Actual source code: snesncg.c

petsc-3.7.3 2016-07-24
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  1: #include <../src/snes/impls/ncg/snesncgimpl.h> /*I "petscsnes.h" I*/
  2: const char *const SNESNCGTypes[] = {"FR","PRP","HS","DY","CD","SNESNCGType","SNES_NCG_",0};

  6: PetscErrorCode SNESReset_NCG(SNES snes)
  7: {
  9:   return(0);
 10: }

 12: #define SNESLINESEARCHNCGLINEAR "ncglinear"

 14: /*
 15:   SNESDestroy_NCG - Destroys the private SNES_NCG context that was created with SNESCreate_NCG().

 17:   Input Parameter:
 18: . snes - the SNES context

 20:   Application Interface Routine: SNESDestroy()
 21: */
 24: PetscErrorCode SNESDestroy_NCG(SNES snes)
 25: {

 29:   PetscFree(snes->data);
 30:   return(0);
 31: }

 33: /*
 34:    SNESSetUp_NCG - Sets up the internal data structures for the later use
 35:    of the SNESNCG nonlinear solver.

 37:    Input Parameters:
 38: +  snes - the SNES context
 39: -  x - the solution vector

 41:    Application Interface Routine: SNESSetUp()
 42:  */

 44: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch);

 48: PetscErrorCode SNESSetUp_NCG(SNES snes)
 49: {

 53:   SNESSetWorkVecs(snes,2);
 54:   if (snes->pcside == PC_RIGHT) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNESNCG only supports left preconditioning");
 55:   if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED;
 56:   return(0);
 57: }
 58: /*
 59:   SNESSetFromOptions_NCG - Sets various parameters for the SNESNCG method.

 61:   Input Parameter:
 62: . snes - the SNES context

 64:   Application Interface Routine: SNESSetFromOptions()
 65: */
 68: static PetscErrorCode SNESSetFromOptions_NCG(PetscOptionItems *PetscOptionsObject,SNES snes)
 69: {
 70:   SNES_NCG       *ncg = (SNES_NCG*)snes->data;
 72:   PetscBool      debug = PETSC_FALSE;
 73:   SNESLineSearch linesearch;
 74:   SNESNCGType    ncgtype=ncg->type;

 77:   PetscOptionsHead(PetscOptionsObject,"SNES NCG options");
 78:   PetscOptionsBool("-snes_ncg_monitor","Monitor NCG iterations","SNES",ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL);
 79:   if (debug) {
 80:     ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
 81:   }
 82:   PetscOptionsEnum("-snes_ncg_type","NCG Beta type used","SNESNCGSetType",SNESNCGTypes,(PetscEnum)ncg->type,(PetscEnum*)&ncgtype,NULL);
 83:   SNESNCGSetType(snes, ncgtype);
 84:   PetscOptionsTail();
 85:   if (!snes->linesearch) {
 86:     SNESGetLineSearch(snes, &linesearch);
 87:     if (!snes->pc) {
 88:       SNESLineSearchSetType(linesearch, SNESLINESEARCHCP);
 89:     } else {
 90:       SNESLineSearchSetType(linesearch, SNESLINESEARCHL2);
 91:     }
 92:   }
 93:   SNESLineSearchRegister(SNESLINESEARCHNCGLINEAR, SNESLineSearchCreate_NCGLinear);
 94:   return(0);
 95: }

 97: /*
 98:   SNESView_NCG - Prints info from the SNESNCG data structure.

100:   Input Parameters:
101: + SNES - the SNES context
102: - viewer - visualization context

104:   Application Interface Routine: SNESView()
105: */
108: static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer)
109: {
110:   SNES_NCG      *ncg = (SNES_NCG *) snes->data;
111:   PetscBool      iascii;

115:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
116:   if (iascii) {
117:     PetscViewerASCIIPrintf(viewer, "ncg type: %s\n", SNESNCGTypes[ncg->type]);
118:   }
119:   return(0);
120: }

124: PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch)
125: {
126:   PetscScalar    alpha, ptAp;
127:   Vec            X, Y, F, W;
128:   SNES           snes;
130:   PetscReal      *fnorm, *xnorm, *ynorm;

133:   SNESLineSearchGetSNES(linesearch, &snes);
134:   X     = linesearch->vec_sol;
135:   W     = linesearch->vec_sol_new;
136:   F     = linesearch->vec_func;
137:   Y     = linesearch->vec_update;
138:   fnorm = &linesearch->fnorm;
139:   xnorm = &linesearch->xnorm;
140:   ynorm = &linesearch->ynorm;

