[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) 2008-2012 Gael Guennebaud <gael.guennebaud@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_SIMPLICIAL_CHOLESKY_H
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| 11 | #define EIGEN_SIMPLICIAL_CHOLESKY_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | enum SimplicialCholeskyMode {
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| 16 | SimplicialCholeskyLLT,
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| 17 | SimplicialCholeskyLDLT
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| 18 | };
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| 19 |
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| 20 | /** \ingroup SparseCholesky_Module
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| 21 | * \brief A direct sparse Cholesky factorizations
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| 22 | *
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| 23 | * These classes provide LL^T and LDL^T Cholesky factorizations of sparse matrices that are
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| 24 | * selfadjoint and positive definite. The factorization allows for solving A.X = B where
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| 25 | * X and B can be either dense or sparse.
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| 26 | *
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| 27 | * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
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| 28 | * such that the factorized matrix is P A P^-1.
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| 29 | *
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| 30 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
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| 31 | * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
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| 32 | * or Upper. Default is Lower.
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| 33 | *
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| 34 | */
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| 35 | template<typename Derived>
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| 36 | class SimplicialCholeskyBase : internal::noncopyable
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| 37 | {
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| 38 | public:
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| 39 | typedef typename internal::traits<Derived>::MatrixType MatrixType;
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| 40 | typedef typename internal::traits<Derived>::OrderingType OrderingType;
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| 41 | enum { UpLo = internal::traits<Derived>::UpLo };
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| 42 | typedef typename MatrixType::Scalar Scalar;
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| 43 | typedef typename MatrixType::RealScalar RealScalar;
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| 44 | typedef typename MatrixType::Index Index;
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| 45 | typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
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| 46 | typedef Matrix<Scalar,Dynamic,1> VectorType;
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| 47 |
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| 48 | public:
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| 49 |
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| 50 | /** Default constructor */
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| 51 | SimplicialCholeskyBase()
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| 52 | : m_info(Success), m_isInitialized(false), m_shiftOffset(0), m_shiftScale(1)
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| 53 | {}
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| 54 |
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| 55 | SimplicialCholeskyBase(const MatrixType& matrix)
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| 56 | : m_info(Success), m_isInitialized(false), m_shiftOffset(0), m_shiftScale(1)
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| 57 | {
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| 58 | derived().compute(matrix);
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| 59 | }
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| 60 |
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| 61 | ~SimplicialCholeskyBase()
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| 62 | {
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| 63 | }
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| 64 |
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| 65 | Derived& derived() { return *static_cast<Derived*>(this); }
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| 66 | const Derived& derived() const { return *static_cast<const Derived*>(this); }
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| 67 |
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| 68 | inline Index cols() const { return m_matrix.cols(); }
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| 69 | inline Index rows() const { return m_matrix.rows(); }
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| 70 |
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| 71 | /** \brief Reports whether previous computation was successful.
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| 72 | *
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| 73 | * \returns \c Success if computation was succesful,
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| 74 | * \c NumericalIssue if the matrix.appears to be negative.
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| 75 | */
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| 76 | ComputationInfo info() const
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| 77 | {
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| 78 | eigen_assert(m_isInitialized && "Decomposition is not initialized.");
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| 79 | return m_info;
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| 80 | }
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| 81 |
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| 82 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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| 83 | *
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| 84 | * \sa compute()
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| 85 | */
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| 86 | template<typename Rhs>
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| 87 | inline const internal::solve_retval<SimplicialCholeskyBase, Rhs>
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| 88 | solve(const MatrixBase<Rhs>& b) const
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| 89 | {
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| 90 | eigen_assert(m_isInitialized && "Simplicial LLT or LDLT is not initialized.");
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| 91 | eigen_assert(rows()==b.rows()
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| 92 | && "SimplicialCholeskyBase::solve(): invalid number of rows of the right hand side matrix b");
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| 93 | return internal::solve_retval<SimplicialCholeskyBase, Rhs>(*this, b.derived());
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| 94 | }
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| 95 |
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| 96 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
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| 97 | *
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| 98 | * \sa compute()
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| 99 | */
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| 100 | template<typename Rhs>
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| 101 | inline const internal::sparse_solve_retval<SimplicialCholeskyBase, Rhs>
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| 102 | solve(const SparseMatrixBase<Rhs>& b) const
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| 103 | {
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| 104 | eigen_assert(m_isInitialized && "Simplicial LLT or LDLT is not initialized.");
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| 105 | eigen_assert(rows()==b.rows()
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| 106 | && "SimplicialCholesky::solve(): invalid number of rows of the right hand side matrix b");
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| 107 | return internal::sparse_solve_retval<SimplicialCholeskyBase, Rhs>(*this, b.derived());
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| 108 | }
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| 109 |
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| 110 | /** \returns the permutation P
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| 111 | * \sa permutationPinv() */
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| 112 | const PermutationMatrix<Dynamic,Dynamic,Index>& permutationP() const
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| 113 | { return m_P; }
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| 114 |
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| 115 | /** \returns the inverse P^-1 of the permutation P
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| 116 | * \sa permutationP() */
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| 117 | const PermutationMatrix<Dynamic,Dynamic,Index>& permutationPinv() const
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| 118 | { return m_Pinv; }
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| 119 |
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| 120 | /** Sets the shift parameters that will be used to adjust the diagonal coefficients during the numerical factorization.
