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Unify unit test for BDC and Jacobi SVD. This reveals some numerical issues in BDCSVD.
This commit is contained in:
Gael Guennebaud
parent
0a18eecab3
commit
03dd4dd91a
@ -1,7 +1,7 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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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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@ -14,273 +14,47 @@
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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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#define SVD_DEFAULT(M) JacobiSVD<M>
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#define SVD_FOR_MIN_NORM(M) JacobiSVD<M,ColPivHouseholderQRPreconditioner>
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#include "svd_common.h"
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// Check all variants of JacobiSVD
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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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svd_fill_random(m);
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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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CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> >(m, true) )); // check full only
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CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner> >(m, false) ));
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CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, HouseholderQRPreconditioner> >(m, false) ));
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if(m.rows()==m.cols())
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CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, NoQRPreconditioner> >(m, false) ));
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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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svd_verify_assert<JacobiSVD<MatrixType> >(m);
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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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@ -296,165 +70,17 @@ void jacobisvd_method()
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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());
|
||||
|
||||
#if defined __INTEL_COMPILER
|
||||
#pragma warning pop
|
||||
#endif
|
||||
|
||||
// Check for overflow:
|
||||
Matrix3d M3;
|
||||
M3 << 4.4331978442502944e+307, -5.8585363752028680e+307, 6.4527017443412964e+307,
|
||||
3.7841695601406358e+307, 2.4331702789740617e+306, -3.5235707140272905e+307,
|
||||
-8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
|
||||
|
||||
JacobiSVD<Matrix3d> svd3;
|
||||
svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
|
||||
jacobisvd_check_full(M3,svd3);
|
||||
}
|
||||
|
||||
void jacobisvd_preallocate()
|
||||
{
|
||||
Vector3f v(3.f, 2.f, 1.f);
|
||||
MatrixXf m = v.asDiagonal();
|
||||
|
||||
internal::set_is_malloc_allowed(false);
|
||||
VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
|
||||
JacobiSVD<MatrixXf> svd;
|
||||
internal::set_is_malloc_allowed(true);
|
||||
svd.compute(m);
|
||||
VERIFY_IS_APPROX(svd.singularValues(), v);
|
||||
|
||||
JacobiSVD<MatrixXf> svd2(3,3);
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
VERIFY_IS_APPROX(svd2.singularValues(), v);
|
||||
VERIFY_RAISES_ASSERT(svd2.matrixU());
|
||||
VERIFY_RAISES_ASSERT(svd2.matrixV());
|
||||
svd2.compute(m, ComputeFullU | ComputeFullV);
|
||||
VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
|
||||
VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
|
||||
JacobiSVD<MatrixXf> svd3(3,3,ComputeFullU|ComputeFullV);
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
VERIFY_IS_APPROX(svd2.singularValues(), v);
|
||||
VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
|
||||
VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m, ComputeFullU|ComputeFullV);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
}
|
||||
|
||||
void test_jacobisvd()
|
||||
{
|
||||
CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) ));
|
||||
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)) ));
|
||||
|
||||
svd_all_trivial_2x2(jacobisvd<Matrix2cd>);
|
||||
svd_all_trivial_2x2(jacobisvd<Matrix2d>);
|
||||
|
||||
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> >() ));
|
||||
@ -473,8 +99,8 @@ void test_jacobisvd()
|
||||
(void) c;
|
||||
|
||||
// Test on inf/nan matrix
|
||||
CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() );
|
||||
CALL_SUBTEST_10( jacobisvd_inf_nan<MatrixXd>() );
|
||||
CALL_SUBTEST_7( (svd_inf_nan<JacobiSVD<MatrixXf>, MatrixXf>()) );
|
||||
CALL_SUBTEST_10( (svd_inf_nan<JacobiSVD<MatrixXd>, 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))) ));
|
||||
@ -488,8 +114,7 @@ void test_jacobisvd()
|
||||
CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) );
|
||||
|
||||
// Check that preallocation avoids subsequent mallocs
|
||||
CALL_SUBTEST_9( jacobisvd_preallocate() );
|
||||
CALL_SUBTEST_9( svd_preallocate() );
|
||||
|
||||
// Regression check for bug 286
|
||||
CALL_SUBTEST_2( jacobisvd_underoverflow() );
|
||||
CALL_SUBTEST_2( svd_underoverflow() );
|
||||
}
|
||||
|
||||
454
test/svd_common.h
Normal file
454
test/svd_common.h
Normal file
@ -0,0 +1,454 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef SVD_DEFAULT
|
||||
#error a macro SVD_DEFAULT(MatrixType) must be defined prior to including svd_common.h
|
||||
#endif
|
||||
|
||||
#ifndef SVD_FOR_MIN_NORM
|
||||
#error a macro SVD_FOR_MIN_NORM(MatrixType) must be defined prior to including svd_common.h
|
||||
#endif
|
||||
|
||||
// Check that the matrix m is properly reconstructed and that the U and V factors are unitary
|
||||
// The SVD must have already been computed.
|
||||
template<typename SvdType, typename MatrixType>
|
||||
void svd_check_full(const MatrixType& m, const SvdType& svd)
|
||||
{
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
|
||||
|
||||
MatrixType sigma = MatrixType::Zero(rows,cols);
|
||||
sigma.diagonal() = svd.singularValues().template cast<Scalar>();
|
||||
MatrixUType u = svd.matrixU();
|
||||
MatrixVType v = svd.matrixV();
|
||||
|
||||
VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
|
||||
VERIFY_IS_UNITARY(u);
|
||||
VERIFY_IS_UNITARY(v);
|
||||
}
|
||||
|
||||
// Compare partial SVD defined by computationOptions to a full SVD referenceSvd
|
||||
template<typename SvdType, typename MatrixType>
|
||||
void svd_compare_to_full(const MatrixType& m,
|
||||
unsigned int computationOptions,
|
||||
const SvdType& referenceSvd)
|
||||
{
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
Index diagSize = (std::min)(rows, cols);
|
||||
|
||||
SvdType svd(m, computationOptions);
|
||||
|
||||
VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
|
||||
if(computationOptions & ComputeFullU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
|
||||
if(computationOptions & ComputeThinU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
|
||||
if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
|
||||
if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
|
||||
}
|
||||
|
||||
//
|
||||
template<typename SvdType, typename MatrixType>
|
||||
void svd_least_square(const MatrixType& m, unsigned int computationOptions)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
|
||||
|
||||
RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
|
||||
SvdType svd(m, computationOptions);
|
||||
|
||||
if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
|
||||
else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(1e-4);
|
||||
|
||||
SolutionType x = svd.solve(rhs);
|
||||
|
||||
RealScalar residual = (m*x-rhs).norm();
|
||||
// Check that there is no significantly better solution in the neighborhood of x
|
||||
if(!test_isMuchSmallerThan(residual,rhs.norm()))
|
||||
{
|
||||
// If the residual is very small, then we have an exact solution, so we are already good.
