[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 David Harmon <dharmon@gmail.com>
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| 5 | //
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| 6 | // Eigen is free software; you can redistribute it and/or
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| 7 | // modify it under the terms of the GNU Lesser General Public
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| 8 | // License as published by the Free Software Foundation; either
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| 9 | // version 3 of the License, or (at your option) any later version.
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| 10 | //
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| 11 | // Alternatively, you can redistribute it and/or
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| 12 | // modify it under the terms of the GNU General Public License as
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| 13 | // published by the Free Software Foundation; either version 2 of
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| 14 | // the License, or (at your option) any later version.
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| 15 | //
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| 16 | // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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| 17 | // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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| 18 | // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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| 19 | // GNU General Public License for more details.
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| 20 | //
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| 21 | // You should have received a copy of the GNU Lesser General Public
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| 22 | // License and a copy of the GNU General Public License along with
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| 23 | // Eigen. If not, see <http://www.gnu.org/licenses/>.
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| 24 |
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| 25 | #ifndef EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
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| 26 | #define EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
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| 27 |
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| 28 | #include <Eigen/Dense>
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| 29 |
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| 30 | namespace Eigen {
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| 31 |
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| 32 | namespace internal {
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| 33 | template<typename Scalar, typename RealScalar> struct arpack_wrapper;
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| 34 | template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD> struct OP;
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| 35 | }
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| 36 |
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| 37 |
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| 38 |
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| 39 | template<typename MatrixType, typename MatrixSolver=SimplicialLLT<MatrixType>, bool BisSPD=false>
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| 40 | class ArpackGeneralizedSelfAdjointEigenSolver
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| 41 | {
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| 42 | public:
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| 43 | //typedef typename MatrixSolver::MatrixType MatrixType;
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| 44 |
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| 45 | /** \brief Scalar type for matrices of type \p MatrixType. */
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| 46 | typedef typename MatrixType::Scalar Scalar;
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| 47 | typedef typename MatrixType::Index Index;
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| 48 |
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| 49 | /** \brief Real scalar type for \p MatrixType.
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| 50 | *
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| 51 | * This is just \c Scalar if #Scalar is real (e.g., \c float or
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| 52 | * \c Scalar), and the type of the real part of \c Scalar if #Scalar is
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| 53 | * complex.
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| 54 | */
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| 55 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 56 |
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| 57 | /** \brief Type for vector of eigenvalues as returned by eigenvalues().
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| 58 | *
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| 59 | * This is a column vector with entries of type #RealScalar.
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| 60 | * The length of the vector is the size of \p nbrEigenvalues.
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| 61 | */
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| 62 | typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;
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| 63 |
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| 64 | /** \brief Default constructor.
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| 65 | *
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| 66 | * The default constructor is for cases in which the user intends to
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| 67 | * perform decompositions via compute().
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| 68 | *
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| 69 | */
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| 70 | ArpackGeneralizedSelfAdjointEigenSolver()
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| 71 | : m_eivec(),
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| 72 | m_eivalues(),
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| 73 | m_isInitialized(false),
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| 74 | m_eigenvectorsOk(false),
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| 75 | m_nbrConverged(0),
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| 76 | m_nbrIterations(0)
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| 77 | { }
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| 78 |
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| 79 | /** \brief Constructor; computes generalized eigenvalues of given matrix with respect to another matrix.
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| 80 | *
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| 81 | * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
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| 82 | * computed. By default, the upper triangular part is used, but can be changed
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| 83 | * through the template parameter.
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| 84 | * \param[in] B Self-adjoint matrix for the generalized eigenvalue problem.
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| 85 | * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
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| 86 | * Must be less than the size of the input matrix, or an error is returned.
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| 87 | * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
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| 88 | * respective meanings to find the largest magnitude , smallest magnitude,
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| 89 | * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
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| 90 | * value can contain floating point value in string form, in which case the
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| 91 | * eigenvalues closest to this value will be found.
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| 92 | * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
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| 93 | * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
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| 94 | * means machine precision.
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| 95 | *
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| 96 | * This constructor calls compute(const MatrixType&, const MatrixType&, Index, string, int, RealScalar)
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| 97 | * to compute the eigenvalues of the matrix \p A with respect to \p B. The eigenvectors are computed if
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| 98 | * \p options equals #ComputeEigenvectors.
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| 99 | *
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| 100 | */
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| 101 | ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A, const MatrixType& B,
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| 102 | Index nbrEigenvalues, std::string eigs_sigma="LM",
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| 103 | int options=ComputeEigenvectors, RealScalar tol=0.0)
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| 104 | : m_eivec(),
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| 105 | m_eivalues(),
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| 106 | m_isInitialized(false),
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| 107 | m_eigenvectorsOk(false),
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| 108 | m_nbrConverged(0),
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| 109 | m_nbrIterations(0)
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| 110 | {
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| 111 | compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
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| 112 | }
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| 113 |
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| 114 | /** \brief Constructor; computes eigenvalues of given matrix.
