diff options
| author | Stanislaw Halik <sthalik@misaki.pl> | 2019-03-03 21:09:10 +0100 |
|---|---|---|
| committer | Stanislaw Halik <sthalik@misaki.pl> | 2019-03-03 21:10:13 +0100 |
| commit | f0238cfb6997c4acfc2bd200de7295f3fa36968f (patch) | |
| tree | b215183760e4f615b9c1dabc1f116383b72a1b55 /eigen/Eigen/src/SparseCholesky | |
| parent | 543edd372a5193d04b3de9f23c176ab439e51b31 (diff) | |
don't index Eigen
Diffstat (limited to 'eigen/Eigen/src/SparseCholesky')
| -rw-r--r-- | eigen/Eigen/src/SparseCholesky/SimplicialCholesky.h | 689 | ||||
| -rw-r--r-- | eigen/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h | 199 |
2 files changed, 0 insertions, 888 deletions
diff --git a/eigen/Eigen/src/SparseCholesky/SimplicialCholesky.h b/eigen/Eigen/src/SparseCholesky/SimplicialCholesky.h deleted file mode 100644 index 2907f65..0000000 --- a/eigen/Eigen/src/SparseCholesky/SimplicialCholesky.h +++ /dev/null @@ -1,689 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.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/. - -#ifndef EIGEN_SIMPLICIAL_CHOLESKY_H -#define EIGEN_SIMPLICIAL_CHOLESKY_H - -namespace Eigen { - -enum SimplicialCholeskyMode { - SimplicialCholeskyLLT, - SimplicialCholeskyLDLT -}; - -namespace internal { - template<typename CholMatrixType, typename InputMatrixType> - struct simplicial_cholesky_grab_input { - typedef CholMatrixType const * ConstCholMatrixPtr; - static void run(const InputMatrixType& input, ConstCholMatrixPtr &pmat, CholMatrixType &tmp) - { - tmp = input; - pmat = &tmp; - } - }; - - template<typename MatrixType> - struct simplicial_cholesky_grab_input<MatrixType,MatrixType> { - typedef MatrixType const * ConstMatrixPtr; - static void run(const MatrixType& input, ConstMatrixPtr &pmat, MatrixType &/*tmp*/) - { - pmat = &input; - } - }; -} // end namespace internal - -/** \ingroup SparseCholesky_Module - * \brief A base class for direct sparse Cholesky factorizations - * - * This is a base class for LL^T and LDL^T Cholesky factorizations of sparse matrices that are - * selfadjoint and positive definite. These factorizations allow for solving A.X = B where - * X and B can be either dense or sparse. - * - * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization - * such that the factorized matrix is P A P^-1. - * - * \tparam Derived the type of the derived class, that is the actual factorization type. - * - */ -template<typename Derived> -class SimplicialCholeskyBase : public SparseSolverBase<Derived> -{ - typedef SparseSolverBase<Derived> Base; - using Base::m_isInitialized; - - public: - typedef typename internal::traits<Derived>::MatrixType MatrixType; - typedef typename internal::traits<Derived>::OrderingType OrderingType; - enum { UpLo = internal::traits<Derived>::UpLo }; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::StorageIndex StorageIndex; - typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType; - typedef CholMatrixType const * ConstCholMatrixPtr; - typedef Matrix<Scalar,Dynamic,1> VectorType; - typedef Matrix<StorageIndex,Dynamic,1> VectorI; - - enum { - ColsAtCompileTime = MatrixType::ColsAtCompileTime, - MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime - }; - - public: - - using Base::derived; - - /** Default constructor */ - SimplicialCholeskyBase() - : m_info(Success), m_shiftOffset(0), m_shiftScale(1) - {} - - explicit SimplicialCholeskyBase(const MatrixType& matrix) - : m_info(Success), m_shiftOffset(0), m_shiftScale(1) - { - derived().compute(matrix); - } - - ~SimplicialCholeskyBase() - { - } - - Derived& derived() { return *static_cast<Derived*>(this); } - const Derived& derived() const { return *static_cast<const Derived*>(this); } - - inline Index cols() const { return m_matrix.cols(); } - inline Index rows() const { return m_matrix.rows(); } - - /** \brief Reports whether previous computation was successful. - * - * \returns \c Success if computation was succesful, - * \c NumericalIssue if the