Actual source code: fnbasic.c

slepc-3.11.2 2019-07-30
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  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:    Basic FN routines
 12: */

 14: #include <slepc/private/fnimpl.h>      /*I "slepcfn.h" I*/
 15: #include <slepcblaslapack.h>

 17: PetscFunctionList FNList = 0;
 18: PetscBool         FNRegisterAllCalled = PETSC_FALSE;
 19: PetscClassId      FN_CLASSID = 0;
 20: PetscLogEvent     FN_Evaluate = 0;
 21: static PetscBool  FNPackageInitialized = PETSC_FALSE;

 23: const char *FNParallelTypes[] = {"REDUNDANT","SYNCHRONIZED","FNParallelType","FN_PARALLEL_",0};

 25: /*@C
 26:    FNFinalizePackage - This function destroys everything in the Slepc interface
 27:    to the FN package. It is called from SlepcFinalize().

 29:    Level: developer

 31: .seealso: SlepcFinalize()
 32: @*/
 33: PetscErrorCode FNFinalizePackage(void)
 34: {

 38:   PetscFunctionListDestroy(&FNList);
 39:   FNPackageInitialized = PETSC_FALSE;
 40:   FNRegisterAllCalled  = PETSC_FALSE;
 41:   return(0);
 42: }

 44: /*@C
 45:   FNInitializePackage - This function initializes everything in the FN package.
 46:   It is called from PetscDLLibraryRegister() when using dynamic libraries, and
 47:   on the first call to FNCreate() when using static libraries.

 49:   Level: developer

 51: .seealso: SlepcInitialize()
 52: @*/
 53: PetscErrorCode FNInitializePackage(void)
 54: {
 55:   char           logList[256];
 56:   PetscBool      opt,pkg;

 60:   if (FNPackageInitialized) return(0);
 61:   FNPackageInitialized = PETSC_TRUE;
 62:   /* Register Classes */
 63:   PetscClassIdRegister("Math Function",&FN_CLASSID);
 64:   /* Register Constructors */
 65:   FNRegisterAll();
 66:   /* Register Events */
 67:   PetscLogEventRegister("FNEvaluate",FN_CLASSID,&FN_Evaluate);
 68:   /* Process info exclusions */
 69:   PetscOptionsGetString(NULL,NULL,"-info_exclude",logList,sizeof(logList),&opt);
 70:   if (opt) {
 71:     PetscStrInList("fn",logList,',',&pkg);
 72:     if (pkg) { PetscInfoDeactivateClass(FN_CLASSID); }
 73:   }
 74:   /* Process summary exclusions */
 75:   PetscOptionsGetString(NULL,NULL,"-log_exclude",logList,sizeof(logList),&opt);
 76:   if (opt) {
 77:     PetscStrInList("fn",logList,',',&pkg);
 78:     if (pkg) { PetscLogEventDeactivateClass(FN_CLASSID); }
 79:   }
 80:   /* Register package finalizer */
 81:   PetscRegisterFinalize(FNFinalizePackage);
 82:   return(0);
 83: }

 85: /*@
 86:    FNCreate - Creates an FN context.

 88:    Collective on MPI_Comm

 90:    Input Parameter:
 91: .  comm - MPI communicator

 93:    Output Parameter:
 94: .  newfn - location to put the FN context

 96:    Level: beginner

 98: .seealso: FNDestroy(), FN
 99: @*/
100: PetscErrorCode FNCreate(MPI_Comm comm,FN *newfn)
101: {
102:   FN             fn;

107:   *newfn = 0;
108:   FNInitializePackage();
109:   SlepcHeaderCreate(fn,FN_CLASSID,"FN","Math Function","FN",comm,FNDestroy,FNView);

111:   fn->alpha    = 1.0;
112:   fn->beta     = 1.0;
113:   fn->method   = 0;

115:   fn->nw       = 0;
116:   fn->cw       = 0;
117:   fn->data     = NULL;

119:   *newfn = fn;
120:   return(0);
121: }

123: /*@C
124:    FNSetOptionsPrefix - Sets the prefix used for searching for all
125:    FN options in the database.

127:    Logically Collective on FN

129:    Input Parameters:
130: +  fn - the math function context
131: -  prefix - the prefix string to prepend to all FN option requests

133:    Notes:
134:    A hyphen (-) must NOT be given at the beginning of the prefix name.
135:    The first character of all runtime options is AUTOMATICALLY the
136:    hyphen.