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| 115 | *
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| 116 | * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
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| 117 | * computed. By default, the upper triangular part is used, but can be changed
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| 118 | * through the template parameter.
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| 119 | * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
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| 120 | * Must be less than the size of the input matrix, or an error is returned.
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| 121 | * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
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| 122 | * respective meanings to find the largest magnitude , smallest magnitude,
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| 123 | * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
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| 124 | * value can contain floating point value in string form, in which case the
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| 125 | * eigenvalues closest to this value will be found.
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| 126 | * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
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| 127 | * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
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| 128 | * means machine precision.
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| 129 | *
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| 130 | * This constructor calls compute(const MatrixType&, Index, string, int, RealScalar)
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| 131 | * to compute the eigenvalues of the matrix \p A. The eigenvectors are computed if
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| 132 | * \p options equals #ComputeEigenvectors.
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| 133 | *
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| 134 | */
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| 135 |
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| 136 | ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A,
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| 137 | Index nbrEigenvalues, std::string eigs_sigma="LM",
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| 138 | int options=ComputeEigenvectors, RealScalar tol=0.0)
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| 139 | : m_eivec(),
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| 140 | m_eivalues(),
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| 141 | m_isInitialized(false),
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| 142 | m_eigenvectorsOk(false),
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| 143 | m_nbrConverged(0),
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| 144 | m_nbrIterations(0)
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| 145 | {
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| 146 | compute(A, nbrEigenvalues, eigs_sigma, options, tol);
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| 147 | }
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| 148 |
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| 149 |
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| 150 | /** \brief Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPACK library.
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| 151 | *
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| 152 | * \param[in] A Selfadjoint matrix whose eigendecomposition is to be computed.
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| 153 | * \param[in] B Selfadjoint matrix for generalized eigenvalues.
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| 154 | * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
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| 155 | * Must be less than the size of the input matrix, or an error is returned.
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| 156 | * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
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| 157 | * respective meanings to find the largest magnitude , smallest magnitude,
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| 158 | * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
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| 159 | * value can contain floating point value in string form, in which case the
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| 160 | * eigenvalues closest to this value will be found.
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| 161 | * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
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| 162 | * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
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| 163 | * means machine precision.
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| 164 | *
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| 165 | * \returns Reference to \c *this
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| 166 | *
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| 167 | * This function computes the generalized eigenvalues of \p A with respect to \p B using ARPACK. The eigenvalues()
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| 168 | * function can be used to retrieve them. If \p options equals #ComputeEigenvectors,
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| 169 | * then the eigenvectors are also computed and can be retrieved by
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| 170 | * calling eigenvectors().
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| 171 | *
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| 172 | */
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| 173 | ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A, const MatrixType& B,
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| 174 | Index nbrEigenvalues, std::string eigs_sigma="LM",
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| 175 | int options=ComputeEigenvectors, RealScalar tol=0.0);
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| 176 |
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| 177 | /** \brief Computes eigenvalues / eigenvectors of given matrix using the external ARPACK library.
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| 178 | *
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| 179 | * \param[in] A Selfadjoint matrix whose eigendecomposition is to be computed.
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| 180 | * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
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| 181 | * Must be less than the size of the input matrix, or an error is returned.
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| 182 | * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
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| 183 | * respective meanings to find the largest magnitude , smallest magnitude,
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| 184 | * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
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| 185 | * value can contain floating point value in string form, in which case the
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| 186 | * eigenvalues closest to this value will be found.
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| 187 | * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
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| 188 | * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
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| 189 | * means machine precision.
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| 190 | *
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| 191 | * \returns Reference to \c *this
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| 192 | *
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| 193 | * This function computes the eigenvalues of \p A using ARPACK. The eigenvalues()
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| 194 | * function can be used to retrieve them. If \p options equals #ComputeEigenvectors,
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| 195 | * then the eigenvectors are also computed and can be retrieved by
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| 196 | * calling eigenvectors().
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| 197 | *
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| 198 | */
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| 199 | ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A,
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| 200 | Index nbrEigenvalues, std::string eigs_sigma="LM",
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| 201 | int options=ComputeEigenvectors, RealScalar tol=0.0);
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| 202 |
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| 203 |
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| 204 | /** \brief Returns the eigenvectors of given matrix.
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| 205 | *
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| 206 | * \returns A const reference to the matrix whose columns are the eigenvectors.
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| 207 | *
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| 208 | * \pre The eigenvectors have been computed before.
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| 209 | *
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| 210 | * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
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| 211 | * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
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| 212 | * eigenvectors are normalized to have (Euclidean) norm equal to one. If
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| 213 | * this object was used to solve the eigenproblem for the selfadjoint
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| 214 | * matrix \f$ A \f$, then the matrix returned by this function is the
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| 215 | * matrix \f$ V \f$ in the eigendecomposition \f$ A V = D V \f$.
