Date: 2015-10-02T22:23:46+00:00

Actual source code: tr.c
petsc-3.6.2 2015-10-02
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      2: #include <../src/snes/impls/tr/trimpl.h>                /*I   "petscsnes.h"   I*/

      4: typedef struct {
      5:   void *ctx;
      6:   SNES snes;
      7: } SNES_TR_KSPConverged_Ctx;

      9: /*
     10:    This convergence test determines if the two norm of the
     11:    solution lies outside the trust region, if so it halts.
     12: */
     15: PetscErrorCode SNES_TR_KSPConverged_Private(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *cctx)
     16: {
     17:   SNES_TR_KSPConverged_Ctx *ctx = (SNES_TR_KSPConverged_Ctx*)cctx;
     18:   SNES                     snes = ctx->snes;
     19:   SNES_NEWTONTR            *neP = (SNES_NEWTONTR*)snes->data;
     20:   Vec                      x;
     21:   PetscReal                nrm;
     22:   PetscErrorCode           ierr;

     25:   KSPConvergedDefault(ksp,n,rnorm,reason,ctx->ctx);
     26:   if (*reason) {
     27:     PetscInfo2(snes,"default convergence test KSP iterations=%D, rnorm=%g\n",n,(double)rnorm);
     28:   }
     29:   /* Determine norm of solution */
     30:   KSPBuildSolution(ksp,0,&x);
     31:   VecNorm(x,NORM_2,&nrm);
     32:   if (nrm >= neP->delta) {
     33:     PetscInfo2(snes,"Ending linear iteration early, delta=%g, length=%g\n",(double)neP->delta,(double)nrm);
     34:     *reason = KSP_CONVERGED_STEP_LENGTH;
     35:   }
     36:   return(0);
     37: }

     41: PetscErrorCode SNES_TR_KSPConverged_Destroy(void *cctx)
     42: {
     43:   SNES_TR_KSPConverged_Ctx *ctx = (SNES_TR_KSPConverged_Ctx*)cctx;
     44:   PetscErrorCode           ierr;

     47:   KSPConvergedDefaultDestroy(ctx->ctx);
     48:   PetscFree(ctx);
     49:   return(0);
     50: }

     52: /* ---------------------------------------------------------------- */
     55: /*
     56:    SNES_TR_Converged_Private -test convergence JUST for
     57:    the trust region tolerance.

     59: */
     60: static PetscErrorCode SNES_TR_Converged_Private(SNES snes,PetscInt it,PetscReal xnorm,PetscReal pnorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
     61: {
     62:   SNES_NEWTONTR  *neP = (SNES_NEWTONTR*)snes->data;

     66:   *reason = SNES_CONVERGED_ITERATING;
     67:   if (neP->delta < xnorm * snes->deltatol) {
     68:     PetscInfo3(snes,"Converged due to trust region param %g<%g*%g\n",(double)neP->delta,(double)xnorm,(double)snes->deltatol);
     69:     *reason = SNES_CONVERGED_TR_DELTA;
     70:   } else if (snes->nfuncs >= snes->max_funcs) {
     71:     PetscInfo1(snes,"Exceeded maximum number of function evaluations: %D\n",snes->max_funcs);
     72:     *reason = SNES_DIVERGED_FUNCTION_COUNT;
     73:   }
     74:   return(0);
     75: }

     78: /*
     79:    SNESSolve_NEWTONTR - Implements Newton's Method with a very simple trust
     80:    region approach for solving systems of nonlinear equations.

