Actual source code: snesncg.c
petsc-3.10.5 2019-03-28
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      1:  #include <../src/snes/impls/ncg/snesncgimpl.h>
      2: const char *const SNESNCGTypes[] = {"FR","PRP","HS","DY","CD","SNESNCGType","SNES_NCG_",0};

      4: PetscErrorCode SNESReset_NCG(SNES snes)
      5: {
      7:   return(0);
      8: }

     10: #define SNESLINESEARCHNCGLINEAR "ncglinear"

     12: /*
     13:   SNESDestroy_NCG - Destroys the private SNES_NCG context that was created with SNESCreate_NCG().

     15:   Input Parameter:
     16: . snes - the SNES context

     18:   Application Interface Routine: SNESDestroy()
     19: */
     20: PetscErrorCode SNESDestroy_NCG(SNES snes)
     21: {

     25:   PetscFree(snes->data);
     26:   return(0);
     27: }

     29: /*
     30:    SNESSetUp_NCG - Sets up the internal data structures for the later use
     31:    of the SNESNCG nonlinear solver.

     33:    Input Parameters:
     34: +  snes - the SNES context
     35: -  x - the solution vector

     37:    Application Interface Routine: SNESSetUp()
     38:  */

     40: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch);

     42: PetscErrorCode SNESSetUp_NCG(SNES snes)
     43: {

     47:   SNESSetWorkVecs(snes,2);
     48:   if (snes->npcside== PC_RIGHT) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNESNCG only supports left preconditioning");
     49:   if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED;
     50:   return(0);
     51: }
     52: /*
     53:   SNESSetFromOptions_NCG - Sets various parameters for the SNESNCG method.

     55:   Input Parameter:
     56: . snes - the SNES context

     58:   Application Interface Routine: SNESSetFromOptions()
     59: */
     60: static PetscErrorCode SNESSetFromOptions_NCG(PetscOptionItems *PetscOptionsObject,SNES snes)
     61: {
     62:   SNES_NCG       *ncg = (SNES_NCG*)snes->data;
     64:   PetscBool      debug = PETSC_FALSE;
     65:   SNESLineSearch linesearch;
     66:   SNESNCGType    ncgtype=ncg->type;

     69:   PetscOptionsHead(PetscOptionsObject,"SNES NCG options");
     70:   PetscOptionsBool("-snes_ncg_monitor","Monitor NCG iterations","SNES",ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL);
     71:   if (debug) {
     72:     ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
     73:   }
     74:   PetscOptionsEnum("-snes_ncg_type","NCG Beta type used","SNESNCGSetType",SNESNCGTypes,(PetscEnum)ncg->type,(PetscEnum*)&ncgtype,NULL);
     75:   SNESNCGSetType(snes, ncgtype);
     76:   PetscOptionsTail();
     77:   if (!snes->linesearch) {
     78:     SNESGetLineSearch(snes, &linesearch);
     79:     if (!snes->npc) {
     80:       SNESLineSearchSetType(linesearch, SNESLINESEARCHCP);
     81:     } else {
     82:       SNESLineSearchSetType(linesearch, SNESLINESEARCHL2);
     83:     }
     84:   }
     85:   SNESLineSearchRegister(SNESLINESEARCHNCGLINEAR, SNESLineSearchCreate_NCGLinear);
     86:   return(0);
     87: }

     89: /*
     90:   SNESView_NCG - Prints info from the SNESNCG data structure.

     92:   Input Parameters:
     93: + SNES - the SNES context
     94: - viewer - visualization context

     96:   Application Interface Routine: SNESView()
     97: */
     98: static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer)
     99: {
    100:   SNES_NCG      *ncg = (SNES_NCG *) snes->data;
    101:   PetscBool      iascii;

    105:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    106:   if (iascii) {
    107:     PetscViewerASCIIPrintf(viewer, "  type: %s\n", SNESNCGTypes[ncg->type]);
    108:   }
    109:   return(0);
    110: }

    112: PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch)
    113: {
    114:   PetscScalar    alpha, ptAp;
    115:   Vec            X, Y, F, W;
    116:   SNES           snes;
    118:   PetscReal      *fnorm, *xnorm, *ynorm;

    121:   SNESLineSearchGetSNES(linesearch, &snes);
    122:   X     = linesearch->vec_sol;
    123:   W     = linesearch->vec_sol_new;
    124:   F     = linesearch->vec_func;
    125:   Y     = linesearch->vec_update;
    126:   fnorm = &linesearch->fnorm;
    127:   xnorm = &linesearch->xnorm;
    128:   ynorm = &linesearch->ynorm;