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| 216 | * For the generalized eigenproblem, the matrix returned is the solution \f$ A V = D B V \f$
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| 217 | *
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| 218 | * Example: \include SelfAdjointEigenSolver_eigenvectors.cpp
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| 219 | * Output: \verbinclude SelfAdjointEigenSolver_eigenvectors.out
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| 220 | *
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| 221 | * \sa eigenvalues()
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| 222 | */
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| 223 | const Matrix<Scalar, Dynamic, Dynamic>& eigenvectors() const
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| 224 | {
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| 225 | eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
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| 226 | eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
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| 227 | return m_eivec;
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| 228 | }
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| 229 |
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| 230 | /** \brief Returns the eigenvalues of given matrix.
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| 231 | *
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| 232 | * \returns A const reference to the column vector containing the eigenvalues.
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| 233 | *
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| 234 | * \pre The eigenvalues have been computed before.
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| 235 | *
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| 236 | * The eigenvalues are repeated according to their algebraic multiplicity,
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| 237 | * so there are as many eigenvalues as rows in the matrix. The eigenvalues
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| 238 | * are sorted in increasing order.
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| 239 | *
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| 240 | * Example: \include SelfAdjointEigenSolver_eigenvalues.cpp
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| 241 | * Output: \verbinclude SelfAdjointEigenSolver_eigenvalues.out
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| 242 | *
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| 243 | * \sa eigenvectors(), MatrixBase::eigenvalues()
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| 244 | */
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| 245 | const Matrix<Scalar, Dynamic, 1>& eigenvalues() const
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| 246 | {
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| 247 | eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
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| 248 | return m_eivalues;
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| 249 | }
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| 250 |
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| 251 | /** \brief Computes the positive-definite square root of the matrix.
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| 252 | *
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| 253 | * \returns the positive-definite square root of the matrix
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| 254 | *
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| 255 | * \pre The eigenvalues and eigenvectors of a positive-definite matrix
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| 256 | * have been computed before.
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| 257 | *
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| 258 | * The square root of a positive-definite matrix \f$ A \f$ is the
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| 259 | * positive-definite matrix whose square equals \f$ A \f$. This function
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| 260 | * uses the eigendecomposition \f$ A = V D V^{-1} \f$ to compute the
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| 261 | * square root as \f$ A^{1/2} = V D^{1/2} V^{-1} \f$.
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| 262 | *
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| 263 | * Example: \include SelfAdjointEigenSolver_operatorSqrt.cpp
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| 264 | * Output: \verbinclude SelfAdjointEigenSolver_operatorSqrt.out
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| 265 | *
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| 266 | * \sa operatorInverseSqrt(),
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| 267 | * \ref MatrixFunctions_Module "MatrixFunctions Module"
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| 268 | */
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| 269 | Matrix<Scalar, Dynamic, Dynamic> operatorSqrt() const
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| 270 | {
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| 271 | eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
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| 272 | eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
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| 273 | return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
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| 274 | }
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| 275 |
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| 276 | /** \brief Computes the inverse square root of the matrix.
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| 277 | *
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| 278 | * \returns the inverse positive-definite square root of the matrix
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| 279 | *
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| 280 | * \pre The eigenvalues and eigenvectors of a positive-definite matrix
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| 281 | * have been computed before.
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| 282 | *
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| 283 | * This function uses the eigendecomposition \f$ A = V D V^{-1} \f$ to
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| 284 | * compute the inverse square root as \f$ V D^{-1/2} V^{-1} \f$. This is
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| 285 | * cheaper than first computing the square root with operatorSqrt() and
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| 286 | * then its inverse with MatrixBase::inverse().
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| 287 | *
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| 288 | * Example: \include SelfAdjointEigenSolver_operatorInverseSqrt.cpp
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| 289 | * Output: \verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out
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| 290 | *
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| 291 | * \sa operatorSqrt(), MatrixBase::inverse(),
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| 292 | * \ref MatrixFunctions_Module "MatrixFunctions Module"
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| 293 | */
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| 294 | Matrix<Scalar, Dynamic, Dynamic> operatorInverseSqrt() const
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| 295 | {
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| 296 | eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
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| 297 | eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
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| 298 | return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
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| 299 | }
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| 300 |
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| 301 | /** \brief Reports whether previous computation was successful.
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| 302 | *
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| 303 | * \returns \c Success if computation was succesful, \c NoConvergence otherwise.
