Actual source code: stsolve.c

slepc-3.16.1 2021-11-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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:    ST interface routines, callable by users
 12: */

 14: #include <slepc/private/stimpl.h>

 16: PetscErrorCode STApply_Generic(ST st,Vec x,Vec y)
 17: {

 21:   if (st->M && st->P) {
 22:     MatMult(st->M,x,st->work[0]);
 23:     STMatSolve(st,st->work[0],y);
 24:   } else if (st->M) {
 25:     MatMult(st->M,x,y);
 26:   } else {
 27:     STMatSolve(st,x,y);
 28:   }
 29:   return(0);
 30: }

 32: /*@
 33:    STApply - Applies the spectral transformation operator to a vector, for
 34:    instance (A - sB)^-1 B in the case of the shift-and-invert transformation
 35:    and generalized eigenproblem.

 37:    Collective on st

 39:    Input Parameters:
 40: +  st - the spectral transformation context
 41: -  x  - input vector

 43:    Output Parameter:
 44: .  y - output vector

 46:    Level: developer

 48: .seealso: STApplyTranspose(), STApplyHermitianTranspose()
 49: @*/
 50: PetscErrorCode STApply(ST st,Vec x,Vec y)
 51: {
 53:   Mat            Op;

 60:   STCheckMatrices(st,1);
 61:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_IDN,"x and y must be different vectors");
 62:   VecSetErrorIfLocked(y,3);
 63:   if (!st->ops->apply) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST does not have apply");
 64:   STGetOperator_Private(st,&Op);
 65:   MatMult(Op,x,y);
 66:   return(0);
 67: }

 69: PetscErrorCode STApplyMat_Generic(ST st,Mat B,Mat C)
 70: {
 72:   Mat            work;

 75:   if (st->M && st->P) {
 76:     MatMatMult(st->M,B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&work);
 77:     STMatMatSolve(st,work,C);
 78:     MatDestroy(&work);
 79:   } else if (st->M) {
 80:     MatMatMult(st->M,B,MAT_REUSE_MATRIX,PETSC_DEFAULT,&C);
 81:   } else {
 82:     STMatMatSolve(st,B,C);
 83:   }
 84:   return(0);
 85: }

 87: /*@
 88:    STApplyMat - Applies the spectral transformation operator to a matrix, for
 89:    instance (A - sB)^-1 B in the case of the shift-and-invert transformation
 90:    and generalized eigenproblem.

 92:    Collective on st

 94:    Input Parameters:
 95: +  st - the spectral transformation context
 96: -  X  - input matrix

 98:    Output Parameter:
 99: .  y - output matrix

101:    Level: developer

103: .seealso: STApply()
104: @*/
105: PetscErrorCode STApplyMat(ST st,Mat X,Mat Y)
106: {

114:   STCheckMatrices(st,1);
115:   if (X == Y) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_IDN,"X and Y must be different matrices");
116:   if (!st->ops->applymat) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST does not have applymat");
117:   (*st->ops->applymat)(st,X,Y);
118:   return(0);
119: }

121: PetscErrorCode STApplyTranspose_Generic(ST st,Vec x,Vec y)
122: {

126:   if (st->M && st->P) {
127:     STMatSolveTranspose(st,x,st->work[0]);
128:     MatMultTranspose(st->M,st->work[0],y);
129:   } else if (st->M) {
130:     MatMultTranspose(st->M,x,y);
131:   } else {
132:     STMatSolveTranspose(st,x,y);
133:   }
134:   return(0);
135: }

137: /*@
138:    STApplyTranspose - Applies the transpose of the operator to a vector, for
139:    instance B^T(A - sB)^-T in the case of the shift-and-invert transformation
140:    and generalized eigenproblem.

