Actual source code: mffd.c

petsc-3.4.4 2014-03-13
  2: #include <petsc-private/matimpl.h>
  3: #include <../src/mat/impls/mffd/mffdimpl.h>   /*I  "petscmat.h"   I*/

  5: PetscFunctionList MatMFFDList              = 0;
  6: PetscBool         MatMFFDRegisterAllCalled = PETSC_FALSE;

  8: PetscClassId  MATMFFD_CLASSID;
  9: PetscLogEvent MATMFFD_Mult;

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

 18:   Level: developer

 20: .keywords: Petsc, destroy, package
 21: .seealso: PetscFinalize()
 22: @*/
 23: PetscErrorCode  MatMFFDFinalizePackage(void)
 24: {

 28:   PetscFunctionListDestroy(&MatMFFDList);
 29:   MatMFFDPackageInitialized = PETSC_FALSE;
 30:   MatMFFDRegisterAllCalled  = PETSC_FALSE;
 31:   return(0);
 32: }

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

 41:   Level: developer

 43: .keywords: Vec, initialize, package
 44: .seealso: PetscInitialize()
 45: @*/
 46: PetscErrorCode  MatMFFDInitializePackage(void)
 47: {
 48:   char           logList[256];
 49:   char           *className;
 50:   PetscBool      opt;

 54:   if (MatMFFDPackageInitialized) return(0);
 55:   MatMFFDPackageInitialized = PETSC_TRUE;
 56:   /* Register Classes */
 57:   PetscClassIdRegister("MatMFFD",&MATMFFD_CLASSID);
 58:   /* Register Constructors */
 59:   MatMFFDRegisterAll();
 60:   /* Register Events */
 61:   PetscLogEventRegister("MatMult MF",          MATMFFD_CLASSID,&MATMFFD_Mult);

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

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

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

 94:     Level: advanced

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

100:                         F(x+ha) - F(x)
101:           F'(u)a  ~=  ----------------
102:                               h

104: .seealso: MatCreateSNESMF(), MatMFFDRegister(), MatMFFDSetFunction()
105: @*/
106: PetscErrorCode  MatMFFDSetType(Mat mat,MatMFFDType ftype)
107: {
108:   PetscErrorCode ierr,(*r)(MatMFFD);
109:   MatMFFD        ctx = (MatMFFD)mat->data;
110:   PetscBool      match;


116:   PetscObjectTypeCompare((PetscObject)mat,MATMFFD,&match);
117:   if (!match) return(0);

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

123:   /* destroy the old one if it exists */
124:   if (ctx->ops->destroy) {
125:     (*ctx->ops->destroy)(ctx);
126:   }

128:    PetscFunctionListFind(MatMFFDList,ftype,&r);
129:   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown MatMFFD type %s given",ftype);
130:   (*r)(ctx);
131:   PetscObjectChangeTypeName((PetscObject)ctx,ftype);
132:   return(0);
133: }

135: typedef PetscErrorCode (*FCN1)(void*,Vec); /* force argument to next function to not be extern C*/
138: PetscErrorCode  MatMFFDSetFunctioniBase_MFFD(Mat mat,FCN1 func)
139: {
140:   MatMFFD ctx = (MatMFFD)mat->data;

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

147: typedef PetscErrorCode (*FCN2)(void*,PetscInt,Vec,PetscScalar*); /* force argument to next function to not be extern C*/
150: PetscErrorCode  MatMFFDSetFunctioni_MFFD(Mat mat,FCN2 funci)
151: {
152:   MatMFFD ctx = (MatMFFD)mat->data;

155:   ctx->funci = funci;
156:   return(0);
157: }

161: PetscErrorCode  MatMFFDResetHHistory_MFFD(Mat J)
162: {
163:   MatMFFD ctx = (MatMFFD)J->data;

166:   ctx->ncurrenth = 0;
167:   return(0);
168: }

172: /*@C
173:    MatMFFDRegister - Adds a method to the MatMFFD registry.

175:    Not Collective

177:    Input Parameters:
178: +  name_solver - name of a new user-defined compute-h module
179: -  routine_create - routine to create method context

181:    Level: developer

183:    Notes:
184:    MatMFFDRegister() may be called multiple times to add several user-defined solvers.