138:    Level: advanced

140: .seealso: FNAppendOptionsPrefix()
141: @*/
142: PetscErrorCode FNSetOptionsPrefix(FN fn,const char *prefix)
143: {

148:   PetscObjectSetOptionsPrefix((PetscObject)fn,prefix);
149:   return(0);
150: }

152: /*@C
153:    FNAppendOptionsPrefix - Appends to the prefix used for searching for all
154:    FN options in the database.

156:    Logically Collective on FN

158:    Input Parameters:
159: +  fn - the math function context
160: -  prefix - the prefix string to prepend to all FN option requests

162:    Notes:
163:    A hyphen (-) must NOT be given at the beginning of the prefix name.
164:    The first character of all runtime options is AUTOMATICALLY the hyphen.

166:    Level: advanced

168: .seealso: FNSetOptionsPrefix()
169: @*/
170: PetscErrorCode FNAppendOptionsPrefix(FN fn,const char *prefix)
171: {

176:   PetscObjectAppendOptionsPrefix((PetscObject)fn,prefix);
177:   return(0);
178: }

180: /*@C
181:    FNGetOptionsPrefix - Gets the prefix used for searching for all
182:    FN options in the database.

184:    Not Collective

186:    Input Parameters:
187: .  fn - the math function context

189:    Output Parameters:
190: .  prefix - pointer to the prefix string used is returned

192:    Note:
193:    On the Fortran side, the user should pass in a string 'prefix' of
194:    sufficient length to hold the prefix.

196:    Level: advanced

198: .seealso: FNSetOptionsPrefix(), FNAppendOptionsPrefix()
199: @*/
200: PetscErrorCode FNGetOptionsPrefix(FN fn,const char *prefix[])
201: {

207:   PetscObjectGetOptionsPrefix((PetscObject)fn,prefix);
208:   return(0);
209: }

211: /*@C
212:    FNSetType - Selects the type for the FN object.

214:    Logically Collective on FN

216:    Input Parameter:
217: +  fn   - the math function context
218: -  type - a known type

220:    Notes:
221:    The default is FNRATIONAL, which includes polynomials as a particular
222:    case as well as simple functions such as f(x)=x and f(x)=constant.

224:    Level: intermediate

226: .seealso: FNGetType()
227: @*/
228: PetscErrorCode FNSetType(FN fn,FNType type)
229: {
230:   PetscErrorCode ierr,(*r)(FN);
231:   PetscBool      match;


237:   PetscObjectTypeCompare((PetscObject)fn,type,&match);
238:   if (match) return(0);

240:    PetscFunctionListFind(FNList,type,&r);
241:   if (!r) SETERRQ1(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_UNKNOWN_TYPE,"Unable to find requested FN type %s",type);

243:   if (fn->ops->destroy) { (*fn->ops->destroy)(fn); }
244:   PetscMemzero(fn->ops,sizeof(struct _FNOps));

246:   PetscObjectChangeTypeName((PetscObject)fn,type);
247:   (*r)(fn);
248:   return(0);
249: }

251: /*@C
252:    FNGetType - Gets the FN type name (as a string) from the FN context.

254:    Not Collective

256:    Input Parameter:
257: .  fn - the math function context

259:    Output Parameter:
260: .  name - name of the math function

262:    Level: intermediate

264: .seealso: FNSetType()
265: @*/
266: PetscErrorCode FNGetType(FN fn,FNType *type)
267: {
271:   *type = ((PetscObject)fn)->type_name;
272:   return(0);
273: }

275: /*@
276:    FNSetScale - Sets the scaling parameters that define the matematical function.

278:    Logically Collective on FN

280:    Input Parameters:
281: +  fn    - the math function context
282: .  alpha - inner scaling (argument)
283: -  beta  - outer scaling (result)

285:    Notes:
286:    Given a function f(x) specified by the FN type, the scaling parameters can
287:    be used to realize the function beta*f(alpha*x). So when these values are given,
288:    the procedure for function evaluation will first multiply the argument by alpha,
289:    then evaluate the function itself, and finally scale the result by beta.
290:    Likewise, these values are also considered when evaluating the derivative.

292:    If you want to provide only one of the two scaling factors, set the other
293:    one to 1.0.

295:    Level: intermediate

297: .seealso: FNGetScale(), FNEvaluateFunction()
298: @*/
299: PetscErrorCode FNSetScale(FN fn,PetscScalar alpha,PetscScalar beta)
300: {
305:   if (PetscAbsScalar(alpha)==0.0 || PetscAbsScalar(beta)==0.0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_WRONG,"Scaling factors must be nonzero");
306:   fn->alpha = alpha;
307:   fn->beta  = beta;
308:   return(0);
309: }

311: /*@
312:    FNGetScale - Gets the scaling parameters that define the matematical function.

