Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2012 David Harmon <dharmon@gmail.com> |
| 5 | // |
| 6 | // Eigen is free software; you can redistribute it and/or |
| 7 | // modify it under the terms of the GNU Lesser General Public |
| 8 | // License as published by the Free Software Foundation; either |
| 9 | // version 3 of the License, or (at your option) any later version. |
| 10 | // |
| 11 | // Alternatively, you can redistribute it and/or |
| 12 | // modify it under the terms of the GNU General Public License as |
| 13 | // published by the Free Software Foundation; either version 2 of |
| 14 | // the License, or (at your option) any later version. |
| 15 | // |
| 16 | // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY |
| 17 | // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
| 18 | // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the |
| 19 | // GNU General Public License for more details. |
| 20 | // |
| 21 | // You should have received a copy of the GNU Lesser General Public |
| 22 | // License and a copy of the GNU General Public License along with |
| 23 | // Eigen. If not, see <http://www.gnu.org/licenses/>. |
| 24 | |
| 25 | #ifndef EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H |
| 26 | #define EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H |
| 27 | |
| 28 | #include <Eigen/Dense> |
| 29 | |
| 30 | namespace Eigen { |
| 31 | |
| 32 | namespace internal { |
| 33 | template<typename Scalar, typename RealScalar> struct arpack_wrapper; |
| 34 | template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD> struct OP; |
| 35 | } |
| 36 | |
| 37 | |
| 38 | |
| 39 | template<typename MatrixType, typename MatrixSolver=SimplicialLLT<MatrixType>, bool BisSPD=false> |
| 40 | class ArpackGeneralizedSelfAdjointEigenSolver |
| 41 | { |
| 42 | public: |
| 43 | //typedef typename MatrixSolver::MatrixType MatrixType; |
| 44 | |
| 45 | /** \brief Scalar type for matrices of type \p MatrixType. */ |
| 46 | typedef typename MatrixType::Scalar Scalar; |
| 47 | typedef typename MatrixType::Index Index; |
| 48 | |
| 49 | /** \brief Real scalar type for \p MatrixType. |
| 50 | * |
| 51 | * This is just \c Scalar if #Scalar is real (e.g., \c float or |
| 52 | * \c Scalar), and the type of the real part of \c Scalar if #Scalar is |
| 53 | * complex. |
| 54 | */ |
| 55 | typedef typename NumTraits<Scalar>::Real RealScalar; |
| 56 | |
| 57 | /** \brief Type for vector of eigenvalues as returned by eigenvalues(). |
| 58 | * |
| 59 | * This is a column vector with entries of type #RealScalar. |
| 60 | * The length of the vector is the size of \p nbrEigenvalues. |
| 61 | */ |
| 62 | typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType; |
| 63 | |
| 64 | /** \brief Default constructor. |
| 65 | * |
| 66 | * The default constructor is for cases in which the user intends to |
| 67 | * perform decompositions via compute(). |
| 68 | * |
| 69 | */ |
| 70 | ArpackGeneralizedSelfAdjointEigenSolver() |
| 71 | : m_eivec(), |
| 72 | m_eivalues(), |
| 73 | m_isInitialized(false), |
| 74 | m_eigenvectorsOk(false), |
| 75 | m_nbrConverged(0), |
| 76 | m_nbrIterations(0) |
| 77 | { } |
| 78 | |
| 79 | /** \brief Constructor; computes generalized eigenvalues of given matrix with respect to another matrix. |
| 80 | * |
| 81 | * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will |
| 82 | * computed. By default, the upper triangular part is used, but can be changed |
| 83 | * through the template parameter. |
| 84 | * \param[in] B Self-adjoint matrix for the generalized eigenvalue problem. |
| 85 | * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute. |
| 86 | * Must be less than the size of the input matrix, or an error is returned. |
| 87 | * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with |