186:    Sample usage:
187: .vb
188:    MatMFFDRegister("my_h",MyHCreate);
189: .ve

191:    Then, your solver can be chosen with the procedural interface via
192: $     MatMFFDSetType(mfctx,"my_h")
193:    or at runtime via the option
194: $     -snes_mf_type my_h

196: .keywords: MatMFFD, register

198: .seealso: MatMFFDRegisterAll(), MatMFFDRegisterDestroy()
199:  @*/
200: PetscErrorCode  MatMFFDRegister(const char sname[],PetscErrorCode (*function)(MatMFFD))
201: {

205:   PetscFunctionListAdd(&MatMFFDList,sname,function);
206:   return(0);
207: }

211: PetscErrorCode  MatMFFDAddNullSpace_MFFD(Mat J,MatNullSpace nullsp)
212: {
214:   MatMFFD        ctx = (MatMFFD)J->data;

217:   PetscObjectReference((PetscObject)nullsp);
218:   if (ctx->sp) { MatNullSpaceDestroy(&ctx->sp); }
219:   ctx->sp = nullsp;
220:   return(0);
221: }

223: /* ----------------------------------------------------------------------------------------*/
226: PetscErrorCode MatDestroy_MFFD(Mat mat)
227: {
229:   MatMFFD        ctx = (MatMFFD)mat->data;

232:   VecDestroy(&ctx->w);
233:   VecDestroy(&ctx->drscale);
234:   VecDestroy(&ctx->dlscale);
235:   VecDestroy(&ctx->dshift);
236:   if (ctx->current_f_allocated) {
237:     VecDestroy(&ctx->current_f);
238:   }
239:   if (ctx->ops->destroy) {(*ctx->ops->destroy)(ctx);}
240:   MatNullSpaceDestroy(&ctx->sp);
241:   PetscHeaderDestroy(&ctx);
242:   mat->data = 0;

244:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetBase_C",NULL);
245:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioniBase_C",NULL);
246:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioni_C",NULL);
247:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunction_C",NULL);
248:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctionError_C",NULL);
249:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetCheckh_C",NULL);
250:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetPeriod_C",NULL);
251:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDResetHHistory_C",NULL);
252:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDAddNullSpace_C",NULL);
253:   return(0);
254: }

258: /*
259:    MatMFFDView_MFFD - Views matrix-free parameters.

261: */
262: PetscErrorCode MatView_MFFD(Mat J,PetscViewer viewer)
263: {
265:   MatMFFD        ctx = (MatMFFD)J->data;
266:   PetscBool      iascii, viewbase, viewfunction;
267:   const char     *prefix;

270:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
271:   if (iascii) {
272:     PetscViewerASCIIPrintf(viewer,"Matrix-free approximation:\n");
273:     PetscViewerASCIIPushTab(viewer);
274:     PetscViewerASCIIPrintf(viewer,"err=%G (relative error in function evaluation)\n",ctx->error_rel);
275:     if (!((PetscObject)ctx)->type_name) {
276:       PetscViewerASCIIPrintf(viewer,"The compute h routine has not yet been set\n");
277:     } else {
278:       PetscViewerASCIIPrintf(viewer,"Using %s compute h routine\n",((PetscObject)ctx)->type_name);
279:     }
280:     if (ctx->ops->view) {
281:       (*ctx->ops->view)(ctx,viewer);
282:     }
283:     PetscObjectGetOptionsPrefix((PetscObject)J, &prefix);

285:     PetscOptionsHasName(prefix, "-mat_mffd_view_base", &viewbase);
286:     if (viewbase) {
287:       PetscViewerASCIIPrintf(viewer, "Base:\n");
288:       VecView(ctx->current_u, viewer);
289:     }
290:     PetscOptionsHasName(prefix, "-mat_mffd_view_function", &viewfunction);
291:     if (viewfunction) {
292:       PetscViewerASCIIPrintf(viewer, "Function:\n");
293:       VecView(ctx->current_f, viewer);
294:     }
295:     PetscViewerASCIIPopTab(viewer);
296:   }
297:   return(0);
298: }

302: /*
303:    MatAssemblyEnd_MFFD - Resets the ctx->ncurrenth to zero. This
304:    allows the user to indicate the beginning of a new linear solve by calling
305:    MatAssemblyXXX() on the matrix free matrix. This then allows the
306:    MatCreateMFFD_WP() to properly compute ||U|| only the first time
307:    in the linear solver rather than every time.

309:    This function is referenced directly from MatAssemblyEnd_SNESMF(), which may be in a different shared library.
310: */
311: PETSC_EXTERN PetscErrorCode MatAssemblyEnd_MFFD(Mat J,MatAssemblyType mt)
312: {
314:   MatMFFD        j = (MatMFFD)J->data;

317:   MatMFFDResetHHistory(J);
318:   j->vshift = 0.0;
319:   j->vscale = 1.0;
320:   return(0);
321: }

325: /*
326:   MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:

328:         y ~= (F(u + ha) - F(u))/h,
329:   where F = nonlinear function, as set by SNESSetFunction()
330:         u = current iterate
331:         h = difference interval
332: */
333: PetscErrorCode MatMult_MFFD(Mat mat,Vec a,Vec y)
334: {
335:   MatMFFD        ctx = (MatMFFD)mat->data;
336:   PetscScalar    h;
337:   Vec            w,U,F;
339:   PetscBool      zeroa;

