[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_DGMRES_H
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| 11 | #define EIGEN_DGMRES_H
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| 12 |
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| 13 | #include <Eigen/Eigenvalues>
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| 14 |
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| 15 | namespace Eigen {
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| 16 |
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| 17 | template< typename _MatrixType,
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| 18 | typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
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| 19 | class DGMRES;
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| 20 |
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| 21 | namespace internal {
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| 22 |
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| 23 | template< typename _MatrixType, typename _Preconditioner>
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| 24 | struct traits<DGMRES<_MatrixType,_Preconditioner> >
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| 25 | {
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| 26 | typedef _MatrixType MatrixType;
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| 27 | typedef _Preconditioner Preconditioner;
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| 28 | };
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| 29 |
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| 30 | /** \brief Computes a permutation vector to have a sorted sequence
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| 31 | * \param vec The vector to reorder.
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| 32 | * \param perm gives the sorted sequence on output. Must be initialized with 0..n-1
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| 33 | * \param ncut Put the ncut smallest elements at the end of the vector
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| 34 | * WARNING This is an expensive sort, so should be used only
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| 35 | * for small size vectors
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| 36 | * TODO Use modified QuickSplit or std::nth_element to get the smallest values
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| 37 | */
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| 38 | template <typename VectorType, typename IndexType>
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| 39 | void sortWithPermutation (VectorType& vec, IndexType& perm, typename IndexType::Scalar& ncut)
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| 40 | {
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| 41 | eigen_assert(vec.size() == perm.size());
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| 42 | typedef typename IndexType::Scalar Index;
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| 43 | typedef typename VectorType::Scalar Scalar;
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| 44 | bool flag;
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| 45 | for (Index k = 0; k < ncut; k++)
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| 46 | {
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| 47 | flag = false;
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| 48 | for (Index j = 0; j < vec.size()-1; j++)
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| 49 | {
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| 50 | if ( vec(perm(j)) < vec(perm(j+1)) )
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| 51 | {
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| 52 | std::swap(perm(j),perm(j+1));
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| 53 | flag = true;
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| 54 | }
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| 55 | if (!flag) break; // The vector is in sorted order
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| 56 | }
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| 57 | }
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| 58 | }
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| 59 |
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| 60 | }
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| 61 | /**
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| 62 | * \ingroup IterativeLInearSolvers_Module
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| 63 | * \brief A Restarted GMRES with deflation.
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| 64 | * This class implements a modification of the GMRES solver for
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| 65 | * sparse linear systems. The basis is built with modified
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| 66 | * Gram-Schmidt. At each restart, a few approximated eigenvectors
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| 67 | * corresponding to the smallest eigenvalues are used to build a
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| 68 | * preconditioner for the next cycle. This preconditioner
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| 69 | * for deflation can be combined with any other preconditioner,
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| 70 | * the IncompleteLUT for instance. The preconditioner is applied
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| 71 | * at right of the matrix and the combination is multiplicative.
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| 72 | *
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| 73 | * \tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix.
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| 74 | * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner
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| 75 | * Typical usage :
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| 76 | * \code
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| 77 | * SparseMatrix<double> A;
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| 78 | * VectorXd x, b;
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| 79 | * //Fill A and b ...
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| 80 | * DGMRES<SparseMatrix<double> > solver;
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| 81 | * solver.set_restart(30); // Set restarting value
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| 82 | * solver.setEigenv(1); // Set the number of eigenvalues to deflate
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| 83 | * solver.compute(A);
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| 84 | * x = solver.solve(b);
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| 85 | * \endcode
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| 86 | *
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| 87 | * References :
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| 88 | * [1] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid
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| 89 | * Algebraic Solvers for Linear Systems Arising from Compressible
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| 90 | * Flows, Computers and Fluids, In Press,
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| 91 | * http://dx.doi.org/10.1016/j.compfluid.2012.03.023
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| 92 | * [2] K. Burrage and J. Erhel, On the performance of various
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| 93 | * adaptive preconditioned GMRES strategies, 5(1998), 101-121.
