Actual source code: mffd.c

petsc-master 2018-01-18
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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:   char           *className;
 46:   PetscBool      opt;

 50:   if (MatMFFDPackageInitialized) return(0);
 51:   MatMFFDPackageInitialized = PETSC_TRUE;
 52:   /* Register Classes */
 53:   PetscClassIdRegister("MatMFFD",&MATMFFD_CLASSID);
 54:   /* Register Constructors */
 55:   MatMFFDRegisterAll();
 56:   /* Register Events */
 57:   PetscLogEventRegister("MatMult MF",          MATMFFD_CLASSID,&MATMFFD_Mult);

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

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

 83:     Input Parameters:
 84: +   mat - the "matrix-free" matrix created via MatCreateSNESMF(), or MatCreateMFFD()
 85:           or MatSetType(mat,MATMFFD);
 86: -   ftype - the type requested, either MATMFFD_WP or MATMFFD_DS

 88:     Level: advanced

 90:     Notes:
 91:     For example, such routines can compute h for use in
 92:     Jacobian-vector products of the form

 94:                         F(x+ha) - F(x)
 95:           F'(u)a  ~=  ----------------
 96:                               h

 98: .seealso: MatCreateSNESMF(), MatMFFDRegister(), MatMFFDSetFunction(), MatCreateMFFD()
 99: @*/
100: PetscErrorCode  MatMFFDSetType(Mat mat,MatMFFDType ftype)
101: {
102:   PetscErrorCode ierr,(*r)(MatMFFD);
103:   MatMFFD        ctx = (MatMFFD)mat->data;
104:   PetscBool      match;


110:   PetscObjectTypeCompare((PetscObject)mat,MATMFFD,&match);
111:   if (!match) return(0);

113:   /* already set, so just return */
114:   PetscObjectTypeCompare((PetscObject)ctx,ftype,&match);
115:   if (match) return(0);

117:   /* destroy the old one if it exists */
118:   if (ctx->ops->destroy) {
119:     (*ctx->ops->destroy)(ctx);
120:   }

122:    PetscFunctionListFind(MatMFFDList,ftype,&r);
123:   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown MatMFFD type %s given",ftype);
124:   (*r)(ctx);
125:   PetscObjectChangeTypeName((PetscObject)ctx,ftype);
126:   return(0);
127: }

129: static PetscErrorCode MatGetDiagonal_MFFD(Mat,Vec);

131: typedef PetscErrorCode (*FCN1)(void*,Vec); /* force argument to next function to not be extern C*/
132: static PetscErrorCode  MatMFFDSetFunctioniBase_MFFD(Mat mat,FCN1 func)
133: {
134:   MatMFFD ctx = (MatMFFD)mat->data;

137:   ctx->funcisetbase = func;
138:   /* allow users to compose their own getdiagonal and allow MatHasOperation
139:      to return false if the two functions pointers are not set */
140:   if (!mat->ops->getdiagonal && func) {
141:     mat->ops->getdiagonal = MatGetDiagonal_MFFD;
142:   }
143:   return(0);
144: }

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

152:   ctx->funci = funci;
153:   /* allow users to compose their own getdiagonal and allow MatHasOperation
154:      to return false if the two functions pointers are not set */
155:   if (!mat->ops->getdiagonal && funci) {
156:     mat->ops->getdiagonal = MatGetDiagonal_MFFD;
157:   }
158:   return(0);
159: }

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

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

170: /*@C
171:    MatMFFDRegister - Adds a method to the MatMFFD registry.

173:    Not Collective

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

179:    Level: developer

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

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

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

194: .keywords: MatMFFD, register

196: .seealso: MatMFFDRegisterAll(), MatMFFDRegisterDestroy()
197:  @*/
198: PetscErrorCode  MatMFFDRegister(const char sname[],PetscErrorCode (*function)(MatMFFD))
199: {

203:   PetscFunctionListAdd(&MatMFFDList,sname,function);
204:   return(0);
205: }

207: /* ----------------------------------------------------------------------------------------*/
208: static PetscErrorCode MatDestroy_MFFD(Mat mat)
209: {
211:   MatMFFD        ctx = (MatMFFD)mat->data;

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

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

238: /*
239:    MatMFFDView_MFFD - Views matrix-free parameters.