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| 304 | */
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| 305 | ComputationInfo info() const
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| 306 | {
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| 307 | eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
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| 308 | return m_info;
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| 309 | }
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| 310 |
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| 311 | size_t getNbrConvergedEigenValues() const
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| 312 | { return m_nbrConverged; }
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| 313 |
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| 314 | size_t getNbrIterations() const
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| 315 | { return m_nbrIterations; }
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| 316 |
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| 317 | protected:
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| 318 | Matrix<Scalar, Dynamic, Dynamic> m_eivec;
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| 319 | Matrix<Scalar, Dynamic, 1> m_eivalues;
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| 320 | ComputationInfo m_info;
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| 321 | bool m_isInitialized;
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| 322 | bool m_eigenvectorsOk;
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| 323 |
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| 324 | size_t m_nbrConverged;
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| 325 | size_t m_nbrIterations;
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| 326 | };
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| 327 |
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| 328 |
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| 329 |
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| 330 |
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| 331 |
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| 332 | template<typename MatrixType, typename MatrixSolver, bool BisSPD>
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| 333 | ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
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| 334 | ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>
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| 335 | ::compute(const MatrixType& A, Index nbrEigenvalues,
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| 336 | std::string eigs_sigma, int options, RealScalar tol)
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| 337 | {
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| 338 | MatrixType B(0,0);
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| 339 | compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
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| 340 |
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| 341 | return *this;
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| 342 | }
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| 343 |
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| 344 |
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| 345 | template<typename MatrixType, typename MatrixSolver, bool BisSPD>
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| 346 | ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
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| 347 | ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>
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| 348 | ::compute(const MatrixType& A, const MatrixType& B, Index nbrEigenvalues,
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| 349 | std::string eigs_sigma, int options, RealScalar tol)
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| 350 | {
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| 351 | eigen_assert(A.cols() == A.rows());
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| 352 | eigen_assert(B.cols() == B.rows());
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| 353 | eigen_assert(B.rows() == 0 || A.cols() == B.rows());
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| 354 | eigen_assert((options &~ (EigVecMask | GenEigMask)) == 0
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| 355 | && (options & EigVecMask) != EigVecMask
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| 356 | && "invalid option parameter");
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| 357 |
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| 358 | bool isBempty = (B.rows() == 0) || (B.cols() == 0);
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| 359 |
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| 360 | // For clarity, all parameters match their ARPACK name
