[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #ifndef EIGEN_PASTIXSUPPORT_H
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| 11 | #define EIGEN_PASTIXSUPPORT_H
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| 12 |
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| 13 | #if defined(DCOMPLEX)
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| 14 | #define PASTIX_COMPLEX COMPLEX
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| 15 | #define PASTIX_DCOMPLEX DCOMPLEX
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| 16 | #else
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| 17 | #define PASTIX_COMPLEX std::complex<float>
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| 18 | #define PASTIX_DCOMPLEX std::complex<double>
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| 19 | #endif
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| 20 |
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| 21 | namespace Eigen {
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| 22 |
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| 23 | /** \ingroup PaStiXSupport_Module
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| 24 | * \brief Interface to the PaStix solver
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| 25 | *
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| 26 | * This class is used to solve the linear systems A.X = B via the PaStix library.
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| 27 | * The matrix can be either real or complex, symmetric or not.
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| 28 | *
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| 29 | * \sa TutorialSparseDirectSolvers
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| 30 | */
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| 31 | template<typename _MatrixType, bool IsStrSym = false> class PastixLU;
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| 32 | template<typename _MatrixType, int Options> class PastixLLT;
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| 33 | template<typename _MatrixType, int Options> class PastixLDLT;
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| 34 |
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| 35 | namespace internal
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| 36 | {
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| 37 |
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| 38 | template<class Pastix> struct pastix_traits;
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| 39 |
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| 40 | template<typename _MatrixType>
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| 41 | struct pastix_traits< PastixLU<_MatrixType> >
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| 42 | {
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| 43 | typedef _MatrixType MatrixType;
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| 44 | typedef typename _MatrixType::Scalar Scalar;
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| 45 | typedef typename _MatrixType::RealScalar RealScalar;
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| 46 | typedef typename _MatrixType::Index Index;
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| 47 | };
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| 48 |
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| 49 | template<typename _MatrixType, int Options>
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| 50 | struct pastix_traits< PastixLLT<_MatrixType,Options> >
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| 51 | {
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| 52 | typedef _MatrixType MatrixType;
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| 53 | typedef typename _MatrixType::Scalar Scalar;
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| 54 | typedef typename _MatrixType::RealScalar RealScalar;
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| 55 | typedef typename _MatrixType::Index Index;
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| 56 | };
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| 57 |
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| 58 | template<typename _MatrixType, int Options>
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| 59 | struct pastix_traits< PastixLDLT<_MatrixType,Options> >
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| 60 | {
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| 61 | typedef _MatrixType MatrixType;
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| 62 | typedef typename _MatrixType::Scalar Scalar;
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| 63 | typedef typename _MatrixType::RealScalar RealScalar;
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| 64 | typedef typename _MatrixType::Index Index;
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| 65 | };
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| 66 |
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| 67 | void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, float *vals, int *perm, int * invp, float *x, int nbrhs, int *iparm, double *dparm)
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| 68 | {
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| 69 | if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
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| 70 | if (nbrhs == 0) {x = NULL; nbrhs=1;}
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| 71 | s_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
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| 72 | }
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| 73 |
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| 74 | void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, double *vals, int *perm, int * invp, double *x, int nbrhs, int *iparm, double *dparm)
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| 75 | {
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| 76 | if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
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| 77 | if (nbrhs == 0) {x = NULL; nbrhs=1;}
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| 78 | d_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
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| 79 | }
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| 80 |
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| 81 | void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<float> *vals, int *perm, int * invp, std::complex<float> *x, int nbrhs, int *iparm, double *dparm)
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| 82 | {
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| 83 | if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
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| 84 | if (nbrhs == 0) {x = NULL; nbrhs=1;}
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| 85 | c_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_COMPLEX*>(vals), perm, invp, reinterpret_cast<PASTIX_COMPLEX*>(x), nbrhs, iparm, dparm);
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| 86 | }
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| 87 |
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| 88 | void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<double> *vals, int *perm, int * invp, std::complex<double> *x, int nbrhs, int *iparm, double *dparm)
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| 89 | {
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| 90 | if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
