1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: EPS routines related to problem setup
12: */
14: #include <slepc/private/epsimpl.h> /*I "slepceps.h" I*/
16: /*
17: Let the solver choose the ST type that should be used by default,
18: otherwise set it to SHIFT.
19: This is called at EPSSetFromOptions (before STSetFromOptions)
20: and also at EPSSetUp (in case EPSSetFromOptions was not called).
21: */
22: PetscErrorCode EPSSetDefaultST(EPS eps) 23: {
27: if (eps->ops->setdefaultst) { (*eps->ops->setdefaultst)(eps); }
28: if (!((PetscObject)eps->st)->type_name) {
29: STSetType(eps->st,STSHIFT);
30: }
31: return(0);
32: }
34: /*
35: This is done by preconditioned eigensolvers that use the PC only.
36: It sets STPRECOND with KSPPREONLY.
37: */
38: PetscErrorCode EPSSetDefaultST_Precond(EPS eps) 39: {
41: KSP ksp;
44: if (!((PetscObject)eps->st)->type_name) {
45: STSetType(eps->st,STPRECOND);
46: STPrecondSetKSPHasMat(eps->st,PETSC_TRUE);
47: }
48: STGetKSP(eps->st,&ksp);
49: if (!((PetscObject)ksp)->type_name) {
50: KSPSetType(ksp,KSPPREONLY);
51: }
52: return(0);
53: }
55: /*
56: This is done by preconditioned eigensolvers that can also use the KSP.
57: It sets STPRECOND with the default KSP (GMRES).
58: */
59: PetscErrorCode EPSSetDefaultST_GMRES(EPS eps) 60: {
62: KSP ksp;
65: if (!((PetscObject)eps->st)->type_name) {
66: STSetType(eps->st,STPRECOND);
67: STPrecondSetKSPHasMat(eps->st,PETSC_TRUE);
68: }
69: STGetKSP(eps->st,&ksp);
70: KSPSetTolerances(ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,5);
71: return(0);
72: }
74: /*@
75: EPSSetUp - Sets up all the internal data structures necessary for the
76: execution of the eigensolver. Then calls STSetUp() for any set-up
77: operations associated to the ST object.
79: Collective on EPS 81: Input Parameter:
82: . eps - eigenproblem solver context
84: Notes:
85: This function need not be called explicitly in most cases, since EPSSolve()
86: calls it. It can be useful when one wants to measure the set-up time
87: separately from the solve time.
89: Level: developer
91: .seealso: EPSCreate(), EPSSolve(), EPSDestroy(), STSetUp(), EPSSetInitialSpace()
92: @*/
93: PetscErrorCode EPSSetUp(EPS eps) 94: {
96: Mat A,B;
97: SlepcSC sc;
98: PetscInt k,nmat;
99: PetscBool flg,istrivial,precond;
100: #if defined(PETSC_USE_COMPLEX)
101: PetscScalar sigma;
102: #endif
106: if (eps->state) return(0);
107: PetscLogEventBegin(EPS_SetUp,eps,0,0,0);
109: /* reset the convergence flag from the previous solves */
110: eps->reason = EPS_CONVERGED_ITERATING;
112: /* Set default solver type (EPSSetFromOptions was not called) */
113: if (!((PetscObject)eps)->type_name) {
114: EPSSetType(eps,EPSKRYLOVSCHUR);
115: }
116: if (!eps->st) { EPSGetST(eps,&eps->st); }
117: EPSSetDefaultST(eps);
119: PetscObjectTypeCompare((PetscObject)eps->st,STPRECOND,&precond);
120: if (eps->categ==EPS_CATEGORY_PRECOND && !precond) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver requires ST=PRECOND");
121: if (eps->categ!=EPS_CATEGORY_PRECOND && precond) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"STPRECOND is intended for preconditioned eigensolvers only");
123: STSetTransform(eps->st,PETSC_TRUE);
124: if (eps->useds && !eps->ds) { EPSGetDS(eps,&eps->ds); }
125: if (eps->twosided) {
126: if (!eps->hasts) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support computing left eigenvectors (no two-sided variant)");
127: if (eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Two-sided methods are not intended for symmetric problems");
