Actual source code: mffd.c

  1: #define PETSCMAT_DLL

 3:  #include private/matimpl.h
 4:  #include ../src/mat/impls/mffd/mffdimpl.h

  6: PetscFList MatMFFDList        = 0;
  7: PetscTruth MatMFFDRegisterAllCalled = PETSC_FALSE;

  9: PetscCookie  MATMFFD_COOKIE;
 10: PetscLogEvent  MATMFFD_Mult;

 12: static PetscTruth MatMFFDPackageInitialized = PETSC_FALSE;
 15: /*@C
 16:   MatMFFDFinalizePackage - This function destroys everything in the MatMFFD package. It is
 17:   called from PetscFinalize().

 19:   Level: developer

 21: .keywords: Petsc, destroy, package
 22: .seealso: PetscFinalize()
 23: @*/
 24: PetscErrorCode  MatMFFDFinalizePackage(void)
 25: {
 27:   MatMFFDPackageInitialized = PETSC_FALSE;
 28:   MatMFFDRegisterAllCalled  = PETSC_FALSE;
 29:   MatMFFDList               = PETSC_NULL;
 30:   return(0);
 31: }

 35: /*@C
 36:   MatMFFDInitializePackage - This function initializes everything in the MatMFFD package. It is called
 37:   from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to MatCreate_MFFD()
 38:   when using static libraries.

 40:   Input Parameter:
 41: . path - The dynamic library path, or PETSC_NULL

 43:   Level: developer

 45: .keywords: Vec, initialize, package
 46: .seealso: PetscInitialize()
 47: @*/
 48: PetscErrorCode  MatMFFDInitializePackage(const char path[])
 49: {
 50:   char              logList[256];
 51:   char              *className;
 52:   PetscTruth        opt;
 53:   PetscErrorCode    ierr;

 56:   if (MatMFFDPackageInitialized) return(0);
 57:   MatMFFDPackageInitialized = PETSC_TRUE;
 58:   /* Register Classes */
 59:   PetscCookieRegister("MatMFFD",&MATMFFD_COOKIE);
 60:   /* Register Constructors */
 61:   MatMFFDRegisterAll(path);
 62:   /* Register Events */
 63:   PetscLogEventRegister("MatMult MF",          MATMFFD_COOKIE,&MATMFFD_Mult);

 65:   /* Process info exclusions */
 66:   PetscOptionsGetString(PETSC_NULL, "-info_exclude", logList, 256, &opt);
 67:   if (opt) {
 68:     PetscStrstr(logList, "matmffd", &className);
 69:     if (className) {
 70:       PetscInfoDeactivateClass(MATMFFD_COOKIE);
 71:     }
 72:   }
 73:   /* Process summary exclusions */
 74:   PetscOptionsGetString(PETSC_NULL, "-log_summary_exclude", logList, 256, &opt);
 75:   if (opt) {
 76:     PetscStrstr(logList, "matmffd", &className);
 77:     if (className) {
 78:       PetscLogEventDeactivateClass(MATMFFD_COOKIE);
 79:     }
 80:   }
 81:   PetscRegisterFinalize(MatMFFDFinalizePackage);
 82:   return(0);
 83: }

 87: /*@C
 88:     MatMFFDSetType - Sets the method that is used to compute the 
 89:     differencing parameter for finite differene matrix-free formulations. 

 91:     Input Parameters:
 92: +   mat - the "matrix-free" matrix created via MatCreateSNESMF(), or MatCreateMFFD()
 93:           or MatSetType(mat,MATMFFD);
 94: -   ftype - the type requested, either MATMFFD_WP or MATMFFD_DS

 96:     Level: advanced

 98:     Notes:
 99:     For example, such routines can compute h for use in
100:     Jacobian-vector products of the form

102:                         F(x+ha) - F(x)
103:           F'(u)a  ~=  ----------------
104:                               h

106: .seealso: MatCreateSNESMF(), MatMFFDRegisterDynamic(), MatMFFDSetFunction()
107: @*/
108: PetscErrorCode  MatMFFDSetType(Mat mat,const MatMFFDType ftype)
109: {
110:   PetscErrorCode ierr,(*r)(MatMFFD);
111:   MatMFFD        ctx = (MatMFFD)mat->data;
112:   PetscTruth     match;
113: 

118:   /* already set, so just return */
119:   PetscTypeCompare((PetscObject)ctx,ftype,&match);
120:   if (match) return(0);

122:   /* destroy the old one if it exists */
123:   if (ctx->ops->destroy) {
124:     (*ctx->ops->destroy)(ctx);
125:   }

