Actual source code: mffd.c

petsc-3.10.2 2018-10-09
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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: .keywords: Petsc, destroy, package
 19: .seealso: PetscFinalize(), MatCreateMFFD(), MatCreateSNESMF()
 20: @*/
 21: PetscErrorCode  MatMFFDFinalizePackage(void)
 22: {

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

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

 37:   Level: developer

 39: .keywords: Vec, initialize, package
 40: .seealso: PetscInitialize()
 41: @*/
 42: PetscErrorCode  MatMFFDInitializePackage(void)
 43: {
 44:   char           logList[256];
 45:   PetscBool      opt,pkg;

 49:   if (MatMFFDPackageInitialized) return(0);
 50:   MatMFFDPackageInitialized = PETSC_TRUE;
 51:   /* Register Classes */
 52:   PetscClassIdRegister("MatMFFD",&MATMFFD_CLASSID);
 53:   /* Register Constructors */
 54:   MatMFFDRegisterAll();
 55:   /* Register Events */
 56:   PetscLogEventRegister("MatMult MF",MATMFFD_CLASSID,&MATMFFD_Mult);
 57:   /* Process info exclusions */
 58:   PetscOptionsGetString(NULL,NULL,"-info_exclude",logList,sizeof(logList),&opt);
 59:   if (opt) {
 60:     PetscStrInList("matmffd",logList,',',&pkg);
 61:     if (pkg) {PetscInfoDeactivateClass(MATMFFD_CLASSID);}
 62:   }
 63:   /* Process summary exclusions */
 64:   PetscOptionsGetString(NULL,NULL,"-log_exclude",logList,sizeof(logList),&opt);
 65:   if (opt) {
 66:     PetscStrInList("matmffd",logList,',',&pkg);
 67:     if (pkg) {PetscLogEventExcludeClass(MATMFFD_CLASSID);}
 68:   }
 69:   /* Register package finalizer */
 70:   PetscRegisterFinalize(MatMFFDFinalizePackage);
 71:   return(0);
 72: }

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

 78:     Input Parameters:
 79: +   mat - the "matrix-free" matrix created via MatCreateSNESMF(), or MatCreateMFFD()
 80:           or MatSetType(mat,MATMFFD);
 81: -   ftype - the type requested, either MATMFFD_WP or MATMFFD_DS

 83:     Level: advanced

 85:     Notes:
 86:     For example, such routines can compute h for use in
 87:     Jacobian-vector products of the form

 89:                         F(x+ha) - F(x)
 90:           F'(u)a  ~=  ----------------
 91:                               h

 93: .seealso: MatCreateSNESMF(), MatMFFDRegister(), MatMFFDSetFunction(), MatCreateMFFD()
 94: @*/
 95: PetscErrorCode  MatMFFDSetType(Mat mat,MatMFFDType ftype)
 96: {
 97:   PetscErrorCode ierr,(*r)(MatMFFD);
 98:   MatMFFD        ctx = (MatMFFD)mat->data;
 99:   PetscBool      match;


105:   PetscObjectTypeCompare((PetscObject)mat,MATMFFD,&match);
106:   if (!match) return(0);

108:   /* already set, so just return */
109:   PetscObjectTypeCompare((PetscObject)ctx,ftype,&match);
110:   if (match) return(0);

112:   /* destroy the old one if it exists */
113:   if (ctx->ops->destroy) {
114:     (*ctx->ops->destroy)(ctx);
115:   }

117:    PetscFunctionListFind(MatMFFDList,ftype,&r);
118:   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown MatMFFD type %s given",ftype);
119:   (*r)(ctx);
120:   PetscObjectChangeTypeName((PetscObject)ctx,ftype);
121:   return(0);
122: }

124: static PetscErrorCode MatGetDiagonal_MFFD(Mat,Vec);

126: typedef PetscErrorCode (*FCN1)(void*,Vec); /* force argument to next function to not be extern C*/
127: static PetscErrorCode  MatMFFDSetFunctioniBase_MFFD(Mat mat,FCN1 func)
128: {
129:   MatMFFD ctx = (MatMFFD)mat->data;

132:   ctx->funcisetbase = func;
133:   /* allow users to compose their own getdiagonal and allow MatHasOperation
134:      to return false if the two functions pointers are not set */
135:   if (!mat->ops->getdiagonal && func) {
136:     mat->ops->getdiagonal = MatGetDiagonal_MFFD;
137:   }
138:   return(0);
139: }

141: typedef PetscErrorCode (*FCN2)(void*,PetscInt,Vec,PetscScalar*); /* force argument to next function to not be extern C*/
142: static PetscErrorCode  MatMFFDSetFunctioni_MFFD(Mat mat,FCN2 funci)
143: {
144:   MatMFFD ctx = (MatMFFD)mat->data;

147:   ctx->funci = funci;
148:   /* allow users to compose their own getdiagonal and allow MatHasOperation
149:      to return false if the two functions pointers are not set */
150:   if (!mat->ops->getdiagonal && funci) {
151:     mat->ops->getdiagonal = MatGetDiagonal_MFFD;
152:   }
153:   return(0);
154: }

156: static PetscErrorCode  MatMFFDResetHHistory_MFFD(Mat J)
157: {
158:   MatMFFD ctx = (MatMFFD)J->data;

161:   ctx->ncurrenth = 0;
162:   return(0);
163: }

165: /*@C
166:    MatMFFDRegister - Adds a method to the MatMFFD registry.