|
||||
for(int k=0;k<x.rows();++k)
|
||||
{
|
||||
SolutionType y(x);
|
||||
y.row(k).array() += 2*NumTraits<RealScalar>::epsilon();
|
||||
RealScalar residual_y = (m*y-rhs).norm();
|
||||
VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
|
||||
|
||||
y.row(k) = x.row(k).array() - 2*NumTraits<RealScalar>::epsilon();
|
||||
residual_y = (m*y-rhs).norm();
|
||||
VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
|
||||
}
|
||||
}
|
||||
|
||||
// evaluate normal equation which works also for least-squares solutions
|
||||
if(internal::is_same<RealScalar,double>::value)
|
||||
{
|
||||
// This test is not stable with single precision.
|
||||
// This is probably because squaring m signicantly affects the precision.
|
||||
VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
|
||||
}
|
||||
}
|
||||
|
||||
// check minimal norm solutions, the inoput matrix m is only used to recover problem size
|
||||
template<typename MatrixType>
|
||||
void svd_min_norm(const MatrixType& m, unsigned int computationOptions)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index cols = m.cols();
|
||||
|
||||
enum {
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
|
||||
|
||||
// generate a full-rank m x n problem with m<n
|
||||
enum {
|
||||
RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,
|
||||
RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1
|
||||
};
|
||||
typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;
|
||||
typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;
|
||||
Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);
|
||||
MatrixType2 m2(rank,cols);
|
||||
int guard = 0;
|
||||
do {
|
||||
m2.setRandom();
|
||||
} while(SVD_FOR_MIN_NORM(MatrixType2)(m2).setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);
|
||||
VERIFY(guard<10);
|
||||
RhsType2 rhs2 = RhsType2::Random(rank);
|
||||
// use QR to find a reference minimal norm solution
|
||||
HouseholderQR<MatrixType2T> qr(m2.adjoint());
|
||||
Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);
|
||||
tmp.conservativeResize(cols);
|
||||
tmp.tail(cols-rank).setZero();
|
||||
SolutionType x21 = qr.householderQ() * tmp;
|
||||
// now check with SVD
|
||||
SVD_FOR_MIN_NORM(MatrixType2) svd2(m2, computationOptions);
|
||||
SolutionType x22 = svd2.solve(rhs2);
|
||||
VERIFY_IS_APPROX(m2*x21, rhs2);
|
||||
VERIFY_IS_APPROX(m2*x22, rhs2);
|
||||
VERIFY_IS_APPROX(x21, x22);
|
||||
|
||||
// Now check with a rank deficient matrix
|
||||
typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;
|
||||
typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;
|
||||
Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);
|
||||
Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);
|
||||
MatrixType3 m3 = C * m2;
|
||||
RhsType3 rhs3 = C * rhs2;
|
||||
SVD_FOR_MIN_NORM(MatrixType3) svd3(m3, computationOptions);
|
||||
SolutionType x3 = svd3.solve(rhs3);
|
||||
VERIFY_IS_APPROX(m3*x3, rhs3);
|
||||
VERIFY_IS_APPROX(m3*x21, rhs3);
|
||||
VERIFY_IS_APPROX(m2*x3, rhs2);
|
||||
|
||||
VERIFY_IS_APPROX(x21, x3);
|
||||
}
|
||||
|
||||
// Check full, compare_to_full, least_square, and min_norm for all possible compute-options
|
||||
template<typename SvdType, typename MatrixType>
|
||||
void svd_test_all_computation_options(const MatrixType& m, bool full_only)
|
||||
{
|
||||
// if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
|
||||
// return;
|
||||
SvdType fullSvd(m, ComputeFullU|ComputeFullV);
|
||||
CALL_SUBTEST(( svd_check_full(m, fullSvd) ));
|
||||
CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeFullV) ));
|
||||
CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeFullV) ));
|
||||
|
||||
#if defined __INTEL_COMPILER
|
||||
// remark #111: statement is unreachable
|
||||
#pragma warning disable 111
|
||||
#endif
|
||||
if(full_only)
|
||||
return;
|
||||
|
||||
CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU, fullSvd) ));
|
||||
CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullV, fullSvd) ));
|
||||
CALL_SUBTEST(( svd_compare_to_full(m, 0, fullSvd) ));
|
||||
|
||||
if (MatrixType::ColsAtCompileTime == Dynamic) {
|
||||
// thin U/V are only available with dynamic number of columns
|
||||
CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));
|
||||
CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinV, fullSvd) ));
|
||||
CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));
|
||||
CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU , fullSvd) ));
|
||||
CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));
|
||||
|
||||
CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeThinV) ));
|
||||
CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeFullV) ));
|
||||
CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeThinV) ));
|
||||
|
||||
CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeThinV) ));
|
||||
CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeFullV) ));
|
||||
CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeThinV) ));
|
||||
|
||||
// test reconstruction
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index diagSize = (std::min)(m.rows(), m.cols());
|
||||
SvdType svd(m, ComputeThinU | ComputeThinV);
|
||||
VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void svd_fill_random(MatrixType &m)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index diagSize = (std::min)(m.rows(), m.cols());
|
||||
RealScalar s = std::numeric_limits<RealScalar>::max_exponent10/4;
|
||||
s = internal::random<RealScalar>(1,s);
|
||||
Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(diagSize);
|
||||
for(Index k=0; k<diagSize; ++k)
|
||||
d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s));
|
||||
m = Matrix<Scalar,Dynamic,Dynamic>::Random(m.rows(),diagSize) * d.asDiagonal() * Matrix<Scalar,Dynamic,Dynamic>::Random(diagSize,m.cols());
|
||||
// cancel some coeffs
|
||||
Index n = internal::random<Index>(0,m.size()-1);
|
||||
for(Index i=0; i<n; ++i)
|
||||
m(internal::random<Index>(0,m.rows()-1), internal::random<Index>(0,m.cols()-1)) = Scalar(0);
|
||||
}
|
||||
|
||||
|
||||
// work around stupid msvc error when constructing at compile time an expression that involves
|
||||
// a division by zero, even if the numeric type has floating point
|
||||
template<typename Scalar>
|
||||
EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
|
||||
|
||||
// workaround aggressive optimization in ICC
|
||||
template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
|
||||
|
||||
// all this function does is verify we don't iterate infinitely on nan/inf values
|
||||
template<typename SvdType, typename MatrixType>
|
||||
void svd_inf_nan()
|
||||
{
|
||||
SvdType svd;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
Scalar some_inf = Scalar(1) / zero<Scalar>();
|
||||
VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
|
||||
svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
|
||||
|
||||
Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
|
||||
VERIFY(nan != nan);
|
||||
svd.compute(MatrixType::Constant(10,10,nan), ComputeFullU | ComputeFullV);
|
||||
|
||||
MatrixType m = MatrixType::Zero(10,10);
|
||||
m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
|
||||
svd.compute(m, ComputeFullU | ComputeFullV);
|
||||
|
||||
m = MatrixType::Zero(10,10);
|
||||
m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;
|
||||
svd.compute(m, ComputeFullU | ComputeFullV);
|
||||
|
||||
// regression test for bug 791
|
||||
m.resize(3,3);
|
||||
m << 0, 2*NumTraits<Scalar>::epsilon(), 0.5,
|
||||
0, -0.5, 0,
|
||||
nan, 0, 0;
|
||||
svd.compute(m, ComputeFullU | ComputeFullV);
|
||||
|
||||
m.resize(4,4);
|
||||
m << 1, 0, 0, 0,
|
||||
0, 3, 1, 2e-308,
|
||||
1, 0, 1, nan,
|
||||
0, nan, nan, 0;
|
||||
svd.compute(m, ComputeFullU | ComputeFullV);
|
||||
}
|
||||
|
||||
// Regression test for bug 286: JacobiSVD loops indefinitely with some
|
||||
// matrices containing denormal numbers.
|
||||
void svd_underoverflow()
|
||||
{
|
||||
#if defined __INTEL_COMPILER
|
||||
// shut up warning #239: floating point underflow
|
||||
#pragma warning push
|
||||
#pragma warning disable 239
|
||||
#endif
|
||||
Matrix2d M;
|
||||
M << -7.90884e-313, -4.94e-324,
|
||||
0, 5.60844e-313;
|
||||
SVD_DEFAULT(Matrix2d) svd;
|
||||
svd.compute(M,ComputeFullU|ComputeFullV);
|
||||
svd_check_full(M,svd);
|
||||
|
||||
// Check all 2x2 matrices made with the following coefficients:
|
||||
VectorXd value_set(9);
|
||||
value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
|
||||
Array4i id(0,0,0,0);
|
||||
int k = 0;
|
||||
do
|
||||
{
|
||||
M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
|
||||
svd.compute(M,ComputeFullU|ComputeFullV);
|
||||
svd_check_full(M,svd);
|
||||
|
||||
id(k)++;
|
||||
if(id(k)>=value_set.size())
|
||||
{
|
||||
while(k<3 && id(k)>=value_set.size()) id(++k)++;
|
||||
id.head(k).setZero();
|
||||
k=0;
|
||||
}
|
||||
|
||||
} while((id<int(value_set.size())).all());
|
||||
|
||||
#if defined __INTEL_COMPILER
|
||||
#pragma warning pop
|
||||
#endif
|
||||
|
||||
// Check for overflow:
|
||||
Matrix3d M3;
|
||||
M3 << 4.4331978442502944e+307, -5.8585363752028680e+307, 6.4527017443412964e+307,
|
||||
3.7841695601406358e+307, 2.4331702789740617e+306, -3.5235707140272905e+307,
|
||||
-8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
|
||||
|
||||
SVD_DEFAULT(Matrix3d) svd3;
|
||||
svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
|
||||
svd_check_full(M3,svd3);
|
||||
}
|
||||
|
||||
// void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
|
||||
|
||||
template<typename MatrixType>
|
||||
void svd_all_trivial_2x2( void (*cb)(const MatrixType&,bool) )
|
||||
{
|
||||
MatrixType M;
|
||||
VectorXd value_set(3);
|
||||
value_set << 0, 1, -1;
|
||||
Array4i id(0,0,0,0);
|
||||
int k = 0;
|
||||
do
|
||||
{
|
||||
M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
|
||||
|
||||
cb(M,false);
|
||||
|
||||
id(k)++;
|
||||
if(id(k)>=value_set.size())
|
||||
{
|
||||
while(k<3 && id(k)>=value_set.size()) id(++k)++;
|
||||
id.head(k).setZero();
|
||||
k=0;
|
||||
}
|
||||
|
||||
} while((id<int(value_set.size())).all());
|
||||
}
|
||||
|
||||
void svd_preallocate()
|
||||
{
|
||||
Vector3f v(3.f, 2.f, 1.f);
|
||||
MatrixXf m = v.asDiagonal();
|
||||
|
||||
internal::set_is_malloc_allowed(false);
|
||||
VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
|
||||
SVD_DEFAULT(MatrixXf) svd;
|
||||
internal::set_is_malloc_allowed(true);
|
||||
svd.compute(m);
|
||||
VERIFY_IS_APPROX(svd.singularValues(), v);
