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: }