128: if (!eps->dsts) { DSDuplicate(eps->ds,&eps->dsts); }
129: }
130: if (!eps->rg) { EPSGetRG(eps,&eps->rg); }
131: if (!((PetscObject)eps->rg)->type_name) {
132: RGSetType(eps->rg,RGINTERVAL);
133: }
135: /* Set problem dimensions */
136: STGetNumMatrices(eps->st,&nmat);
137: if (!nmat) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"EPSSetOperators must be called first");
138: STMatGetSize(eps->st,&eps->n,NULL);
139: STMatGetLocalSize(eps->st,&eps->nloc,NULL);
141: /* Set default problem type */
142: if (!eps->problem_type) {
143: if (nmat==1) {
144: EPSSetProblemType(eps,EPS_NHEP);
145: } else {
146: EPSSetProblemType(eps,EPS_GNHEP);
147: }
148: } else if (nmat==1 && eps->isgeneralized) {
149: PetscInfo(eps,"Eigenproblem set as generalized but no matrix B was provided; reverting to a standard eigenproblem\n");
150: eps->isgeneralized = PETSC_FALSE;
151: eps->problem_type = eps->ishermitian? EPS_HEP: EPS_NHEP;
152: } else if (nmat>1 && !eps->isgeneralized) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"Inconsistent EPS state");
154: if (eps->nev > eps->n) eps->nev = eps->n;
155: if (eps->ncv > eps->n) eps->ncv = eps->n;
157: /* initialization of matrix norms */
158: if (eps->conv==EPS_CONV_NORM) {
159: if (!eps->nrma) {
160: STGetMatrix(eps->st,0,&A);
161: MatNorm(A,NORM_INFINITY,&eps->nrma);
162: }
163: if (nmat>1 && !eps->nrmb) {
164: STGetMatrix(eps->st,1,&B);
165: MatNorm(B,NORM_INFINITY,&eps->nrmb);
166: }
167: }
169: /* call specific solver setup */
170: (*eps->ops->setup)(eps);
172: /* if purification is set, check that it really makes sense */
173: if (eps->purify) {
174: if (eps->categ==EPS_CATEGORY_PRECOND || eps->categ==EPS_CATEGORY_CONTOUR) eps->purify = PETSC_FALSE;
175: else {
176: if (!eps->isgeneralized) eps->purify = PETSC_FALSE;
177: else if (!eps->ishermitian && !eps->ispositive) eps->purify = PETSC_FALSE;
178: else {
179: PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&flg);
180: if (flg) eps->purify = PETSC_FALSE;
181: }
182: }
183: }
185: /* check extraction */
186: PetscObjectTypeCompareAny((PetscObject)eps->st,&flg,STPRECOND,STSHIFT,"");
187: if (!flg && eps->extraction && eps->extraction!=EPS_RITZ) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cannot use a spectral transformation combined with harmonic extraction");
189: /* set tolerance if not yet set */
190: if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
192: /* fill sorting criterion context */
193: switch (eps->which) {
194: case EPS_LARGEST_MAGNITUDE:
195: eps->sc->comparison = SlepcCompareLargestMagnitude;
196: eps->sc->comparisonctx = NULL;
197: break;
198: case EPS_SMALLEST_MAGNITUDE:
199: eps->sc->comparison = SlepcCompareSmallestMagnitude;
200: eps->sc->comparisonctx = NULL;
201: break;
202: case EPS_LARGEST_REAL:
203: eps->sc->comparison = SlepcCompareLargestReal;
204: eps->sc->comparisonctx = NULL;
205: break;
206: case EPS_SMALLEST_REAL:
207: eps->sc->comparison = SlepcCompareSmallestReal;
208: eps->sc->comparisonctx = NULL;
209: break;
210: case EPS_LARGEST_IMAGINARY:
211: eps->sc->comparison = SlepcCompareLargestImaginary;
212: eps->sc->comparisonctx = NULL;
213: break;
214: case EPS_SMALLEST_IMAGINARY:
215: eps->sc->comparison = SlepcCompareSmallestImaginary;
216: eps->sc->comparisonctx = NULL;
217: break;
218: case EPS_TARGET_MAGNITUDE:
219: eps->sc->comparison = SlepcCompareTargetMagnitude;
220: eps->sc->comparisonctx = &eps->target;