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| 94 | * [3] J. Erhel, K. Burrage and B. Pohl, Restarted GMRES
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| 95 | * preconditioned by deflation,J. Computational and Applied
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| 96 | * Mathematics, 69(1996), 303-318.
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| 97 |
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| 98 | *
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| 99 | */
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| 100 | template< typename _MatrixType, typename _Preconditioner>
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| 101 | class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
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| 102 | {
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| 103 | typedef IterativeSolverBase<DGMRES> Base;
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| 104 | using Base::mp_matrix;
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| 105 | using Base::m_error;
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| 106 | using Base::m_iterations;
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| 107 | using Base::m_info;
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| 108 | using Base::m_isInitialized;
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| 109 | using Base::m_tolerance;
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| 110 | public:
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| 111 | typedef _MatrixType MatrixType;
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| 112 | typedef typename MatrixType::Scalar Scalar;
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| 113 | typedef typename MatrixType::Index Index;
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| 114 | typedef typename MatrixType::RealScalar RealScalar;
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| 115 | typedef _Preconditioner Preconditioner;
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| 116 | typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
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| 117 | typedef Matrix<RealScalar,Dynamic,Dynamic> DenseRealMatrix;
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| 118 | typedef Matrix<Scalar,Dynamic,1> DenseVector;
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| 119 | typedef Matrix<RealScalar,Dynamic,1> DenseRealVector;
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| 120 | typedef Matrix<std::complex<RealScalar>, Dynamic, 1> ComplexVector;
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| 121 |
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| 122 |
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| 123 | /** Default constructor. */
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| 124 | DGMRES() : Base(),m_restart(30),m_neig(0),m_r(0),m_maxNeig(5),m_isDeflAllocated(false),m_isDeflInitialized(false) {}
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| 125 |
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| 126 | /** Initialize the solver with matrix \a A for further \c Ax=b solving.
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| 127 | *
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| 128 | * This constructor is a shortcut for the default constructor followed
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| 129 | * by a call to compute().
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| 130 | *
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| 131 | * \warning this class stores a reference to the matrix A as well as some
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| 132 | * precomputed values that depend on it. Therefore, if \a A is changed
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| 133 | * this class becomes invalid. Call compute() to update it with the new
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| 134 | * matrix A, or modify a copy of A.
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| 135 | */
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| 136 | template<typename MatrixDerived>
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| 137 | explicit DGMRES(const EigenBase<MatrixDerived>& A) : Base(A.derived()), m_restart(30),m_neig(0),m_r(0),m_maxNeig(5),m_isDeflAllocated(false),m_isDeflInitialized(false) {}
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| 138 |
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| 139 | ~DGMRES() {}
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| 140 |
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| 141 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A
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| 142 | * \a x0 as an initial solution.