314:    Not Collective

316:    Input Parameter:
317: .  fn    - the math function context

319:    Output Parameters:
320: +  alpha - inner scaling (argument)
321: -  beta  - outer scaling (result)

323:    Level: intermediate

325: .seealso: FNSetScale()
326: @*/
327: PetscErrorCode FNGetScale(FN fn,PetscScalar *alpha,PetscScalar *beta)
328: {
331:   if (alpha) *alpha = fn->alpha;
332:   if (beta)  *beta  = fn->beta;
333:   return(0);
334: }

336: /*@
337:    FNSetMethod - Selects the method to be used to evaluate functions of matrices.

339:    Logically Collective on FN

341:    Input Parameter:
342: +  fn   - the math function context
343: -  meth - an index indentifying the method

345:    Options Database Key:
346: .  -fn_method <meth> - Sets the method

348:    Notes:
349:    In some FN types there are more than one algorithms available for computing
350:    matrix functions. In that case, this function allows choosing the wanted method.

352:    If meth is currently set to 0 (the default) and the input argument A of
353:    FNEvaluateFunctionMat() is a symmetric/Hermitian matrix, then the computation
354:    is done via the eigendecomposition of A, rather than with the general algorithm.

356:    Level: intermediate

358: .seealso: FNGetMethod(), FNEvaluateFunctionMat()
359: @*/
360: PetscErrorCode FNSetMethod(FN fn,PetscInt meth)
361: {
365:   if (meth<0) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"The method must be a non-negative integer");
366:   if (meth>FN_MAX_SOLVE) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"Too large value for the method");
367:   fn->method = meth;
368:   return(0);
369: }

371: /*@
372:    FNGetMethod - Gets the method currently used in the FN.

374:    Not Collective

376:    Input Parameter:
377: .  fn - the math function context

379:    Output Parameter:
380: .  meth - identifier of the method

382:    Level: intermediate

384: .seealso: FNSetMethod()
385: @*/
386: PetscErrorCode FNGetMethod(FN fn,PetscInt *meth)
387: {
391:   *meth = fn->method;
392:   return(0);
393: }

395: /*@
396:    FNSetParallel - Selects the mode of operation in parallel runs.

398:    Logically Collective on FN

400:    Input Parameter:
401: +  fn    - the math function context
402: -  pmode - the parallel mode

404:    Options Database Key:
405: .  -fn_parallel <mode> - Sets the parallel mode, either 'redundant' or 'synchronized'

407:    Notes:
408:    This is relevant only when the function is evaluated on a matrix, with
409:    either FNEvaluateFunctionMat() or FNEvaluateFunctionMatVec().

411:    In the 'redundant' parallel mode, all processes will make the computation
412:    redundantly, starting from the same data, and producing the same result.
413:    This result may be slightly different in the different processes if using a
414:    multithreaded BLAS library, which may cause issues in ill-conditioned problems.

416:    In the 'synchronized' parallel mode, only the first MPI process performs the
417:    computation and then the computed matrix is broadcast to the other
418:    processes in the communicator. This communication is done automatically at
419:    the end of FNEvaluateFunctionMat() or FNEvaluateFunctionMatVec().

421:    Level: advanced

423: .seealso: FNEvaluateFunctionMat() or FNEvaluateFunctionMatVec(), FNGetParallel()
424: @*/
425: PetscErrorCode FNSetParallel(FN fn,FNParallelType pmode)
426: {
430:   fn->pmode = pmode;
431:   return(0);
432: }

434: /*@
435:    FNGetParallel - Gets the mode of operation in parallel runs.

437:    Not Collective

439:    Input Parameter:
440: .  fn - the math function context

442:    Output Parameter:
443: .  pmode - the parallel mode

445:    Level: advanced

447: .seealso: FNSetParallel()
448: @*/
449: PetscErrorCode FNGetParallel(FN fn,FNParallelType *pmode)
450: {
454:   *pmode = fn->pmode;
455:   return(0);
456: }

458: /*@
459:    FNEvaluateFunction - Computes the value of the function f(x) for a given x.

461:    Not collective

463:    Input Parameters:
464: +  fn - the math function context
465: -  x  - the value where the function must be evaluated

467:    Output Parameter:
468: .  y  - the result of f(x)

470:    Note:
471:    Scaling factors are taken into account, so the actual function evaluation
472:    will return beta*f(alpha*x).