221: break;
222: case EPS_TARGET_REAL:
223: eps->sc->comparison = SlepcCompareTargetReal;
224: eps->sc->comparisonctx = &eps->target;
225: break;
226: case EPS_TARGET_IMAGINARY:
227: #if defined(PETSC_USE_COMPLEX)
228: eps->sc->comparison = SlepcCompareTargetImaginary;
229: eps->sc->comparisonctx = &eps->target;
230: #endif
231: break;
232: case EPS_ALL:
233: eps->sc->comparison = SlepcCompareSmallestReal;
234: eps->sc->comparisonctx = NULL;
235: break;
236: case EPS_WHICH_USER:
237: break;
238: }
239: eps->sc->map = NULL;
240: eps->sc->mapobj = NULL;
242: /* fill sorting criterion for DS */
243: if (eps->useds && eps->which!=EPS_ALL) {
244: DSGetSlepcSC(eps->ds,&sc);
245: RGIsTrivial(eps->rg,&istrivial);
246: sc->rg = istrivial? NULL: eps->rg;
247: sc->comparison = eps->sc->comparison;
248: sc->comparisonctx = eps->sc->comparisonctx;
249: sc->map = SlepcMap_ST;
250: sc->mapobj = (PetscObject)eps->st;
251: if (eps->twosided) {
252: DSSetSlepcSC(eps->dsts,sc);
253: }
254: }
256: /* Build balancing matrix if required */
257: if (!eps->ishermitian && (eps->balance==EPS_BALANCE_ONESIDE || eps->balance==EPS_BALANCE_TWOSIDE)) {
258: if (!eps->D) {
259: BVCreateVec(eps->V,&eps->D);
260: PetscLogObjectParent((PetscObject)eps,(PetscObject)eps->D);
261: } else {
262: VecSet(eps->D,1.0);
263: }
264: EPSBuildBalance_Krylov(eps);
265: STSetBalanceMatrix(eps->st,eps->D);
266: }
268: /* Setup ST */
269: STSetUp(eps->st);
271: #if defined(PETSC_USE_COMPLEX)
272: STGetShift(eps->st,&sigma);
273: if (eps->ishermitian && PetscImaginaryPart(sigma) != 0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Hermitian problems are not compatible with complex shifts");
274: #endif
275: PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&flg);
276: if (flg && eps->problem_type == EPS_PGNHEP) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cayley spectral transformation is not compatible with PGNHEP");
277: PetscObjectTypeCompareAny((PetscObject)eps->st,&flg,STSINVERT,STCAYLEY,"");
278: if (flg && (eps->categ==EPS_CATEGORY_KRYLOV || eps->categ==EPS_CATEGORY_OTHER) && (eps->which!=EPS_TARGET_MAGNITUDE && eps->which!=EPS_TARGET_REAL && eps->which!=EPS_TARGET_IMAGINARY && eps->which!=EPS_ALL && eps->which!=EPS_WHICH_USER)) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Shift-and-invert requires a target 'which' (see EPSSetWhichEigenpairs), for instance -st_type sinvert -eps_target 0 -eps_target_magnitude");
280: /* process deflation and initial vectors */
281: if (eps->nds<0) {
282: k = -eps->nds;
283: BVInsertConstraints(eps->V,&k,eps->defl);
284: SlepcBasisDestroy_Private(&eps->nds,&eps->defl);
285: eps->nds = k;
286: STCheckNullSpace(eps->st,eps->V);
287: }
288: if (eps->nini<0) {
289: k = -eps->nini;
290: if (k>eps->ncv) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The number of initial vectors is larger than ncv");
291: BVInsertVecs(eps->V,0,&k,eps->IS,PETSC_TRUE);
292: SlepcBasisDestroy_Private(&eps->nini,&eps->IS);
293: eps->nini = k;
294: }
296: PetscLogEventEnd(EPS_SetUp,eps,0,0,0);
297: eps->state = EPS_STATE_SETUP;
298: return(0);
299: }
301: /*@
302: EPSSetOperators - Sets the matrices associated with the eigenvalue problem.
304: Collective on EPS and Mat
306: Input Parameters:
307: + eps - the eigenproblem solver context
308: . A - the matrix associated with the eigensystem
309: - B - the second matrix in the case of generalized eigenproblems
311: Notes:
312: To specify a standard eigenproblem, use NULL for parameter B.