168:    Not Collective

170:    Input Parameters:
171: +  name_solver - name of a new user-defined compute-h module
172: -  routine_create - routine to create method context

174:    Level: developer

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

179:    Sample usage:
180: .vb
181:    MatMFFDRegister("my_h",MyHCreate);
182: .ve

184:    Then, your solver can be chosen with the procedural interface via
185: $     MatMFFDSetType(mfctx,"my_h")
186:    or at runtime via the option
187: $     -mat_mffd_type my_h

189: .keywords: MatMFFD, register

191: .seealso: MatMFFDRegisterAll(), MatMFFDRegisterDestroy()
192:  @*/
193: PetscErrorCode  MatMFFDRegister(const char sname[],PetscErrorCode (*function)(MatMFFD))
194: {

198:   MatInitializePackage();
199:   PetscFunctionListAdd(&MatMFFDList,sname,function);
200:   return(0);
201: }

203: /* ----------------------------------------------------------------------------------------*/
204: static PetscErrorCode MatDestroy_MFFD(Mat mat)
205: {
207:   MatMFFD        ctx = (MatMFFD)mat->data;

210:   VecDestroy(&ctx->w);
211:   VecDestroy(&ctx->drscale);
212:   VecDestroy(&ctx->dlscale);
213:   VecDestroy(&ctx->dshift);
214:   VecDestroy(&ctx->dshiftw);
215:   VecDestroy(&ctx->current_u);
216:   if (ctx->current_f_allocated) {
217:     VecDestroy(&ctx->current_f);
218:   }
219:   if (ctx->ops->destroy) {(*ctx->ops->destroy)(ctx);}
220:   PetscHeaderDestroy(&ctx);
221:   mat->data = 0;

223:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetBase_C",NULL);
224:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioniBase_C",NULL);
225:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioni_C",NULL);
226:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunction_C",NULL);
227:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctionError_C",NULL);
228:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetCheckh_C",NULL);
229:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetPeriod_C",NULL);
230:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDResetHHistory_C",NULL);
231:   return(0);
232: }

234: /*
235:    MatMFFDView_MFFD - Views matrix-free parameters.

237: */
238: static PetscErrorCode MatView_MFFD(Mat J,PetscViewer viewer)
239: {
241:   MatMFFD        ctx = (MatMFFD)J->data;
242:   PetscBool      iascii, viewbase, viewfunction;
243:   const char     *prefix;

246:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
247:   if (iascii) {
248:     PetscViewerASCIIPrintf(viewer,"Matrix-free approximation:\n");
249:     PetscViewerASCIIPushTab(viewer);
250:     PetscViewerASCIIPrintf(viewer,"err=%g (relative error in function evaluation)\n",(double)ctx->error_rel);
251:     if (!((PetscObject)ctx)->type_name) {
252:       PetscViewerASCIIPrintf(viewer,"The compute h routine has not yet been set\n");
253:     } else {
254:       PetscViewerASCIIPrintf(viewer,"Using %s compute h routine\n",((PetscObject)ctx)->type_name);
255:     }
256:     if (ctx->ops->view) {
257:       (*ctx->ops->view)(ctx,viewer);
258:     }
259:     PetscObjectGetOptionsPrefix((PetscObject)J, &prefix);

261:     PetscOptionsHasName(((PetscObject)J)->options,prefix, "-mat_mffd_view_base", &viewbase);
262:     if (viewbase) {
263:       PetscViewerASCIIPrintf(viewer, "Base:\n");
264:       VecView(ctx->current_u, viewer);
265:     }
266:     PetscOptionsHasName(((PetscObject)J)->options,prefix, "-mat_mffd_view_function", &viewfunction);
267:     if (viewfunction) {
268:       PetscViewerASCIIPrintf(viewer, "Function:\n");
269:       VecView(ctx->current_f, viewer);
270:     }
271:     PetscViewerASCIIPopTab(viewer);
272:   }
273:   return(0);
274: }

276: /*
277:    MatAssemblyEnd_MFFD - Resets the ctx->ncurrenth to zero. This
278:    allows the user to indicate the beginning of a new linear solve by calling
279:    MatAssemblyXXX() on the matrix free matrix. This then allows the
280:    MatCreateMFFD_WP() to properly compute ||U|| only the first time
281:    in the linear solver rather than every time.