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| 143 | *
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| 144 | * \sa compute()
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| 145 | */
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| 146 | template<typename Rhs,typename Guess>
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| 147 | inline const internal::solve_retval_with_guess<DGMRES, Rhs, Guess>
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| 148 | solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
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| 149 | {
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| 150 | eigen_assert(m_isInitialized && "DGMRES is not initialized.");
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| 151 | eigen_assert(Base::rows()==b.rows()
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| 152 | && "DGMRES::solve(): invalid number of rows of the right hand side matrix b");
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| 153 | return internal::solve_retval_with_guess
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| 154 | <DGMRES, Rhs, Guess>(*this, b.derived(), x0);
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| 155 | }
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| 156 |
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| 157 | /** \internal */
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| 158 | template<typename Rhs,typename Dest>
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| 159 | void _solveWithGuess(const Rhs& b, Dest& x) const
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| 160 | {
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| 161 | bool failed = false;
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| 162 | for(int j=0; j<b.cols(); ++j)
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| 163 | {
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| 164 | m_iterations = Base::maxIterations();
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| 165 | m_error = Base::m_tolerance;
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| 166 |
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| 167 | typename Dest::ColXpr xj(x,j);
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| 168 | dgmres(*mp_matrix, b.col(j), xj, Base::m_preconditioner);
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| 169 | }
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| 170 | m_info = failed ? NumericalIssue
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| 171 | : m_error <= Base::m_tolerance ? Success
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| 172 | : NoConvergence;
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| 173 | m_isInitialized = true;
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| 174 | }
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| 175 |
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| 176 | /** \internal */
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| 177 | template<typename Rhs,typename Dest>
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| 178 | void _solve(const Rhs& b, Dest& x) const
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| 179 | {
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| 180 | x = b;
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| 181 | _solveWithGuess(b,x);
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| 182 | }
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| 183 | /**
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| 184 | * Get the restart value
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| 185 | */
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| 186 | int restart() { return m_restart; }
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| 187 |
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| 188 | /**
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| 189 | * Set the restart value (default is 30)
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| 190 | */
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| 191 | void set_restart(const int restart) { m_restart=restart; }
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| 192 |
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| 193 | /**
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| 194 | * Set the number of eigenvalues to deflate at each restart
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| 195 | */
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| 196 | void setEigenv(const int neig)
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| 197 | {
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| 198 | m_neig = neig;
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| 199 | if (neig+1 > m_maxNeig) m_maxNeig = neig+1; // To allow for complex conjugates
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| 200 | }
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| 201 |
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| 202 | /**
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| 203 | * Get the size of the deflation subspace size
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| 204 | */
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| 205 | int deflSize() {return m_r; }
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| 206 |
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| 207 | /**
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| 208 | * Set the maximum size of the deflation subspace
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| 209 | */
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| 210 | void setMaxEigenv(const int maxNeig) { m_maxNeig = maxNeig; }
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| 211 |
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| 212 | protected:
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| 213 | // DGMRES algorithm
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| 214 | template<typename Rhs, typename Dest>
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| 215 | void dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x, const Preconditioner& precond) const;
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| 216 | // Perform one cycle of GMRES
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| 217 | template<typename Dest>
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| 218 | int dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, int& nbIts) const;
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| 219 | // Compute data to use for deflation
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| 220 | int dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, Index& neig) const;
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| 221 | // Apply deflation to a vector
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| 222 | template<typename RhsType, typename DestType>
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| 223 | int dgmresApplyDeflation(const RhsType& In, DestType& Out) const;
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| 224 | ComplexVector schurValues(const ComplexSchur<DenseMatrix>& schurofH) const;
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| 225 | ComplexVector schurValues(const RealSchur<DenseMatrix>& schurofH) const;
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| 226 | // Init data for deflation
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| 227 | void dgmresInitDeflation(Index& rows) const;
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| 228 | mutable DenseMatrix m_V; // Krylov basis vectors
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| 229 | mutable DenseMatrix m_H; // Hessenberg matrix
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| 230 | mutable DenseMatrix m_Hes; // Initial hessenberg matrix wihout Givens rotations applied
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| 231 | mutable Index m_restart; // Maximum size of the Krylov subspace
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| 232 | mutable DenseMatrix m_U; // Vectors that form the basis of the invariant subspace
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| 233 | mutable DenseMatrix m_MU; // matrix operator applied to m_U (for next cycles)
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| 234 | mutable DenseMatrix m_T; /* T=U^T*M^{-1}*A*U */
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| 235 | mutable PartialPivLU<DenseMatrix> m_luT; // LU factorization of m_T
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| 236 | mutable int m_neig; //Number of eigenvalues to extract at each restart
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| 237 | mutable int m_r; // Current number of deflated eigenvalues, size of m_U
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| 238 | mutable int m_maxNeig; // Maximum number of eigenvalues to deflate
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| 239 | mutable RealScalar m_lambdaN; //Modulus of the largest eigenvalue of A
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| 240 | mutable bool m_isDeflAllocated;
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| 241 | mutable bool m_isDeflInitialized;
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| 242 |
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| 243 | //Adaptive strategy
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| 244 | mutable RealScalar m_smv; // Smaller multiple of the remaining number of steps allowed
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| 245 | mutable bool m_force; // Force the use of deflation at each restart
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| 246 |
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| 247 | };
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| 248 | /**
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| 249 | * \brief Perform several cycles of restarted GMRES with modified Gram Schmidt,
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| 250 | *
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| 251 | * A right preconditioner is used combined with deflation.