142:   if (!snes->jacobian) {
143:     SNESSetUpMatrices(snes);
144:   }

146:   /*

148:    The exact step size for unpreconditioned linear CG is just:
149:    alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy)
150:    */
151:   SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre);
152:   VecDot(F, F, &alpha);
153:   MatMult(snes->jacobian, Y, W);
154:   VecDot(Y, W, &ptAp);
155:   alpha = alpha / ptAp;
156:   VecAXPY(X,-alpha,Y);
157:   SNESComputeFunction(snes,X,F);

159:   VecNorm(F,NORM_2,fnorm);
160:   VecNorm(X,NORM_2,xnorm);
161:   VecNorm(Y,NORM_2,ynorm);
162:   return(0);
163: }

167: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch)
168: {
170:   linesearch->ops->apply          = SNESLineSearchApply_NCGLinear;
171:   linesearch->ops->destroy        = NULL;
172:   linesearch->ops->setfromoptions = NULL;
173:   linesearch->ops->reset          = NULL;
174:   linesearch->ops->view           = NULL;
175:   linesearch->ops->setup          = NULL;
176:   return(0);
177: }

181: /*

183:  Assuming F = SNESComputeFunction(X) compute Y^tJ^tF using a simple secant approximation of the jacobian.

185:  */
186: PetscErrorCode SNESNCGComputeYtJtF_Private(SNES snes, Vec X, Vec F, Vec Y, Vec W, Vec G, PetscScalar * ytJtf)
187: {
189:   PetscScalar    ftf, ftg, fty, h;

192:   VecDot(F, F, &ftf);
193:   VecDot(F, Y, &fty);
194:   h      = 1e-5*fty / fty;
195:   VecCopy(X, W);
196:   VecAXPY(W, -h, Y);          /* this is arbitrary */
197:   SNESComputeFunction(snes, W, G);
198:   VecDot(G, F, &ftg);
199:   *ytJtf = (ftg - ftf) / h;
200:   return(0);
201: }

205: /*@
206:     SNESNCGSetType - Sets the conjugate update type for SNESNCG.

208:     Logically Collective on SNES

210:     Input Parameters:
211: +   snes - the iterative context
212: -   btype - update type

214:     Options Database:
215: .   -snes_ncg_type<prp,fr,hs,dy,cd>

217:     Level: intermediate

219:     SNESNCGSelectTypes:
220: +   SNES_NCG_FR - Fletcher-Reeves update
221: .   SNES_NCG_PRP - Polak-Ribiere-Polyak update
222: .   SNES_NCG_HS - Hestenes-Steifel update
223: .   SNES_NCG_DY - Dai-Yuan update
224: -   SNES_NCG_CD - Conjugate Descent update

226:    Notes:
227:    PRP is the default, and the only one that tolerates generalized search directions.

229: .keywords: SNES, SNESNCG, selection, type, set
230: @*/
231: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
232: {

237:   PetscTryMethod(snes,"SNESNCGSetType_C",(SNES,SNESNCGType),(snes,btype));
238:   return(0);
239: }

243: PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
244: {
245:   SNES_NCG *ncg = (SNES_NCG*)snes->data;

248:   ncg->type = btype;
249:   return(0);
250: }

252: /*
253:   SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.

255:   Input Parameters:
256: . snes - the SNES context

258:   Output Parameter:
259: . outits - number of iterations until termination

261:   Application Interface Routine: SNESSolve()
262: */
265: PetscErrorCode SNESSolve_NCG(SNES snes)
266: {
267:   SNES_NCG             *ncg = (SNES_NCG*)snes->data;
268:   Vec                  X,dX,lX,F,dXold;
269:   PetscReal            fnorm, ynorm, xnorm, beta = 0.0;
270:   PetscScalar          dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
271:   PetscInt             maxits, i;
272:   PetscErrorCode       ierr;
273:   SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
274:   SNESLineSearch       linesearch;
275:   SNESConvergedReason  reason;

278:   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);

280:   PetscCitationsRegister(SNESCitation,&SNEScite);
281:   snes->reason = SNES_CONVERGED_ITERATING;

