114 lines
3.5 KiB
C++
114 lines
3.5 KiB
C++
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 Gael Guennebaud <g.gael@free.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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#define EIGEN_NO_ASSERTION_CHECKING
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#include "main.h"
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#include <Eigen/Cholesky>
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#include <Eigen/LU>
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#ifdef HAS_GSL
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#include "gsl_helper.h"
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#endif
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template<typename MatrixType> void cholesky(const MatrixType& m)
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{
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/* this test covers the following files:
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LLT.h LDLT.h
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*/
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int rows = m.rows();
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int cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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MatrixType a0 = MatrixType::Random(rows,cols);
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VectorType vecB = VectorType::Random(rows), vecX(rows);
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MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
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SquareMatrixType symm = a0 * a0.adjoint();
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// let's make sure the matrix is not singular or near singular
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MatrixType a1 = MatrixType::Random(rows,cols);
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symm += a1 * a1.adjoint();
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#ifdef HAS_GSL
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if (ei_is_same_type<RealScalar,double>::ret)
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{
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typedef GslTraits<Scalar> Gsl;
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typename Gsl::Matrix gMatA=0, gSymm=0;
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typename Gsl::Vector gVecB=0, gVecX=0;
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convert<MatrixType>(symm, gSymm);
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convert<MatrixType>(symm, gMatA);
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convert<VectorType>(vecB, gVecB);
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convert<VectorType>(vecB, gVecX);
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Gsl::cholesky(gMatA);
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Gsl::cholesky_solve(gMatA, gVecB, gVecX);
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VectorType vecX(rows), _vecX, _vecB;
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convert(gVecX, _vecX);
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symm.llt().solve(vecB, &vecX);
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Gsl::prod(gSymm, gVecX, gVecB);
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convert(gVecB, _vecB);
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// test gsl itself !
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VERIFY_IS_APPROX(vecB, _vecB);
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VERIFY_IS_APPROX(vecX, _vecX);
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Gsl::free(gMatA);
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Gsl::free(gSymm);
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Gsl::free(gVecB);
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Gsl::free(gVecX);
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}
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#endif
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{
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LDLT<SquareMatrixType> ldlt(symm);
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VERIFY(ldlt.isPositiveDefinite());
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// in eigen3, LDLT is pivoting
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//VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
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ldlt.solve(vecB, &vecX);
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VERIFY_IS_APPROX(symm * vecX, vecB);
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ldlt.solve(matB, &matX);
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VERIFY_IS_APPROX(symm * matX, matB);
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}
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{
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LLT<SquareMatrixType> chol(symm);
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VERIFY(chol.isPositiveDefinite());
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VERIFY_IS_APPROX(symm, chol.matrixL() * chol.matrixL().adjoint());
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chol.solve(vecB, &vecX);
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VERIFY_IS_APPROX(symm * vecX, vecB);
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chol.solve(matB, &matX);
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VERIFY_IS_APPROX(symm * matX, matB);
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}
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#if 0 // cholesky is not rank-revealing anyway
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// test isPositiveDefinite on non definite matrix
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if (rows>4)
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{
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SquareMatrixType symm = a0.block(0,0,rows,cols-4) * a0.block(0,0,rows,cols-4).adjoint();
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LLT<SquareMatrixType> chol(symm);
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VERIFY(!chol.isPositiveDefinite());
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LDLT<SquareMatrixType> cholnosqrt(symm);
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VERIFY(!cholnosqrt.isPositiveDefinite());
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}
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#endif
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}
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void test_eigen2_cholesky()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( cholesky(Matrix<double,1,1>()) );
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CALL_SUBTEST_2( cholesky(Matrix2d()) );
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CALL_SUBTEST_3( cholesky(Matrix3f()) );
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CALL_SUBTEST_4( cholesky(Matrix4d()) );
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CALL_SUBTEST_5( cholesky(MatrixXcd(7,7)) );
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CALL_SUBTEST_6( cholesky(MatrixXf(17,17)) );
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CALL_SUBTEST_7( cholesky(MatrixXd(33,33)) );
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}
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}
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