|
||||
|
||||
SVD_DEFAULT(MatrixXf) svd2(3,3);
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
VERIFY_IS_APPROX(svd2.singularValues(), v);
|
||||
VERIFY_RAISES_ASSERT(svd2.matrixU());
|
||||
VERIFY_RAISES_ASSERT(svd2.matrixV());
|
||||
svd2.compute(m, ComputeFullU | ComputeFullV);
|
||||
VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
|
||||
VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
|
||||
SVD_DEFAULT(MatrixXf) svd3(3,3,ComputeFullU|ComputeFullV);
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
VERIFY_IS_APPROX(svd2.singularValues(), v);
|
||||
VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
|
||||
VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m, ComputeFullU|ComputeFullV);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
}
|
||||
|
||||
template<typename SvdType,typename MatrixType>
|
||||
void svd_verify_assert(const MatrixType& m)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
|
||||
RhsType rhs(rows);
|
||||
SvdType svd;
|
||||
VERIFY_RAISES_ASSERT(svd.matrixU())
|
||||
VERIFY_RAISES_ASSERT(svd.singularValues())
|
||||
VERIFY_RAISES_ASSERT(svd.matrixV())
|
||||
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
||||
MatrixType a = MatrixType::Zero(rows, cols);
|
||||
a.setZero();
|
||||
svd.compute(a, 0);
|
||||
VERIFY_RAISES_ASSERT(svd.matrixU())
|
||||
VERIFY_RAISES_ASSERT(svd.matrixV())
|
||||
svd.singularValues();
|
||||
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
||||
|
||||
if (ColsAtCompileTime == Dynamic)
|
||||
{
|
||||
svd.compute(a, ComputeThinU);
|
||||
svd.matrixU();
|
||||
VERIFY_RAISES_ASSERT(svd.matrixV())
|
||||
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
||||
svd.compute(a, ComputeThinV);
|
||||
svd.matrixV();
|
||||
VERIFY_RAISES_ASSERT(svd.matrixU())
|
||||
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
||||
}
|
||||
else
|
||||
{
|
||||
VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
|
||||
VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
|
||||
}
|
||||
}
|
||||
|
||||
#undef SVD_DEFAULT
|
||||
#undef SVD_FOR_MIN_NORM
|
||||
@ -10,204 +10,105 @@
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/
|
||||
|
||||
#include "svd_common.h"
|
||||
// discard stack allocation as that too bypasses malloc
|
||||
#define EIGEN_STACK_ALLOCATION_LIMIT 0
|
||||
#define EIGEN_RUNTIME_NO_MALLOC
|
||||
|
||||
#include "main.h"
|
||||
#include <unsupported/Eigen/BDCSVD>
|
||||
#include <iostream>
|
||||
#include <Eigen/LU>
|
||||
|
||||
// check if "svd" is the good image of "m"
|
||||
template<typename MatrixType>
|
||||
void bdcsvd_check_full(const MatrixType& m, const BDCSVD<MatrixType>& svd)
|
||||
{
|
||||
svd_check_full< MatrixType, BDCSVD< MatrixType > >(m, svd);
|
||||
}
|
||||
|
||||
// Compare to a reference value
|
||||
template<typename MatrixType>
|
||||
void bdcsvd_compare_to_full(const MatrixType& m,
|
||||
unsigned int computationOptions,
|
||||
const BDCSVD<MatrixType>& referenceSvd)
|
||||
{
|
||||
svd_compare_to_full< MatrixType, BDCSVD< MatrixType > >(m, computationOptions, referenceSvd);
|
||||
} // end bdcsvd_compare_to_full
|
||||
#define SVD_DEFAULT(M) BDCSVD<M>
|
||||
// #define SVD_FOR_MIN_NORM(M) BDCSVD<M>
|
||||
#define SVD_FOR_MIN_NORM(M) JacobiSVD<M,ColPivHouseholderQRPreconditioner>
|
||||
#include "../../test/svd_common.h"
|
||||
|
||||
|
||||
template<typename MatrixType>
|
||||
void bdcsvd_solve(const MatrixType& m, unsigned int computationOptions)
|
||||
{
|
||||
svd_solve< MatrixType, BDCSVD< MatrixType > >(m, computationOptions);
|
||||
} // end template bdcsvd_solve
|
||||
|
||||
|
||||
// test the computations options
|
||||
template<typename MatrixType>
|
||||
void bdcsvd_test_all_computation_options(const MatrixType& m)
|
||||
{
|
||||
BDCSVD<MatrixType> fullSvd(m, ComputeFullU|ComputeFullV);
|
||||
svd_test_computation_options_1< MatrixType, BDCSVD< MatrixType > >(m, fullSvd);
|
||||
svd_test_computation_options_2< MatrixType, BDCSVD< MatrixType > >(m, fullSvd);
|
||||
} // end bdcsvd_test_all_computation_options
|
||||
|
||||
|
||||
// Call a test with all the computations options
|
||||
// Check all variants of JacobiSVD
|
||||
template<typename MatrixType>
|
||||
void bdcsvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
|
||||
{
|
||||
MatrixType m = pickrandom ? MatrixType::Random(a.rows(), a.cols()) : a;
|
||||
bdcsvd_test_all_computation_options<MatrixType>(m);
|
||||
} // end template bdcsvd
|
||||
MatrixType m = a;
|
||||
if(pickrandom)
|
||||
svd_fill_random(m);
|
||||
|
||||
CALL_SUBTEST(( svd_test_all_computation_options<BDCSVD<MatrixType> >(m, false) ));
|
||||
}
|
||||
|
||||
// verify assert
|
||||
template<typename MatrixType>
|
||||
void bdcsvd_verify_assert(const MatrixType& m)
|
||||
{
|
||||
svd_verify_assert< MatrixType, BDCSVD< MatrixType > >(m);
|
||||
}// end template bdcsvd_verify_assert
|
||||
|
||||
|
||||
// test weird values
|
||||
template<typename MatrixType>
|
||||
void bdcsvd_inf_nan()
|
||||
{
|
||||
svd_inf_nan< MatrixType, BDCSVD< MatrixType > >();
|
||||
}// end template bdcsvd_inf_nan
|
||||
|
||||
|
||||
|
||||
void bdcsvd_preallocate()
|
||||
{
|
||||
svd_preallocate< BDCSVD< MatrixXf > >();
|
||||
} // end bdcsvd_preallocate
|
||||
|
||||