127:    PetscFListFind(MatMFFDList,((PetscObject)ctx)->comm,ftype,(void (**)(void)) &r);
128:   if (!r) SETERRQ1(PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown MatMFFD type %s given",ftype);
129:   (*r)(ctx);
130:   PetscObjectChangeTypeName((PetscObject)ctx,ftype);
131:   return(0);
132: }

138: PetscErrorCode  MatMFFDSetFunctioniBase_MFFD(Mat mat,FCN1 func)
139: {
140:   MatMFFD ctx = (MatMFFD)mat->data;

143:   ctx->funcisetbase = func;
144:   return(0);
145: }

152: PetscErrorCode  MatMFFDSetFunctioni_MFFD(Mat mat,FCN2 funci)
153: {
154:   MatMFFD ctx = (MatMFFD)mat->data;

157:   ctx->funci = funci;
158:   return(0);
159: }


165: PetscErrorCode  MatMFFDRegister(const char sname[],const char path[],const char name[],PetscErrorCode (*function)(MatMFFD))
166: {
168:   char           fullname[PETSC_MAX_PATH_LEN];

171:   PetscFListConcat(path,name,fullname);
172:   PetscFListAdd(&MatMFFDList,sname,fullname,(void (*)(void))function);
173:   return(0);
174: }


179: /*@C
180:    MatMFFDRegisterDestroy - Frees the list of MatMFFD methods that were
181:    registered by MatMFFDRegisterDynamic).

183:    Not Collective

185:    Level: developer

187: .keywords: MatMFFD, register, destroy

189: .seealso: MatMFFDRegisterDynamic), MatMFFDRegisterAll()
190: @*/
191: PetscErrorCode  MatMFFDRegisterDestroy(void)
192: {

196:   PetscFListDestroy(&MatMFFDList);
197:   MatMFFDRegisterAllCalled = PETSC_FALSE;
198:   return(0);
199: }

201: /* ----------------------------------------------------------------------------------------*/
204: PetscErrorCode MatDestroy_MFFD(Mat mat)
205: {
207:   MatMFFD        ctx = (MatMFFD)mat->data;

210:   if (ctx->w) {
211:     VecDestroy(ctx->w);
212:   }
213:   if (ctx->current_f_allocated) {
214:     VecDestroy(ctx->current_f);
215:   }
216:   if (ctx->ops->destroy) {(*ctx->ops->destroy)(ctx);}
217:   if (ctx->sp) {MatNullSpaceDestroy(ctx->sp);}
218:   PetscHeaderDestroy(ctx);

220:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetBase_C","",PETSC_NULL);
221:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioniBase_C","",PETSC_NULL);
222:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioni_C","",PETSC_NULL);
223:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetCheckh_C","",PETSC_NULL);

225:   return(0);
226: }

230: /*
231:    MatMFFDView_MFFD - Views matrix-free parameters.

233: */
234: PetscErrorCode MatView_MFFD(Mat J,PetscViewer viewer)
235: {
237:   MatMFFD        ctx = (MatMFFD)J->data;
238:   PetscTruth     iascii;

241:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
242:   if (iascii) {
243:      PetscViewerASCIIPrintf(viewer,"  matrix-free approximation:\n");
244:      PetscViewerASCIIPrintf(viewer,"    err=%G (relative error in function evaluation)\n",ctx->error_rel);
245:      if (!((PetscObject)ctx)->type_name) {
246:        PetscViewerASCIIPrintf(viewer,"    The compute h routine has not yet been set\n");
247:      } else {
248:        PetscViewerASCIIPrintf(viewer,"    Using %s compute h routine\n",((PetscObject)ctx)->type_name);
249:      }
250:      if (ctx->ops->view) {
251:        (*ctx->ops->view)(ctx,viewer);
252:      }
253:   } else {
254:     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for matrix-free matrix",((PetscObject)viewer)->type_name);
255:   }
256:   return(0);
257: }

261: /*
262:    MatAssemblyEnd_MFFD - Resets the ctx->ncurrenth to zero. This 
263:    allows the user to indicate the beginning of a new linear solve by calling
264:    MatAssemblyXXX() on the matrix free matrix. This then allows the 
265:    MatCreateMFFD_WP() to properly compute ||U|| only the first time
266:    in the linear solver rather than every time.
267: */
268: PetscErrorCode MatAssemblyEnd_MFFD(Mat J,MatAssemblyType mt)
269: {
271:   MatMFFD        j = (MatMFFD)J->data;

274:   MatMFFDResetHHistory(J);
275:   j->vshift = 0.0;
276:   j->vscale = 1.0;
277:   return(0);
278: }

282: /*
283:   MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:

285:         y ~= (F(u + ha) - F(u))/h, 
286:   where F = nonlinear function, as set by SNESSetFunction()
287:         u = current iterate
288:         h = difference interval
289: */
290: PetscErrorCode MatMult_MFFD(Mat mat,Vec a,Vec y)
291: {
292:   MatMFFD        ctx = (MatMFFD)mat->data;
293:   PetscScalar    h;
294:   Vec            w,U,F;
296:   PetscTruth     zeroa;

299:   /* We log matrix-free matrix-vector products separately, so that we can
300:      separate the performance monitoring from the cases that use conventional
301:      storage.  We may eventually modify event logging to associate events
302:      with particular objects, hence alleviating the more general problem. */
303:   PetscLogEventBegin(MATMFFD_Mult,a,y,0,0);

305:   w    = ctx->w;
306:   U    = ctx->current_u;
307:   F    = ctx->current_f;
308:   /* 
309:       Compute differencing parameter 
310:   */
311:   if (!ctx->ops->compute) {
312:     MatMFFDSetType(mat,MATMFFD_WP);
313:     MatMFFDSetFromOptions(mat);
314:   }
315:   (*ctx->ops->compute)(ctx,U,a,&h,&zeroa);
316:   if (zeroa) {
317:     VecSet(y,0.0);
318:     return(0);
319:   }

321:   if (h != h) SETERRQ(PETSC_ERR_PLIB,"Computed Nan differencing parameter h");
322:   if (ctx->checkh) {
323:     (*ctx->checkh)(ctx->checkhctx,U,a,&h);
324:   }

326:   /* keep a record of the current differencing parameter h */
327:   ctx->currenth = h;
328: #if defined(PETSC_USE_COMPLEX)
329:   PetscInfo2(mat,"Current differencing parameter: %G + %G i\n",PetscRealPart(h),PetscImaginaryPart(h));
330: #else
331:   PetscInfo1(mat,"Current differencing parameter: %15.12e\n",h);
332: #endif
333:   if (ctx->historyh && ctx->ncurrenth < ctx->maxcurrenth) {
334:     ctx->historyh[ctx->ncurrenth] = h;
335:   }
336:   ctx->ncurrenth++;

338:   /* w = u + ha */
339:   VecWAXPY(w,h,a,U);

341:   /* compute func(U) as base for differencing; only needed first time in and not when provided by user */
342:   if (ctx->ncurrenth == 1 && ctx->current_f_allocated) {
343:     (*ctx->func)(ctx->funcctx,U,F);
344:   }
345:   (*ctx->func)(ctx->funcctx,w,y);

347:   VecAXPY(y,-1.0,F);
348:   VecScale(y,1.0/h);

350:   VecAXPBY(y,ctx->vshift,ctx->vscale,a);

352:   if (ctx->sp) {MatNullSpaceRemove(ctx->sp,y,PETSC_NULL);}

354:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
355:   return(0);
356: }

360: /*
361:   MatGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix

363:         y ~= (F(u + ha) - F(u))/h, 
364:   where F = nonlinear function, as set by SNESSetFunction()
365:         u = current iterate
366:         h = difference interval
367: */
368: PetscErrorCode MatGetDiagonal_MFFD(Mat mat,Vec a)
369: {
370:   MatMFFD        ctx = (MatMFFD)mat->data;
371:   PetscScalar    h,*aa,*ww,v;
372:   PetscReal      epsilon = PETSC_SQRT_MACHINE_EPSILON,umin = 100.0*PETSC_SQRT_MACHINE_EPSILON;
373:   Vec            w,U;
375:   PetscInt       i,rstart,rend;

378:   if (!ctx->funci) {
379:     SETERRQ(PETSC_ERR_ORDER,"Requires calling MatMFFDSetFunctioni() first");
380:   }

382:   w    = ctx->w;
383:   U    = ctx->current_u;
384:   (*ctx->func)(ctx->funcctx,U,a);
385:   (*ctx->funcisetbase)(ctx->funcctx,U);
386:   VecCopy(U,w);

388:   VecGetOwnershipRange(a,&rstart,&rend);
389:   VecGetArray(a,&aa);
390:   for (i=rstart; i<rend; i++) {
391:     VecGetArray(w,&ww);
392:     h  = ww[i-rstart];
393:     if (h == 0.0) h = 1.0;
394: #if !defined(PETSC_USE_COMPLEX)
395:     if (h < umin && h >= 0.0)      h = umin;
396:     else if (h < 0.0 && h > -umin) h = -umin;
397: #else
398:     if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0)     h = umin;
399:     else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
400: #endif
401:     h     *= epsilon;
402: 
403:     ww[i-rstart] += h;
404:     VecRestoreArray(w,&ww);
405:     (*ctx->funci)(ctx->funcctx,i,w,&v);
406:     aa[i-rstart]  = (v - aa[i-rstart])/h;

408:     /* possibly shift and scale result */
409:     aa[i - rstart] = ctx->vshift + ctx->vscale*aa[i-rstart];