283:    This function is referenced directly from MatAssemblyEnd_SNESMF(), which may be in a different shared library hence
284:    it must be labeled as PETSC_EXTERN
285: */
286: PETSC_EXTERN PetscErrorCode MatAssemblyEnd_MFFD(Mat J,MatAssemblyType mt)
287: {
289:   MatMFFD        j = (MatMFFD)J->data;

292:   MatMFFDResetHHistory(J);
293:   j->vshift = 0.0;
294:   j->vscale = 1.0;
295:   return(0);
296: }

298: /*
299:   MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:

301:         y ~= (F(u + ha) - F(u))/h,
302:   where F = nonlinear function, as set by SNESSetFunction()
303:         u = current iterate
304:         h = difference interval
305: */
306: static PetscErrorCode MatMult_MFFD(Mat mat,Vec a,Vec y)
307: {
308:   MatMFFD        ctx = (MatMFFD)mat->data;
309:   PetscScalar    h;
310:   Vec            w,U,F;
312:   PetscBool      zeroa;

315:   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");
316:   /* We log matrix-free matrix-vector products separately, so that we can
317:      separate the performance monitoring from the cases that use conventional
318:      storage.  We may eventually modify event logging to associate events
319:      with particular objects, hence alleviating the more general problem. */
320:   PetscLogEventBegin(MATMFFD_Mult,a,y,0,0);

322:   w = ctx->w;
323:   U = ctx->current_u;
324:   F = ctx->current_f;
325:   /*
326:       Compute differencing parameter
327:   */
328:   if (!((PetscObject)ctx)->type_name) {
329:     MatMFFDSetType(mat,MATMFFD_WP);
330:     MatSetFromOptions(mat);
331:   }
332:   (*ctx->ops->compute)(ctx,U,a,&h,&zeroa);
333:   if (zeroa) {
334:     VecSet(y,0.0);
335:     return(0);
336:   }

338:   if (mat->erroriffailure && PetscIsInfOrNanScalar(h)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed Nan differencing parameter h");
339:   if (ctx->checkh) {
340:     (*ctx->checkh)(ctx->checkhctx,U,a,&h);
341:   }

343:   /* keep a record of the current differencing parameter h */
344:   ctx->currenth = h;
345: #if defined(PETSC_USE_COMPLEX)
346:   PetscInfo2(mat,"Current differencing parameter: %g + %g i\n",(double)PetscRealPart(h),(double)PetscImaginaryPart(h));
347: #else
348:   PetscInfo1(mat,"Current differencing parameter: %15.12e\n",h);
349: #endif
350:   if (ctx->historyh && ctx->ncurrenth < ctx->maxcurrenth) {
351:     ctx->historyh[ctx->ncurrenth] = h;
352:   }
353:   ctx->ncurrenth++;

355:   /* w = u + ha */
356:   if (ctx->drscale) {
357:     VecPointwiseMult(ctx->drscale,a,U);
358:     VecAYPX(U,h,w);
359:   } else {
360:     VecWAXPY(w,h,a,U);
361:   }

363:   /* compute func(U) as base for differencing; only needed first time in and not when provided by user */
364:   if (ctx->ncurrenth == 1 && ctx->current_f_allocated) {
365:     (*ctx->func)(ctx->funcctx,U,F);
366:   }
367:   (*ctx->func)(ctx->funcctx,w,y);

369:   VecAXPY(y,-1.0,F);
370:   VecScale(y,1.0/h);

372:   if ((ctx->vshift != 0.0) || (ctx->vscale != 1.0)) {
373:     VecAXPBY(y,ctx->vshift,ctx->vscale,a);
374:   }
375:   if (ctx->dlscale) {
376:     VecPointwiseMult(y,ctx->dlscale,y);
377:   }
378:   if (ctx->dshift) {
379:     if (!ctx->dshiftw) {
380:       VecDuplicate(y,&ctx->dshiftw);
381:     }
382:     VecPointwiseMult(ctx->dshift,a,ctx->dshiftw);
383:     VecAXPY(y,1.0,ctx->dshiftw);
384:   }

386:   if (mat->nullsp) {MatNullSpaceRemove(mat->nullsp,y);}

388:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
389:   return(0);
390: }