474:    Level: intermediate

476: .seealso: FNEvaluateDerivative(), FNEvaluateFunctionMat(), FNSetScale()
477: @*/
478: PetscErrorCode FNEvaluateFunction(FN fn,PetscScalar x,PetscScalar *y)
479: {
481:   PetscScalar    xf,yf;

487:   PetscLogEventBegin(FN_Evaluate,fn,0,0,0);
488:   xf = fn->alpha*x;
489:   (*fn->ops->evaluatefunction)(fn,xf,&yf);
490:   *y = fn->beta*yf;
491:   PetscLogEventEnd(FN_Evaluate,fn,0,0,0);
492:   return(0);
493: }

495: /*@
496:    FNEvaluateDerivative - Computes the value of the derivative f'(x) for a given x.

498:    Not Collective

500:    Input Parameters:
501: +  fn - the math function context
502: -  x  - the value where the derivative must be evaluated

504:    Output Parameter:
505: .  y  - the result of f'(x)

507:    Note:
508:    Scaling factors are taken into account, so the actual derivative evaluation will
509:    return alpha*beta*f'(alpha*x).

511:    Level: intermediate

513: .seealso: FNEvaluateFunction()
514: @*/
515: PetscErrorCode FNEvaluateDerivative(FN fn,PetscScalar x,PetscScalar *y)
516: {
518:   PetscScalar    xf,yf;

524:   PetscLogEventBegin(FN_Evaluate,fn,0,0,0);
525:   xf = fn->alpha*x;
526:   (*fn->ops->evaluatederivative)(fn,xf,&yf);
527:   *y = fn->alpha*fn->beta*yf;
528:   PetscLogEventEnd(FN_Evaluate,fn,0,0,0);
529:   return(0);
530: }

532: static PetscErrorCode FNEvaluateFunctionMat_Sym_Private(FN fn,PetscScalar *As,PetscScalar *Bs,PetscInt m,PetscBool firstonly)
533: {
534: #if defined(PETSC_MISSING_LAPACK_SYEV) || defined(SLEPC_MISSING_LAPACK_LACPY)
536:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SYEV/LACPY - Lapack routines are unavailable");
537: #else
539:   PetscInt       i,j;
540:   PetscBLASInt   n,k,ld,lwork,info;
541:   PetscScalar    *Q,*W,*work,a,x,y,one=1.0,zero=0.0;
542:   PetscReal      *eig,dummy;
543: #if defined(PETSC_USE_COMPLEX)
544:   PetscReal      *rwork,rdummy;
545: #endif

548:   PetscBLASIntCast(m,&n);
549:   ld = n;
550:   k = firstonly? 1: n;

552:   /* workspace query and memory allocation */
553:   lwork = -1;
554: #if defined(PETSC_USE_COMPLEX)
555:   PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n,As,&ld,&dummy,&a,&lwork,&rdummy,&info));
556:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
557:   PetscMalloc5(m,&eig,m*m,&Q,m*k,&W,lwork,&work,PetscMax(1,3*m-2),&rwork);
558: #else
559:   PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n,As,&ld,&dummy,&a,&lwork,&info));
560:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
561:   PetscMalloc4(m,&eig,m*m,&Q,m*k,&W,lwork,&work);
562: #endif

564:   /* compute eigendecomposition */
565:   PetscStackCallBLAS("LAPACKlacpy",LAPACKlacpy_("L",&n,&n,As,&ld,Q,&ld));
566: #if defined(PETSC_USE_COMPLEX)
567:   PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n,Q,&ld,eig,work,&lwork,rwork,&info));
568: #else
569:   PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&n,Q,&ld,eig,work,&lwork,&info));
570: #endif
571:   SlepcCheckLapackInfo("syev",info);

573:   /* W = f(Lambda)*Q' */
574:   for (i=0;i<n;i++) {
575:     x = fn->alpha*eig[i];
576:     (*fn->ops->evaluatefunction)(fn,x,&y);  /* y = f(x) */
577:     for (j=0;j<k;j++) W[i+j*ld] = PetscConj(Q[j+i*ld])*fn->beta*y;
578:   }
579:   /* Bs = Q*W */
580:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&k,&n,&one,Q,&ld,W,&ld,&zero,Bs,&ld));
581: #if defined(PETSC_USE_COMPLEX)
582:   PetscFree5(eig,Q,W,work,rwork);
583: #else
584:   PetscFree4(eig,Q,W,work);
585: #endif
586:   PetscLogFlops(9.0*n*n*n+2.0*n*n*n);
587:   return(0);
588: #endif
589: }