314: It must be called before EPSSetUp(). If it is called again after EPSSetUp() then
315: the EPS object is reset.
317: Level: beginner
319: .seealso: EPSSolve(), EPSSetUp(), EPSReset(), EPSGetST(), STGetMatrix()
320: @*/
321: PetscErrorCode EPSSetOperators(EPS eps,Mat A,Mat B)322: {
324: PetscInt m,n,m0,nmat;
325: Mat mat[2];
334: /* Check for square matrices */
335: MatGetSize(A,&m,&n);
336: if (m!=n) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"A is a non-square matrix");
337: if (B) {
338: MatGetSize(B,&m0,&n);
339: if (m0!=n) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"B is a non-square matrix");
340: if (m!=m0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"Dimensions of A and B do not match");
341: }
342: if (eps->state && n!=eps->n) { EPSReset(eps); }
343: eps->nrma = 0.0;
344: eps->nrmb = 0.0;
345: if (!eps->st) { EPSGetST(eps,&eps->st); }
346: mat[0] = A;
347: if (B) {
348: mat[1] = B;
349: nmat = 2;
350: } else nmat = 1;
351: STSetMatrices(eps->st,nmat,mat);
352: eps->state = EPS_STATE_INITIAL;
353: return(0);
354: }
356: /*@
357: EPSGetOperators - Gets the matrices associated with the eigensystem.
359: Collective on EPS and Mat
361: Input Parameter:
362: . eps - the EPS context
364: Output Parameters:
365: + A - the matrix associated with the eigensystem
366: - B - the second matrix in the case of generalized eigenproblems
368: Level: intermediate
370: .seealso: EPSSolve(), EPSGetST(), STGetMatrix(), STSetMatrices()
371: @*/
372: PetscErrorCode EPSGetOperators(EPS eps,Mat *A,Mat *B)373: {
375: ST st;
376: PetscInt k;
380: EPSGetST(eps,&st);
381: if (A) { STGetMatrix(st,0,A); }
382: if (B) {
383: STGetNumMatrices(st,&k);
384: if (k==1) B = NULL;
385: else {
386: STGetMatrix(st,1,B);
387: }
388: }
389: return(0);
390: }
392: /*@
393: EPSSetDeflationSpace - Specify a basis of vectors that constitute the deflation
394: space.
396: Collective on EPS and Vec
398: Input Parameter:
399: + eps - the eigenproblem solver context
400: . n - number of vectors
401: - v - set of basis vectors of the deflation space
403: Notes:
404: When a deflation space is given, the eigensolver seeks the eigensolution
405: in the restriction of the problem to the orthogonal complement of this
406: space. This can be used for instance in the case that an invariant
407: subspace is known beforehand (such as the nullspace of the matrix).
409: These vectors do not persist from one EPSSolve() call to the other, so the
410: deflation space should be set every time.
412: The vectors do not need to be mutually orthonormal, since they are explicitly
413: orthonormalized internally.
415: Level: intermediate
417: .seealso: EPSSetInitialSpace()
418: @*/
419: PetscErrorCode EPSSetDeflationSpace(EPS eps,PetscInt n,Vec *v)420: {
426: if (n<0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n out of range");
427: SlepcBasisReference_Private(n,v,&eps->nds,&eps->defl);
428: if (n>0) eps->state = EPS_STATE_INITIAL;
429: return(0);
430: }
432: /*@C
433: EPSSetInitialSpace - Specify a basis of vectors that constitute the initial
434: space, that is, the subspace from which the solver starts to iterate.
436: Collective on EPS and Vec
438: Input Parameter:
439: + eps - the eigenproblem solver context
440: . n - number of vectors
441: - is - set of basis vectors of the initial space
443: Notes:
444: Some solvers start to iterate on a single vector (initial vector). In that case,
445: the other vectors are ignored.
447: These vectors do not persist from one EPSSolve() call to the other, so the
448: initial space should be set every time.
450: The vectors do not need to be mutually orthonormal, since they are explicitly
451: orthonormalized internally.
453: Common usage of this function is when the user can provide a rough approximation
454: of the wanted eigenspace. Then, convergence may be faster.
