Date: 2016-07-24T17:09:06+00:00

Actual source code: tr.c
petsc-3.7.3 2016-07-24
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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;

     99:   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);

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

    108:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    109:   snes->iter = 0;
    110:   PetscObjectSAWsGrantAccess((PetscObject)snes);

    112:   if (!snes->vec_func_init_set) {
    113:     SNESComputeFunction(snes,X,F);          /* F(X) */
    114:   } else snes->vec_func_init_set = PETSC_FALSE;

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

    127:   /* test convergence */
    128:   (*snes->ops->converged)(snes,snes->iter,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    129:   if (snes->reason) return(0);

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

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

    145:     /* Call general purpose update function */
    146:     if (snes->ops->update) {
    147:       (*snes->ops->update)(snes, snes->iter);
    148:     }

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

    156:     snes->linear_its += lits;

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

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

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

    193:       neP->delta = delta;
    194:       if (rho > neP->sigma) break;
    195:       PetscInfo(snes,"Trying again in smaller region\n");
    196:       /* check to see if progress is hopeless */
    197:       neP->itflag = PETSC_FALSE;
    198:       SNES_TR_Converged_Private(snes,snes->iter,xnorm,ynorm,fnorm,&reason,snes->cnvP);
    199:       if (!reason) { (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&reason,snes->cnvP); }
    200:       if (reason) {
    201:         /* We're not progressing, so return with the current iterate */
    202:         SNESMonitor(snes,i+1,fnorm);
    203:         breakout = PETSC_TRUE;
    204:         break;
    205:       }
    206:       snes->numFailures++;
    207:     }
    208:     if (!breakout) {
    209:       /* Update function and solution vectors */
    210:       fnorm = gnorm;
    211:       VecCopy(G,F);
    212:       VecCopy(Y,X);
    213:       /* Monitor convergence */
    214:       PetscObjectSAWsTakeAccess((PetscObject)snes);
    215:       snes->iter = i+1;
    216:       snes->norm = fnorm;
    217:       PetscObjectSAWsGrantAccess((PetscObject)snes);
    218:       SNESLogConvergenceHistory(snes,snes->norm,lits);
    219:       SNESMonitor(snes,snes->iter,snes->norm);
    220:       /* Test for convergence, xnorm = || X || */
    221:       neP->itflag = PETSC_TRUE;
    222:       if (snes->ops->converged != SNESConvergedSkip) { VecNorm(X,NORM_2,&xnorm); }
    223:       (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&reason,snes->cnvP);
    224:       if (reason) break;
    225:     } else break;
    226:   }
    227:   if (i == maxits) {
    228:     PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);
    229:     if (!reason) reason = SNES_DIVERGED_MAX_IT;
    230:   }
    231:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    232:   snes->reason = reason;
    233:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    234:   return(0);
    235: }
    236: /*------------------------------------------------------------*/
    239: static PetscErrorCode SNESSetUp_NEWTONTR(SNES snes)
    240: {

    244:   SNESSetWorkVecs(snes,3);
    245:   SNESSetUpMatrices(snes);
    246:   return(0);
    247: }

    251: PetscErrorCode SNESReset_NEWTONTR(SNES snes)
    252: {

    255:   return(0);
    256: }

    260: static PetscErrorCode SNESDestroy_NEWTONTR(SNES snes)
    261: {

    265:   SNESReset_NEWTONTR(snes);
    266:   PetscFree(snes->data);
    267:   return(0);
    268: }
    269: /*------------------------------------------------------------*/

    273: static PetscErrorCode SNESSetFromOptions_NEWTONTR(PetscOptionItems *PetscOptionsObject,SNES snes)
    274: {
    275:   SNES_NEWTONTR  *ctx = (SNES_NEWTONTR*)snes->data;

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

    294: static PetscErrorCode SNESView_NEWTONTR(SNES snes,PetscViewer viewer)
    295: {
    296:   SNES_NEWTONTR  *tr = (SNES_NEWTONTR*)snes->data;
    298:   PetscBool      iascii;

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

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

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

    326:    Level: intermediate

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

    330: M*/
    333: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONTR(SNES snes)
    334: {
    335:   SNES_NEWTONTR  *neP;

    339:   snes->ops->setup          = SNESSetUp_NEWTONTR;
    340:   snes->ops->solve          = SNESSolve_NEWTONTR;
    341:   snes->ops->destroy        = SNESDestroy_NEWTONTR;
    342:   snes->ops->setfromoptions = SNESSetFromOptions_NEWTONTR;
    343:   snes->ops->view           = SNESView_NEWTONTR;
    344:   snes->ops->reset          = SNESReset_NEWTONTR;

    346:   snes->usesksp = PETSC_TRUE;
    347:   snes->usespc  = PETSC_FALSE;

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