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| 91 | if (nbrhs == 0) {x = NULL; nbrhs=1;}
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| 92 | z_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_DCOMPLEX*>(vals), perm, invp, reinterpret_cast<PASTIX_DCOMPLEX*>(x), nbrhs, iparm, dparm);
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| 93 | }
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| 94 |
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| 95 | // Convert the matrix to Fortran-style Numbering
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| 96 | template <typename MatrixType>
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| 97 | void c_to_fortran_numbering (MatrixType& mat)
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| 98 | {
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| 99 | if ( !(mat.outerIndexPtr()[0]) )
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| 100 | {
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| 101 | int i;
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| 102 | for(i = 0; i <= mat.rows(); ++i)
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| 103 | ++mat.outerIndexPtr()[i];
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| 104 | for(i = 0; i < mat.nonZeros(); ++i)
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| 105 | ++mat.innerIndexPtr()[i];
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| 106 | }
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| 107 | }
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| 108 |
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| 109 | // Convert to C-style Numbering
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| 110 | template <typename MatrixType>
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| 111 | void fortran_to_c_numbering (MatrixType& mat)
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| 112 | {
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| 113 | // Check the Numbering
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| 114 | if ( mat.outerIndexPtr()[0] == 1 )
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| 115 | { // Convert to C-style numbering
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| 116 | int i;
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| 117 | for(i = 0; i <= mat.rows(); ++i)
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| 118 | --mat.outerIndexPtr()[i];
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| 119 | for(i = 0; i < mat.nonZeros(); ++i)
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| 120 | --mat.innerIndexPtr()[i];
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| 121 | }
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| 122 | }
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| 123 | }
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| 124 |
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| 125 | // This is the base class to interface with PaStiX functions.
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| 126 | // Users should not used this class directly.
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| 127 | template <class Derived>
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| 128 | class PastixBase : internal::noncopyable
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| 129 | {
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| 130 | public:
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| 131 | typedef typename internal::pastix_traits<Derived>::MatrixType _MatrixType;
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| 132 | typedef _MatrixType MatrixType;
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| 133 | typedef typename MatrixType::Scalar Scalar;
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| 134 | typedef typename MatrixType::RealScalar RealScalar;
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| 135 | typedef typename MatrixType::Index Index;
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| 136 | typedef Matrix<Scalar,Dynamic,1> Vector;
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| 137 | typedef SparseMatrix<Scalar, ColMajor> ColSpMatrix;
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| 138 |
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| 139 | public:
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| 140 |
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| 141 | PastixBase() : m_initisOk(false), m_analysisIsOk(false), m_factorizationIsOk(false), m_isInitialized(false), m_pastixdata(0), m_size(0)
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| 142 | {
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| 143 | init();
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| 144 | }
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| 145 |
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| 146 | ~PastixBase()
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| 147 | {
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| 148 | clean();
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| 149 | }
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| 150 |
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| 151 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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| 152 | *
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| 153 | * \sa compute()
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| 154 | */
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| 155 | template<typename Rhs>
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| 156 | inline const internal::solve_retval<PastixBase, Rhs>
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| 157 | solve(const MatrixBase<Rhs>& b) const
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| 158 | {
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| 159 | eigen_assert(m_isInitialized && "Pastix solver is not initialized.");
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| 160 | eigen_assert(rows()==b.rows()
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| 161 | && "PastixBase::solve(): invalid number of rows of the right hand side matrix b");
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| 162 | return internal::solve_retval<PastixBase, Rhs>(*this, b.derived());
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| 163 | }
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| 164 |
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| 165 | template<typename Rhs,typename Dest>
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| 166 | bool _solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const;
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| 167 |
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| 168 | Derived& derived()
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| 169 | {
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| 170 | return *static_cast<Derived*>(this);
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| 171 | }
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| 172 | const Derived& derived() const
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| 173 | {
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| 174 | return *static_cast<const Derived*>(this);
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| 175 | }
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| 176 |
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| 177 | /** Returns a reference to the integer vector IPARM of PaStiX parameters
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| 178 | * to modify the default parameters.