411:     VecGetArray(w,&ww);
412:     ww[i-rstart] -= h;
413:     VecRestoreArray(w,&ww);
414:   }
415:   VecRestoreArray(a,&aa);
416:   return(0);
417: }

421: PetscErrorCode MatShift_MFFD(Mat Y,PetscScalar a)
422: {
423:   MatMFFD shell = (MatMFFD)Y->data;
425:   shell->vshift += a;
426:   return(0);
427: }

431: PetscErrorCode MatScale_MFFD(Mat Y,PetscScalar a)
432: {
433:   MatMFFD shell = (MatMFFD)Y->data;
435:   shell->vscale *= a;
436:   return(0);
437: }

442: PetscErrorCode  MatMFFDSetBase_MFFD(Mat J,Vec U,Vec F)
443: {
445:   MatMFFD        ctx = (MatMFFD)J->data;

448:   MatMFFDResetHHistory(J);
449:   ctx->current_u = U;
450:   if (F) {
451:     if (ctx->current_f_allocated) {VecDestroy(ctx->current_f);}
452:     ctx->current_f           = F;
453:     ctx->current_f_allocated = PETSC_FALSE;
454:   } else if (!ctx->current_f_allocated) {
455:     VecDuplicate(ctx->current_u, &ctx->current_f);
456:     ctx->current_f_allocated = PETSC_TRUE;
457:   }
458:   if (!ctx->w) {
459:     VecDuplicate(ctx->current_u, &ctx->w);
460:   }
461:   J->assembled = PETSC_TRUE;
462:   return(0);
463: }
469: PetscErrorCode  MatMFFDSetCheckh_MFFD(Mat J,FCN3 fun,void*ectx)
470: {
471:   MatMFFD ctx = (MatMFFD)J->data;

474:   ctx->checkh    = fun;
475:   ctx->checkhctx = ectx;
476:   return(0);
477: }

482: /*@C
483:    MatMFFDSetOptionsPrefix - Sets the prefix used for searching for all 
484:    MatMFFD options in the database.

486:    Collective on Mat

488:    Input Parameter:
489: +  A - the Mat context
490: -  prefix - the prefix to prepend to all option names

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

496:    Level: advanced

498: .keywords: SNES, matrix-free, parameters

500: .seealso: MatMFFDSetFromOptions(), MatCreateSNESMF()
501: @*/
502: PetscErrorCode  MatMFFDSetOptionsPrefix(Mat mat,const char prefix[])

504: {
505:   MatMFFD        mfctx = mat ? (MatMFFD)mat->data : PETSC_NULL;
510:   PetscObjectSetOptionsPrefix((PetscObject)mfctx,prefix);
511:   return(0);
512: }

516: /*@
517:    MatMFFDSetFromOptions - Sets the MatMFFD options from the command line
518:    parameter.

520:    Collective on Mat

522:    Input Parameters:
523: .  mat - the matrix obtained with MatCreateMFFD() or MatCreateSNESMF()

525:    Options Database Keys:
526: +  -mat_mffd_type - wp or ds (see MATMFFD_WP or MATMFFD_DS)
527: -  -mat_mffd_err - square root of estimated relative error in function evaluation
528: -  -mat_mffd_period - how often h is recomputed, defaults to 1, everytime

530:    Level: advanced

532: .keywords: SNES, matrix-free, parameters

534: .seealso: MatCreateSNESMF(),MatMFFDSetHHistory(), MatMFFDResetHHistory()
535: @*/
536: PetscErrorCode  MatMFFDSetFromOptions(Mat mat)
537: {
538:   MatMFFD        mfctx = mat ? (MatMFFD)mat->data : PETSC_NULL;
540:   PetscTruth     flg;
541:   char           ftype[256];

546:   PetscOptionsBegin(((PetscObject)mfctx)->comm,((PetscObject)mfctx)->prefix,"Set matrix free computation parameters","MatMFFD");
547:   PetscOptionsList("-mat_mffd_type","Matrix free type","MatMFFDSetType",MatMFFDList,((PetscObject)mfctx)->type_name,ftype,256,&flg);
548:   if (flg) {
549:     MatMFFDSetType(mat,ftype);
550:   }

552:   PetscOptionsReal("-mat_mffd_err","set sqrt relative error in function","MatMFFDSetFunctionError",mfctx->error_rel,&mfctx->error_rel,0);
553:   PetscOptionsInt("-mat_mffd_period","how often h is recomputed","MatMFFDSetPeriod",mfctx->recomputeperiod,&mfctx->recomputeperiod,0);

555:   flg  = PETSC_FALSE;
556:   PetscOptionsTruth("-mat_mffd_check_positivity","Insure that U + h*a is nonnegative","MatMFFDSetCheckh",flg,&flg,PETSC_NULL);
557:   if (flg) {
558:     MatMFFDSetCheckh(mat,MatMFFDCheckPositivity,0);
559:   }
560:   if (mfctx->ops->setfromoptions) {
561:     (*mfctx->ops->setfromoptions)(mfctx);
562:   }
563:   PetscOptionsEnd();
564:   return(0);
565: }

567: /*MC
568:   MATMFFD - MATMFFD = "mffd" - A matrix free matrix type.

