262 lines
8.7 KiB
C
262 lines
8.7 KiB
C
|
// 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);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|