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| 179 | * The statistics related to the different phases of factorization and solve are saved here as well
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| 180 | * \sa analyzePattern() factorize()
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| 181 | */
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| 182 | Array<Index,IPARM_SIZE,1>& iparm()
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| 183 | {
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| 184 | return m_iparm;
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| 185 | }
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| 186 |
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| 187 | /** Return a reference to a particular index parameter of the IPARM vector
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| 188 | * \sa iparm()
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| 189 | */
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| 190 |
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| 191 | int& iparm(int idxparam)
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| 192 | {
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| 193 | return m_iparm(idxparam);
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| 194 | }
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| 195 |
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| 196 | /** Returns a reference to the double vector DPARM of PaStiX parameters
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| 197 | * The statistics related to the different phases of factorization and solve are saved here as well
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| 198 | * \sa analyzePattern() factorize()
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| 199 | */
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| 200 | Array<RealScalar,IPARM_SIZE,1>& dparm()
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| 201 | {
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| 202 | return m_dparm;
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| 203 | }
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| 204 |
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| 205 |
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| 206 | /** Return a reference to a particular index parameter of the DPARM vector
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| 207 | * \sa dparm()
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| 208 | */
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| 209 | double& dparm(int idxparam)
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| 210 | {
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| 211 | return m_dparm(idxparam);
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| 212 | }
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| 213 |
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| 214 | inline Index cols() const { return m_size; }
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| 215 | inline Index rows() const { return m_size; }
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| 216 |
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| 217 | /** \brief Reports whether previous computation was successful.
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| 218 | *
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| 219 | * \returns \c Success if computation was succesful,
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| 220 | * \c NumericalIssue if the PaStiX reports a problem
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| 221 | * \c InvalidInput if the input matrix is invalid
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| 222 | *
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| 223 | * \sa iparm()
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| 224 | */
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| 225 | ComputationInfo info() const
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| 226 | {
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| 227 | eigen_assert(m_isInitialized && "Decomposition is not initialized.");
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| 228 | return m_info;
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| 229 | }
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| 230 |
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| 231 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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| 232 | *
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| 233 | * \sa compute()
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| 234 | */
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| 235 | template<typename Rhs>
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| 236 | inline const internal::sparse_solve_retval<PastixBase, Rhs>
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| 237 | solve(const SparseMatrixBase<Rhs>& b) const
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| 238 | {
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| 239 | eigen_assert(m_isInitialized && "Pastix LU, LLT or LDLT is not initialized.");
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| 240 | eigen_assert(rows()==b.rows()
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| 241 | && "PastixBase::solve(): invalid number of rows of the right hand side matrix b");
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| 242 | return internal::sparse_solve_retval<PastixBase, Rhs>(*this, b.derived());
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| 243 | }
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| 244 |
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| 245 | protected:
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| 246 |
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| 247 | // Initialize the Pastix data structure, check the matrix
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| 248 | void init();
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| 249 |
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| 250 | // Compute the ordering and the symbolic factorization
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| 251 | void analyzePattern(ColSpMatrix& mat);
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| 252 |
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| 253 | // Compute the numerical factorization
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| 254 | void factorize(ColSpMatrix& mat);
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| 255 |
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| 256 | // Free all the data allocated by Pastix
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| 257 | void clean()
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| 258 | {
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| 259 | eigen_assert(m_initisOk && "The Pastix structure should be allocated first");
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| 260 | m_iparm(IPARM_START_TASK) = API_TASK_CLEAN;
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| 261 | m_iparm(IPARM_END_TASK) = API_TASK_CLEAN;
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| 262 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,
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| 263 | m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
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| 264 | }
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| 265 |
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| 266 | void compute(ColSpMatrix& mat);
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| 267 |
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| 268 | int m_initisOk;
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| 269 | int m_analysisIsOk;
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| 270 | int m_factorizationIsOk;
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| 271 | bool m_isInitialized;
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| 272 | mutable ComputationInfo m_info;
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| 273 | mutable pastix_data_t *m_pastixdata; // Data structure for pastix
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| 274 | mutable int m_comm; // The MPI communicator identifier
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| 275 | mutable Matrix<int,IPARM_SIZE,1> m_iparm; // integer vector for the input parameters
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| 276 | mutable Matrix<double,DPARM_SIZE,1> m_dparm; // Scalar vector for the input parameters
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| 277 | mutable Matrix<Index,Dynamic,1> m_perm; // Permutation vector
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| 278 | mutable Matrix<Index,Dynamic,1> m_invp; // Inverse permutation vector
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| 279 | mutable int m_size; // Size of the matrix
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| 280 | };
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| 281 |
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| 282 | /** Initialize the PaStiX data structure.
