Actual source code: tr.c

  1: /*$Id: tr.c,v 1.128 2001/08/07 03:04:11 balay Exp $*/
  2: 
 3:  #include src/snes/impls/tr/tr.h

  5: /*
  6:    This convergence test determines if the two norm of the 
  7:    solution lies outside the trust region, if so it halts.
  8: */
 11: int SNES_TR_KSPConverged_Private(KSP ksp,int n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
 12: {
 13:   SNES                snes = (SNES) ctx;
 14:   SNES_KSP_EW_ConvCtx *kctx = (SNES_KSP_EW_ConvCtx*)snes->kspconvctx;
 15:   SNES_TR             *neP = (SNES_TR*)snes->data;
 16:   Vec                 x;
 17:   PetscReal           nrm;
 18:   int                 ierr;

 21:   if (snes->ksp_ewconv) {
 22:     if (!kctx) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Eisenstat-Walker onvergence context not created");
 23:     if (!n) {SNES_KSP_EW_ComputeRelativeTolerance_Private(snes,ksp);}
 24:     kctx->lresid_last = rnorm;
 25:   }
 26:   KSPDefaultConverged(ksp,n,rnorm,reason,ctx);
 27:   if (*reason) {
 28:     PetscLogInfo(snes,"SNES_TR_KSPConverged_Private: regular convergence test KSP iterations=%d, rnorm=%g\n",n,rnorm);
 29:   }

 31:   /* Determine norm of solution */
 32:   KSPBuildSolution(ksp,0,&x);
 33:   VecNorm(x,NORM_2,&nrm);
 34:   if (nrm >= neP->delta) {
 35:     PetscLogInfo(snes,"SNES_TR_KSPConverged_Private: KSP iterations=%d, rnorm=%g\n",n,rnorm);
 36:     PetscLogInfo(snes,"SNES_TR_KSPConverged_Private: Ending linear iteration early, delta=%g, length=%g\n",neP->delta,nrm);
 37:     *reason = KSP_CONVERGED_STEP_LENGTH;
 38:   }
 39:   return(0);
 40: }

 42: /*
 43:    SNESSolve_TR - Implements Newton's Method with a very simple trust 
 44:    region approach for solving systems of nonlinear equations. 

 46:  
 47: */
 50: static int SNESSolve_TR(SNES snes)
 51: {
 52:   SNES_TR             *neP = (SNES_TR*)snes->data;
 53:   Vec                 X,F,Y,G,TMP,Ytmp;
 54:   int                 maxits,i,ierr,lits,breakout = 0;
 55:   MatStructure        flg = DIFFERENT_NONZERO_PATTERN;
 56:   PetscReal           rho,fnorm,gnorm,gpnorm,xnorm,delta,nrm,ynorm,norm1;
 57:   PetscScalar         mone = -1.0,cnorm;
 58:   KSP                 ksp;
 59:   SNESConvergedReason reason;
 60:   PetscTruth          conv;

 63:   maxits        = snes->max_its;        /* maximum number of iterations */
 64:   X                = snes->vec_sol;        /* solution vector */
 65:   F                = snes->vec_func;        /* residual vector */
 66:   Y                = snes->work[0];        /* work vectors */
 67:   G                = snes->work[1];
 68:   Ytmp          = snes->work[2];

 70:   PetscObjectTakeAccess(snes);
 71:   snes->iter = 0;
 72:   PetscObjectGrantAccess(snes);
 73:   VecNorm(X,NORM_2,&xnorm);         /* xnorm = || X || */

 75:   SNESComputeFunction(snes,X,F);          /* F(X) */
 76:   VecNorm(F,NORM_2,&fnorm);             /* fnorm <- || F || */
 77:   PetscObjectTakeAccess(snes);
 78:   snes->norm = fnorm;
 79:   PetscObjectGrantAccess(snes);
 80:   delta = neP->delta0*fnorm;
 81:   neP->delta = delta;
 82:   SNESLogConvHistory(snes,fnorm,0);
 83:   SNESMonitor(snes,0,fnorm);
 84:   SNESGetKSP(snes,&ksp);

 86:  if (fnorm < snes->atol) {snes->reason = SNES_CONVERGED_FNORM_ABS; return(0);}

 88:   /* set parameter for default relative tolerance convergence test */
 89:   snes->ttol = fnorm*snes->rtol;