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

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

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

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

287:    This function is referenced directly from MatAssemblyEnd_SNESMF(), which may be in a different shared library hence
288:    it must be labeled as PETSC_EXTERN
289: */
290: PETSC_EXTERN PetscErrorCode MatAssemblyEnd_MFFD(Mat J,MatAssemblyType mt)
291: {
293:   MatMFFD        j = (MatMFFD)J->data;

296:   MatMFFDResetHHistory(J);
297:   j->vshift = 0.0;
298:   j->vscale = 1.0;
299:   return(0);
300: }

302: /*
303:   MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:

305:         y ~= (F(u + ha) - F(u))/h,
306:   where F = nonlinear function, as set by SNESSetFunction()
307:         u = current iterate
308:         h = difference interval
309: */
310: static PetscErrorCode MatMult_MFFD(Mat mat,Vec a,Vec y)
311: {
312:   MatMFFD        ctx = (MatMFFD)mat->data;
313:   PetscScalar    h;
314:   Vec            w,U,F;
316:   PetscBool      zeroa;

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

326:   w = ctx->w;
327:   U = ctx->current_u;
328:   F = ctx->current_f;
329:   /*
330:       Compute differencing parameter
331:   */
332:   if (!((PetscObject)ctx)->type_name) {
333:     MatMFFDSetType(mat,MATMFFD_WP);
334:     MatSetFromOptions(mat);
335:   }
336:   (*ctx->ops->compute)(ctx,U,a,&h,&zeroa);
337:   if (zeroa) {
338:     VecSet(y,0.0);
339:     return(0);
340:   }

342:   if (mat->erroriffailure && PetscIsInfOrNanScalar(h)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed Nan differencing parameter h");
343:   if (ctx->checkh) {
344:     (*ctx->checkh)(ctx->checkhctx,U,a,&h);
345:   }

347:   /* keep a record of the current differencing parameter h */
348:   ctx->currenth = h;
349: #if defined(PETSC_USE_COMPLEX)
350:   PetscInfo2(mat,"Current differencing parameter: %g + %g i\n",(double)PetscRealPart(h),(double)PetscImaginaryPart(h));
351: #else
352:   PetscInfo1(mat,"Current differencing parameter: %15.12e\n",h);
353: #endif
354:   if (ctx->historyh && ctx->ncurrenth < ctx->maxcurrenth) {
355:     ctx->historyh[ctx->ncurrenth] = h;
356:   }
357:   ctx->ncurrenth++;

359:   /* w = u + ha */
360:   if (ctx->drscale) {
361:     VecPointwiseMult(ctx->drscale,a,U);
362:     VecAYPX(U,h,w);
363:   } else {
364:     VecWAXPY(w,h,a,U);
365:   }

367:   /* compute func(U) as base for differencing; only needed first time in and not when provided by user */
368:   if (ctx->ncurrenth == 1 && ctx->current_f_allocated) {
369:     (*ctx->func)(ctx->funcctx,U,F);
370:   }
371:   (*ctx->func)(ctx->funcctx,w,y);

373:   VecAXPY(y,-1.0,F);
374:   VecScale(y,1.0/h);

376:   if ((ctx->vshift != 0.0) || (ctx->vscale != 1.0)) {
377:     VecAXPBY(y,ctx->vshift,ctx->vscale,a);
378:   }
379:   if (ctx->dlscale) {
380:     VecPointwiseMult(y,ctx->dlscale,y);
381:   }
382:   if (ctx->dshift) {
383:     if (!ctx->dshiftw) {
384:       VecDuplicate(y,&ctx->dshiftw);
385:     }
386:     VecPointwiseMult(ctx->dshift,a,ctx->dshiftw);
387:     VecAXPY(y,1.0,ctx->dshiftw);
388:   }