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| 283 | *A first call to this function fills iparm and dparm with the default PaStiX parameters
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| 284 | * \sa iparm() dparm()
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| 285 | */
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| 286 | template <class Derived>
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| 287 | void PastixBase<Derived>::init()
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| 288 | {
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| 289 | m_size = 0;
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| 290 | m_iparm.setZero(IPARM_SIZE);
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| 291 | m_dparm.setZero(DPARM_SIZE);
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| 292 |
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| 293 | m_iparm(IPARM_MODIFY_PARAMETER) = API_NO;
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| 294 | pastix(&m_pastixdata, MPI_COMM_WORLD,
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| 295 | 0, 0, 0, 0,
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| 296 | 0, 0, 0, 1, m_iparm.data(), m_dparm.data());
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| 297 |
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| 298 | m_iparm[IPARM_MATRIX_VERIFICATION] = API_NO;
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| 299 | m_iparm[IPARM_VERBOSE] = 2;
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| 300 | m_iparm[IPARM_ORDERING] = API_ORDER_SCOTCH;
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| 301 | m_iparm[IPARM_INCOMPLETE] = API_NO;
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| 302 | m_iparm[IPARM_OOC_LIMIT] = 2000;
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| 303 | m_iparm[IPARM_RHS_MAKING] = API_RHS_B;
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| 304 | m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
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| 305 |
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| 306 | m_iparm(IPARM_START_TASK) = API_TASK_INIT;
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| 307 | m_iparm(IPARM_END_TASK) = API_TASK_INIT;
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| 308 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,
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| 309 | 0, 0, 0, 0, m_iparm.data(), m_dparm.data());
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| 310 |
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| 311 | // Check the returned error
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| 312 | if(m_iparm(IPARM_ERROR_NUMBER)) {
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| 313 | m_info = InvalidInput;
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| 314 | m_initisOk = false;
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| 315 | }
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| 316 | else {
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| 317 | m_info = Success;
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| 318 | m_initisOk = true;
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| 319 | }
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| 320 | }
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| 321 |
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| 322 | template <class Derived>
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| 323 | void PastixBase<Derived>::compute(ColSpMatrix& mat)
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| 324 | {
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| 325 | eigen_assert(mat.rows() == mat.cols() && "The input matrix should be squared");
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| 326 |
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| 327 | analyzePattern(mat);
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| 328 | factorize(mat);
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| 329 |
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| 330 | m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
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| 331 | m_isInitialized = m_factorizationIsOk;
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| 332 | }
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| 333 |
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| 334 |
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| 335 | template <class Derived>
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| 336 | void PastixBase<Derived>::analyzePattern(ColSpMatrix& mat)
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| 337 | {
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| 338 | eigen_assert(m_initisOk && "The initialization of PaSTiX failed");
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| 339 |
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| 340 | // clean previous calls
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| 341 | if(m_size>0)
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| 342 | clean();
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| 343 |
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| 344 | m_size = mat.rows();
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| 345 | m_perm.resize(m_size);
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| 346 | m_invp.resize(m_size);
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| 347 |
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| 348 | m_iparm(IPARM_START_TASK) = API_TASK_ORDERING;
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| 349 | m_iparm(IPARM_END_TASK) = API_TASK_ANALYSE;
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| 350 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
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| 351 | mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
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| 352 |
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| 353 | // Check the returned error
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| 354 | if(m_iparm(IPARM_ERROR_NUMBER))
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| 355 | {
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| 356 | m_info = NumericalIssue;
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| 357 | m_analysisIsOk = false;
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| 358 | }
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| 359 | else
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| 360 | {
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| 361 | m_info = Success;
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| 362 | m_analysisIsOk = true;
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| 363 | }
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| 364 | }
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| 365 |
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| 366 | template <class Derived>
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| 367 | void PastixBase<Derived>::factorize(ColSpMatrix& mat)
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| 368 | {
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| 369 | // if(&m_cpyMat != &mat) m_cpyMat = mat;
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| 370 | eigen_assert(m_analysisIsOk && "The analysis phase should be called before the factorization phase");