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| 121 | *
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| 122 | * During the numerical factorization, the diagonal coefficients are transformed by the following linear model:\n
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| 123 | * \c d_ii = \a offset + \a scale * \c d_ii
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| 124 | *
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| 125 | * The default is the identity transformation with \a offset=0, and \a scale=1.
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| 126 | *
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| 127 | * \returns a reference to \c *this.
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| 128 | */
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| 129 | Derived& setShift(const RealScalar& offset, const RealScalar& scale = 1)
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| 130 | {
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| 131 | m_shiftOffset = offset;
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| 132 | m_shiftScale = scale;
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| 133 | return derived();
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| 134 | }
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| 135 |
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| 136 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 137 | /** \internal */
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| 138 | template<typename Stream>
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| 139 | void dumpMemory(Stream& s)
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| 140 | {
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| 141 | int total = 0;
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| 142 | s << " L: " << ((total+=(m_matrix.cols()+1) * sizeof(int) + m_matrix.nonZeros()*(sizeof(int)+sizeof(Scalar))) >> 20) << "Mb" << "\n";
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| 143 | s << " diag: " << ((total+=m_diag.size() * sizeof(Scalar)) >> 20) << "Mb" << "\n";
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| 144 | s << " tree: " << ((total+=m_parent.size() * sizeof(int)) >> 20) << "Mb" << "\n";
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| 145 | s << " nonzeros: " << ((total+=m_nonZerosPerCol.size() * sizeof(int)) >> 20) << "Mb" << "\n";
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| 146 | s << " perm: " << ((total+=m_P.size() * sizeof(int)) >> 20) << "Mb" << "\n";
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| 147 | s << " perm^-1: " << ((total+=m_Pinv.size() * sizeof(int)) >> 20) << "Mb" << "\n";
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| 148 | s << " TOTAL: " << (total>> 20) << "Mb" << "\n";
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| 149 | }
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| 150 |
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| 151 | /** \internal */
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| 152 | template<typename Rhs,typename Dest>
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| 153 | void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
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| 154 | {
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| 155 | eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
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| 156 | eigen_assert(m_matrix.rows()==b.rows());
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| 157 |
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| 158 | if(m_info!=Success)
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| 159 | return;
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| 160 |
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| 161 | if(m_P.size()>0)
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| 162 | dest = m_P * b;
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| 163 | else
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| 164 | dest = b;
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| 165 |
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| 166 | if(m_matrix.nonZeros()>0) // otherwise L==I
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| 167 | derived().matrixL().solveInPlace(dest);
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| 168 |
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| 169 | if(m_diag.size()>0)
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| 170 | dest = m_diag.asDiagonal().inverse() * dest;
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| 171 |
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| 172 | if (m_matrix.nonZeros()>0) // otherwise U==I
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| 173 | derived().matrixU().solveInPlace(dest);
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| 174 |
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| 175 | if(m_P.size()>0)
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| 176 | dest = m_Pinv * dest;
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| 177 | }
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| 178 |
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| 179 | #endif // EIGEN_PARSED_BY_DOXYGEN
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| 180 |
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| 181 | protected:
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| 182 |
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| 183 | /** Computes the sparse Cholesky decomposition of \a matrix */
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| 184 | template<bool DoLDLT>
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| 185 | void compute(const MatrixType& matrix)
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| 186 | {
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| 187 | eigen_assert(matrix.rows()==matrix.cols());
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| 188 | Index size = matrix.cols();
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| 189 | CholMatrixType ap(size,size);
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| 190 | ordering(matrix, ap);
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| 191 | analyzePattern_preordered(ap, DoLDLT);
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| 192 | factorize_preordered<DoLDLT>(ap);
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| 193 | }
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| 194 |
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| 195 | template<bool DoLDLT>
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| 196 | void factorize(const MatrixType& a)
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| 197 | {
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| 198 | eigen_assert(a.rows()==a.cols());
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| 199 | int size = a.cols();
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| 200 | CholMatrixType ap(size,size);
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| 201 | ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);
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| 202 | factorize_preordered<DoLDLT>(ap);
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| 203 | }
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| 204 |
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| 205 | template<bool DoLDLT>
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| 206 | void factorize_preordered(const CholMatrixType& a);
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| 207 |
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| 208 | void analyzePattern(const MatrixType& a, bool doLDLT)
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| 209 | {
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| 210 | eigen_assert(a.rows()==a.cols());
