Actual source code: mffd.c
petsc-3.7.1 2016-05-15
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      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: }