Actual source code: snesncg.c

  1: #include <../src/snes/impls/ncg/snesncgimpl.h>
  2: const char *const SNESNCGTypes[] = {"FR", "PRP", "HS", "DY", "CD", "SNESNCGType", "SNES_NCG_", NULL};

  4: static PetscErrorCode SNESReset_NCG(SNES snes)
  5: {
  6:   PetscFunctionBegin;
  7:   PetscFunctionReturn(PETSC_SUCCESS);
  8: }

 10: static PetscErrorCode SNESDestroy_NCG(SNES snes)
 11: {
 12:   PetscFunctionBegin;
 13:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", NULL));
 14:   PetscCall(PetscFree(snes->data));
 15:   PetscFunctionReturn(PETSC_SUCCESS);
 16: }

 18: static PetscErrorCode SNESSetUp_NCG(SNES snes)
 19: {
 20:   PetscFunctionBegin;
 21:   PetscCall(SNESSetWorkVecs(snes, 2));
 22:   PetscCheck(snes->npcside != PC_RIGHT, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNESNCG only supports left preconditioning");
 23:   if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED;
 24:   PetscFunctionReturn(PETSC_SUCCESS);
 25: }

 27: static PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch)
 28: {
 29:   PetscScalar alpha, ptAp;
 30:   Vec         X, Y, F, W;
 31:   SNES        snes;
 32:   PetscReal  *fnorm, *xnorm, *ynorm;

 34:   PetscFunctionBegin;
 35:   PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
 36:   X     = linesearch->vec_sol;
 37:   W     = linesearch->vec_sol_new;
 38:   F     = linesearch->vec_func;
 39:   Y     = linesearch->vec_update;
 40:   fnorm = &linesearch->fnorm;
 41:   xnorm = &linesearch->xnorm;
 42:   ynorm = &linesearch->ynorm;

 44:   if (!snes->jacobian) PetscCall(SNESSetUpMatrices(snes));

 46:   /*
 47:    The exact step size for unpreconditioned linear CG is just:
 48:    alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy)
 49:    */
 50:   PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre));
 51:   PetscCall(VecDot(F, F, &alpha));
 52:   PetscCall(MatMult(snes->jacobian, Y, W));
 53:   PetscCall(VecDot(Y, W, &ptAp));
 54:   alpha = alpha / ptAp;
 55:   PetscCall(VecAXPY(X, -alpha, Y));
 56:   PetscCall(SNESComputeFunction(snes, X, F));

 58:   PetscCall(VecNorm(F, NORM_2, fnorm));
 59:   PetscCall(VecNorm(X, NORM_2, xnorm));
 60:   PetscCall(VecNorm(Y, NORM_2, ynorm));
 61:   PetscFunctionReturn(PETSC_SUCCESS);
 62: }

 64: /*MC
 65:    SNESLINESEARCHNCGLINEAR - Special line search only for the nonlinear CG solver `SNESNCG`

 67:    This line search uses the length "as if" the problem is linear (that is what is computed by the linear CG method) using the Jacobian of the function.
 68:    alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy) where r (f) is the current residual (function value), p (y) is the current search direction.

 70:    Notes:
 71:    This requires a Jacobian-vector product but does not require the solution of a linear system with the Jacobian

 73:    This is a "odd-ball" line search, we don't know if it is in the literature or used in practice by anyone.

 75:    Level: advanced

 77: .seealso: `SNESLineSearchCreate()`, `SNESLineSearchSetType()`
 78: M*/

 80: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch)
 81: {
 82:   PetscFunctionBegin;
 83:   linesearch->ops->apply          = SNESLineSearchApply_NCGLinear;
 84:   linesearch->ops->destroy        = NULL;
 85:   linesearch->ops->setfromoptions = NULL;
 86:   linesearch->ops->reset          = NULL;
 87:   linesearch->ops->view           = NULL;
 88:   linesearch->ops->setup          = NULL;
 89:   PetscFunctionReturn(PETSC_SUCCESS);
 90: }

 92: static PetscErrorCode SNESSetFromOptions_NCG(SNES snes, PetscOptionItems *PetscOptionsObject)
 93: {
 94:   SNES_NCG      *ncg     = (SNES_NCG *)snes->data;
 95:   PetscBool      debug   = PETSC_FALSE;
 96:   SNESNCGType    ncgtype = ncg->type;
 97:   SNESLineSearch linesearch;