142:    Collective on st

144:    Input Parameters:
145: +  st - the spectral transformation context
146: -  x  - input vector

148:    Output Parameter:
149: .  y - output vector

151:    Level: developer

153: .seealso: STApply(), STApplyHermitianTranspose()
154: @*/
155: PetscErrorCode STApplyTranspose(ST st,Vec x,Vec y)
156: {
158:   Mat            Op;

165:   STCheckMatrices(st,1);
166:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_IDN,"x and y must be different vectors");
167:   VecSetErrorIfLocked(y,3);
168:   if (!st->ops->applytrans) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST does not have applytrans");
169:   STGetOperator_Private(st,&Op);
170:   MatMultTranspose(Op,x,y);
171:   return(0);
172: }

174: /*@
175:    STApplyHermitianTranspose - Applies the hermitian-transpose of the operator
176:    to a vector, for instance B^H(A - sB)^-H in the case of the shift-and-invert
177:    transformation and generalized eigenproblem.

179:    Collective on st

181:    Input Parameters:
182: +  st - the spectral transformation context
183: -  x  - input vector

185:    Output Parameter:
186: .  y - output vector

188:    Note:
189:    Currently implemented via STApplyTranspose() with appropriate conjugation.

191:    Level: developer

193: .seealso: STApply(), STApplyTranspose()
194: @*/
195: PetscErrorCode STApplyHermitianTranspose(ST st,Vec x,Vec y)
196: {
198:   Mat            Op;

205:   STCheckMatrices(st,1);
206:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_IDN,"x and y must be different vectors");
207:   VecSetErrorIfLocked(y,3);
208:   if (!st->ops->applytrans) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST does not have applytrans");
209:   STGetOperator_Private(st,&Op);
210:   MatMultHermitianTranspose(Op,x,y);
211:   return(0);
212: }

214: /*@
215:    STGetBilinearForm - Returns the matrix used in the bilinear form with a
216:    generalized problem with semi-definite B.

218:    Not collective, though a parallel Mat may be returned

220:    Input Parameters:
221: .  st - the spectral transformation context

223:    Output Parameter:
224: .  B - output matrix

226:    Notes:
227:    The output matrix B must be destroyed after use. It will be NULL in
228:    case of standard eigenproblems.

230:    Level: developer
231: @*/
232: PetscErrorCode STGetBilinearForm(ST st,Mat *B)
233: {

240:   STCheckMatrices(st,1);
241:   (*st->ops->getbilinearform)(st,B);
242:   return(0);
243: }

245: PetscErrorCode STGetBilinearForm_Default(ST st,Mat *B)
246: {

250:   if (st->nmat==1) *B = NULL;
251:   else {
252:     *B = st->A[1];
253:     PetscObjectReference((PetscObject)*B);
254:   }
255:   return(0);
256: }

258: static PetscErrorCode MatMult_STOperator(Mat Op,Vec x,Vec y)
259: {
261:   ST             st;

264:   MatShellGetContext(Op,&st);
265:   STSetUp(st);
266:   PetscLogEventBegin(ST_Apply,st,x,y,0);
267:   if (st->D) { /* with balancing */
268:     VecPointwiseDivide(st->wb,x,st->D);
269:     (*st->ops->apply)(st,st->wb,y);
270:     VecPointwiseMult(y,y,st->D);
271:   } else {
272:     (*st->ops->apply)(st,x,y);
273:   }
274:   PetscLogEventEnd(ST_Apply,st,x,y,0);
275:   return(0);
276: }

278: static PetscErrorCode MatMultTranspose_STOperator(Mat Op,Vec x,Vec y)
279: {
281:   ST             st;

284:   MatShellGetContext(Op,&st);
285:   STSetUp(st);
286:   PetscLogEventBegin(ST_ApplyTranspose,st,x,y,0);
287:   if (st->D) { /* with balancing */
288:     VecPointwiseMult(st->wb,x,st->D);
289:     (*st->ops->applytrans)(st,st->wb,y);
290:     VecPointwiseDivide(y,y,st->D);
291:   } else {
292:     (*st->ops->applytrans)(st,x,y);
293:   }
294:   PetscLogEventEnd(ST_ApplyTranspose,st,x,y,0);
295:   return(0);
296: }

298: #if defined(PETSC_USE_COMPLEX)
299: static PetscErrorCode MatMultHermitianTranspose_STOperator(Mat Op,Vec x,Vec y)
300: {
302:   ST             st;