342:   if (!ctx->current_u) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatMFFDSetBase() has not been called, this is often caused by forgetting to call \n\t\tMatAssemblyBegin/End on the first Mat in the SNES compute function");
343:   /* We log matrix-free matrix-vector products separately, so that we can
344:      separate the performance monitoring from the cases that use conventional
345:      storage.  We may eventually modify event logging to associate events
346:      with particular objects, hence alleviating the more general problem. */
347:   PetscLogEventBegin(MATMFFD_Mult,a,y,0,0);

349:   w = ctx->w;
350:   U = ctx->current_u;
351:   F = ctx->current_f;
352:   /*
353:       Compute differencing parameter
354:   */
355:   if (!ctx->ops->compute) {
356:     MatMFFDSetType(mat,MATMFFD_WP);
357:     MatSetFromOptions(mat);
358:   }
359:   (*ctx->ops->compute)(ctx,U,a,&h,&zeroa);
360:   if (zeroa) {
361:     VecSet(y,0.0);
362:     return(0);
363:   }

365:   if (PetscIsInfOrNanScalar(h)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed Nan differencing parameter h");
366:   if (ctx->checkh) {
367:     (*ctx->checkh)(ctx->checkhctx,U,a,&h);
368:   }

370:   /* keep a record of the current differencing parameter h */
371:   ctx->currenth = h;
372: #if defined(PETSC_USE_COMPLEX)
373:   PetscInfo2(mat,"Current differencing parameter: %G + %G i\n",PetscRealPart(h),PetscImaginaryPart(h));
374: #else
375:   PetscInfo1(mat,"Current differencing parameter: %15.12e\n",h);
376: #endif
377:   if (ctx->historyh && ctx->ncurrenth < ctx->maxcurrenth) {
378:     ctx->historyh[ctx->ncurrenth] = h;
379:   }
380:   ctx->ncurrenth++;

382:   /* w = u + ha */
383:   if (ctx->drscale) {
384:     VecPointwiseMult(ctx->drscale,a,U);
385:     VecAYPX(U,h,w);
386:   } else {
387:     VecWAXPY(w,h,a,U);
388:   }

390:   /* compute func(U) as base for differencing; only needed first time in and not when provided by user */
391:   if (ctx->ncurrenth == 1 && ctx->current_f_allocated) {
392:     (*ctx->func)(ctx->funcctx,U,F);
393:   }
394:   (*ctx->func)(ctx->funcctx,w,y);

396:   VecAXPY(y,-1.0,F);
397:   VecScale(y,1.0/h);

399:   if ((ctx->vshift != 0.0) || (ctx->vscale != 1.0)) {
400:     VecAXPBY(y,ctx->vshift,ctx->vscale,a);
401:   }
402:   if (ctx->dlscale) {
403:     VecPointwiseMult(y,ctx->dlscale,y);
404:   }
405:   if (ctx->dshift) {
406:     VecPointwiseMult(ctx->dshift,a,U);
407:     VecAXPY(y,1.0,U);
408:   }

410:   if (ctx->sp) {MatNullSpaceRemove(ctx->sp,y,NULL);}

412:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
413:   return(0);
414: }

418: /*
419:   MatGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix

421:         y ~= (F(u + ha) - F(u))/h,
422:   where F = nonlinear function, as set by SNESSetFunction()
423:         u = current iterate
424:         h = difference interval
425: */
426: PetscErrorCode MatGetDiagonal_MFFD(Mat mat,Vec a)
427: {
428:   MatMFFD        ctx = (MatMFFD)mat->data;
429:   PetscScalar    h,*aa,*ww,v;
430:   PetscReal      epsilon = PETSC_SQRT_MACHINE_EPSILON,umin = 100.0*PETSC_SQRT_MACHINE_EPSILON;
431:   Vec            w,U;
433:   PetscInt       i,rstart,rend;

436:   if (!ctx->funci) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Requires calling MatMFFDSetFunctioni() first");

438:   w    = ctx->w;
439:   U    = ctx->current_u;
440:   (*ctx->func)(ctx->funcctx,U,a);
441:   (*ctx->funcisetbase)(ctx->funcctx,U);
442:   VecCopy(U,w);

444:   VecGetOwnershipRange(a,&rstart,&rend);
445:   VecGetArray(a,&aa);
446:   for (i=rstart; i<rend; i++) {
447:     VecGetArray(w,&ww);
448:     h    = ww[i-rstart];
449:     if (h == 0.0) h = 1.0;
450:     if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0)     h = umin;
451:     else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
452:     h *= epsilon;

454:     ww[i-rstart] += h;
455:     VecRestoreArray(w,&ww);
456:     (*ctx->funci)(ctx->funcctx,i,w,&v);
457:     aa[i-rstart]  = (v - aa[i-rstart])/h;

