Actual source code: tr.c

petsc-3.11.0 2019-03-29
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  2:  #include <../src/snes/impls/tr/trimpl.h>

  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: */
 13: static PetscErrorCode SNESTR_KSPConverged_Private(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *cctx)
 14: {
 15:   SNES_TR_KSPConverged_Ctx *ctx = (SNES_TR_KSPConverged_Ctx*)cctx;
 16:   SNES                     snes = ctx->snes;
 17:   SNES_NEWTONTR            *neP = (SNES_NEWTONTR*)snes->data;
 18:   Vec                      x;
 19:   PetscReal                nrm;
 20:   PetscErrorCode           ierr;

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

 37: static PetscErrorCode SNESTR_KSPConverged_Destroy(void *cctx)
 38: {
 39:   SNES_TR_KSPConverged_Ctx *ctx = (SNES_TR_KSPConverged_Ctx*)cctx;
 40:   PetscErrorCode           ierr;

 43:   KSPConvergedDefaultDestroy(ctx->ctx);
 44:   PetscFree(ctx);
 45:   return(0);
 46: }

 48: /* ---------------------------------------------------------------- */
 49: /*
 50:    SNESTR_Converged_Private -test convergence JUST for
 51:    the trust region tolerance.

 53: */
 54: static PetscErrorCode SNESTR_Converged_Private(SNES snes,PetscInt it,PetscReal xnorm,PetscReal pnorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
 55: {
 56:   SNES_NEWTONTR  *neP = (SNES_NEWTONTR*)snes->data;

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


 72: /*
 73:    SNESSolve_NEWTONTR - Implements Newton's Method with a very simple trust
 74:    region approach for solving systems of nonlinear equations.


 77: */
 78: static PetscErrorCode SNESSolve_NEWTONTR(SNES snes)
 79: {
 80:   SNES_NEWTONTR       *neP = (SNES_NEWTONTR*)snes->data;
 81:   Vec                 X,F,Y,G,Ytmp;
 82:   PetscErrorCode      ierr;
 83:   PetscInt            maxits,i,lits;
 84:   PetscReal           rho,fnorm,gnorm,gpnorm,xnorm=0,delta,nrm,ynorm,norm1;
 85:   PetscScalar         cnorm;
 86:   KSP                 ksp;
 87:   SNESConvergedReason reason = SNES_CONVERGED_ITERATING;
 88:   PetscBool           conv   = PETSC_FALSE,breakout = PETSC_FALSE;

 91:   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);

 93:   maxits = snes->max_its;               /* maximum number of iterations */
 94:   X      = snes->vec_sol;               /* solution vector */
 95:   F      = snes->vec_func;              /* residual vector */
 96:   Y      = snes->work[0];               /* work vectors */
 97:   G      = snes->work[1];
 98:   Ytmp   = snes->work[2];

100:   PetscObjectSAWsTakeAccess((PetscObject)snes);
101:   snes->iter = 0;
102:   PetscObjectSAWsGrantAccess((PetscObject)snes);

104:   if (!snes->vec_func_init_set) {
105:     SNESComputeFunction(snes,X,F);          /* F(X) */
106:   } else snes->vec_func_init_set = PETSC_FALSE;

108:   VecNorm(F,NORM_2,&fnorm);             /* fnorm <- || F || */
109:   SNESCheckFunctionNorm(snes,fnorm);
110:   VecNorm(X,NORM_2,&xnorm);             /* fnorm <- || F || */
111:   PetscObjectSAWsTakeAccess((PetscObject)snes);
112:   snes->norm = fnorm;
113:   PetscObjectSAWsGrantAccess((PetscObject)snes);
114:   delta      = xnorm ? neP->delta0*xnorm : neP->delta0;
115:   neP->delta = delta;
116:   SNESLogConvergenceHistory(snes,fnorm,0);
117:   SNESMonitor(snes,0,fnorm);

119:   /* test convergence */
120:   (*snes->ops->converged)(snes,snes->iter,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
121:   if (snes->reason) return(0);

123:   /* Set the stopping criteria to use the More' trick. */
124:   PetscOptionsGetBool(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_tr_ksp_regular_convergence_test",&conv,NULL);
125:   if (!conv) {
126:     SNES_TR_KSPConverged_Ctx *ctx;
127:     SNESGetKSP(snes,&ksp);
128:     PetscNew(&ctx);
129:     ctx->snes = snes;
130:     KSPConvergedDefaultCreate(&ctx->ctx);
131:     KSPSetConvergenceTest(ksp,SNESTR_KSPConverged_Private,ctx,SNESTR_KSPConverged_Destroy);
132:     PetscInfo(snes,"Using Krylov convergence test SNESTR_KSPConverged_Private\n");
133:   }

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

137:     /* Call general purpose update function */
138:     if (snes->ops->update) {
139:       (*snes->ops->update)(snes, snes->iter);
140:     }

142:     /* Solve J Y = F, where J is Jacobian matrix */
143:     SNESComputeJacobian(snes,X,snes->jacobian,snes->jacobian_pre);
144:     SNESCheckJacobianDomainerror(snes);
145:     KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre);
146:     KSPSolve(snes->ksp,F,Ytmp);
147:     KSPGetIterationNumber(snes->ksp,&lits);

149:     snes->linear_its += lits;

151:     PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);
152:     VecNorm(Ytmp,NORM_2,&nrm);
153:     norm1 = nrm;
154:     while (1) {
155:       VecCopy(Ytmp,Y);
156:       nrm  = norm1;

