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new unsupported and not finished SVD, using a divide and conquert algorithm, with tests and benchmark
This commit is contained in:
Gauthier Brun
261
unsupported/test/svd_common.h
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261
unsupported/test/svd_common.h
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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) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
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// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
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// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
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// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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// discard stack allocation as that too bypasses malloc
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#define EIGEN_STACK_ALLOCATION_LIMIT 0
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#define EIGEN_RUNTIME_NO_MALLOC
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#include "main.h"
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#include <unsupported/Eigen/SVD>
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#include <Eigen/LU>
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// check if "svd" is the good image of "m"
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template<typename MatrixType, typename SVD>
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void svd_check_full(const MatrixType& m, const SVD& 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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} // end svd_check_full
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// Compare to a reference value
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template<typename MatrixType, typename SVD>
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void svd_compare_to_full(const MatrixType& m,
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unsigned int computationOptions,
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const SVD& 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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SVD 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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} // end svd_compare_to_full
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template<typename MatrixType, typename SVD>
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void svd_solve(const MatrixType& m, unsigned int computationOptions)
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{
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::Index Index;
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Index rows = m.rows();
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Index cols = m.cols();
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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = MatrixType::ColsAtCompileTime
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};
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typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
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typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
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RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
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SVD svd(m, computationOptions);
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SolutionType x = svd.solve(rhs);
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// evaluate normal equation which works also for least-squares solutions
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VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
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} // end svd_solve
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// test computations options
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// 2 functions because Jacobisvd can return before the second function
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template<typename MatrixType, typename SVD>
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void svd_test_computation_options_1(const MatrixType& m, const SVD& fullSvd)
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{
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svd_check_full< MatrixType, SVD >(m, fullSvd);
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svd_solve< MatrixType, SVD >(m, ComputeFullU | ComputeFullV);
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}
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template<typename MatrixType, typename SVD>
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void svd_test_computation_options_2(const MatrixType& m, const SVD& fullSvd)
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{
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svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU, fullSvd);
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svd_compare_to_full< MatrixType, SVD >(m, ComputeFullV, fullSvd);
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svd_compare_to_full< MatrixType, SVD >(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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svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU|ComputeThinV, fullSvd);
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svd_compare_to_full< MatrixType, SVD >(m, ComputeThinV, fullSvd);
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svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeFullV, fullSvd);
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svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU , fullSvd);
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svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeThinV, fullSvd);
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svd_solve<MatrixType, SVD>(m, ComputeFullU | ComputeThinV);
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svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeFullV);
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svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeThinV);
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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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SVD svd(m, ComputeThinU | ComputeThinV);
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VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
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}
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}
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template<typename MatrixType, typename SVD>
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void svd_verify_assert(const MatrixType& m)
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{
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::Index Index;
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Index rows = m.rows();
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Index cols = m.cols();
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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = MatrixType::ColsAtCompileTime
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};
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typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
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RhsType rhs(rows);
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SVD 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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}
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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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// 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, typename SVD>
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void svd_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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SVD 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 some_nan = zero<Scalar> () / zero<Scalar> ();
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VERIFY(some_nan != some_nan);
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svd.compute(MatrixType::Constant(10,10,some_nan), ComputeFullU | ComputeFullV);
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MatrixType m = MatrixType::Zero(10,10);
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m(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)) = some_nan;
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svd.compute(m, ComputeFullU | ComputeFullV);
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}
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template<typename SVD>
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void svd_preallocate()
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{
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Vector3f v(3.f, 2.f, 1.f);
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MatrixXf m = v.asDiagonal();
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internal::set_is_malloc_allowed(false);
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VERIFY_RAISES_ASSERT(VectorXf v(10);)
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SVD svd;
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internal::set_is_malloc_allowed(true);
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svd.compute(m);
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VERIFY_IS_APPROX(svd.singularValues(), v);
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SVD svd2(3,3);
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internal::set_is_malloc_allowed(false);
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svd2.compute(m);
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internal::set_is_malloc_allowed(true);
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VERIFY_IS_APPROX(svd2.singularValues(), v);
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VERIFY_RAISES_ASSERT(svd2.matrixU());
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VERIFY_RAISES_ASSERT(svd2.matrixV());
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svd2.compute(m, ComputeFullU | ComputeFullV);
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VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
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VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
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internal::set_is_malloc_allowed(false);
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svd2.compute(m);
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internal::set_is_malloc_allowed(true);
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SVD svd3(3,3,ComputeFullU|ComputeFullV);
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internal::set_is_malloc_allowed(false);
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svd2.compute(m);
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internal::set_is_malloc_allowed(true);
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VERIFY_IS_APPROX(svd2.singularValues(), v);
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VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
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VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
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internal::set_is_malloc_allowed(false);
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svd2.compute(m, ComputeFullU|ComputeFullV);
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internal::set_is_malloc_allowed(true);
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}
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