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:    Level: advanced

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

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

 77: .seealso: [](ch_snes), `SNES`, `SNESNCG` `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: /*@
131:   SNESNCGSetType - Sets the conjugate update type for nonlinear CG `SNESNCG`.

133:   Logically Collective

135:   Input Parameters:
136: + snes  - the iterative context
137: - btype - update type, see `SNESNCGType`

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

142:   Level: intermediate

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

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

150: .seealso: [](ch_snes), `SNES`, `SNESNCG`, `SNESNCGType`, `SNES_NCG_FR`, `SNES_NCG_PRP`, `SNES_NCG_HS`, `SNES_NCG_DY`, `SNES_NCG_CD`
151: @*/
152: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
153: {
154:   PetscFunctionBegin;
156:   PetscTryMethod(snes, "SNESNCGSetType_C", (SNES, SNESNCGType), (snes, btype));
157:   PetscFunctionReturn(PETSC_SUCCESS);
158: }

160: static PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
161: {
162:   SNES_NCG *ncg = (SNES_NCG *)snes->data;

164:   PetscFunctionBegin;
165:   ncg->type = btype;
166:   PetscFunctionReturn(PETSC_SUCCESS);
167: }

169: /*
170:   SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.

172:   Input Parameter:
173: . snes - the `SNES` context

175:   Output Parameter:
176: . outits - number of iterations until termination

178:   Application Interface Routine: SNESSolve()
179: */
180: static PetscErrorCode SNESSolve_NCG(SNES snes)
181: {
182:   SNES_NCG            *ncg = (SNES_NCG *)snes->data;
183:   Vec                  X, dX, lX, F, dXold;
184:   PetscReal            fnorm, ynorm, xnorm, beta = 0.0;
185:   PetscScalar          dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
186:   PetscInt             maxits, i;
187:   SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
188:   SNESLineSearch       linesearch;
189:   SNESConvergedReason  reason;

191:   PetscFunctionBegin;
192:   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);

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

197:   maxits = snes->max_its;        /* maximum number of iterations */
198:   X      = snes->vec_sol;        /* X^n */
199:   dXold  = snes->work[0];        /* The previous iterate of X */
200:   dX     = snes->work[1];        /* the preconditioned direction */
201:   lX     = snes->vec_sol_update; /* the conjugate direction */
202:   F      = snes->vec_func;       /* residual vector */

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

206:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
207:   snes->iter = 0;
208:   snes->norm = 0.;
209:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));

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

213:   if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
214:     PetscCall(SNESApplyNPC(snes, X, NULL, dX));
215:     PetscCall(SNESGetConvergedReason(snes->npc, &reason));
216:     if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
217:       snes->reason = SNES_DIVERGED_INNER;
218:       PetscFunctionReturn(PETSC_SUCCESS);
219:     }
220:     PetscCall(VecCopy(dX, F));
221:     PetscCall(VecNorm(F, NORM_2, &fnorm));
222:   } else {
223:     if (!snes->vec_func_init_set) {
224:       PetscCall(SNESComputeFunction(snes, X, F));
225:     } else snes->vec_func_init_set = PETSC_FALSE;

227:     /* convergence test */
228:     PetscCall(VecNorm(F, NORM_2, &fnorm));
229:     SNESCheckFunctionNorm(snes, fnorm);
230:     PetscCall(VecCopy(F, dX));
231:   }
232:   if (snes->npc) {
233:     if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
234:       PetscCall(SNESApplyNPC(snes, X, F, dX));
235:       PetscCall(SNESGetConvergedReason(snes->npc, &reason));
236:       if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
237:         snes->reason = SNES_DIVERGED_INNER;
238:         PetscFunctionReturn(PETSC_SUCCESS);
239:       }
240:     }
241:   }
242:   PetscCall(VecCopy(dX, lX));
243:   PetscCall(VecDot(dX, dX, &dXdotdX));

245:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
246:   snes->norm = fnorm;
247:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
248:   PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));

250:   /* test convergence */
251:   PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm));
252:   PetscCall(SNESMonitor(snes, 0, fnorm));
253:   if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

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

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

260:   for (i = 1; i < maxits + 1; i++) {
261:     /* some update types require the old update direction or conjugate direction */
262:     if (ncg->type != SNES_NCG_FR) PetscCall(VecCopy(dX, dXold));
263:     PetscCall(SNESLineSearchApply(linesearch, X, F, &fnorm, lX));
264:     PetscCall(SNESLineSearchGetReason(linesearch, &lsresult));
265:     PetscCall(SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm));
266:     if (lsresult) {
267:       if (++snes->numFailures >= snes->maxFailures) {
268:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
269:         PetscFunctionReturn(PETSC_SUCCESS);
270:       }
271:     }
272:     if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
273:       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
274:       PetscFunctionReturn(PETSC_SUCCESS);
275:     }
276:     /* Monitor convergence */
277:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
278:     snes->iter  = i;
279:     snes->norm  = fnorm;
280:     snes->xnorm = xnorm;
281:     snes->ynorm = ynorm;
282:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
283:     PetscCall(SNESLogConvergenceHistory(snes, snes->norm, 0));