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

392:   PetscLogEventEnd(MATMFFD_Mult,a,y,0,0);
393:   return(0);
394: }

396: /*
397:   MatGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix

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

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

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

433:     ww[i-rstart] += h;
434:     VecRestoreArray(w,&ww);
435:     (*ctx->funci)(ctx->funcctx,i,w,&v);
436:     aa[i-rstart]  = (v - aa[i-rstart])/h;

438:     /* possibly shift and scale result */
439:     if ((ctx->vshift != 0.0) || (ctx->vscale != 1.0)) {
440:       aa[i - rstart] = ctx->vshift + ctx->vscale*aa[i-rstart];
441:     }

443:     VecGetArray(w,&ww);
444:     ww[i-rstart] -= h;
445:     VecRestoreArray(w,&ww);
446:   }
447:   VecRestoreArray(a,&aa);
448:   return(0);
449: }

451: static PetscErrorCode MatDiagonalScale_MFFD(Mat mat,Vec ll,Vec rr)
452: {
453:   MatMFFD        aij = (MatMFFD)mat->data;

457:   if (ll && !aij->dlscale) {
458:     VecDuplicate(ll,&aij->dlscale);
459:   }
460:   if (rr && !aij->drscale) {
461:     VecDuplicate(rr,&aij->drscale);
462:   }
463:   if (ll) {
464:     VecCopy(ll,aij->dlscale);
465:   }
466:   if (rr) {
467:     VecCopy(rr,aij->drscale);
468:   }
469:   return(0);
470: }

472: static PetscErrorCode MatDiagonalSet_MFFD(Mat mat,Vec ll,InsertMode mode)
473: {
474:   MatMFFD        aij = (MatMFFD)mat->data;

478:   if (mode == INSERT_VALUES) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No diagonal set with INSERT_VALUES");
479:   if (!aij->dshift) {
480:     VecDuplicate(ll,&aij->dshift);
481:   }
482:   VecAXPY(aij->dshift,1.0,ll);
483:   return(0);
484: }

486: static PetscErrorCode MatShift_MFFD(Mat Y,PetscScalar a)
487: {
488:   MatMFFD shell = (MatMFFD)Y->data;

491:   shell->vshift += a;
492:   return(0);
493: }

495: static PetscErrorCode MatScale_MFFD(Mat Y,PetscScalar a)
496: {
497:   MatMFFD shell = (MatMFFD)Y->data;

500:   shell->vscale *= a;
501:   return(0);
502: }

504: PETSC_EXTERN PetscErrorCode MatMFFDSetBase_MFFD(Mat J,Vec U,Vec F)
505: {
507:   MatMFFD        ctx = (MatMFFD)J->data;

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

525:     ctx->current_f_allocated = PETSC_TRUE;
526:   }
527:   if (!ctx->w) {
528:     VecDuplicate(ctx->current_u,&ctx->w);
529:   }
530:   J->assembled = PETSC_TRUE;
531:   return(0);
532: }

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

536: static PetscErrorCode  MatMFFDSetCheckh_MFFD(Mat J,FCN3 fun,void *ectx)
537: {
538:   MatMFFD ctx = (MatMFFD)J->data;

541:   ctx->checkh    = fun;
542:   ctx->checkhctx = ectx;
543:   return(0);
544: }

546: /*@C
547:    MatMFFDSetOptionsPrefix - Sets the prefix used for searching for all
548:    MatMFFD options in the database.