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| 371 | m_iparm(IPARM_START_TASK) = API_TASK_NUMFACT;
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| 372 | m_iparm(IPARM_END_TASK) = API_TASK_NUMFACT;
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| 373 | m_size = mat.rows();
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| 374 |
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| 375 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
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| 376 | mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
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| 377 |
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| 378 | // Check the returned error
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| 379 | if(m_iparm(IPARM_ERROR_NUMBER))
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| 380 | {
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| 381 | m_info = NumericalIssue;
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| 382 | m_factorizationIsOk = false;
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| 383 | m_isInitialized = false;
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| 384 | }
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| 385 | else
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| 386 | {
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| 387 | m_info = Success;
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| 388 | m_factorizationIsOk = true;
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| 389 | m_isInitialized = true;
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| 390 | }
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| 391 | }
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| 392 |
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| 393 | /* Solve the system */
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| 394 | template<typename Base>
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| 395 | template<typename Rhs,typename Dest>
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| 396 | bool PastixBase<Base>::_solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const
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| 397 | {
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| 398 | eigen_assert(m_isInitialized && "The matrix should be factorized first");
|
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| 399 | EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
|
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| 400 | THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
|
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| 401 | int rhs = 1;
|
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| 402 |
|
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| 403 | x = b; /* on return, x is overwritten by the computed solution */
|
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| 404 |
|
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| 405 | for (int i = 0; i < b.cols(); i++){
|
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| 406 | m_iparm[IPARM_START_TASK] = API_TASK_SOLVE;
|
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| 407 | m_iparm[IPARM_END_TASK] = API_TASK_REFINE;
|
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| 408 |
|
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| 409 | internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, x.rows(), 0, 0, 0,
|
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| 410 | m_perm.data(), m_invp.data(), &x(0, i), rhs, m_iparm.data(), m_dparm.data());
|
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| 411 | }
|
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| 412 |
|
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| 413 | // Check the returned error
|
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| 414 | m_info = m_iparm(IPARM_ERROR_NUMBER)==0 ? Success : NumericalIssue;
|
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| 415 |
|
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| 416 | return m_iparm(IPARM_ERROR_NUMBER)==0;
|
---|
| 417 | }
|
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| 418 |
|
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| 419 | /** \ingroup PaStiXSupport_Module
|
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| 420 | * \class PastixLU
|
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| 421 | * \brief Sparse direct LU solver based on PaStiX library
|
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| 422 | *
|
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| 423 | * This class is used to solve the linear systems A.X = B with a supernodal LU
|
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| 424 | * factorization in the PaStiX library. The matrix A should be squared and nonsingular
|
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| 425 | * PaStiX requires that the matrix A has a symmetric structural pattern.
|
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| 426 | * This interface can symmetrize the input matrix otherwise.
|
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| 427 | * The vectors or matrices X and B can be either dense or sparse.
|
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| 428 | *
|
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| 429 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
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| 430 | * \tparam IsStrSym Indicates if the input matrix has a symmetric pattern, default is false
|
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| 431 | * NOTE : Note that if the analysis and factorization phase are called separately,
|
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| 432 | * the input matrix will be symmetrized at each call, hence it is advised to
|
---|
| 433 | * symmetrize the matrix in a end-user program and set \p IsStrSym to true
|
---|
| 434 | *
|
---|
| 435 | * \sa \ref TutorialSparseDirectSolvers
|
---|
| 436 | *
|
---|
| 437 | */
|
---|
| 438 | template<typename _MatrixType, bool IsStrSym>
|
---|
| 439 | class PastixLU : public PastixBase< PastixLU<_MatrixType> >
|
---|
| 440 | {
|
---|
| 441 | public:
|
---|
| 442 | typedef _MatrixType MatrixType;
|
---|
| 443 | typedef PastixBase<PastixLU<MatrixType> > Base;
|
---|
| 444 | typedef typename Base::ColSpMatrix ColSpMatrix;
|
---|
| 445 | typedef typename MatrixType::Index Index;
|
---|
| 446 |
|
---|
| 447 | public:
|
---|
| 448 | PastixLU() : Base()
|
---|
| 449 | {
|
---|
| 450 | init();
|
---|
| 451 | }
|
---|
| 452 |
|
---|
| 453 | PastixLU(const MatrixType& matrix):Base()
|
---|
| 454 | {
|
---|
| 455 | init();
|
---|
| 456 | compute(matrix);
|
---|
| 457 | }
|
---|
| 458 | /** Compute the LU supernodal factorization of \p matrix.
|
---|
| 459 | * iparm and dparm can be used to tune the PaStiX parameters.
|
---|
| 460 | * see the PaStiX user's manual
|
---|
| 461 | * \sa analyzePattern() factorize()
|
---|
| 462 | */
|
---|
| 463 | void compute (const MatrixType& matrix)
|
---|
| 464 | {
|
---|
| 465 | m_structureIsUptodate = false;
|
---|
| 466 | ColSpMatrix temp;
|
---|
| 467 | grabMatrix(matrix, temp);
|
---|
| 468 | Base::compute(temp);
|
---|
| 469 | }
|
---|
| 470 | /** Compute the LU symbolic factorization of \p matrix using its sparsity pattern.
