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: /*
11: SNESDestroy_NCG - Destroys the private SNES_NCG context that was created with SNESCreate_NCG().
13: Input Parameter:
14: . snes - the SNES context
16: Application Interface Routine: SNESDestroy()
17: */
18: static PetscErrorCode SNESDestroy_NCG(SNES snes)
19: {
20: PetscFunctionBegin;
21: PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", NULL));
22: PetscCall(PetscFree(snes->data));
23: PetscFunctionReturn(PETSC_SUCCESS);
24: }
26: /*
27: SNESSetUp_NCG - Sets up the internal data structures for the later use
28: of the SNESNCG nonlinear solver.
30: Input Parameters:
31: + snes - the SNES context
32: - x - the solution vector
34: Application Interface Routine: SNESSetUp()
35: */
37: static PetscErrorCode SNESSetUp_NCG(SNES snes)
38: {
39: PetscFunctionBegin;
40: PetscCall(SNESSetWorkVecs(snes, 2));
41: PetscCheck(snes->npcside != PC_RIGHT, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNESNCG only supports left preconditioning");
42: if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED;
43: PetscFunctionReturn(PETSC_SUCCESS);
44: }
46: static PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch)
47: {
48: PetscScalar alpha, ptAp;
49: Vec X, Y, F, W;
50: SNES snes;
51: PetscReal *fnorm, *xnorm, *ynorm;
53: PetscFunctionBegin;
54: PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
55: X = linesearch->vec_sol;
56: W = linesearch->vec_sol_new;
57: F = linesearch->vec_func;
58: Y = linesearch->vec_update;
59: fnorm = &linesearch->fnorm;
60: xnorm = &linesearch->xnorm;
61: ynorm = &linesearch->ynorm;
63: if (!snes->jacobian) PetscCall(SNESSetUpMatrices(snes));
65: /*
67: The exact step size for unpreconditioned linear CG is just:
68: alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy)
69: */
70: PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre));
71: PetscCall(VecDot(F, F, &alpha));
72: PetscCall(MatMult(snes->jacobian, Y, W));
73: PetscCall(VecDot(Y, W, &ptAp));
74: alpha = alpha / ptAp;
75: PetscCall(VecAXPY(X, -alpha, Y));
76: PetscCall(SNESComputeFunction(snes, X, F));
78: PetscCall(VecNorm(F, NORM_2, fnorm));
79: PetscCall(VecNorm(X, NORM_2, xnorm));
80: PetscCall(VecNorm(Y, NORM_2, ynorm));
81: PetscFunctionReturn(PETSC_SUCCESS);
82: }
84: /*MC
85: SNESLINESEARCHNCGLINEAR - Special line search only for the nonlinear CG solver `SNESNCG`
87: 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.
88: 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.
90: Notes:
91: This requires a Jacobian-vector product but does not require the solution of a linear system with the Jacobian
93: This is a "odd-ball" line search, we don't know if it is in the literature or used in practice by anyone.
95: Level: advanced
97: .seealso: `SNESLineSearchCreate()`, `SNESLineSearchSetType()`
98: M*/
100: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch)
101: {
102: PetscFunctionBegin;
103: linesearch->ops->apply = SNESLineSearchApply_NCGLinear;
104: linesearch->ops->destroy = NULL;
105: linesearch->ops->setfromoptions = NULL;
106: linesearch->ops->reset = NULL;
107: linesearch->ops->view = NULL;
108: linesearch->ops->setup = NULL;
109: PetscFunctionReturn(PETSC_SUCCESS);
110: }
112: /*
113: SNESSetFromOptions_NCG - Sets various parameters for the SNESNCG method.
115: Input Parameter:
116: . snes - the SNES context
118: Application Interface Routine: SNESSetFromOptions()
119: */
120: static PetscErrorCode SNESSetFromOptions_NCG(SNES snes, PetscOptionItems *PetscOptionsObject)
121: {
122: SNES_NCG *ncg = (SNES_NCG *)snes->data;
123: PetscBool debug = PETSC_FALSE;
124: SNESNCGType ncgtype = ncg->type;
125: SNESLineSearch linesearch;
127: PetscFunctionBegin;
128: PetscOptionsHeadBegin(PetscOptionsObject, "SNES NCG options");
129: PetscCall(PetscOptionsBool("-snes_ncg_monitor", "Monitor the beta values used in the NCG iterations", "SNES", ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL));
130: if (debug) ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
131: PetscCall(PetscOptionsEnum("-snes_ncg_type", "NCG Beta type used", "SNESNCGSetType", SNESNCGTypes, (PetscEnum)ncg->type, (PetscEnum *)&ncgtype, NULL));
132: PetscCall(SNESNCGSetType(snes, ncgtype));
133: PetscOptionsHeadEnd();
134: if (!snes->linesearch) {
135: PetscCall(SNESGetLineSearch(snes, &linesearch));
136: if (!((PetscObject)linesearch)->type_name) {
137: if (!snes->npc) {
138: PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHCP));
139: } else {
140: PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHL2));
141: }
142: }
143: }
144: PetscFunctionReturn(PETSC_SUCCESS);
145: }
147: /*
148: SNESView_NCG - Prints info from the SNESNCG data structure.