283:   maxits = snes->max_its;            /* maximum number of iterations */
284:   X      = snes->vec_sol;            /* X^n */
285:   dXold  = snes->work[0];            /* The previous iterate of X */
286:   dX     = snes->work[1];            /* the preconditioned direction */
287:   lX     = snes->vec_sol_update;     /* the conjugate direction */
288:   F      = snes->vec_func;           /* residual vector */

290:   SNESGetLineSearch(snes, &linesearch);

292:   PetscObjectSAWsTakeAccess((PetscObject)snes);
293:   snes->iter = 0;
294:   snes->norm = 0.;
295:   PetscObjectSAWsGrantAccess((PetscObject)snes);

297:   /* compute the initial function and preconditioned update dX */

299:   if (snes->pc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
300:     SNESApplyNPC(snes,X,NULL,dX);
301:     SNESGetConvergedReason(snes->pc,&reason);
302:     if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
303:       snes->reason = SNES_DIVERGED_INNER;
304:       return(0);
305:     }
306:     VecCopy(dX,F);
307:     VecNorm(F,NORM_2,&fnorm);
308:   } else {
309:     if (!snes->vec_func_init_set) {
310:       SNESComputeFunction(snes,X,F);
311:     } else snes->vec_func_init_set = PETSC_FALSE;

313:     /* convergence test */
314:     VecNorm(F,NORM_2,&fnorm);
315:     SNESCheckFunctionNorm(snes,fnorm);
316:     VecCopy(F,dX);
317:   }
318:   if (snes->pc) {
319:     if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
320:       SNESApplyNPC(snes,X,F,dX);
321:       SNESGetConvergedReason(snes->pc,&reason);
322:       if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
323:         snes->reason = SNES_DIVERGED_INNER;
324:         return(0);
325:       }
326:     }
327:   }
328:   VecCopy(dX,lX);
329:   VecDot(dX, dX, &dXdotdX);


332:   PetscObjectSAWsTakeAccess((PetscObject)snes);
333:   snes->norm = fnorm;
334:   PetscObjectSAWsGrantAccess((PetscObject)snes);
335:   SNESLogConvergenceHistory(snes,fnorm,0);
336:   SNESMonitor(snes,0,fnorm);

338:   /* test convergence */
339:   (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
340:   if (snes->reason) return(0);

342:   /* Call general purpose update function */
343:   if (snes->ops->update) {
344:     (*snes->ops->update)(snes, snes->iter);
345:   }

347:   /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */

349:   for (i = 1; i < maxits + 1; i++) {
350:     /* some update types require the old update direction or conjugate direction */
351:     if (ncg->type != SNES_NCG_FR) {
352:       VecCopy(dX, dXold);
353:     }
354:     SNESLineSearchApply(linesearch,X,F,&fnorm,lX);
355:     SNESLineSearchGetReason(linesearch, &lsresult);
356:     SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
357:     if (lsresult) {
358:       if (++snes->numFailures >= snes->maxFailures) {
359:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
360:         return(0);
361:       }
362:     }
363:     if (snes->nfuncs >= snes->max_funcs) {
364:       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
365:       return(0);
366:     }
367:     /* Monitor convergence */
368:     PetscObjectSAWsTakeAccess((PetscObject)snes);
369:     snes->iter = i;
370:     snes->norm = fnorm;
371:     PetscObjectSAWsGrantAccess((PetscObject)snes);
372:     SNESLogConvergenceHistory(snes,snes->norm,0);
373:     SNESMonitor(snes,snes->iter,snes->norm);

375:     /* Test for convergence */
376:     (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
377:     if (snes->reason) return(0);

379:     /* Call general purpose update function */
380:     if (snes->ops->update) {
381:       (*snes->ops->update)(snes, snes->iter);
382:     }
383:     if (snes->pc) {
384:       if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
385:         SNESApplyNPC(snes,X,NULL,dX);
386:         SNESGetConvergedReason(snes->pc,&reason);
387:         if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
388:           snes->reason = SNES_DIVERGED_INNER;
389:           return(0);
390:         }
391:         VecCopy(dX,F);
392:       } else {
393:         SNESApplyNPC(snes,X,F,dX);
394:         SNESGetConvergedReason(snes->pc,&reason);
395:         if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
396:           snes->reason = SNES_DIVERGED_INNER;
397:           return(0);
398:         }
399:       }
400:     } else {
401:       VecCopy(F,dX);
402:     }