591: /*
592:    FNEvaluateFunctionMat_Sym_Default - given a symmetric matrix A,
593:    compute the matrix function as f(A)=Q*f(D)*Q' where the spectral
594:    decomposition of A is A=Q*D*Q'
595: */
596: static PetscErrorCode FNEvaluateFunctionMat_Sym_Default(FN fn,Mat A,Mat B)
597: {
599:   PetscInt       m;
600:   PetscScalar    *As,*Bs;

603:   MatDenseGetArray(A,&As);
604:   MatDenseGetArray(B,&Bs);
605:   MatGetSize(A,&m,NULL);
606:   FNEvaluateFunctionMat_Sym_Private(fn,As,Bs,m,PETSC_FALSE);
607:   MatDenseRestoreArray(A,&As);
608:   MatDenseRestoreArray(B,&Bs);
609:   return(0);
610: }

612: PetscErrorCode FNEvaluateFunctionMat_Private(FN fn,Mat A,Mat B,PetscBool sync)
613: {
615:   PetscBool      set,flg,symm=PETSC_FALSE;
616:   PetscInt       m,n;
617:   PetscMPIInt    size,rank;
618:   PetscScalar    *pF;
619:   Mat            M,F;

622:   /* destination matrix */
623:   F = B?B:A;

625:   /* check symmetry of A */
626:   MatIsHermitianKnown(A,&set,&flg);
627:   symm = set? flg: PETSC_FALSE;

629:   MPI_Comm_size(PetscObjectComm((PetscObject)fn),&size);
630:   MPI_Comm_rank(PetscObjectComm((PetscObject)fn),&rank);
631:   if (size==1 || fn->pmode==FN_PARALLEL_REDUNDANT || (fn->pmode==FN_PARALLEL_SYNCHRONIZED && !rank)) {
632:     
633:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
634:     if (symm && !fn->method) {  /* prefer diagonalization */
635:       PetscInfo(fn,"Computing matrix function via diagonalization\n");
636:       FNEvaluateFunctionMat_Sym_Default(fn,A,F);
637:     } else {
638:       /* scale argument */
639:       if (fn->alpha!=(PetscScalar)1.0) {
640:         FN_AllocateWorkMat(fn,A,&M);
641:         MatScale(M,fn->alpha);
642:       } else M = A;
643:       if (fn->ops->evaluatefunctionmat[fn->method]) {
644:         (*fn->ops->evaluatefunctionmat[fn->method])(fn,M,F);
645:       } else if (!fn->method) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Matrix functions not implemented in this FN type");
646:       else SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"The specified method number does not exist for this FN type");
647:       if (fn->alpha!=(PetscScalar)1.0) {
648:         FN_FreeWorkMat(fn,&M);
649:       }
650:       /* scale result */
651:       MatScale(F,fn->beta);
652:     }
653:     PetscFPTrapPop();
654:   }
655:   if (size>1 && fn->pmode==FN_PARALLEL_SYNCHRONIZED && sync) {  /* synchronize */
656:     MatGetSize(A,&m,&n);
657:     MatDenseGetArray(F,&pF);
658:     MPI_Bcast(pF,n*n,MPIU_SCALAR,0,PetscObjectComm((PetscObject)fn));
659:     MatDenseRestoreArray(F,&pF);
660:   }
661:   return(0);
662: }

664: /*@
665:    FNEvaluateFunctionMat - Computes the value of the function f(A) for a given
666:    matrix A, where the result is also a matrix.

668:    Logically Collective on FN

670:    Input Parameters:
671: +  fn - the math function context
672: -  A  - matrix on which the function must be evaluated

674:    Output Parameter:
675: .  B  - (optional) matrix resulting from evaluating f(A)

677:    Notes:
678:    Matrix A must be a square sequential dense Mat, with all entries equal on
679:    all processes (otherwise each process will compute different results).
680:    If matrix B is provided, it must also be a square sequential dense Mat, and
681:    both matrices must have the same dimensions. If B is NULL (or B=A) then the
682:    function will perform an in-place computation, overwriting A with f(A).

684:    If A is known to be real symmetric or complex Hermitian then it is
685:    recommended to set the appropriate flag with MatSetOption(), because
686:    symmetry can sometimes be exploited by the algorithm.

688:    Scaling factors are taken into account, so the actual function evaluation
689:    will return beta*f(alpha*A).

