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: /*@
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: Developer Notes:
151: There should be a `SNESNCGSetType()`
153: .seealso: `SNESNCG`, `SNESNCGType`, `SNES_NCG_FR`, `SNES_NCG_PRP`, `SNES_NCG_HS`, `SNES_NCG_DY`, `SNES_NCG_CD`
154: @*/
155: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
156: {
157: PetscFunctionBegin;
159: PetscTryMethod(snes, "SNESNCGSetType_C", (SNES, SNESNCGType), (snes, btype));
160: PetscFunctionReturn(PETSC_SUCCESS);
161: }
163: static PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
164: {
165: SNES_NCG *ncg = (SNES_NCG *)snes->data;
167: PetscFunctionBegin;
168: ncg->type = btype;
169: PetscFunctionReturn(PETSC_SUCCESS);
170: }
172: /*
173: SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.
175: Input Parameter:
176: . snes - the `SNES` context
178: Output Parameter:
179: . outits - number of iterations until termination
181: Application Interface Routine: SNESSolve()
182: */
183: static PetscErrorCode SNESSolve_NCG(SNES snes)
184: {
185: SNES_NCG *ncg = (SNES_NCG *)snes->data;
186: Vec X, dX, lX, F, dXold;
187: PetscReal fnorm, ynorm, xnorm, beta = 0.0;
188: PetscScalar dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
189: PetscInt maxits, i;
190: SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
191: SNESLineSearch linesearch;
192: SNESConvergedReason reason;
194: PetscFunctionBegin;
195: 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);
197: PetscCall(PetscCitationsRegister(SNESCitation, &SNEScite));
198: snes->reason = SNES_CONVERGED_ITERATING;
200: maxits = snes->max_its; /* maximum number of iterations */
201: X = snes->vec_sol; /* X^n */
202: dXold = snes->work[0]; /* The previous iterate of X */
203: dX = snes->work[1]; /* the preconditioned direction */
204: lX = snes->vec_sol_update; /* the conjugate direction */
205: F = snes->vec_func; /* residual vector */
207: PetscCall(SNESGetLineSearch(snes, &linesearch));
209: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
210: snes->iter = 0;
211: snes->norm = 0.;
212: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
214: /* compute the initial function and preconditioned update dX */
216: if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
217: PetscCall(SNESApplyNPC(snes, X, NULL, dX));
218: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
219: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
220: snes->reason = SNES_DIVERGED_INNER;
221: PetscFunctionReturn(PETSC_SUCCESS);
222: }
223: PetscCall(VecCopy(dX, F));
224: PetscCall(VecNorm(F, NORM_2, &fnorm));
225: } else {
226: if (!snes->vec_func_init_set) {
227: PetscCall(SNESComputeFunction(snes, X, F));
228: } else snes->vec_func_init_set = PETSC_FALSE;
230: /* convergence test */
231: PetscCall(VecNorm(F, NORM_2, &fnorm));
232: SNESCheckFunctionNorm(snes, fnorm);
233: PetscCall(VecCopy(F, dX));
234: }
235: if (snes->npc) {
236: if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
237: PetscCall(SNESApplyNPC(snes, X, F, dX));
238: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
239: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
240: snes->reason = SNES_DIVERGED_INNER;
241: PetscFunctionReturn(PETSC_SUCCESS);
242: }
243: }
244: }
245: PetscCall(VecCopy(dX, lX));
246: PetscCall(VecDot(dX, dX, &dXdotdX));
248: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
249: snes->norm = fnorm;
250: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
251: PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));
253: /* test convergence */
254: PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm));
255: PetscCall(SNESMonitor(snes, 0, fnorm));
256: if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);
258: /* Call general purpose update function */
259: PetscTryTypeMethod(snes, update, snes->iter);
261: /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */
263: for (i = 1; i < maxits + 1; i++) {
264: /* some update types require the old update direction or conjugate direction */
265: if (ncg->type != SNES_NCG_FR) PetscCall(VecCopy(dX, dXold));
266: PetscCall(SNESLineSearchApply(linesearch, X, F, &fnorm, lX));
267: PetscCall(SNESLineSearchGetReason(linesearch, &lsresult));
268: PetscCall(SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm));
269: if (lsresult) {
270: if (++snes->numFailures >= snes->maxFailures) {
271: snes->reason = SNES_DIVERGED_LINE_SEARCH;
272: PetscFunctionReturn(PETSC_SUCCESS);
273: }
274: }
275: if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
276: snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
277: PetscFunctionReturn(PETSC_SUCCESS);
278: }
279: /* Monitor convergence */
280: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
281: snes->iter = i;
282: snes->norm = fnorm;
283: snes->xnorm = xnorm;
284: snes->ynorm = ynorm;
285: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
286: PetscCall(SNESLogConvergenceHistory(snes, snes->norm, 0));
288: /* Test for convergence */
289: PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