404:     /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
405:     switch (ncg->type) {
406:     case SNES_NCG_FR: /* Fletcher-Reeves */
407:       dXolddotdXold= dXdotdX;
408:       VecDot(dX, dX, &dXdotdX);
409:       beta         = PetscRealPart(dXdotdX / dXolddotdXold);
410:       break;
411:     case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
412:       dXolddotdXold= dXdotdX;
413:       VecDotBegin(dX, dX, &dXdotdXold);
414:       VecDotBegin(dXold, dX, &dXdotdXold);
415:       VecDotEnd(dX, dX, &dXdotdX);
416:       VecDotEnd(dXold, dX, &dXdotdXold);
417:       beta         = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
418:       if (beta < 0.0) beta = 0.0; /* restart */
419:       break;
420:     case SNES_NCG_HS: /* Hestenes-Stiefel */
421:       VecDotBegin(dX, dX, &dXdotdX);
422:       VecDotBegin(dX, dXold, &dXdotdXold);
423:       VecDotBegin(lX, dX, &lXdotdX);
424:       VecDotBegin(lX, dXold, &lXdotdXold);
425:       VecDotEnd(dX, dX, &dXdotdX);
426:       VecDotEnd(dX, dXold, &dXdotdXold);
427:       VecDotEnd(lX, dX, &lXdotdX);
428:       VecDotEnd(lX, dXold, &lXdotdXold);
429:       beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
430:       break;
431:     case SNES_NCG_DY: /* Dai-Yuan */
432:       VecDotBegin(dX, dX, &dXdotdX);
433:       VecDotBegin(lX, dX, &lXdotdX);
434:       VecDotBegin(lX, dXold, &lXdotdXold);
435:       VecDotEnd(dX, dX, &dXdotdX);
436:       VecDotEnd(lX, dX, &lXdotdX);
437:       VecDotEnd(lX, dXold, &lXdotdXold);
438:       beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
439:       break;
440:     case SNES_NCG_CD: /* Conjugate Descent */
441:       VecDotBegin(dX, dX, &dXdotdX);
442:       VecDotBegin(lX, dXold, &lXdotdXold);
443:       VecDotEnd(dX, dX, &dXdotdX);
444:       VecDotEnd(lX, dXold, &lXdotdXold);
445:       beta = PetscRealPart(dXdotdX / lXdotdXold);
446:       break;
447:     }
448:     if (ncg->monitor) {
449:       PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta);
450:     }
451:     VecAYPX(lX, beta, dX);
452:   }
453:   PetscInfo1(snes, "Maximum number of iterations has been reached: %D\n", maxits);
454:   if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
455:   return(0);
456: }



460: /*MC
461:   SNESNCG - Nonlinear Conjugate-Gradient method for the solution of general nonlinear systems.

463:   Level: beginner

465:   Options Database:
466: +   -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
467: .   -snes_linesearch_type <cp,l2,basic> - Line search type.
468: -   -snes_ncg_monitor - Print relevant information about the ncg iteration.

470:    Notes: This solves the nonlinear system of equations F(x) = 0 using the nonlinear generalization of the conjugate
471:           gradient method.  This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise
472:           chooses the initial search direction as F(x) for the initial guess x.

474:    References:
475: .  1. -  Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
476:    SIAM Review, 57(4), 2015


479: .seealso:  SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESNEWTONTR, SNESNGMRES, SNESNQN
480: M*/
483: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
484: {
486:   SNES_NCG       * neP;

489:   snes->ops->destroy        = SNESDestroy_NCG;
490:   snes->ops->setup          = SNESSetUp_NCG;
491:   snes->ops->setfromoptions = SNESSetFromOptions_NCG;
492:   snes->ops->view           = SNESView_NCG;
493:   snes->ops->solve          = SNESSolve_NCG;
494:   snes->ops->reset          = SNESReset_NCG;

496:   snes->usesksp = PETSC_FALSE;
497:   snes->usespc  = PETSC_TRUE;
498:   snes->pcside  = PC_LEFT;

500:   if (!snes->tolerancesset) {
501:     snes->max_funcs = 30000;
502:     snes->max_its   = 10000;
503:     snes->stol      = 1e-20;
504:   }

506:   PetscNewLog(snes,&neP);
507:   snes->data   = (void*) neP;
508:   neP->monitor = NULL;
509:   neP->type    = SNES_NCG_PRP;
510:   PetscObjectComposeFunction((PetscObject)snes,"SNESNCGSetType_C", SNESNCGSetType_NCG);
511:   return(0);
512: }