| 88 | * respective meanings to find the largest magnitude , smallest magnitude, |
| 89 | * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this |
| 90 | * value can contain floating point value in string form, in which case the |
| 91 | * eigenvalues closest to this value will be found. |
| 92 | * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly. |
| 93 | * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which |
| 94 | * means machine precision. |
| 95 | * |
| 96 | * This constructor calls compute(const MatrixType&, const MatrixType&, Index, string, int, RealScalar) |
| 97 | * to compute the eigenvalues of the matrix \p A with respect to \p B. The eigenvectors are computed if |
| 98 | * \p options equals #ComputeEigenvectors. |
| 99 | * |
| 100 | */ |
| 101 | ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A, const MatrixType& B, |
| 102 | Index nbrEigenvalues, std::string eigs_sigma="LM", |
| 103 | int options=ComputeEigenvectors, RealScalar tol=0.0) |
| 104 | : m_eivec(), |
| 105 | m_eivalues(), |
| 106 | m_isInitialized(false), |
| 107 | m_eigenvectorsOk(false), |
| 108 | m_nbrConverged(0), |
| 109 | m_nbrIterations(0) |
| 110 | { |
| 111 | compute(A, B, nbrEigenvalues, eigs_sigma, options, tol); |
| 112 | } |
| 113 | |
| 114 | /** \brief Constructor; computes eigenvalues of given matrix. |
| 115 | * |
| 116 | * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will |
| 117 | * computed. By default, the upper triangular part is used, but can be changed |
| 118 | * through the template parameter. |
| 119 | * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute. |
| 120 | * Must be less than the size of the input matrix, or an error is returned. |
| 121 | * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with |
| 122 | * respective meanings to find the largest magnitude , smallest magnitude, |
| 123 | * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this |
| 124 | * value can contain floating point value in string form, in which case the |
| 125 | * eigenvalues closest to this value will be found. |
| 126 | * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly. |
| 127 | * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which |
| 128 | * means machine precision. |
| 129 | * |
| 130 | * This constructor calls compute(const MatrixType&, Index, string, int, RealScalar) |
| 131 | * to compute the eigenvalues of the matrix \p A. The eigenvectors are computed if |
| 132 | * \p options equals #ComputeEigenvectors. |
| 133 | * |
| 134 | */ |
| 135 | |
| 136 | ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A, |
| 137 | Index nbrEigenvalues, std::string eigs_sigma="LM", |
| 138 | int options=ComputeEigenvectors, RealScalar tol=0.0) |
| 139 | : m_eivec(), |
| 140 | m_eivalues(), |
| 141 | m_isInitialized(false), |
| 142 | m_eigenvectorsOk(false), |
| 143 | m_nbrConverged(0), |
| 144 | m_nbrIterations(0) |
| 145 | { |
| 146 | compute(A, nbrEigenvalues, eigs_sigma, options, tol); |
| 147 | } |
| 148 | |
| 149 | |
| 150 | /** \brief Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPACK library. |
| 151 | * |
| 152 | * \param[in] A Selfadjoint matrix whose eigendecomposition is to be computed. |
| 153 | * \param[in] B Selfadjoint matrix for generalized eigenvalues. |
| 154 | * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute. |
| 155 | * Must be less than the size of the input matrix, or an error is returned. |
| 156 | * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with |
| 157 | * respective meanings to find the largest magnitude , smallest magnitude, |
| 158 | * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this |
| 159 | * value can contain floating point value in string form, in which case the |
| 160 | * eigenvalues closest to this value will be found. |