 99:   PetscFunctionBegin;
100:   PetscOptionsHeadBegin(PetscOptionsObject, "SNES NCG options");
101:   PetscCall(PetscOptionsBool("-snes_ncg_monitor", "Monitor the beta values used in the NCG iterations", "SNES", ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL));
102:   if (debug) ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
103:   PetscCall(PetscOptionsEnum("-snes_ncg_type", "NCG Beta type used", "SNESNCGSetType", SNESNCGTypes, (PetscEnum)ncg->type, (PetscEnum *)&ncgtype, NULL));
104:   PetscCall(SNESNCGSetType(snes, ncgtype));
105:   PetscOptionsHeadEnd();
106:   if (!snes->linesearch) {
107:     PetscCall(SNESGetLineSearch(snes, &linesearch));
108:     if (!((PetscObject)linesearch)->type_name) {
109:       if (!snes->npc) {
110:         PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHCP));
111:       } else {
112:         PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHL2));
113:       }
114:     }
115:   }
116:   PetscFunctionReturn(PETSC_SUCCESS);
117: }

119: static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer)
120: {
121:   SNES_NCG *ncg = (SNES_NCG *)snes->data;
122:   PetscBool iascii;

124:   PetscFunctionBegin;
125:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
126:   if (iascii) PetscCall(PetscViewerASCIIPrintf(viewer, "  type: %s\n", SNESNCGTypes[ncg->type]));
127:   PetscFunctionReturn(PETSC_SUCCESS);
128: }

130: /*

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

134:  This routine is not currently used. I don't know what its intended purpose is.

136:  Note it has a hardwired differencing parameter of 1e-5

138:  */
139: PetscErrorCode SNESNCGComputeYtJtF_Private(SNES snes, Vec X, Vec F, Vec Y, Vec W, Vec G, PetscScalar *ytJtf)
140: {
141:   PetscScalar ftf, ftg, fty, h;

143:   PetscFunctionBegin;
144:   PetscCall(VecDot(F, F, &ftf));
145:   PetscCall(VecDot(F, Y, &fty));
146:   h = 1e-5 * fty / fty;
147:   PetscCall(VecCopy(X, W));
148:   PetscCall(VecAXPY(W, -h, Y)); /* this is arbitrary */
149:   PetscCall(SNESComputeFunction(snes, W, G));
150:   PetscCall(VecDot(G, F, &ftg));
151:   *ytJtf = (ftg - ftf) / h;
152:   PetscFunctionReturn(PETSC_SUCCESS);
153: }

155: /*@
156:     SNESNCGSetType - Sets the conjugate update type for nonlinear CG `SNESNCG`.

158:     Logically Collective

160:     Input Parameters:
161: +   snes - the iterative context
162: -   btype - update type

164:     Options Database Key:
165: .   -snes_ncg_type <prp,fr,hs,dy,cd> -strategy for selecting algorithm for computing beta

167:     Level: intermediate

169:     `SNESNCGType`s:
170: +   `SNES_NCG_FR` - Fletcher-Reeves update
171: .   `SNES_NCG_PRP` - Polak-Ribiere-Polyak update
172: .   `SNES_NCG_HS` - Hestenes-Steifel update
173: .   `SNES_NCG_DY` - Dai-Yuan update
174: -   `SNES_NCG_CD` - Conjugate Descent update

176:    Notes:
177:    `SNES_NCG_PRP` is the default, and the only one that tolerates generalized search directions.

179:    It is not clear what "generalized search directions" means, does it mean use with a nonlinear preconditioner,
180:    that is using -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()`?

182:    Developer Note:
183:    There should be a `SNESNCGSetType()`

185: .seealso: `SNESNCGType`, `SNES_NCG_FR`, `SNES_NCG_PRP`, `SNES_NCG_HS`, `SNES_NCG_DY`, `SNES_NCG_CD`
186: @*/
187: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
188: {
189:   PetscFunctionBegin;
191:   PetscTryMethod(snes, "SNESNCGSetType_C", (SNES, SNESNCGType), (snes, btype));
192:   PetscFunctionReturn(PETSC_SUCCESS);
193: }

195: static PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
196: {
197:   SNES_NCG *ncg = (SNES_NCG *)snes->data;

199:   PetscFunctionBegin;
200:   ncg->type = btype;
201:   PetscFunctionReturn(PETSC_SUCCESS);
202: }

204: /*
205:   SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.