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| 361 | //
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| 362 | // Always 0 on the first call
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| 363 | //
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| 364 | int ido = 0;
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| 365 |
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| 366 | int n = (int)A.cols();
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| 367 |
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| 368 | // User options: "LA", "SA", "SM", "LM", "BE"
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| 369 | //
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| 370 | char whch[3] = "LM";
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| 371 |
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| 372 | // Specifies the shift if iparam[6] = { 3, 4, 5 }, not used if iparam[6] = { 1, 2 }
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| 373 | //
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| 374 | RealScalar sigma = 0.0;
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| 375 |
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| 376 | if (eigs_sigma.length() >= 2 && isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1]))
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| 377 | {
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| 378 | eigs_sigma[0] = toupper(eigs_sigma[0]);
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| 379 | eigs_sigma[1] = toupper(eigs_sigma[1]);
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| 380 |
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| 381 | // In the following special case we're going to invert the problem, since solving
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| 382 | // for larger magnitude is much much faster
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| 383 | // i.e., if 'SM' is specified, we're going to really use 'LM', the default
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| 384 | //
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| 385 | if (eigs_sigma.substr(0,2) != "SM")
|
---|
| 386 | {
|
---|
| 387 | whch[0] = eigs_sigma[0];
|
---|
| 388 | whch[1] = eigs_sigma[1];
|
---|
| 389 | }
|
---|
| 390 | }
|
---|
| 391 | else
|
---|
| 392 | {
|
---|
| 393 | eigen_assert(false && "Specifying clustered eigenvalues is not yet supported!");
|
---|
| 394 |
|
---|
| 395 | // If it's not scalar values, then the user may be explicitly
|
---|
| 396 | // specifying the sigma value to cluster the evs around
|
---|
| 397 | //
|
---|
| 398 | sigma = atof(eigs_sigma.c_str());
|
---|
| 399 |
|
---|
| 400 | // If atof fails, it returns 0.0, which is a fine default
|
---|
| 401 | //
|
---|
| 402 | }
|
---|
| 403 |
|
---|
| 404 | // "I" means normal eigenvalue problem, "G" means generalized
|
---|
| 405 | //
|
---|
| 406 | char bmat[2] = "I";
|
---|
| 407 | if (eigs_sigma.substr(0,2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])) || (!isBempty && !BisSPD))
|
---|
| 408 | bmat[0] = 'G';
|
---|
| 409 |
|
---|
| 410 | // Now we determine the mode to use
|
---|
| 411 | //
|
---|
| 412 | int mode = (bmat[0] == 'G') + 1;
|
---|
| 413 | if (eigs_sigma.substr(0,2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])))
|
---|
| 414 | {
|
---|
| 415 | // We're going to use shift-and-invert mode, and basically find
|
---|
| 416 | // the largest eigenvalues of the inverse operator
|
---|
| 417 | //
|
---|
| 418 | mode = 3;
|
---|
| 419 | }
|
---|
| 420 |
|
---|
| 421 | // The user-specified number of eigenvalues/vectors to compute
|
---|
| 422 | //
|
---|
| 423 | int nev = (int)nbrEigenvalues;
|
---|
| 424 |
|
---|
| 425 | // Allocate space for ARPACK to store the residual
|
---|
| 426 | //
|
---|
| 427 | Scalar *resid = new Scalar[n];
|
---|
| 428 |
|
---|
| 429 | // Number of Lanczos vectors, must satisfy nev < ncv <= n
|
---|
| 430 | // Note that this indicates that nev != n, and we cannot compute
|
---|
| 431 | // all eigenvalues of a mtrix
|
---|
| 432 | //
|
---|
| 433 | int ncv = std::min(std::max(2*nev, 20), n);
|
---|
| 434 |
|
---|
| 435 | // The working n x ncv matrix, also store the final eigenvectors (if computed)
|
---|
| 436 | //
|
---|
| 437 | Scalar *v = new Scalar[n*ncv];
|
---|
| 438 | int ldv = n;
|
---|
| 439 |
|
---|
| 440 | // Working space
|
---|
| 441 | //
|
---|
| 442 | Scalar *workd = new Scalar[3*n];
|
---|
| 443 | int lworkl = ncv*ncv+8*ncv; // Must be at least this length
|
---|
| 444 | Scalar *workl = new Scalar[lworkl];
|
---|
| 445 |
|
---|
| 446 | int *iparam= new int[11];
|
---|
| 447 | iparam[0] = 1; // 1 means we let ARPACK perform the shifts, 0 means we'd have to do it
|
---|
| 448 | iparam[2] = std::max(300, (int)std::ceil(2*n/std::max(ncv,1)));
|
---|
| 449 | iparam[6] = mode; // The mode, 1 is standard ev problem, 2 for generalized ev, 3 for shift-and-invert
|
---|
| 450 |
|
---|
| 451 | // Used during reverse communicate to notify where arrays start