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| 211 | int size = a.cols();
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| 212 | CholMatrixType ap(size,size);
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| 213 | ordering(a, ap);
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| 214 | analyzePattern_preordered(ap,doLDLT);
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| 215 | }
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| 216 | void analyzePattern_preordered(const CholMatrixType& a, bool doLDLT);
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| 217 |
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| 218 | void ordering(const MatrixType& a, CholMatrixType& ap);
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| 219 |
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| 220 | /** keeps off-diagonal entries; drops diagonal entries */
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| 221 | struct keep_diag {
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| 222 | inline bool operator() (const Index& row, const Index& col, const Scalar&) const
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| 223 | {
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| 224 | return row!=col;
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| 225 | }
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| 226 | };
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| 227 |
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| 228 | mutable ComputationInfo m_info;
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| 229 | bool m_isInitialized;
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| 230 | bool m_factorizationIsOk;
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| 231 | bool m_analysisIsOk;
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| 232 |
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| 233 | CholMatrixType m_matrix;
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| 234 | VectorType m_diag; // the diagonal coefficients (LDLT mode)
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| 235 | VectorXi m_parent; // elimination tree
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| 236 | VectorXi m_nonZerosPerCol;
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| 237 | PermutationMatrix<Dynamic,Dynamic,Index> m_P; // the permutation
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| 238 | PermutationMatrix<Dynamic,Dynamic,Index> m_Pinv; // the inverse permutation
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| 239 |
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| 240 | RealScalar m_shiftOffset;
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| 241 | RealScalar m_shiftScale;
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| 242 | };
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| 243 |
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| 244 | template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialLLT;
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| 245 | template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialLDLT;
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| 246 | template<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::Index> > class SimplicialCholesky;
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| 247 |
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| 248 | namespace internal {
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| 249 |
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| 250 | template<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialLLT<_MatrixType,_UpLo,_Ordering> >
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| 251 | {
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| 252 | typedef _MatrixType MatrixType;
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| 253 | typedef _Ordering OrderingType;
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| 254 | enum { UpLo = _UpLo };
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| 255 | typedef typename MatrixType::Scalar Scalar;
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| 256 | typedef typename MatrixType::Index Index;
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| 257 | typedef SparseMatrix<Scalar, ColMajor, Index> CholMatrixType;
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| 258 | typedef SparseTriangularView<CholMatrixType, Eigen::Lower> MatrixL;
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| 259 | typedef SparseTriangularView<typename CholMatrixType::AdjointReturnType, Eigen::Upper> MatrixU;
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| 260 | static inline MatrixL getL(const MatrixType& m) { return m; }
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| 261 | static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
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| 262 | };
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| 263 |
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| 264 | template<typename _MatrixType,int _UpLo, typename _Ordering> struct traits<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> >
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| 265 | {
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| 266 | typedef _MatrixType MatrixType;
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| 267 | typedef _Ordering OrderingType;
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| 268 | enum { UpLo = _UpLo };
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| 269 | typedef typename MatrixType::Scalar Scalar;
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| 270 | typedef typename MatrixType::Index Index;
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| 271 | typedef SparseMatrix<Scalar, ColMajor, Index> CholMatrixType;
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| 272 | typedef SparseTriangularView<CholMatrixType, Eigen::UnitLower> MatrixL;
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| 273 | typedef SparseTriangularView<typename CholMatrixType::AdjointReturnType, Eigen::UnitUpper> MatrixU;
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| 274 | static inline MatrixL getL(const MatrixType& m) { return m; }
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| 275 | static inline MatrixU getU(const MatrixType& m) { return m.adjoint(); }
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| 276 | };
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| 277 |
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| 278 | template<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> >
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| 279 | {
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| 280 | typedef _MatrixType MatrixType;
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| 281 | typedef _Ordering OrderingType;
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| 282 | enum { UpLo = _UpLo };
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| 283 | };
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| 284 |
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| 285 | }
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| 286 |
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| 287 | /** \ingroup SparseCholesky_Module
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| 288 | * \class SimplicialLLT
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| 289 | * \brief A direct sparse LLT Cholesky factorizations
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| 290 | *
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| 291 | * This class provides a LL^T Cholesky factorizations of sparse matrices that are
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| 292 | * selfadjoint and positive definite. The factorization allows for solving A.X = B where
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| 293 | * X and B can be either dense or sparse.