| 161 | * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly. |
| 162 | * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which |
| 163 | * means machine precision. |
| 164 | * |
| 165 | * \returns Reference to \c *this |
| 166 | * |
| 167 | * This function computes the generalized eigenvalues of \p A with respect to \p B using ARPACK. The eigenvalues() |
| 168 | * function can be used to retrieve them. If \p options equals #ComputeEigenvectors, |
| 169 | * then the eigenvectors are also computed and can be retrieved by |
| 170 | * calling eigenvectors(). |
| 171 | * |
| 172 | */ |
| 173 | ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A, const MatrixType& B, |
| 174 | Index nbrEigenvalues, std::string eigs_sigma="LM", |
| 175 | int options=ComputeEigenvectors, RealScalar tol=0.0); |
| 176 | |
| 177 | /** \brief Computes eigenvalues / eigenvectors of given matrix using the external ARPACK library. |
| 178 | * |
| 179 | * \param[in] A Selfadjoint matrix whose eigendecomposition is to be computed. |
| 180 | * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute. |
| 181 | * Must be less than the size of the input matrix, or an error is returned. |
| 182 | * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with |
| 183 | * respective meanings to find the largest magnitude , smallest magnitude, |
| 184 | * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this |
| 185 | * value can contain floating point value in string form, in which case the |
| 186 | * eigenvalues closest to this value will be found. |
| 187 | * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly. |
| 188 | * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which |
| 189 | * means machine precision. |
| 190 | * |
| 191 | * \returns Reference to \c *this |
| 192 | * |
| 193 | * This function computes the eigenvalues of \p A using ARPACK. The eigenvalues() |
| 194 | * function can be used to retrieve them. If \p options equals #ComputeEigenvectors, |
| 195 | * then the eigenvectors are also computed and can be retrieved by |
| 196 | * calling eigenvectors(). |
| 197 | * |
| 198 | */ |
| 199 | ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A, |
| 200 | Index nbrEigenvalues, std::string eigs_sigma="LM", |
| 201 | int options=ComputeEigenvectors, RealScalar tol=0.0); |
| 202 | |
| 203 | |
| 204 | /** \brief Returns the eigenvectors of given matrix. |
| 205 | * |
| 206 | * \returns A const reference to the matrix whose columns are the eigenvectors. |
| 207 | * |
| 208 | * \pre The eigenvectors have been computed before. |
| 209 | * |
| 210 | * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding |
| 211 | * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The |
| 212 | * eigenvectors are normalized to have (Euclidean) norm equal to one. If |
| 213 | * this object was used to solve the eigenproblem for the selfadjoint |
| 214 | * matrix \f$ A \f$, then the matrix returned by this function is the |
| 215 | * matrix \f$ V \f$ in the eigendecomposition \f$ A V = D V \f$. |
| 216 | * For the generalized eigenproblem, the matrix returned is the solution \f$ A V = D B V \f$ |
| 217 | * |
| 218 | * Example: \include SelfAdjointEigenSolver_eigenvectors.cpp |
| 219 | * Output: \verbinclude SelfAdjointEigenSolver_eigenvectors.out |
| 220 | * |
| 221 | * \sa eigenvalues() |
| 222 | */ |
| 223 | const Matrix<Scalar, Dynamic, Dynamic>& eigenvectors() const |
| 224 | { |
| 225 | eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized."); |
| 226 | eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues."); |
| 227 | return m_eivec; |
| 228 | } |
| 229 | |
| 230 | /** \brief Returns the eigenvalues of given matrix. |
| 231 | * |
| 232 | * \returns A const reference to the column vector containing the eigenvalues. |
| 233 | * |