|
---|
| 452 | //
|
---|
| 453 | int *ipntr = new int[11];
|
---|
| 454 |
|
---|
| 455 | // Error codes are returned in here, initial value of 0 indicates a random initial
|
---|
| 456 | // residual vector is used, any other values means resid contains the initial residual
|
---|
| 457 | // vector, possibly from a previous run
|
---|
| 458 | //
|
---|
| 459 | int info = 0;
|
---|
| 460 |
|
---|
| 461 | Scalar scale = 1.0;
|
---|
| 462 | //if (!isBempty)
|
---|
| 463 | //{
|
---|
| 464 | //Scalar scale = B.norm() / std::sqrt(n);
|
---|
| 465 | //scale = std::pow(2, std::floor(std::log(scale+1)));
|
---|
| 466 | ////M /= scale;
|
---|
| 467 | //for (size_t i=0; i<(size_t)B.outerSize(); i++)
|
---|
| 468 | // for (typename MatrixType::InnerIterator it(B, i); it; ++it)
|
---|
| 469 | // it.valueRef() /= scale;
|
---|
| 470 | //}
|
---|
| 471 |
|
---|
| 472 | MatrixSolver OP;
|
---|
| 473 | if (mode == 1 || mode == 2)
|
---|
| 474 | {
|
---|
| 475 | if (!isBempty)
|
---|
| 476 | OP.compute(B);
|
---|
| 477 | }
|
---|
| 478 | else if (mode == 3)
|
---|
| 479 | {
|
---|
| 480 | if (sigma == 0.0)
|
---|
| 481 | {
|
---|
| 482 | OP.compute(A);
|
---|
| 483 | }
|
---|
| 484 | else
|
---|
| 485 | {
|
---|
| 486 | // Note: We will never enter here because sigma must be 0.0
|
---|
| 487 | //
|
---|
| 488 | if (isBempty)
|
---|
| 489 | {
|
---|
| 490 | MatrixType AminusSigmaB(A);
|
---|
| 491 | for (Index i=0; i<A.rows(); ++i)
|
---|
| 492 | AminusSigmaB.coeffRef(i,i) -= sigma;
|
---|
| 493 |
|
---|
| 494 | OP.compute(AminusSigmaB);
|
---|
| 495 | }
|
---|
| 496 | else
|
---|
| 497 | {
|
---|
| 498 | MatrixType AminusSigmaB = A - sigma * B;
|
---|
| 499 | OP.compute(AminusSigmaB);
|
---|
| 500 | }
|
---|
| 501 | }
|
---|
| 502 | }
|
---|
| 503 |
|
---|
| 504 | if (!(mode == 1 && isBempty) && !(mode == 2 && isBempty) && OP.info() != Success)
|
---|
| 505 | std::cout << "Error factoring matrix" << std::endl;
|
---|
| 506 |
|
---|
| 507 | do
|
---|
| 508 | {
|
---|
| 509 | internal::arpack_wrapper<Scalar, RealScalar>::saupd(&ido, bmat, &n, whch, &nev, &tol, resid,
|
---|
| 510 | &ncv, v, &ldv, iparam, ipntr, workd, workl,
|
---|
| 511 | &lworkl, &info);
|
---|
| 512 |
|
---|
| 513 | if (ido == -1 || ido == 1)
|
---|
| 514 | {
|
---|
| 515 | Scalar *in = workd + ipntr[0] - 1;
|
---|
| 516 | Scalar *out = workd + ipntr[1] - 1;
|
---|
| 517 |
|
---|
| 518 | if (ido == 1 && mode != 2)
|
---|
| 519 | {
|
---|
| 520 | Scalar *out2 = workd + ipntr[2] - 1;
|
---|
| 521 | if (isBempty || mode == 1)
|
---|
| 522 | Matrix<Scalar, Dynamic, 1>::Map(out2, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
|
---|
| 523 | else
|
---|
| 524 | Matrix<Scalar, Dynamic, 1>::Map(out2, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
|
---|
| 525 |
|
---|
| 526 | in = workd + ipntr[2] - 1;
|
---|
| 527 | }
|
---|
| 528 |
|
---|
| 529 | if (mode == 1)
|
---|
| 530 | {
|
---|
| 531 | if (isBempty)
|
---|
| 532 | {
|
---|
| 533 | // OP = A
|
---|
| 534 | //
|
---|
| 535 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
|
---|
| 536 | }
|
---|
| 537 | else
|
---|
| 538 | {
|
---|
| 539 | // OP = L^{-1}AL^{-T}
|
---|
| 540 | //
|
---|
| 541 | internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::applyOP(OP, A, n, in, out);
|
---|
| 542 | }
|
---|
| 543 | }
|
---|
| 544 | else if (mode == 2)
|
---|
| 545 | {
|
---|
| 546 | if (ido == 1)
|
---|
| 547 | Matrix<Scalar, Dynamic, 1>::Map(in, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
|
---|
| 548 |
|
---|
| 549 | // OP = B^{-1} A
|
---|
| 550 | //
|
---|
| 551 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
|
---|
| 552 | }
|
---|
| 553 | else if (mode == 3)
|
---|
| 554 | {
|
---|
| 555 | // OP = (A-\sigmaB)B (\sigma could be 0, and B could be I)
|
---|
| 556 | // The B * in is already computed and stored at in if ido == 1
|
---|
| 557 | //
|
---|
| 558 | if (ido == 1 || isBempty)
|
---|
| 559 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
|
---|
| 560 | else
|
---|
| 561 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(B * Matrix<Scalar, Dynamic, 1>::Map(in, n));
|
---|
| 562 | }
|
---|
| 563 | }
|
---|
| 564 | else if (ido == 2)
|
---|
| 565 | {
|
---|
| 566 | Scalar *in = workd + ipntr[0] - 1;
|
---|
| 567 | Scalar *out = workd + ipntr[1] - 1;
|
---|
| 568 |
|
---|
| 569 | if (isBempty || mode == 1)
|
---|
| 570 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
|
---|
| 571 | else
|
---|
| 572 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
|
---|
| 573 | }
|
---|
| 574 | } while (ido != 99);
|
---|
| 575 |
|
---|
| 576 | if (info == 1)
|
---|
| 577 | m_info = NoConvergence;
|
---|
| 578 | else if (info == 3)
|
---|
| 579 | m_info = NumericalIssue;
|
---|
| 580 | else if (info < 0)
|
---|
| 581 | m_info = InvalidInput;
|
---|
| 582 | else if (info != 0)
|
---|
| 583 | eigen_assert(false && "Unknown ARPACK return value!");
|
---|
| 584 | else
|
---|
| 585 | {
|
---|
| 586 | // Do we compute eigenvectors or not?