459:     /* possibly shift and scale result */
460:     if ((ctx->vshift != 0.0) || (ctx->vscale != 1.0)) {
461:       aa[i - rstart] = ctx->vshift + ctx->vscale*aa[i-rstart];
462:     }

464:     VecGetArray(w,&ww);
465:     ww[i-rstart] -= h;
466:     VecRestoreArray(w,&ww);
467:   }
468:   VecRestoreArray(a,&aa);
469:   return(0);
470: }

474: PetscErrorCode MatDiagonalScale_MFFD(Mat mat,Vec ll,Vec rr)
475: {
476:   MatMFFD        aij = (MatMFFD)mat->data;

480:   if (ll && !aij->dlscale) {
481:     VecDuplicate(ll,&aij->dlscale);
482:   }
483:   if (rr && !aij->drscale) {
484:     VecDuplicate(rr,&aij->drscale);
485:   }
486:   if (ll) {
487:     VecCopy(ll,aij->dlscale);
488:   }
489:   if (rr) {
490:     VecCopy(rr,aij->drscale);
491:   }
492:   return(0);
493: }

497: PetscErrorCode MatDiagonalSet_MFFD(Mat mat,Vec ll,InsertMode mode)
498: {
499:   MatMFFD        aij = (MatMFFD)mat->data;

503:   if (mode == INSERT_VALUES) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No diagonal set with INSERT_VALUES");
504:   if (!aij->dshift) {
505:     VecDuplicate(ll,&aij->dshift);
506:   }
507:   VecAXPY(aij->dshift,1.0,ll);
508:   return(0);
509: }

513: PetscErrorCode MatShift_MFFD(Mat Y,PetscScalar a)
514: {
515:   MatMFFD shell = (MatMFFD)Y->data;

518:   shell->vshift += a;
519:   return(0);
520: }

524: PetscErrorCode MatScale_MFFD(Mat Y,PetscScalar a)
525: {
526:   MatMFFD shell = (MatMFFD)Y->data;

529:   shell->vscale *= a;
530:   return(0);
531: }

535: PETSC_EXTERN PetscErrorCode MatMFFDSetBase_MFFD(Mat J,Vec U,Vec F)
536: {
538:   MatMFFD        ctx = (MatMFFD)J->data;

541:   MatMFFDResetHHistory(J);

543:   ctx->current_u = U;
544:   if (F) {
545:     if (ctx->current_f_allocated) {VecDestroy(&ctx->current_f);}
546:     ctx->current_f           = F;
547:     ctx->current_f_allocated = PETSC_FALSE;
548:   } else if (!ctx->current_f_allocated) {
549:     VecDuplicate(ctx->current_u, &ctx->current_f);

551:     ctx->current_f_allocated = PETSC_TRUE;
552:   }
553:   if (!ctx->w) {
554:     VecDuplicate(ctx->current_u, &ctx->w);
555:   }
556:   J->assembled = PETSC_TRUE;
557:   return(0);
558: }

560: typedef PetscErrorCode (*FCN3)(void*,Vec,Vec,PetscScalar*); /* force argument to next function to not be extern C*/

564: PetscErrorCode  MatMFFDSetCheckh_MFFD(Mat J,FCN3 fun,void *ectx)
565: {
566:   MatMFFD ctx = (MatMFFD)J->data;

569:   ctx->checkh    = fun;
570:   ctx->checkhctx = ectx;
571:   return(0);
572: }

576: /*@C
577:    MatMFFDSetOptionsPrefix - Sets the prefix used for searching for all
578:    MatMFFD options in the database.

580:    Collective on Mat

582:    Input Parameter:
583: +  A - the Mat context
584: -  prefix - the prefix to prepend to all option names

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

590:    Level: advanced

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

594: .seealso: MatSetFromOptions(), MatCreateSNESMF()
595: @*/
596: PetscErrorCode  MatMFFDSetOptionsPrefix(Mat mat,const char prefix[])

598: {
599:   MatMFFD        mfctx = mat ? (MatMFFD)mat->data : (MatMFFD)NULL;

605:   PetscObjectSetOptionsPrefix((PetscObject)mfctx,prefix);
606:   return(0);
607: }

611: PetscErrorCode  MatSetFromOptions_MFFD(Mat mat)
612: {
613:   MatMFFD        mfctx = (MatMFFD)mat->data;
615:   PetscBool      flg;
616:   char           ftype[256];

621:   PetscObjectOptionsBegin((PetscObject)mfctx);
622:   PetscOptionsList("-mat_mffd_type","Matrix free type","MatMFFDSetType",MatMFFDList,((PetscObject)mfctx)->type_name,ftype,256,&flg);
623:   if (flg) {
624:     MatMFFDSetType(mat,ftype);
625:   }

