Actual source code: mffd.c

petsc-master 2020-07-09
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  2:  #include <petsc/private/matimpl.h>
  3:  #include <../src/mat/impls/mffd/mffdimpl.h>

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

  8: PetscClassId  MATMFFD_CLASSID;
  9: PetscLogEvent MATMFFD_Mult;

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

 16:   Level: developer

 18: .seealso: PetscFinalize(), MatCreateMFFD(), MatCreateSNESMF()
 19: @*/
 20: PetscErrorCode  MatMFFDFinalizePackage(void)
 21: {

 25:   PetscFunctionListDestroy(&MatMFFDList);
 26:   MatMFFDPackageInitialized = PETSC_FALSE;
 27:   MatMFFDRegisterAllCalled  = PETSC_FALSE;
 28:   return(0);
 29: }

 31: /*@C
 32:   MatMFFDInitializePackage - This function initializes everything in the MatMFFD package. It is called
 33:   from MatInitializePackage().

 35:   Level: developer

 37: .seealso: PetscInitialize()
 38: @*/
 39: PetscErrorCode  MatMFFDInitializePackage(void)
 40: {
 41:   char           logList[256];
 42:   PetscBool      opt,pkg;

 46:   if (MatMFFDPackageInitialized) return(0);
 47:   MatMFFDPackageInitialized = PETSC_TRUE;
 48:   /* Register Classes */
 49:   PetscClassIdRegister("MatMFFD",&MATMFFD_CLASSID);
 50:   /* Register Constructors */
 51:   MatMFFDRegisterAll();
 52:   /* Register Events */
 53:   PetscLogEventRegister("MatMult MF",MATMFFD_CLASSID,&MATMFFD_Mult);
 54:  /* Process Info */
 55:   {
 56:     PetscClassId  classids[1];

 58:     classids[0] = MATMFFD_CLASSID;
 59:     PetscInfoProcessClass("matmffd", 1, classids);
 60:   }
 61:   /* Process summary exclusions */
 62:   PetscOptionsGetString(NULL,NULL,"-log_exclude",logList,sizeof(logList),&opt);
 63:   if (opt) {
 64:     PetscStrInList("matmffd",logList,',',&pkg);
 65:     if (pkg) {PetscLogEventExcludeClass(MATMFFD_CLASSID);}
 66:   }
 67:   /* Register package finalizer */
 68:   PetscRegisterFinalize(MatMFFDFinalizePackage);
 69:   return(0);
 70: }

 72: static PetscErrorCode  MatMFFDSetType_MFFD(Mat mat,MatMFFDType ftype)
 73: {
 74:   PetscErrorCode ierr,(*r)(MatMFFD);
 75:   MatMFFD        ctx;
 76:   PetscBool      match;

 81:   MatShellGetContext(mat,&ctx);

 83:   /* already set, so just return */
 84:   PetscObjectTypeCompare((PetscObject)ctx,ftype,&match);
 85:   if (match) return(0);

 87:   /* destroy the old one if it exists */
 88:   if (ctx->ops->destroy) {
 89:     (*ctx->ops->destroy)(ctx);
 90:   }

 92:    PetscFunctionListFind(MatMFFDList,ftype,&r);
 93:   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown MatMFFD type %s given",ftype);
 94:   (*r)(ctx);
 95:   PetscObjectChangeTypeName((PetscObject)ctx,ftype);
 96:   return(0);
 97: }

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

103:     Input Parameters:
104: +   mat - the "matrix-free" matrix created via MatCreateSNESMF(), or MatCreateMFFD()
105:           or MatSetType(mat,MATMFFD);
106: -   ftype - the type requested, either MATMFFD_WP or MATMFFD_DS

108:     Level: advanced

110:     Notes:
111:     For example, such routines can compute h for use in
112:     Jacobian-vector products of the form

114:                         F(x+ha) - F(x)
115:           F'(u)a  ~=  ----------------
116:                               h

118: .seealso: MatCreateSNESMF(), MatMFFDRegister(), MatMFFDSetFunction(), MatCreateMFFD()
119: @*/
120: PetscErrorCode  MatMFFDSetType(Mat mat,MatMFFDType ftype)
121: {

127:   PetscTryMethod(mat,"MatMFFDSetType_C",(Mat,MatMFFDType),(mat,ftype));
128:   return(0);
129: }

131: static PetscErrorCode MatGetDiagonal_MFFD(Mat,Vec);

133: typedef PetscErrorCode (*FCN1)(void*,Vec); /* force argument to next function to not be extern C*/
134: static PetscErrorCode  MatMFFDSetFunctioniBase_MFFD(Mat mat,FCN1 func)
135: {
136:   MatMFFD        ctx;

140:   MatShellGetContext(mat,&ctx);
141:   ctx->funcisetbase = func;
142:   return(0);
143: }