550:    Collective on Mat

552:    Input Parameter:
553: +  A - the Mat context
554: -  prefix - the prefix to prepend to all option names

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

560:    Level: advanced

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

564: .seealso: MatSetFromOptions(), MatCreateSNESMF(), MatCreateMFFD()
565: @*/
566: PetscErrorCode  MatMFFDSetOptionsPrefix(Mat mat,const char prefix[])

568: {
569:   MatMFFD        mfctx = mat ? (MatMFFD)mat->data : (MatMFFD)NULL;

575:   PetscObjectSetOptionsPrefix((PetscObject)mfctx,prefix);
576:   return(0);
577: }

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

589:   PetscObjectOptionsBegin((PetscObject)mfctx);
590:   PetscOptionsFList("-mat_mffd_type","Matrix free type","MatMFFDSetType",MatMFFDList,((PetscObject)mfctx)->type_name,ftype,256,&flg);
591:   if (flg) {
592:     MatMFFDSetType(mat,ftype);
593:   }

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

598:   flg  = PETSC_FALSE;
599:   PetscOptionsBool("-mat_mffd_check_positivity","Insure that U + h*a is nonnegative","MatMFFDSetCheckh",flg,&flg,NULL);
600:   if (flg) {
601:     MatMFFDSetCheckh(mat,MatMFFDCheckPositivity,0);
602:   }
603:   if (mfctx->ops->setfromoptions) {
604:     (*mfctx->ops->setfromoptions)(PetscOptionsObject,mfctx);
605:   }
606:   PetscOptionsEnd();
607:   return(0);
608: }

610: static PetscErrorCode  MatMFFDSetPeriod_MFFD(Mat mat,PetscInt period)
611: {
612:   MatMFFD ctx = (MatMFFD)mat->data;

615:   ctx->recomputeperiod = period;
616:   return(0);
617: }

619: static PetscErrorCode  MatMFFDSetFunction_MFFD(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
620: {
621:   MatMFFD ctx = (MatMFFD)mat->data;

624:   ctx->func    = func;
625:   ctx->funcctx = funcctx;
626:   return(0);
627: }

629: static PetscErrorCode  MatMFFDSetFunctionError_MFFD(Mat mat,PetscReal error)
630: {
631:   MatMFFD ctx = (MatMFFD)mat->data;

634:   if (error != PETSC_DEFAULT) ctx->error_rel = error;
635:   return(0);
636: }

638: static PetscErrorCode MatMissingDiagonal_MFFD(Mat A,PetscBool  *missing,PetscInt *d)
639: {
641:   *missing = PETSC_FALSE;
642:   return(0);
643: }

645: /*MC
646:   MATMFFD - MATMFFD = "mffd" - A matrix free matrix type.

648:   Level: advanced

650: .seealso: MatCreateMFFD(), MatCreateSNESMF(), MatMFFDSetFunction(), MatMFFDSetType(),  
651:           MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
652:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
653:           MatMFFDGetH(),
654: M*/
655: PETSC_EXTERN PetscErrorCode MatCreate_MFFD(Mat A)
656: {
657:   MatMFFD        mfctx;

661:   MatMFFDInitializePackage();

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

665:   mfctx->error_rel                = PETSC_SQRT_MACHINE_EPSILON;
666:   mfctx->recomputeperiod          = 1;
667:   mfctx->count                    = 0;
668:   mfctx->currenth                 = 0.0;
669:   mfctx->historyh                 = NULL;
670:   mfctx->ncurrenth                = 0;
671:   mfctx->maxcurrenth              = 0;
672:   ((PetscObject)mfctx)->type_name = 0;

674:   mfctx->vshift = 0.0;
675:   mfctx->vscale = 1.0;

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

689:   mfctx->func    = 0;
690:   mfctx->funcctx = 0;
691:   mfctx->w       = NULL;

693:   A->data = mfctx;

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

707:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetBase_C",MatMFFDSetBase_MFFD);
708:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioniBase_C",MatMFFDSetFunctioniBase_MFFD);
709:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioni_C",MatMFFDSetFunctioni_MFFD);
710:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunction_C",MatMFFDSetFunction_MFFD);
711:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetCheckh_C",MatMFFDSetCheckh_MFFD);
712:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetPeriod_C",MatMFFDSetPeriod_MFFD);
713:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctionError_C",MatMFFDSetFunctionError_MFFD);
714:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDResetHHistory_C",MatMFFDResetHHistory_MFFD);