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| 252 | *
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| 253 | */
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| 254 | template< typename _MatrixType, typename _Preconditioner>
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| 255 | template<typename Rhs, typename Dest>
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| 256 | void DGMRES<_MatrixType, _Preconditioner>::dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x,
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| 257 | const Preconditioner& precond) const
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| 258 | {
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| 259 | //Initialization
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| 260 | int n = mat.rows();
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| 261 | DenseVector r0(n);
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| 262 | int nbIts = 0;
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| 263 | m_H.resize(m_restart+1, m_restart);
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| 264 | m_Hes.resize(m_restart, m_restart);
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| 265 | m_V.resize(n,m_restart+1);
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| 266 | //Initial residual vector and intial norm
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| 267 | x = precond.solve(x);
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| 268 | r0 = rhs - mat * x;
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| 269 | RealScalar beta = r0.norm();
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| 270 | RealScalar normRhs = rhs.norm();
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| 271 | m_error = beta/normRhs;
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| 272 | if(m_error < m_tolerance)
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| 273 | m_info = Success;
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| 274 | else
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| 275 | m_info = NoConvergence;
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| 276 |
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| 277 | // Iterative process
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| 278 | while (nbIts < m_iterations && m_info == NoConvergence)
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| 279 | {
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| 280 | dgmresCycle(mat, precond, x, r0, beta, normRhs, nbIts);
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| 281 |
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| 282 | // Compute the new residual vector for the restart
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| 283 | if (nbIts < m_iterations && m_info == NoConvergence)
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| 284 | r0 = rhs - mat * x;
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| 285 | }
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| 286 | }
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| 287 |
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| 288 | /**
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| 289 | * \brief Perform one restart cycle of DGMRES
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| 290 | * \param mat The coefficient matrix
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| 291 | * \param precond The preconditioner
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| 292 | * \param x the new approximated solution
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| 293 | * \param r0 The initial residual vector
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| 294 | * \param beta The norm of the residual computed so far
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| 295 | * \param normRhs The norm of the right hand side vector
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| 296 | * \param nbIts The number of iterations
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| 297 | */
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| 298 | template< typename _MatrixType, typename _Preconditioner>
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| 299 | template<typename Dest>
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| 300 | int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, int& nbIts) const
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| 301 | {
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| 302 | //Initialization
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| 303 | DenseVector g(m_restart+1); // Right hand side of the least square problem
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| 304 | g.setZero();
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| 305 | g(0) = Scalar(beta);
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| 306 | m_V.col(0) = r0/beta;
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| 307 | m_info = NoConvergence;
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| 308 | std::vector<JacobiRotation<Scalar> >gr(m_restart); // Givens rotations
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| 309 | int it = 0; // Number of inner iterations
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| 310 | int n = mat.rows();
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| 311 | DenseVector tv1(n), tv2(n); //Temporary vectors
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| 312 | while (m_info == NoConvergence && it < m_restart && nbIts < m_iterations)
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| 313 | {
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| 314 | // Apply preconditioner(s) at right
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| 315 | if (m_isDeflInitialized )
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| 316 | {
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| 317 | dgmresApplyDeflation(m_V.col(it), tv1); // Deflation
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| 318 | tv2 = precond.solve(tv1);
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| 319 | }
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| 320 | else
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| 321 | {
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| 322 | tv2 = precond.solve(m_V.col(it)); // User's selected preconditioner
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| 323 | }