    130:   if (!snes->jacobian) {
    131:     SNESSetUpMatrices(snes);
    132:   }

    134:   /*

    136:    The exact step size for unpreconditioned linear CG is just:
    137:    alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy)
    138:    */
    139:   SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre);
    140:   VecDot(F, F, &alpha);
    141:   MatMult(snes->jacobian, Y, W);
    142:   VecDot(Y, W, &ptAp);
    143:   alpha = alpha / ptAp;
    144:   VecAXPY(X,-alpha,Y);
    145:   SNESComputeFunction(snes,X,F);

    147:   VecNorm(F,NORM_2,fnorm);
    148:   VecNorm(X,NORM_2,xnorm);
    149:   VecNorm(Y,NORM_2,ynorm);
    150:   return(0);
    151: }

    153: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch)
    154: {
    156:   linesearch->ops->apply          = SNESLineSearchApply_NCGLinear;
    157:   linesearch->ops->destroy        = NULL;
    158:   linesearch->ops->setfromoptions = NULL;
    159:   linesearch->ops->reset          = NULL;
    160:   linesearch->ops->view           = NULL;
    161:   linesearch->ops->setup          = NULL;
    162:   return(0);
    163: }

    165: /*

    167:  Assuming F = SNESComputeFunction(X) compute Y^tJ^tF using a simple secant approximation of the jacobian.

    169:  */
    170: PetscErrorCode SNESNCGComputeYtJtF_Private(SNES snes, Vec X, Vec F, Vec Y, Vec W, Vec G, PetscScalar * ytJtf)
    171: {
    173:   PetscScalar    ftf, ftg, fty, h;

    176:   VecDot(F, F, &ftf);
    177:   VecDot(F, Y, &fty);
    178:   h      = 1e-5*fty / fty;
    179:   VecCopy(X, W);
    180:   VecAXPY(W, -h, Y);          /* this is arbitrary */
    181:   SNESComputeFunction(snes, W, G);
    182:   VecDot(G, F, &ftg);
    183:   *ytJtf = (ftg - ftf) / h;
    184:   return(0);
    185: }

    187: /*@
    188:     SNESNCGSetType - Sets the conjugate update type for SNESNCG.

    190:     Logically Collective on SNES

    192:     Input Parameters:
    193: +   snes - the iterative context
    194: -   btype - update type

    196:     Options Database:
    197: .   -snes_ncg_type<prp,fr,hs,dy,cd>

    199:     Level: intermediate

    201:     SNESNCGSelectTypes:
    202: +   SNES_NCG_FR - Fletcher-Reeves update
    203: .   SNES_NCG_PRP - Polak-Ribiere-Polyak update
    204: .   SNES_NCG_HS - Hestenes-Steifel update
    205: .   SNES_NCG_DY - Dai-Yuan update
    206: -   SNES_NCG_CD - Conjugate Descent update

    208:    Notes:
    209:    PRP is the default, and the only one that tolerates generalized search directions.

    211: .keywords: SNES, SNESNCG, selection, type, set
    212: @*/
    213: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
    214: {

    219:   PetscTryMethod(snes,"SNESNCGSetType_C",(SNES,SNESNCGType),(snes,btype));
    220:   return(0);
    221: }

    223: PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
    224: {
    225:   SNES_NCG *ncg = (SNES_NCG*)snes->data;

    228:   ncg->type = btype;
    229:   return(0);
    230: }

    232: /*
    233:   SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.

    235:   Input Parameters:
    236: . snes - the SNES context

    238:   Output Parameter:
    239: . outits - number of iterations until termination

    241:   Application Interface Routine: SNESSolve()
    242: */
    243: PetscErrorCode SNESSolve_NCG(SNES snes)
    244: {
    245:   SNES_NCG             *ncg = (SNES_NCG*)snes->data;
    246:   Vec                  X,dX,lX,F,dXold;
    247:   PetscReal            fnorm, ynorm, xnorm, beta = 0.0;
    248:   PetscScalar          dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
    249:   PetscInt             maxits, i;
    250:   PetscErrorCode       ierr;
    251:   SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
    252:   SNESLineSearch       linesearch;
    253:   SNESConvergedReason  reason;

    256:   if (snes->xl || snes->xu || snes->ops->computevariablebounds) SETERRQ1(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

    258:   PetscCitationsRegister(SNESCitation,&SNEScite);
    259:   snes->reason = SNES_CONVERGED_ITERATING;