matrix.appears to be negative. - */ - ComputationInfo info() const - { - eigen_assert(m_isInitialized && "Decomposition is not initialized."); - return m_info; - } - - /** \returns the permutation P - * \sa permutationPinv() */ - const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& permutationP() const - { return m_P; } - - /** \returns the inverse P^-1 of the permutation P - * \sa permutationP() */ - const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& permutationPinv() const - { return m_Pinv; } - - /** Sets the shift parameters that will be used to adjust the diagonal coefficients during the numerical factorization. - * - * During the numerical factorization, the diagonal coefficients are transformed by the following linear model:\n - * \c d_ii = \a offset + \a scale * \c d_ii - * - * The default is the identity transformation with \a offset=0, and \a scale=1. - * - * \returns a reference to \c *this. - */ - Derived& setShift(const RealScalar& offset, const RealScalar& scale = 1) - { - m_shiftOffset = offset; - m_shiftScale = scale; - return derived(); - } - -#ifndef EIGEN_PARSED_BY_DOXYGEN - /** \internal */ - template<typename Stream> - void dumpMemory(Stream& s) - { - int total = 0; - s << " L: " << ((total+=(m_matrix.cols()+1) * sizeof(int) + m_matrix.nonZeros()*(sizeof(int)+sizeof(Scalar))) >> 20) << "Mb" << "\n"; - s << " diag: " << ((total+=m_diag.size() * sizeof(Scalar)) >> 20) << "Mb" << "\n"; - s << " tree: " << ((total+=m_parent.size() * sizeof(int)) >> 20) << "Mb" << "\n"; - s << " nonzeros: " << ((total+=m_nonZerosPerCol.size() * sizeof(int)) >> 20) << "Mb" << "\n"; - s << " perm: " << ((total+=m_P.size() * sizeof(int)) >> 20) << "Mb" << "\n"; - s << " perm^-1: " << ((total+=m_Pinv.size() * sizeof(int)) >> 20) << "Mb" << "\n"; - s << " TOTAL: " << (total>> 20) << "Mb" << "\n"; - } - - /** \internal */ - template<typename Rhs,typename Dest> - void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const - { - eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()"); - eigen_assert(m_matrix.rows()==b.rows()); - - if(m_info!=Success) - return; - - if(m_P.size()>0) - dest = m_P * b; - else - dest = b; - - if(m_matrix.nonZeros()>0) // otherwise L==I - derived().matrixL().solveInPlace(dest); - - if(m_diag.size()>0) - dest = m_diag.asDiagonal().inverse() * dest; - - if (m_matrix.nonZeros()>0) // otherwise U==I - derived().matrixU().solveInPlace(dest); - - if(m_P.size()>0) - dest = m_Pinv * dest; - } - - template<typename Rhs,typename Dest> - void _solve_impl(const SparseMatrixBase<Rhs> &b, SparseMatrixBase<Dest> &dest) const - { - internal::solve_sparse_through_dense_panels(derived(), b, dest); - } - -#endif // EIGEN_PARSED_BY_DOXYGEN - - protected: - - /** Computes the sparse Cholesky decomposition of \a matrix */ - template<bool DoLDLT> - void compute(const MatrixType& matrix) - { - eigen_assert(matrix.rows()==matrix.cols()); - Index size = matrix.cols(); - CholMatrixType tmp(size,size); - ConstCholMatrixPtr pmat; - ordering(matrix, pmat, tmp); - analyzePattern_preordered(*pmat, DoLDLT); - factorize_preordered<DoLDLT>(*pmat); - } - - template<bool DoLDLT> - void factorize(const MatrixType& a) - { - eigen_assert(a.rows()==a.cols()); - Index size = a.cols(); - CholMatrixType tmp(size,size); - ConstCholMatrixPtr pmat; - - if(m_P.size()==0 && (UpLo&Upper)==Upper) - { - // If there is no ordering, try to directly use the input matrix without any copy - internal::simplicial_cholesky_grab_input<CholMatrixType,MatrixType>::run(a, pmat, tmp); - } - else - { - tmp.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P); - pmat = &tmp; - } - - factorize_preordered<DoLDLT>(*pmat); - } - - template<bool DoLDLT> - void factorize_preordered(const CholMatrixType& a); - - void analyzePattern(const MatrixType& a, bool doLDLT) - { - eigen_assert(a.rows()==a.cols()); - Index size = a.cols(); - CholMatrixType tmp(size,size); - ConstCholMatrixPtr pmat; - ordering(a, pmat, tmp); - analyzePattern_preordered(*pmat,doLDLT); - } - void analyzePattern_preordered(const CholMatrixType& a, bool doLDLT); - - void ordering(const MatrixType& a, ConstCholMatrixPtr &pmat, CholMatrixType& ap); - - /** keeps off-diagonal entries; drops diagonal entries */ - struct keep_diag { - inline bool operator() (const Index& row, const Index& col, const Scalar&) const - { - return row!