Date: 2015-10-02T22:10:31+00:00

Actual source code: mffd.c
petsc-3.6.2 2015-10-02
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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, "-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, "-log_summary_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(prefix, "-mat_mffd_view_base", &viewbase);
    270:     if (viewbase) {
    271:       PetscViewerASCIIPrintf(viewer, "Base:\n");
    272:       VecView(ctx->current_u, viewer);
    273:     }
    274:     PetscOptionsHasName(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.
    294: */
    295: PETSC_EXTERN PetscErrorCode MatAssemblyEnd_MFFD(Mat J,MatAssemblyType mt)
    296: {
    298:   MatMFFD        j = (MatMFFD)J->data;

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

    309: /*
    310:   MatMult_MFFD - Default matrix-free form for Jacobian-vector product, y = F'(u)*a:

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

    326:   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");
    327:   /* We log matrix-free matrix-vector products separately, so that we can
    328:      separate the performance monitoring from the cases that use conventional
    329:      storage.  We may eventually modify event logging to associate events
    330:      with particular objects, hence alleviating the more general problem. */
    331:   PetscLogEventBegin(MATMFFD_Mult,a,y,0,0);

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

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

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

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

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

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

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

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

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

    402: /*
    403:   MatGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix

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

    420:   if (!ctx->funci) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Requires calling MatMFFDSetFunctioni() first");

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    525:   MatMFFDResetHHistory(J);

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

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

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

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

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

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

    564:    Collective on Mat

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

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

    574:    Level: advanced

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

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

    582: {
    583:   MatMFFD        mfctx = mat ? (MatMFFD)mat->data : (MatMFFD)NULL;

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

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

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

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

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

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

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

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

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

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

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

    662: /*MC
    663:   MATMFFD - MATMFFD = "mffd" - A matrix free matrix type.

    665:   Level: advanced

    667: .seealso: MatCreateMFFD(), MatCreateSNESMF(), MatMFFDSetFunction()
    668: M*/
    671: PETSC_EXTERN PetscErrorCode MatCreate_MFFD(Mat A)
    672: {
    673:   MatMFFD        mfctx;

    677:   MatMFFDInitializePackage();

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

    681:   mfctx->error_rel                = PETSC_SQRT_MACHINE_EPSILON;
    682:   mfctx->recomputeperiod          = 1;
    683:   mfctx->count                    = 0;
    684:   mfctx->currenth                 = 0.0;
    685:   mfctx->historyh                 = NULL;
    686:   mfctx->ncurrenth                = 0;
    687:   mfctx->maxcurrenth              = 0;
    688:   ((PetscObject)mfctx)->type_name = 0;

    690:   mfctx->vshift = 0.0;
    691:   mfctx->vscale = 1.0;

    693:   /*
    694:      Create the empty data structure to contain compute-h routines.
    695:      These will be filled in below from the command line options or
    696:      a later call with MatMFFDSetType() or if that is not called
    697:      then it will default in the first use of MatMult_MFFD()
    698:   */
    699:   mfctx->ops->compute        = 0;
    700:   mfctx->ops->destroy        = 0;
    701:   mfctx->ops->view           = 0;
    702:   mfctx->ops->setfromoptions = 0;
    703:   mfctx->hctx                = 0;

    705:   mfctx->func    = 0;
    706:   mfctx->funcctx = 0;
    707:   mfctx->w       = NULL;

    709:   A->data = mfctx;

    711:   A->ops->mult           = MatMult_MFFD;
    712:   A->ops->destroy        = MatDestroy_MFFD;
    713:   A->ops->view           = MatView_MFFD;
    714:   A->ops->assemblyend    = MatAssemblyEnd_MFFD;
    715:   A->ops->getdiagonal    = MatGetDiagonal_MFFD;
    716:   A->ops->scale          = MatScale_MFFD;
    717:   A->ops->shift          = MatShift_MFFD;
    718:   A->ops->diagonalscale  = MatDiagonalScale_MFFD;
    719:   A->ops->diagonalset    = MatDiagonalSet_MFFD;
    720:   A->ops->setfromoptions = MatSetFromOptions_MFFD;
    721:   A->assembled           = PETSC_TRUE;

    723:   PetscLayoutSetUp(A->rmap);
    724:   PetscLayoutSetUp(A->cmap);

    726:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetBase_C",MatMFFDSetBase_MFFD);
    727:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioniBase_C",MatMFFDSetFunctioniBase_MFFD);
    728:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctioni_C",MatMFFDSetFunctioni_MFFD);
    729:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunction_C",MatMFFDSetFunction_MFFD);
    730:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetCheckh_C",MatMFFDSetCheckh_MFFD);
    731:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetPeriod_C",MatMFFDSetPeriod_MFFD);
    732:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDSetFunctionError_C",MatMFFDSetFunctionError_MFFD);
    733:   PetscObjectComposeFunction((PetscObject)A,"MatMFFDResetHHistory_C",MatMFFDResetHHistory_MFFD);