    261:   maxits = snes->max_its;            /* maximum number of iterations */
    262:   X      = snes->vec_sol;            /* X^n */
    263:   dXold  = snes->work[0];            /* The previous iterate of X */
    264:   dX     = snes->work[1];            /* the preconditioned direction */
    265:   lX     = snes->vec_sol_update;     /* the conjugate direction */
    266:   F      = snes->vec_func;           /* residual vector */

    268:   SNESGetLineSearch(snes, &linesearch);

    270:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    271:   snes->iter = 0;
    272:   snes->norm = 0.;
    273:   PetscObjectSAWsGrantAccess((PetscObject)snes);

    275:   /* compute the initial function and preconditioned update dX */

    277:   if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
    278:     SNESApplyNPC(snes,X,NULL,dX);
    279:     SNESGetConvergedReason(snes->npc,&reason);
    280:     if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    281:       snes->reason = SNES_DIVERGED_INNER;
    282:       return(0);
    283:     }
    284:     VecCopy(dX,F);
    285:     VecNorm(F,NORM_2,&fnorm);
    286:   } else {
    287:     if (!snes->vec_func_init_set) {
    288:       SNESComputeFunction(snes,X,F);
    289:     } else snes->vec_func_init_set = PETSC_FALSE;

    291:     /* convergence test */
    292:     VecNorm(F,NORM_2,&fnorm);
    293:     SNESCheckFunctionNorm(snes,fnorm);
    294:     VecCopy(F,dX);
    295:   }
    296:   if (snes->npc) {
    297:     if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
    298:       SNESApplyNPC(snes,X,F,dX);
    299:       SNESGetConvergedReason(snes->npc,&reason);
    300:       if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    301:         snes->reason = SNES_DIVERGED_INNER;
    302:         return(0);
    303:       }
    304:     }
    305:   }
    306:   VecCopy(dX,lX);
    307:   VecDot(dX, dX, &dXdotdX);

    310:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    311:   snes->norm = fnorm;
    312:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    313:   SNESLogConvergenceHistory(snes,fnorm,0);
    314:   SNESMonitor(snes,0,fnorm);

    316:   /* test convergence */
    317:   (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    318:   if (snes->reason) return(0);

    320:   /* Call general purpose update function */
    321:   if (snes->ops->update) {
    322:     (*snes->ops->update)(snes, snes->iter);
    323:   }

    325:   /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */

    327:   for (i = 1; i < maxits + 1; i++) {
    328:     /* some update types require the old update direction or conjugate direction */
    329:     if (ncg->type != SNES_NCG_FR) {
    330:       VecCopy(dX, dXold);
    331:     }
    332:     SNESLineSearchApply(linesearch,X,F,&fnorm,lX);
    333:     SNESLineSearchGetReason(linesearch, &lsresult);
    334:     SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
    335:     if (lsresult) {
    336:       if (++snes->numFailures >= snes->maxFailures) {
    337:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
    338:         return(0);
    339:       }
    340:     }
    341:     if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
    342:       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
    343:       return(0);
    344:     }
    345:     /* Monitor convergence */
    346:     PetscObjectSAWsTakeAccess((PetscObject)snes);
    347:     snes->iter = i;
    348:     snes->norm = fnorm;
    349:     PetscObjectSAWsGrantAccess((PetscObject)snes);
    350:     SNESLogConvergenceHistory(snes,snes->norm,0);
    351:     SNESMonitor(snes,snes->iter,snes->norm);

    353:     /* Test for convergence */
    354:     (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
    355:     if (snes->reason) return(0);

    357:     /* Call general purpose update function */
    358:     if (snes->ops->update) {
    359:       (*snes->ops->update)(snes, snes->iter);
    360:     }
    361:     if (snes->npc) {
    362:       if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
    363:         SNESApplyNPC(snes,X,NULL,dX);
    364:         SNESGetConvergedReason(snes->npc,&reason);
    365:         if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    366:           snes->reason = SNES_DIVERGED_INNER;
    367:           return(0);
    368:         }
    369:         VecCopy(dX,F);
    370:       } else {
    371:         SNESApplyNPC(snes,X,F,dX);
    372:         SNESGetConvergedReason(snes->npc,&reason);
    373:         if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    374:           snes->reason = SNES_DIVERGED_INNER;
    375:           return(0);
    376:         }
    377:       }
    378:     } else {
    379:       VecCopy(F,dX);
    380:     }