|
---|
| 471 | * Several ordering methods can be used at this step. See the PaStiX user's manual.
|
---|
| 472 | * The result of this operation can be used with successive matrices having the same pattern as \p matrix
|
---|
| 473 | * \sa factorize()
|
---|
| 474 | */
|
---|
| 475 | void analyzePattern(const MatrixType& matrix)
|
---|
| 476 | {
|
---|
| 477 | m_structureIsUptodate = false;
|
---|
| 478 | ColSpMatrix temp;
|
---|
| 479 | grabMatrix(matrix, temp);
|
---|
| 480 | Base::analyzePattern(temp);
|
---|
| 481 | }
|
---|
| 482 |
|
---|
| 483 | /** Compute the LU supernodal factorization of \p matrix
|
---|
| 484 | * WARNING The matrix \p matrix should have the same structural pattern
|
---|
| 485 | * as the same used in the analysis phase.
|
---|
| 486 | * \sa analyzePattern()
|
---|
| 487 | */
|
---|
| 488 | void factorize(const MatrixType& matrix)
|
---|
| 489 | {
|
---|
| 490 | ColSpMatrix temp;
|
---|
| 491 | grabMatrix(matrix, temp);
|
---|
| 492 | Base::factorize(temp);
|
---|
| 493 | }
|
---|
| 494 | protected:
|
---|
| 495 |
|
---|
| 496 | void init()
|
---|
| 497 | {
|
---|
| 498 | m_structureIsUptodate = false;
|
---|
| 499 | m_iparm(IPARM_SYM) = API_SYM_NO;
|
---|
| 500 | m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;
|
---|
| 501 | }
|
---|
| 502 |
|
---|
| 503 | void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
|
---|
| 504 | {
|
---|
| 505 | if(IsStrSym)
|
---|
| 506 | out = matrix;
|
---|
| 507 | else
|
---|
| 508 | {
|
---|
| 509 | if(!m_structureIsUptodate)
|
---|
| 510 | {
|
---|
| 511 | // update the transposed structure
|
---|
| 512 | m_transposedStructure = matrix.transpose();
|
---|
| 513 |
|
---|
| 514 | // Set the elements of the matrix to zero
|
---|
| 515 | for (Index j=0; j<m_transposedStructure.outerSize(); ++j)
|
---|
| 516 | for(typename ColSpMatrix::InnerIterator it(m_transposedStructure, j); it; ++it)
|
---|
| 517 | it.valueRef() = 0.0;
|
---|
| 518 |
|
---|
| 519 | m_structureIsUptodate = true;
|
---|
| 520 | }
|
---|
| 521 |
|
---|
| 522 | out = m_transposedStructure + matrix;
|
---|
| 523 | }
|
---|
| 524 | internal::c_to_fortran_numbering(out);
|
---|
| 525 | }
|
---|
| 526 |
|
---|
| 527 | using Base::m_iparm;
|
---|
| 528 | using Base::m_dparm;
|
---|
| 529 |
|
---|
| 530 | ColSpMatrix m_transposedStructure;
|
---|
| 531 | bool m_structureIsUptodate;
|
---|
| 532 | };
|
---|
| 533 |
|
---|
| 534 | /** \ingroup PaStiXSupport_Module
|
---|
| 535 | * \class PastixLLT
|
---|
| 536 | * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
|
---|
| 537 | *
|
---|
| 538 | * This class is used to solve the linear systems A.X = B via a LL^T supernodal Cholesky factorization
|
---|
| 539 | * available in the PaStiX library. The matrix A should be symmetric and positive definite
|
---|
| 540 | * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
|
---|
| 541 | * The vectors or matrices X and B can be either dense or sparse
|
---|
| 542 | *
|
---|
| 543 | * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
---|
| 544 | * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
|
---|
| 545 | *
|
---|
| 546 | * \sa \ref TutorialSparseDirectSolvers
|
---|
| 547 | */
|
---|
| 548 | template<typename _MatrixType, int _UpLo>
|
---|
| 549 | class PastixLLT : public PastixBase< PastixLLT<_MatrixType, _UpLo> >
|
---|
| 550 | {
|
---|
| 551 | public:
|
---|
| 552 | typedef _MatrixType MatrixType;
|
---|