305:   MatShellGetContext(Op,&st);
306:   STSetUp(st);
307:   PetscLogEventBegin(ST_ApplyTranspose,st,x,y,0);
308:   if (!st->wht) {
309:     MatCreateVecs(st->A[0],&st->wht,NULL);
310:     PetscLogObjectParent((PetscObject)st,(PetscObject)st->wht);
311:   }
312:   VecCopy(x,st->wht);
313:   VecConjugate(st->wht);
314:   if (st->D) { /* with balancing */
315:     VecPointwiseMult(st->wb,st->wht,st->D);
316:     (*st->ops->applytrans)(st,st->wb,y);
317:     VecPointwiseDivide(y,y,st->D);
318:   } else {
319:     (*st->ops->applytrans)(st,st->wht,y);
320:   }
321:   VecConjugate(y);
322:   PetscLogEventEnd(ST_ApplyTranspose,st,x,y,0);
323:   return(0);
324: }
325: #endif

327: static PetscErrorCode MatMatMult_STOperator(Mat Op,Mat B,Mat C,void *ctx)
328: {
330:   ST             st;

333:   MatShellGetContext(Op,&st);
334:   STSetUp(st);
335:   PetscLogEventBegin(ST_Apply,st,B,C,0);
336:   STApplyMat_Generic(st,B,C);
337:   PetscLogEventEnd(ST_Apply,st,B,C,0);
338:   return(0);
339: }

341: PetscErrorCode STGetOperator_Private(ST st,Mat *Op)
342: {
344:   PetscInt       m,n,M,N;
345:   Vec            v;
346:   VecType        vtype;

349:   if (!st->Op) {
350:     if (Op) *Op = NULL;
351:     /* create the shell matrix */
352:     MatGetLocalSize(st->A[0],&m,&n);
353:     MatGetSize(st->A[0],&M,&N);
354:     MatCreateShell(PetscObjectComm((PetscObject)st),m,n,M,N,st,&st->Op);
355:     MatShellSetOperation(st->Op,MATOP_MULT,(void(*)(void))MatMult_STOperator);
356:     MatShellSetOperation(st->Op,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_STOperator);
357: #if defined(PETSC_USE_COMPLEX)
358:     MatShellSetOperation(st->Op,MATOP_MULT_HERMITIAN_TRANSPOSE,(void(*)(void))MatMultHermitianTranspose_STOperator);
359: #else
360:     MatShellSetOperation(st->Op,MATOP_MULT_HERMITIAN_TRANSPOSE,(void(*)(void))MatMultTranspose_STOperator);
361: #endif
362:     if (!st->D && st->ops->apply==STApply_Generic) {
363:       MatShellSetMatProductOperation(st->Op,MATPRODUCT_AB,NULL,MatMatMult_STOperator,NULL,MATDENSE,MATDENSE);
364:     }
365:     /* make sure the shell matrix generates a vector of the same type as the problem matrices */
366:     MatCreateVecs(st->A[0],&v,NULL);
367:     VecGetType(v,&vtype);
368:     MatShellSetVecType(st->Op,vtype);
369:     VecDestroy(&v);
370:     /* build the operator matrices */
371:     STComputeOperator(st);
372:   }
373:   if (Op) *Op = st->Op;
374:   return(0);
375: }

377: /*@
378:    STGetOperator - Returns a shell matrix that represents the operator of the
379:    spectral transformation.

381:    Collective on st

383:    Input Parameter:
384: .  st - the spectral transformation context

386:    Output Parameter:
387: .  Op - operator matrix

389:    Notes:
390:    The operator is defined in linear eigenproblems only, not in polynomial ones,
391:    so the call will fail if more than 2 matrices were passed in STSetMatrices().

393:    The returned shell matrix is essentially a wrapper to the STApply() and
394:    STApplyTranspose() operations. The operator can often be expressed as

396: .vb
397:       Op = D*inv(K)*M*inv(D)
398: .ve

400:    where D is the balancing matrix, and M and K are two matrices corresponding
401:    to the numerator and denominator for spectral transformations that represent
402:    a rational matrix function. In the case of STSHELL, the inner part inv(K)*M
403:    is replaced by the user-provided operation from STShellSetApply().

