Actual source code: mffd.c

petsc-3.7.3 2016-07-24
Report Typos and Errors
  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,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,NULL, "-log_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: $     -mat_mffd_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: }

209: /* ----------------------------------------------------------------------------------------*/
212: PetscErrorCode MatDestroy_MFFD(Mat mat)
213: {
215:   MatMFFD        ctx = (MatMFFD)mat->data;

218:   VecDestroy(&ctx->w);
219:   VecDestroy(&ctx->drscale);
220:   VecDestroy(&ctx->dlscale);
221:   VecDestroy(&ctx->dshift);
222:   if (ctx->current_f_allocated) {
223:     VecDestroy(&ctx->current_f);
224:   }
225:   if (ctx->ops->destroy) {(*ctx->ops->destroy)(ctx);}
226:   PetscHeaderDestroy(&ctx);
227:   mat->data = 0;

229:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetBase_C",NULL);
230:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioniBase_C",NULL);
231:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctioni_C",NULL);
232:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunction_C",NULL);
233:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetFunctionError_C",NULL);
234:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetCheckh_C",NULL);
235:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDSetPeriod_C",NULL);
236:   PetscObjectComposeFunction((PetscObject)mat,"MatMFFDResetHHistory_C",NULL);
237:   return(0);
238: }

242: /*
243:    MatMFFDView_MFFD - Views matrix-free parameters.

245: */
246: PetscErrorCode MatView_MFFD(Mat J,PetscViewer viewer)
247: {
249:   MatMFFD        ctx = (MatMFFD)J->data;
250:   PetscBool      iascii, viewbase, viewfunction;
251:   const char     *prefix;

254:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
255:   if (iascii) {
256:     PetscViewerASCIIPrintf(viewer,"Matrix-free approximation:\n");
257:     PetscViewerASCIIPushTab(viewer);
258:     PetscViewerASCIIPrintf(viewer,"err=%g (relative error in function evaluation)\n",(double)ctx->error_rel);
259:     if (!((PetscObject)ctx)->type_name) {
260:       PetscViewerASCIIPrintf(viewer,"The compute h routine has not yet been set\n");
261:     } else {
262:       PetscViewerASCIIPrintf(viewer,"Using %s compute h routine\n",((PetscObject)ctx)->type_name);
263:     }
264:     if (ctx->ops->view) {
265:       (*ctx->ops->view)(ctx,viewer);
266:     }
267:     PetscObjectGetOptionsPrefix((PetscObject)J, &prefix);

269:     PetscOptionsHasName(((PetscObject)J)->options,prefix, "-mat_mffd_view_base", &viewbase);
270:     if (viewbase) {
271:       PetscViewerASCIIPrintf(viewer, "Base:\n");
272:       VecView(ctx->current_u, viewer);
273:     }
274:     PetscOptionsHasName(((PetscObject)J)->options,prefix, "-mat_mffd_view_function", &viewfunction);
275:     if (viewfunction) {
276:       PetscViewerASCIIPrintf(viewer, "Function:\n");
277:       VecView(ctx->current_f, viewer);
278:     }
279:     PetscViewerASCIIPopTab(viewer);
280:   }
281:   return(0);
282: }

286: /*
287:    MatAssemblyEnd_MFFD - Resets the ctx->ncurrenth to zero. This
288:    allows the user to indicate the beginning of a new linear solve by calling
289:    MatAssemblyXXX() on the matrix free matrix. This then allows the
290:    MatCreateMFFD_WP() to properly compute ||U|| only the first time
291:    in the linear solver rather than every time.

