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ArpackSelfAdjointEigenSolver.h
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
30namespace Eigen {
31
32namespace 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
39template<typename MatrixType, typename MatrixSolver=SimplicialLLT<MatrixType>, bool BisSPD=false>
40class ArpackGeneralizedSelfAdjointEigenSolver
41{
42public:
43 //typedef typename MatrixSolver::MatrixType MatrixType;
44
46 typedef typename MatrixType::Scalar Scalar;
47 typedef typename MatrixType::Index Index;
48
55 typedef typename NumTraits<Scalar>::Real RealScalar;
56
62 typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;
63
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
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
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
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
199 ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A,
200 Index nbrEigenvalues, std::string eigs_sigma="LM",
201 int options=ComputeEigenvectors, RealScalar tol=0.0);
202
203
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
245 const Matrix<Scalar, Dynamic, 1>& eigenvalues() const
246 {
247 eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
248 return m_eivalues;
249 }
250
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
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
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
317protected:
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
332template<typename MatrixType, typename MatrixSolver, bool BisSPD>
333ArpackGeneralizedSelfAdjointEigenSolver<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
345template<typename MatrixType, typename MatrixSolver, bool BisSPD>
346ArpackGeneralizedSelfAdjointEigenSolver<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)));
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//
649extern "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
655extern "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//
664extern "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
670extern "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
678namespace internal {
679
680template<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
701template <> 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
723template <> 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
746template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD>
747struct 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
753template<typename MatrixSolver, typename MatrixType, typename Scalar>
754struct 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
785template<typename MatrixSolver, typename MatrixType, typename Scalar>
786struct 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
Namespace containing all symbols from the Eigen library.
Definition: AdolcForward:45