| 234 | * \pre The eigenvalues have been computed before. |
| 235 | * |
| 236 | * The eigenvalues are repeated according to their algebraic multiplicity, |
| 237 | * so there are as many eigenvalues as rows in the matrix. The eigenvalues |
| 238 | * are sorted in increasing order. |
| 239 | * |
| 240 | * Example: \include SelfAdjointEigenSolver_eigenvalues.cpp |
| 241 | * Output: \verbinclude SelfAdjointEigenSolver_eigenvalues.out |
| 242 | * |
| 243 | * \sa eigenvectors(), MatrixBase::eigenvalues() |
| 244 | */ |
| 245 | const Matrix<Scalar, Dynamic, 1>& eigenvalues() const |
| 246 | { |
| 247 | eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized."); |
| 248 | return m_eivalues; |
| 249 | } |
| 250 | |
| 251 | /** \brief Computes the positive-definite square root of the matrix. |
| 252 | * |
| 253 | * \returns the positive-definite square root of the matrix |
| 254 | * |
| 255 | * \pre The eigenvalues and eigenvectors of a positive-definite matrix |
| 256 | * have been computed before. |
| 257 | * |
| 258 | * The square root of a positive-definite matrix \f$ A \f$ is the |
| 259 | * positive-definite matrix whose square equals \f$ A \f$. This function |
| 260 | * uses the eigendecomposition \f$ A = V D V^{-1} \f$ to compute the |
| 261 | * square root as \f$ A^{1/2} = V D^{1/2} V^{-1} \f$. |
| 262 | * |
| 263 | * Example: \include SelfAdjointEigenSolver_operatorSqrt.cpp |
| 264 | * Output: \verbinclude SelfAdjointEigenSolver_operatorSqrt.out |
| 265 | * |
| 266 | * \sa operatorInverseSqrt(), |
| 267 | * \ref MatrixFunctions_Module "MatrixFunctions Module" |
| 268 | */ |
| 269 | Matrix<Scalar, Dynamic, Dynamic> operatorSqrt() const |
| 270 | { |
| 271 | eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized."); |
| 272 | eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues."); |
| 273 | return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint(); |
| 274 | } |
| 275 | |
| 276 | /** \brief Computes the inverse square root of the matrix. |
| 277 | * |
| 278 | * \returns the inverse positive-definite square root of the matrix |
| 279 | * |
| 280 | * \pre The eigenvalues and eigenvectors of a positive-definite matrix |
| 281 | * have been computed before. |
| 282 | * |
| 283 | * This function uses the eigendecomposition \f$ A = V D V^{-1} \f$ to |
| 284 | * compute the inverse square root as \f$ V D^{-1/2} V^{-1} \f$. This is |
| 285 | * cheaper than first computing the square root with operatorSqrt() and |
| 286 | * then its inverse with MatrixBase::inverse(). |
| 287 | * |
| 288 | * Example: \include SelfAdjointEigenSolver_operatorInverseSqrt.cpp |
| 289 | * Output: \verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out |
| 290 | * |
| 291 | * \sa operatorSqrt(), MatrixBase::inverse(), |
| 292 | * \ref MatrixFunctions_Module "MatrixFunctions Module" |
| 293 | */ |
| 294 | Matrix<Scalar, Dynamic, Dynamic> operatorInverseSqrt() const |
| 295 | { |
| 296 | eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized."); |
| 297 | eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues."); |
| 298 | return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint(); |
| 299 | } |
| 300 | |
| 301 | /** \brief Reports whether previous computation was successful. |
| 302 | * |
| 303 | * \returns \c Success if computation was succesful, \c NoConvergence otherwise. |
| 304 | */ |
| 305 | ComputationInfo info() const |
| 306 | { |
| 307 | eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized."); |
| 308 | return m_info; |
| 309 | } |
| 310 | |
| 311 | size_t getNbrConvergedEigenValues() const |
| 312 | { return m_nbrConverged; } |
| 313 | |
| 314 | size_t getNbrIterations() const |
| 315 | { return m_nbrIterations; } |
| 316 | |
| 317 | protected: |
| 318 | Matrix<Scalar, Dynamic, Dynamic> m_eivec; |