293:    This function is referenced directly from MatAssemblyEnd_SNESMF(), which may be in a different shared library hence
294:    it must be labeled as PETSC_EXTERN
295: */
296: PETSC_EXTERN PetscErrorCode MatAssemblyEnd_MFFD(Mat J,MatAssemblyType mt)
297: {
299:   MatMFFD        j = (MatMFFD)J->data;

302:   MatMFFDResetHHistory(J);
303:   j->vshift = 0.0;
304:   j->vscale = 1.0;
305:   return(0);
306: }

310: /*
311:   MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:

313:         y ~= (F(u + ha) - F(u))/h,
314:   where F = nonlinear function, as set by SNESSetFunction()
315:         u = current iterate
316:         h = difference interval
317: */
318: PetscErrorCode MatMult_MFFD(Mat mat,Vec a,Vec y)
319: {
320:   MatMFFD        ctx = (MatMFFD)mat->data;
321:   PetscScalar    h;
322:   Vec            w,U,F;
324:   PetscBool      zeroa;

327:   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");
328:   /* We log matrix-free matrix-vector products separately, so that we can
329:      separate the performance monitoring from the cases that use conventional
330:      storage.  We may eventually modify event logging to associate events
331:      with particular objects, hence alleviating the more general problem. */
332:   PetscLogEventBegin(MATMFFD_Mult,a,y,0,0);

334:   w = ctx->w;
335:   U = ctx->current_u;
336:   F = ctx->current_f;
337:   /*
338:       Compute differencing parameter
339:   */
340:   if (!ctx->ops->compute) {
341:     MatMFFDSetType(mat,MATMFFD_WP);
342:     MatSetFromOptions(mat);
343:   }
344:   (*ctx->ops->compute)(ctx,U,a,&h,&zeroa);
345:   if (zeroa) {
346:     VecSet(y,0.0);
347:     return(0);
348:   }

350:   if (mat->erroriffailure && PetscIsInfOrNanScalar(h)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed Nan differencing parameter h");
351:   if (ctx->checkh) {
352:     (*ctx->checkh)(ctx->checkhctx,U,a,&h);
353:   }

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

367:   /* w = u + ha */
368:   if (ctx->drscale) {
369:     VecPointwiseMult(ctx->drscale,a,U);
370:     VecAYPX(U,h,w);
371:   } else {
372:     VecWAXPY(w,h,a,U);
373:   }

375:   /* compute func(U) as base for differencing; only needed first time in and not when provided by user */
376:   if (ctx->ncurrenth == 1 && ctx->current_f_allocated) {
377:     (*ctx->func)(ctx->funcctx,U,F);
378:   }
379:   (*ctx->func)(ctx->funcctx,w,y);

381:   VecAXPY(y,-1.0,F);
382:   VecScale(y,1.0/h);

384:   if ((ctx->vshift != 0.0) || (ctx->vscale != 1.0)) {
385:     VecAXPBY(y,ctx->vshift,ctx->vscale,a);
386:   }
387:   if (ctx->dlscale) {
388:     VecPointwiseMult(y,ctx->dlscale,y);
389:   }
390:   if (ctx->dshift) {
391:     VecPointwiseMult(ctx->dshift,a,U);
392:     VecAXPY(y,1.0,U);
393:   }

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

397:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
398:   return(0);
399: }

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 = (MatMFFD)mat->data;
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:   if (!ctx->funci) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Requires calling MatMFFDSetFunctioni() first");

423:   w    = ctx->w;
424:   U    = ctx->current_u;
425:   (*ctx->func)(ctx->funcctx,U,a);
426:   (*ctx->funcisetbase)(ctx->funcctx,U);
427:   VecCopy(U,w);

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

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

444:     /* possibly shift and scale result */
445:     if ((ctx->vshift != 0.0) || (ctx->vscale != 1.0)) {
446:       aa[i - rstart] = ctx->vshift + ctx->vscale*aa[i-rstart];
447:     }

449:     VecGetArray(w,&ww);
450:     ww[i-rstart] -= h;
451:     VecRestoreArray(w,&ww);
452:   }
453:   VecRestoreArray(a,&aa);
454:   return(0);
455: }

459: PetscErrorCode MatDiagonalScale_MFFD(Mat mat,Vec ll,Vec rr)
460: {
461:   MatMFFD        aij = (MatMFFD)mat->data;

465:   if (ll && !aij->dlscale) {
466:     VecDuplicate(ll,&aij->dlscale);
467:   }
468:   if (rr && !aij->drscale) {
469:     VecDuplicate(rr,&aij->drscale);
470:   }
471:   if (ll) {
472:     VecCopy(ll,aij->dlscale);
473:   }
474:   if (rr) {
475:     VecCopy(rr,aij->drscale);
476:   }
477:   return(0);
478: }