405:    The preconditioner matrix K typically depends on the value of the shift, and
406:    its inverse is handled via an internal KSP object. Normal usage does not
407:    require explicitly calling STGetOperator(), but it can be used to force the
408:    creation of K and M, and then K is passed to the KSP. This is useful for
409:    setting options associated with the PCFactor (to set MUMPS options, for instance).

411:    The returned matrix must NOT be destroyed by the user. Instead, when no
412:    longer needed it must be returned with STRestoreOperator(). In particular,
413:    this is required before modifying the ST matrices or the shift.

415:    A NULL pointer can be passed in Op in case the matrix is not required but we
416:    want to force its creation. In this case, STRestoreOperator() should not be
417:    called.

419:    Level: advanced

421: .seealso: STApply(), STApplyTranspose(), STSetBalanceMatrix(), STShellSetApply(),
422:           STGetKSP(), STSetShift(), STRestoreOperator(), STSetMatrices()
423: @*/
424: PetscErrorCode STGetOperator(ST st,Mat *Op)
425: {

431:   STCheckMatrices(st,1);
432:   STCheckNotSeized(st,1);
433:   if (st->nmat>2) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_WRONGSTATE,"The operator is not defined in polynomial eigenproblems");
434:   STGetOperator_Private(st,Op);
435:   if (Op) st->opseized = PETSC_TRUE;
436:   return(0);
437: }

439: /*@
440:    STRestoreOperator - Restore the previously seized operator matrix.

442:    Collective on st

444:    Input Parameters:
445: +  st - the spectral transformation context
446: -  Op - operator matrix

448:    Notes:
449:    The arguments must match the corresponding call to STGetOperator().

451:    Level: advanced

453: .seealso: STGetOperator()
454: @*/
455: PetscErrorCode STRestoreOperator(ST st,Mat *Op)
456: {
461:   if (!st->opseized) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_WRONGSTATE,"Must be called after STGetOperator()");
462:   *Op = NULL;
463:   st->opseized = PETSC_FALSE;
464:   return(0);
465: }

467: /*
468:    STComputeOperator - Computes the matrices that constitute the operator

470:       Op = D*inv(K)*M*inv(D).

472:    K and M are computed here (D is user-provided) from the system matrices
473:    and the shift sigma (whenever these are changed, this function recomputes
474:    K and M). This is used only in linear eigenproblems (nmat<3).

476:    K is the "preconditioner matrix": it is the denominator in rational operators,
477:    e.g. (A-sigma*B) in shift-and-invert. In non-rational transformations such
478:    as STFILTER, K=NULL which means identity. After computing K, it is passed to
479:    the internal KSP object via KSPSetOperators.

481:    M is the numerator in rational operators. If unused it is set to NULL (e.g.
482:    in STPRECOND).

484:    STSHELL does not compute anything here, but sets the flag as if it was ready.
485: */
486: PetscErrorCode STComputeOperator(ST st)
487: {
489:   PC             pc;

494:   if (!st->opready && st->ops->computeoperator) {
495:     PetscInfo(st,"Building the operator matrices\n");
496:     STCheckMatrices(st,1);
497:     if (!st->T) {
498:       PetscCalloc1(PetscMax(2,st->nmat),&st->T);
499:       PetscLogObjectMemory((PetscObject)st,PetscMax(2,st->nmat)*sizeof(Mat));
500:     }
501:     PetscLogEventBegin(ST_ComputeOperator,st,0,0,0);
502:     (*st->ops->computeoperator)(st);
503:     PetscLogEventEnd(ST_ComputeOperator,st,0,0,0);
504:     if (st->usesksp) {
505:       if (!st->ksp) { STGetKSP(st,&st->ksp); }
506:       if (st->P) {
507:         STSetDefaultKSP(st);
508:         STKSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P);
509:       } else {
510:         /* STPRECOND defaults to PCNONE if st->P is empty */
511:         KSPGetPC(st->ksp,&pc);
512:         PCSetType(pc,PCNONE);
513:       }
514:     }
515:   }
516:   st->opready = PETSC_TRUE;
517:   return(0);
518: }

520: /*@
521:    STSetUp - Prepares for the use of a spectral transformation.