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

630:   flg  = PETSC_FALSE;
631:   PetscOptionsBool("-mat_mffd_check_positivity","Insure that U + h*a is nonnegative","MatMFFDSetCheckh",flg,&flg,NULL);
632:   if (flg) {
633:     MatMFFDSetCheckh(mat,MatMFFDCheckPositivity,0);
634:   }
635:   if (mfctx->ops->setfromoptions) {
636:     (*mfctx->ops->setfromoptions)(mfctx);
637:   }
638:   PetscOptionsEnd();
639:   return(0);
640: }

644: PetscErrorCode  MatMFFDSetPeriod_MFFD(Mat mat,PetscInt period)
645: {
646:   MatMFFD ctx = (MatMFFD)mat->data;

650:   ctx->recomputeperiod = period;
651:   return(0);
652: }

656: PetscErrorCode  MatMFFDSetFunction_MFFD(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
657: {
658:   MatMFFD ctx = (MatMFFD)mat->data;

661:   ctx->func    = func;
662:   ctx->funcctx = funcctx;
663:   return(0);
664: }

668: PetscErrorCode  MatMFFDSetFunctionError_MFFD(Mat mat,PetscReal error)
669: {
670:   MatMFFD ctx = (MatMFFD)mat->data;

674:   if (error != PETSC_DEFAULT) ctx->error_rel = error;
675:   return(0);
676: }

678: /*MC
679:   MATMFFD - MATMFFD = "mffd" - A matrix free matrix type.

681:   Level: advanced

683: .seealso: MatCreateMFFD(), MatCreateSNESMF(), MatMFFDSetFunction()
684: M*/
687: PETSC_EXTERN PetscErrorCode MatCreate_MFFD(Mat A)
688: {
689:   MatMFFD        mfctx;

693: #if !defined(PETSC_USE_DYNAMIC_LIBRARIES)
694:   MatMFFDInitializePackage();
695: #endif

697:   PetscHeaderCreate(mfctx,_p_MatMFFD,struct _MFOps,MATMFFD_CLASSID,"MatMFFD","Matrix-free Finite Differencing","Mat",PetscObjectComm((PetscObject)A),MatDestroy_MFFD,MatView_MFFD);

699:   mfctx->sp                       = 0;
700:   mfctx->error_rel                = PETSC_SQRT_MACHINE_EPSILON;
701:   mfctx->recomputeperiod          = 1;
702:   mfctx->count                    = 0;
703:   mfctx->currenth                 = 0.0;
704:   mfctx->historyh                 = NULL;
705:   mfctx->ncurrenth                = 0;
706:   mfctx->maxcurrenth              = 0;
707:   ((PetscObject)mfctx)->type_name = 0;

709:   mfctx->vshift = 0.0;
710:   mfctx->vscale = 1.0;

712:   /*
713:      Create the empty data structure to contain compute-h routines.
714:      These will be filled in below from the command line options or
715:      a later call with MatMFFDSetType() or if that is not called
716:      then it will default in the first use of MatMult_MFFD()
717:   */
718:   mfctx->ops->compute        = 0;
719:   mfctx->ops->destroy        = 0;
720:   mfctx->ops->view           = 0;
721:   mfctx->ops->setfromoptions = 0;
722:   mfctx->hctx                = 0;

724:   mfctx->func    = 0;
725:   mfctx->funcctx = 0;
726:   mfctx->w       = NULL;

728:   A->data = mfctx;

730:   A->ops->mult           = MatMult_MFFD;
731:   A->ops->destroy        = MatDestroy_MFFD;
732:   A->ops->view           = MatView_MFFD;
733:   A->ops->assemblyend    = MatAssemblyEnd_MFFD;
734:   A->ops->getdiagonal    = MatGetDiagonal_MFFD;
735:   A->ops->scale          = MatScale_MFFD;
736:   A->ops->shift          = MatShift_MFFD;
737:   A->ops->diagonalscale  = MatDiagonalScale_MFFD;
738:   A->ops->diagonalset    = MatDiagonalSet_MFFD;
739:   A->ops->setfromoptions = MatSetFromOptions_MFFD;
740:   A->assembled           = PETSC_TRUE;

742:   PetscLayoutSetUp(A->rmap);
743:   PetscLayoutSetUp(A->cmap);

745:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetBase_C",MatMFFDSetBase_MFFD);
746:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioniBase_C",MatMFFDSetFunctioniBase_MFFD);
747:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioni_C",MatMFFDSetFunctioni_MFFD);
748:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunction_C",MatMFFDSetFunction_MFFD);
749:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetCheckh_C",MatMFFDSetCheckh_MFFD);
750:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetPeriod_C",MatMFFDSetPeriod_MFFD);
751:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctionError_C",MatMFFDSetFunctionError_MFFD);
752:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDResetHHistory_C",MatMFFDResetHHistory_MFFD);
753:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDAddNullSpace_C",MatMFFDAddNullSpace_MFFD);