     83: */
     86: static PetscErrorCode SNESSolve_NEWTONTR(SNES snes)
     87: {
     88:   SNES_NEWTONTR       *neP = (SNES_NEWTONTR*)snes->data;
     89:   Vec                 X,F,Y,G,Ytmp;
     90:   PetscErrorCode      ierr;
     91:   PetscInt            maxits,i,lits;
     92:   PetscReal           rho,fnorm,gnorm,gpnorm,xnorm=0,delta,nrm,ynorm,norm1;
     93:   PetscScalar         cnorm;
     94:   KSP                 ksp;
     95:   SNESConvergedReason reason = SNES_CONVERGED_ITERATING;
     96:   PetscBool           conv   = PETSC_FALSE,breakout = PETSC_FALSE;

    100:   if (snes->xl || snes->xu || snes->ops->computevariablebounds) {
    101:     SETERRQ1(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);
    102:   }

    104:   maxits = snes->max_its;               /* maximum number of iterations */
    105:   X      = snes->vec_sol;               /* solution vector */
    106:   F      = snes->vec_func;              /* residual vector */
    107:   Y      = snes->work[0];               /* work vectors */
    108:   G      = snes->work[1];
    109:   Ytmp   = snes->work[2];

    111:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    112:   snes->iter = 0;
    113:   PetscObjectSAWsGrantAccess((PetscObject)snes);

    115:   if (!snes->vec_func_init_set) {
    116:     SNESComputeFunction(snes,X,F);          /* F(X) */
    117:   } else snes->vec_func_init_set = PETSC_FALSE;

    119:   VecNorm(F,NORM_2,&fnorm);             /* fnorm <- || F || */
    120:   SNESCheckFunctionNorm(snes,fnorm);
    121:   VecNorm(X,NORM_2,&xnorm);             /* fnorm <- || F || */
    122:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    123:   snes->norm = fnorm;
    124:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    125:   delta      = xnorm ? neP->delta0*xnorm : neP->delta0;
    126:   neP->delta = delta;
    127:   SNESLogConvergenceHistory(snes,fnorm,0);
    128:   SNESMonitor(snes,0,fnorm);

    130:   /* test convergence */
    131:   (*snes->ops->converged)(snes,snes->iter,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    132:   if (snes->reason) return(0);

    134:   /* Set the stopping criteria to use the More' trick. */
    135:   PetscOptionsGetBool(NULL,"-snes_tr_ksp_regular_convergence_test",&conv,NULL);
    136:   if (!conv) {
    137:     SNES_TR_KSPConverged_Ctx *ctx;
    138:     SNESGetKSP(snes,&ksp);
    139:     PetscNew(&ctx);
    140:     ctx->snes = snes;
    141:     KSPConvergedDefaultCreate(&ctx->ctx);
    142:     KSPSetConvergenceTest(ksp,SNES_TR_KSPConverged_Private,ctx,SNES_TR_KSPConverged_Destroy);
    143:     PetscInfo(snes,"Using Krylov convergence test SNES_TR_KSPConverged_Private\n");
    144:   }

    146:   for (i=0; i<maxits; i++) {

    148:     /* Call general purpose update function */
    149:     if (snes->ops->update) {
    150:       (*snes->ops->update)(snes, snes->iter);
    151:     }

    153:     /* Solve J Y = F, where J is Jacobian matrix */
    154:     SNESComputeJacobian(snes,X,snes->jacobian,snes->jacobian_pre);
    155:     KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre);
    156:     KSPSolve(snes->ksp,F,Ytmp);
    157:     KSPGetIterationNumber(snes->ksp,&lits);

    159:     snes->linear_its += lits;

    161:     PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);
    162:     VecNorm(Ytmp,NORM_2,&nrm);
    163:     norm1 = nrm;
    164:     while (1) {
    165:       VecCopy(Ytmp,Y);
    166:       nrm  = norm1;

    168:       /* Scale Y if need be and predict new value of F norm */
    169:       if (nrm >= delta) {
    170:         nrm    = delta/nrm;
    171:         gpnorm = (1.0 - nrm)*fnorm;
    172:         cnorm  = nrm;
    173:         PetscInfo1(snes,"Scaling direction by %g\n",(double)nrm);
    174:         VecScale(Y,cnorm);
    175:         nrm    = gpnorm;
    176:         ynorm  = delta;
    177:       } else {
    178:         gpnorm = 0.0;
    179:         PetscInfo(snes,"Direction is in Trust Region\n");
    180:         ynorm  = nrm;
    181:       }
    182:       VecAYPX(Y,-1.0,X);            /* Y <- X - Y */
    183:       VecCopy(X,snes->vec_sol_update);
    184:       SNESComputeFunction(snes,Y,G); /*  F(X) */
    185:       VecNorm(G,NORM_2,&gnorm);      /* gnorm <- || g || */
    186:       if (fnorm == gpnorm) rho = 0.0;
    187:       else rho = (fnorm*fnorm - gnorm*gnorm)/(fnorm*fnorm - gpnorm*gpnorm);