    735:   mfctx->mat = A;

    737:   PetscObjectChangeTypeName((PetscObject)A,MATMFFD);
    738:   return(0);
    739: }

    743: /*@
    744:    MatCreateMFFD - Creates a matrix-free matrix. See also MatCreateSNESMF()

    746:    Collective on Vec

    748:    Input Parameters:
    749: +  comm - MPI communicator
    750: .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
    751:            This value should be the same as the local size used in creating the
    752:            y vector for the matrix-vector product y = Ax.
    753: .  n - This value should be the same as the local size used in creating the
    754:        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
    755:        calculated if N is given) For square matrices n is almost always m.
    756: .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
    757: -  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)

    760:    Output Parameter:
    761: .  J - the matrix-free matrix

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

    769:    Level: advanced

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

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

    778: .vb
    779:      F'(u)*a = [F(u+h*a) - F(u)]/h where
    780:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
    781:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
    782:  where
    783:      error_rel = square root of relative error in function evaluation
    784:      umin = minimum iterate parameter
    785: .ve

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

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

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

    796:    Options Database Keys:
    797: +  -mat_mffd_err <error_rel> - Sets error_rel
    798: .  -mat_mffd_unim <umin> - Sets umin (for default PETSc routine that computes h only)
    799: -  -mat_mffd_check_positivity

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

    803: .seealso: MatDestroy(), MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction()
    804:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(),
    805:           MatMFFDGetH(), MatMFFDRegister(), MatMFFDComputeJacobian()

    807: @*/
    808: PetscErrorCode  MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)
    809: {

    813:   MatCreate(comm,J);
    814:   MatSetSizes(*J,m,n,M,N);
    815:   MatSetType(*J,MATMFFD);
    816:   MatSetUp(*J);
    817:   return(0);
    818: }

    823: /*@
    824:    MatMFFDGetH - Gets the last value that was used as the differencing
    825:    parameter.

    827:    Not Collective

    829:    Input Parameters:
    830: .  mat - the matrix obtained with MatCreateSNESMF()

    832:    Output Paramter:
    833: .  h - the differencing step size

    835:    Level: advanced

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

    839: .seealso: MatCreateSNESMF(),MatMFFDSetHHistory(), MatCreateMFFD(), MATMFFD, MatMFFDResetHHistory()
    840: @*/
    841: PetscErrorCode  MatMFFDGetH(Mat mat,PetscScalar *h)
    842: {
    843:   MatMFFD        ctx = (MatMFFD)mat->data;
    845:   PetscBool      match;

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

    851:   *h = ctx->currenth;
    852:   return(0);
    853: }

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

    860:    Logically Collective on Mat

    862:    Input Parameters:
    863: +  mat - the matrix free matrix created via MatCreateSNESMF() or MatCreateMFFD()
    864: .  func - the function to use
    865: -  funcctx - optional function context passed to function

    867:    Calling Sequence of func:
    868: $     func (void *funcctx, Vec x, Vec f)

    870: +  funcctx - user provided context
    871: .  x - input vector
    872: -  f - computed output function

    874:    Level: advanced

    876:    Notes:
    877:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
    878:     matrix inside your compute Jacobian routine

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

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

    884: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD,
    885:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
    886: @*/
    887: PetscErrorCode  MatMFFDSetFunction(Mat mat,PetscErrorCode (*func)(void*,Vec,Vec),void *funcctx)
    888: {

    892:   PetscTryMethod(mat,"MatMFFDSetFunction_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec),void*),(mat,func,funcctx));
    893:   return(0);
    894: }

    898: /*@C
    899:    MatMFFDSetFunctioni - Sets the function for a single component

    901:    Logically Collective on Mat

    903:    Input Parameters:
    904: +  mat - the matrix free matrix created via MatCreateSNESMF()
    905: -  funci - the function to use

    907:    Level: advanced

    909:    Notes:
    910:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
    911:     matrix inside your compute Jacobian routine

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

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

    918: @*/
    919: PetscErrorCode  MatMFFDSetFunctioni(Mat mat,PetscErrorCode (*funci)(void*,PetscInt,Vec,PetscScalar*))
    920: {

    925:   PetscTryMethod(mat,"MatMFFDSetFunctioni_C",(Mat,PetscErrorCode (*)(void*,PetscInt,Vec,PetscScalar*)),(mat,funci));
    926:   return(0);
    927: }

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

    935:    Logically Collective on Mat

    937:    Input Parameters:
    938: +  mat - the matrix free matrix created via MatCreateSNESMF()
    939: -  func - the function to use