523:    Collective on st

525:    Input Parameter:
526: .  st - the spectral transformation context

528:    Level: advanced

530: .seealso: STCreate(), STApply(), STDestroy()
531: @*/
532: PetscErrorCode STSetUp(ST st)
533: {
534:   PetscInt       i,n,k;

540:   STCheckMatrices(st,1);
541:   switch (st->state) {
542:     case ST_STATE_INITIAL:
543:       PetscInfo(st,"Setting up new ST\n");
544:       if (!((PetscObject)st)->type_name) {
545:         STSetType(st,STSHIFT);
546:       }
547:       break;
548:     case ST_STATE_SETUP:
549:       return(0);
550:     case ST_STATE_UPDATED:
551:       PetscInfo(st,"Setting up updated ST\n");
552:       break;
553:   }
554:   PetscLogEventBegin(ST_SetUp,st,0,0,0);
555:   if (st->state!=ST_STATE_UPDATED) {
556:     if (!(st->nmat<3 && st->opready)) {
557:       if (st->T) {
558:         for (i=0;i<PetscMax(2,st->nmat);i++) {
559:           MatDestroy(&st->T[i]);
560:         }
561:       }
562:       MatDestroy(&st->P);
563:     }
564:   }
565:   if (st->D) {
566:     MatGetLocalSize(st->A[0],NULL,&n);
567:     VecGetLocalSize(st->D,&k);
568:     if (n != k) SETERRQ2(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_SIZ,"Balance matrix has wrong dimension %D (should be %D)",k,n);
569:     if (!st->wb) {
570:       VecDuplicate(st->D,&st->wb);
571:       PetscLogObjectParent((PetscObject)st,(PetscObject)st->wb);
572:     }
573:   }
574:   if (st->nmat<3 && st->transform) {
575:     STComputeOperator(st);
576:   } else {
577:     if (!st->T) {
578:       PetscCalloc1(PetscMax(2,st->nmat),&st->T);
579:       PetscLogObjectMemory((PetscObject)st,PetscMax(2,st->nmat)*sizeof(Mat));
580:     }
581:   }
582:   if (st->ops->setup) { (*st->ops->setup)(st); }
583:   st->state = ST_STATE_SETUP;
584:   PetscLogEventEnd(ST_SetUp,st,0,0,0);
585:   return(0);
586: }

588: /*
589:    Computes coefficients for the transformed polynomial,
590:    and stores the result in argument S.

592:    alpha - value of the parameter of the transformed polynomial
593:    beta - value of the previous shift (only used in inplace mode)
594:    k - index of first matrix included in the computation
595:    coeffs - coefficients of the expansion
596:    initial - true if this is the first time (only relevant for shell mode)
597: */
598: PetscErrorCode STMatMAXPY_Private(ST st,PetscScalar alpha,PetscScalar beta,PetscInt k,PetscScalar *coeffs,PetscBool initial,Mat *S)
599: {
601:   PetscInt       *matIdx=NULL,nmat,i,ini=-1;
602:   PetscScalar    t=1.0,ta,gamma;
603:   PetscBool      nz=PETSC_FALSE;

