Actual source code: tr.c

petsc-3.8.3 2017-12-09
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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: PetscErrorCode SNES_TR_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: PetscErrorCode SNES_TR_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:    SNES_TR_Converged_Private -test convergence JUST for
 51:    the trust region tolerance.

 53: */
 54: static PetscErrorCode SNES_TR_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) {
 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,SNES_TR_KSPConverged_Private,ctx,SNES_TR_KSPConverged_Destroy);
132:     PetscInfo(snes,"Using Krylov convergence test SNES_TR_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:     KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre);
145:     KSPSolve(snes->ksp,F,Ytmp);
146:     KSPGetIterationNumber(snes->ksp,&lits);

148:     snes->linear_its += lits;

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

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

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

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

234:   SNESSetWorkVecs(snes,3);
235:   SNESSetUpMatrices(snes);
236:   return(0);
237: }

239: PetscErrorCode SNESReset_NEWTONTR(SNES snes)
240: {

243:   return(0);
244: }

246: static PetscErrorCode SNESDestroy_NEWTONTR(SNES snes)
247: {

251:   SNESReset_NEWTONTR(snes);
252:   PetscFree(snes->data);
253:   return(0);
254: }
255: /*------------------------------------------------------------*/

257: static PetscErrorCode SNESSetFromOptions_NEWTONTR(PetscOptionItems *PetscOptionsObject,SNES snes)
258: {
259:   SNES_NEWTONTR  *ctx = (SNES_NEWTONTR*)snes->data;

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

276: static PetscErrorCode SNESView_NEWTONTR(SNES snes,PetscViewer viewer)
277: {
278:   SNES_NEWTONTR  *tr = (SNES_NEWTONTR*)snes->data;
280:   PetscBool      iascii;

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

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

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

308:    Level: intermediate

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

312: M*/
313: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONTR(SNES snes)
314: {
315:   SNES_NEWTONTR  *neP;

319:   snes->ops->setup          = SNESSetUp_NEWTONTR;
320:   snes->ops->solve          = SNESSolve_NEWTONTR;
321:   snes->ops->destroy        = SNESDestroy_NEWTONTR;
322:   snes->ops->setfromoptions = SNESSetFromOptions_NEWTONTR;
323:   snes->ops->view           = SNESView_NEWTONTR;
324:   snes->ops->reset          = SNESReset_NEWTONTR;

326:   snes->usesksp = PETSC_TRUE;
327:   snes->usesnpc = PETSC_FALSE;

329:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

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