 91:   /* Set the stopping criteria to use the More' trick. */
 92:   PetscOptionsHasName(PETSC_NULL,"-snes_tr_ksp_regular_convergence_test",&conv);
 93:   if (!conv) {
 94:     KSPSetConvergenceTest(ksp,SNES_TR_KSPConverged_Private,(void *)snes);
 95:     PetscLogInfo(snes,"SNESSolve_TR: Using Krylov convergence test SNES_TR_KSPConverged_Private\n");
 96:   }
 97: 
 98:   for (i=0; i<maxits; i++) {
 99:     SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);
100:     KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);

102:     /* Solve J Y = F, where J is Jacobian matrix */
103:     KSPSetRhs(snes->ksp,F);
104:     KSPSetSolution(snes->ksp,Ytmp);
105:     KSPSolve(snes->ksp);
106:     KSPGetIterationNumber(ksp,&lits);
107:     snes->linear_its += lits;
108:     PetscLogInfo(snes,"SNESSolve_TR: iter=%d, linear solve iterations=%d\n",snes->iter,lits);
109:     VecNorm(Ytmp,NORM_2,&nrm);
110:     norm1 = nrm;
111:     while(1) {
112:       VecCopy(Ytmp,Y);
113:       nrm = norm1;

115:       /* Scale Y if need be and predict new value of F norm */
116:       if (nrm >= delta) {
117:         nrm = delta/nrm;
118:         gpnorm = (1.0 - nrm)*fnorm;
119:         cnorm = nrm;
120:         PetscLogInfo(snes,"SNESSolve_TR: Scaling direction by %g\n",nrm);
121:         VecScale(&cnorm,Y);
122:         nrm = gpnorm;
123:         ynorm = delta;
124:       } else {
125:         gpnorm = 0.0;
126:         PetscLogInfo(snes,"SNESSolve_TR: Direction is in Trust Region\n");
127:         ynorm = nrm;
128:       }
129:       VecAYPX(&mone,X,Y);            /* Y <- X - Y */
130:       VecCopy(X,snes->vec_sol_update_always);
131:       SNESComputeFunction(snes,Y,G); /*  F(X) */
132:       VecNorm(G,NORM_2,&gnorm);      /* gnorm <- || g || */
133:       if (fnorm == gpnorm) rho = 0.0;
134:       else rho = (fnorm*fnorm - gnorm*gnorm)/(fnorm*fnorm - gpnorm*gpnorm);

136:       /* Update size of trust region */
137:       if      (rho < neP->mu)  delta *= neP->delta1;
138:       else if (rho < neP->eta) delta *= neP->delta2;
139:       else                     delta *= neP->delta3;
140:       PetscLogInfo(snes,"SNESSolve_TR: fnorm=%g, gnorm=%g, ynorm=%g\n",fnorm,gnorm,ynorm);
141:       PetscLogInfo(snes,"SNESSolve_TR: gpred=%g, rho=%g, delta=%g\n",gpnorm,rho,delta);
142:       neP->delta = delta;
143:       if (rho > neP->sigma) break;
144:       PetscLogInfo(snes,"SNESSolve_TR: Trying again in smaller region\n");
145:       /* check to see if progress is hopeless */
146:       neP->itflag = 0;
147:       (*snes->converged)(snes,xnorm,ynorm,fnorm,&reason,snes->cnvP);
148:       if (reason) {
149:         /* We're not progressing, so return with the current iterate */
150:         SNESMonitor(snes,i+1,fnorm);
151:         breakout = 1;
152:         break;
153:       }
154:       snes->numFailures++;
155:     }
156:     if (!breakout) {
157:       fnorm = gnorm;
158:       PetscObjectTakeAccess(snes);
159:       snes->iter = i+1;
160:       snes->norm = fnorm;
161:       PetscObjectGrantAccess(snes);
162:       TMP = F; F = G; snes->vec_func_always = F; G = TMP;
163:       TMP = X; X = Y; snes->vec_sol_always  = X; Y = TMP;
164:       VecNorm(X,NORM_2,&xnorm);                /* xnorm = || X || */
165:       SNESLogConvHistory(snes,fnorm,lits);
166:       SNESMonitor(snes,i+1,fnorm);