606:   nmat = st->nmat-k;
607:   switch (st->matmode) {
608:   case ST_MATMODE_INPLACE:
609:     if (st->nmat>2) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST_MATMODE_INPLACE not supported for polynomial eigenproblems");
610:     if (initial) {
611:       PetscObjectReference((PetscObject)st->A[0]);
612:       *S = st->A[0];
613:       gamma = alpha;
614:     } else gamma = alpha-beta;
615:     if (gamma != 0.0) {
616:       if (st->nmat>1) {
617:         MatAXPY(*S,gamma,st->A[1],st->str);
618:       } else {
619:         MatShift(*S,gamma);
620:       }
621:     }
622:     break;
623:   case ST_MATMODE_SHELL:
624:     if (initial) {
625:       if (st->nmat>2) {
626:         PetscMalloc1(nmat,&matIdx);
627:         for (i=0;i<nmat;i++) matIdx[i] = k+i;
628:       }
629:       STMatShellCreate(st,alpha,nmat,matIdx,coeffs,S);
630:       PetscLogObjectParent((PetscObject)st,(PetscObject)*S);
631:       if (st->nmat>2) { PetscFree(matIdx); }
632:     } else {
633:       STMatShellShift(*S,alpha);
634:     }
635:     break;
636:   case ST_MATMODE_COPY:
637:     if (coeffs) {
638:       for (i=0;i<nmat && ini==-1;i++) {
639:         if (coeffs[i]!=0.0) ini = i;
640:         else t *= alpha;
641:       }
642:       if (coeffs[ini] != 1.0) nz = PETSC_TRUE;
643:       for (i=ini+1;i<nmat&&!nz;i++) if (coeffs[i]!=0.0) nz = PETSC_TRUE;
644:     } else { nz = PETSC_TRUE; ini = 0; }
645:     if ((alpha == 0.0 || !nz) && t==1.0) {
646:       PetscObjectReference((PetscObject)st->A[k+ini]);
647:       MatDestroy(S);
648:       *S = st->A[k+ini];
649:     } else {
650:       if (*S && *S!=st->A[k+ini]) {
651:         MatSetOption(*S,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
652:         MatCopy(st->A[k+ini],*S,DIFFERENT_NONZERO_PATTERN);
653:       } else {
654:         MatDestroy(S);
655:         MatDuplicate(st->A[k+ini],MAT_COPY_VALUES,S);
656:         MatSetOption(*S,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
657:         PetscLogObjectParent((PetscObject)st,(PetscObject)*S);
658:       }
659:       if (coeffs && coeffs[ini]!=1.0) {
660:         MatScale(*S,coeffs[ini]);
661:       }
662:       for (i=ini+k+1;i<PetscMax(2,st->nmat);i++) {
663:         t *= alpha;
664:         ta = t;
665:         if (coeffs) ta *= coeffs[i-k];
666:         if (ta!=0.0) {
667:           if (st->nmat>1) {
668:             MatAXPY(*S,ta,st->A[i],st->str);
669:           } else {
670:             MatShift(*S,ta);
671:           }
672:         }
673:       }
674:     }
675:   }
676:   MatSetOption(*S,MAT_SYMMETRIC,st->asymm);
677:   MatSetOption(*S,MAT_HERMITIAN,(PetscImaginaryPart(st->sigma)==0.0)?st->aherm:PETSC_FALSE);
678:   return(0);
679: }

681: /*
682:    Computes the values of the coefficients required by STMatMAXPY_Private
683:    for the case of monomial basis.
684: */
685: PetscErrorCode STCoeffs_Monomial(ST st, PetscScalar *coeffs)
686: {
687:   PetscInt  k,i,ini,inip;

690:   /* Compute binomial coefficients */
691:   ini = (st->nmat*(st->nmat-1))/2;
692:   for (i=0;i<st->nmat;i++) coeffs[ini+i]=1.0;
693:   for (k=st->nmat-1;k>=1;k--) {
694:     inip = ini+1;
695:     ini = (k*(k-1))/2;
696:     coeffs[ini] = 1.0;
697:     for (i=1;i<k;i++) coeffs[ini+i] = coeffs[ini+i-1]+coeffs[inip+i-1];
698:   }
699:   return(0);
700: }

702: /*@
703:    STPostSolve - Optional post-solve phase, intended for any actions that must
704:    be performed on the ST object after the eigensolver has finished.

