Actual source code: tr.c

  1: #define PETSCSNES_DLL
  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: PetscErrorCode SNES_TR_KSPConverged_Private(KSP ksp,PetscInt 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:   PetscErrorCode      ierr;

 21:   if (snes->ksp_ewconv) {
 22:     if (!kctx) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Eisenstat-Walker convergence 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:     PetscInfo2(snes,"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:     PetscInfo2(snes,"KSP iterations=%D, rnorm=%G\n",n,rnorm);
 36:     PetscInfo2(snes,"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 PetscErrorCode SNESSolve_TR(SNES snes)
 51: {
 52:   SNES_TR             *neP = (SNES_TR*)snes->data;
 53:   Vec                 X,F,Y,G,TMP,Ytmp;
 54:   PetscErrorCode      ierr;
 55:   PetscInt            maxits,i,lits;
 56:   MatStructure        flg = DIFFERENT_NONZERO_PATTERN;
 57:   PetscReal           rho,fnorm,gnorm,gpnorm,xnorm,delta,nrm,ynorm,norm1;
 58:   PetscScalar         cnorm;
 59:   KSP                 ksp;
 60:   SNESConvergedReason reason;
 61:   PetscTruth          conv,breakout = PETSC_FALSE;

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

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

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

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

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

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

101:     /* Call general purpose update function */
102:     if (snes->ops->update) {
103:       (*snes->ops->update)(snes, snes->iter);
104:     }

106:     SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);
107:     KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);

109:     /* Solve J Y = F, where J is Jacobian matrix */
110:     KSPSolve(snes->ksp,F,Ytmp);
111:     KSPGetIterationNumber(ksp,&lits);
112:     snes->linear_its += lits;
113:     PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);
114:     VecNorm(Ytmp,NORM_2,&nrm);
115:     norm1 = nrm;
116:     while(1) {
117:       VecCopy(Ytmp,Y);
118:       nrm = norm1;

120:       /* Scale Y if need be and predict new value of F norm */
121:       if (nrm >= delta) {
122:         nrm = delta/nrm;
123:         gpnorm = (1.0 - nrm)*fnorm;
124:         cnorm = nrm;
125:         PetscInfo1(snes,"Scaling direction by %G\n",nrm);
126:         VecScale(Y,cnorm);
127:         nrm = gpnorm;
128:         ynorm = delta;
129:       } else {
130:         gpnorm = 0.0;
131:         PetscInfo(snes,"Direction is in Trust Region\n");
132:         ynorm = nrm;
133:       }
134:       VecAYPX(Y,-1.0,X);            /* Y <- X - Y */
135:       VecCopy(X,snes->vec_sol_update_always);
136:       SNESComputeFunction(snes,Y,G); /*  F(X) */
137:       VecNorm(G,NORM_2,&gnorm);      /* gnorm <- || g || */
138:       if (fnorm == gpnorm) rho = 0.0;
139:       else rho = (fnorm*fnorm - gnorm*gnorm)/(fnorm*fnorm - gpnorm*gpnorm);

141:       /* Update size of trust region */
142:       if      (rho < neP->mu)  delta *= neP->delta1;
143:       else if (rho < neP->eta) delta *= neP->delta2;
144:       else                     delta *= neP->delta3;
145:       PetscInfo3(snes,"fnorm=%G, gnorm=%G, ynorm=%G\n",fnorm,gnorm,ynorm);
146:       PetscInfo3(snes,"gpred=%G, rho=%G, delta=%G\n",gpnorm,rho,delta);
147:       neP->delta = delta;
148:       if (rho > neP->sigma) break;
149:       PetscInfo(snes,"Trying again in smaller region\n");
150:       /* check to see if progress is hopeless */
151:       neP->itflag = PETSC_FALSE;
152:       (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&reason,snes->cnvP);
153:       if (reason) {
154:         /* We're not progressing, so return with the current iterate */
155:         SNESMonitor(snes,i+1,fnorm);
156:         breakout = PETSC_TRUE;
157:         break;
158:       }
159:       snes->numFailures++;
160:     }
161:     if (!breakout) {
162:       fnorm = gnorm;
163:       PetscObjectTakeAccess(snes);
164:       snes->iter = i+1;
165:       snes->norm = fnorm;
166:       PetscObjectGrantAccess(snes);
167:       TMP = F; F = G; snes->vec_func_always = F; G = TMP;
168:       TMP = X; X = Y; snes->vec_sol_always  = X; Y = TMP;
169:       VecNorm(X,NORM_2,&xnorm);                /* xnorm = || X || */
170:       SNESLogConvHistory(snes,fnorm,lits);
171:       SNESMonitor(snes,i+1,fnorm);