150: Input Parameters:
151: + SNES - the SNES context
152: - viewer - visualization context
154: Application Interface Routine: SNESView()
155: */
156: static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer)
157: {
158: SNES_NCG *ncg = (SNES_NCG *)snes->data;
159: PetscBool iascii;
161: PetscFunctionBegin;
162: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
163: if (iascii) PetscCall(PetscViewerASCIIPrintf(viewer, " type: %s\n", SNESNCGTypes[ncg->type]));
164: PetscFunctionReturn(PETSC_SUCCESS);
165: }
167: /*
169: Assuming F = SNESComputeFunction(X) compute Y^tJ^tF using a simple secant approximation of the jacobian.
171: This routine is not currently used. I don't know what its intended purpose is.
173: Note it has a hardwired differencing parameter of 1e-5
175: */
176: PetscErrorCode SNESNCGComputeYtJtF_Private(SNES snes, Vec X, Vec F, Vec Y, Vec W, Vec G, PetscScalar *ytJtf)
177: {
178: PetscScalar ftf, ftg, fty, h;
180: PetscFunctionBegin;
181: PetscCall(VecDot(F, F, &ftf));
182: PetscCall(VecDot(F, Y, &fty));
183: h = 1e-5 * fty / fty;
184: PetscCall(VecCopy(X, W));
185: PetscCall(VecAXPY(W, -h, Y)); /* this is arbitrary */
186: PetscCall(SNESComputeFunction(snes, W, G));
187: PetscCall(VecDot(G, F, &ftg));
188: *ytJtf = (ftg - ftf) / h;
189: PetscFunctionReturn(PETSC_SUCCESS);
190: }
192: /*@
193: SNESNCGSetType - Sets the conjugate update type for nonlinear CG `SNESNCG`.
195: Logically Collective
197: Input Parameters:
198: + snes - the iterative context
199: - btype - update type
201: Options Database Key:
202: . -snes_ncg_type <prp,fr,hs,dy,cd> -strategy for selecting algorithm for computing beta
204: Level: intermediate
206: `SNESNCGType`s:
207: + `SNES_NCG_FR` - Fletcher-Reeves update
208: . `SNES_NCG_PRP` - Polak-Ribiere-Polyak update
209: . `SNES_NCG_HS` - Hestenes-Steifel update
210: . `SNES_NCG_DY` - Dai-Yuan update
211: - `SNES_NCG_CD` - Conjugate Descent update
213: Notes:
214: `SNES_NCG_PRP` is the default, and the only one that tolerates generalized search directions.
216: It is not clear what "generalized search directions" means, does it mean use with a nonlinear preconditioner,
217: that is using -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()`?
219: Developer Note:
220: There should be a `SNESNCGSetType()`
222: .seealso: `SNESNCGType`, `SNES_NCG_FR`, `SNES_NCG_PRP`, `SNES_NCG_HS`, `SNES_NCG_DY`, `SNES_NCG_CD`
223: @*/
224: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
225: {
226: PetscFunctionBegin;
228: PetscTryMethod(snes, "SNESNCGSetType_C", (SNES, SNESNCGType), (snes, btype));
229: PetscFunctionReturn(PETSC_SUCCESS);
230: }
232: static PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
233: {
234: SNES_NCG *ncg = (SNES_NCG *)snes->data;
236: PetscFunctionBegin;
237: ncg->type = btype;
238: PetscFunctionReturn(PETSC_SUCCESS);
239: }
241: /*
242: SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.