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| 324 | tv1 = mat * tv2;
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| 325 |
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| 326 | // Orthogonalize it with the previous basis in the basis using modified Gram-Schmidt
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| 327 | Scalar coef;
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| 328 | for (int i = 0; i <= it; ++i)
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| 329 | {
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| 330 | coef = tv1.dot(m_V.col(i));
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| 331 | tv1 = tv1 - coef * m_V.col(i);
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| 332 | m_H(i,it) = coef;
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| 333 | m_Hes(i,it) = coef;
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| 334 | }
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| 335 | // Normalize the vector
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| 336 | coef = tv1.norm();
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| 337 | m_V.col(it+1) = tv1/coef;
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| 338 | m_H(it+1, it) = coef;
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| 339 | // m_Hes(it+1,it) = coef;
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| 340 |
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| 341 | // FIXME Check for happy breakdown
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| 342 |
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| 343 | // Update Hessenberg matrix with Givens rotations
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| 344 | for (int i = 1; i <= it; ++i)
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| 345 | {
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| 346 | m_H.col(it).applyOnTheLeft(i-1,i,gr[i-1].adjoint());
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| 347 | }
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| 348 | // Compute the new plane rotation
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| 349 | gr[it].makeGivens(m_H(it, it), m_H(it+1,it));
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| 350 | // Apply the new rotation
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| 351 | m_H.col(it).applyOnTheLeft(it,it+1,gr[it].adjoint());
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| 352 | g.applyOnTheLeft(it,it+1, gr[it].adjoint());
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| 353 |
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| 354 | beta = std::abs(g(it+1));
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| 355 | m_error = beta/normRhs;
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| 356 | std::cerr << nbIts << " Relative Residual Norm " << m_error << std::endl;
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| 357 | it++; nbIts++;
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| 358 |
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| 359 | if (m_error < m_tolerance)
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| 360 | {
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| 361 | // The method has converged
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| 362 | m_info = Success;
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| 363 | break;
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| 364 | }
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| 365 | }
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| 366 |
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| 367 | // Compute the new coefficients by solving the least square problem
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| 368 | // it++;
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| 369 | //FIXME Check first if the matrix is singular ... zero diagonal
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| 370 | DenseVector nrs(m_restart);
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| 371 | nrs = m_H.topLeftCorner(it,it).template triangularView<Upper>().solve(g.head(it));
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| 372 |
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| 373 | // Form the new solution
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| 374 | if (m_isDeflInitialized)
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| 375 | {
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| 376 | tv1 = m_V.leftCols(it) * nrs;
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| 377 | dgmresApplyDeflation(tv1, tv2);
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| 378 | x = x + precond.solve(tv2);
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| 379 | }
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| 380 | else
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| 381 | x = x + precond.solve(m_V.leftCols(it) * nrs);
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| 382 |
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| 383 | // Go for a new cycle and compute data for deflation
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| 384 | if(nbIts < m_iterations && m_info == NoConvergence && m_neig > 0 && (m_r+m_neig) < m_maxNeig)
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| 385 | dgmresComputeDeflationData(mat, precond, it, m_neig);
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| 386 | return 0;
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| 387 |
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| 388 | }
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| 389 |
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| 390 |
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| 391 | template< typename _MatrixType, typename _Preconditioner>
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| 392 | void DGMRES<_MatrixType, _Preconditioner>::dgmresInitDeflation(Index& rows) const
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| 393 | {
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| 394 | m_U.resize(rows, m_maxNeig);
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| 395 | m_MU.resize(rows, m_maxNeig);
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| 396 | m_T.resize(m_maxNeig, m_maxNeig);
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| 397 | m_lambdaN = 0.0;
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| 398 | m_isDeflAllocated = true;
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| 399 | }