691:    Level: advanced

693: .seealso: FNEvaluateFunction(), FNEvaluateFunctionMatVec(), FNSetMethod()
694: @*/
695: PetscErrorCode FNEvaluateFunctionMat(FN fn,Mat A,Mat B)
696: {
698:   PetscBool      match,inplace=PETSC_FALSE;
699:   PetscInt       m,n,n1;

706:   if (B) {
709:   } else inplace = PETSC_TRUE;
710:   PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&match);
711:   if (!match) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Mat A must be of type seqdense");
712:   MatGetSize(A,&m,&n);
713:   if (m!=n) SETERRQ2(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Mat A is not square (has %D rows, %D cols)",m,n);
714:   if (!inplace) {
715:     PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&match);
716:     if (!match) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Mat B must be of type seqdense");
717:     n1 = n;
718:     MatGetSize(B,&m,&n);
719:     if (m!=n) SETERRQ2(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Mat B is not square (has %D rows, %D cols)",m,n);
720:     if (n1!=n) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Matrices A and B must have the same dimension");
721:   }

723:   /* evaluate matrix function */
724:   PetscLogEventBegin(FN_Evaluate,fn,0,0,0);
725:   FNEvaluateFunctionMat_Private(fn,A,B,PETSC_TRUE);
726:   PetscLogEventEnd(FN_Evaluate,fn,0,0,0);
727:   return(0);
728: }

730: /*
731:    FNEvaluateFunctionMatVec_Default - computes the full matrix f(A)
732:    and then copies the first column.
733: */
734: static PetscErrorCode FNEvaluateFunctionMatVec_Default(FN fn,Mat A,Vec v)
735: {
737:   Mat            F;

740:   FN_AllocateWorkMat(fn,A,&F);
741:   if (fn->ops->evaluatefunctionmat[fn->method]) {
742:     (*fn->ops->evaluatefunctionmat[fn->method])(fn,A,F);
743:   } else if (!fn->method) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Matrix functions not implemented in this FN type");
744:   else SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_OUTOFRANGE,"The specified method number does not exist for this FN type");
745:   MatGetColumnVector(F,v,0);
746:   FN_FreeWorkMat(fn,&F);
747:   return(0);
748: }

750: /*
751:    FNEvaluateFunctionMatVec_Sym_Default - given a symmetric matrix A,
752:    compute the matrix function as f(A)=Q*f(D)*Q' where the spectral
753:    decomposition of A is A=Q*D*Q'. Only the first column is computed.
754: */
755: static PetscErrorCode FNEvaluateFunctionMatVec_Sym_Default(FN fn,Mat A,Vec v)
756: {
758:   PetscInt       m;
759:   PetscScalar    *As,*vs;

762:   MatDenseGetArray(A,&As);
763:   VecGetArray(v,&vs);
764:   MatGetSize(A,&m,NULL);
765:   FNEvaluateFunctionMat_Sym_Private(fn,As,vs,m,PETSC_TRUE);
766:   MatDenseRestoreArray(A,&As);
767:   VecRestoreArray(v,&vs);
768:   return(0);
769: }

771: PetscErrorCode FNEvaluateFunctionMatVec_Private(FN fn,Mat A,Vec v,PetscBool sync)
772: {
774:   PetscBool      set,flg,symm=PETSC_FALSE;
775:   PetscInt       m,n;
776:   Mat            M;
777:   PetscMPIInt    size,rank;
778:   PetscScalar    *pv;

781:   /* check symmetry of A */
782:   MatIsHermitianKnown(A,&set,&flg);
783:   symm = set? flg: PETSC_FALSE;

785:   /* evaluate matrix function */
786:   MPI_Comm_size(PetscObjectComm((PetscObject)fn),&size);
787:   MPI_Comm_rank(PetscObjectComm((PetscObject)fn),&rank);
788:   if (size==1 || fn->pmode==FN_PARALLEL_REDUNDANT || (fn->pmode==FN_PARALLEL_SYNCHRONIZED && !rank)) {
789:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
790:     if (symm && !fn->method) {  /* prefer diagonalization */
791:       PetscInfo(fn,"Computing matrix function via diagonalization\n");
792:       FNEvaluateFunctionMatVec_Sym_Default(fn,A,v);
793:     } else {
794:       /* scale argument */
795:       if (fn->alpha!=(PetscScalar)1.0) {
796:         FN_AllocateWorkMat(fn,A,&M);
797:         MatScale(M,fn->alpha);
798:       } else M = A;
799:       if (fn->ops->evaluatefunctionmatvec[fn->method]) {
800:         (*fn->ops->evaluatefunctionmatvec[fn->method])(fn,M,v);
801:       } else {
802:         FNEvaluateFunctionMatVec_Default(fn,M,v);
803:       }
804:       if (fn->alpha!=(PetscScalar)1.0) {
805:         FN_FreeWorkMat(fn,&M);
806:       }
807:       /* scale result */
808:       VecScale(v,fn->beta);
809:     }
810:     PetscFPTrapPop();
811:   }