145: typedef PetscErrorCode (*FCN2)(void*,PetscInt,Vec,PetscScalar*); /* force argument to next function to not be extern C*/
146: static PetscErrorCode  MatMFFDSetFunctioni_MFFD(Mat mat,FCN2 funci)
147: {
148:   MatMFFD        ctx;

152:   MatShellGetContext(mat,&ctx);
153:   ctx->funci = funci;
154:   MatShellSetOperation(mat,MATOP_GET_DIAGONAL,(void (*)(void))MatGetDiagonal_MFFD);
155:   return(0);
156: }

158: static PetscErrorCode MatMFFDGetH_MFFD(Mat mat,PetscScalar *h)
159: {
160:   MatMFFD        ctx;

164:   MatShellGetContext(mat,&ctx);
165:   *h = ctx->currenth;
166:   return(0);
167: }

169: static PetscErrorCode  MatMFFDResetHHistory_MFFD(Mat J)
170: {
171:   MatMFFD        ctx;

175:   MatShellGetContext(J,&ctx);
176:   ctx->ncurrenth = 0;
177:   return(0);
178: }

180: /*@C
181:    MatMFFDRegister - Adds a method to the MatMFFD registry.

183:    Not Collective

185:    Input Parameters:
186: +  name_solver - name of a new user-defined compute-h module
187: -  routine_create - routine to create method context

189:    Level: developer

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

194:    Sample usage:
195: .vb
196:    MatMFFDRegister("my_h",MyHCreate);
197: .ve

199:    Then, your solver can be chosen with the procedural interface via
200: $     MatMFFDSetType(mfctx,"my_h")
201:    or at runtime via the option
202: $     -mat_mffd_type my_h

204: .seealso: MatMFFDRegisterAll(), MatMFFDRegisterDestroy()
205:  @*/
206: PetscErrorCode  MatMFFDRegister(const char sname[],PetscErrorCode (*function)(MatMFFD))
207: {

211:   MatInitializePackage();
212:   PetscFunctionListAdd(&MatMFFDList,sname,function);
213:   return(0);
214: }

216: /* ----------------------------------------------------------------------------------------*/
217: static PetscErrorCode MatDestroy_MFFD(Mat mat)
218: {
220:   MatMFFD        ctx;

223:   MatShellGetContext(mat,&ctx);
224:   VecDestroy(&ctx->w);
225:   VecDestroy(&ctx->current_u);
226:   if (ctx->current_f_allocated) {
227:     VecDestroy(&ctx->current_f);
228:   }
229:   if (ctx->ops->destroy) {(*ctx->ops->destroy)(ctx);}
230:   PetscHeaderDestroy(&ctx);

232:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetBase_C",NULL);
233:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioniBase_C",NULL);
234:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioni_C",NULL);
235:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunction_C",NULL);
236:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctionError_C",NULL);
237:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetCheckh_C",NULL);
238:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetPeriod_C",NULL);
239:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDResetHHistory_C",NULL);
240:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetHHistory_C",NULL);
241:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetType_C",NULL);
242:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDGetH_C",NULL);
243:   return(0);
244: }

246: /*
247:    MatMFFDView_MFFD - Views matrix-free parameters.

249: */
250: static PetscErrorCode MatView_MFFD(Mat J,PetscViewer viewer)
251: {
253:   MatMFFD        ctx;
254:   PetscBool      iascii, viewbase, viewfunction;
255:   const char     *prefix;

258:   MatShellGetContext(J,&ctx);
259:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
260:   if (iascii) {
261:     PetscViewerASCIIPrintf(viewer,"Matrix-free approximation:\n");
262:     PetscViewerASCIIPushTab(viewer);
263:     PetscViewerASCIIPrintf(viewer,"err=%g (relative error in function evaluation)\n",(double)ctx->error_rel);
264:     if (!((PetscObject)ctx)->type_name) {
265:       PetscViewerASCIIPrintf(viewer,"The compute h routine has not yet been set\n");
266:     } else {
267:       PetscViewerASCIIPrintf(viewer,"Using %s compute h routine\n",((PetscObject)ctx)->type_name);
268:     }
269: #if defined(PETSC_USE_COMPLEX)
270:     if (ctx->usecomplex) {
271:       PetscViewerASCIIPrintf(viewer,"Using Lyness complex number trick to compute the matrix-vector product\n");
272:     }
273: #endif
274:     if (ctx->ops->view) {
275:       (*ctx->ops->view)(ctx,viewer);
276:     }
277:     PetscObjectGetOptionsPrefix((PetscObject)J, &prefix);