706:    Collective on st

708:    Input Parameters:
709: .  st  - the spectral transformation context

711:    Level: developer

713: .seealso: EPSSolve()
714: @*/
715: PetscErrorCode STPostSolve(ST st)
716: {

722:   if (st->ops->postsolve) {
723:     (*st->ops->postsolve)(st);
724:   }
725:   return(0);
726: }

728: /*@
729:    STBackTransform - Back-transformation phase, intended for
730:    spectral transformations which require to transform the computed
731:    eigenvalues back to the original eigenvalue problem.

733:    Not Collective

735:    Input Parameters:
736: +  st   - the spectral transformation context
737:    eigr - real part of a computed eigenvalue
738: -  eigi - imaginary part of a computed eigenvalue

740:    Level: developer

742: .seealso: STIsInjective()
743: @*/
744: PetscErrorCode STBackTransform(ST st,PetscInt n,PetscScalar* eigr,PetscScalar* eigi)
745: {

751:   if (st->ops->backtransform) {
752:     (*st->ops->backtransform)(st,n,eigr,eigi);
753:   }
754:   return(0);
755: }

757: /*@
758:    STIsInjective - Ask if this spectral transformation is injective or not
759:    (that is, if it corresponds to a one-to-one mapping). If not, then it
760:    does not make sense to call STBackTransform().

762:    Not collective

764:    Input Parameter:
765: .  st   - the spectral transformation context

767:    Output Parameter:
768: .  is - the answer

770:    Level: developer

772: .seealso: STBackTransform()
773: @*/
774: PetscErrorCode STIsInjective(ST st,PetscBool* is)
775: {
777:   PetscBool      shell;


784:   PetscObjectTypeCompare((PetscObject)st,STSHELL,&shell);
785:   if (shell) {
786:     STIsInjective_Shell(st,is);
787:   } else *is = st->ops->backtransform? PETSC_TRUE: PETSC_FALSE;
788:   return(0);
789: }

791: /*@
792:    STMatSetUp - Build the preconditioner matrix used in STMatSolve().

794:    Collective on st

796:    Input Parameters:
797: +  st     - the spectral transformation context
798: .  sigma  - the shift
799: -  coeffs - the coefficients (may be NULL)

801:    Note:
802:    This function is not intended to be called by end users, but by SLEPc
803:    solvers that use ST. It builds matrix st->P as follows, then calls KSPSetUp().
804: .vb
805:     If (coeffs):  st->P = Sum_{i=0:nmat-1} coeffs[i]*sigma^i*A_i.
806:     else          st->P = Sum_{i=0:nmat-1} sigma^i*A_i
807: .ve

809:    Level: developer

811: .seealso: STMatSolve()
812: @*/
813: PetscErrorCode STMatSetUp(ST st,PetscScalar sigma,PetscScalar *coeffs)
814: {

820:   STCheckMatrices(st,1);

822:   PetscLogEventBegin(ST_MatSetUp,st,0,0,0);
823:   STMatMAXPY_Private(st,sigma,0.0,0,coeffs,PETSC_TRUE,&st->P);
824:   STKSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P);
825:   KSPSetUp(st->ksp);
826:   PetscLogEventEnd(ST_MatSetUp,st,0,0,0);
827:   return(0);
828: }

830: /*@
831:    STSetWorkVecs - Sets a number of work vectors into the ST object.

833:    Collective on st

835:    Input Parameters:
836: +  st - the spectral transformation context
837: -  nw - number of work vectors to allocate

839:    Developers Note:
840:    This is SLEPC_EXTERN because it may be required by shell STs.

842:    Level: developer
843: @*/
844: PetscErrorCode STSetWorkVecs(ST st,PetscInt nw)
845: {
847:   PetscInt       i;

852:   if (nw <= 0) SETERRQ1(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_OUTOFRANGE,"nw must be > 0: nw = %D",nw);
853:   if (st->nwork < nw) {
854:     VecDestroyVecs(st->nwork,&st->work);
855:     st->nwork = nw;
856:     PetscMalloc1(nw,&st->work);
857:     for (i=0;i<nw;i++) { STMatCreateVecs(st,&st->work[i],NULL); }
858:     PetscLogObjectParents(st,nw,st->work);
859:   }
860:   return(0);
861: }