570:   Level: advanced

572: .seealso: MatCreateMFFD(), MatCreateSNESMF(), MatMFFDSetFunction()
573: M*/
577: PetscErrorCode  MatCreate_MFFD(Mat A)
578: {
579:   MatMFFD         mfctx;
580:   PetscErrorCode  ierr;

583: #ifndef PETSC_USE_DYNAMIC_LIBRARIES
584:   MatMFFDInitializePackage(PETSC_NULL);
585: #endif

587:   PetscHeaderCreate(mfctx,_p_MatMFFD,struct _MFOps,MATMFFD_COOKIE,0,"MatMFFD",((PetscObject)A)->comm,MatDestroy_MFFD,MatView_MFFD);
588:   mfctx->sp              = 0;
589:   mfctx->error_rel       = PETSC_SQRT_MACHINE_EPSILON;
590:   mfctx->recomputeperiod = 1;
591:   mfctx->count           = 0;
592:   mfctx->currenth        = 0.0;
593:   mfctx->historyh        = PETSC_NULL;
594:   mfctx->ncurrenth       = 0;
595:   mfctx->maxcurrenth     = 0;
596:   ((PetscObject)mfctx)->type_name       = 0;

598:   mfctx->vshift          = 0.0;
599:   mfctx->vscale          = 1.0;

601:   /* 
602:      Create the empty data structure to contain compute-h routines.
603:      These will be filled in below from the command line options or 
604:      a later call with MatMFFDSetType() or if that is not called 
605:      then it will default in the first use of MatMult_MFFD()
606:   */
607:   mfctx->ops->compute        = 0;
608:   mfctx->ops->destroy        = 0;
609:   mfctx->ops->view           = 0;
610:   mfctx->ops->setfromoptions = 0;
611:   mfctx->hctx                = 0;

613:   mfctx->func                = 0;
614:   mfctx->funcctx             = 0;
615:   mfctx->w                   = PETSC_NULL;

617:   A->data                = mfctx;

619:   A->ops->mult           = MatMult_MFFD;
620:   A->ops->destroy        = MatDestroy_MFFD;
621:   A->ops->view           = MatView_MFFD;
622:   A->ops->assemblyend    = MatAssemblyEnd_MFFD;
623:   A->ops->getdiagonal    = MatGetDiagonal_MFFD;
624:   A->ops->scale          = MatScale_MFFD;
625:   A->ops->shift          = MatShift_MFFD;
626:   A->ops->setfromoptions = MatMFFDSetFromOptions;
627:   A->assembled = PETSC_TRUE;

629:   PetscLayoutSetBlockSize(A->rmap,1);
630:   PetscLayoutSetBlockSize(A->cmap,1);
631:   PetscLayoutSetUp(A->rmap);
632:   PetscLayoutSetUp(A->cmap);

634:   PetscObjectComposeFunctionDynamic((PetscObject)A,"MatMFFDSetBase_C","MatMFFDSetBase_MFFD",MatMFFDSetBase_MFFD);
635:   PetscObjectComposeFunctionDynamic((PetscObject)A,"MatMFFDSetFunctioniBase_C","MatMFFDSetFunctioniBase_MFFD",MatMFFDSetFunctioniBase_MFFD);
636:   PetscObjectComposeFunctionDynamic((PetscObject)A,"MatMFFDSetFunctioni_C","MatMFFDSetFunctioni_MFFD",MatMFFDSetFunctioni_MFFD);
637:   PetscObjectComposeFunctionDynamic((PetscObject)A,"MatMFFDSetCheckh_C","MatMFFDSetCheckh_MFFD",MatMFFDSetCheckh_MFFD);
638:   mfctx->mat = A;
639:   PetscObjectChangeTypeName((PetscObject)A,MATMFFD);
640:   return(0);
641: }

646: /*@
647:    MatCreateMFFD - Creates a matrix-free matrix. See also MatCreateSNESMF() 

649:    Collective on Vec

651:    Input Parameters:
652: +  comm - MPI communicator
653: .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
654:            This value should be the same as the local size used in creating the 
655:            y vector for the matrix-vector product y = Ax.
656: .  n - This value should be the same as the local size used in creating the 
657:        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
658:        calculated if N is given) For square matrices n is almost always m.
659: .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
660: -  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)