716:   mfctx->mat = A;

718:   PetscObjectChangeTypeName((PetscObject)A,MATMFFD);
719:   return(0);
720: }

722: /*@
723:    MatCreateMFFD - Creates a matrix-free matrix. See also MatCreateSNESMF()

725:    Collective on Vec

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


739:    Output Parameter:
740: .  J - the matrix-free matrix

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


748:    Level: advanced

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

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

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

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

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

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

775:    Options Database Keys:
776: +  -mat_mffd_err <error_rel> - Sets error_rel
777: .  -mat_mffd_unim <umin> - Sets umin (for default PETSc routine that computes h only)
778: -  -mat_mffd_check_positivity

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

782: .seealso: MatDestroy(), MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
783:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
784:           MatMFFDGetH(), MatMFFDRegister(), MatMFFDComputeJacobian()

786: @*/
787: PetscErrorCode  MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)
788: {

792:   MatCreate(comm,J);
793:   MatSetSizes(*J,m,n,M,N);
794:   MatSetType(*J,MATMFFD);
795:   MatSetUp(*J);
796:   return(0);
797: }

799: /*@
800:    MatMFFDGetH - Gets the last value that was used as the differencing
801:    parameter.

803:    Not Collective

805:    Input Parameters:
806: .  mat - the matrix obtained with MatCreateSNESMF()

808:    Output Paramter:
809: .  h - the differencing step size

811:    Level: advanced

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

815: .seealso: MatCreateSNESMF(),MatMFFDSetHHistory(), MatCreateMFFD(), MATMFFD, MatMFFDResetHHistory()
816: @*/
817: PetscErrorCode  MatMFFDGetH(Mat mat,PetscScalar *h)
818: {
819:   MatMFFD        ctx = (MatMFFD)mat->data;
821:   PetscBool      match;

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

829:   *h = ctx->currenth;
830:   return(0);
831: }

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

836:    Logically Collective on Mat

838:    Input Parameters:
839: +  mat - the matrix free matrix created via MatCreateSNESMF() or MatCreateMFFD()
840: .  func - the function to use
841: -  funcctx - optional function context passed to function

843:    Calling Sequence of func:
844: $     func (void *funcctx, Vec x, Vec f)

846: +  funcctx - user provided context
847: .  x - input vector
848: -  f - computed output function

850:    Level: advanced

852:    Notes:
853:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
854:     matrix inside your compute Jacobian routine

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

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

860: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD,
861:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
862: @*/
863: PetscErrorCode  MatMFFDSetFunction(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
864: {

869:   PetscTryMethod(mat,"MatMFFDSetFunction_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec),void*),(mat,func,funcctx));
870:   return(0);
871: }

873: /*@C
874:    MatMFFDSetFunctioni - Sets the function for a single component

876:    Logically Collective on Mat

878:    Input Parameters:
879: +  mat - the matrix free matrix created via MatCreateSNESMF()
880: -  funci - the function to use

882:    Level: advanced

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

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

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

894: @*/
895: PetscErrorCode  MatMFFDSetFunctioni(Mat mat,PetscErrorCode (*funci)(void*,PetscInt,Vec,PetscScalar*))
896: {

901:   PetscTryMethod(mat,"MatMFFDSetFunctioni_C",(Mat,PetscErrorCode (*)(void*,PetscInt,Vec,PetscScalar*)),(mat,funci));
902:   return(0);
903: }

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

908:    Logically Collective on Mat

910:    Input Parameters:
911: +  mat - the matrix free matrix created via MatCreateSNESMF()
912: -  func - the function to use

914:    Level: advanced

916:    Notes:
917:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
918:     matrix inside your compute Jacobian routine.
919:     This function is necessary to compute the diagonal of the matrix.