| 319 | Matrix<Scalar, Dynamic, 1> m_eivalues; |
| 320 | ComputationInfo m_info; |
| 321 | bool m_isInitialized; |
| 322 | bool m_eigenvectorsOk; |
| 323 | |
| 324 | size_t m_nbrConverged; |
| 325 | size_t m_nbrIterations; |
| 326 | }; |
| 327 | |
| 328 | |
| 329 | |
| 330 | |
| 331 | |
| 332 | template<typename MatrixType, typename MatrixSolver, bool BisSPD> |
| 333 | ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>& |
| 334 | ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD> |
| 335 | ::compute(const MatrixType& A, Index nbrEigenvalues, |
| 336 | std::string eigs_sigma, int options, RealScalar tol) |
| 337 | { |
| 338 | MatrixType B(0,0); |
| 339 | compute(A, B, nbrEigenvalues, eigs_sigma, options, tol); |
| 340 | |
| 341 | return *this; |
| 342 | } |
| 343 | |
| 344 | |
| 345 | template<typename MatrixType, typename MatrixSolver, bool BisSPD> |
| 346 | ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>& |
| 347 | ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD> |
| 348 | ::compute(const MatrixType& A, const MatrixType& B, Index nbrEigenvalues, |
| 349 | std::string eigs_sigma, int options, RealScalar tol) |
| 350 | { |
| 351 | eigen_assert(A.cols() == A.rows()); |
| 352 | eigen_assert(B.cols() == B.rows()); |
| 353 | eigen_assert(B.rows() == 0 || A.cols() == B.rows()); |
| 354 | eigen_assert((options &~ (EigVecMask | GenEigMask)) == 0 |
| 355 | && (options & EigVecMask) != EigVecMask |
| 356 | && "invalid option parameter"); |
| 357 | |
| 358 | bool isBempty = (B.rows() == 0) || (B.cols() == 0); |
| 359 | |
| 360 | // For clarity, all parameters match their ARPACK name |
| 361 | // |
| 362 | // Always 0 on the first call |
| 363 | // |
| 364 | int ido = 0; |
| 365 | |
| 366 | int n = (int)A.cols(); |
| 367 | |
| 368 | // User options: "LA", "SA", "SM", "LM", "BE" |
| 369 | // |
| 370 | char whch[3] = "LM"; |
| 371 | |
| 372 | // Specifies the shift if iparam[6] = { 3, 4, 5 }, not used if iparam[6] = { 1, 2 } |
| 373 | // |
| 374 | RealScalar sigma = 0.0; |
| 375 | |
| 376 | if (eigs_sigma.length() >= 2 && isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])) |
| 377 | { |
| 378 | eigs_sigma[0] = toupper(eigs_sigma[0]); |
| 379 | eigs_sigma[1] = toupper(eigs_sigma[1]); |
| 380 | |
| 381 | // In the following special case we're going to invert the problem, since solving |
| 382 | // for larger magnitude is much much faster |
| 383 | // i.e., if 'SM' is specified, we're going to really use 'LM', the default |
| 384 | // |
| 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); |
| 772 | Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixL().solve(Matrix<Scalar, Dynamic, 1>::Map(out, n)); |
| 773 | } |
| 774 | |
| 775 | static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs) |
| 776 | { |
| 777 | // Solve L^T out = in |
| 778 | // |
| 779 | Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.matrixU().solve(Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k)); |
| 780 | Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.permutationPinv() * Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k); |
| 781 | } |
| 782 | |
| 783 | }; |
| 784 | |
| 785 | template<typename MatrixSolver, typename MatrixType, typename Scalar> |
| 786 | struct OP<MatrixSolver, MatrixType, Scalar, false> |
| 787 | { |
| 788 | static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out) |
| 789 | { |
| 790 | eigen_assert(false && "Should never be in here..."); |
| 791 | } |
| 792 | |
| 793 | static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs) |
| 794 | { |
| 795 | eigen_assert(false && "Should never be in here..."); |
| 796 | } |
| 797 | |
| 798 | }; |
| 799 | |
| 800 | } // end namespace internal |
| 801 | |
| 802 | } // end namespace Eigen |
| 803 | |
| 804 | #endif // EIGEN_ARPACKSELFADJOINTEIGENSOLVER_H |
| 805 | |