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Diffstat (limited to 'extern/Eigen2/Eigen/src/Cholesky/LLT.h')
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diff --git a/extern/Eigen2/Eigen/src/Cholesky/LLT.h b/extern/Eigen2/Eigen/src/Cholesky/LLT.h deleted file mode 100644 index 42c959f83a2..00000000000 --- a/extern/Eigen2/Eigen/src/Cholesky/LLT.h +++ /dev/null @@ -1,219 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// 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/>. - -#ifndef EIGEN_LLT_H -#define EIGEN_LLT_H - -/** \ingroup cholesky_Module - * - * \class LLT - * - * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features - * - * \param MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition - * - * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite - * matrix A such that A = LL^* = U^*U, where L is lower triangular. - * - * While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, - * for that purpose, we recommend the Cholesky decomposition without square root which is more stable - * and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other - * situations like generalised eigen problems with hermitian matrices. - * - * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices, - * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations - * has a solution. - * - * \sa MatrixBase::llt(), class LDLT - */ - /* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH) - * Note that during the decomposition, only the upper triangular part of A is considered. Therefore, - * the strict lower part does not have to store correct values. - */ -template<typename MatrixType> class LLT -{ - private: - typedef typename MatrixType::Scalar Scalar; - typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; - typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; - - enum { - PacketSize = ei_packet_traits<Scalar>::size, - AlignmentMask = int(PacketSize)-1 - }; - - public: - - /** - * \brief Default Constructor. - * - * The default constructor is useful in cases in which the user intends to - * perform decompositions via LLT::compute(const MatrixType&). - */ - LLT() : m_matrix(), m_isInitialized(false) {} - - LLT(const MatrixType& matrix) - : m_matrix(matrix.rows(), matrix.cols()), - m_isInitialized(false) - { - compute(matrix); - } - - /** \returns the lower triangular matrix L */ - inline Part<MatrixType, LowerTriangular> matrixL(void) const - { - ei_assert(m_isInitialized && "LLT is not initialized."); - return m_matrix; - } - - /** \deprecated */ - inline bool isPositiveDefinite(void) const { return m_isInitialized && m_isPositiveDefinite; } - - template<typename RhsDerived, typename ResultType> - bool solve(const MatrixBase<RhsDerived> &b, ResultType *result) const; - - template<typename Derived> - bool solveInPlace(MatrixBase<Derived> &bAndX) const; - - void compute(const MatrixType& matrix); - - protected: - /** \internal - * Used to compute and store L - * The strict upper part is not used and even not initialized. - */ - MatrixType m_matrix; - bool m_isInitialized; - bool m_isPositiveDefinite; -}; - -/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix - */ -template<typename MatrixType> -void LLT<MatrixType>::compute(const MatrixType& a) -{ - assert(a.rows()==a.cols()); - m_isPositiveDefinite = true; - const int size = a.rows(); - m_matrix.resize(size, size); - // The biggest overall is the point of reference to which further diagonals - // are compared; if any diagonal is negligible compared - // to the largest overall, the algorithm bails. This cutoff is suggested - // in "Analysis of the Cholesky Decomposition of a Semi-definite Matrix" by - // Nicholas J. Higham. Also see "Accuracy and Stability of Numerical - // Algorithms" page 217, also by Higham. - const RealScalar cutoff = machine_epsilon<Scalar>() * size * a.diagonal().cwise().abs().maxCoeff(); - RealScalar x; - x = ei_real(a.coeff(0,0)); - m_matrix.coeffRef(0,0) = ei_sqrt(x); - if(size==1) - { - m_isInitialized = true; - return; - } - m_matrix.col(0).end(size-1) = a.row(0).end(size-1).adjoint() / ei_real(m_matrix.coeff(0,0)); - for (int j = 1; j < size; ++j) - { - x = ei_real(a.coeff(j,j)) - m_matrix.row(j).start(j).squaredNorm(); - if (x < cutoff) - { - m_isPositiveDefinite = false; - continue; - } - - m_matrix.coeffRef(j,j) = x = ei_sqrt(x); - - int endSize = size-j-1; - if (endSize>0) { - // Note that when all matrix columns have good alignment, then the following - // product is guaranteed to be optimal with respect to alignment. - m_matrix.col(j).end(endSize) = - (m_matrix.block(j+1, 0, endSize, j) * m_matrix.row(j).start(j).adjoint()).lazy(); - - // FIXME could use a.col instead of a.row - m_matrix.col(j).end(endSize) = (a.row(j).end(endSize).adjoint() - - m_matrix.col(j).end(endSize) ) / x; - } - } - - m_isInitialized = true; -} - -/** Computes the solution x of \f$ A x = b \f$ using the current decomposition of A. - * The result is stored in \a result - * - * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD. - * - * In other words, it computes \f$ b = A^{-1} b \f$ with - * \f$ {L^{*}}^{-1} L^{-1} b \f$ from right to left. - * - * Example: \include LLT_solve.cpp - * Output: \verbinclude LLT_solve.out - * - * \sa LLT::solveInPlace(), MatrixBase::llt() - */ -template<typename MatrixType> -template<typename RhsDerived, typename ResultType> -bool LLT<MatrixType>::solve(const MatrixBase<RhsDerived> &b, ResultType *result) const -{ - ei_assert(m_isInitialized && "LLT is not initialized."); - const int size = m_matrix.rows(); - ei_assert(size==b.rows() && "LLT::solve(): invalid number of rows of the right hand side matrix b"); - return solveInPlace((*result) = b); -} - -/** This is the \em in-place version of solve(). - * - * \param bAndX represents both the right-hand side matrix b and result x. - * - * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD. - * - * This version avoids a copy when the right hand side matrix b is not - * needed anymore. - * - * \sa LLT::solve(), MatrixBase::llt() - */ -template<typename MatrixType> -template<typename Derived> -bool LLT<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const -{ - ei_assert(m_isInitialized && "LLT is not initialized."); - const int size = m_matrix.rows(); - ei_assert(size==bAndX.rows()); - matrixL().solveTriangularInPlace(bAndX); - m_matrix.adjoint().template part<UpperTriangular>().solveTriangularInPlace(bAndX); - return true; -} - -/** \cholesky_module - * \returns the LLT decomposition of \c *this - */ -template<typename Derived> -inline const LLT<typename MatrixBase<Derived>::PlainMatrixType> -MatrixBase<Derived>::llt() const -{ - return LLT<PlainMatrixType>(derived()); -} - -#endif // EIGEN_LLT_H |