285:     /* Test for convergence */
286:     PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
287:     PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
288:     if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

290:     /* Call general purpose update function */
291:     PetscTryTypeMethod(snes, update, snes->iter);
292:     if (snes->npc) {
293:       if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
294:         PetscCall(SNESApplyNPC(snes, X, NULL, dX));
295:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
296:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
297:           snes->reason = SNES_DIVERGED_INNER;
298:           PetscFunctionReturn(PETSC_SUCCESS);
299:         }
300:         PetscCall(VecCopy(dX, F));
301:       } else {
302:         PetscCall(SNESApplyNPC(snes, X, F, dX));
303:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
304:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
305:           snes->reason = SNES_DIVERGED_INNER;
306:           PetscFunctionReturn(PETSC_SUCCESS);
307:         }
308:       }
309:     } else {
310:       PetscCall(VecCopy(F, dX));
311:     }

313:     /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
314:     switch (ncg->type) {
315:     case SNES_NCG_FR: /* Fletcher-Reeves */
316:       dXolddotdXold = dXdotdX;
317:       PetscCall(VecDot(dX, dX, &dXdotdX));
318:       beta = PetscRealPart(dXdotdX / dXolddotdXold);
319:       break;
320:     case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
321:       dXolddotdXold = dXdotdX;
322:       PetscCall(VecDotBegin(dX, dX, &dXdotdXold));
323:       PetscCall(VecDotBegin(dXold, dX, &dXdotdXold));
324:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
325:       PetscCall(VecDotEnd(dXold, dX, &dXdotdXold));
326:       beta = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
327:       if (beta < 0.0) beta = 0.0; /* restart */
328:       break;
329:     case SNES_NCG_HS: /* Hestenes-Stiefel */
330:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
331:       PetscCall(VecDotBegin(dX, dXold, &dXdotdXold));
332:       PetscCall(VecDotBegin(lX, dX, &lXdotdX));
333:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
334:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
335:       PetscCall(VecDotEnd(dX, dXold, &dXdotdXold));
336:       PetscCall(VecDotEnd(lX, dX, &lXdotdX));
337:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
338:       beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
339:       break;
340:     case SNES_NCG_DY: /* Dai-Yuan */
341:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
342:       PetscCall(VecDotBegin(lX, dX, &lXdotdX));
343:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
344:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
345:       PetscCall(VecDotEnd(lX, dX, &lXdotdX));
346:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
347:       beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
348:       break;
349:     case SNES_NCG_CD: /* Conjugate Descent */
350:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
351:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
352:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
353:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
354:       beta = PetscRealPart(dXdotdX / lXdotdXold);
355:       break;
356:     }
357:     if (ncg->monitor) PetscCall(PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta));
358:     PetscCall(VecAYPX(lX, beta, dX));
359:   }
360:   PetscFunctionReturn(PETSC_SUCCESS);
361: }

363: /*MC
364:   SNESNCG - Nonlinear Conjugate-Gradient method for the solution of nonlinear systems {cite}`bruneknepleysmithtu15`.

366:   Level: beginner

368:   Options Database Keys:
369: +   -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
370: .   -snes_linesearch_type <cp,l2,basic>  - Line search type.
371: -   -snes_ncg_monitor                    - Print the beta values nonlinear Conjugate-Gradient used in the  iteration, .

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

378:    Only supports left non-linear preconditioning.

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

383: .seealso: [](ch_snes), `SNES`, `SNESNCG`, `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNEWTONTR`, `SNESNGMRES`, `SNESQN`, `SNESLINESEARCHNCGLINEAR`, `SNESNCGSetType()`, `SNESLineSearchSetType()`
384: M*/
385: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
386: {
387:   SNES_NCG *neP;

389:   PetscFunctionBegin;
390:   snes->ops->destroy        = SNESDestroy_NCG;
391:   snes->ops->setup          = SNESSetUp_NCG;
392:   snes->ops->setfromoptions = SNESSetFromOptions_NCG;
393:   snes->ops->view           = SNESView_NCG;
394:   snes->ops->solve          = SNESSolve_NCG;
395:   snes->ops->reset          = SNESReset_NCG;

397:   snes->usesksp = PETSC_FALSE;
398:   snes->usesnpc = PETSC_TRUE;
399:   snes->npcside = PC_LEFT;

401:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

403:   if (!snes->tolerancesset) {
404:     snes->max_funcs = 30000;
405:     snes->max_its   = 10000;
406:     snes->stol      = 1e-20;
407:   }

409:   PetscCall(PetscNew(&neP));
410:   snes->data   = (void *)neP;
411:   neP->monitor = NULL;
412:   neP->type    = SNES_NCG_PRP;
413:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", SNESNCGSetType_NCG));
414:   PetscFunctionReturn(PETSC_SUCCESS);
415: }