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

924: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
925:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction(), MatGetDiagonal()
926: @*/
927: PetscErrorCode  MatMFFDSetFunctioniBase(Mat mat,PetscErrorCode (*func)(void*,Vec))
928: {

933:   PetscTryMethod(mat,"MatMFFDSetFunctioniBase_C",(Mat,PetscErrorCode (*)(void*,Vec)),(mat,func));
934:   return(0);
935: }

937: /*@
938:    MatMFFDSetPeriod - Sets how often h is recomputed, by default it is everytime

940:    Logically Collective on Mat

942:    Input Parameters:
943: +  mat - the matrix free matrix created via MatCreateSNESMF()
944: -  period - 1 for everytime, 2 for every second etc

946:    Options Database Keys:
947: +  -mat_mffd_period <period>

949:    Level: advanced


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

954: .seealso: MatCreateSNESMF(),MatMFFDGetH(),
955:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
956: @*/
957: PetscErrorCode  MatMFFDSetPeriod(Mat mat,PetscInt period)
958: {

964:   PetscTryMethod(mat,"MatMFFDSetPeriod_C",(Mat,PetscInt),(mat,period));
965:   return(0);
966: }

968: /*@
969:    MatMFFDSetFunctionError - Sets the error_rel for the approximation of
970:    matrix-vector products using finite differences.

972:    Logically Collective on Mat

974:    Input Parameters:
975: +  mat - the matrix free matrix created via MatCreateMFFD() or MatCreateSNESMF()
976: -  error_rel - relative error (should be set to the square root of
977:                the relative error in the function evaluations)

979:    Options Database Keys:
980: +  -mat_mffd_err <error_rel> - Sets error_rel

982:    Level: advanced

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

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

994: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
995:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
996: @*/
997: PetscErrorCode  MatMFFDSetFunctionError(Mat mat,PetscReal error)
998: {

1004:   PetscTryMethod(mat,"MatMFFDSetFunctionError_C",(Mat,PetscReal),(mat,error));
1005:   return(0);
1006: }

1008: /*@
1009:    MatMFFDSetHHistory - Sets an array to collect a history of the
1010:    differencing values (h) computed for the matrix-free product.

1012:    Logically Collective on Mat

1014:    Input Parameters:
1015: +  J - the matrix-free matrix context
1016: .  histroy - space to hold the history
1017: -  nhistory - number of entries in history, if more entries are generated than
1018:               nhistory, then the later ones are discarded

1020:    Level: advanced

1022:    Notes:
1023:    Use MatMFFDResetHHistory() to reset the history counter and collect
1024:    a new batch of differencing parameters, h.

1026: .keywords: SNES, matrix-free, h history, differencing history

1028: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1029:           MatMFFDResetHHistory(), MatMFFDSetFunctionError()

1031: @*/
1032: PetscErrorCode  MatMFFDSetHHistory(Mat J,PetscScalar history[],PetscInt nhistory)
1033: {
1034:   MatMFFD        ctx = (MatMFFD)J->data;
1036:   PetscBool      match;

1042:   PetscObjectTypeCompare((PetscObject)J,MATMFFD,&match);
1043:   if (!match) SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_WRONG,"Not a MFFD matrix");
1044:   ctx->historyh    = history;
1045:   ctx->maxcurrenth = nhistory;
1046:   ctx->currenth    = 0.;
1047:   return(0);
1048: }

1050: /*@
1051:    MatMFFDResetHHistory - Resets the counter to zero to begin
1052:    collecting a new set of differencing histories.

1054:    Logically Collective on Mat

1056:    Input Parameters:
1057: .  J - the matrix-free matrix context

1059:    Level: advanced

1061:    Notes:
1062:    Use MatMFFDSetHHistory() to create the original history counter.