    941:    Level: advanced

    943:    Notes:
    944:     If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
    945:     matrix inside your compute Jacobian routine

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

    950: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
    951:           MatMFFDSetHHistory(), MatMFFDResetHHistory(), SNESetFunction()
    952: @*/
    953: PetscErrorCode  MatMFFDSetFunctioniBase(Mat mat,PetscErrorCode (*func)(void*,Vec))
    954: {

    959:   PetscTryMethod(mat,"MatMFFDSetFunctioniBase_C",(Mat,PetscErrorCode (*)(void*,Vec)),(mat,func));
    960:   return(0);
    961: }

    965: /*@
    966:    MatMFFDSetPeriod - Sets how often h is recomputed, by default it is everytime

    968:    Logically Collective on Mat

    970:    Input Parameters:
    971: +  mat - the matrix free matrix created via MatCreateSNESMF()
    972: -  period - 1 for everytime, 2 for every second etc

    974:    Options Database Keys:
    975: +  -mat_mffd_period <period>

    977:    Level: advanced

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

    982: .seealso: MatCreateSNESMF(),MatMFFDGetH(),
    983:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
    984: @*/
    985: PetscErrorCode  MatMFFDSetPeriod(Mat mat,PetscInt period)
    986: {

    990:   PetscTryMethod(mat,"MatMFFDSetPeriod_C",(Mat,PetscInt),(mat,period));
    991:   return(0);
    992: }

    996: /*@
    997:    MatMFFDSetFunctionError - Sets the error_rel for the approximation of
    998:    matrix-vector products using finite differences.

    1000:    Logically Collective on Mat

    1002:    Input Parameters:
    1003: +  mat - the matrix free matrix created via MatCreateMFFD() or MatCreateSNESMF()
    1004: -  error_rel - relative error (should be set to the square root of
    1005:                the relative error in the function evaluations)

    1007:    Options Database Keys:
    1008: +  -mat_mffd_err <error_rel> - Sets error_rel

    1010:    Level: advanced

    1012:    Notes:
    1013:    The default matrix-free matrix-vector product routine computes
    1014: .vb
    1015:      F'(u)*a = [F(u+h*a) - F(u)]/h where
    1016:      h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
    1017:        = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
    1018: .ve

    1020: .keywords: SNES, matrix-free, parameters

    1022: .seealso: MatCreateSNESMF(),MatMFFDGetH(), MatCreateMFFD(), MATMFFD
    1023:           MatMFFDSetHHistory(), MatMFFDResetHHistory()
    1024: @*/
    1025: PetscErrorCode  MatMFFDSetFunctionError(Mat mat,PetscReal error)
    1026: {

    1030:   PetscTryMethod(mat,"MatMFFDSetFunctionError_C",(Mat,PetscReal),(mat,error));
    1031:   return(0);
    1032: }

    1036: /*@
    1037:    MatMFFDSetHHistory - Sets an array to collect a history of the
    1038:    differencing values (h) computed for the matrix-free product.

    1040:    Logically Collective on Mat

    1042:    Input Parameters:
    1043: +  J - the matrix-free matrix context
    1044: .  histroy - space to hold the history
    1045: -  nhistory - number of entries in history, if more entries are generated than
    1046:               nhistory, then the later ones are discarded

    1048:    Level: advanced

    1050:    Notes:
    1051:    Use MatMFFDResetHHistory() to reset the history counter and collect
    1052:    a new batch of differencing parameters, h.

    1054: .keywords: SNES, matrix-free, h history, differencing history

    1056: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
    1057:           MatMFFDResetHHistory(), MatMFFDSetFunctionError()

    1059: @*/
    1060: PetscErrorCode  MatMFFDSetHHistory(Mat J,PetscScalar history[],PetscInt nhistory)
    1061: {
    1062:   MatMFFD        ctx = (MatMFFD)J->data;
    1064:   PetscBool      match;

    1067:   PetscObjectTypeCompare((PetscObject)J,MATMFFD,&match);
    1068:   if (!match) SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_WRONG,"Not a MFFD matrix");
    1069:   ctx->historyh    = history;
    1070:   ctx->maxcurrenth = nhistory;
    1071:   ctx->currenth    = 0.;
    1072:   return(0);
    1073: }

    1078: /*@
    1079:    MatMFFDResetHHistory - Resets the counter to zero to begin
    1080:    collecting a new set of differencing histories.

    1082:    Logically Collective on Mat

    1084:    Input Parameters:
    1085: .  J - the matrix-free matrix context

    1087:    Level: advanced

    1089:    Notes:
    1090:    Use MatMFFDSetHHistory() to create the original history counter.

