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765219aa51
* rename Cholesky to LLT
* rename CholeskyWithoutSquareRoot to LDLT
* rename MatrixBase::cholesky() to llt()
* rename MatrixBase::choleskyNoSqrt() to ldlt()
* make {LLT,LDLT}::solve() API consistent with other modules
Note that we are going to keep a source compatibility untill the next beta release.
E.g., the "old" Cholesky* classes, etc are still available for some time.
To be clear, Eigen beta2 should be (hopefully) source compatible with beta1,
and so beta2 will contain all the deprecated API of beta1. Those features marked
as deprecated will be removed in beta3 (or in the final 2.0 if there is no beta 3 !).
Also includes various updated in sparse Cholesky.
125 lines
4.1 KiB
C++
125 lines
4.1 KiB
C++
// 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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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#define EIGEN_DONT_VECTORIZE
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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, _vecX, _vecB;
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convert(gVecX, _vecX);
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vecX = symm.cholesky().solve(vecB);
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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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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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// 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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}
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void test_cholesky()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST( cholesky(Matrix<double,1,1>()) );
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CALL_SUBTEST( cholesky(Matrix2d()) );
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CALL_SUBTEST( cholesky(Matrix3f()) );
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CALL_SUBTEST( cholesky(Matrix4d()) );
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CALL_SUBTEST( cholesky(MatrixXcd(7,7)) );
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CALL_SUBTEST( cholesky(MatrixXf(17,17)) );
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CALL_SUBTEST( cholesky(MatrixXd(33,33)) );
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}
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}
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