    189:       /* Update size of trust region */
    190:       if      (rho < neP->mu)  delta *= neP->delta1;
    191:       else if (rho < neP->eta) delta *= neP->delta2;
    192:       else                     delta *= neP->delta3;
    193:       PetscInfo3(snes,"fnorm=%g, gnorm=%g, ynorm=%g\n",(double)fnorm,(double)gnorm,(double)ynorm);
    194:       PetscInfo3(snes,"gpred=%g, rho=%g, delta=%g\n",(double)gpnorm,(double)rho,(double)delta);

    196:       neP->delta = delta;
    197:       if (rho > neP->sigma) break;
    198:       PetscInfo(snes,"Trying again in smaller region\n");
    199:       /* check to see if progress is hopeless */
    200:       neP->itflag = PETSC_FALSE;
    201:       SNES_TR_Converged_Private(snes,snes->iter,xnorm,ynorm,fnorm,&reason,snes->cnvP);
    202:       if (!reason) { (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&reason,snes->cnvP); }
    203:       if (reason) {
    204:         /* We're not progressing, so return with the current iterate */
    205:         SNESMonitor(snes,i+1,fnorm);
    206:         breakout = PETSC_TRUE;
    207:         break;
    208:       }
    209:       snes->numFailures++;
    210:     }
    211:     if (!breakout) {
    212:       /* Update function and solution vectors */
    213:       fnorm = gnorm;
    214:       VecCopy(G,F);
    215:       VecCopy(Y,X);
    216:       /* Monitor convergence */
    217:       PetscObjectSAWsTakeAccess((PetscObject)snes);
    218:       snes->iter = i+1;
    219:       snes->norm = fnorm;
    220:       PetscObjectSAWsGrantAccess((PetscObject)snes);
    221:       SNESLogConvergenceHistory(snes,snes->norm,lits);
    222:       SNESMonitor(snes,snes->iter,snes->norm);
    223:       /* Test for convergence, xnorm = || X || */
    224:       neP->itflag = PETSC_TRUE;
    225:       if (snes->ops->converged != SNESConvergedSkip) { VecNorm(X,NORM_2,&xnorm); }
    226:       (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&reason,snes->cnvP);
    227:       if (reason) break;
    228:     } else break;
    229:   }
    230:   if (i == maxits) {
    231:     PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);
    232:     if (!reason) reason = SNES_DIVERGED_MAX_IT;
    233:   }
    234:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    235:   snes->reason = reason;
    236:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    237:   return(0);
    238: }
    239: /*------------------------------------------------------------*/
    242: static PetscErrorCode SNESSetUp_NEWTONTR(SNES snes)
    243: {

    247:   SNESSetWorkVecs(snes,3);
    248:   SNESSetUpMatrices(snes);
    249:   return(0);
    250: }

    254: PetscErrorCode SNESReset_NEWTONTR(SNES snes)
    255: {

    258:   return(0);
    259: }

    263: static PetscErrorCode SNESDestroy_NEWTONTR(SNES snes)
    264: {

    268:   SNESReset_NEWTONTR(snes);
    269:   PetscFree(snes->data);
    270:   return(0);
    271: }
    272: /*------------------------------------------------------------*/

    276: static PetscErrorCode SNESSetFromOptions_NEWTONTR(PetscOptions *PetscOptionsObject,SNES snes)
    277: {
    278:   SNES_NEWTONTR  *ctx = (SNES_NEWTONTR*)snes->data;