663:    Output Parameter:
664: .  J - the matrix-free matrix

666:    Level: advanced

668:    Notes:
669:    The matrix-free matrix context merely contains the function pointers
670:    and work space for performing finite difference approximations of
671:    Jacobian-vector products, F'(u)*a, 

673:    The default code uses the following approach to compute h

675: .vb
676:      F'(u)*a = [F(u+h*a) - F(u)]/h where
677:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
678:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
679:  where
680:      error_rel = square root of relative error in function evaluation
681:      umin = minimum iterate parameter
682: .ve

684:    The user can set the error_rel via MatMFFDSetFunctionError() and 
685:    umin via MatMFFDDSSetUmin(); see the nonlinear solvers chapter
686:    of the users manual for details.

688:    The user should call MatDestroy() when finished with the matrix-free
689:    matrix context.

691:    Options Database Keys:
692: +  -mat_mffd_err <error_rel> - Sets error_rel
693: .  -mat_mffd_unim <umin> - Sets umin (for default PETSc routine that computes h only)
694: -  -mat_mffd_check_positivity

696: .keywords: default, matrix-free, create, matrix

698: .seealso: MatDestroy(), MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
699:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(), 
700:           MatMFFDGetH(), MatMFFDRegisterDynamic), MatMFFDComputeJacobian()
701:  
702: @*/
703: PetscErrorCode  MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)
704: {

708:   MatCreate(comm,J);
709:   MatSetSizes(*J,m,n,M,N);
710:   MatSetType(*J,MATMFFD);
711:   return(0);
712: }


717: /*@
718:    MatMFFDGetH - Gets the last value that was used as the differencing 
719:    parameter.

721:    Not Collective

723:    Input Parameters:
724: .  mat - the matrix obtained with MatCreateSNESMF()

726:    Output Paramter:
727: .  h - the differencing step size

729:    Level: advanced

731: .keywords: SNES, matrix-free, parameters

733: .seealso: MatCreateSNESMF(),MatMFFDSetHHistory(), MatCreateMFFD(), MATMFFD, MatMFFDResetHHistory()
734: @*/
735: PetscErrorCode  MatMFFDGetH(Mat mat,PetscScalar *h)
736: {
737:   MatMFFD ctx = (MatMFFD)mat->data;

740:   *h = ctx->currenth;
741:   return(0);
742: }


747: /*@C
748:    MatMFFDSetFunction - Sets the function used in applying the matrix free.

750:    Collective on Mat

752:    Input Parameters:
753: +  mat - the matrix free matrix created via MatCreateSNESMF()
754: .  func - the function to use
755: -  funcctx - optional function context passed to function

757:    Level: advanced

759:    Notes:
760:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
761:     matrix inside your compute Jacobian routine

763:     If this is not set then it will use the function set with SNESSetFunction() if MatCreateSNESMF() was used.

765: .keywords: SNES, matrix-free, function

767: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD,
768:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
769: @*/
770: PetscErrorCode  MatMFFDSetFunction(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
771: {
772:   MatMFFD ctx = (MatMFFD)mat->data;

775:   ctx->func    = func;
776:   ctx->funcctx = funcctx;
777:   return(0);
778: }

782: /*@C
783:    MatMFFDSetFunctioni - Sets the function for a single component

785:    Collective on Mat

787:    Input Parameters:
788: +  mat - the matrix free matrix created via MatCreateSNESMF()
789: -  funci - the function to use

791:    Level: advanced

793:    Notes:
794:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
795:     matrix inside your compute Jacobian routine


798: .keywords: SNES, matrix-free, function

800: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()

802: @*/
803: PetscErrorCode  MatMFFDSetFunctioni(Mat mat,PetscErrorCode (*funci)(void*,PetscInt,Vec,PetscScalar*))
804: {
805:   PetscErrorCode ierr,(*f)(Mat,PetscErrorCode (*)(void*,PetscInt,Vec,PetscScalar*));

809:   PetscObjectQueryFunction((PetscObject)mat,"MatMFFDSetFunctioni_C",(void (**)(void))&f);
810:   if (f) {
811:     (*f)(mat,funci);
812:   }
813:   return(0);
814: }


819: /*@C
820:    MatMFFDSetFunctioniBase - Sets the base vector for a single component function evaluation

822:    Collective on Mat

824:    Input Parameters:
825: +  mat - the matrix free matrix created via MatCreateSNESMF()
826: -  func - the function to use

828:    Level: advanced

830:    Notes:
831:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
832:     matrix inside your compute Jacobian routine