392: /*
393:   MatGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix

395:         y ~= (F(u + ha) - F(u))/h,
396:   where F = nonlinear function, as set by SNESSetFunction()
397:         u = current iterate
398:         h = difference interval
399: */
400: PetscErrorCode MatGetDiagonal_MFFD(Mat mat,Vec a)
401: {
402:   MatMFFD        ctx = (MatMFFD)mat->data;
403:   PetscScalar    h,*aa,*ww,v;
404:   PetscReal      epsilon = PETSC_SQRT_MACHINE_EPSILON,umin = 100.0*PETSC_SQRT_MACHINE_EPSILON;
405:   Vec            w,U;
407:   PetscInt       i,rstart,rend;

410:   if (!ctx->func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Requires calling MatMFFDSetFunction() first");
411:   if (!ctx->funci) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Requires calling MatMFFDSetFunctioni() first");
412:   if (!ctx->funcisetbase) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Requires calling MatMFFDSetFunctioniBase() first");
413:   w    = ctx->w;
414:   U    = ctx->current_u;
415:   (*ctx->func)(ctx->funcctx,U,a);
416:   (*ctx->funcisetbase)(ctx->funcctx,U);
417:   VecCopy(U,w);

419:   VecGetOwnershipRange(a,&rstart,&rend);
420:   VecGetArray(a,&aa);
421:   for (i=rstart; i<rend; i++) {
422:     VecGetArray(w,&ww);
423:     h    = ww[i-rstart];
424:     if (h == 0.0) h = 1.0;
425:     if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0)     h = umin;
426:     else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
427:     h *= epsilon;

429:     ww[i-rstart] += h;
430:     VecRestoreArray(w,&ww);
431:     (*ctx->funci)(ctx->funcctx,i,w,&v);
432:     aa[i-rstart]  = (v - aa[i-rstart])/h;

434:     /* possibly shift and scale result */
435:     if ((ctx->vshift != 0.0) || (ctx->vscale != 1.0)) {
436:       aa[i - rstart] = ctx->vshift + ctx->vscale*aa[i-rstart];
437:     }

439:     VecGetArray(w,&ww);
440:     ww[i-rstart] -= h;
441:     VecRestoreArray(w,&ww);
442:   }
443:   VecRestoreArray(a,&aa);
444:   return(0);
445: }

447: static PetscErrorCode MatDiagonalScale_MFFD(Mat mat,Vec ll,Vec rr)
448: {
449:   MatMFFD        aij = (MatMFFD)mat->data;

453:   if (ll && !aij->dlscale) {
454:     VecDuplicate(ll,&aij->dlscale);
455:   }
456:   if (rr && !aij->drscale) {
457:     VecDuplicate(rr,&aij->drscale);
458:   }
459:   if (ll) {
460:     VecCopy(ll,aij->dlscale);
461:   }
462:   if (rr) {
463:     VecCopy(rr,aij->drscale);
464:   }
465:   return(0);
466: }

468: static PetscErrorCode MatDiagonalSet_MFFD(Mat mat,Vec ll,InsertMode mode)
469: {
470:   MatMFFD        aij = (MatMFFD)mat->data;

474:   if (mode == INSERT_VALUES) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No diagonal set with INSERT_VALUES");
475:   if (!aij->dshift) {
476:     VecDuplicate(ll,&aij->dshift);
477:   }
478:   VecAXPY(aij->dshift,1.0,ll);
479:   return(0);
480: }

482: static PetscErrorCode MatShift_MFFD(Mat Y,PetscScalar a)
483: {
484:   MatMFFD shell = (MatMFFD)Y->data;

487:   shell->vshift += a;
488:   return(0);
489: }

491: static PetscErrorCode MatScale_MFFD(Mat Y,PetscScalar a)
492: {
493:   MatMFFD shell = (MatMFFD)Y->data;

496:   shell->vscale *= a;
497:   return(0);
498: }

500: PETSC_EXTERN PetscErrorCode MatMFFDSetBase_MFFD(Mat J,Vec U,Vec F)
501: {
503:   MatMFFD        ctx = (MatMFFD)J->data;

506:   MatMFFDResetHHistory(J);
507:   if (!ctx->current_u) {
508:     VecDuplicate(U,&ctx->current_u);
509:     VecLockPush(ctx->current_u);
510:   }
511:   VecLockPop(ctx->current_u);
512:   VecCopy(U,ctx->current_u);
513:   VecLockPush(ctx->current_u);
514:   if (F) {
515:     if (ctx->current_f_allocated) {VecDestroy(&ctx->current_f);}
516:     ctx->current_f           = F;
517:     ctx->current_f_allocated = PETSC_FALSE;
518:   } else if (!ctx->current_f_allocated) {
519:     MatCreateVecs(J,NULL,&ctx->current_f);

521:     ctx->current_f_allocated = PETSC_TRUE;
522:   }
523:   if (!ctx->w) {
524:     VecDuplicate(ctx->current_u,&ctx->w);
525:   }
526:   J->assembled = PETSC_TRUE;
527:   return(0);
528: }

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

532: static PetscErrorCode  MatMFFDSetCheckh_MFFD(Mat J,FCN3 fun,void *ectx)
533: {
534:   MatMFFD ctx = (MatMFFD)J->data;

537:   ctx->checkh    = fun;
538:   ctx->checkhctx = ectx;
539:   return(0);
540: }

542: /*@C
543:    MatMFFDSetOptionsPrefix - Sets the prefix used for searching for all
544:    MatMFFD options in the database.