=col; - } - }; - - mutable ComputationInfo m_info; - bool m_factorizationIsOk; - bool m_analysisIsOk; - - CholMatrixType m_matrix; - VectorType m_diag; // the diagonal coefficients (LDLT mode) - VectorI m_parent; // elimination tree - VectorI m_nonZerosPerCol; - PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_P; // the permutation - PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_Pinv; // the inverse permutation - - RealScalar m_shiftOffset; - RealScalar m_shiftScale; -}; - -template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::StorageIndex> > class SimplicialLLT; -template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::StorageIndex> > class SimplicialLDLT; -template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::StorageIndex> > class SimplicialCholesky; - -namespace internal { - -template<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialLLT<_MatrixType,_UpLo,_Ordering> > -{ - typedef _MatrixType MatrixType; - typedef _Ordering OrderingType; - enum { UpLo = _UpLo }; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::StorageIndex StorageIndex; - typedef SparseMatrix<Scalar, ColMajor, StorageIndex> CholMatrixType; - typedef TriangularView<const CholMatrixType, Eigen::Lower> MatrixL; - typedef TriangularView<const typename CholMatrixType::AdjointReturnType, Eigen::Upper> MatrixU; - static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); } - static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); } -}; - -template<typename _MatrixType,int _UpLo, typename _Ordering> struct traits<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> > -{ - typedef _MatrixType MatrixType; - typedef _Ordering OrderingType; - enum { UpLo = _UpLo }; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::StorageIndex StorageIndex; - typedef SparseMatrix<Scalar, ColMajor, StorageIndex> CholMatrixType; - typedef TriangularView<const CholMatrixType, Eigen::UnitLower> MatrixL; - typedef TriangularView<const typename CholMatrixType::AdjointReturnType, Eigen::UnitUpper> MatrixU; - static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); } - static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); } -}; - -template<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> > -{ - typedef _MatrixType MatrixType; - typedef _Ordering OrderingType; - enum { UpLo = _UpLo }; -}; - -} - -/** \ingroup SparseCholesky_Module - * \class SimplicialLLT - * \brief A direct sparse LLT Cholesky factorizations - * - * This class provides a LL^T Cholesky factorizations of sparse matrices that are - * selfadjoint and positive definite. The factorization allows for solving A.X = B where - * X and B can be either dense or sparse. - * - * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization - * such that the factorized matrix is P A P^-1. - * - * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> - * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower - * or Upper. Default is Lower. - * \tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<> - * - * \implsparsesolverconcept - * - * \sa class SimplicialLDLT, class AMDOrdering, class NaturalOrdering - */ -template<typename _MatrixType, int _UpLo, typename _Ordering> - class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<_MatrixType,_UpLo,_Ordering> > -{ -public: - typedef _MatrixType MatrixType; - enum { UpLo = _UpLo }; - typedef SimplicialCholeskyBase<SimplicialLLT> Base; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::StorageIndex StorageIndex; - typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType; - typedef