813:   /* synchronize */
814:   if (size>1 && fn->pmode==FN_PARALLEL_SYNCHRONIZED && sync) { 
815:     MatGetSize(A,&m,&n);
816:     VecGetArray(v,&pv);
817:     MPI_Bcast(pv,n,MPIU_SCALAR,0,PetscObjectComm((PetscObject)fn));
818:     VecRestoreArray(v,&pv);
819:   }
820:   return(0);
821: }

823: /*@
824:    FNEvaluateFunctionMatVec - Computes the first column of the matrix f(A)
825:    for a given matrix A.

827:    Logically Collective on FN

829:    Input Parameters:
830: +  fn - the math function context
831: -  A  - matrix on which the function must be evaluated

833:    Output Parameter:
834: .  v  - vector to hold the first column of f(A)

836:    Notes:
837:    This operation is similar to FNEvaluateFunctionMat() but returns only
838:    the first column of f(A), hence saving computations in most cases.

840:    Level: advanced

842: .seealso: FNEvaluateFunction(), FNEvaluateFunctionMat(), FNSetMethod()
843: @*/
844: PetscErrorCode FNEvaluateFunctionMatVec(FN fn,Mat A,Vec v)
845: {
847:   PetscBool      match;
848:   PetscInt       m,n;

857:   PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&match);
858:   if (!match) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_SUP,"Mat A must be of type seqdense");
859:   MatGetSize(A,&m,&n);
860:   if (m!=n) SETERRQ2(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Mat A is not square (has %D rows, %D cols)",m,n);
861:   VecGetSize(v,&m);
862:   if (m!=n) SETERRQ(PetscObjectComm((PetscObject)fn),PETSC_ERR_ARG_SIZ,"Matrix A and vector v must have the same size");
863:   PetscLogEventBegin(FN_Evaluate,fn,0,0,0);
864:   FNEvaluateFunctionMatVec_Private(fn,A,v,PETSC_TRUE);
865:   PetscLogEventEnd(FN_Evaluate,fn,0,0,0);
866:   return(0);
867: }

869: /*@
870:    FNSetFromOptions - Sets FN options from the options database.

872:    Collective on FN

874:    Input Parameters:
875: .  fn - the math function context

877:    Notes:
878:    To see all options, run your program with the -help option.

880:    Level: beginner
881: @*/
882: PetscErrorCode FNSetFromOptions(FN fn)
883: {
885:   char           type[256];
886:   PetscScalar    array[2];
887:   PetscInt       k,meth;
888:   PetscBool      flg;
889:   FNParallelType pmode;

893:   FNRegisterAll();
894:   PetscObjectOptionsBegin((PetscObject)fn);
895:     PetscOptionsFList("-fn_type","Math function type","FNSetType",FNList,(char*)(((PetscObject)fn)->type_name?((PetscObject)fn)->type_name:FNRATIONAL),type,256,&flg);
896:     if (flg) {
897:       FNSetType(fn,type);
898:     } else if (!((PetscObject)fn)->type_name) {
899:       FNSetType(fn,FNRATIONAL);
900:     }

902:     k = 2;
903:     array[0] = 0.0; array[1] = 0.0;
904:     PetscOptionsScalarArray("-fn_scale","Scale factors (one or two scalar values separated with a comma without spaces)","FNSetScale",array,&k,&flg);
905:     if (flg) {
906:       if (k<2) array[1] = 1.0;
907:       FNSetScale(fn,array[0],array[1]);
908:     }

910:     PetscOptionsInt("-fn_method","Method to be used for computing matrix functions","FNSetMethod",fn->method,&meth,&flg);
911:     if (flg) { FNSetMethod(fn,meth); }

913:     PetscOptionsEnum("-fn_parallel","Operation mode in parallel runs","FNSetParallel",FNParallelTypes,(PetscEnum)fn->pmode,(PetscEnum*)&pmode,&flg);
914:     if (flg) { FNSetParallel(fn,pmode); }

916:     if (fn->ops->setfromoptions) {
917:       (*fn->ops->setfromoptions)(PetscOptionsObject,fn);
918:     }
919:     PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)fn);
920:   PetscOptionsEnd();
921:   return(0);
922: }

924: /*@C
925:    FNView - Prints the FN data structure.