279:     PetscOptionsHasName(((PetscObject)J)->options,prefix, "-mat_mffd_view_base", &viewbase);
280:     if (viewbase) {
281:       PetscViewerASCIIPrintf(viewer, "Base:\n");
282:       VecView(ctx->current_u, viewer);
283:     }
284:     PetscOptionsHasName(((PetscObject)J)->options,prefix, "-mat_mffd_view_function", &viewfunction);
285:     if (viewfunction) {
286:       PetscViewerASCIIPrintf(viewer, "Function:\n");
287:       VecView(ctx->current_f, viewer);
288:     }
289:     PetscViewerASCIIPopTab(viewer);
290:   }
291:   return(0);
292: }

294: /*
295:    MatAssemblyEnd_MFFD - Resets the ctx->ncurrenth to zero. This
296:    allows the user to indicate the beginning of a new linear solve by calling
297:    MatAssemblyXXX() on the matrix free matrix. This then allows the
298:    MatCreateMFFD_WP() to properly compute ||U|| only the first time
299:    in the linear solver rather than every time.

301:    This function is referenced directly from MatAssemblyEnd_SNESMF(), which may be in a different shared library hence
302:    it must be labeled as PETSC_EXTERN
303: */
304: PETSC_EXTERN PetscErrorCode MatAssemblyEnd_MFFD(Mat J,MatAssemblyType mt)
305: {
307:   MatMFFD        j;

310:   MatShellGetContext(J,&j);
311:   MatMFFDResetHHistory(J);
312:   return(0);
313: }

315: /*
316:   MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:

318:         y ~= (F(u + ha) - F(u))/h,
319:   where F = nonlinear function, as set by SNESSetFunction()
320:         u = current iterate
321:         h = difference interval
322: */
323: static PetscErrorCode MatMult_MFFD(Mat mat,Vec a,Vec y)
324: {
325:   MatMFFD        ctx;
326:   PetscScalar    h;
327:   Vec            w,U,F;
329:   PetscBool      zeroa;

332:   MatShellGetContext(mat,&ctx);
333:   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");
334:   /* We log matrix-free matrix-vector products separately, so that we can
335:      separate the performance monitoring from the cases that use conventional
336:      storage.  We may eventually modify event logging to associate events
337:      with particular objects, hence alleviating the more general problem. */
338:   PetscLogEventBegin(MATMFFD_Mult,a,y,0,0);

340:   w = ctx->w;
341:   U = ctx->current_u;
342:   F = ctx->current_f;
343:   /*
344:       Compute differencing parameter
345:   */
346:   if (!((PetscObject)ctx)->type_name) {
347:     MatMFFDSetType(mat,MATMFFD_WP);
348:     MatSetFromOptions(mat);
349:   }
350:   (*ctx->ops->compute)(ctx,U,a,&h,&zeroa);
351:   if (zeroa) {
352:     VecSet(y,0.0);
353:     return(0);
354:   }

356:   if (mat->erroriffailure && PetscIsInfOrNanScalar(h)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed Nan differencing parameter h");
357:   if (ctx->checkh) {
358:     (*ctx->checkh)(ctx->checkhctx,U,a,&h);
359:   }

361:   /* keep a record of the current differencing parameter h */
362:   ctx->currenth = h;
363: #if defined(PETSC_USE_COMPLEX)
364:   PetscInfo2(mat,"Current differencing parameter: %g + %g i\n",(double)PetscRealPart(h),(double)PetscImaginaryPart(h));
365: #else
366:   PetscInfo1(mat,"Current differencing parameter: %15.12e\n",h);
367: #endif
368:   if (ctx->historyh && ctx->ncurrenth < ctx->maxcurrenth) {
369:     ctx->historyh[ctx->ncurrenth] = h;
370:   }
371:   ctx->ncurrenth++;

373: #if defined(PETSC_USE_COMPLEX)
374:   if (ctx->usecomplex) h = PETSC_i*h;
375: #endif

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

380:   /* compute func(U) as base for differencing; only needed first time in and not when provided by user */
381:   if (ctx->ncurrenth == 1 && ctx->current_f_allocated) {
382:     (*ctx->func)(ctx->funcctx,U,F);
383:   }
384:   (*ctx->func)(ctx->funcctx,w,y);

386: #if defined(PETSC_USE_COMPLEX)  
387:   if (ctx->usecomplex) {
388:     VecImaginaryPart(y);
389:     h    = PetscImaginaryPart(h);
390:   } else {
391:     VecAXPY(y,-1.0,F);
392:   }
393: #else
394:   VecAXPY(y,-1.0,F);
395: #endif
396:   VecScale(y,1.0/h);
397:   if (mat->nullsp) {MatNullSpaceRemove(mat->nullsp,y);}

399:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
400:   return(0);
401: }