835: .keywords: SNES, matrix-free, function

837: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
838:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
839: @*/
840: PetscErrorCode  MatMFFDSetFunctioniBase(Mat mat,PetscErrorCode (*func)(void*,Vec))
841: {
842:   PetscErrorCode ierr,(*f)(Mat,PetscErrorCode (*)(void*,Vec));

846:   PetscObjectQueryFunction((PetscObject)mat,"MatMFFDSetFunctioniBase_C",(void (**)(void))&f);
847:   if (f) {
848:     (*f)(mat,func);
849:   }
850:   return(0);
851: }


856: /*@
857:    MatMFFDSetPeriod - Sets how often h is recomputed, by default it is everytime

859:    Collective on Mat

861:    Input Parameters:
862: +  mat - the matrix free matrix created via MatCreateSNESMF()
863: -  period - 1 for everytime, 2 for every second etc

865:    Options Database Keys:
866: +  -mat_mffd_period <period>

868:    Level: advanced


871: .keywords: SNES, matrix-free, parameters

873: .seealso: MatCreateSNESMF(),MatMFFDGetH(),
874:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
875: @*/
876: PetscErrorCode  MatMFFDSetPeriod(Mat mat,PetscInt period)
877: {
878:   MatMFFD ctx = (MatMFFD)mat->data;

881:   ctx->recomputeperiod = period;
882:   return(0);
883: }

887: /*@
888:    MatMFFDSetFunctionError - Sets the error_rel for the approximation of
889:    matrix-vector products using finite differences.

891:    Collective on Mat

893:    Input Parameters:
894: +  mat - the matrix free matrix created via MatCreateMFFD() or MatCreateSNESMF()
895: -  error_rel - relative error (should be set to the square root of
896:                the relative error in the function evaluations)

898:    Options Database Keys:
899: +  -mat_mffd_err <error_rel> - Sets error_rel

901:    Level: advanced

903:    Notes:
904:    The default matrix-free matrix-vector product routine computes
905: .vb
906:      F'(u)*a = [F(u+h*a) - F(u)]/h where
907:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
908:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
909: .ve

911: .keywords: SNES, matrix-free, parameters

913: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
914:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
915: @*/
916: PetscErrorCode  MatMFFDSetFunctionError(Mat mat,PetscReal error)
917: {
918:   MatMFFD ctx = (MatMFFD)mat->data;

921:   if (error != PETSC_DEFAULT) ctx->error_rel = error;
922:   return(0);
923: }

927: /*@
928:    MatMFFDAddNullSpace - Provides a null space that an operator is
929:    supposed to have.  Since roundoff will create a small component in
930:    the null space, if you know the null space you may have it
931:    automatically removed.

933:    Collective on Mat 

935:    Input Parameters:
936: +  J - the matrix-free matrix context
937: -  nullsp - object created with MatNullSpaceCreate()

939:    Level: advanced

941: .keywords: SNES, matrix-free, null space

943: .seealso: MatNullSpaceCreate(), MatMFFDGetH(), MatCreateSNESMF(), MatCreateMFFD(), MATMFFD
944:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
945: @*/
946: PetscErrorCode  MatMFFDAddNullSpace(Mat J,MatNullSpace nullsp)
947: {
949:   MatMFFD      ctx = (MatMFFD)J->data;

952:   PetscObjectReference((PetscObject)nullsp);
953:   if (ctx->sp) { MatNullSpaceDestroy(ctx->sp); }
954:   ctx->sp = nullsp;
955:   return(0);
956: }

960: /*@
961:    MatMFFDSetHHistory - Sets an array to collect a history of the
962:    differencing values (h) computed for the matrix-free product.

964:    Collective on Mat 

966:    Input Parameters:
967: +  J - the matrix-free matrix context
968: .  histroy - space to hold the history
969: -  nhistory - number of entries in history, if more entries are generated than
970:               nhistory, then the later ones are discarded

972:    Level: advanced

974:    Notes:
975:    Use MatMFFDResetHHistory() to reset the history counter and collect
976:    a new batch of differencing parameters, h.

978: .keywords: SNES, matrix-free, h history, differencing history

980: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
981:           MatMFFDResetHHistory(), MatMFFDSetFunctionError()

983: @*/
984: PetscErrorCode  MatMFFDSetHHistory(Mat J,PetscScalar history[],PetscInt nhistory)
985: {
986:   MatMFFD ctx = (MatMFFD)J->data;

989:   ctx->historyh    = history;
990:   ctx->maxcurrenth = nhistory;
991:   ctx->currenth    = 0.;
992:   return(0);
993: }

997: /*@
998:    MatMFFDResetHHistory - Resets the counter to zero to begin 
999:    collecting a new set of differencing histories.

1001:    Collective on Mat 

1003:    Input Parameters:
1004: .  J - the matrix-free matrix context

1006:    Level: advanced

1008:    Notes:
1009:    Use MatMFFDSetHHistory() to create the original history counter.

