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Diffstat (limited to 'eigen/test/jacobisvd.cpp')
| -rw-r--r-- | eigen/test/jacobisvd.cpp | 462 |
1 files changed, 462 insertions, 0 deletions
diff --git a/eigen/test/jacobisvd.cpp b/eigen/test/jacobisvd.cpp new file mode 100644 index 0000000..12c556e --- /dev/null +++ b/eigen/test/jacobisvd.cpp @@ -0,0 +1,462 @@ +// 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/. + +// discard stack allocation as that too bypasses malloc +#define EIGEN_STACK_ALLOCATION_LIMIT 0 +#define EIGEN_RUNTIME_NO_MALLOC +#include "main.h" +#include <Eigen/SVD> + +template<typename MatrixType, int QRPreconditioner> +void jacobisvd_check_full(const MatrixType& m, const JacobiSVD<MatrixType, QRPreconditioner>& 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); +} + +template<typename MatrixType, int QRPreconditioner> +void jacobisvd_compare_to_full(const MatrixType& m, + unsigned int computationOptions, + const JacobiSVD<MatrixType, QRPreconditioner>& referenceSvd) +{ + typedef typename MatrixType::Index Index; + Index rows = m.rows(); + Index cols = m.cols(); + Index diagSize = (std::min)(rows, cols); + + JacobiSVD<MatrixType, QRPreconditioner> 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 MatrixType, int QRPreconditioner> +void jacobisvd_solve(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)); + JacobiSVD<MatrixType, QRPreconditioner> 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 + { + // 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(m2.jacobiSvd().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 + JacobiSVD<MatrixType2, ColPivHouseholderQRPreconditioner> 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; + JacobiSVD<MatrixType3, ColPivHouseholderQRPreconditioner> svd3(m3, computationOptions); + SolutionType x3 = svd3.solve(rhs3); + if(svd3.rank()!=rank) { + std::cout << m3 << "\n\n"; + std::cout << svd3.singularValues().transpose() << "\n"; + std::cout << svd3.rank() << " == " << rank << "\n"; + std::cout << x21.norm() << " == " << x3.norm() << "\n"; + } +// VERIFY_IS_APPROX(m3*x3, rhs3); + VERIFY_IS_APPROX(m3*x21, rhs3); + VERIFY_IS_APPROX(m2*x3, rhs2); + + VERIFY_IS_APPROX(x21, x3); + } +} + +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); + CALL_SUBTEST(( jacobisvd_check_full(m, fullSvd) )); + CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeFullV) )); + + #if defined __INTEL_COMPILER + // remark #111: statement is unreachable + #pragma warning disable 111 + #endif + if(QRPreconditioner == FullPivHouseholderQRPreconditioner) + return; + + CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullU, fullSvd) )); + CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullV, fullSvd) )); + CALL_SUBTEST(( jacobisvd_compare_to_full(m, 0, fullSvd) )); + + if (MatrixType::ColsAtCompileTime == Dynamic) { + // thin U/V are only available with dynamic number of columns + CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) )); + CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinV, fullSvd) )); + CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) )); + CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU , fullSvd) )); + CALL_SUBTEST(( jacobisvd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) )); + CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeThinV) )); + CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeFullV) )); + CALL_SUBTEST(( jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeThinV) )); + + // test reconstruction + typedef typename MatrixType::Index Index; + Index diagSize = (std::min)(m.rows(), m.cols()); + JacobiSVD<MatrixType, QRPreconditioner> svd(m, ComputeThinU | ComputeThinV); + VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint()); + } +} + +template<typename MatrixType> +void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true) +{ + MatrixType m = a; + if(pickrandom) + { + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef typename MatrixType::Index Index; + Index diagSize = (std::min)(a.rows(), a.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(a.rows(),diagSize) * d.asDiagonal() * Matrix<Scalar,Dynamic,Dynamic>::Random(diagSize,a.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); + } + + CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m) )); + CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m) )); + CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m) )); + CALL_SUBTEST(( jacobisvd_test_all_computation_options<MatrixType, NoQRPreconditioner>(m) )); +} + +template<typename MatrixType> void jacobisvd_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); + + JacobiSVD<MatrixType> 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)) + + 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)) + } + else + { + VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU)) + VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV)) + } +} + +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); +} + +// 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> +void jacobisvd_inf_nan() +{ + // all this function does is verify we don't iterate infinitely on nan/inf values + + JacobiSVD<MatrixType> 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); +} + +// 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() +{ + 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)) )); + + 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_bug286() ); +} |