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| 294 | *
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| 295 | * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
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| 296 | * such that the factorized matrix is P A P^-1.
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| 297 | *
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| 298 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
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| 299 | * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
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| 300 | * or Upper. Default is Lower.
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| 301 | * \tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
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| 302 | *
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| 303 | * \sa class SimplicialLDLT, class AMDOrdering, class NaturalOrdering
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| 304 | */
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| 305 | template<typename _MatrixType, int _UpLo, typename _Ordering>
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| 306 | class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<_MatrixType,_UpLo,_Ordering> >
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| 307 | {
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| 308 | public:
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| 309 | typedef _MatrixType MatrixType;
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| 310 | enum { UpLo = _UpLo };
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| 311 | typedef SimplicialCholeskyBase<SimplicialLLT> Base;
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| 312 | typedef typename MatrixType::Scalar Scalar;
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| 313 | typedef typename MatrixType::RealScalar RealScalar;
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| 314 | typedef typename MatrixType::Index Index;
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| 315 | typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
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| 316 | typedef Matrix<Scalar,Dynamic,1> VectorType;
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| 317 | typedef internal::traits<SimplicialLLT> Traits;
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| 318 | typedef typename Traits::MatrixL MatrixL;
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| 319 | typedef typename Traits::MatrixU MatrixU;
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| 320 | public:
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| 321 | /** Default constructor */
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| 322 | SimplicialLLT() : Base() {}
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| 323 | /** Constructs and performs the LLT factorization of \a matrix */
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| 324 | SimplicialLLT(const MatrixType& matrix)
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| 325 | : Base(matrix) {}
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| 326 |
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| 327 | /** \returns an expression of the factor L */
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| 328 | inline const MatrixL matrixL() const {
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| 329 | eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized");
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| 330 | return Traits::getL(Base::m_matrix);
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| 331 | }
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| 332 |
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| 333 | /** \returns an expression of the factor U (= L^*) */
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| 334 | inline const MatrixU matrixU() const {
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| 335 | eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized");
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| 336 | return Traits::getU(Base::m_matrix);
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| 337 | }
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| 338 |
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| 339 | /** Computes the sparse Cholesky decomposition of \a matrix */
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| 340 | SimplicialLLT& compute(const MatrixType& matrix)
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| 341 | {
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| 342 | Base::template compute<false>(matrix);
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| 343 | return *this;
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| 344 | }
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| 345 |
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| 346 | /** Performs a symbolic decomposition on the sparcity of \a matrix.
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| 347 | *
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| 348 | * This function is particularly useful when solving for several problems having the same structure.