173:       /* Test for convergence */
174:       neP->itflag = PETSC_TRUE;
175:       (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&reason,snes->cnvP);
176:       if (reason) {
177:         break;
178:       }
179:     } else {
180:       break;
181:     }
182:   }
183:   /* Verify solution is in corect location */
184:   if (X != snes->vec_sol) {
185:     VecCopy(X,snes->vec_sol);
186:   }
187:   if (F != snes->vec_func) {
188:     VecCopy(F,snes->vec_func);
189:   }
190:   snes->vec_sol_always  = snes->vec_sol;
191:   snes->vec_func_always = snes->vec_func;
192:   if (i == maxits) {
193:     PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);
194:     reason = SNES_DIVERGED_MAX_IT;
195:   }
196:   PetscObjectTakeAccess(snes);
197:   snes->reason = reason;
198:   PetscObjectGrantAccess(snes);
199:   return(0);
200: }
201: /*------------------------------------------------------------*/
204: static PetscErrorCode SNESSetUp_TR(SNES snes)
205: {

209:   if (!snes->work) {
210:     snes->nwork = 4;
211:     VecDuplicateVecs(snes->vec_sol,snes->nwork,&snes->work);
212:     PetscLogObjectParents(snes,snes->nwork,snes->work);
213:   }
214:   snes->vec_sol_update_always = snes->work[3];
215:   return(0);
216: }
217: /*------------------------------------------------------------*/
220: static PetscErrorCode SNESDestroy_TR(SNES snes)
221: {

225:   if (snes->nwork) {
226:     VecDestroyVecs(snes->work,snes->nwork);
227:   }
228:   PetscFree(snes->data);
229:   return(0);
230: }
231: /*------------------------------------------------------------*/

235: static PetscErrorCode SNESSetFromOptions_TR(SNES snes)
236: {
237:   SNES_TR *ctx = (SNES_TR *)snes->data;

241:   PetscOptionsHead("SNES trust region options for nonlinear equations");
242:     PetscOptionsReal("-snes_trtol","Trust region tolerance","SNESSetTrustRegionTolerance",snes->deltatol,&snes->deltatol,0);
243:     PetscOptionsReal("-snes_tr_mu","mu","None",ctx->mu,&ctx->mu,0);
244:     PetscOptionsReal("-snes_tr_eta","eta","None",ctx->eta,&ctx->eta,0);
245:     PetscOptionsReal("-snes_tr_sigma","sigma","None",ctx->sigma,&ctx->sigma,0);
246:     PetscOptionsReal("-snes_tr_delta0","delta0","None",ctx->delta0,&ctx->delta0,0);
247:     PetscOptionsReal("-snes_tr_delta1","delta1","None",ctx->delta1,&ctx->delta1,0);
248:     PetscOptionsReal("-snes_tr_delta2","delta2","None",ctx->delta2,&ctx->delta2,0);
249:     PetscOptionsReal("-snes_tr_delta3","delta3","None",ctx->delta3,&ctx->delta3,0);
250:   PetscOptionsTail();
251:   return(0);
252: }

256: static PetscErrorCode SNESView_TR(SNES snes,PetscViewer viewer)
257: {
258:   SNES_TR *tr = (SNES_TR *)snes->data;
260:   PetscTruth iascii;

263:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
264:   if (iascii) {
265:     PetscViewerASCIIPrintf(viewer,"  mu=%G, eta=%G, sigma=%G\n",tr->mu,tr->eta,tr->sigma);
266:     PetscViewerASCIIPrintf(viewer,"  delta0=%G, delta1=%G, delta2=%G, delta3=%G\n",tr->delta0,tr->delta1,tr->delta2,tr->delta3);
267:   } else {
268:     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for SNES EQ TR",((PetscObject)viewer)->type_name);
269:   }
270:   return(0);
271: }

273: /* ---------------------------------------------------------------- */
276: /*@C
277:    SNESConverged_TR - Monitors the convergence of the trust region
278:    method SNESTR for solving systems of nonlinear equations (default).