// template<typename MatrixType>
|
||||
// void bdcsvd_method()
|
||||
// {
|
||||
// enum { Size = MatrixType::RowsAtCompileTime };
|
||||
// typedef typename MatrixType::RealScalar RealScalar;
|
||||
// typedef Matrix<RealScalar, Size, 1> RealVecType;
|
||||
// MatrixType m = MatrixType::Identity();
|
||||
// VERIFY_IS_APPROX(m.bdcSvd().singularValues(), RealVecType::Ones());
|
||||
// VERIFY_RAISES_ASSERT(m.bdcSvd().matrixU());
|
||||
// VERIFY_RAISES_ASSERT(m.bdcSvd().matrixV());
|
||||
// VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).solve(m), m);
|
||||
// }
|
||||
|
||||
// compare the Singular values returned with Jacobi and Bdc
|
||||
template<typename MatrixType>
|
||||
void compare_bdc_jacobi(const MatrixType& a = MatrixType(), unsigned int computationOptions = 0)
|
||||
{
|
||||
std::cout << "debut compare" << std::endl;
|
||||
MatrixType m = MatrixType::Random(a.rows(), a.cols());
|
||||
BDCSVD<MatrixType> bdc_svd(m);
|
||||
JacobiSVD<MatrixType> jacobi_svd(m);
|
||||
VERIFY_IS_APPROX(bdc_svd.singularValues(), jacobi_svd.singularValues());
|
||||
if(computationOptions & ComputeFullU)
|
||||
VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());
|
||||
if(computationOptions & ComputeThinU)
|
||||
VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());
|
||||
if(computationOptions & ComputeFullV)
|
||||
VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());
|
||||
if(computationOptions & ComputeThinV)
|
||||
VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());
|
||||
std::cout << "fin compare" << std::endl;
|
||||
} // end template compare_bdc_jacobi
|
||||
if(computationOptions & ComputeFullU) VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());
|
||||
if(computationOptions & ComputeThinU) VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());
|
||||
if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());
|
||||
if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());
|
||||
}
|
||||
|
||||
|
||||
// call the tests
|
||||
void test_bdcsvd()
|
||||
{
|
||||
// test of Dynamic defined Matrix (42, 42) of float
|
||||
CALL_SUBTEST_11(( bdcsvd_verify_assert<Matrix<float,Dynamic,Dynamic> >
|
||||
(Matrix<float,Dynamic,Dynamic>(42,42)) ));
|
||||
CALL_SUBTEST_11(( compare_bdc_jacobi<Matrix<float,Dynamic,Dynamic> >
|
||||
(Matrix<float,Dynamic,Dynamic>(42,42), 0) ));
|
||||
CALL_SUBTEST_11(( bdcsvd<Matrix<float,Dynamic,Dynamic> >
|
||||
(Matrix<float,Dynamic,Dynamic>(42,42)) ));
|
||||
|
||||
// test of Dynamic defined Matrix (50, 50) of double
|
||||
CALL_SUBTEST_13(( bdcsvd_verify_assert<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(50,50)) ));
|
||||
CALL_SUBTEST_13(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(50,50), 0) ));
|
||||
CALL_SUBTEST_13(( bdcsvd<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(50, 50)) ));
|
||||
|
||||
// test of Dynamic defined Matrix (22, 22) of complex double
|
||||
CALL_SUBTEST_14(( bdcsvd_verify_assert<Matrix<std::complex<double>,Dynamic,Dynamic> >
|
||||
(Matrix<std::complex<double>,Dynamic,Dynamic>(22,22)) ));
|
||||
CALL_SUBTEST_14(( compare_bdc_jacobi<Matrix<std::complex<double>,Dynamic,Dynamic> >
|
||||
(Matrix<std::complex<double>, Dynamic, Dynamic> (22,22), 0) ));
|
||||
CALL_SUBTEST_14(( bdcsvd<Matrix<std::complex<double>,Dynamic,Dynamic> >
|
||||
(Matrix<std::complex<double>,Dynamic,Dynamic>(22, 22)) ));
|
||||
|
||||
// test of Dynamic defined Matrix (10, 10) of int
|
||||
//CALL_SUBTEST_15(( bdcsvd_verify_assert<Matrix<int,Dynamic,Dynamic> >
|
||||
// (Matrix<int,Dynamic,Dynamic>(10,10)) ));
|
||||
//CALL_SUBTEST_15(( compare_bdc_jacobi<Matrix<int,Dynamic,Dynamic> >
|
||||
// (Matrix<int,Dynamic,Dynamic>(10,10), 0) ));
|
||||
//CALL_SUBTEST_15(( bdcsvd<Matrix<int,Dynamic,Dynamic> >
|
||||
// (Matrix<int,Dynamic,Dynamic>(10, 10)) ));
|
||||
CALL_SUBTEST_3(( svd_verify_assert<BDCSVD<Matrix3f> >(Matrix3f()) ));
|
||||
CALL_SUBTEST_4(( svd_verify_assert<BDCSVD<Matrix4d> >(Matrix4d()) ));
|
||||
CALL_SUBTEST_7(( svd_verify_assert<BDCSVD<MatrixXf> >(MatrixXf(10,12)) ));
|
||||
CALL_SUBTEST_8(( svd_verify_assert<BDCSVD<MatrixXcd> >(MatrixXcd(7,5)) ));
|
||||
|
||||
// svd_all_trivial_2x2(bdcsvd<Matrix2cd>);
|
||||
// svd_all_trivial_2x2(bdcsvd<Matrix2d>);
|
||||
|
||||
// test of Dynamic defined Matrix (8, 6) of double
|
||||
|
||||
CALL_SUBTEST_16(( bdcsvd_verify_assert<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(8,6)) ));
|
||||
CALL_SUBTEST_16(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(8, 6), 0) ));
|
||||
CALL_SUBTEST_16(( bdcsvd<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(8, 6)) ));
|
||||
|
||||
|
||||
|
||||
// test of Dynamic defined Matrix (36, 12) of float
|
||||
CALL_SUBTEST_17(( compare_bdc_jacobi<Matrix<float,Dynamic,Dynamic> >
|
||||
(Matrix<float,Dynamic,Dynamic>(36, 12), 0) ));
|
||||
CALL_SUBTEST_17(( bdcsvd<Matrix<float,Dynamic,Dynamic> >
|
||||
(Matrix<float,Dynamic,Dynamic>(36, 12)) ));
|
||||
|
||||
// test of Dynamic defined Matrix (5, 8) of double
|
||||
CALL_SUBTEST_18(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(5, 8), 0) ));
|
||||
CALL_SUBTEST_18(( bdcsvd<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(5, 8)) ));
|
||||
|
||||
|
||||
// non regression tests
|
||||
