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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#define EIGEN_NO_ASSERTION_CHECKING
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/LU>
#ifdef HAS_GSL
#include "gsl_helper.h"
#endif
template<typename MatrixType> void cholesky(const MatrixType& m)
{
/* this test covers the following files:
LLT.h LDLT.h
*/
int rows = m.rows();
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
MatrixType a0 = MatrixType::Random(rows,cols);
VectorType vecB = VectorType::Random(rows), vecX(rows);
MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
SquareMatrixType symm = a0 * a0.adjoint();
// let's make sure the matrix is not singular or near singular
MatrixType a1 = MatrixType::Random(rows,cols);
symm += a1 * a1.adjoint();
#ifdef HAS_GSL
if (ei_is_same_type<RealScalar,double>::ret)
{
typedef GslTraits<Scalar> Gsl;
typename Gsl::Matrix gMatA=0, gSymm=0;
typename Gsl::Vector gVecB=0, gVecX=0;
convert<MatrixType>(symm, gSymm);
convert<MatrixType>(symm, gMatA);
convert<VectorType>(vecB, gVecB);
convert<VectorType>(vecB, gVecX);
Gsl::cholesky(gMatA);
Gsl::cholesky_solve(gMatA, gVecB, gVecX);
VectorType vecX(rows), _vecX, _vecB;
convert(gVecX, _vecX);
symm.llt().solve(vecB, &vecX);
Gsl::prod(gSymm, gVecX, gVecB);
convert(gVecB, _vecB);
// test gsl itself !
VERIFY_IS_APPROX(vecB, _vecB);
VERIFY_IS_APPROX(vecX, _vecX);
Gsl::free(gMatA);
Gsl::free(gSymm);
Gsl::free(gVecB);
Gsl::free(gVecX);
}
#endif
{
LDLT<SquareMatrixType> ldlt(symm);
VERIFY(ldlt.isPositiveDefinite());
VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
ldlt.solve(vecB, &vecX);
VERIFY_IS_APPROX(symm * vecX, vecB);
ldlt.solve(matB, &matX);
VERIFY_IS_APPROX(symm * matX, matB);
}
{
LLT<SquareMatrixType> chol(symm);
VERIFY(chol.isPositiveDefinite());
VERIFY_IS_APPROX(symm, chol.matrixL() * chol.matrixL().adjoint());
chol.solve(vecB, &vecX);
VERIFY_IS_APPROX(symm * vecX, vecB);
chol.solve(matB, &matX);
VERIFY_IS_APPROX(symm * matX, matB);
}
#if 0 // cholesky is not rank-revealing anyway
// test isPositiveDefinite on non definite matrix
if (rows>4)
{
SquareMatrixType symm = a0.block(0,0,rows,cols-4) * a0.block(0,0,rows,cols-4).adjoint();
LLT<SquareMatrixType> chol(symm);
VERIFY(!chol.isPositiveDefinite());
LDLT<SquareMatrixType> cholnosqrt(symm);
VERIFY(!cholnosqrt.isPositiveDefinite());
}
#endif
}
void test_cholesky()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( cholesky(Matrix<double,1,1>()) );
CALL_SUBTEST( cholesky(Matrix2d()) );
CALL_SUBTEST( cholesky(Matrix3f()) );
CALL_SUBTEST( cholesky(Matrix4d()) );
CALL_SUBTEST( cholesky(MatrixXcd(7,7)) );
CALL_SUBTEST( cholesky(MatrixXf(17,17)) );
CALL_SUBTEST( cholesky(MatrixXd(33,33)) );
}
MatrixXf m = MatrixXf::Zero(10,10);
VectorXf b = VectorXf::Zero(10);
VERIFY(!m.llt().isPositiveDefinite());
}
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