    282:   PetscOptionsHead(PetscOptionsObject,"SNES trust region options for nonlinear equations");
    283:   PetscOptionsReal("-snes_trtol","Trust region tolerance","SNESSetTrustRegionTolerance",snes->deltatol,&snes->deltatol,NULL);
    284:   PetscOptionsReal("-snes_tr_mu","mu","None",ctx->mu,&ctx->mu,NULL);
    285:   PetscOptionsReal("-snes_tr_eta","eta","None",ctx->eta,&ctx->eta,NULL);
    286:   PetscOptionsReal("-snes_tr_sigma","sigma","None",ctx->sigma,&ctx->sigma,NULL);
    287:   PetscOptionsReal("-snes_tr_delta0","delta0","None",ctx->delta0,&ctx->delta0,NULL);
    288:   PetscOptionsReal("-snes_tr_delta1","delta1","None",ctx->delta1,&ctx->delta1,NULL);
    289:   PetscOptionsReal("-snes_tr_delta2","delta2","None",ctx->delta2,&ctx->delta2,NULL);
    290:   PetscOptionsReal("-snes_tr_delta3","delta3","None",ctx->delta3,&ctx->delta3,NULL);
    291:   PetscOptionsTail();
    292:   return(0);
    293: }

    297: static PetscErrorCode SNESView_NEWTONTR(SNES snes,PetscViewer viewer)
    298: {
    299:   SNES_NEWTONTR  *tr = (SNES_NEWTONTR*)snes->data;
    301:   PetscBool      iascii;

    304:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    305:   if (iascii) {
    306:     PetscViewerASCIIPrintf(viewer,"  mu=%g, eta=%g, sigma=%g\n",(double)tr->mu,(double)tr->eta,(double)tr->sigma);
    307:     PetscViewerASCIIPrintf(viewer,"  delta0=%g, delta1=%g, delta2=%g, delta3=%g\n",(double)tr->delta0,(double)tr->delta1,(double)tr->delta2,(double)tr->delta3);
    308:   }
    309:   return(0);
    310: }
    311: /* ------------------------------------------------------------ */
    312: /*MC
    313:       SNESNEWTONTR - Newton based nonlinear solver that uses a trust region

    315:    Options Database:
    316: +    -snes_trtol <tol> Trust region tolerance
    317: .    -snes_tr_mu <mu>
    318: .    -snes_tr_eta <eta>
    319: .    -snes_tr_sigma <sigma>
    320: .    -snes_tr_delta0 <delta0> -  initial size of the trust region is delta0*norm2(x)
    321: .    -snes_tr_delta1 <delta1>
    322: .    -snes_tr_delta2 <delta2>
    323: -    -snes_tr_delta3 <delta3>

    325:    The basic algorithm is taken from "The Minpack Project", by More',
    326:    Sorensen, Garbow, Hillstrom, pages 88-111 of "Sources and Development
    327:    of Mathematical Software", Wayne Cowell, editor.

    329:    Level: intermediate

    331: .seealso:  SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESSetTrustRegionTolerance()

    333: M*/
    336: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONTR(SNES snes)
    337: {
    338:   SNES_NEWTONTR  *neP;

    342:   snes->ops->setup          = SNESSetUp_NEWTONTR;
    343:   snes->ops->solve          = SNESSolve_NEWTONTR;
    344:   snes->ops->destroy        = SNESDestroy_NEWTONTR;
    345:   snes->ops->setfromoptions = SNESSetFromOptions_NEWTONTR;
    346:   snes->ops->view           = SNESView_NEWTONTR;
    347:   snes->ops->reset          = SNESReset_NEWTONTR;

    349:   snes->usesksp = PETSC_TRUE;
    350:   snes->usespc  = PETSC_FALSE;

    352:   PetscNewLog(snes,&neP);
    353:   snes->data  = (void*)neP;
    354:   neP->mu     = 0.25;
    355:   neP->eta    = 0.75;
    356:   neP->delta  = 0.0;
    357:   neP->delta0 = 0.2;
    358:   neP->delta1 = 0.3;
    359:   neP->delta2 = 0.75;
    360:   neP->delta3 = 2.0;
    361:   neP->sigma  = 0.0001;
    362:   neP->itflag = PETSC_FALSE;
    363:   neP->rnorm0 = 0.0;
    364:   neP->ttol   = 0.0;
    365:   return(0);
    366: }