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| 349 | *
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| 350 | * \sa factorize()
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| 351 | */
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| 352 | void analyzePattern(const MatrixType& a)
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| 353 | {
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| 354 | Base::analyzePattern(a, false);
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| 355 | }
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| 356 |
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| 357 | /** Performs a numeric decomposition of \a matrix
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| 358 | *
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| 359 | * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
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| 360 | *
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| 361 | * \sa analyzePattern()
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| 362 | */
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| 363 | void factorize(const MatrixType& a)
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| 364 | {
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| 365 | Base::template factorize<false>(a);
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| 366 | }
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| 367 |
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| 368 | /** \returns the determinant of the underlying matrix from the current factorization */
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| 369 | Scalar determinant() const
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| 370 | {
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| 371 | Scalar detL = Base::m_matrix.diagonal().prod();
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| 372 | return numext::abs2(detL);
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| 373 | }
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| 374 | };
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| 375 |
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| 376 | /** \ingroup SparseCholesky_Module
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| 377 | * \class SimplicialLDLT
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| 378 | * \brief A direct sparse LDLT Cholesky factorizations without square root.
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| 379 | *
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| 380 | * This class provides a LDL^T Cholesky factorizations without square root of sparse matrices that are
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| 381 | * selfadjoint and positive definite. The factorization allows for solving A.X = B where
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| 382 | * X and B can be either dense or sparse.
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| 383 | *
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| 384 | * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
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| 385 | * such that the factorized matrix is P A P^-1.
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| 386 | *
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| 387 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
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| 388 | * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
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| 389 | * or Upper. Default is Lower.
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| 390 | * \tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
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| 391 | *
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| 392 | * \sa class SimplicialLLT, class AMDOrdering, class NaturalOrdering
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| 393 | */
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| 394 | template<typename _MatrixType, int _UpLo, typename _Ordering>
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| 395 | class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> >
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| 396 | {
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| 397 | public:
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| 398 | typedef _MatrixType MatrixType;
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| 399 | enum { UpLo = _UpLo };
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| 400 | typedef SimplicialCholeskyBase<SimplicialLDLT> Base;
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| 401 | typedef typename MatrixType::Scalar Scalar;
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| 402 | typedef typename MatrixType::RealScalar RealScalar;
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| 403 | typedef typename MatrixType::Index Index;
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| 404 | typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
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| 405 | typedef Matrix<Scalar,Dynamic,1> VectorType;
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| 406 | typedef internal::traits<SimplicialLDLT> Traits;
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| 407 | typedef typename Traits::MatrixL MatrixL;
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| 408 | typedef typename Traits::MatrixU MatrixU;
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| 409 | public:
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| 410 | /** Default constructor */
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| 411 | SimplicialLDLT() : Base() {}
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| 412 |
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| 413 | /** Constructs and performs the LLT factorization of \a matrix */
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| 414 | SimplicialLDLT(const MatrixType& matrix)
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| 415 | : Base(matrix) {}
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| 416 |
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| 417 | /** \returns a vector expression of the diagonal D */
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| 418 | inline const VectorType vectorD() const {
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| 419 | eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
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| 420 | return Base::m_diag;
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| 421 | }
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| 422 | /** \returns an expression of the factor L */
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| 423 | inline const MatrixL matrixL() const {
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| 424 | eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
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| 425 | return Traits::getL(Base::m_matrix);
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| 426 | }
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| 427 |
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| 428 | /** \returns an expression of the factor U (= L^*) */
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| 429 | inline const MatrixU matrixU() const {
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| 430 | eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
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| 431 | return Traits::getU(Base::m_matrix);
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| 432 | }
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| 433 |
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| 434 | /** Computes the sparse Cholesky decomposition of \a matrix */
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| 435 | SimplicialLDLT& compute(const MatrixType& matrix)
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| 436 | {
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| 437 | Base::template compute<true>(matrix);
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| 438 | return *this;
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| 439 | }
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| 440 |
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| 441 | /** Performs a symbolic decomposition on the sparcity of \a matrix.
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| 442 | *
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| 443 | * This function is particularly useful when solving for several problems having the same structure.