CALL_SUBTEST_3(( bdcsvd_verify_assert(Matrix3f()) ));
|
||||
CALL_SUBTEST_4(( bdcsvd_verify_assert(Matrix4d()) ));
|
||||
CALL_SUBTEST_7(( bdcsvd_verify_assert(MatrixXf(10,12)) ));
|
||||
CALL_SUBTEST_8(( bdcsvd_verify_assert(MatrixXcd(7,5)) ));
|
||||
|
||||
// SUBTESTS 1 and 2 on specifics matrix
|
||||
for(int i = 0; i < g_repeat; i++) {
|
||||
Matrix2cd m;
|
||||
m << 0, 1,
|
||||
0, 1;
|
||||
CALL_SUBTEST_1(( bdcsvd(m, false) ));
|
||||
m << 1, 0,
|
||||
1, 0;
|
||||
CALL_SUBTEST_1(( bdcsvd(m, false) ));
|
||||
// CALL_SUBTEST_3(( bdcsvd<Matrix3f>() ));
|
||||
// CALL_SUBTEST_4(( bdcsvd<Matrix4d>() ));
|
||||
// CALL_SUBTEST_5(( bdcsvd<Matrix<float,3,5> >() ));
|
||||
|
||||
Matrix2d n;
|
||||
n << 0, 0,
|
||||
0, 0;
|
||||
CALL_SUBTEST_2(( bdcsvd(n, false) ));
|
||||
n << 0, 0,
|
||||
0, 1;
|
||||
CALL_SUBTEST_2(( bdcsvd(n, false) ));
|
||||
int r = internal::random<int>(1, EIGEN_TEST_MAX_SIZE/2),
|
||||
c = internal::random<int>(1, EIGEN_TEST_MAX_SIZE/2);
|
||||
|
||||
// Statics matrix don't work with BDSVD yet
|
||||
// bdc algo on a random 3x3 float matrix
|
||||
// CALL_SUBTEST_3(( bdcsvd<Matrix3f>() ));
|
||||
// bdc algo on a random 4x4 double matrix
|
||||
// CALL_SUBTEST_4(( bdcsvd<Matrix4d>() ));
|
||||
// bdc algo on a random 3x5 float matrix
|
||||
// CALL_SUBTEST_5(( bdcsvd<Matrix<float,3,5> >() ));
|
||||
|
||||
int r = internal::random<int>(1, 30),
|
||||
c = internal::random<int>(1, 30);
|
||||
CALL_SUBTEST_7(( bdcsvd<MatrixXf>(MatrixXf(r,c)) ));
|
||||
CALL_SUBTEST_8(( bdcsvd<MatrixXcd>(MatrixXcd(r,c)) ));
|
||||
TEST_SET_BUT_UNUSED_VARIABLE(r)
|
||||
TEST_SET_BUT_UNUSED_VARIABLE(c)
|
||||
|
||||
CALL_SUBTEST_6(( bdcsvd(Matrix<double,Dynamic,2>(r,2)) ));
|
||||
CALL_SUBTEST_7(( bdcsvd(MatrixXf(r,c)) ));
|
||||
CALL_SUBTEST_7(( compare_bdc_jacobi(MatrixXf(r,c)) ));
|
||||
CALL_SUBTEST_10(( bdcsvd(MatrixXd(r,c)) ));
|
||||
CALL_SUBTEST_10(( compare_bdc_jacobi(MatrixXd(r,c)) ));
|
||||
CALL_SUBTEST_8(( bdcsvd(MatrixXcd(r,c)) ));
|
||||
CALL_SUBTEST_8(( compare_bdc_jacobi(MatrixXcd(r,c)) ));
|
||||
(void) r;
|
||||
(void) c;
|
||||
|
||||
// Test on inf/nan matrix
|
||||
CALL_SUBTEST_7( bdcsvd_inf_nan<MatrixXf>() );
|
||||
CALL_SUBTEST_7( (svd_inf_nan<BDCSVD<MatrixXf>, MatrixXf>()) );
|
||||
CALL_SUBTEST_10( (svd_inf_nan<BDCSVD<MatrixXd>, MatrixXd>()) );
|
||||
}
|
||||
|
||||
CALL_SUBTEST_7(( bdcsvd<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(( bdcsvd<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(( bdcsvd_method<Matrix2cd>() ));
|
||||
// CALL_SUBTEST_3(( bdcsvd_method<Matrix3f>() ));
|
||||
|
||||
// Test problem size constructors
|
||||
CALL_SUBTEST_7( BDCSVD<MatrixXf>(10,10) );
|
||||
|
||||
} // end test_bdcsvd
|
||||
// Check that preallocation avoids subsequent mallocs
|
||||
CALL_SUBTEST_9( svd_preallocate() );
|
||||
|
||||
CALL_SUBTEST_2( svd_underoverflow() );
|
||||
}
|
||||
|
||||
|
||||
@ -1,198 +0,0 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#include "svd_common.h"
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner>
|
||||
void jacobisvd_check_full(const MatrixType& m, const JacobiSVD<MatrixType, QRPreconditioner>& svd)
|
||||
{
|
||||
svd_check_full<MatrixType, JacobiSVD<MatrixType, QRPreconditioner > >(m, svd);
|
||||
}
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner>
|
||||
void jacobisvd_compare_to_full(const MatrixType& m,
|
||||
unsigned int computationOptions,
|
||||
const JacobiSVD<MatrixType, QRPreconditioner>& referenceSvd)
|
||||
{
|
||||
svd_compare_to_full<MatrixType, JacobiSVD<MatrixType, QRPreconditioner> >(m, computationOptions, referenceSvd);
|
||||
}
|
||||
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner>
|
||||
void jacobisvd_solve(const MatrixType& m, unsigned int computationOptions)
|
||||
{
|
||||
svd_solve< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, computationOptions);
|
||||
}
|
||||
|
||||
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner>
|
||||
void jacobisvd_test_all_computation_options(const MatrixType& m)
|
||||
{
|
||||
|
||||
if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
|
||||
return;
|
||||
|
||||
JacobiSVD< MatrixType, QRPreconditioner > fullSvd(m, ComputeFullU|ComputeFullV);
|
||||
svd_test_computation_options_1< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, fullSvd);
|
||||
|
||||
if(QRPreconditioner == FullPivHouseholderQRPreconditioner)
|
||||
return;
|
||||
svd_test_computation_options_2< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, fullSvd);
|
||||
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
|
||||
{
|
||||
MatrixType m = pickrandom ? MatrixType::Random(a.rows(), a.cols()) : a;
|
||||
|
||||
jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m);
|
||||
jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m);
|
||||
jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m);
|
||||
jacobisvd_test_all_computation_options<MatrixType, NoQRPreconditioner>(m);
|
||||
}
|
||||
|
||||
|
||||
template<typename MatrixType>
|
||||
void jacobisvd_verify_assert(const MatrixType& m)
|
||||
{
|
||||
|
||||
svd_verify_assert<MatrixType, JacobiSVD< MatrixType > >(m);
|
||||
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
||||
};
|
||||
|
||||
MatrixType a = MatrixType::Zero(rows, cols);
|
||||