927:    Collective on FN

929:    Input Parameters:
930: +  fn - the math function context
931: -  viewer - optional visualization context

933:    Note:
934:    The available visualization contexts include
935: +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
936: -     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
937:          output where only the first processor opens
938:          the file.  All other processors send their
939:          data to the first processor to print.

941:    The user can open an alternative visualization context with
942:    PetscViewerASCIIOpen() - output to a specified file.

944:    Level: beginner
945: @*/
946: PetscErrorCode FNView(FN fn,PetscViewer viewer)
947: {
948:   PetscBool      isascii;
950:   PetscMPIInt    size;

954:   if (!viewer) {
955:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)fn),&viewer);
956:   }
959:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
960:   if (isascii) {
961:     PetscObjectPrintClassNamePrefixType((PetscObject)fn,viewer);
962:     MPI_Comm_size(PetscObjectComm((PetscObject)fn),&size);
963:     if (size>1) {
964:       PetscViewerASCIIPrintf(viewer,"  parallel operation mode: %s\n",FNParallelTypes[fn->pmode]);
965:     }
966:     if (fn->ops->view) {
967:       PetscViewerASCIIPushTab(viewer);
968:       (*fn->ops->view)(fn,viewer);
969:       PetscViewerASCIIPopTab(viewer);
970:     }
971:   }
972:   return(0);
973: }

975: /*@
976:    FNDuplicate - Duplicates a math function, copying all parameters, possibly with a
977:    different communicator.

979:    Collective on FN

981:    Input Parameters:
982: +  fn   - the math function context
983: -  comm - MPI communicator

985:    Output Parameter:
986: .  newfn - location to put the new FN context

988:    Note:
989:    In order to use the same MPI communicator as in the original object,
990:    use PetscObjectComm((PetscObject)fn).

992:    Level: developer

994: .seealso: FNCreate()
995: @*/
996: PetscErrorCode FNDuplicate(FN fn,MPI_Comm comm,FN *newfn)
997: {
999:   FNType         type;
1000:   PetscScalar    alpha,beta;
1001:   PetscInt       meth;
1002:   FNParallelType ptype;

1008:   FNCreate(comm,newfn);
1009:   FNGetType(fn,&type);
1010:   FNSetType(*newfn,type);
1011:   FNGetScale(fn,&alpha,&beta);
1012:   FNSetScale(*newfn,alpha,beta);
1013:   FNGetMethod(fn,&meth);
1014:   FNSetMethod(*newfn,meth);
1015:   FNGetParallel(fn,&ptype);
1016:   FNSetParallel(*newfn,ptype);
1017:   if (fn->ops->duplicate) {
1018:     (*fn->ops->duplicate)(fn,comm,newfn);
1019:   }
1020:   return(0);
1021: }

1023: /*@
1024:    FNDestroy - Destroys FN context that was created with FNCreate().

1026:    Collective on FN

1028:    Input Parameter:
1029: .  fn - the math function context

1031:    Level: beginner

1033: .seealso: FNCreate()
1034: @*/
1035: PetscErrorCode FNDestroy(FN *fn)
1036: {
1038:   PetscInt       i;

1041:   if (!*fn) return(0);
1043:   if (--((PetscObject)(*fn))->refct > 0) { *fn = 0; return(0); }
1044:   if ((*fn)->ops->destroy) { (*(*fn)->ops->destroy)(*fn); }
1045:   for (i=0;i<(*fn)->nw;i++) {
1046:     MatDestroy(&(*fn)->W[i]);
1047:   }
1048:   PetscHeaderDestroy(fn);
1049:   return(0);
1050: }

1052: /*@C
1053:    FNRegister - Adds a mathematical function to the FN package.

1055:    Not collective

1057:    Input Parameters:
1058: +  name - name of a new user-defined FN
1059: -  function - routine to create context

1061:    Notes:
1062:    FNRegister() may be called multiple times to add several user-defined functions.

1064:    Level: advanced

1066: .seealso: FNRegisterAll()
1067: @*/
1068: PetscErrorCode FNRegister(const char *name,PetscErrorCode (*function)(FN))
1069: {

1073:   FNInitializePackage();
1074:   PetscFunctionListAdd(&FNList,name,function);
1075:   return(0);
1076: }