1064: .keywords: SNES, matrix-free, h history, differencing history

1066: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
1067:           MatMFFDSetHHistory(), MatMFFDSetFunctionError()

1069: @*/
1070: PetscErrorCode  MatMFFDResetHHistory(Mat J)
1071: {

1076:   PetscTryMethod(J,"MatMFFDResetHHistory_C",(Mat),(J));
1077:   return(0);
1078: }

1080: /*@
1081:     MatMFFDSetBase - Sets the vector U at which matrix vector products of the
1082:         Jacobian are computed

1084:     Logically Collective on Mat

1086:     Input Parameters:
1087: +   J - the MatMFFD matrix
1088: .   U - the vector
1089: -   F - (optional) vector that contains F(u) if it has been already computed

1091:     Notes: This is rarely used directly

1093:     If F is provided then it is not recomputed. Otherwise the function is evaluated at the base
1094:     point during the first MatMult() after each call to MatMFFDSetBase().

1096:     Level: advanced

1098: @*/
1099: PetscErrorCode  MatMFFDSetBase(Mat J,Vec U,Vec F)
1100: {

1107:   PetscTryMethod(J,"MatMFFDSetBase_C",(Mat,Vec,Vec),(J,U,F));
1108:   return(0);
1109: }

1111: /*@C
1112:     MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
1113:         it to satisfy some criteria

1115:     Logically Collective on Mat

1117:     Input Parameters:
1118: +   J - the MatMFFD matrix
1119: .   fun - the function that checks h
1120: -   ctx - any context needed by the function

1122:     Options Database Keys:
1123: .   -mat_mffd_check_positivity

1125:     Level: advanced

1127:     Notes: For example, MatMFFDCheckPositivity() insures that all entries
1128:        of U + h*a are non-negative

1130:      The function you provide is called after the default h has been computed and allows you to
1131:      modify it.

1133: .seealso:  MatMFFDCheckPositivity()
1134: @*/
1135: PetscErrorCode  MatMFFDSetCheckh(Mat J,PetscErrorCode (*fun)(void*,Vec,Vec,PetscScalar*),void *ctx)
1136: {

1141:   PetscTryMethod(J,"MatMFFDSetCheckh_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec,PetscScalar*),void*),(J,fun,ctx));
1142:   return(0);
1143: }

1145: /*@
1146:     MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
1147:         zero, decreases h until this is satisfied.

1149:     Logically Collective on Vec

1151:     Input Parameters:
1152: +   U - base vector that is added to
1153: .   a - vector that is added
1154: .   h - scaling factor on a
1155: -   dummy - context variable (unused)

1157:     Options Database Keys:
1158: .   -mat_mffd_check_positivity

1160:     Level: advanced

1162:     Notes: This is rarely used directly, rather it is passed as an argument to
1163:            MatMFFDSetCheckh()

1165: .seealso:  MatMFFDSetCheckh()
1166: @*/
1167: PetscErrorCode  MatMFFDCheckPositivity(void *dummy,Vec U,Vec a,PetscScalar *h)
1168: {
1169:   PetscReal      val, minval;
1170:   PetscScalar    *u_vec, *a_vec;
1172:   PetscInt       i,n;
1173:   MPI_Comm       comm;

1179:   PetscObjectGetComm((PetscObject)U,&comm);
1180:   VecGetArray(U,&u_vec);
1181:   VecGetArray(a,&a_vec);
1182:   VecGetLocalSize(U,&n);
1183:   minval = PetscAbsScalar(*h)*PetscRealConstant(1.01);
1184:   for (i=0; i<n; i++) {
1185:     if (PetscRealPart(u_vec[i] + *h*a_vec[i]) <= 0.0) {
1186:       val = PetscAbsScalar(u_vec[i]/a_vec[i]);
1187:       if (val < minval) minval = val;
1188:     }
1189:   }
1190:   VecRestoreArray(U,&u_vec);
1191:   VecRestoreArray(a,&a_vec);
1192:   MPIU_Allreduce(&minval,&val,1,MPIU_REAL,MPIU_MIN,comm);
1193:   if (val <= PetscAbsScalar(*h)) {
1194:     PetscInfo2(U,"Scaling back h from %g to %g\n",(double)PetscRealPart(*h),(double)(.99*val));
1195:     if (PetscRealPart(*h) > 0.0) *h =  0.99*val;
1196:     else                         *h = -0.99*val;
1197:   }
1198:   return(0);
1199: }