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| 400 |
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| 401 | template< typename _MatrixType, typename _Preconditioner>
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| 402 | inline typename DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_MatrixType, _Preconditioner>::schurValues(const ComplexSchur<DenseMatrix>& schurofH) const
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| 403 | {
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| 404 | return schurofH.matrixT().diagonal();
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| 405 | }
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| 406 |
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| 407 | template< typename _MatrixType, typename _Preconditioner>
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| 408 | inline typename DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_MatrixType, _Preconditioner>::schurValues(const RealSchur<DenseMatrix>& schurofH) const
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| 409 | {
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| 410 | typedef typename MatrixType::Index Index;
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| 411 | const DenseMatrix& T = schurofH.matrixT();
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| 412 | Index it = T.rows();
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| 413 | ComplexVector eig(it);
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| 414 | Index j = 0;
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| 415 | while (j < it-1)
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| 416 | {
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| 417 | if (T(j+1,j) ==Scalar(0))
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| 418 | {
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| 419 | eig(j) = std::complex<RealScalar>(T(j,j),RealScalar(0));
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| 420 | j++;
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| 421 | }
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| 422 | else
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| 423 | {
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| 424 | eig(j) = std::complex<RealScalar>(T(j,j),T(j+1,j));
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| 425 | eig(j+1) = std::complex<RealScalar>(T(j,j+1),T(j+1,j+1));
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| 426 | j++;
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| 427 | }
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| 428 | }
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| 429 | if (j < it-1) eig(j) = std::complex<RealScalar>(T(j,j),RealScalar(0));
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| 430 | return eig;
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| 431 | }
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| 432 |
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| 433 | template< typename _MatrixType, typename _Preconditioner>
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| 434 | int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, Index& neig) const
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| 435 | {
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| 436 | // First, find the Schur form of the Hessenberg matrix H
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| 437 | typename internal::conditional<NumTraits<Scalar>::IsComplex, ComplexSchur<DenseMatrix>, RealSchur<DenseMatrix> >::type schurofH;
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| 438 | bool computeU = true;
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| 439 | DenseMatrix matrixQ(it,it);
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| 440 | matrixQ.setIdentity();
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| 441 | schurofH.computeFromHessenberg(m_Hes.topLeftCorner(it,it), matrixQ, computeU);
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| 442 |
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| 443 | ComplexVector eig(it);
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| 444 | Matrix<Index,Dynamic,1>perm(it);
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| 445 | eig = this->schurValues(schurofH);
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| 446 |
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| 447 | // Reorder the absolute values of Schur values
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| 448 | DenseRealVector modulEig(it);
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| 449 | for (int j=0; j<it; ++j) modulEig(j) = std::abs(eig(j));
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| 450 | perm.setLinSpaced(it,0,it-1);
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| 451 | internal::sortWithPermutation(modulEig, perm, neig);
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| 452 |
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| 453 | if (!m_lambdaN)
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| 454 | {
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| 455 | m_lambdaN = (std::max)(modulEig.maxCoeff(), m_lambdaN);
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| 456 | }
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| 457 | //Count the real number of extracted eigenvalues (with complex conjugates)
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| 458 | int nbrEig = 0;
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| 459 | while (nbrEig < neig)
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| 460 | {
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| 461 | if(eig(perm(it-nbrEig-1)).imag() == RealScalar(0)) nbrEig++;
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| 462 | else nbrEig += 2;
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| 463 | }
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| 464 | // Extract the Schur vectors corresponding to the smallest Ritz values
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| 465 | DenseMatrix Sr(it, nbrEig);
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| 466 | Sr.setZero();
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| 467 | for (int j = 0; j < nbrEig; j++)
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| 468 | {
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| 469 | Sr.col(j) = schurofH.matrixU().col(perm(it-j-1));