207:   Input Parameter:
208: . snes - the `SNES` context

210:   Output Parameter:
211: . outits - number of iterations until termination

213:   Application Interface Routine: SNESSolve()
214: */
215: static PetscErrorCode SNESSolve_NCG(SNES snes)
216: {
217:   SNES_NCG            *ncg = (SNES_NCG *)snes->data;
218:   Vec                  X, dX, lX, F, dXold;
219:   PetscReal            fnorm, ynorm, xnorm, beta = 0.0;
220:   PetscScalar          dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
221:   PetscInt             maxits, i;
222:   SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
223:   SNESLineSearch       linesearch;
224:   SNESConvergedReason  reason;

226:   PetscFunctionBegin;
227:   PetscCheck(!snes->xl && !snes->xu && !snes->ops->computevariablebounds, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

229:   PetscCall(PetscCitationsRegister(SNESCitation, &SNEScite));
230:   snes->reason = SNES_CONVERGED_ITERATING;

232:   maxits = snes->max_its;        /* maximum number of iterations */
233:   X      = snes->vec_sol;        /* X^n */
234:   dXold  = snes->work[0];        /* The previous iterate of X */
235:   dX     = snes->work[1];        /* the preconditioned direction */
236:   lX     = snes->vec_sol_update; /* the conjugate direction */
237:   F      = snes->vec_func;       /* residual vector */

239:   PetscCall(SNESGetLineSearch(snes, &linesearch));

241:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
242:   snes->iter = 0;
243:   snes->norm = 0.;
244:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));

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

248:   if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
249:     PetscCall(SNESApplyNPC(snes, X, NULL, dX));
250:     PetscCall(SNESGetConvergedReason(snes->npc, &reason));
251:     if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
252:       snes->reason = SNES_DIVERGED_INNER;
253:       PetscFunctionReturn(PETSC_SUCCESS);
254:     }
255:     PetscCall(VecCopy(dX, F));
256:     PetscCall(VecNorm(F, NORM_2, &fnorm));
257:   } else {
258:     if (!snes->vec_func_init_set) {
259:       PetscCall(SNESComputeFunction(snes, X, F));
260:     } else snes->vec_func_init_set = PETSC_FALSE;

262:     /* convergence test */
263:     PetscCall(VecNorm(F, NORM_2, &fnorm));
264:     SNESCheckFunctionNorm(snes, fnorm);
265:     PetscCall(VecCopy(F, dX));
266:   }
267:   if (snes->npc) {
268:     if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
269:       PetscCall(SNESApplyNPC(snes, X, F, dX));
270:       PetscCall(SNESGetConvergedReason(snes->npc, &reason));
271:       if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
272:         snes->reason = SNES_DIVERGED_INNER;
273:         PetscFunctionReturn(PETSC_SUCCESS);
274:       }
275:     }
276:   }
277:   PetscCall(VecCopy(dX, lX));
278:   PetscCall(VecDot(dX, dX, &dXdotdX));

280:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
281:   snes->norm = fnorm;
282:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
283:   PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));
284:   PetscCall(SNESMonitor(snes, 0, fnorm));

286:   /* test convergence */
287:   PetscUseTypeMethod(snes, converged, 0, 0.0, 0.0, fnorm, &snes->reason, snes->cnvP);
288:   if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

290:   /* Call general purpose update function */
291:   PetscTryTypeMethod(snes, update, snes->iter);

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

295:   for (i = 1; i < maxits + 1; i++) {
296:     /* some update types require the old update direction or conjugate direction */
297:     if (ncg->type != SNES_NCG_FR) PetscCall(VecCopy(dX, dXold));
298:     PetscCall(SNESLineSearchApply(linesearch, X, F, &fnorm, lX));
299:     PetscCall(SNESLineSearchGetReason(linesearch, &lsresult));
300:     PetscCall(SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm));
301:     if (lsresult) {
302:       if (++snes->numFailures >= snes->maxFailures) {
303:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
304:         PetscFunctionReturn(PETSC_SUCCESS);
305:       }
306:     }
307:     if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
308:       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
309:       PetscFunctionReturn(PETSC_SUCCESS);
310:     }
311:     /* Monitor convergence */
312:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
313:     snes->iter  = i;
314:     snes->norm  = fnorm;
315:     snes->xnorm = xnorm;
316:     snes->ynorm = ynorm;
317:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
318:     PetscCall(SNESLogConvergenceHistory(snes, snes->norm, 0));
319:     PetscCall(SNESMonitor(snes, snes->iter, snes->norm));

321:     /* Test for convergence */
322:     PetscUseTypeMethod(snes, converged, snes->iter, xnorm, ynorm, fnorm, &snes->reason, snes->cnvP);
323:     if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

325:     /* Call general purpose update function */
326:     PetscTryTypeMethod(snes, update, snes->iter);
327:     if (snes->npc) {
328:       if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
329:         PetscCall(SNESApplyNPC(snes, X, NULL, dX));
330:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
331:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
332:           snes->reason = SNES_DIVERGED_INNER;
333:           PetscFunctionReturn(PETSC_SUCCESS);
334:         }
335:         PetscCall(VecCopy(dX, F));
336:       } else {
337:         PetscCall(SNESApplyNPC(snes, X, F, dX));
338:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
339:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
340:           snes->reason = SNES_DIVERGED_INNER;
341:           PetscFunctionReturn(PETSC_SUCCESS);
342:         }
343:       }
344:     } else {
345:       PetscCall(VecCopy(F, dX));
346:     }