546:    Collective on Mat

548:    Input Parameter:
549: +  A - the Mat context
550: -  prefix - the prefix to prepend to all option names

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

556:    Level: advanced

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

560: .seealso: MatSetFromOptions(), MatCreateSNESMF(), MatCreateMFFD()
561: @*/
562: PetscErrorCode  MatMFFDSetOptionsPrefix(Mat mat,const char prefix[])

564: {
565:   MatMFFD        mfctx = mat ? (MatMFFD)mat->data : (MatMFFD)NULL;

571:   PetscObjectSetOptionsPrefix((PetscObject)mfctx,prefix);
572:   return(0);
573: }

575: static PetscErrorCode  MatSetFromOptions_MFFD(PetscOptionItems *PetscOptionsObject,Mat mat)
576: {
577:   MatMFFD        mfctx = (MatMFFD)mat->data;
579:   PetscBool      flg;
580:   char           ftype[256];

585:   PetscObjectOptionsBegin((PetscObject)mfctx);
586:   PetscOptionsFList("-mat_mffd_type","Matrix free type","MatMFFDSetType",MatMFFDList,((PetscObject)mfctx)->type_name,ftype,256,&flg);
587:   if (flg) {
588:     MatMFFDSetType(mat,ftype);
589:   }

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

594:   flg  = PETSC_FALSE;
595:   PetscOptionsBool("-mat_mffd_check_positivity","Insure that U + h*a is nonnegative","MatMFFDSetCheckh",flg,&flg,NULL);
596:   if (flg) {
597:     MatMFFDSetCheckh(mat,MatMFFDCheckPositivity,0);
598:   }
599:   if (mfctx->ops->setfromoptions) {
600:     (*mfctx->ops->setfromoptions)(PetscOptionsObject,mfctx);
601:   }
602:   PetscOptionsEnd();
603:   return(0);
604: }

606: static PetscErrorCode  MatMFFDSetPeriod_MFFD(Mat mat,PetscInt period)
607: {
608:   MatMFFD ctx = (MatMFFD)mat->data;

611:   ctx->recomputeperiod = period;
612:   return(0);
613: }

615: static PetscErrorCode  MatMFFDSetFunction_MFFD(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
616: {
617:   MatMFFD ctx = (MatMFFD)mat->data;

620:   ctx->func    = func;
621:   ctx->funcctx = funcctx;
622:   return(0);
623: }

625: static PetscErrorCode  MatMFFDSetFunctionError_MFFD(Mat mat,PetscReal error)
626: {
627:   MatMFFD ctx = (MatMFFD)mat->data;

630:   if (error != PETSC_DEFAULT) ctx->error_rel = error;
631:   return(0);
632: }

634: static PetscErrorCode MatMissingDiagonal_MFFD(Mat A,PetscBool  *missing,PetscInt *d)
635: {
637:   *missing = PETSC_FALSE;
638:   return(0);
639: }

641: /*MC
642:   MATMFFD - MATMFFD = "mffd" - A matrix free matrix type.

644:   Level: advanced

646: .seealso: MatCreateMFFD(), MatCreateSNESMF(), MatMFFDSetFunction(), MatMFFDSetType(),  
647:           MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
648:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
649:           MatMFFDGetH(),
650: M*/
651: PETSC_EXTERN PetscErrorCode MatCreate_MFFD(Mat A)
652: {
653:   MatMFFD        mfctx;

657:   MatMFFDInitializePackage();

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

661:   mfctx->error_rel                = PETSC_SQRT_MACHINE_EPSILON;
662:   mfctx->recomputeperiod          = 1;
663:   mfctx->count                    = 0;
664:   mfctx->currenth                 = 0.0;
665:   mfctx->historyh                 = NULL;
666:   mfctx->ncurrenth                = 0;
667:   mfctx->maxcurrenth              = 0;
668:   ((PetscObject)mfctx)->type_name = 0;

670:   mfctx->vshift = 0.0;
671:   mfctx->vscale = 1.0;

673:   /*
674:      Create the empty data structure to contain compute-h routines.
675:      These will be filled in below from the command line options or
676:      a later call with MatMFFDSetType() or if that is not called
677:      then it will default in the first use of MatMult_MFFD()
678:   */
679:   mfctx->ops->compute        = 0;
680:   mfctx->ops->destroy        = 0;
681:   mfctx->ops->view           = 0;
682:   mfctx->ops->setfromoptions = 0;
683:   mfctx->hctx                = 0;