|
---|
| 587 | //
|
---|
| 588 | int rvec = (options & ComputeEigenvectors) == ComputeEigenvectors;
|
---|
| 589 |
|
---|
| 590 | // "A" means "All", use "S" to choose specific eigenvalues (not yet supported in ARPACK))
|
---|
| 591 | //
|
---|
| 592 | char howmny[2] = "A";
|
---|
| 593 |
|
---|
| 594 | // if howmny == "S", specifies the eigenvalues to compute (not implemented in ARPACK)
|
---|
| 595 | //
|
---|
| 596 | int *select = new int[ncv];
|
---|
| 597 |
|
---|
| 598 | // Final eigenvalues
|
---|
| 599 | //
|
---|
| 600 | m_eivalues.resize(nev, 1);
|
---|
| 601 |
|
---|
| 602 | internal::arpack_wrapper<Scalar, RealScalar>::seupd(&rvec, howmny, select, m_eivalues.data(), v, &ldv,
|
---|
| 603 | &sigma, bmat, &n, whch, &nev, &tol, resid, &ncv,
|
---|
| 604 | v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info);
|
---|
| 605 |
|
---|
| 606 | if (info == -14)
|
---|
| 607 | m_info = NoConvergence;
|
---|
| 608 | else if (info != 0)
|
---|
| 609 | m_info = InvalidInput;
|
---|
| 610 | else
|
---|
| 611 | {
|
---|
| 612 | if (rvec)
|
---|
| 613 | {
|
---|
| 614 | m_eivec.resize(A.rows(), nev);
|
---|
| 615 | for (int i=0; i<nev; i++)
|
---|
| 616 | for (int j=0; j<n; j++)
|
---|
| 617 | m_eivec(j,i) = v[i*n+j] / scale;
|
---|
| 618 |
|
---|
| 619 | if (mode == 1 && !isBempty && BisSPD)
|
---|
| 620 | internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::project(OP, n, nev, m_eivec.data());
|
---|
| 621 |
|
---|
| 622 | m_eigenvectorsOk = true;
|
---|
| 623 | }
|
---|
| 624 |
|
---|
| 625 | m_nbrIterations = iparam[2];
|
---|
| 626 | m_nbrConverged = iparam[4];
|
---|
| 627 |
|
---|
| 628 | m_info = Success;
|
---|
| 629 | }
|
---|
| 630 |
|
---|
| 631 | delete select;
|
---|
| 632 | }
|
---|
| 633 |
|
---|
| 634 | delete v;
|
---|
| 635 | delete iparam;
|
---|
| 636 | delete ipntr;
|
---|
| 637 | delete workd;
|
---|
| 638 | delete workl;
|
---|
| 639 | delete resid;
|
---|
| 640 |
|
---|
| 641 | m_isInitialized = true;
|
---|
| 642 |
|
---|
| 643 | return *this;
|
---|
| 644 | }
|
---|
| 645 |
|
---|
| 646 |
|
---|
| 647 | // Single precision
|
---|
| 648 | //
|
---|
| 649 | extern "C" void ssaupd_(int *ido, char *bmat, int *n, char *which,
|
---|
| 650 | int *nev, float *tol, float *resid, int *ncv,
|
---|
| 651 | float *v, int *ldv, int *iparam, int *ipntr,
|
---|
| 652 | float *workd, float *workl, int *lworkl,
|
---|
| 653 | int *info);
|
---|
| 654 |
|
---|
| 655 | extern "C" void sseupd_(int *rvec, char *All, int *select, float *d,
|
---|
| 656 | float *z, int *ldz, float *sigma,
|
---|
| 657 | char *bmat, int *n, char *which, int *nev,
|
---|
| 658 | float *tol, float *resid, int *ncv, float *v,
|
---|
| 659 | int *ldv, int *iparam, int *ipntr, float *workd,
|
---|
| 660 | float *workl, int *lworkl, int *ierr);
|
---|
| 661 |
|
---|
| 662 | // Double precision
|
---|
| 663 | //
|
---|
| 664 | extern "C" void dsaupd_(int *ido, char *bmat, int *n, char *which,
|
---|
| 665 | int *nev, double *tol, double *resid, int *ncv,
|
---|
| 666 | double *v, int *ldv, int *iparam, int *ipntr,
|
---|
| 667 | double *workd, double *workl, int *lworkl,
|
---|
| 668 | int *info);
|
---|
| 669 |
|
---|
| 670 | extern "C" void dseupd_(int *rvec, char *All, int *select, double *d,
|
---|
| 671 | double *z, int *ldz, double *sigma,
|
---|
| 672 | char *bmat, int *n, char *which, int *nev,
|
---|
| 673 | double *tol, double *resid, int *ncv, double *v,
|
---|
| 674 | int *ldv, int *iparam, int *ipntr, double *workd,
|
---|
| 675 | double *workl, int *lworkl, int *ierr);
|
---|
| 676 |
|
---|
| 677 |
|
---|
| 678 | namespace internal {
|
---|
| 679 |
|
---|
| 680 | template<typename Scalar, typename RealScalar> struct arpack_wrapper
|
---|
| 681 | {
|
---|
| 682 | static inline void saupd(int *ido, char *bmat, int *n, char *which,
|
---|
| 683 | int *nev, RealScalar *tol, Scalar *resid, int *ncv,
|
---|
| 684 | Scalar *v, int *ldv, int *iparam, int *ipntr,
|
---|
| 685 | Scalar *workd, Scalar *workl, int *lworkl, int *info)
|
---|
| 686 | {
|
---|
| 687 | EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
|
---|
| 688 | }
|
---|
| 689 |
|
---|
| 690 | static inline void seupd(int *rvec, char *All, int *select, Scalar *d,
|
---|
| 691 | Scalar *z, int *ldz, RealScalar *sigma,
|
---|
| 692 | char *bmat, int *n, char *which, int *nev,
|
---|
| 693 | RealScalar *tol, Scalar *resid, int *ncv, Scalar *v,
|
---|
| 694 | int *ldv, int *iparam, int *ipntr, Scalar *workd,
|
---|
| 695 | Scalar *workl, int *lworkl, int *ierr)
|
---|
| 696 | {
|
---|
| 697 | EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
|
---|
| 698 | }
|
---|
| 699 | };
|
---|
| 700 |
|
---|
| 701 | template <> struct arpack_wrapper<float, float>
|
---|
| 702 | {
|
---|
| 703 | static inline void saupd(int *ido, char *bmat, int *n, char *which,
|
---|
| 704 | int *nev, float *tol, float *resid, int *ncv,
|
---|
| 705 | float *v, int *ldv, int *iparam, int *ipntr,
|
---|
| 706 | float *workd, float *workl, int *lworkl, int *info)
|
---|
| 707 | {
|
---|
| 708 | ssaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
|
---|
| 709 | }
|
---|
| 710 |
|
---|
| 711 | static inline void seupd(int *rvec, char *All, int *select, float *d,
|
---|
| 712 | float *z, int *ldz, float *sigma,
|
---|
| 713 | char *bmat, int *n, char *which, int *nev,
|
---|
| 714 | float *tol, float *resid, int *ncv, float *v,
|
---|
| 715 | int *ldv, int *iparam, int *ipntr, float *workd,
|
---|
| 716 | float *workl, int *lworkl, int *ierr)
|
---|
| 717 | {
|
---|
| 718 | sseupd_(rvec, All, select, d, z, ldz, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,