348:     /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
349:     switch (ncg->type) {
350:     case SNES_NCG_FR: /* Fletcher-Reeves */
351:       dXolddotdXold = dXdotdX;
352:       PetscCall(VecDot(dX, dX, &dXdotdX));
353:       beta = PetscRealPart(dXdotdX / dXolddotdXold);
354:       break;
355:     case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
356:       dXolddotdXold = dXdotdX;
357:       PetscCall(VecDotBegin(dX, dX, &dXdotdXold));
358:       PetscCall(VecDotBegin(dXold, dX, &dXdotdXold));
359:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
360:       PetscCall(VecDotEnd(dXold, dX, &dXdotdXold));
361:       beta = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
362:       if (beta < 0.0) beta = 0.0; /* restart */
363:       break;
364:     case SNES_NCG_HS: /* Hestenes-Stiefel */
365:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
366:       PetscCall(VecDotBegin(dX, dXold, &dXdotdXold));
367:       PetscCall(VecDotBegin(lX, dX, &lXdotdX));
368:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
369:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
370:       PetscCall(VecDotEnd(dX, dXold, &dXdotdXold));
371:       PetscCall(VecDotEnd(lX, dX, &lXdotdX));
372:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
373:       beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
374:       break;
375:     case SNES_NCG_DY: /* Dai-Yuan */
376:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
377:       PetscCall(VecDotBegin(lX, dX, &lXdotdX));
378:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
379:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
380:       PetscCall(VecDotEnd(lX, dX, &lXdotdX));
381:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
382:       beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
383:       break;
384:     case SNES_NCG_CD: /* Conjugate Descent */
385:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
386:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
387:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
388:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
389:       beta = PetscRealPart(dXdotdX / lXdotdXold);
390:       break;
391:     }
392:     if (ncg->monitor) PetscCall(PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta));
393:     PetscCall(VecAYPX(lX, beta, dX));
394:   }
395:   PetscCall(PetscInfo(snes, "Maximum number of iterations has been reached: %" PetscInt_FMT "\n", maxits));
396:   if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
397:   PetscFunctionReturn(PETSC_SUCCESS);
398: }

400: /*MC
401:   SNESNCG - Nonlinear Conjugate-Gradient method for the solution of nonlinear systems.

403:   Level: beginner

405:   Options Database Keys:
406: +   -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
407: .   -snes_linesearch_type <cp,l2,basic> - Line search type.
408: -   -snes_ncg_monitor - Print the beta values used in the ncg iteration, .

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

415:    Only supports left non-linear preconditioning.

417:    Default line search is `SNESLINESEARCHCP`, unless a nonlinear preconditioner is used with -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()` then
418:    `SNESLINESEARCHL2` is used. Also supports the special purpose line search `SNESLINESEARCHNCGLINEAR`

420:    References:
421: .  * -  Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
422:    SIAM Review, 57(4), 2015

424: .seealso: `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNEWTONTR`, `SNESNGMRES`, `SNESQN`, `SNESLINESEARCHNCGLINEAR`, `SNESNCGSetType()`, `SNESLineSearchSetType()`
425: M*/
426: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
427: {
428:   SNES_NCG *neP;

430:   PetscFunctionBegin;
431:   snes->ops->destroy        = SNESDestroy_NCG;
432:   snes->ops->setup          = SNESSetUp_NCG;
433:   snes->ops->setfromoptions = SNESSetFromOptions_NCG;
434:   snes->ops->view           = SNESView_NCG;
435:   snes->ops->solve          = SNESSolve_NCG;
436:   snes->ops->reset          = SNESReset_NCG;

438:   snes->usesksp = PETSC_FALSE;
439:   snes->usesnpc = PETSC_TRUE;
440:   snes->npcside = PC_LEFT;

442:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

444:   if (!snes->tolerancesset) {
445:     snes->max_funcs = 30000;
446:     snes->max_its   = 10000;
447:     snes->stol      = 1e-20;
448:   }

450:   PetscCall(PetscNew(&neP));
451:   snes->data   = (void *)neP;
452:   neP->monitor = NULL;
453:   neP->type    = SNES_NCG_PRP;
454:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", SNESNCGSetType_NCG));
455:   PetscFunctionReturn(PETSC_SUCCESS);
456: }