    1092: .keywords: SNES, matrix-free, h history, differencing history

    1094: .seealso: MatMFFDGetH(), MatCreateSNESMF(),
    1095:           MatMFFDSetHHistory(), MatMFFDSetFunctionError()

    1097: @*/
    1098: PetscErrorCode  MatMFFDResetHHistory(Mat J)
    1099: {

    1103:   PetscTryMethod(J,"MatMFFDResetHHistory_C",(Mat),(J));
    1104:   return(0);
    1105: }

    1110: /*@
    1111:     MatMFFDSetBase - Sets the vector U at which matrix vector products of the
    1112:         Jacobian are computed

    1114:     Logically Collective on Mat

    1116:     Input Parameters:
    1117: +   J - the MatMFFD matrix
    1118: .   U - the vector
    1119: -   F - (optional) vector that contains F(u) if it has been already computed

    1121:     Notes: This is rarely used directly

    1123:     If F is provided then it is not recomputed. Otherwise the function is evaluated at the base
    1124:     point during the first MatMult() after each call to MatMFFDSetBase().

    1126:     Level: advanced

    1128: @*/
    1129: PetscErrorCode  MatMFFDSetBase(Mat J,Vec U,Vec F)
    1130: {

    1137:   PetscTryMethod(J,"MatMFFDSetBase_C",(Mat,Vec,Vec),(J,U,F));
    1138:   return(0);
    1139: }

    1143: /*@C
    1144:     MatMFFDSetCheckh - Sets a function that checks the computed h and adjusts
    1145:         it to satisfy some criteria

    1147:     Logically Collective on Mat

    1149:     Input Parameters:
    1150: +   J - the MatMFFD matrix
    1151: .   fun - the function that checks h
    1152: -   ctx - any context needed by the function

    1154:     Options Database Keys:
    1155: .   -mat_mffd_check_positivity

    1157:     Level: advanced

    1159:     Notes: For example, MatMFFDSetCheckPositivity() insures that all entries
    1160:        of U + h*a are non-negative

    1162: .seealso:  MatMFFDSetCheckPositivity()
    1163: @*/
    1164: PetscErrorCode  MatMFFDSetCheckh(Mat J,PetscErrorCode (*fun)(void*,Vec,Vec,PetscScalar*),void *ctx)
    1165: {

    1170:   PetscTryMethod(J,"MatMFFDSetCheckh_C",(Mat,PetscErrorCode (*)(void*,Vec,Vec,PetscScalar*),void*),(J,fun,ctx));
    1171:   return(0);
    1172: }

    1176: /*@
    1177:     MatMFFDCheckPositivity - Checks that all entries in U + h*a are positive or
    1178:         zero, decreases h until this is satisfied.

    1180:     Logically Collective on Vec

    1182:     Input Parameters:
    1183: +   U - base vector that is added to
    1184: .   a - vector that is added
    1185: .   h - scaling factor on a
    1186: -   dummy - context variable (unused)

    1188:     Options Database Keys:
    1189: .   -mat_mffd_check_positivity

    1191:     Level: advanced

    1193:     Notes: This is rarely used directly, rather it is passed as an argument to
    1194:            MatMFFDSetCheckh()

    1196: .seealso:  MatMFFDSetCheckh()
    1197: @*/
    1198: PetscErrorCode  MatMFFDCheckPositivity(void *dummy,Vec U,Vec a,PetscScalar *h)
    1199: {
    1200:   PetscReal      val, minval;
    1201:   PetscScalar    *u_vec, *a_vec;
    1203:   PetscInt       i,n;
    1204:   MPI_Comm       comm;

    1207:   PetscObjectGetComm((PetscObject)U,&comm);
    1208:   VecGetArray(U,&u_vec);
    1209:   VecGetArray(a,&a_vec);
    1210:   VecGetLocalSize(U,&n);
    1211:   minval = PetscAbsScalar(*h*1.01);
    1212:   for (i=0; i<n; i++) {
    1213:     if (PetscRealPart(u_vec[i] + *h*a_vec[i]) <= 0.0) {
    1214:       val = PetscAbsScalar(u_vec[i]/a_vec[i]);
    1215:       if (val < minval) minval = val;
    1216:     }
    1217:   }
    1218:   VecRestoreArray(U,&u_vec);
    1219:   VecRestoreArray(a,&a_vec);
    1220:   MPI_Allreduce(&minval,&val,1,MPIU_REAL,MPIU_MIN,comm);
    1221:   if (val <= PetscAbsScalar(*h)) {
    1222:     PetscInfo2(U,"Scaling back h from %g to %g\n",(double)PetscRealPart(*h),(double)(.99*val));
    1223:     if (PetscRealPart(*h) > 0.0) *h =  0.99*val;
    1224:     else                         *h = -0.99*val;
    1225:   }
    1226:   return(0);
    1227: }