Matrix<Scalar,Dynamic,1> VectorType; - typedef internal::traits<SimplicialLLT> Traits; - typedef typename Traits::MatrixL MatrixL; - typedef typename Traits::MatrixU MatrixU; -public: - /** Default constructor */ - SimplicialLLT() : Base() {} - /** Constructs and performs the LLT factorization of \a matrix */ - explicit SimplicialLLT(const MatrixType& matrix) - : Base(matrix) {} - - /** \returns an expression of the factor L */ - inline const MatrixL matrixL() const { - eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized"); - return Traits::getL(Base::m_matrix); - } - - /** \returns an expression of the factor U (= L^*) */ - inline const MatrixU matrixU() const { - eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized"); - return Traits::getU(Base::m_matrix); - } - - /** Computes the sparse Cholesky decomposition of \a matrix */ - SimplicialLLT& compute(const MatrixType& matrix) - { - Base::template compute<false>(matrix); - return *this; - } - - /** Performs a symbolic decomposition on the sparcity of \a matrix. - * - * This function is particularly useful when solving for several problems having the same structure. - * - * \sa factorize() - */ - void analyzePattern(const MatrixType& a) - { - Base::analyzePattern(a, false); - } - - /** Performs a numeric decomposition of \a matrix - * - * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed. - * - * \sa analyzePattern() - */ - void factorize(const MatrixType& a) - { - Base::template factorize<false>(a); - } - - /** \returns the determinant of the underlying matrix from the current factorization */ - Scalar determinant() const - { - Scalar detL = Base::m_matrix.diagonal().prod(); - return numext::abs2(detL); - } -}; - -/** \ingroup SparseCholesky_Module - * \class SimplicialLDLT - * \brief A direct sparse LDLT Cholesky factorizations without square root. - * - * This class provides a LDL^T Cholesky factorizations without square root of sparse matrices that are - * selfadjoint and positive definite. The factorization allows for solving A.X = B where - * X and B can be either dense or sparse. - * - * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization - * such that the factorized matrix is P A P^-1. - * - * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<> - * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower - * or Upper. Default is Lower. - * \tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<> - * - * \implsparsesolverconcept - * - * \sa class SimplicialLLT, class AMDOrdering, class NaturalOrdering - */ -template<typename _MatrixType, int _UpLo, typename _Ordering> - class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> > -{ -public: - typedef _MatrixType MatrixType; - enum { UpLo = _UpLo }; - typedef SimplicialCholeskyBase<SimplicialLDLT> Base; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::StorageIndex StorageIndex; - typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType; - typedef Matrix<Scalar,Dynamic,1> VectorType; - typedef internal::traits<SimplicialLDLT> Traits; - typedef typename Traits::MatrixL MatrixL; - typedef typename Traits::MatrixU MatrixU; -public: - /** Default constructor */ - SimplicialLDLT() : Base() {} - - /** Constructs and performs the LLT factorization of \a matrix */ - explicit SimplicialLDLT(const MatrixType& matrix) - : Base(matrix) {} - - /** \returns a vector expression of the diagonal D */ - inline const VectorType vectorD() const { - eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized"); - return Base::m_diag; - } - /** \returns an expression of the factor L */ - inline const MatrixL matrixL() const { - eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized"); - return Traits::getL(Base::m_matrix); - } - - /** \returns an expression of the factor U (= L^*) */ - inline const MatrixU matrixU() const { - eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized"); - return Traits::getU(Base::m_matrix); - } - - /** Computes