482: PetscErrorCode MatDiagonalSet_MFFD(Mat mat,Vec ll,InsertMode mode)
483: {
484:   MatMFFD        aij = (MatMFFD)mat->data;

488:   if (mode == INSERT_VALUES) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No diagonal set with INSERT_VALUES");
489:   if (!aij->dshift) {
490:     VecDuplicate(ll,&aij->dshift);
491:   }
492:   VecAXPY(aij->dshift,1.0,ll);
493:   return(0);
494: }

498: PetscErrorCode MatShift_MFFD(Mat Y,PetscScalar a)
499: {
500:   MatMFFD shell = (MatMFFD)Y->data;

503:   shell->vshift += a;
504:   return(0);
505: }

509: PetscErrorCode MatScale_MFFD(Mat Y,PetscScalar a)
510: {
511:   MatMFFD shell = (MatMFFD)Y->data;

514:   shell->vscale *= a;
515:   return(0);
516: }

520: PETSC_EXTERN PetscErrorCode MatMFFDSetBase_MFFD(Mat J,Vec U,Vec F)
521: {
523:   MatMFFD        ctx = (MatMFFD)J->data;

526:   MatMFFDResetHHistory(J);

528:   ctx->current_u = U;
529:   if (F) {
530:     if (ctx->current_f_allocated) {VecDestroy(&ctx->current_f);}
531:     ctx->current_f           = F;
532:     ctx->current_f_allocated = PETSC_FALSE;
533:   } else if (!ctx->current_f_allocated) {
534:     MatCreateVecs(J,NULL,&ctx->current_f);

536:     ctx->current_f_allocated = PETSC_TRUE;
537:   }
538:   if (!ctx->w) {
539:     VecDuplicate(ctx->current_u, &ctx->w);
540:   }
541:   J->assembled = PETSC_TRUE;
542:   return(0);
543: }

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

549: PetscErrorCode  MatMFFDSetCheckh_MFFD(Mat J,FCN3 fun,void *ectx)
550: {
551:   MatMFFD ctx = (MatMFFD)J->data;

554:   ctx->checkh    = fun;
555:   ctx->checkhctx = ectx;
556:   return(0);
557: }

561: /*@C
562:    MatMFFDSetOptionsPrefix - Sets the prefix used for searching for all
563:    MatMFFD options in the database.

565:    Collective on Mat

567:    Input Parameter:
568: +  A - the Mat context
569: -  prefix - the prefix to prepend to all option names

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

575:    Level: advanced

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

579: .seealso: MatSetFromOptions(), MatCreateSNESMF()
580: @*/
581: PetscErrorCode  MatMFFDSetOptionsPrefix(Mat mat,const char prefix[])

583: {
584:   MatMFFD        mfctx = mat ? (MatMFFD)mat->data : (MatMFFD)NULL;

590:   PetscObjectSetOptionsPrefix((PetscObject)mfctx,prefix);
591:   return(0);
592: }

596: PetscErrorCode  MatSetFromOptions_MFFD(PetscOptionItems *PetscOptionsObject,Mat mat)
597: {
598:   MatMFFD        mfctx = (MatMFFD)mat->data;
600:   PetscBool      flg;
601:   char           ftype[256];

606:   PetscObjectOptionsBegin((PetscObject)mfctx);
607:   PetscOptionsFList("-mat_mffd_type","Matrix free type","MatMFFDSetType",MatMFFDList,((PetscObject)mfctx)->type_name,ftype,256,&flg);
608:   if (flg) {
609:     MatMFFDSetType(mat,ftype);
610:   }

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

615:   flg  = PETSC_FALSE;
616:   PetscOptionsBool("-mat_mffd_check_positivity","Insure that U + h*a is nonnegative","MatMFFDSetCheckh",flg,&flg,NULL);
617:   if (flg) {
618:     MatMFFDSetCheckh(mat,MatMFFDCheckPositivity,0);
619:   }
620:   if (mfctx->ops->setfromoptions) {
621:     (*mfctx->ops->setfromoptions)(PetscOptionsObject,mfctx);
622:   }
623:   PetscOptionsEnd();
624:   return(0);
625: }