685:   mfctx->func    = 0;
686:   mfctx->funcctx = 0;
687:   mfctx->w       = NULL;

689:   A->data = mfctx;

691:   A->ops->mult            = MatMult_MFFD;
692:   A->ops->destroy         = MatDestroy_MFFD;
693:   A->ops->view            = MatView_MFFD;
694:   A->ops->assemblyend     = MatAssemblyEnd_MFFD;
695:   A->ops->scale           = MatScale_MFFD;
696:   A->ops->shift           = MatShift_MFFD;
697:   A->ops->diagonalscale   = MatDiagonalScale_MFFD;
698:   A->ops->diagonalset     = MatDiagonalSet_MFFD;
699:   A->ops->setfromoptions  = MatSetFromOptions_MFFD;
700:   A->ops->missingdiagonal = MatMissingDiagonal_MFFD;
701:   A->assembled            = PETSC_TRUE;

703:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetBase_C",MatMFFDSetBase_MFFD);
704:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioniBase_C",MatMFFDSetFunctioniBase_MFFD);
705:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioni_C",MatMFFDSetFunctioni_MFFD);
706:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunction_C",MatMFFDSetFunction_MFFD);
707:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetCheckh_C",MatMFFDSetCheckh_MFFD);
708:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetPeriod_C",MatMFFDSetPeriod_MFFD);
709:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctionError_C",MatMFFDSetFunctionError_MFFD);
710:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDResetHHistory_C",MatMFFDResetHHistory_MFFD);

712:   mfctx->mat = A;

714:   PetscObjectChangeTypeName((PetscObject)A,MATMFFD);
715:   return(0);
716: }

718: /*@
719:    MatCreateMFFD - Creates a matrix-free matrix. See also MatCreateSNESMF()

721:    Collective on Vec

723:    Input Parameters:
724: +  comm - MPI communicator
725: .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
726:            This value should be the same as the local size used in creating the
727:            y vector for the matrix-vector product y = Ax.
728: .  n - This value should be the same as the local size used in creating the
729:        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
730:        calculated if N is given) For square matrices n is almost always m.
731: .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
732: -  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)


735:    Output Parameter:
736: .  J - the matrix-free matrix

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


744:    Level: advanced

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

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

753: .vb
754:      F'(u)*a = [F(u+h*a) - F(u)]/h where
755:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
756:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
757:  where
758:      error_rel = square root of relative error in function evaluation
759:      umin = minimum iterate parameter
760: .ve

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

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

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

771:    Options Database Keys:
772: +  -mat_mffd_err <error_rel> - Sets error_rel
773: .  -mat_mffd_unim <umin> - Sets umin (for default PETSc routine that computes h only)
774: -  -mat_mffd_check_positivity

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

778: .seealso: MatDestroy(), MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
779:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
780:           MatMFFDGetH(), MatMFFDRegister(), MatMFFDComputeJacobian()

782: @*/
783: PetscErrorCode  MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)
784: {

788:   MatCreate(comm,J);
789:   MatSetSizes(*J,m,n,M,N);
790:   MatSetType(*J,MATMFFD);
791:   MatSetUp(*J);
792:   return(0);
793: }

795: /*@
796:    MatMFFDGetH - Gets the last value that was used as the differencing
797:    parameter.

799:    Not Collective

801:    Input Parameters:
802: .  mat - the matrix obtained with MatCreateSNESMF()

804:    Output Paramter:
805: .  h - the differencing step size

807:    Level: advanced

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

811: .seealso: MatCreateSNESMF(),MatMFFDSetHHistory(), MatCreateMFFD(), MATMFFD, MatMFFDResetHHistory()
812: @*/
813: PetscErrorCode  MatMFFDGetH(Mat mat,PetscScalar *h)
814: {
815:   MatMFFD        ctx = (MatMFFD)mat->data;
817:   PetscBool      match;

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

825:   *h = ctx->currenth;
826:   return(0);
827: }

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

832:    Logically Collective on Mat

834:    Input Parameters:
835: +  mat - the matrix free matrix created via MatCreateSNESMF() or MatCreateMFFD()
836: .  func - the function to use
837: -  funcctx - optional function context passed to function

839:    Calling Sequence of func:
840: $     func (void *funcctx, Vec x, Vec f)

842: +  funcctx - user provided context
843: .  x - input vector
844: -  f - computed output function

846:    Level: advanced

848:    Notes:
849:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
850:     matrix inside your compute Jacobian routine

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

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

856: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD,
857:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
858: @*/
859: PetscErrorCode  MatMFFDSetFunction(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
860: {

