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// 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/SVD>
#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);}
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