629: PetscErrorCode  MatMFFDSetPeriod_MFFD(Mat mat,PetscInt period)
630: {
631:   MatMFFD ctx = (MatMFFD)mat->data;

635:   ctx->recomputeperiod = period;
636:   return(0);
637: }

641: PetscErrorCode  MatMFFDSetFunction_MFFD(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
642: {
643:   MatMFFD ctx = (MatMFFD)mat->data;

646:   ctx->func    = func;
647:   ctx->funcctx = funcctx;
648:   return(0);
649: }

653: PetscErrorCode  MatMFFDSetFunctionError_MFFD(Mat mat,PetscReal error)
654: {
655:   MatMFFD ctx = (MatMFFD)mat->data;

659:   if (error != PETSC_DEFAULT) ctx->error_rel = error;
660:   return(0);
661: }

665: static PetscErrorCode MatMissingDiagonal_MFFD(Mat A,PetscBool  *missing,PetscInt *d)
666: {
668:   *missing = PETSC_FALSE;
669:   return(0);
670: }

672: /*MC
673:   MATMFFD - MATMFFD = "mffd" - A matrix free matrix type.

675:   Level: advanced

677: .seealso: MatCreateMFFD(), MatCreateSNESMF(), MatMFFDSetFunction()
678: M*/
681: PETSC_EXTERN PetscErrorCode MatCreate_MFFD(Mat A)
682: {
683:   MatMFFD        mfctx;

687:   MatMFFDInitializePackage();

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

691:   mfctx->error_rel                = PETSC_SQRT_MACHINE_EPSILON;
692:   mfctx->recomputeperiod          = 1;
693:   mfctx->count                    = 0;
694:   mfctx->currenth                 = 0.0;
695:   mfctx->historyh                 = NULL;
696:   mfctx->ncurrenth                = 0;
697:   mfctx->maxcurrenth              = 0;
698:   ((PetscObject)mfctx)->type_name = 0;

700:   mfctx->vshift = 0.0;
701:   mfctx->vscale = 1.0;

703:   /*
704:      Create the empty data structure to contain compute-h routines.
705:      These will be filled in below from the command line options or
706:      a later call with MatMFFDSetType() or if that is not called
707:      then it will default in the first use of MatMult_MFFD()
708:   */
709:   mfctx->ops->compute        = 0;
710:   mfctx->ops->destroy        = 0;
711:   mfctx->ops->view           = 0;
712:   mfctx->ops->setfromoptions = 0;
713:   mfctx->hctx                = 0;

715:   mfctx->func    = 0;
716:   mfctx->funcctx = 0;
717:   mfctx->w       = NULL;

719:   A->data = mfctx;

721:   A->ops->mult            = MatMult_MFFD;
722:   A->ops->destroy         = MatDestroy_MFFD;
723:   A->ops->view            = MatView_MFFD;
724:   A->ops->assemblyend     = MatAssemblyEnd_MFFD;
725:   A->ops->getdiagonal     = MatGetDiagonal_MFFD;
726:   A->ops->scale           = MatScale_MFFD;
727:   A->ops->shift           = MatShift_MFFD;
728:   A->ops->diagonalscale   = MatDiagonalScale_MFFD;
729:   A->ops->diagonalset     = MatDiagonalSet_MFFD;
730:   A->ops->setfromoptions  = MatSetFromOptions_MFFD;
731:   A->ops->missingdiagonal = MatMissingDiagonal_MFFD;
732:   A->assembled           = PETSC_TRUE;

734:   PetscLayoutSetUp(A->rmap);
735:   PetscLayoutSetUp(A->cmap);

737:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetBase_C",MatMFFDSetBase_MFFD);
738:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioniBase_C",MatMFFDSetFunctioniBase_MFFD);
739:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioni_C",MatMFFDSetFunctioni_MFFD);
740:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunction_C",MatMFFDSetFunction_MFFD);
741:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetCheckh_C",MatMFFDSetCheckh_MFFD);
742:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetPeriod_C",MatMFFDSetPeriod_MFFD);
743:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctionError_C",MatMFFDSetFunctionError_MFFD);
744:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDResetHHistory_C",MatMFFDResetHHistory_MFFD);

746:   mfctx->mat = A;

748:   PetscObjectChangeTypeName((PetscObject)A,MATMFFD);
749:   return(0);
750: }

754: /*@
755:    MatCreateMFFD - Creates a matrix-free matrix. See also MatCreateSNESMF()

757:    Collective on Vec

759:    Input Parameters:
760: +  comm - MPI communicator
761: .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
762:            This value should be the same as the local size used in creating the
763:            y vector for the matrix-vector product y = Ax.
764: .  n - This value should be the same as the local size used in creating the
765:        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
766:        calculated if N is given) For square matrices n is almost always m.
767: .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
768: -  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)


771:    Output Parameter:
772: .  J - the matrix-free matrix

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


780:    Level: advanced

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

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

789: .vb
790:      F'(u)*a = [F(u+h*a) - F(u)]/h where
791:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
792:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
793:  where
794:      error_rel = square root of relative error in function evaluation
795:      umin = minimum iterate parameter
796: .ve

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

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

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

807:    Options Database Keys:
808: +  -mat_mffd_err <error_rel> - Sets error_rel
809: .  -mat_mffd_unim <umin> - Sets umin (for default PETSc routine that computes h only)
810: -  -mat_mffd_check_positivity

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

814: .seealso: MatDestroy(), MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
815:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
816:           MatMFFDGetH(), MatMFFDRegister(), MatMFFDComputeJacobian()

818: @*/
819: PetscErrorCode  MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)
820: {

824:   MatCreate(comm,J);
825:   MatSetSizes(*J,m,n,M,N);
826:   MatSetType(*J,MATMFFD);
827:   MatSetUp(*J);
828:   return(0);
829: }


834: /*@
835:    MatMFFDGetH - Gets the last value that was used as the differencing
836:    parameter.

838:    Not Collective

840:    Input Parameters:
841: .  mat - the matrix obtained with MatCreateSNESMF()

843:    Output Paramter:
844: .  h - the differencing step size

846:    Level: advanced

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

850: .seealso: MatCreateSNESMF(),MatMFFDSetHHistory(), MatCreateMFFD(), MATMFFD, MatMFFDResetHHistory()
851: @*/
852: PetscErrorCode  MatMFFDGetH(Mat mat,PetscScalar *h)
853: {
854:   MatMFFD        ctx = (MatMFFD)mat->data;
856:   PetscBool      match;

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

862:   *h = ctx->currenth;
863:   return(0);
864: }

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

871:    Logically Collective on Mat

873:    Input Parameters:
874: +  mat - the matrix free matrix created via MatCreateSNESMF() or MatCreateMFFD()
875: .  func - the function to use
876: -  funcctx - optional function context passed to function

878:    Calling Sequence of func:
879: $     func (void *funcctx, Vec x, Vec f)

881: +  funcctx - user provided context
882: .  x - input vector
883: -  f - computed output function

885:    Level: advanced

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

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

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

895: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD,
896:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
897: @*/
898: PetscErrorCode  MatMFFDSetFunction(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
899: {

903:   PetscTryMethod(mat,"MatMFFDSetFunction_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec),void*),(mat,func,funcctx));
904:   return(0);
905: }

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

912:    Logically Collective on Mat

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

918:    Level: advanced

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


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

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

929: @*/
930: PetscErrorCode  MatMFFDSetFunctioni(Mat mat,PetscErrorCode (*funci)(void*,PetscInt,Vec,PetscScalar*))
931: {

936:   PetscTryMethod(mat,"MatMFFDSetFunctioni_C",(Mat,PetscErrorCode (*)(void*,PetscInt,Vec,PetscScalar*)),(mat,funci));
937:   return(0);
938: }