456: Level: intermediate
458: .seealso: EPSSetDeflationSpace()
459: @*/
460: PetscErrorCode EPSSetInitialSpace(EPS eps,PetscInt n,Vec *is)461: {
467: if (n<0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n cannot be negative");
468: SlepcBasisReference_Private(n,is,&eps->nini,&eps->IS);
469: if (n>0) eps->state = EPS_STATE_INITIAL;
470: return(0);
471: }
473: /*
474: EPSSetDimensions_Default - Set reasonable values for ncv, mpd if not set
475: by the user. This is called at setup.
476: */
477: PetscErrorCode EPSSetDimensions_Default(EPS eps,PetscInt nev,PetscInt *ncv,PetscInt *mpd)478: {
480: PetscBool krylov;
483: if (*ncv) { /* ncv set */
484: PetscObjectTypeCompareAny((PetscObject)eps,&krylov,EPSKRYLOVSCHUR,EPSARNOLDI,EPSLANCZOS,"");
485: if (krylov) {
486: if (*ncv<nev+1 && !(*ncv==nev && *ncv==eps->n)) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must be at least nev+1");
487: } else {
488: if (*ncv<nev) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must be at least nev");
489: }
490: } else if (*mpd) { /* mpd set */
491: *ncv = PetscMin(eps->n,nev+(*mpd));
492: } else { /* neither set: defaults depend on nev being small or large */
493: if (nev<500) *ncv = PetscMin(eps->n,PetscMax(2*nev,nev+15));
494: else {
495: *mpd = 500;
496: *ncv = PetscMin(eps->n,nev+(*mpd));
497: }
498: }
499: if (!*mpd) *mpd = *ncv;
500: return(0);
501: }
503: /*@
504: EPSAllocateSolution - Allocate memory storage for common variables such
505: as eigenvalues and eigenvectors.
507: Collective on EPS509: Input Parameters:
510: + eps - eigensolver context
511: - extra - number of additional positions, used for methods that require a
512: working basis slightly larger than ncv
514: Developers Note:
515: This is SLEPC_EXTERN because it may be required by user plugin EPS516: implementations.
518: Level: developer
519: @*/
520: PetscErrorCode EPSAllocateSolution(EPS eps,PetscInt extra)521: {
523: PetscInt oldsize,newc,requested;
524: PetscLogDouble cnt;
525: Vec t;
528: requested = eps->ncv + extra;
530: /* oldsize is zero if this is the first time setup is called */
531: BVGetSizes(eps->V,NULL,NULL,&oldsize);
532: newc = PetscMax(0,requested-oldsize);
534: /* allocate space for eigenvalues and friends */
535: if (requested != oldsize || !eps->eigr) {
536: PetscFree4(eps->eigr,eps->eigi,eps->errest,eps->perm);
537: PetscMalloc4(requested,&eps->eigr,requested,&eps->eigi,requested,&eps->errest,requested,&eps->perm);
538: cnt = 2*newc*sizeof(PetscScalar) + 2*newc*sizeof(PetscReal) + newc*sizeof(PetscInt);
539: PetscLogObjectMemory((PetscObject)eps,cnt);
540: }
542: /* workspace for the case of arbitrary selection */
543: if (eps->arbitrary) {
544: if (eps->rr) {
545: PetscFree2(eps->rr,eps->ri);
546: }
547: PetscMalloc2(requested,&eps->rr,requested,&eps->ri);
548: PetscLogObjectMemory((PetscObject)eps,2*newc*sizeof(PetscScalar));
549: }
551: /* allocate V */
552: if (!eps->V) { EPSGetBV(eps,&eps->V); }
553: if (!oldsize) {
554: if (!((PetscObject)(eps->V))->type_name) {
555: BVSetType(eps->V,BVSVEC);
556: }
557: STMatCreateVecsEmpty(eps->st,&t,NULL);
558: BVSetSizesFromVec(eps->V,t,requested);
559: VecDestroy(&t);
560: } else {
561: BVResize(eps->V,requested,PETSC_FALSE);
562: }
564: /* allocate W */
565: if (eps->twosided) {
566: BVDestroy(&eps->W);
567: BVDuplicate(eps->V,&eps->W);
568: }
569: return(0);
570: }