a.setZero();
|
||||
|
||||
if (ColsAtCompileTime == Dynamic)
|
||||
{
|
||||
JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> svd_fullqr;
|
||||
VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV))
|
||||
VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV))
|
||||
VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV))
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void jacobisvd_method()
|
||||
{
|
||||
enum { Size = MatrixType::RowsAtCompileTime };
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef Matrix<RealScalar, Size, 1> RealVecType;
|
||||
MatrixType m = MatrixType::Identity();
|
||||
VERIFY_IS_APPROX(m.jacobiSvd().singularValues(), RealVecType::Ones());
|
||||
VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixU());
|
||||
VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixV());
|
||||
VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m);
|
||||
}
|
||||
|
||||
|
||||
|
||||
template<typename MatrixType>
|
||||
void jacobisvd_inf_nan()
|
||||
{
|
||||
svd_inf_nan<MatrixType, JacobiSVD< MatrixType > >();
|
||||
}
|
||||
|
||||
|
||||
// Regression test for bug 286: JacobiSVD loops indefinitely with some
|
||||
// matrices containing denormal numbers.
|
||||
void jacobisvd_bug286()
|
||||
{
|
||||
#if defined __INTEL_COMPILER
|
||||
// shut up warning #239: floating point underflow
|
||||
#pragma warning push
|
||||
#pragma warning disable 239
|
||||
#endif
|
||||
Matrix2d M;
|
||||
M << -7.90884e-313, -4.94e-324,
|
||||
0, 5.60844e-313;
|
||||
#if defined __INTEL_COMPILER
|
||||
#pragma warning pop
|
||||
#endif
|
||||
JacobiSVD<Matrix2d> svd;
|
||||
svd.compute(M); // just check we don't loop indefinitely
|
||||
}
|
||||
|
||||
|
||||
void jacobisvd_preallocate()
|
||||
{
|
||||
svd_preallocate< JacobiSVD <MatrixXf> >();
|
||||
}
|
||||
|
||||
void test_jacobisvd()
|
||||
{
|
||||
CALL_SUBTEST_11(( jacobisvd<Matrix<double,Dynamic,Dynamic> >
|
||||
(Matrix<double,Dynamic,Dynamic>(16, 6)) ));
|
||||
|
||||
CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) ));
|
||||
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);
|
||||
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_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_bug286() );
|
||||
}
|
||||
@ -1,261 +0,0 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
//
|
||||
// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
|
||||
// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
|
||||
// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
|
||||
// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
// discard stack allocation as that too bypasses malloc
|
||||
#define EIGEN_STACK_ALLOCATION_LIMIT 0
|
||||
#define EIGEN_RUNTIME_NO_MALLOC
|
||||
|
||||
#include "main.h"
|
||||
#include <unsupported/Eigen/BDCSVD>
|
||||
#include <Eigen/LU>
|
||||
|
||||
|
||||
// check if "svd" is the good image of "m"
|
||||
template<typename MatrixType, typename SVD>
|
||||
void svd_check_full(const MatrixType& m, const SVD& svd)
|
||||
{
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
|
||||
|
||||
|
||||
MatrixType sigma = MatrixType::Zero(rows, cols);
|
||||
sigma.diagonal() = svd.singularValues().template cast<Scalar>();
|
||||
MatrixUType u = svd.matrixU();
|
||||
MatrixVType v = svd.matrixV();
|
||||
VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
|
||||
VERIFY_IS_UNITARY(u);
|
||||
VERIFY_IS_UNITARY(v);
|
||||
} // end svd_check_full
|
||||
|
||||
|
||||
|
||||
// Compare to a reference value
|
||||
template<typename MatrixType, typename SVD>
|
||||
void svd_compare_to_full(const MatrixType& m,
|
||||
unsigned int computationOptions,
|
||||
const SVD& referenceSvd)
|
||||
{
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
Index diagSize = (std::min)(rows, cols);
|
||||
|
||||
SVD svd(m, computationOptions);
|
||||
|
||||
VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
|
||||
if(computationOptions & ComputeFullU)
|
||||
VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
|
||||
if(computationOptions & ComputeThinU)
|
||||
VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
|
||||
if(computationOptions & ComputeFullV)
|
||||
VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
|
||||
if(computationOptions & ComputeThinV)
|
||||
VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
|
||||
} // end svd_compare_to_full
|
||||
|
||||
|
||||
|
||||
template<typename MatrixType, typename SVD>
|
||||
void svd_solve(const MatrixType& m, unsigned int computationOptions)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
|
||||
|
||||
RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
|
||||
SVD svd(m, computationOptions);
|
||||
SolutionType x = svd.solve(rhs);
|
||||
// evaluate normal equation which works also for least-squares solutions
|
||||
VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
|
||||
} // end svd_solve
|
||||
|
||||
|
||||
// test computations options
|
||||
// 2 functions because Jacobisvd can return before the second function
|
||||
template<typename MatrixType, typename SVD>
|
||||
void svd_test_computation_options_1(const MatrixType& m, const SVD& fullSvd)
|
||||
{
|
||||
svd_check_full< MatrixType, SVD >(m, fullSvd);
|
||||
svd_solve< MatrixType, SVD >(m, ComputeFullU | ComputeFullV);