403: /*
404:   MatGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix

406:         y ~= (F(u + ha) - F(u))/h,
407:   where F = nonlinear function, as set by SNESSetFunction()
408:         u = current iterate
409:         h = difference interval
410: */
411: PetscErrorCode MatGetDiagonal_MFFD(Mat mat,Vec a)
412: {
413:   MatMFFD        ctx;
414:   PetscScalar    h,*aa,*ww,v;
415:   PetscReal      epsilon = PETSC_SQRT_MACHINE_EPSILON,umin = 100.0*PETSC_SQRT_MACHINE_EPSILON;
416:   Vec            w,U;
418:   PetscInt       i,rstart,rend;

421:   MatShellGetContext(mat,&ctx);
422:   if (!ctx->func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Requires calling MatMFFDSetFunction() first");
423:   if (!ctx->funci) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Requires calling MatMFFDSetFunctioni() first");
424:   w    = ctx->w;
425:   U    = ctx->current_u;
426:   (*ctx->func)(ctx->funcctx,U,a);
427:   if (ctx->funcisetbase) {
428:     (*ctx->funcisetbase)(ctx->funcctx,U);
429:   }
430:   VecCopy(U,w);

432:   VecGetOwnershipRange(a,&rstart,&rend);
433:   VecGetArray(a,&aa);
434:   for (i=rstart; i<rend; i++) {
435:     VecGetArray(w,&ww);
436:     h    = ww[i-rstart];
437:     if (h == 0.0) h = 1.0;
438:     if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0)     h = umin;
439:     else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
440:     h *= epsilon;

442:     ww[i-rstart] += h;
443:     VecRestoreArray(w,&ww);
444:     (*ctx->funci)(ctx->funcctx,i,w,&v);
445:     aa[i-rstart]  = (v - aa[i-rstart])/h;

447:     VecGetArray(w,&ww);
448:     ww[i-rstart] -= h;
449:     VecRestoreArray(w,&ww);
450:   }
451:   VecRestoreArray(a,&aa);
452:   return(0);
453: }

455: PETSC_EXTERN PetscErrorCode MatMFFDSetBase_MFFD(Mat J,Vec U,Vec F)
456: {
458:   MatMFFD        ctx;

461:   MatShellGetContext(J,&ctx);
462:   MatMFFDResetHHistory(J);
463:   if (!ctx->current_u) {
464:     VecDuplicate(U,&ctx->current_u);
465:     VecLockReadPush(ctx->current_u);
466:   }
467:   VecLockReadPop(ctx->current_u);
468:   VecCopy(U,ctx->current_u);
469:   VecLockReadPush(ctx->current_u);
470:   if (F) {
471:     if (ctx->current_f_allocated) {VecDestroy(&ctx->current_f);}
472:     ctx->current_f           = F;
473:     ctx->current_f_allocated = PETSC_FALSE;
474:   } else if (!ctx->current_f_allocated) {
475:     MatCreateVecs(J,NULL,&ctx->current_f);

477:     ctx->current_f_allocated = PETSC_TRUE;
478:   }
479:   if (!ctx->w) {
480:     VecDuplicate(ctx->current_u,&ctx->w);
481:   }
482:   J->assembled = PETSC_TRUE;
483:   return(0);
484: }

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

488: static PetscErrorCode  MatMFFDSetCheckh_MFFD(Mat J,FCN3 fun,void *ectx)
489: {
490:   MatMFFD        ctx;

494:   MatShellGetContext(J,&ctx);
495:   ctx->checkh    = fun;
496:   ctx->checkhctx = ectx;
497:   return(0);
498: }

500: /*@C
501:    MatMFFDSetOptionsPrefix - Sets the prefix used for searching for all
502:    MatMFFD options in the database.

504:    Collective on Mat

506:    Input Parameter:
507: +  A - the Mat context
508: -  prefix - the prefix to prepend to all option names

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

514:    Level: advanced

516: .seealso: MatSetFromOptions(), MatCreateSNESMF(), MatCreateMFFD()
517: @*/
518: PetscErrorCode  MatMFFDSetOptionsPrefix(Mat mat,const char prefix[])

520: {
521:   MatMFFD        mfctx;

526:   MatShellGetContext(mat,&mfctx);
528:   PetscObjectSetOptionsPrefix((PetscObject)mfctx,prefix);
529:   return(0);
530: }

532: static PetscErrorCode  MatSetFromOptions_MFFD(PetscOptionItems *PetscOptionsObject,Mat mat)
533: {
534:   MatMFFD        mfctx;
536:   PetscBool      flg;
537:   char           ftype[256];

541:   MatShellGetContext(mat,&mfctx);
543:   PetscObjectOptionsBegin((PetscObject)mfctx);
544:   PetscOptionsFList("-mat_mffd_type","Matrix free type","MatMFFDSetType",MatMFFDList,((PetscObject)mfctx)->type_name,ftype,256,&flg);
545:   if (flg) {
546:     MatMFFDSetType(mat,ftype);
547:   }