168:       /* Test for convergence */
169:       neP->itflag = 1;
170:       (*snes->converged)(snes,xnorm,ynorm,fnorm,&reason,snes->cnvP);
171:       if (reason) {
172:         break;
173:       }
174:     } else {
175:       break;
176:     }
177:   }
178:   /* Verify solution is in corect location */
179:   if (X != snes->vec_sol) {
180:     VecCopy(X,snes->vec_sol);
181:   }
182:   if (F != snes->vec_func) {
183:     VecCopy(F,snes->vec_func);
184:   }
185:   snes->vec_sol_always  = snes->vec_sol;
186:   snes->vec_func_always = snes->vec_func;
187:   if (i == maxits) {
188:     PetscLogInfo(snes,"SNESSolve_TR: Maximum number of iterations has been reached: %d\n",maxits);
189:     reason = SNES_DIVERGED_MAX_IT;
190:   }
191:   PetscObjectTakeAccess(snes);
192:   snes->reason = reason;
193:   PetscObjectGrantAccess(snes);
194:   return(0);
195: }
196: /*------------------------------------------------------------*/
199: static int SNESSetUp_TR(SNES snes)
200: {

204:   snes->nwork = 4;
205:   VecDuplicateVecs(snes->vec_sol,snes->nwork,&snes->work);
206:   PetscLogObjectParents(snes,snes->nwork,snes->work);
207:   snes->vec_sol_update_always = snes->work[3];
208:   return(0);
209: }
210: /*------------------------------------------------------------*/
213: static int SNESDestroy_TR(SNES snes)
214: {
215:   int  ierr;

218:   if (snes->nwork) {
219:     VecDestroyVecs(snes->work,snes->nwork);
220:   }
221:   PetscFree(snes->data);
222:   return(0);
223: }
224: /*------------------------------------------------------------*/

228: static int SNESSetFromOptions_TR(SNES snes)
229: {
230:   SNES_TR *ctx = (SNES_TR *)snes->data;
231:   int     ierr;

234:   PetscOptionsHead("SNES trust region options for nonlinear equations");
235:     PetscOptionsReal("-snes_trtol","Trust region tolerance","SNESSetTrustRegionTolerance",snes->deltatol,&snes->deltatol,0);
236:     PetscOptionsReal("-snes_tr_mu","mu","None",ctx->mu,&ctx->mu,0);
237:     PetscOptionsReal("-snes_tr_eta","eta","None",ctx->eta,&ctx->eta,0);
238:     PetscOptionsReal("-snes_tr_sigma","sigma","None",ctx->sigma,&ctx->sigma,0);
239:     PetscOptionsReal("-snes_tr_delta0","delta0","None",ctx->delta0,&ctx->delta0,0);
240:     PetscOptionsReal("-snes_tr_delta1","delta1","None",ctx->delta1,&ctx->delta1,0);
241:     PetscOptionsReal("-snes_tr_delta2","delta2","None",ctx->delta2,&ctx->delta2,0);
242:     PetscOptionsReal("-snes_tr_delta3","delta3","None",ctx->delta3,&ctx->delta3,0);
243:   PetscOptionsTail();
244:   return(0);
245: }

249: static int SNESView_TR(SNES snes,PetscViewer viewer)
250: {
251:   SNES_TR *tr = (SNES_TR *)snes->data;
252:   int        ierr;
253:   PetscTruth isascii;

256:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&isascii);
257:   if (isascii) {
258:     PetscViewerASCIIPrintf(viewer,"  mu=%g, eta=%g, sigma=%g\n",tr->mu,tr->eta,tr->sigma);
259:     PetscViewerASCIIPrintf(viewer,"  delta0=%g, delta1=%g, delta2=%g, delta3=%g\n",tr->delta0,tr->delta1,tr->delta2,tr->delta3);
260:   } else {
261:     SETERRQ1(1,"Viewer type %s not supported for SNES EQ TR",((PetscObject)viewer)->type_name);
262:   }
263:   return(0);
264: }

266: /* ---------------------------------------------------------------- */
269: /*@C
270:    SNESConverged_TR - Monitors the convergence of the trust region
271:    method SNESTR for solving systems of nonlinear equations (default).