755:   mfctx->mat = A;

757:   PetscObjectChangeTypeName((PetscObject)A,MATMFFD);
758:   return(0);
759: }

763: /*@
764:    MatCreateMFFD - Creates a matrix-free matrix. See also MatCreateSNESMF()

766:    Collective on Vec

768:    Input Parameters:
769: +  comm - MPI communicator
770: .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
771:            This value should be the same as the local size used in creating the
772:            y vector for the matrix-vector product y = Ax.
773: .  n - This value should be the same as the local size used in creating the
774:        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
775:        calculated if N is given) For square matrices n is almost always m.
776: .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
777: -  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)


780:    Output Parameter:
781: .  J - the matrix-free matrix

783:    Options Database Keys: call MatSetFromOptions() to trigger these
784: +  -mat_mffd_type - wp or ds (see MATMFFD_WP or MATMFFD_DS)
785: -  -mat_mffd_err - square root of estimated relative error in function evaluation
786: -  -mat_mffd_period - how often h is recomputed, defaults to 1, everytime


789:    Level: advanced

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

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

798: .vb
799:      F'(u)*a = [F(u+h*a) - F(u)]/h where
800:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
801:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
802:  where
803:      error_rel = square root of relative error in function evaluation
804:      umin = minimum iterate parameter
805: .ve

807:    The user can set the error_rel via MatMFFDSetFunctionError() and
808:    umin via MatMFFDDSSetUmin(); see the <A href="../../docs/manual.pdf#nameddest=ch_snes">SNES chapter of the users manual</A> for details.

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

813:    Options Database Keys:
814: +  -mat_mffd_err <error_rel> - Sets error_rel
815: .  -mat_mffd_unim <umin> - Sets umin (for default PETSc routine that computes h only)
816: -  -mat_mffd_check_positivity

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

820: .seealso: MatDestroy(), MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
821:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
822:           MatMFFDGetH(), MatMFFDRegister(), MatMFFDComputeJacobian()

824: @*/
825: PetscErrorCode  MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)
826: {

830:   MatCreate(comm,J);
831:   MatSetSizes(*J,m,n,M,N);
832:   MatSetType(*J,MATMFFD);
833:   MatSetUp(*J);
834:   return(0);
835: }


840: /*@
841:    MatMFFDGetH - Gets the last value that was used as the differencing
842:    parameter.

844:    Not Collective

846:    Input Parameters:
847: .  mat - the matrix obtained with MatCreateSNESMF()

849:    Output Paramter:
850: .  h - the differencing step size

852:    Level: advanced

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

856: .seealso: MatCreateSNESMF(),MatMFFDSetHHistory(), MatCreateMFFD(), MATMFFD, MatMFFDResetHHistory()
857: @*/
858: PetscErrorCode  MatMFFDGetH(Mat mat,PetscScalar *h)
859: {
860:   MatMFFD        ctx = (MatMFFD)mat->data;
862:   PetscBool      match;

865:   PetscObjectTypeCompare((PetscObject)mat,MATMFFD,&match);
866:   if (!match) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Not a MFFD matrix");

868:   *h = ctx->currenth;
869:   return(0);
870: }

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

877:    Logically Collective on Mat

879:    Input Parameters:
880: +  mat - the matrix free matrix created via MatCreateSNESMF()
881: .  func - the function to use
882: -  funcctx - optional function context passed to function

884:    Level: advanced

886:    Notes:
887:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
888:     matrix inside your compute Jacobian routine

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

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

894: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD,
895:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
896: @*/
897: PetscErrorCode  MatMFFDSetFunction(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
898: {

902:   PetscTryMethod(mat,"MatMFFDSetFunction_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec),void*),(mat,func,funcctx));
903:   return(0);
904: }

908: /*@C
909:    MatMFFDSetFunctioni - Sets the function for a single component

911:    Logically Collective on Mat

913:    Input Parameters:
914: +  mat - the matrix free matrix created via MatCreateSNESMF()
915: -  funci - the function to use

917:    Level: advanced

919:    Notes:
920:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
921:     matrix inside your compute Jacobian routine


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

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

928: @*/
929: PetscErrorCode  MatMFFDSetFunctioni(Mat mat,PetscErrorCode (*funci)(void*,PetscInt,Vec,PetscScalar*))
930: {

935:   PetscTryMethod(mat,"MatMFFDSetFunctioni_C",(Mat,PetscErrorCode (*)(void*,PetscInt,Vec,PetscScalar*)),(mat,funci));
936:   return(0);
937: }