the sparse Cholesky decomposition of \a matrix */ - SimplicialLDLT& compute(const MatrixType& matrix) - { - Base::template compute<true>(matrix); - return *this; - } - - /** Performs a symbolic decomposition on the sparcity of \a matrix. - * - * This function is particularly useful when solving for several problems having the same structure. - * - * \sa factorize() - */ - void analyzePattern(const MatrixType& a) - { - Base::analyzePattern(a, true); - } - - /** Performs a numeric decomposition of \a matrix - * - * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed. - * - * \sa analyzePattern() - */ - void factorize(const MatrixType& a) - { - Base::template factorize<true>(a); - } - - /** \returns the determinant of the underlying matrix from the current factorization */ - Scalar determinant() const - { - return Base::m_diag.prod(); - } -}; - -/** \deprecated use SimplicialLDLT or class SimplicialLLT - * \ingroup SparseCholesky_Module - * \class SimplicialCholesky - * - * \sa class SimplicialLDLT, class SimplicialLLT - */ -template<typename _MatrixType, int _UpLo, typename _Ordering> - class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> > -{ -public: - typedef _MatrixType MatrixType; - enum { UpLo = _UpLo }; - typedef SimplicialCholeskyBase<SimplicialCholesky> Base; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::StorageIndex StorageIndex; - typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType; - typedef Matrix<Scalar,Dynamic,1> VectorType; - typedef internal::traits<SimplicialCholesky> Traits; - typedef internal::traits<SimplicialLDLT<MatrixType,UpLo> > LDLTTraits; - typedef internal::traits<SimplicialLLT<MatrixType,UpLo> > LLTTraits; - public: - SimplicialCholesky() : Base(), m_LDLT(true) {} - - explicit SimplicialCholesky(const MatrixType& matrix) - : Base(), m_LDLT(true) - { - compute(matrix); - } - - SimplicialCholesky& setMode(SimplicialCholeskyMode mode) - { - switch(mode) - { - case SimplicialCholeskyLLT: - m_LDLT = false; - break; - case SimplicialCholeskyLDLT: - m_LDLT = true; - break; - default: - break; - } - - return *this; - } - - inline const VectorType vectorD() const { - eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky not factorized"); - return Base::m_diag; - } - inline const CholMatrixType rawMatrix() const { - eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky not factorized"); - return Base::m_matrix; - } - - /** Computes the sparse Cholesky decomposition of \a matrix */ - SimplicialCholesky& compute(const MatrixType& matrix) - { - if(m_LDLT) - Base::template compute<true>(matrix); - else - Base::template compute<false>(matrix); - return *this; - } - - /** Performs a symbolic decomposition on the sparcity of \a matrix. - * - * This function is particularly useful when solving for several problems having the same structure. - * - * \sa factorize() - */ - void analyzePattern(const MatrixType& a) - { - Base::analyzePattern(a, m_LDLT); - } - - /** Performs a numeric decomposition of \a matrix - * - * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed. - * - * \sa analyzePattern() - */ - void factorize(const MatrixType& a) - { - if(m_LDLT) - Base::template factorize<true>(a); - else - Base::template factorize<false>(a); - } - - /** \internal */ - template<typename Rhs,typename Dest> - void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const - { - eigen_assert(Base::m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()"); - eigen_assert(Base::m_matrix.rows()==b.rows()); - - if(Base::m_info!