| 553 | typedef PastixBase<PastixLLT<MatrixType, _UpLo> > Base;
|
---|
| 554 | typedef typename Base::ColSpMatrix ColSpMatrix;
|
---|
| 555 |
|
---|
| 556 | public:
|
---|
| 557 | enum { UpLo = _UpLo };
|
---|
| 558 | PastixLLT() : Base()
|
---|
| 559 | {
|
---|
| 560 | init();
|
---|
| 561 | }
|
---|
| 562 |
|
---|
| 563 | PastixLLT(const MatrixType& matrix):Base()
|
---|
| 564 | {
|
---|
| 565 | init();
|
---|
| 566 | compute(matrix);
|
---|
| 567 | }
|
---|
| 568 |
|
---|
| 569 | /** Compute the L factor of the LL^T supernodal factorization of \p matrix
|
---|
| 570 | * \sa analyzePattern() factorize()
|
---|
| 571 | */
|
---|
| 572 | void compute (const MatrixType& matrix)
|
---|
| 573 | {
|
---|
| 574 | ColSpMatrix temp;
|
---|
| 575 | grabMatrix(matrix, temp);
|
---|
| 576 | Base::compute(temp);
|
---|
| 577 | }
|
---|
| 578 |
|
---|
| 579 | /** Compute the LL^T symbolic factorization of \p matrix using its sparsity pattern
|
---|
| 580 | * The result of this operation can be used with successive matrices having the same pattern as \p matrix
|
---|
| 581 | * \sa factorize()
|
---|
| 582 | */
|
---|
| 583 | void analyzePattern(const MatrixType& matrix)
|
---|
| 584 | {
|
---|
| 585 | ColSpMatrix temp;
|
---|
| 586 | grabMatrix(matrix, temp);
|
---|
| 587 | Base::analyzePattern(temp);
|
---|
| 588 | }
|
---|
| 589 | /** Compute the LL^T supernodal numerical factorization of \p matrix
|
---|
| 590 | * \sa analyzePattern()
|
---|
| 591 | */
|
---|
| 592 | void factorize(const MatrixType& matrix)
|
---|
| 593 | {
|
---|
| 594 | ColSpMatrix temp;
|
---|
| 595 | grabMatrix(matrix, temp);
|
---|
| 596 | Base::factorize(temp);
|
---|
| 597 | }
|
---|
| 598 | protected:
|
---|
| 599 | using Base::m_iparm;
|
---|
| 600 |
|
---|
| 601 | void init()
|
---|
| 602 | {
|
---|
| 603 | m_iparm(IPARM_SYM) = API_SYM_YES;
|
---|
| 604 | m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;
|
---|
| 605 | }
|
---|
| 606 |
|
---|
| 607 | void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
|
---|
| 608 | {
|
---|
| 609 | // Pastix supports only lower, column-major matrices
|
---|
| 610 | out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
|
---|
| 611 | internal::c_to_fortran_numbering(out);
|
---|
| 612 | }
|
---|
| 613 | };
|
---|
| 614 |
|
---|
| 615 | /** \ingroup PaStiXSupport_Module
|
---|
| 616 | * \class PastixLDLT
|
---|
| 617 | * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
|
---|
| 618 | *
|
---|
| 619 | * This class is used to solve the linear systems A.X = B via a LDL^T supernodal Cholesky factorization
|
---|
| 620 | * available in the PaStiX library. The matrix A should be symmetric and positive definite
|
---|
| 621 | * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
|
---|
| 622 | * The vectors or matrices X and B can be either dense or sparse
|
---|
| 623 | *
|
---|
| 624 | * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
---|
| 625 | * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
|
---|
| 626 | *
|
---|
| 627 | * \sa \ref TutorialSparseDirectSolvers
|
---|
| 628 | */
|
---|
| 629 | template<typename _MatrixType, int _UpLo>
|
---|
| 630 | class PastixLDLT : public PastixBase< PastixLDLT<_MatrixType, _UpLo> >
|
---|
| 631 | {
|
---|
| 632 | public:
|
---|
| 633 | typedef _MatrixType MatrixType;
|
---|
| 634 | typedef PastixBase<PastixLDLT<MatrixType, _UpLo> > Base;
|
---|
| 635 | typedef typename Base::ColSpMatrix ColSpMatrix;