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

946:    Logically Collective on Mat

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

952:    Level: advanced

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


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

961: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
962:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
963: @*/
964: PetscErrorCode  MatMFFDSetFunctioniBase(Mat mat,PetscErrorCode (*func)(void*,Vec))
965: {

970:   PetscTryMethod(mat,"MatMFFDSetFunctioniBase_C",(Mat,PetscErrorCode (*)(void*,Vec)),(mat,func));
971:   return(0);
972: }

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

979:    Logically Collective on Mat

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

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

988:    Level: advanced


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

993: .seealso: MatCreateSNESMF(),MatMFFDGetH(),
994:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
995: @*/
996: PetscErrorCode  MatMFFDSetPeriod(Mat mat,PetscInt period)
997: {

1001:   PetscTryMethod(mat,"MatMFFDSetPeriod_C",(Mat,PetscInt),(mat,period));
1002:   return(0);
1003: }

1007: /*@
1008:    MatMFFDSetFunctionError - Sets the error_rel for the approximation of
1009:    matrix-vector products using finite differences.

1011:    Logically Collective on Mat

1013:    Input Parameters:
1014: +  mat - the matrix free matrix created via MatCreateMFFD() or MatCreateSNESMF()
1015: -  error_rel - relative error (should be set to the square root of
1016:                the relative error in the function evaluations)

1018:    Options Database Keys:
1019: +  -mat_mffd_err <error_rel> - Sets error_rel

1021:    Level: advanced

1023:    Notes:
1024:    The default matrix-free matrix-vector product routine computes
1025: .vb
1026:      F'(u)*a = [F(u+h*a) - F(u)]/h where
1027:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
1028:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
1029: .ve

1031: .keywords: SNES, matrix-free, parameters

1033: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
1034:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
1035: @*/
1036: PetscErrorCode  MatMFFDSetFunctionError(Mat mat,PetscReal error)
1037: {

1041:   PetscTryMethod(mat,"MatMFFDSetFunctionError_C",(Mat,PetscReal),(mat,error));
1042:   return(0);
1043: }

1047: /*@
1048:    MatMFFDSetHHistory - Sets an array to collect a history of the
1049:    differencing values (h) computed for the matrix-free product.

1051:    Logically Collective on Mat

1053:    Input Parameters:
1054: +  J - the matrix-free matrix context
1055: .  histroy - space to hold the history
1056: -  nhistory - number of entries in history, if more entries are generated than
1057:               nhistory, then the later ones are discarded

1059:    Level: advanced

1061:    Notes:
1062:    Use MatMFFDResetHHistory() to reset the history counter and collect
1063:    a new batch of differencing parameters, h.

1065: .keywords: SNES, matrix-free, h history, differencing history

1067: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1068:           MatMFFDResetHHistory(), MatMFFDSetFunctionError()

1070: @*/
1071: PetscErrorCode  MatMFFDSetHHistory(Mat J,PetscScalar history[],PetscInt nhistory)
1072: {
1073:   MatMFFD        ctx = (MatMFFD)J->data;
1075:   PetscBool      match;

1078:   PetscObjectTypeCompare((PetscObject)J,MATMFFD,&match);
1079:   if (!match) SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_WRONG,"Not a MFFD matrix");
1080:   ctx->historyh    = history;
1081:   ctx->maxcurrenth = nhistory;
1082:   ctx->currenth    = 0.;
1083:   return(0);
1084: }


1089: /*@
1090:    MatMFFDResetHHistory - Resets the counter to zero to begin
1091:    collecting a new set of differencing histories.

1093:    Logically Collective on Mat

1095:    Input Parameters:
1096: .  J - the matrix-free matrix context

1098:    Level: advanced

1100:    Notes:
1101:    Use MatMFFDSetHHistory() to create the original history counter.