865:   PetscTryMethod(mat,"MatMFFDSetFunction_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec),void*),(mat,func,funcctx));
866:   return(0);
867: }

869: /*@C
870:    MatMFFDSetFunctioni - Sets the function for a single component

872:    Logically Collective on Mat

874:    Input Parameters:
875: +  mat - the matrix free matrix created via MatCreateSNESMF()
876: -  funci - the function to use

878:    Level: advanced

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

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

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

890: @*/
891: PetscErrorCode  MatMFFDSetFunctioni(Mat mat,PetscErrorCode (*funci)(void*,PetscInt,Vec,PetscScalar*))
892: {

897:   PetscTryMethod(mat,"MatMFFDSetFunctioni_C",(Mat,PetscErrorCode (*)(void*,PetscInt,Vec,PetscScalar*)),(mat,funci));
898:   return(0);
899: }

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

904:    Logically Collective on Mat

906:    Input Parameters:
907: +  mat - the matrix free matrix created via MatCreateSNESMF()
908: -  func - the function to use

910:    Level: advanced

912:    Notes:
913:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
914:     matrix inside your compute Jacobian routine.
915:     This function is necessary to compute the diagonal of the matrix.


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

920: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
921:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction(), MatGetDiagonal()
922: @*/
923: PetscErrorCode  MatMFFDSetFunctioniBase(Mat mat,PetscErrorCode (*func)(void*,Vec))
924: {

929:   PetscTryMethod(mat,"MatMFFDSetFunctioniBase_C",(Mat,PetscErrorCode (*)(void*,Vec)),(mat,func));
930:   return(0);
931: }

933: /*@
934:    MatMFFDSetPeriod - Sets how often h is recomputed, by default it is everytime

936:    Logically Collective on Mat

938:    Input Parameters:
939: +  mat - the matrix free matrix created via MatCreateSNESMF()
940: -  period - 1 for everytime, 2 for every second etc

942:    Options Database Keys:
943: +  -mat_mffd_period <period>

945:    Level: advanced


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

950: .seealso: MatCreateSNESMF(),MatMFFDGetH(),
951:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
952: @*/
953: PetscErrorCode  MatMFFDSetPeriod(Mat mat,PetscInt period)
954: {

960:   PetscTryMethod(mat,"MatMFFDSetPeriod_C",(Mat,PetscInt),(mat,period));
961:   return(0);
962: }

964: /*@
965:    MatMFFDSetFunctionError - Sets the error_rel for the approximation of
966:    matrix-vector products using finite differences.

968:    Logically Collective on Mat

970:    Input Parameters:
971: +  mat - the matrix free matrix created via MatCreateMFFD() or MatCreateSNESMF()
972: -  error_rel - relative error (should be set to the square root of
973:                the relative error in the function evaluations)

975:    Options Database Keys:
976: +  -mat_mffd_err <error_rel> - Sets error_rel

978:    Level: advanced

980:    Notes:
981:    The default matrix-free matrix-vector product routine computes
982: .vb
983:      F'(u)*a = [F(u+h*a) - F(u)]/h where
984:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
985:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
986: .ve

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

990: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
991:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
992: @*/
993: PetscErrorCode  MatMFFDSetFunctionError(Mat mat,PetscReal error)
994: {

1000:   PetscTryMethod(mat,"MatMFFDSetFunctionError_C",(Mat,PetscReal),(mat,error));
1001:   return(0);
1002: }

1004: /*@
1005:    MatMFFDSetHHistory - Sets an array to collect a history of the
1006:    differencing values (h) computed for the matrix-free product.

1008:    Logically Collective on Mat

1010:    Input Parameters:
1011: +  J - the matrix-free matrix context
1012: .  histroy - space to hold the history
1013: -  nhistory - number of entries in history, if more entries are generated than
1014:               nhistory, then the later ones are discarded

1016:    Level: advanced

1018:    Notes:
1019:    Use MatMFFDResetHHistory() to reset the history counter and collect
1020:    a new batch of differencing parameters, h.

1022: .keywords: SNES, matrix-free, h history, differencing history

1024: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1025:           MatMFFDResetHHistory(), MatMFFDSetFunctionError()

1027: @*/
1028: PetscErrorCode  MatMFFDSetHHistory(Mat J,PetscScalar history[],PetscInt nhistory)
1029: {
1030:   MatMFFD        ctx = (MatMFFD)J->data;
1032:   PetscBool      match;

1038:   PetscObjectTypeCompare((PetscObject)J,MATMFFD,&match);
1039:   if (!match) SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_WRONG,"Not a MFFD matrix");
1040:   ctx->historyh    = history;
1041:   ctx->maxcurrenth = nhistory;
1042:   ctx->currenth    = 0.;
1043:   return(0);
1044: }

1046: /*@
1047:    MatMFFDResetHHistory - Resets the counter to zero to begin
1048:    collecting a new set of differencing histories.