|
---|
| 636 |
|
---|
| 637 | public:
|
---|
| 638 | enum { UpLo = _UpLo };
|
---|
| 639 | PastixLDLT():Base()
|
---|
| 640 | {
|
---|
| 641 | init();
|
---|
| 642 | }
|
---|
| 643 |
|
---|
| 644 | PastixLDLT(const MatrixType& matrix):Base()
|
---|
| 645 | {
|
---|
| 646 | init();
|
---|
| 647 | compute(matrix);
|
---|
| 648 | }
|
---|
| 649 |
|
---|
| 650 | /** Compute the L and D factors of the LDL^T factorization of \p matrix
|
---|
| 651 | * \sa analyzePattern() factorize()
|
---|
| 652 | */
|
---|
| 653 | void compute (const MatrixType& matrix)
|
---|
| 654 | {
|
---|
| 655 | ColSpMatrix temp;
|
---|
| 656 | grabMatrix(matrix, temp);
|
---|
| 657 | Base::compute(temp);
|
---|
| 658 | }
|
---|
| 659 |
|
---|
| 660 | /** Compute the LDL^T symbolic factorization of \p matrix using its sparsity pattern
|
---|
| 661 | * The result of this operation can be used with successive matrices having the same pattern as \p matrix
|
---|
| 662 | * \sa factorize()
|
---|
| 663 | */
|
---|
| 664 | void analyzePattern(const MatrixType& matrix)
|
---|
| 665 | {
|
---|
| 666 | ColSpMatrix temp;
|
---|
| 667 | grabMatrix(matrix, temp);
|
---|
| 668 | Base::analyzePattern(temp);
|
---|
| 669 | }
|
---|
| 670 | /** Compute the LDL^T supernodal numerical factorization of \p matrix
|
---|
| 671 | *
|
---|
| 672 | */
|
---|
| 673 | void factorize(const MatrixType& matrix)
|
---|
| 674 | {
|
---|
| 675 | ColSpMatrix temp;
|
---|
| 676 | grabMatrix(matrix, temp);
|
---|
| 677 | Base::factorize(temp);
|
---|
| 678 | }
|
---|
| 679 |
|
---|
| 680 | protected:
|
---|
| 681 | using Base::m_iparm;
|
---|
| 682 |
|
---|
| 683 | void init()
|
---|
| 684 | {
|
---|
| 685 | m_iparm(IPARM_SYM) = API_SYM_YES;
|
---|
| 686 | m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;
|
---|
| 687 | }
|
---|
| 688 |
|
---|
| 689 | void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
|
---|
| 690 | {
|
---|
| 691 | // Pastix supports only lower, column-major matrices
|
---|
| 692 | out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
|
---|
| 693 | internal::c_to_fortran_numbering(out);
|
---|
| 694 | }
|
---|
| 695 | };
|
---|
| 696 |
|
---|
| 697 | namespace internal {
|
---|
| 698 |
|
---|
| 699 | template<typename _MatrixType, typename Rhs>
|
---|
| 700 | struct solve_retval<PastixBase<_MatrixType>, Rhs>
|
---|
| 701 | : solve_retval_base<PastixBase<_MatrixType>, Rhs>
|
---|
| 702 | {
|
---|
| 703 | typedef PastixBase<_MatrixType> Dec;
|
---|
| 704 | EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
|
---|
| 705 |
|
---|
| 706 | template<typename Dest> void evalTo(Dest& dst) const
|
---|
| 707 | {
|
---|
| 708 | dec()._solve(rhs(),dst);
|
---|
| 709 | }
|
---|
| 710 | };
|
---|
| 711 |
|
---|
| 712 | template<typename _MatrixType, typename Rhs>
|
---|
| 713 | struct sparse_solve_retval<PastixBase<_MatrixType>, Rhs>
|
---|
| 714 | : sparse_solve_retval_base<PastixBase<_MatrixType>, Rhs>
|
---|
| 715 | {
|
---|
| 716 | typedef PastixBase<_MatrixType> Dec;
|
---|
| 717 | EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
|
---|
| 718 |
|
---|
| 719 | template<typename Dest> void evalTo(Dest& dst) const
|
---|
| 720 | {
|
---|
| 721 | this->defaultEvalTo(dst);
|
---|
| 722 | }
|
---|
| 723 | };
|
---|
| 724 |
|
---|
| 725 | } // end namespace internal
|
---|
| 726 |
|
---|
| 727 | } // end namespace Eigen
|
---|
| 728 |
|
---|
| 729 | #endif
|
---|