273:    Collective on SNES

275:    Input Parameters:
276: +  snes - the SNES context
277: .  xnorm - 2-norm of current iterate
278: .  pnorm - 2-norm of current step 
279: .  fnorm - 2-norm of function
280: -  dummy - unused context

282:    Output Parameter:
283: .   reason - one of
284: $  SNES_CONVERGED_FNORM_ABS       - (fnorm < atol),
285: $  SNES_CONVERGED_PNORM_RELATIVE  - (pnorm < xtol*xnorm),
286: $  SNES_CONVERGED_FNORM_RELATIVE  - (fnorm < rtol*fnorm0),
287: $  SNES_DIVERGED_FUNCTION_COUNT   - (nfct > maxf),
288: $  SNES_DIVERGED_FNORM_NAN        - (fnorm == NaN),
289: $  SNES_CONVERGED_TR_DELTA        - (delta < xnorm*deltatol),
290: $  SNES_CONVERGED_ITERATING       - (otherwise)

292:    where
293: +    delta    - trust region paramenter
294: .    deltatol - trust region size tolerance,
295:                 set with SNESSetTrustRegionTolerance()
296: .    maxf - maximum number of function evaluations,
297:             set with SNESSetTolerances()
298: .    nfct - number of function evaluations,
299: .    atol - absolute function norm tolerance,
300:             set with SNESSetTolerances()
301: -    xtol - relative function norm tolerance,
302:             set with SNESSetTolerances()

304:    Level: intermediate

306: .keywords: SNES, nonlinear, default, converged, convergence

308: .seealso: SNESSetConvergenceTest(), SNESEisenstatWalkerConverged()
309: @*/
310: int SNESConverged_TR(SNES snes,PetscReal xnorm,PetscReal pnorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
311: {
312:   SNES_TR *neP = (SNES_TR *)snes->data;
313:   int     ierr;

316:   if (fnorm != fnorm) {
317:     PetscLogInfo(snes,"SNESConverged_TR:Failed to converged, function norm is NaN\n");
318:     *reason = SNES_DIVERGED_FNORM_NAN;
319:   } else if (neP->delta < xnorm * snes->deltatol) {
320:     PetscLogInfo(snes,"SNESConverged_TR: Converged due to trust region param %g<%g*%g\n",neP->delta,xnorm,snes->deltatol);
321:     *reason = SNES_CONVERGED_TR_DELTA;
322:   } else if (neP->itflag) {
323:     SNESConverged_LS(snes,xnorm,pnorm,fnorm,reason,dummy);
324:   } else if (snes->nfuncs > snes->max_funcs) {
325:     PetscLogInfo(snes,"SNESConverged_TR: Exceeded maximum number of function evaluations: %d > %d\n",snes->nfuncs,snes->max_funcs);
326:     *reason = SNES_DIVERGED_FUNCTION_COUNT;
327:   } else {
328:     *reason = SNES_CONVERGED_ITERATING;
329:   }
330:   return(0);
331: }
332: /* ------------------------------------------------------------ */
333: /*MC
334:       SNESTR - Newton based nonlinear solver that uses a trust region

336:    Options Database:
337: +    -snes_trtol <tol> Trust region tolerance
338: .    -snes_tr_mu <mu>
339: .    -snes_tr_eta <eta>
340: .    -snes_tr_sigma <sigma>
341: .    -snes_tr_delta0 <delta0>
342: .    -snes_tr_delta1 <delta1>
343: .    -snes_tr_delta2 <delta2>
344: -    -snes_tr_delta3 <delta3>

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

350:    This is intended as a model implementation, since it does not 
351:    necessarily have many of the bells and whistles of other 
352:    implementations.  

354: .seealso:  SNESCreate(), SNES, SNESSetType(), SNESLS, SNESSetTrustRegionTolerance()

356: M*/
357: EXTERN_C_BEGIN
360: int SNESCreate_TR(SNES snes)
361: {
362:   SNES_TR *neP;
363:   int     ierr;

366:   snes->setup                = SNESSetUp_TR;
367:   snes->solve                = SNESSolve_TR;
368:   snes->destroy                = SNESDestroy_TR;
369:   snes->converged        = SNESConverged_TR;
370:   snes->setfromoptions  = SNESSetFromOptions_TR;
371:   snes->view            = SNESView_TR;
372:   snes->nwork           = 0;
373: 
374:   ierr                        = PetscNew(SNES_TR,&neP);
375:   PetscLogObjectMemory(snes,sizeof(SNES_TR));
376:   snes->data                = (void*)neP;
377:   neP->mu                = 0.25;
378:   neP->eta                = 0.75;
379:   neP->delta                = 0.0;
380:   neP->delta0                = 0.2;
381:   neP->delta1                = 0.3;
382:   neP->delta2                = 0.75;
383:   neP->delta3                = 2.0;
384:   neP->sigma                = 0.0001;
385:   neP->itflag                = 0;
386:   neP->rnorm0                = 0;
387:   neP->ttol                = 0;
388:   return(0);
389: }
390: EXTERN_C_END