1050:    Logically Collective on Mat

1052:    Input Parameters:
1053: .  J - the matrix-free matrix context

1055:    Level: advanced

1057:    Notes:
1058:    Use MatMFFDSetHHistory() to create the original history counter.

1060: .keywords: SNES, matrix-free, h history, differencing history

1062: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1063:           MatMFFDSetHHistory(), MatMFFDSetFunctionError()

1065: @*/
1066: PetscErrorCode  MatMFFDResetHHistory(Mat J)
1067: {

1072:   PetscTryMethod(J,"MatMFFDResetHHistory_C",(Mat),(J));
1073:   return(0);
1074: }

1076: /*@
1077:     MatMFFDSetBase - Sets the vector U at which matrix vector products of the
1078:         Jacobian are computed

1080:     Logically Collective on Mat

1082:     Input Parameters:
1083: +   J - the MatMFFD matrix
1084: .   U - the vector
1085: -   F - (optional) vector that contains F(u) if it has been already computed

1087:     Notes:
1088:     This is rarely used directly

1090:     If F is provided then it is not recomputed. Otherwise the function is evaluated at the base
1091:     point during the first MatMult() after each call to MatMFFDSetBase().

1093:     Level: advanced

1095: @*/
1096: PetscErrorCode  MatMFFDSetBase(Mat J,Vec U,Vec F)
1097: {

1104:   PetscTryMethod(J,"MatMFFDSetBase_C",(Mat,Vec,Vec),(J,U,F));
1105:   return(0);
1106: }

1108: /*@C
1109:     MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
1110:         it to satisfy some criteria

1112:     Logically Collective on Mat

1114:     Input Parameters:
1115: +   J - the MatMFFD matrix
1116: .   fun - the function that checks h
1117: -   ctx - any context needed by the function

1119:     Options Database Keys:
1120: .   -mat_mffd_check_positivity

1122:     Level: advanced

1124:     Notes:
1125:     For example, MatMFFDCheckPositivity() insures that all entries
1126:        of U + h*a are non-negative

1128:      The function you provide is called after the default h has been computed and allows you to
1129:      modify it.

1131: .seealso:  MatMFFDCheckPositivity()
1132: @*/
1133: PetscErrorCode  MatMFFDSetCheckh(Mat J,PetscErrorCode (*fun)(void*,Vec,Vec,PetscScalar*),void *ctx)
1134: {

1139:   PetscTryMethod(J,"MatMFFDSetCheckh_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec,PetscScalar*),void*),(J,fun,ctx));
1140:   return(0);
1141: }

1143: /*@
1144:     MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
1145:         zero, decreases h until this is satisfied.

1147:     Logically Collective on Vec

1149:     Input Parameters:
1150: +   U - base vector that is added to
1151: .   a - vector that is added
1152: .   h - scaling factor on a
1153: -   dummy - context variable (unused)

1155:     Options Database Keys:
1156: .   -mat_mffd_check_positivity

1158:     Level: advanced

1160:     Notes:
1161:     This is rarely used directly, rather it is passed as an argument to
1162:            MatMFFDSetCheckh()

1164: .seealso:  MatMFFDSetCheckh()
1165: @*/
1166: PetscErrorCode  MatMFFDCheckPositivity(void *dummy,Vec U,Vec a,PetscScalar *h)
1167: {
1168:   PetscReal      val, minval;
1169:   PetscScalar    *u_vec, *a_vec;
1171:   PetscInt       i,n;
1172:   MPI_Comm       comm;

1178:   PetscObjectGetComm((PetscObject)U,&comm);
1179:   VecGetArray(U,&u_vec);
1180:   VecGetArray(a,&a_vec);
1181:   VecGetLocalSize(U,&n);
1182:   minval = PetscAbsScalar(*h)*PetscRealConstant(1.01);
1183:   for (i=0; i<n; i++) {
1184:     if (PetscRealPart(u_vec[i] + *h*a_vec[i]) <= 0.0) {
1185:       val = PetscAbsScalar(u_vec[i]/a_vec[i]);
1186:       if (val < minval) minval = val;
1187:     }
1188:   }
1189:   VecRestoreArray(U,&u_vec);
1190:   VecRestoreArray(a,&a_vec);
1191:   MPIU_Allreduce(&minval,&val,1,MPIU_REAL,MPIU_MIN,comm);
1192:   if (val <= PetscAbsScalar(*h)) {
1193:     PetscInfo2(U,"Scaling back h from %g to %g\n",(double)PetscRealPart(*h),(double)(.99*val));
1194:     if (PetscRealPart(*h) > 0.0) *h =  0.99*val;
1195:     else                         *h = -0.99*val;
1196:   }
1197:   return(0);
1198: }