1103: .keywords: SNES, matrix-free, h history, differencing history

1105: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1106:           MatMFFDSetHHistory(), MatMFFDSetFunctionError()

1108: @*/
1109: PetscErrorCode  MatMFFDResetHHistory(Mat J)
1110: {

1114:   PetscTryMethod(J,"MatMFFDResetHHistory_C",(Mat),(J));
1115:   return(0);
1116: }


1121: /*@
1122:     MatMFFDSetBase - Sets the vector U at which matrix vector products of the
1123:         Jacobian are computed

1125:     Logically Collective on Mat

1127:     Input Parameters:
1128: +   J - the MatMFFD matrix
1129: .   U - the vector
1130: -   F - (optional) vector that contains F(u) if it has been already computed

1132:     Notes: This is rarely used directly

1134:     If F is provided then it is not recomputed. Otherwise the function is evaluated at the base
1135:     point during the first MatMult() after each call to MatMFFDSetBase().

1137:     Level: advanced

1139: @*/
1140: PetscErrorCode  MatMFFDSetBase(Mat J,Vec U,Vec F)
1141: {

1148:   PetscTryMethod(J,"MatMFFDSetBase_C",(Mat,Vec,Vec),(J,U,F));
1149:   return(0);
1150: }

1154: /*@C
1155:     MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
1156:         it to satisfy some criteria

1158:     Logically Collective on Mat

1160:     Input Parameters:
1161: +   J - the MatMFFD matrix
1162: .   fun - the function that checks h
1163: -   ctx - any context needed by the function

1165:     Options Database Keys:
1166: .   -mat_mffd_check_positivity

1168:     Level: advanced

1170:     Notes: For example, MatMFFDSetCheckPositivity() insures that all entries
1171:        of U + h*a are non-negative

1173: .seealso:  MatMFFDSetCheckPositivity()
1174: @*/
1175: PetscErrorCode  MatMFFDSetCheckh(Mat J,PetscErrorCode (*fun)(void*,Vec,Vec,PetscScalar*),void *ctx)
1176: {

1181:   PetscTryMethod(J,"MatMFFDSetCheckh_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec,PetscScalar*),void*),(J,fun,ctx));
1182:   return(0);
1183: }

1187: /*@
1188:     MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
1189:         zero, decreases h until this is satisfied.

1191:     Logically Collective on Vec

1193:     Input Parameters:
1194: +   U - base vector that is added to
1195: .   a - vector that is added
1196: .   h - scaling factor on a
1197: -   dummy - context variable (unused)

1199:     Options Database Keys:
1200: .   -mat_mffd_check_positivity

1202:     Level: advanced

1204:     Notes: This is rarely used directly, rather it is passed as an argument to
1205:            MatMFFDSetCheckh()

1207: .seealso:  MatMFFDSetCheckh()
1208: @*/
1209: PetscErrorCode  MatMFFDCheckPositivity(void *dummy,Vec U,Vec a,PetscScalar *h)
1210: {
1211:   PetscReal      val, minval;
1212:   PetscScalar    *u_vec, *a_vec;
1214:   PetscInt       i,n;
1215:   MPI_Comm       comm;

1218:   PetscObjectGetComm((PetscObject)U,&comm);
1219:   VecGetArray(U,&u_vec);
1220:   VecGetArray(a,&a_vec);
1221:   VecGetLocalSize(U,&n);
1222:   minval = PetscAbsScalar(*h*1.01);
1223:   for (i=0; i<n; i++) {
1224:     if (PetscRealPart(u_vec[i] + *h*a_vec[i]) <= 0.0) {
1225:       val = PetscAbsScalar(u_vec[i]/a_vec[i]);
1226:       if (val < minval) minval = val;
1227:     }
1228:   }
1229:   VecRestoreArray(U,&u_vec);
1230:   VecRestoreArray(a,&a_vec);
1231:   MPIU_Allreduce(&minval,&val,1,MPIU_REAL,MPIU_MIN,comm);
1232:   if (val <= PetscAbsScalar(*h)) {
1233:     PetscInfo2(U,"Scaling back h from %g to %g\n",(double)PetscRealPart(*h),(double)(.99*val));
1234:     if (PetscRealPart(*h) > 0.0) *h =  0.99*val;
1235:     else                         *h = -0.99*val;
1236:   }
1237:   return(0);
1238: }