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

552:   flg  = PETSC_FALSE;
553:   PetscOptionsBool("-mat_mffd_check_positivity","Insure that U + h*a is nonnegative","MatMFFDSetCheckh",flg,&flg,NULL);
554:   if (flg) {
555:     MatMFFDSetCheckh(mat,MatMFFDCheckPositivity,0);
556:   }
557: #if defined(PETSC_USE_COMPLEX)
558:   PetscOptionsBool("-mat_mffd_complex","Use Lyness complex number trick to compute the matrix-vector product","None",mfctx->usecomplex,&mfctx->usecomplex,NULL);
559: #endif
560:   if (mfctx->ops->setfromoptions) {
561:     (*mfctx->ops->setfromoptions)(PetscOptionsObject,mfctx);
562:   }
563:   PetscOptionsEnd();
564:   return(0);
565: }

567: static PetscErrorCode  MatMFFDSetPeriod_MFFD(Mat mat,PetscInt period)
568: {
569:   MatMFFD        ctx;

573:   MatShellGetContext(mat,&ctx);
574:   ctx->recomputeperiod = period;
575:   return(0);
576: }

578: static PetscErrorCode  MatMFFDSetFunction_MFFD(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
579: {
580:   MatMFFD        ctx;

584:   MatShellGetContext(mat,&ctx);
585:   ctx->func    = func;
586:   ctx->funcctx = funcctx;
587:   return(0);
588: }

590: static PetscErrorCode  MatMFFDSetFunctionError_MFFD(Mat mat,PetscReal error)
591: {
592:   MatMFFD        ctx;

596:   MatShellGetContext(mat,&ctx);
597:   if (error != PETSC_DEFAULT) ctx->error_rel = error;
598:   return(0);
599: }

601: PetscErrorCode  MatMFFDSetHHistory_MFFD(Mat J,PetscScalar history[],PetscInt nhistory)
602: {
603:   MatMFFD        ctx;

607:   MatShellGetContext(J,&ctx);
608:   ctx->historyh    = history;
609:   ctx->maxcurrenth = nhistory;
610:   ctx->currenth    = 0.;
611:   return(0);
612: }

614: /*MC
615:   MATMFFD - MATMFFD = "mffd" - A matrix free matrix type.

617:   Level: advanced

619:   Developers Note: This is implemented on top of MATSHELL to get support for scaling and shifting without requiring duplicate code

621: .seealso: MatCreateMFFD(), MatCreateSNESMF(), MatMFFDSetFunction(), MatMFFDSetType(),  
622:           MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
623:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
624:           MatMFFDGetH(),
625: M*/
626: PETSC_EXTERN PetscErrorCode MatCreate_MFFD(Mat A)
627: {
628:   MatMFFD        mfctx;

632:   MatMFFDInitializePackage();

634:   PetscHeaderCreate(mfctx,MATMFFD_CLASSID,"MatMFFD","Matrix-free Finite Differencing","Mat",PetscObjectComm((PetscObject)A),NULL,NULL);

636:   mfctx->error_rel                = PETSC_SQRT_MACHINE_EPSILON;
637:   mfctx->recomputeperiod          = 1;
638:   mfctx->count                    = 0;
639:   mfctx->currenth                 = 0.0;
640:   mfctx->historyh                 = NULL;
641:   mfctx->ncurrenth                = 0;
642:   mfctx->maxcurrenth              = 0;
643:   ((PetscObject)mfctx)->type_name = 0;

645:   /*
646:      Create the empty data structure to contain compute-h routines.
647:      These will be filled in below from the command line options or
648:      a later call with MatMFFDSetType() or if that is not called
649:      then it will default in the first use of MatMult_MFFD()
650:   */
651:   mfctx->ops->compute        = 0;
652:   mfctx->ops->destroy        = 0;
653:   mfctx->ops->view           = 0;
654:   mfctx->ops->setfromoptions = 0;
655:   mfctx->hctx                = 0;

657:   mfctx->func    = 0;
658:   mfctx->funcctx = 0;
659:   mfctx->w       = NULL;
660:   mfctx->mat     = A;

662:   MatSetType(A,MATSHELL);
663:   MatShellSetContext(A,mfctx);
664:   MatShellSetOperation(A,MATOP_MULT,(void (*)(void))MatMult_MFFD);
665:   MatShellSetOperation(A,MATOP_DESTROY,(void (*)(void))MatDestroy_MFFD);
666:   MatShellSetOperation(A,MATOP_VIEW,(void (*)(void))MatView_MFFD);
667:   MatShellSetOperation(A,MATOP_ASSEMBLY_END,(void (*)(void))MatAssemblyEnd_MFFD);
668:   MatShellSetOperation(A,MATOP_SET_FROM_OPTIONS,(void (*)(void))MatSetFromOptions_MFFD);

670:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetBase_C",MatMFFDSetBase_MFFD);
671:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioniBase_C",MatMFFDSetFunctioniBase_MFFD);
672:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioni_C",MatMFFDSetFunctioni_MFFD);
673:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunction_C",MatMFFDSetFunction_MFFD);
674:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetCheckh_C",MatMFFDSetCheckh_MFFD);
675:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetPeriod_C",MatMFFDSetPeriod_MFFD);
676:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctionError_C",MatMFFDSetFunctionError_MFFD);
677:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDResetHHistory_C",MatMFFDResetHHistory_MFFD);
678:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetHHistory_C",MatMFFDSetHHistory_MFFD);
679:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetType_C",MatMFFDSetType_MFFD);
680:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDGetH_C",MatMFFDGetH_MFFD);
681:   PetscObjectChangeTypeName((PetscObject)A,MATMFFD);
682:   return(0);
683: }

685: /*@
686:    MatCreateMFFD - Creates a matrix-free matrix. See also MatCreateSNESMF()

688:    Collective on Vec

690:    Input Parameters:
691: +  comm - MPI communicator
692: .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
693:            This value should be the same as the local size used in creating the
694:            y vector for the matrix-vector product y = Ax.
695: .  n - This value should be the same as the local size used in creating the
696:        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
697:        calculated if N is given) For square matrices n is almost always m.
698: .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
699: -  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)


702:    Output Parameter:
703: .  J - the matrix-free matrix

705:    Options Database Keys: call MatSetFromOptions() to trigger these
706: +  -mat_mffd_type - wp or ds (see MATMFFD_WP or MATMFFD_DS)
707: .  -mat_mffd_err - square root of estimated relative error in function evaluation
708: .  -mat_mffd_period - how often h is recomputed, defaults to 1, everytime
709: .  -mat_mffd_check_positivity - possibly decrease h until U + h*a has only positive values
710: -  -mat_mffd_complex - use the Lyness trick with complex numbers to compute the matrix-vector product instead of differencing
711:                        (requires real valued functions but that PETSc be configured for complex numbers)


714:    Level: advanced

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

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

723: .vb
724:      F'(u)*a = [F(u+h*a) - F(u)]/h where
725:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
726:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
727:  where
728:      error_rel = square root of relative error in function evaluation
729:      umin = minimum iterate parameter
730: .ve

732:    You can call SNESSetJacobian() with MatMFFDComputeJacobian() if you are using matrix and not a different
733:    preconditioner matrix

735:    The user can set the error_rel via MatMFFDSetFunctionError() and
736:    umin via MatMFFDDSSetUmin(); see Users-Manual: ch_snes for details.

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

741:    Options Database Keys:
742: +  -mat_mffd_err <error_rel> - Sets error_rel
743: .  -mat_mffd_unim <umin> - Sets umin (for default PETSc routine that computes h only)
744: -  -mat_mffd_check_positivity

746: .seealso: MatDestroy(), MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
747:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
748:           MatMFFDGetH(), MatMFFDRegister(), MatMFFDComputeJacobian()

750: @*/
751: PetscErrorCode  MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)
752: {

756:   MatCreate(comm,J);
757:   MatSetSizes(*J,m,n,M,N);
758:   MatSetType(*J,MATMFFD);
759:   MatSetUp(*J);
760:   return(0);
761: }

763: /*@
764:    MatMFFDGetH - Gets the last value that was used as the differencing
765:    parameter.

767:    Not Collective

769:    Input Parameters:
770: .  mat - the matrix obtained with MatCreateSNESMF()

772:    Output Parameter:
773: .  h - the differencing step size

775:    Level: advanced

777: .seealso: MatCreateSNESMF(),MatMFFDSetHHistory(), MatCreateMFFD(), MATMFFD, MatMFFDResetHHistory()
778: @*/
779: PetscErrorCode  MatMFFDGetH(Mat mat,PetscScalar *h)
780: {

786:   PetscUseMethod(mat,"MatMFFDGetH_C",(Mat,PetscScalar*),(mat,h));
787:   return(0);
788: }

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

793:    Logically Collective on Mat

795:    Input Parameters:
796: +  mat - the matrix free matrix created via MatCreateSNESMF() or MatCreateMFFD()
797: .  func - the function to use
798: -  funcctx - optional function context passed to function

800:    Calling Sequence of func:
801: $     func (void *funcctx, Vec x, Vec f)

803: +  funcctx - user provided context
804: .  x - input vector
805: -  f - computed output function

807:    Level: advanced

809:    Notes:
810:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
811:     matrix inside your compute Jacobian routine

