComputeThinV);
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VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
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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 = a;
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if(pickrandom)
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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 typename MatrixType::Index Index;
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Index diagSize = (std::min)(a.rows(), a.cols());
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RealScalar s = std::numeric_limits<RealScalar>::max_exponent10/4;
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s = internal::random<RealScalar>(1,s);
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Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(diagSize);
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for(Index k=0; k<diagSize; ++k)
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d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s));
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m = Matrix<Scalar,Dynamic,Dynamic>::Random(a.rows(),diagSize) * d.asDiagonal() * Matrix<Scalar,Dynamic,Dynamic>::Random(diagSize,a.cols());
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// cancel some coeffs
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Index n = internal::random<Index>(0,m.size()-1);
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for(Index i=0; i<n; ++i)
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m(internal::random<Index>(0,m.rows()-1), internal::random<Index>(0,m.cols()-1)) = Scalar(0);
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}
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CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m) ));
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CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m) ));
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CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m) ));
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CALL_SUBTEST(( 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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// 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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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(sub(some_inf, some_inf) != sub(some_inf, some_inf));
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svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
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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), ComputeFullU | ComputeFullV);
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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, ComputeFullU | ComputeFullV);
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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, ComputeFullU | ComputeFullV);
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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, ComputeFullU | ComputeFullV);
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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, ComputeFullU | ComputeFullV);
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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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void jacobisvd_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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JacobiSVD<Matrix2d> svd;
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svd.compute(M,ComputeFullU|ComputeFullV);
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jacobisvd_check_full(M,svd);
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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,ComputeFullU|ComputeFullV);
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jacobisvd_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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JacobiSVD<Matrix3d> svd3;
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svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
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jacobisvd_check_full(M3,svd3);
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}
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void jacobisvd_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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JacobiSVD<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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JacobiSVD<MatrixXf> 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_RAISES_ASSERT(svd2.matrixU());
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VERIFY_RAISES_ASSERT(svd2.matrixV());
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svd2.compute(m, ComputeFullU | ComputeFullV);
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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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JacobiSVD<MatrixXf> svd3(3,3,ComputeFullU|ComputeFullV);
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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);
|
|
svd2.compute(m, ComputeFullU|ComputeFullV);
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internal::set_is_malloc_allowed(true);
|
|
}
|
|
|
|
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()) ));
|
|
CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) ));
|
|
CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) ));
|
|
|
|
for(int i = 0; i < g_repeat; i++) {
|
|
Matrix2cd m;
|
|
m << 0, 1,
|
|
0, 1;
|
|
CALL_SUBTEST_1(( jacobisvd(m, false) ));
|
|
m << 1, 0,
|
|
1, 0;
|
|
CALL_SUBTEST_1(( jacobisvd(m, false) ));
|
|
|
|
Matrix2d n;
|
|
n << 0, 0,
|
|
0, 0;
|
|
CALL_SUBTEST_2(( jacobisvd(n, false) ));
|
|
n << 0, 0,
|
|
0, 1;
|
|
CALL_SUBTEST_2(( jacobisvd(n, false) ));
|
|
|
|
CALL_SUBTEST_3(( jacobisvd<Matrix3f>() ));
|
|
CALL_SUBTEST_4(( jacobisvd<Matrix4d>() ));
|
|
CALL_SUBTEST_5(( jacobisvd<Matrix<float,3,5> >() ));
|
|
CALL_SUBTEST_6(( jacobisvd<Matrix<double,Dynamic,2> >(Matrix<double,Dynamic,2>(10,2)) ));
|
|
|
|
int r = internal::random<int>(1, 30),
|
|
c = internal::random<int>(1, 30);
|
|
|
|
TEST_SET_BUT_UNUSED_VARIABLE(r)
|
|
TEST_SET_BUT_UNUSED_VARIABLE(c)
|
|
|
|
CALL_SUBTEST_10(( jacobisvd<MatrixXd>(MatrixXd(r,c)) ));
|
|
CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(r,c)) ));
|
|
CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(r,c)) ));
|
|
(void) r;
|
|
(void) c;
|
|
|
|
// Test on inf/nan matrix
|
|
CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() );
|
|
CALL_SUBTEST_10( jacobisvd_inf_nan<MatrixXd>() );
|
|
}
|
|
|
|
CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
|
|
CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3))) ));
|
|
|
|
// test matrixbase method
|
|
CALL_SUBTEST_1(( jacobisvd_method<Matrix2cd>() ));
|
|
CALL_SUBTEST_3(( jacobisvd_method<Matrix3f>() ));
|
|
|
|
// Test problem size constructors
|
|
CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) );
|
|
|
|
// Check that preallocation avoids subsequent mallocs
|
|
CALL_SUBTEST_9( jacobisvd_preallocate() );
|
|
|
|
// Regression check for bug 286
|
|
CALL_SUBTEST_2( jacobisvd_underoverflow() );
|
|
}
|