    382:     /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
    383:     switch (ncg->type) {
    384:     case SNES_NCG_FR: /* Fletcher-Reeves */
    385:       dXolddotdXold= dXdotdX;
    386:       VecDot(dX, dX, &dXdotdX);
    387:       beta         = PetscRealPart(dXdotdX / dXolddotdXold);
    388:       break;
    389:     case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
    390:       dXolddotdXold= dXdotdX;
    391:       VecDotBegin(dX, dX, &dXdotdXold);
    392:       VecDotBegin(dXold, dX, &dXdotdXold);
    393:       VecDotEnd(dX, dX, &dXdotdX);
    394:       VecDotEnd(dXold, dX, &dXdotdXold);
    395:       beta         = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
    396:       if (beta < 0.0) beta = 0.0; /* restart */
    397:       break;
    398:     case SNES_NCG_HS: /* Hestenes-Stiefel */
    399:       VecDotBegin(dX, dX, &dXdotdX);
    400:       VecDotBegin(dX, dXold, &dXdotdXold);
    401:       VecDotBegin(lX, dX, &lXdotdX);
    402:       VecDotBegin(lX, dXold, &lXdotdXold);
    403:       VecDotEnd(dX, dX, &dXdotdX);
    404:       VecDotEnd(dX, dXold, &dXdotdXold);
    405:       VecDotEnd(lX, dX, &lXdotdX);
    406:       VecDotEnd(lX, dXold, &lXdotdXold);
    407:       beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
    408:       break;
    409:     case SNES_NCG_DY: /* Dai-Yuan */
    410:       VecDotBegin(dX, dX, &dXdotdX);
    411:       VecDotBegin(lX, dX, &lXdotdX);
    412:       VecDotBegin(lX, dXold, &lXdotdXold);
    413:       VecDotEnd(dX, dX, &dXdotdX);
    414:       VecDotEnd(lX, dX, &lXdotdX);
    415:       VecDotEnd(lX, dXold, &lXdotdXold);
    416:       beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
    417:       break;
    418:     case SNES_NCG_CD: /* Conjugate Descent */
    419:       VecDotBegin(dX, dX, &dXdotdX);
    420:       VecDotBegin(lX, dXold, &lXdotdXold);
    421:       VecDotEnd(dX, dX, &dXdotdX);
    422:       VecDotEnd(lX, dXold, &lXdotdXold);
    423:       beta = PetscRealPart(dXdotdX / lXdotdXold);
    424:       break;
    425:     }
    426:     if (ncg->monitor) {
    427:       PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta);
    428:     }
    429:     VecAYPX(lX, beta, dX);
    430:   }
    431:   PetscInfo1(snes, "Maximum number of iterations has been reached: %D\n", maxits);
    432:   if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
    433:   return(0);
    434: }

    438: /*MC
    439:   SNESNCG - Nonlinear Conjugate-Gradient method for the solution of general nonlinear systems.

    441:   Level: beginner

    443:   Options Database:
    444: +   -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
    445: .   -snes_linesearch_type <cp,l2,basic> - Line search type.
    446: -   -snes_ncg_monitor - Print relevant information about the ncg iteration.

    448:    Notes:
    449:     This solves the nonlinear system of equations F(x) = 0 using the nonlinear generalization of the conjugate
    450:           gradient method.  This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise
    451:           chooses the initial search direction as F(x) for the initial guess x.

    453:           Only supports left non-linear preconditioning.

    455:    References:
    456: .  1. -  Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
    457:    SIAM Review, 57(4), 2015

    460: .seealso:  SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESNEWTONTR, SNESNGMRES, SNESQN
    461: M*/
    462: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
    463: {
    465:   SNES_NCG       * neP;

    468:   snes->ops->destroy        = SNESDestroy_NCG;
    469:   snes->ops->setup          = SNESSetUp_NCG;
    470:   snes->ops->setfromoptions = SNESSetFromOptions_NCG;
    471:   snes->ops->view           = SNESView_NCG;
    472:   snes->ops->solve          = SNESSolve_NCG;
    473:   snes->ops->reset          = SNESReset_NCG;

    475:   snes->usesksp = PETSC_FALSE;
    476:   snes->usesnpc = PETSC_TRUE;
    477:   snes->npcside = PC_LEFT;

    479:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

    481:   if (!snes->tolerancesset) {
    482:     snes->max_funcs = 30000;
    483:     snes->max_its   = 10000;
    484:     snes->stol      = 1e-20;
    485:   }

    487:   PetscNewLog(snes,&neP);
    488:   snes->data   = (void*) neP;
    489:   neP->monitor = NULL;
    490:   neP->type    = SNES_NCG_PRP;
    491:   PetscObjectComposeFunction((PetscObject)snes,"SNESNCGSetType_C", SNESNCGSetType_NCG);
    492:   return(0);
    493: }