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

815: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD,
816:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
817: @*/
818: PetscErrorCode  MatMFFDSetFunction(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
819: {

824:   PetscTryMethod(mat,"MatMFFDSetFunction_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec),void*),(mat,func,funcctx));
825:   return(0);
826: }

828: /*@C
829:    MatMFFDSetFunctioni - Sets the function for a single component

831:    Logically Collective on Mat

833:    Input Parameters:
834: +  mat - the matrix free matrix created via MatCreateSNESMF()
835: -  funci - the function to use

837:    Level: advanced

839:    Notes:
840:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
841:     matrix inside your compute Jacobian routine.
842:     This function is necessary to compute the diagonal of the matrix.
843:     funci must not contain any MPI call as it is called inside a loop on the local portion of the vector.

845: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction(), MatGetDiagonal()

847: @*/
848: PetscErrorCode  MatMFFDSetFunctioni(Mat mat,PetscErrorCode (*funci)(void*,PetscInt,Vec,PetscScalar*))
849: {

854:   PetscTryMethod(mat,"MatMFFDSetFunctioni_C",(Mat,PetscErrorCode (*)(void*,PetscInt,Vec,PetscScalar*)),(mat,funci));
855:   return(0);
856: }

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

861:    Logically Collective on Mat

863:    Input Parameters:
864: +  mat - the matrix free matrix created via MatCreateSNESMF()
865: -  func - the function to use

867:    Level: advanced

869:    Notes:
870:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
871:     matrix inside your compute Jacobian routine.
872:     This function is necessary to compute the diagonal of the matrix.


875: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
876:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction(), MatGetDiagonal()
877: @*/
878: PetscErrorCode  MatMFFDSetFunctioniBase(Mat mat,PetscErrorCode (*func)(void*,Vec))
879: {

884:   PetscTryMethod(mat,"MatMFFDSetFunctioniBase_C",(Mat,PetscErrorCode (*)(void*,Vec)),(mat,func));
885:   return(0);
886: }

888: /*@
889:    MatMFFDSetPeriod - Sets how often h is recomputed, by default it is everytime

891:    Logically Collective on Mat

893:    Input Parameters:
894: +  mat - the matrix free matrix created via MatCreateSNESMF()
895: -  period - 1 for everytime, 2 for every second etc

897:    Options Database Keys:
898: .  -mat_mffd_period <period>

900:    Level: advanced


903: .seealso: MatCreateSNESMF(),MatMFFDGetH(),
904:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
905: @*/
906: PetscErrorCode  MatMFFDSetPeriod(Mat mat,PetscInt period)
907: {

913:   PetscTryMethod(mat,"MatMFFDSetPeriod_C",(Mat,PetscInt),(mat,period));
914:   return(0);
915: }

917: /*@
918:    MatMFFDSetFunctionError - Sets the error_rel for the approximation of
919:    matrix-vector products using finite differences.

921:    Logically Collective on Mat

923:    Input Parameters:
924: +  mat - the matrix free matrix created via MatCreateMFFD() or MatCreateSNESMF()
925: -  error_rel - relative error (should be set to the square root of
926:                the relative error in the function evaluations)

928:    Options Database Keys:
929: .  -mat_mffd_err <error_rel> - Sets error_rel

931:    Level: advanced

933:    Notes:
934:    The default matrix-free matrix-vector product routine computes
935: .vb
936:      F'(u)*a = [F(u+h*a) - F(u)]/h where
937:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
938:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
939: .ve

941: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
942:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
943: @*/
944: PetscErrorCode  MatMFFDSetFunctionError(Mat mat,PetscReal error)
945: {

951:   PetscTryMethod(mat,"MatMFFDSetFunctionError_C",(Mat,PetscReal),(mat,error));
952:   return(0);
953: }

955: /*@
956:    MatMFFDSetHHistory - Sets an array to collect a history of the
957:    differencing values (h) computed for the matrix-free product.

959:    Logically Collective on Mat

961:    Input Parameters:
962: +  J - the matrix-free matrix context
963: .  histroy - space to hold the history
964: -  nhistory - number of entries in history, if more entries are generated than
965:               nhistory, then the later ones are discarded

967:    Level: advanced

969:    Notes:
970:    Use MatMFFDResetHHistory() to reset the history counter and collect
971:    a new batch of differencing parameters, h.

973: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
974:           MatMFFDResetHHistory(), MatMFFDSetFunctionError()

976: @*/
977: PetscErrorCode  MatMFFDSetHHistory(Mat J,PetscScalar history[],PetscInt nhistory)
978: {

985:   PetscUseMethod(J,"MatMFFDSetHHistory_C",(Mat,PetscScalar[],PetscInt),(J,history,nhistory));
986:   return(0);
987: }

989: /*@
990:    MatMFFDResetHHistory - Resets the counter to zero to begin
991:    collecting a new set of differencing histories.