1011: .keywords: SNES, matrix-free, h history, differencing history

1013: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1014:           MatMFFDSetHHistory(), MatMFFDSetFunctionError()

1016: @*/
1017: PetscErrorCode  MatMFFDResetHHistory(Mat J)
1018: {
1019:   MatMFFD ctx = (MatMFFD)J->data;

1022:   ctx->ncurrenth    = 0;
1023:   return(0);
1024: }


1029: /*@
1030:     MatMFFDSetBase - Sets the vector U at which matrix vector products of the 
1031:         Jacobian are computed

1033:     Collective on Mat

1035:     Input Parameters:
1036: +   J - the MatMFFD matrix
1037: .   U - the vector
1038: -   F - (optional) vector that contains F(u) if it has been already computed

1040:     Notes: This is rarely used directly

1042:     If F is provided then it is not recomputed. Otherwise the function is evaluated at the base
1043:     point during the first MatMult() after each call to MatMFFDSetBase().

1045:     Level: advanced

1047: @*/
1048: PetscErrorCode  MatMFFDSetBase(Mat J,Vec U,Vec F)
1049: {
1050:   PetscErrorCode ierr,(*f)(Mat,Vec,Vec);

1056:   PetscObjectQueryFunction((PetscObject)J,"MatMFFDSetBase_C",(void (**)(void))&f);
1057:   if (f) {
1058:     (*f)(J,U,F);
1059:   }
1060:   return(0);
1061: }

1065: /*@C
1066:     MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
1067:         it to satisfy some criteria

1069:     Collective on Mat

1071:     Input Parameters:
1072: +   J - the MatMFFD matrix
1073: .   fun - the function that checks h
1074: -   ctx - any context needed by the function

1076:     Options Database Keys:
1077: .   -mat_mffd_check_positivity

1079:     Level: advanced

1081:     Notes: For example, MatMFFDSetCheckPositivity() insures that all entries
1082:        of U + h*a are non-negative

1084: .seealso:  MatMFFDSetCheckPositivity()
1085: @*/
1086: PetscErrorCode  MatMFFDSetCheckh(Mat J,PetscErrorCode (*fun)(void*,Vec,Vec,PetscScalar*),void* ctx)
1087: {
1088:   PetscErrorCode ierr,(*f)(Mat,PetscErrorCode (*)(void*,Vec,Vec,PetscScalar*),void*);

1092:   PetscObjectQueryFunction((PetscObject)J,"MatMFFDSetCheckh_C",(void (**)(void))&f);
1093:   if (f) {
1094:     (*f)(J,fun,ctx);
1095:   }
1096:   return(0);
1097: }

1101: /*@
1102:     MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
1103:         zero, decreases h until this is satisfied.

1105:     Collective on Vec

1107:     Input Parameters:
1108: +   U - base vector that is added to
1109: .   a - vector that is added
1110: .   h - scaling factor on a
1111: -   dummy - context variable (unused)

1113:     Options Database Keys:
1114: .   -mat_mffd_check_positivity

1116:     Level: advanced

1118:     Notes: This is rarely used directly, rather it is passed as an argument to 
1119:            MatMFFDSetCheckh()

1121: .seealso:  MatMFFDSetCheckh()
1122: @*/
1123: PetscErrorCode  MatMFFDCheckPositivity(void* dummy,Vec U,Vec a,PetscScalar *h)
1124: {
1125:   PetscReal      val, minval;
1126:   PetscScalar    *u_vec, *a_vec;
1128:   PetscInt       i,n;
1129:   MPI_Comm       comm;

1132:   PetscObjectGetComm((PetscObject)U,&comm);
1133:   VecGetArray(U,&u_vec);
1134:   VecGetArray(a,&a_vec);
1135:   VecGetLocalSize(U,&n);
1136:   minval = PetscAbsScalar(*h*1.01);
1137:   for(i=0;i<n;i++) {
1138:     if (PetscRealPart(u_vec[i] + *h*a_vec[i]) <= 0.0) {
1139:       val = PetscAbsScalar(u_vec[i]/a_vec[i]);
1140:       if (val < minval) minval = val;
1141:     }
1142:   }
1143:   VecRestoreArray(U,&u_vec);
1144:   VecRestoreArray(a,&a_vec);
1145:   PetscGlobalMin(&minval,&val,comm);
1146:   if (val <= PetscAbsScalar(*h)) {
1147:     PetscInfo2(U,"Scaling back h from %G to %G\n",PetscRealPart(*h),.99*val);
1148:     if (PetscRealPart(*h) > 0.0) *h =  0.99*val;
1149:     else                         *h = -0.99*val;
1150:   }
1151:   return(0);
1152: }