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| 444 | *
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| 445 | * \sa factorize()
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| 446 | */
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| 447 | void analyzePattern(const MatrixType& a)
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| 448 | {
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| 449 | Base::analyzePattern(a, true);
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| 450 | }
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| 451 |
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| 452 | /** Performs a numeric decomposition of \a matrix
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| 453 | *
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| 454 | * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
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| 455 | *
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| 456 | * \sa analyzePattern()
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| 457 | */
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| 458 | void factorize(const MatrixType& a)
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| 459 | {
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| 460 | Base::template factorize<true>(a);
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| 461 | }
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| 462 |
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| 463 | /** \returns the determinant of the underlying matrix from the current factorization */
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| 464 | Scalar determinant() const
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| 465 | {
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| 466 | return Base::m_diag.prod();
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| 467 | }
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| 468 | };
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| 469 |
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| 470 | /** \deprecated use SimplicialLDLT or class SimplicialLLT
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| 471 | * \ingroup SparseCholesky_Module
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| 472 | * \class SimplicialCholesky
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| 473 | *
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| 474 | * \sa class SimplicialLDLT, class SimplicialLLT
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| 475 | */
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| 476 | template<typename _MatrixType, int _UpLo, typename _Ordering>
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| 477 | class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> >
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| 478 | {
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| 479 | public:
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| 480 | typedef _MatrixType MatrixType;
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| 481 | enum { UpLo = _UpLo };
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| 482 | typedef SimplicialCholeskyBase<SimplicialCholesky> Base;
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| 483 | typedef typename MatrixType::Scalar Scalar;
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| 484 | typedef typename MatrixType::RealScalar RealScalar;
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| 485 | typedef typename MatrixType::Index Index;
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| 486 | typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
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| 487 | typedef Matrix<Scalar,Dynamic,1> VectorType;
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| 488 | typedef internal::traits<SimplicialCholesky> Traits;
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| 489 | typedef internal::traits<SimplicialLDLT<MatrixType,UpLo> > LDLTTraits;
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| 490 | typedef internal::traits<SimplicialLLT<MatrixType,UpLo> > LLTTraits;
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| 491 | public:
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| 492 | SimplicialCholesky() : Base(), m_LDLT(true) {}
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| 493 |
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| 494 | SimplicialCholesky(const MatrixType& matrix)
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| 495 | : Base(), m_LDLT(true)
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| 496 | {
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| 497 | compute(matrix);
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| 498 | }
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| 499 |
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| 500 | SimplicialCholesky& setMode(SimplicialCholeskyMode mode)
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| 501 | {
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| 502 | switch(mode)
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| 503 | {
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| 504 | case SimplicialCholeskyLLT:
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| 505 | m_LDLT = false;
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| 506 | break;
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| 507 | case SimplicialCholeskyLDLT:
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| 508 | m_LDLT = true;
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| 509 | break;
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| 510 | default:
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| 511 | break;
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| 512 | }
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| 513 |
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| 514 | return *this;
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| 515 | }
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| 516 |
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| 517 | inline const VectorType vectorD() const {
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| 518 | eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky not factorized");
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| 519 | return Base::m_diag;
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| 520 | }
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| 521 | inline const CholMatrixType rawMatrix() const {
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| 522 | eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky not factorized");
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| 523 | return Base::m_matrix;
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| 524 | }
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| 525 |
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| 526 | /** Computes the sparse Cholesky decomposition of \a matrix */
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| 527 | SimplicialCholesky& compute(const MatrixType& matrix)
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| 528 | {
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| 529 | if(m_LDLT)
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| 530 | Base::template compute<true>(matrix);
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| 531 | else
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| 532 | Base::template compute<false>(matrix);
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| 533 | return *this;
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| 534 | }
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| 535 |
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| 536 | /** Performs a symbolic decomposition on the sparcity of \a matrix.
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| 537 | *
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| 538 | * This function is particularly useful when solving for several problems having the same structure.