993:    Logically Collective on Mat

995:    Input Parameters:
996: .  J - the matrix-free matrix context

998:    Level: advanced

1000:    Notes:
1001:    Use MatMFFDSetHHistory() to create the original history counter.

1003: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1004:           MatMFFDSetHHistory(), MatMFFDSetFunctionError()

1006: @*/
1007: PetscErrorCode  MatMFFDResetHHistory(Mat J)
1008: {

1013:   PetscTryMethod(J,"MatMFFDResetHHistory_C",(Mat),(J));
1014:   return(0);
1015: }

1017: /*@
1018:     MatMFFDSetBase - Sets the vector U at which matrix vector products of the
1019:         Jacobian are computed

1021:     Logically Collective on Mat

1023:     Input Parameters:
1024: +   J - the MatMFFD matrix
1025: .   U - the vector
1026: -   F - (optional) vector that contains F(u) if it has been already computed

1028:     Notes:
1029:     This is rarely used directly

1031:     If F is provided then it is not recomputed. Otherwise the function is evaluated at the base
1032:     point during the first MatMult() after each call to MatMFFDSetBase().

1034:     Level: advanced

1036: @*/
1037: PetscErrorCode  MatMFFDSetBase(Mat J,Vec U,Vec F)
1038: {

1045:   PetscTryMethod(J,"MatMFFDSetBase_C",(Mat,Vec,Vec),(J,U,F));
1046:   return(0);
1047: }

1049: /*@C
1050:     MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
1051:         it to satisfy some criteria

1053:     Logically Collective on Mat

1055:     Input Parameters:
1056: +   J - the MatMFFD matrix
1057: .   fun - the function that checks h
1058: -   ctx - any context needed by the function

1060:     Options Database Keys:
1061: .   -mat_mffd_check_positivity

1063:     Level: advanced

1065:     Notes:
1066:     For example, MatMFFDCheckPositivity() insures that all entries
1067:        of U + h*a are non-negative

1069:      The function you provide is called after the default h has been computed and allows you to
1070:      modify it.

1072: .seealso:  MatMFFDCheckPositivity()
1073: @*/
1074: PetscErrorCode  MatMFFDSetCheckh(Mat J,PetscErrorCode (*fun)(void*,Vec,Vec,PetscScalar*),void *ctx)
1075: {

1080:   PetscTryMethod(J,"MatMFFDSetCheckh_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec,PetscScalar*),void*),(J,fun,ctx));
1081:   return(0);
1082: }

1084: /*@
1085:     MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
1086:         zero, decreases h until this is satisfied.

1088:     Logically Collective on Vec

1090:     Input Parameters:
1091: +   U - base vector that is added to
1092: .   a - vector that is added
1093: .   h - scaling factor on a
1094: -   dummy - context variable (unused)

1096:     Options Database Keys:
1097: .   -mat_mffd_check_positivity

1099:     Level: advanced

1101:     Notes:
1102:     This is rarely used directly, rather it is passed as an argument to
1103:            MatMFFDSetCheckh()

1105: .seealso:  MatMFFDSetCheckh()
1106: @*/
1107: PetscErrorCode  MatMFFDCheckPositivity(void *dummy,Vec U,Vec a,PetscScalar *h)
1108: {
1109:   PetscReal      val, minval;
1110:   PetscScalar    *u_vec, *a_vec;
1112:   PetscInt       i,n;
1113:   MPI_Comm       comm;

1119:   PetscObjectGetComm((PetscObject)U,&comm);
1120:   VecGetArray(U,&u_vec);
1121:   VecGetArray(a,&a_vec);
1122:   VecGetLocalSize(U,&n);
1123:   minval = PetscAbsScalar(*h)*PetscRealConstant(1.01);
1124:   for (i=0; i<n; i++) {
1125:     if (PetscRealPart(u_vec[i] + *h*a_vec[i]) <= 0.0) {
1126:       val = PetscAbsScalar(u_vec[i]/a_vec[i]);
1127:       if (val < minval) minval = val;
1128:     }
1129:   }
1130:   VecRestoreArray(U,&u_vec);
1131:   VecRestoreArray(a,&a_vec);
1132:   MPIU_Allreduce(&minval,&val,1,MPIU_REAL,MPIU_MIN,comm);
1133:   if (val <= PetscAbsScalar(*h)) {
1134:     PetscInfo2(U,"Scaling back h from %g to %g\n",(double)PetscRealPart(*h),(double)(.99*val));
1135:     if (PetscRealPart(*h) > 0.0) *h =  0.99*val;
1136:     else                         *h = -0.99*val;
1137:   }
1138:   return(0);
1139: }