Actual source code: tr.c

petsc-3.6.0 2015-06-09
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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: }