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

945:    Logically Collective on Mat

947:    Input Parameters:
948: +  mat - the matrix free matrix created via MatCreateSNESMF()
949: -  func - the function to use

951:    Level: advanced

953:    Notes:
954:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
955:     matrix inside your compute Jacobian routine


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

960: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
961:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
962: @*/
963: PetscErrorCode  MatMFFDSetFunctioniBase(Mat mat,PetscErrorCode (*func)(void*,Vec))
964: {

969:   PetscTryMethod(mat,"MatMFFDSetFunctioniBase_C",(Mat,PetscErrorCode (*)(void*,Vec)),(mat,func));
970:   return(0);
971: }

975: /*@
976:    MatMFFDSetPeriod - Sets how often h is recomputed, by default it is everytime

978:    Logically Collective on Mat

980:    Input Parameters:
981: +  mat - the matrix free matrix created via MatCreateSNESMF()
982: -  period - 1 for everytime, 2 for every second etc

984:    Options Database Keys:
985: +  -mat_mffd_period <period>

987:    Level: advanced


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

992: .seealso: MatCreateSNESMF(),MatMFFDGetH(),
993:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
994: @*/
995: PetscErrorCode  MatMFFDSetPeriod(Mat mat,PetscInt period)
996: {

1000:   PetscTryMethod(mat,"MatMFFDSetPeriod_C",(Mat,PetscInt),(mat,period));
1001:   return(0);
1002: }

1006: /*@
1007:    MatMFFDSetFunctionError - Sets the error_rel for the approximation of
1008:    matrix-vector products using finite differences.

1010:    Logically Collective on Mat

1012:    Input Parameters:
1013: +  mat - the matrix free matrix created via MatCreateMFFD() or MatCreateSNESMF()
1014: -  error_rel - relative error (should be set to the square root of
1015:                the relative error in the function evaluations)

1017:    Options Database Keys:
1018: +  -mat_mffd_err <error_rel> - Sets error_rel

1020:    Level: advanced

1022:    Notes:
1023:    The default matrix-free matrix-vector product routine computes
1024: .vb
1025:      F'(u)*a = [F(u+h*a) - F(u)]/h where
1026:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
1027:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
1028: .ve

1030: .keywords: SNES, matrix-free, parameters

1032: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
1033:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
1034: @*/
1035: PetscErrorCode  MatMFFDSetFunctionError(Mat mat,PetscReal error)
1036: {

1040:   PetscTryMethod(mat,"MatMFFDSetFunctionError_C",(Mat,PetscReal),(mat,error));
1041:   return(0);
1042: }

1046: /*@
1047:    MatMFFDAddNullSpace - Provides a null space that an operator is
1048:    supposed to have.  Since roundoff will create a small component in
1049:    the null space, if you know the null space you may have it
1050:    automatically removed.

1052:    Logically Collective on Mat

1054:    Input Parameters:
1055: +  J - the matrix-free matrix context
1056: -  nullsp - object created with MatNullSpaceCreate()

1058:    Level: advanced

1060: .keywords: SNES, matrix-free, null space

1062: .seealso: MatNullSpaceCreate(), MatMFFDGetH(), MatCreateSNESMF(), MatCreateMFFD(), MATMFFD
1063:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
1064: @*/
1065: PetscErrorCode  MatMFFDAddNullSpace(Mat J,MatNullSpace nullsp)
1066: {

1070:   PetscTryMethod(J,"MatMFFDAddNullSpace_C",(Mat,MatNullSpace),(J,nullsp));
1071:   return(0);
1072: }

1076: /*@
1077:    MatMFFDSetHHistory - Sets an array to collect a history of the
1078:    differencing values (h) computed for the matrix-free product.

1080:    Logically Collective on Mat

1082:    Input Parameters:
1083: +  J - the matrix-free matrix context
1084: .  histroy - space to hold the history
1085: -  nhistory - number of entries in history, if more entries are generated than
1086:               nhistory, then the later ones are discarded

1088:    Level: advanced

1090:    Notes:
1091:    Use MatMFFDResetHHistory() to reset the history counter and collect
1092:    a new batch of differencing parameters, h.

1094: .keywords: SNES, matrix-free, h history, differencing history

1096: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1097:           MatMFFDResetHHistory(), MatMFFDSetFunctionError()

1099: @*/
1100: PetscErrorCode  MatMFFDSetHHistory(Mat J,PetscScalar history[],PetscInt nhistory)
1101: {
1102:   MatMFFD        ctx = (MatMFFD)J->data;
1104:   PetscBool      match;

1107:   PetscObjectTypeCompare((PetscObject)J,MATMFFD,&match);
1108:   if (!match) SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_WRONG,"Not a MFFD matrix");
1109:   ctx->historyh    = history;
1110:   ctx->maxcurrenth = nhistory;
1111:   ctx->currenth    = 0.;
1112:   return(0);
1113: }


1118: /*@
1119:    MatMFFDResetHHistory - Resets the counter to zero to begin
1120:    collecting a new set of differencing histories.