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

179:       /* Update size of trust region */
180:       if      (rho < neP->mu)  delta *= neP->delta1;
181:       else if (rho < neP->eta) delta *= neP->delta2;
182:       else                     delta *= neP->delta3;
183:       PetscInfo3(snes,"fnorm=%g, gnorm=%g, ynorm=%g\n",(double)fnorm,(double)gnorm,(double)ynorm);
184:       PetscInfo3(snes,"gpred=%g, rho=%g, delta=%g\n",(double)gpnorm,(double)rho,(double)delta);

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

237:   SNESSetWorkVecs(snes,3);
238:   SNESSetUpMatrices(snes);
239:   return(0);
240: }

242: PetscErrorCode SNESReset_NEWTONTR(SNES snes)
243: {

246:   return(0);
247: }

249: static PetscErrorCode SNESDestroy_NEWTONTR(SNES snes)
250: {

254:   SNESReset_NEWTONTR(snes);
255:   PetscFree(snes->data);
256:   return(0);
257: }
258: /*------------------------------------------------------------*/

260: static PetscErrorCode SNESSetFromOptions_NEWTONTR(PetscOptionItems *PetscOptionsObject,SNES snes)
261: {
262:   SNES_NEWTONTR  *ctx = (SNES_NEWTONTR*)snes->data;

266:   PetscOptionsHead(PetscOptionsObject,"SNES trust region options for nonlinear equations");
267:   PetscOptionsReal("-snes_trtol","Trust region tolerance","SNESSetTrustRegionTolerance",snes->deltatol,&snes->deltatol,NULL);
268:   PetscOptionsReal("-snes_tr_mu","mu","None",ctx->mu,&ctx->mu,NULL);
269:   PetscOptionsReal("-snes_tr_eta","eta","None",ctx->eta,&ctx->eta,NULL);
270:   PetscOptionsReal("-snes_tr_sigma","sigma","None",ctx->sigma,&ctx->sigma,NULL);
271:   PetscOptionsReal("-snes_tr_delta0","delta0","None",ctx->delta0,&ctx->delta0,NULL);
272:   PetscOptionsReal("-snes_tr_delta1","delta1","None",ctx->delta1,&ctx->delta1,NULL);
273:   PetscOptionsReal("-snes_tr_delta2","delta2","None",ctx->delta2,&ctx->delta2,NULL);
274:   PetscOptionsReal("-snes_tr_delta3","delta3","None",ctx->delta3,&ctx->delta3,NULL);
275:   PetscOptionsTail();
276:   return(0);
277: }

279: static PetscErrorCode SNESView_NEWTONTR(SNES snes,PetscViewer viewer)
280: {
281:   SNES_NEWTONTR  *tr = (SNES_NEWTONTR*)snes->data;
283:   PetscBool      iascii;

286:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
287:   if (iascii) {
288:     PetscViewerASCIIPrintf(viewer,"  Trust region tolerance (-snes_trtol)\n",(double)snes->deltatol);
289:     PetscViewerASCIIPrintf(viewer,"  mu=%g, eta=%g, sigma=%g\n",(double)tr->mu,(double)tr->eta,(double)tr->sigma);
290:     PetscViewerASCIIPrintf(viewer,"  delta0=%g, delta1=%g, delta2=%g, delta3=%g\n",(double)tr->delta0,(double)tr->delta1,(double)tr->delta2,(double)tr->delta3);
291:   }
292:   return(0);
293: }
294: /* ------------------------------------------------------------ */
295: /*MC
296:       SNESNEWTONTR - Newton based nonlinear solver that uses a trust region

298:    Options Database:
299: +    -snes_trtol <tol> - trust region tolerance
300: .    -snes_tr_mu <mu> - trust region parameter
301: .    -snes_tr_eta <eta> - trust region parameter
302: .    -snes_tr_sigma <sigma> - trust region parameter
303: .    -snes_tr_delta0 <delta0> -  initial size of the trust region is delta0*norm2(x)
304: .    -snes_tr_delta1 <delta1> - trust region parameter
305: .    -snes_tr_delta2 <delta2> - trust region parameter
306: -    -snes_tr_delta3 <delta3> - trust region parameter

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

312:    Level: intermediate

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

316: M*/
317: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONTR(SNES snes)
318: {
319:   SNES_NEWTONTR  *neP;

323:   snes->ops->setup          = SNESSetUp_NEWTONTR;
324:   snes->ops->solve          = SNESSolve_NEWTONTR;
325:   snes->ops->destroy        = SNESDestroy_NEWTONTR;
326:   snes->ops->setfromoptions = SNESSetFromOptions_NEWTONTR;
327:   snes->ops->view           = SNESView_NEWTONTR;
328:   snes->ops->reset          = SNESReset_NEWTONTR;

330:   snes->usesksp = PETSC_TRUE;
331:   snes->usesnpc = PETSC_FALSE;

333:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

335:   PetscNewLog(snes,&neP);
336:   snes->data  = (void*)neP;
337:   neP->mu     = 0.25;
338:   neP->eta    = 0.75;
339:   neP->delta  = 0.0;
340:   neP->delta0 = 0.2;
341:   neP->delta1 = 0.3;
342:   neP->delta2 = 0.75;
343:   neP->delta3 = 2.0;
344:   neP->sigma  = 0.0001;
345:   neP->itflag = PETSC_FALSE;
346:   neP->rnorm0 = 0.0;
347:   neP->ttol   = 0.0;
348:   return(0);
349: }