244: Input Parameters:
245: . snes - the SNES context
247: Output Parameter:
248: . outits - number of iterations until termination
250: Application Interface Routine: SNESSolve()
251: */
252: static PetscErrorCode SNESSolve_NCG(SNES snes)
253: {
254: SNES_NCG *ncg = (SNES_NCG *)snes->data;
255: Vec X, dX, lX, F, dXold;
256: PetscReal fnorm, ynorm, xnorm, beta = 0.0;
257: PetscScalar dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
258: PetscInt maxits, i;
259: SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
260: SNESLineSearch linesearch;
261: SNESConvergedReason reason;
263: PetscFunctionBegin;
264: 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);
266: PetscCall(PetscCitationsRegister(SNESCitation, &SNEScite));
267: snes->reason = SNES_CONVERGED_ITERATING;
269: maxits = snes->max_its; /* maximum number of iterations */
270: X = snes->vec_sol; /* X^n */
271: dXold = snes->work[0]; /* The previous iterate of X */
272: dX = snes->work[1]; /* the preconditioned direction */
273: lX = snes->vec_sol_update; /* the conjugate direction */
274: F = snes->vec_func; /* residual vector */
276: PetscCall(SNESGetLineSearch(snes, &linesearch));
278: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
279: snes->iter = 0;
280: snes->norm = 0.;
281: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
283: /* compute the initial function and preconditioned update dX */
285: if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
286: PetscCall(SNESApplyNPC(snes, X, NULL, dX));
287: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
288: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
289: snes->reason = SNES_DIVERGED_INNER;
290: PetscFunctionReturn(PETSC_SUCCESS);
291: }
292: PetscCall(VecCopy(dX, F));
293: PetscCall(VecNorm(F, NORM_2, &fnorm));
294: } else {
295: if (!snes->vec_func_init_set) {
296: PetscCall(SNESComputeFunction(snes, X, F));
297: } else snes->vec_func_init_set = PETSC_FALSE;
299: /* convergence test */
300: PetscCall(VecNorm(F, NORM_2, &fnorm));
301: SNESCheckFunctionNorm(snes, fnorm);
302: PetscCall(VecCopy(F, dX));
303: }
304: if (snes->npc) {
305: if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
306: PetscCall(SNESApplyNPC(snes, X, F, dX));
307: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
308: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
309: snes->reason = SNES_DIVERGED_INNER;
310: PetscFunctionReturn(PETSC_SUCCESS);
311: }
312: }
313: }
314: PetscCall(VecCopy(dX, lX));
315: PetscCall(VecDot(dX, dX, &dXdotdX));
317: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
318: snes->norm = fnorm;
319: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
320: PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));
321: PetscCall(SNESMonitor(snes, 0, fnorm));
323: /* test convergence */
324: PetscUseTypeMethod(snes, converged, 0, 0.0, 0.0, fnorm, &snes->reason, snes->cnvP);
325: if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);
327: /* Call general purpose update function */
328: PetscTryTypeMethod(snes, update, snes->iter);
330: /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */
332: for (i = 1; i < maxits + 1; i++) {
333: /* some update types require the old update direction or conjugate direction */
334: if (ncg->type != SNES_NCG_FR) PetscCall(VecCopy(dX, dXold));
335: PetscCall(SNESLineSearchApply(linesearch, X, F, &fnorm, lX));
336: PetscCall(SNESLineSearchGetReason(linesearch, &lsresult));
337: PetscCall(SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm));
338: if (lsresult) {
339: if (++snes->numFailures >= snes->maxFailures) {
340: snes->reason = SNES_DIVERGED_LINE_SEARCH;
341: PetscFunctionReturn(PETSC_SUCCESS);
342: }
343: }
344: if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
345: snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
346: PetscFunctionReturn(PETSC_SUCCESS);
347: }
348: /* Monitor convergence */
349: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
350: snes->iter = i;
351: snes->norm = fnorm;
352: snes->xnorm = xnorm;
353: snes->ynorm = ynorm;
354: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
355: PetscCall(SNESLogConvergenceHistory(snes, snes->norm, 0));
356: PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
358: /* Test for convergence */
359: PetscUseTypeMethod(snes, converged, snes->iter, xnorm, ynorm, fnorm, &snes->reason, snes->cnvP);
360: if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);
362: /* Call general purpose update function */
363: PetscTryTypeMethod(snes, update, snes->iter);
364: if (snes->npc) {
365: if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
366: PetscCall(SNESApplyNPC(snes, X, NULL, dX));
367: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
368: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
369: snes->reason = SNES_DIVERGED_INNER;
370: PetscFunctionReturn(PETSC_SUCCESS);