1122:    Logically Collective on Mat

1124:    Input Parameters:
1125: .  J - the matrix-free matrix context

1127:    Level: advanced

1129:    Notes:
1130:    Use MatMFFDSetHHistory() to create the original history counter.

1132: .keywords: SNES, matrix-free, h history, differencing history

1134: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1135:           MatMFFDSetHHistory(), MatMFFDSetFunctionError()

1137: @*/
1138: PetscErrorCode  MatMFFDResetHHistory(Mat J)
1139: {

1143:   PetscTryMethod(J,"MatMFFDResetHHistory_C",(Mat),(J));
1144:   return(0);
1145: }


1150: /*@
1151:     MatMFFDSetBase - Sets the vector U at which matrix vector products of the
1152:         Jacobian are computed

1154:     Logically Collective on Mat

1156:     Input Parameters:
1157: +   J - the MatMFFD matrix
1158: .   U - the vector
1159: -   F - (optional) vector that contains F(u) if it has been already computed

1161:     Notes: This is rarely used directly

1163:     If F is provided then it is not recomputed. Otherwise the function is evaluated at the base
1164:     point during the first MatMult() after each call to MatMFFDSetBase().

1166:     Level: advanced

1168: @*/
1169: PetscErrorCode  MatMFFDSetBase(Mat J,Vec U,Vec F)
1170: {

1177:   PetscTryMethod(J,"MatMFFDSetBase_C",(Mat,Vec,Vec),(J,U,F));
1178:   return(0);
1179: }

1183: /*@C
1184:     MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
1185:         it to satisfy some criteria

1187:     Logically Collective on Mat

1189:     Input Parameters:
1190: +   J - the MatMFFD matrix
1191: .   fun - the function that checks h
1192: -   ctx - any context needed by the function

1194:     Options Database Keys:
1195: .   -mat_mffd_check_positivity

1197:     Level: advanced

1199:     Notes: For example, MatMFFDSetCheckPositivity() insures that all entries
1200:        of U + h*a are non-negative

1202: .seealso:  MatMFFDSetCheckPositivity()
1203: @*/
1204: PetscErrorCode  MatMFFDSetCheckh(Mat J,PetscErrorCode (*fun)(void*,Vec,Vec,PetscScalar*),void *ctx)
1205: {

1210:   PetscTryMethod(J,"MatMFFDSetCheckh_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec,PetscScalar*),void*),(J,fun,ctx));
1211:   return(0);
1212: }

1216: /*@
1217:     MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
1218:         zero, decreases h until this is satisfied.

1220:     Logically Collective on Vec

1222:     Input Parameters:
1223: +   U - base vector that is added to
1224: .   a - vector that is added
1225: .   h - scaling factor on a
1226: -   dummy - context variable (unused)

1228:     Options Database Keys:
1229: .   -mat_mffd_check_positivity

1231:     Level: advanced

1233:     Notes: This is rarely used directly, rather it is passed as an argument to
1234:            MatMFFDSetCheckh()

1236: .seealso:  MatMFFDSetCheckh()
1237: @*/
1238: PetscErrorCode  MatMFFDCheckPositivity(void *dummy,Vec U,Vec a,PetscScalar *h)
1239: {
1240:   PetscReal      val, minval;
1241:   PetscScalar    *u_vec, *a_vec;
1243:   PetscInt       i,n;
1244:   MPI_Comm       comm;

1247:   PetscObjectGetComm((PetscObject)U,&comm);
1248:   VecGetArray(U,&u_vec);
1249:   VecGetArray(a,&a_vec);
1250:   VecGetLocalSize(U,&n);
1251:   minval = PetscAbsScalar(*h*1.01);
1252:   for (i=0; i<n; i++) {
1253:     if (PetscRealPart(u_vec[i] + *h*a_vec[i]) <= 0.0) {
1254:       val = PetscAbsScalar(u_vec[i]/a_vec[i]);
1255:       if (val < minval) minval = val;
1256:     }
1257:   }
1258:   VecRestoreArray(U,&u_vec);
1259:   VecRestoreArray(a,&a_vec);
1260:   MPI_Allreduce(&minval,&val,1,MPIU_REAL,MPIU_MIN,comm);
1261:   if (val <= PetscAbsScalar(*h)) {
1262:     PetscInfo2(U,"Scaling back h from %G to %G\n",PetscRealPart(*h),.99*val);
1263:     if (PetscRealPart(*h) > 0.0) *h =  0.99*val;
1264:     else                         *h = -0.99*val;
1265:   }
1266:   return(0);
1267: }