=Success) - return; - - if(Base::m_P.size()>0) - dest = Base::m_P * b; - else - dest = b; - - if(Base::m_matrix.nonZeros()>0) // otherwise L==I - { - if(m_LDLT) - LDLTTraits::getL(Base::m_matrix).solveInPlace(dest); - else - LLTTraits::getL(Base::m_matrix).solveInPlace(dest); - } - - if(Base::m_diag.size()>0) - dest = Base::m_diag.asDiagonal().inverse() * dest; - - if (Base::m_matrix.nonZeros()>0) // otherwise I==I - { - if(m_LDLT) - LDLTTraits::getU(Base::m_matrix).solveInPlace(dest); - else - LLTTraits::getU(Base::m_matrix).solveInPlace(dest); - } - - if(Base::m_P.size()>0) - dest = Base::m_Pinv * dest; - } - - /** \internal */ - template<typename Rhs,typename Dest> - void _solve_impl(const SparseMatrixBase<Rhs> &b, SparseMatrixBase<Dest> &dest) const - { - internal::solve_sparse_through_dense_panels(*this, b, dest); - } - - Scalar determinant() const - { - if(m_LDLT) - { - return Base::m_diag.prod(); - } - else - { - Scalar detL = Diagonal<const CholMatrixType>(Base::m_matrix).prod(); - return numext::abs2(detL); - } - } - - protected: - bool m_LDLT; -}; - -template<typename Derived> -void SimplicialCholeskyBase<Derived>::ordering(const MatrixType& a, ConstCholMatrixPtr &pmat, CholMatrixType& ap) -{ - eigen_assert(a.rows()==a.cols()); - const Index size = a.rows(); - pmat = ≈ - // Note that ordering methods compute the inverse permutation - if(!internal::is_same<OrderingType,NaturalOrdering<Index> >::value) - { - { - CholMatrixType C; - C = a.template selfadjointView<UpLo>(); - - OrderingType ordering; - ordering(C,m_Pinv); - } - - if(m_Pinv.size()>0) m_P = m_Pinv.inverse(); - else m_P.resize(0); - - ap.resize(size,size); - ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P); - } - else - { - m_Pinv.resize(0); - m_P.resize(0); - if(int(UpLo)==int(Lower) || MatrixType::IsRowMajor) - { - // we have to transpose the lower part to to the upper one - ap.resize(size,size); - ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>(); - } - else - internal::simplicial_cholesky_grab_input<CholMatrixType,MatrixType>::run(a, pmat, ap); - } -} - -} // end namespace Eigen - -#endif // EIGEN_SIMPLICIAL_CHOLESKY_H diff --git a/eigen/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h b/eigen/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h deleted file mode 100644 index 31e0699..0000000 --- a/eigen/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h +++ /dev/null @@ -1,199 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr> - -/* - -NOTE: thes functions vave been adapted from the LDL library: - -LDL Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved. - -LDL License: - - Your use or distribution of LDL or any modified version of - LDL implies that you agree to this License. - - This library 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 2.1 of the License, or (at your option) any later version. - - This library 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 for more details. - - You should have received a copy of the GNU Lesser General Public - License along with this library; if not, write to the Free Software - Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 - USA - - Permission is hereby granted to use or copy this program under the - terms of the GNU LGPL, provided that the Copyright, this License, - and the Availability of the original version is retained on all copies. - User documentation of any code that uses this code or any modified - version of this code must cite the Copyright, this License, the - Availability note, and "Used by permission." Permission to modify - the code and to distribute modified code is granted, provided the - Copyright, this License, and the Availability note are retained, - and a notice that the code was modified is included. - */ - -#include "../Core/util/NonMPL2.h" - -#ifndef EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H -#define EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H - -namespace Eigen { - -template<typename Derived> -void SimplicialCholeskyBase<Derived>::analyzePattern_preordered(const CholMatrixType& ap, bool doLDLT) -{ - const StorageIndex size = StorageIndex(ap.rows()); - m_matrix.resize(size, size); - m_parent.resize(size); - m_nonZerosPerCol.resize(size); - - ei_declare_aligned_stack_constructed_variable(StorageIndex, tags, size, 0); - - for(StorageIndex k = 0; k < size; ++k) - { - /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */ - m_parent[k] = -1; /* parent of k is not yet known */ - tags[k] = k; /* mark node k as visited */ - m_nonZerosPerCol[k] = 0; /* count of nonzeros in column k of L */ - for(typename CholMatrixType::InnerIterator it(ap,k); it; ++it) - { - StorageIndex i = it.index(); - if(i < k) - { - /* follow path from i to root of etree, stop at flagged node */ - for(; tags[i] != k; i = m_parent[i]) - { - /* find parent of i if not yet determined */ - if (m_parent[i] == -1) - m_parent[i] = k; - m_nonZerosPerCol[i]++; /* L (k,i) is nonzero */ - tags[i] = k; /* mark i as visited */ - } - } - } - } - - /* construct Lp index array from m_nonZerosPerCol column counts */ - StorageIndex* Lp = m_matrix.outerIndexPtr(); - Lp[0] = 0; - for(StorageIndex k = 0; k < size; ++k) - Lp[k+1] = Lp[k] + m_nonZerosPerCol[k] + (doLDLT ? 0 : 1); - - m_matrix.resizeNonZeros(Lp[size]); - - m_isInitialized = true; - m_info = Success; - m_analysisIsOk = true; - m_factorizationIsOk = false; -} - - -template<typename Derived> -template<bool DoLDLT> -void SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType& ap) -{ - using std::sqrt; - - eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); - eigen_assert(ap.rows()==ap.cols()); - eigen_assert(m_parent.size()==ap.rows()); - eigen_assert(m_nonZerosPerCol.size()==ap.rows()); - - const StorageIndex size = StorageIndex(ap.rows()); - const StorageIndex* Lp = m_matrix.outerIndexPtr(); - StorageIndex* Li = m_matrix.innerIndexPtr(); - Scalar* Lx = m_matrix.valuePtr(); - - ei_declare_aligned_stack_constructed_variable(Scalar, y, size, 0); - ei_declare_aligned_stack_constructed_variable(StorageIndex, pattern, size, 0); - ei_declare_aligned_stack_constructed_variable(StorageIndex, tags, size, 0); - - bool ok = true; - m_diag.resize(DoLDLT ? size : 0); - - for(StorageIndex k = 0; k < size; ++k) - { - // compute nonzero pattern of kth row of L, in topological order - y[k] = 0.0; // Y(0:k) is now all zero - StorageIndex top = size; // stack for pattern is empty - tags[k] = k; // mark node k as visited - m_nonZerosPerCol[k] = 0; // count of nonzeros in column k of L - for(typename CholMatrixType::InnerIterator it(ap,k); it; ++it) - { - StorageIndex i = it.index(); - if(i <= k) - { - y[i] += numext::conj(it.value()); /* scatter A(i,k) into Y (sum duplicates) */ - Index len; - for(len = 0; tags[i] != k; i = m_parent[i]) - { - pattern[len++] = i; /* L(k,i) is nonzero */ - tags[i] = k; /* mark i as visited */ - } - while(len > 0) - pattern[--top] = pattern[--len]; - } - } - - /* compute numerical values kth row of L (a sparse triangular solve) */ - - RealScalar d = numext::real(y[k]) * m_shiftScale + m_shiftOffset; // get D(k,k), apply the shift function, and clear Y(k) - y[k] = 0.0; - for(; top < size; ++top) - { - Index i = pattern[top]; /* pattern[top:n-1] is pattern of L(:,k) */ - Scalar yi = y[i]; /* get and clear Y(i) */ - y[i] = 0.0; - - /* the nonzero entry L(k,i) */ - Scalar l_ki; - if(DoLDLT) - l_ki = yi / m_diag[i]; - else - yi = l_ki = yi / Lx[Lp[i]]; - - Index p2 = Lp[i] + m_nonZerosPerCol[i]; - Index p; - for(p = Lp[i] + (DoLDLT ? 0 : 1); p < p2; ++p) - y[Li[p]] -= numext::conj(Lx[p]) * yi; - d -= numext::real(l_ki * numext::conj(yi)); - Li[p] = k; /* store L(k,i) in column form of L */ - Lx[p] = l_ki; - ++m_nonZerosPerCol[i]; /* increment count of nonzeros in col i */ - } - if(DoLDLT) - { - m_diag[k] = d; - if(d == RealScalar(0)) - { - ok = false; /* failure, D(k,k) is zero */ - break; - } - } - else - { - Index p = Lp[k] + m_nonZerosPerCol[k]++; - Li[p] = k ; /* store L(k,k) = sqrt (d) in column k */ - if(d <= RealScalar(0)) { - ok = false; /* failure, matrix is not positive definite */ - break; - } - Lx[p] = sqrt(d) ; - } - } - - m_info = ok ? Success : NumericalIssue; - m_factorizationIsOk = true; -} - -} // end namespace Eigen - -#endif // EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H |