371: }
372: PetscCall(VecCopy(dX, F));
373: } else {
374: PetscCall(SNESApplyNPC(snes, X, F, dX));
375: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
376: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
377: snes->reason = SNES_DIVERGED_INNER;
378: PetscFunctionReturn(PETSC_SUCCESS);
379: }
380: }
381: } else {
382: PetscCall(VecCopy(F, dX));
383: }
385: /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
386: switch (ncg->type) {
387: case SNES_NCG_FR: /* Fletcher-Reeves */
388: dXolddotdXold = dXdotdX;
389: PetscCall(VecDot(dX, dX, &dXdotdX));
390: beta = PetscRealPart(dXdotdX / dXolddotdXold);
391: break;
392: case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
393: dXolddotdXold = dXdotdX;
394: PetscCall(VecDotBegin(dX, dX, &dXdotdXold));
395: PetscCall(VecDotBegin(dXold, dX, &dXdotdXold));
396: PetscCall(VecDotEnd(dX, dX, &dXdotdX));
397: PetscCall(VecDotEnd(dXold, dX, &dXdotdXold));
398: beta = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
399: if (beta < 0.0) beta = 0.0; /* restart */
400: break;
401: case SNES_NCG_HS: /* Hestenes-Stiefel */
402: PetscCall(VecDotBegin(dX, dX, &dXdotdX));
403: PetscCall(VecDotBegin(dX, dXold, &dXdotdXold));
404: PetscCall(VecDotBegin(lX, dX, &lXdotdX));
405: PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
406: PetscCall(VecDotEnd(dX, dX, &dXdotdX));
407: PetscCall(VecDotEnd(dX, dXold, &dXdotdXold));
408: PetscCall(VecDotEnd(lX, dX, &lXdotdX));
409: PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
410: beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
411: break;
412: case SNES_NCG_DY: /* Dai-Yuan */
413: PetscCall(VecDotBegin(dX, dX, &dXdotdX));
414: PetscCall(VecDotBegin(lX, dX, &lXdotdX));
415: PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
416: PetscCall(VecDotEnd(dX, dX, &dXdotdX));
417: PetscCall(VecDotEnd(lX, dX, &lXdotdX));
418: PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
419: beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
420: break;
421: case SNES_NCG_CD: /* Conjugate Descent */
422: PetscCall(VecDotBegin(dX, dX, &dXdotdX));
423: PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
424: PetscCall(VecDotEnd(dX, dX, &dXdotdX));
425: PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
426: beta = PetscRealPart(dXdotdX / lXdotdXold);
427: break;
428: }
429: if (ncg->monitor) PetscCall(PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta));
430: PetscCall(VecAYPX(lX, beta, dX));
431: }
432: PetscCall(PetscInfo(snes, "Maximum number of iterations has been reached: %" PetscInt_FMT "\n", maxits));
433: if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
434: PetscFunctionReturn(PETSC_SUCCESS);
435: }
437: /*MC
438: SNESNCG - Nonlinear Conjugate-Gradient method for the solution of nonlinear systems.
440: Level: beginner
442: Options Database Keys:
443: + -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
444: . -snes_linesearch_type <cp,l2,basic> - Line search type.
445: - -snes_ncg_monitor - Print the beta values used in the ncg iteration, .
447: Notes:
448: This solves the nonlinear system of equations F(x) = 0 using the nonlinear generalization of the conjugate
449: gradient method. This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise
450: chooses the initial search direction as F(x) for the initial guess x.
452: Only supports left non-linear preconditioning.
454: Default line search is `SNESLINESEARCHCP`, unless a nonlinear preconditioner is used with -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()` then
455: `SNESLINESEARCHL2` is used. Also supports the special purpose line search `SNESLINESEARCHNCGLINEAR`
457: References:
458: . * - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
459: SIAM Review, 57(4), 2015
461: .seealso: `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNEWTONTR`, `SNESNGMRES`, `SNESQN`, `SNESLINESEARCHNCGLINEAR`, `SNESNCGSetType()`, `SNESLineSearchSetType()`
462: M*/
463: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
464: {
465: SNES_NCG *neP;
467: PetscFunctionBegin;
468: snes->ops->destroy = SNESDestroy_NCG;
469: snes->ops->setup = SNESSetUp_NCG;
470: snes->ops->setfromoptions = SNESSetFromOptions_NCG;
471: snes->ops->view = SNESView_NCG;
472: snes->ops->solve = SNESSolve_NCG;
473: snes->ops->reset = SNESReset_NCG;
475: snes->usesksp = PETSC_FALSE;
476: snes->usesnpc = PETSC_TRUE;
477: snes->npcside = PC_LEFT;
479: snes->alwayscomputesfinalresidual = PETSC_TRUE;
481: if (!snes->tolerancesset) {
482: snes->max_funcs = 30000;
483: snes->max_its = 10000;
484: snes->stol = 1e-20;
485: }
487: PetscCall(PetscNew(&neP));
488: snes->data = (void *)neP;
489: neP->monitor = NULL;
490: neP->type = SNES_NCG_PRP;
491: PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", SNESNCGSetType_NCG));
492: PetscFunctionReturn(PETSC_SUCCESS);
493: }