|
||||
}
|
||||
|
||||
|
||||
template<typename MatrixType, typename SVD>
|
||||
void svd_test_computation_options_2(const MatrixType& m, const SVD& fullSvd)
|
||||
{
|
||||
svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU, fullSvd);
|
||||
svd_compare_to_full< MatrixType, SVD >(m, ComputeFullV, fullSvd);
|
||||
svd_compare_to_full< MatrixType, SVD >(m, 0, fullSvd);
|
||||
|
||||
if (MatrixType::ColsAtCompileTime == Dynamic) {
|
||||
// thin U/V are only available with dynamic number of columns
|
||||
|
||||
svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU|ComputeThinV, fullSvd);
|
||||
svd_compare_to_full< MatrixType, SVD >(m, ComputeThinV, fullSvd);
|
||||
svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeFullV, fullSvd);
|
||||
svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU , fullSvd);
|
||||
svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeThinV, fullSvd);
|
||||
svd_solve<MatrixType, SVD>(m, ComputeFullU | ComputeThinV);
|
||||
svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeFullV);
|
||||
svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeThinV);
|
||||
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index diagSize = (std::min)(m.rows(), m.cols());
|
||||
SVD svd(m, ComputeThinU | ComputeThinV);
|
||||
VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType, typename SVD>
|
||||
void svd_verify_assert(const MatrixType& m)
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
Index rows = m.rows();
|
||||
Index cols = m.cols();
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
|
||||
RhsType rhs(rows);
|
||||
SVD svd;
|
||||
VERIFY_RAISES_ASSERT(svd.matrixU())
|
||||
VERIFY_RAISES_ASSERT(svd.singularValues())
|
||||
VERIFY_RAISES_ASSERT(svd.matrixV())
|
||||
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
||||
MatrixType a = MatrixType::Zero(rows, cols);
|
||||
a.setZero();
|
||||
svd.compute(a, 0);
|
||||
VERIFY_RAISES_ASSERT(svd.matrixU())
|
||||
VERIFY_RAISES_ASSERT(svd.matrixV())
|
||||
svd.singularValues();
|
||||
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
||||
|
||||
if (ColsAtCompileTime == Dynamic)
|
||||
{
|
||||
svd.compute(a, ComputeThinU);
|
||||
svd.matrixU();
|
||||
VERIFY_RAISES_ASSERT(svd.matrixV())
|
||||
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
||||
svd.compute(a, ComputeThinV);
|
||||
svd.matrixV();
|
||||
VERIFY_RAISES_ASSERT(svd.matrixU())
|
||||
VERIFY_RAISES_ASSERT(svd.solve(rhs))
|
||||
}
|
||||
else
|
||||
{
|
||||
VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
|
||||
VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
|
||||
}
|
||||
}
|
||||
|
||||
// work around stupid msvc error when constructing at compile time an expression that involves
|
||||
// a division by zero, even if the numeric type has floating point
|
||||
template<typename Scalar>
|
||||
EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
|
||||
|
||||
// workaround aggressive optimization in ICC
|
||||
template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
|
||||
|
||||
|
||||
template<typename MatrixType, typename SVD>
|
||||
void svd_inf_nan()
|
||||
{
|
||||
// all this function does is verify we don't iterate infinitely on nan/inf values
|
||||
|
||||
SVD svd;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
Scalar some_inf = Scalar(1) / zero<Scalar>();
|
||||
VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
|
||||
svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
|
||||
|
||||
Scalar some_nan = zero<Scalar> () / zero<Scalar> ();
|
||||
VERIFY(some_nan != some_nan);
|
||||
svd.compute(MatrixType::Constant(10,10,some_nan), ComputeFullU | ComputeFullV);
|
||||
|
||||
MatrixType m = MatrixType::Zero(10,10);
|
||||
m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
|
||||
svd.compute(m, ComputeFullU | ComputeFullV);
|
||||
|
||||
m = MatrixType::Zero(10,10);
|
||||
m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_nan;
|
||||
svd.compute(m, ComputeFullU | ComputeFullV);
|
||||
}
|
||||
|
||||
|
||||
template<typename SVD>
|
||||
void svd_preallocate()
|
||||
{
|
||||
Vector3f v(3.f, 2.f, 1.f);
|
||||
MatrixXf m = v.asDiagonal();
|
||||
|
||||
internal::set_is_malloc_allowed(false);
|
||||
VERIFY_RAISES_ASSERT(VectorXf v(10);)
|
||||
SVD svd;
|
||||
internal::set_is_malloc_allowed(true);
|
||||
svd.compute(m);
|
||||
VERIFY_IS_APPROX(svd.singularValues(), v);
|
||||
|
||||
SVD svd2(3,3);
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
VERIFY_IS_APPROX(svd2.singularValues(), v);
|
||||
VERIFY_RAISES_ASSERT(svd2.matrixU());
|
||||
VERIFY_RAISES_ASSERT(svd2.matrixV());
|
||||
svd2.compute(m, ComputeFullU | ComputeFullV);
|
||||
VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
|
||||
VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
|
||||
SVD svd3(3,3,ComputeFullU|ComputeFullV);
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
VERIFY_IS_APPROX(svd2.singularValues(), v);
|
||||
VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
|
||||
VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
|
||||
internal::set_is_malloc_allowed(false);
|
||||
svd2.compute(m, ComputeFullU|ComputeFullV);
|
||||
internal::set_is_malloc_allowed(true);
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user