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| 539 | *
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| 540 | * \sa factorize()
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| 541 | */
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| 542 | void analyzePattern(const MatrixType& a)
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| 543 | {
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| 544 | Base::analyzePattern(a, m_LDLT);
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| 545 | }
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| 546 |
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| 547 | /** Performs a numeric decomposition of \a matrix
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| 548 | *
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| 549 | * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
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| 550 | *
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| 551 | * \sa analyzePattern()
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| 552 | */
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| 553 | void factorize(const MatrixType& a)
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| 554 | {
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| 555 | if(m_LDLT)
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| 556 | Base::template factorize<true>(a);
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| 557 | else
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| 558 | Base::template factorize<false>(a);
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| 559 | }
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| 560 |
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| 561 | /** \internal */
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| 562 | template<typename Rhs,typename Dest>
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| 563 | void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
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| 564 | {
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| 565 | eigen_assert(Base::m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
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| 566 | eigen_assert(Base::m_matrix.rows()==b.rows());
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| 567 |
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| 568 | if(Base::m_info!=Success)
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| 569 | return;
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| 570 |
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| 571 | if(Base::m_P.size()>0)
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| 572 | dest = Base::m_P * b;
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| 573 | else
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| 574 | dest = b;
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| 575 |
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| 576 | if(Base::m_matrix.nonZeros()>0) // otherwise L==I
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| 577 | {
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| 578 | if(m_LDLT)
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| 579 | LDLTTraits::getL(Base::m_matrix).solveInPlace(dest);
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| 580 | else
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| 581 | LLTTraits::getL(Base::m_matrix).solveInPlace(dest);
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| 582 | }
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| 583 |
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| 584 | if(Base::m_diag.size()>0)
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| 585 | dest = Base::m_diag.asDiagonal().inverse() * dest;
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| 586 |
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| 587 | if (Base::m_matrix.nonZeros()>0) // otherwise I==I
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| 588 | {
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| 589 | if(m_LDLT)
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| 590 | LDLTTraits::getU(Base::m_matrix).solveInPlace(dest);
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| 591 | else
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| 592 | LLTTraits::getU(Base::m_matrix).solveInPlace(dest);
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| 593 | }
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| 594 |
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| 595 | if(Base::m_P.size()>0)
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| 596 | dest = Base::m_Pinv * dest;
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| 597 | }
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| 598 |
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| 599 | Scalar determinant() const
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| 600 | {
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| 601 | if(m_LDLT)
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| 602 | {
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| 603 | return Base::m_diag.prod();
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| 604 | }
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| 605 | else
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| 606 | {
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| 607 | Scalar detL = Diagonal<const CholMatrixType>(Base::m_matrix).prod();
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| 608 | return numext::abs2(detL);
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| 609 | }
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| 610 | }
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| 611 |
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| 612 | protected:
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| 613 | bool m_LDLT;
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| 614 | };
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| 615 |
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| 616 | template<typename Derived>
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| 617 | void SimplicialCholeskyBase<Derived>::ordering(const MatrixType& a, CholMatrixType& ap)
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| 618 | {
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| 619 | eigen_assert(a.rows()==a.cols());
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| 620 | const Index size = a.rows();
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| 621 | // Note that amd compute the inverse permutation
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| 622 | {
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| 623 | CholMatrixType C;
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| 624 | C = a.template selfadjointView<UpLo>();
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| 625 |
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| 626 | OrderingType ordering;
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| 627 | ordering(C,m_Pinv);
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| 628 | }
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| 629 |
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| 630 | if(m_Pinv.size()>0)
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| 631 | m_P = m_Pinv.inverse();
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| 632 | else
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| 633 | m_P.resize(0);
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| 634 |
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| 635 | ap.resize(size,size);
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| 636 | ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);
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| 637 | }
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| 638 |
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| 639 | namespace internal {
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| 640 |
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| 641 | template<typename Derived, typename Rhs>
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| 642 | struct solve_retval<SimplicialCholeskyBase<Derived>, Rhs>
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| 643 | : solve_retval_base<SimplicialCholeskyBase<Derived>, Rhs>
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| 644 | {
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| 645 | typedef SimplicialCholeskyBase<Derived> Dec;
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| 646 | EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
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| 647 |
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| 648 | template<typename Dest> void evalTo(Dest& dst) const
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| 649 | {
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| 650 | dec().derived()._solve(rhs(),dst);
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| 651 | }
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| 652 | };
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| 653 |
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| 654 | template<typename Derived, typename Rhs>
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| 655 | struct sparse_solve_retval<SimplicialCholeskyBase<Derived>, Rhs>
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| 656 | : sparse_solve_retval_base<SimplicialCholeskyBase<Derived>, Rhs>
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| 657 | {
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| 658 | typedef SimplicialCholeskyBase<Derived> Dec;
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| 659 | EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
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| 660 |
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| 661 | template<typename Dest> void evalTo(Dest& dst) const
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| 662 | {
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| 663 | this->defaultEvalTo(dst);
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| 664 | }
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| 665 | };
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| 666 |
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| 667 | } // end namespace internal
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| 668 |
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| 669 | } // end namespace Eigen
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| 670 |
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| 671 | #endif // EIGEN_SIMPLICIAL_CHOLESKY_H
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