|
---|
| 719 | workd, workl, lworkl, ierr);
|
---|
| 720 | }
|
---|
| 721 | };
|
---|
| 722 |
|
---|
| 723 | template <> struct arpack_wrapper<double, double>
|
---|
| 724 | {
|
---|
| 725 | static inline void saupd(int *ido, char *bmat, int *n, char *which,
|
---|
| 726 | int *nev, double *tol, double *resid, int *ncv,
|
---|
| 727 | double *v, int *ldv, int *iparam, int *ipntr,
|
---|
| 728 | double *workd, double *workl, int *lworkl, int *info)
|
---|
| 729 | {
|
---|
| 730 | dsaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
|
---|
| 731 | }
|
---|
| 732 |
|
---|
| 733 | static inline void seupd(int *rvec, char *All, int *select, double *d,
|
---|
| 734 | double *z, int *ldz, double *sigma,
|
---|
| 735 | char *bmat, int *n, char *which, int *nev,
|
---|
| 736 | double *tol, double *resid, int *ncv, double *v,
|
---|
| 737 | int *ldv, int *iparam, int *ipntr, double *workd,
|
---|
| 738 | double *workl, int *lworkl, int *ierr)
|
---|
| 739 | {
|
---|
| 740 | dseupd_(rvec, All, select, d, v, ldv, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,
|
---|
| 741 | workd, workl, lworkl, ierr);
|
---|
| 742 | }
|
---|
| 743 | };
|
---|
| 744 |
|
---|
| 745 |
|
---|
| 746 | template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD>
|
---|
| 747 | struct OP
|
---|
| 748 | {
|
---|
| 749 | static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out);
|
---|
| 750 | static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs);
|
---|
| 751 | };
|
---|
| 752 |
|
---|
| 753 | template<typename MatrixSolver, typename MatrixType, typename Scalar>
|
---|
| 754 | struct OP<MatrixSolver, MatrixType, Scalar, true>
|
---|
| 755 | {
|
---|
| 756 | static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)
|
---|
| 757 | {
|
---|
| 758 | // OP = L^{-1} A L^{-T} (B = LL^T)
|
---|
| 759 | //
|
---|
| 760 | // First solve L^T out = in
|
---|
| 761 | //
|
---|
| 762 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixU().solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
|
---|
| 763 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationPinv() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
|
---|
| 764 |
|
---|
| 765 | // Then compute out = A out
|
---|
| 766 | //
|
---|
| 767 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(out, n);
|
---|
| 768 |
|
---|
| 769 | // Then solve L out = out
|
---|
| 770 | //
|
---|
| 771 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationP() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
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| 772 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixL().solve(Matrix<Scalar, Dynamic, 1>::Map(out, n));
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| 773 | }
|
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| 774 |
|
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| 775 | static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)
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| 776 | {
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| 777 | // Solve L^T out = in
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| 778 | //
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| 779 | Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.matrixU().solve(Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k));
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| 780 | Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.permutationPinv() * Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k);
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| 781 | }
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| 782 |
|
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| 783 | };
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| 784 |
|
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| 785 | template<typename MatrixSolver, typename MatrixType, typename Scalar>
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| 786 | struct OP<MatrixSolver, MatrixType, Scalar, false>
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| 787 | {
|
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| 788 | static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)
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| 789 | {
|
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| 790 | eigen_assert(false && "Should never be in here...");
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| 791 | }
|
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| 792 |
|
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| 793 | static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)
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| 794 | {
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| 795 | eigen_assert(false && "Should never be in here...");
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| 796 | }
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| 797 |
|
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| 798 | };
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| 799 |
|
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| 800 | } // end namespace internal
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| 801 |
|
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| 802 | } // end namespace Eigen
|
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| 803 |
|
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| 804 | #endif // EIGEN_ARPACKSELFADJOINTEIGENSOLVER_H
|
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| 805 |
|
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