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| 470 | }
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| 471 |
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| 472 | // Form the Schur vectors of the initial matrix using the Krylov basis
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| 473 | DenseMatrix X;
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| 474 | X = m_V.leftCols(it) * Sr;
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| 475 | if (m_r)
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| 476 | {
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| 477 | // Orthogonalize X against m_U using modified Gram-Schmidt
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| 478 | for (int j = 0; j < nbrEig; j++)
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| 479 | for (int k =0; k < m_r; k++)
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| 480 | X.col(j) = X.col(j) - (m_U.col(k).dot(X.col(j)))*m_U.col(k);
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| 481 | }
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| 482 |
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| 483 | // Compute m_MX = A * M^-1 * X
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| 484 | Index m = m_V.rows();
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| 485 | if (!m_isDeflAllocated)
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| 486 | dgmresInitDeflation(m);
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| 487 | DenseMatrix MX(m, nbrEig);
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| 488 | DenseVector tv1(m);
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| 489 | for (int j = 0; j < nbrEig; j++)
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| 490 | {
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| 491 | tv1 = mat * X.col(j);
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| 492 | MX.col(j) = precond.solve(tv1);
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| 493 | }
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| 494 |
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| 495 | //Update m_T = [U'MU U'MX; X'MU X'MX]
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| 496 | m_T.block(m_r, m_r, nbrEig, nbrEig) = X.transpose() * MX;
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| 497 | if(m_r)
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| 498 | {
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| 499 | m_T.block(0, m_r, m_r, nbrEig) = m_U.leftCols(m_r).transpose() * MX;
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| 500 | m_T.block(m_r, 0, nbrEig, m_r) = X.transpose() * m_MU.leftCols(m_r);
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| 501 | }
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| 502 |
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| 503 | // Save X into m_U and m_MX in m_MU
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| 504 | for (int j = 0; j < nbrEig; j++) m_U.col(m_r+j) = X.col(j);
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| 505 | for (int j = 0; j < nbrEig; j++) m_MU.col(m_r+j) = MX.col(j);
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| 506 | // Increase the size of the invariant subspace
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| 507 | m_r += nbrEig;
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| 508 |
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| 509 | // Factorize m_T into m_luT
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| 510 | m_luT.compute(m_T.topLeftCorner(m_r, m_r));
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| 511 |
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| 512 | //FIXME CHeck if the factorization was correctly done (nonsingular matrix)
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| 513 | m_isDeflInitialized = true;
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| 514 | return 0;
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| 515 | }
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| 516 | template<typename _MatrixType, typename _Preconditioner>
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| 517 | template<typename RhsType, typename DestType>
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| 518 | int DGMRES<_MatrixType, _Preconditioner>::dgmresApplyDeflation(const RhsType &x, DestType &y) const
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| 519 | {
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| 520 | DenseVector x1 = m_U.leftCols(m_r).transpose() * x;
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| 521 | y = x + m_U.leftCols(m_r) * ( m_lambdaN * m_luT.solve(x1) - x1);
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| 522 | return 0;
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| 523 | }
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| 524 |
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| 525 | namespace internal {
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| 526 |
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| 527 | template<typename _MatrixType, typename _Preconditioner, typename Rhs>
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| 528 | struct solve_retval<DGMRES<_MatrixType, _Preconditioner>, Rhs>
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| 529 | : solve_retval_base<DGMRES<_MatrixType, _Preconditioner>, Rhs>
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| 530 | {
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| 531 | typedef DGMRES<_MatrixType, _Preconditioner> Dec;
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| 532 | EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
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| 533 |
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| 534 | template<typename Dest> void evalTo(Dest& dst) const
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| 535 | {
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| 536 | dec()._solve(rhs(),dst);
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| 537 | }
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| 538 | };
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| 539 | } // end namespace internal
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| 540 |
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| 541 | } // end namespace Eigen
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| 542 | #endif
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