280:    Collective on SNES

282:    Input Parameters:
283: +  snes - the SNES context
284: .  xnorm - 2-norm of current iterate
285: .  pnorm - 2-norm of current step 
286: .  fnorm - 2-norm of function
287: -  dummy - unused context

289:    Output Parameter:
290: .   reason - one of
291: $  SNES_CONVERGED_FNORM_ABS       - (fnorm < abstol),
292: $  SNES_CONVERGED_PNORM_RELATIVE  - (pnorm < xtol*xnorm),
293: $  SNES_CONVERGED_FNORM_RELATIVE  - (fnorm < rtol*fnorm0),
294: $  SNES_DIVERGED_FUNCTION_COUNT   - (nfct > maxf),
295: $  SNES_DIVERGED_FNORM_NAN        - (fnorm == NaN),
296: $  SNES_CONVERGED_TR_DELTA        - (delta < xnorm*deltatol),
297: $  SNES_CONVERGED_ITERATING       - (otherwise)

299:    where
300: +    delta    - trust region paramenter
301: .    deltatol - trust region size tolerance,
302:                 set with SNESSetTrustRegionTolerance()
303: .    maxf - maximum number of function evaluations,
304:             set with SNESSetTolerances()
305: .    nfct - number of function evaluations,
306: .    abstol - absolute function norm tolerance,
307:             set with SNESSetTolerances()
308: -    xtol - relative function norm tolerance,
309:             set with SNESSetTolerances()

311:    Level: intermediate

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

315: .seealso: SNESSetConvergenceTest(), SNESEisenstatWalkerConverged()
316: @*/
317: PetscErrorCode  SNESConverged_TR(SNES snes,PetscInt it,PetscReal xnorm,PetscReal pnorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
318: {
319:   SNES_TR *neP = (SNES_TR *)snes->data;

323:   if (fnorm != fnorm) {
324:     PetscInfo(snes,"Failed to converged, function norm is NaN\n");
325:     *reason = SNES_DIVERGED_FNORM_NAN;
326:   } else if (neP->delta < xnorm * snes->deltatol) {
327:     PetscInfo3(snes,"Converged due to trust region param %G<%G*%G\n",neP->delta,xnorm,snes->deltatol);
328:     *reason = SNES_CONVERGED_TR_DELTA;
329:   } else if (neP->itflag) {
330:     SNESConverged_LS(snes,it,xnorm,pnorm,fnorm,reason,dummy);
331:   } else if (snes->nfuncs >= snes->max_funcs) {
332:     PetscInfo2(snes,"Exceeded maximum number of function evaluations: %D > %D\n",snes->nfuncs,snes->max_funcs);
333:     *reason = SNES_DIVERGED_FUNCTION_COUNT;
334:   } else {
335:     *reason = SNES_CONVERGED_ITERATING;
336:   }
337:   return(0);
338: }
339: /* ------------------------------------------------------------ */
340: /*MC
341:       SNESTR - Newton based nonlinear solver that uses a trust region

343:    Options Database:
344: +    -snes_trtol <tol> Trust region tolerance
345: .    -snes_tr_mu <mu>
346: .    -snes_tr_eta <eta>
347: .    -snes_tr_sigma <sigma>
348: .    -snes_tr_delta0 <delta0>
349: .    -snes_tr_delta1 <delta1>
350: .    -snes_tr_delta2 <delta2>
351: -    -snes_tr_delta3 <delta3>

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

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

361:    Level: intermediate

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

365: M*/
369: PetscErrorCode  SNESCreate_TR(SNES snes)
370: {
371:   SNES_TR        *neP;

375:   snes->ops->setup             = SNESSetUp_TR;
376:   snes->ops->solve             = SNESSolve_TR;
377:   snes->ops->destroy             = SNESDestroy_TR;
378:   snes->ops->converged             = SNESConverged_TR;
379:   snes->ops->setfromoptions  = SNESSetFromOptions_TR;
380:   snes->ops->view            = SNESView_TR;
381:   snes->nwork                = 0;
382: 
383:   ierr                        = PetscNew(SNES_TR,&neP);
384:   PetscLogObjectMemory(snes,sizeof(SNES_TR));
385:   snes->data                = (void*)neP;
386:   neP->mu                = 0.25;
387:   neP->eta                = 0.75;
388:   neP->delta                = 0.0;
389:   neP->delta0                = 0.2;
390:   neP->delta1                = 0.3;
391:   neP->delta2                = 0.75;
392:   neP->delta3                = 2.0;
393:   neP->sigma                = 0.0001;
394:   neP->itflag                = PETSC_FALSE;
395:   neP->rnorm0                = 0;
396:   neP->ttol                = 0;
397:   return(0);
398: }