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 |
|
---|