290: PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
291: if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);
293: /* Call general purpose update function */
294: PetscTryTypeMethod(snes, update, snes->iter);
295: if (snes->npc) {
296: if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
297: PetscCall(SNESApplyNPC(snes, X, NULL, dX));
298: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
299: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
300: snes->reason = SNES_DIVERGED_INNER;
301: PetscFunctionReturn(PETSC_SUCCESS);
302: }
303: PetscCall(VecCopy(dX, F));
304: } else {
305: PetscCall(SNESApplyNPC(snes, X, F, dX));
306: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
307: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
308: snes->reason = SNES_DIVERGED_INNER;
309: PetscFunctionReturn(PETSC_SUCCESS);
310: }
311: }
312: } else {
313: PetscCall(VecCopy(F, dX));
314: }
316: /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
317: switch (ncg->type) {
318: case SNES_NCG_FR: /* Fletcher-Reeves */
319: dXolddotdXold = dXdotdX;
320: PetscCall(VecDot(dX, dX, &dXdotdX));
321: beta = PetscRealPart(dXdotdX / dXolddotdXold);
322: break;
323: case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
324: dXolddotdXold = dXdotdX;
325: PetscCall(VecDotBegin(dX, dX, &dXdotdXold));
326: PetscCall(VecDotBegin(dXold, dX, &dXdotdXold));
327: PetscCall(VecDotEnd(dX, dX, &dXdotdX));
328: PetscCall(VecDotEnd(dXold, dX, &dXdotdXold));
329: beta = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
330: if (beta < 0.0) beta = 0.0; /* restart */
331: break;
332: case SNES_NCG_HS: /* Hestenes-Stiefel */
333: PetscCall(VecDotBegin(dX, dX, &dXdotdX));
334: PetscCall(VecDotBegin(dX, dXold, &dXdotdXold));
335: PetscCall(VecDotBegin(lX, dX, &lXdotdX));
336: PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
337: PetscCall(VecDotEnd(dX, dX, &dXdotdX));
338: PetscCall(VecDotEnd(dX, dXold, &dXdotdXold));
339: PetscCall(VecDotEnd(lX, dX, &lXdotdX));
340: PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
341: beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
342: break;
343: case SNES_NCG_DY: /* Dai-Yuan */
344: PetscCall(VecDotBegin(dX, dX, &dXdotdX));
345: PetscCall(VecDotBegin(lX, dX, &lXdotdX));
346: PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
347: PetscCall(VecDotEnd(dX, dX, &dXdotdX));
348: PetscCall(VecDotEnd(lX, dX, &lXdotdX));
349: PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
350: beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
351: break;
352: case SNES_NCG_CD: /* Conjugate Descent */
353: PetscCall(VecDotBegin(dX, dX, &dXdotdX));
354: PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
355: PetscCall(VecDotEnd(dX, dX, &dXdotdX));
356: PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
357: beta = PetscRealPart(dXdotdX / lXdotdXold);
358: break;
359: }
360: if (ncg->monitor) PetscCall(PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta));
361: PetscCall(VecAYPX(lX, beta, dX));
362: }
363: PetscFunctionReturn(PETSC_SUCCESS);
364: }
366: /*MC
367: SNESNCG - Nonlinear Conjugate-Gradient method for the solution of nonlinear systems.
369: Level: beginner
371: Options Database Keys:
372: + -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
373: . -snes_linesearch_type <cp,l2,basic> - Line search type.
374: - -snes_ncg_monitor - Print the beta values used in the ncg iteration, .
376: Notes:
377: This solves the nonlinear system of equations F(x) = 0 using the nonlinear generalization of the conjugate
378: gradient method. This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise
379: chooses the initial search direction as F(x) for the initial guess x.
381: Only supports left non-linear preconditioning.
383: Default line search is `SNESLINESEARCHCP`, unless a nonlinear preconditioner is used with -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()` then
384: `SNESLINESEARCHL2` is used. Also supports the special purpose line search `SNESLINESEARCHNCGLINEAR`
386: References:
387: . * - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
388: SIAM Review, 57(4), 2015
390: .seealso: `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNEWTONTR`, `SNESNGMRES`, `SNESQN`, `SNESLINESEARCHNCGLINEAR`, `SNESNCGSetType()`, `SNESLineSearchSetType()`
391: M*/
392: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
393: {
394: SNES_NCG *neP;
396: PetscFunctionBegin;
397: snes->ops->destroy = SNESDestroy_NCG;
398: snes->ops->setup = SNESSetUp_NCG;
399: snes->ops->setfromoptions = SNESSetFromOptions_NCG;
400: snes->ops->view = SNESView_NCG;
401: snes->ops->solve = SNESSolve_NCG;
402: snes->ops->reset = SNESReset_NCG;
404: snes->usesksp = PETSC_FALSE;
405: snes->usesnpc = PETSC_TRUE;
406: snes->npcside = PC_LEFT;
408: snes->alwayscomputesfinalresidual = PETSC_TRUE;
410: if (!snes->tolerancesset) {
411: snes->max_funcs = 30000;
412: snes->max_its = 10000;
413: snes->stol = 1e-20;
414: }
416: PetscCall(PetscNew(&neP));
417: snes->data = (void *)neP;
418: neP->monitor = NULL;
419: neP->type = SNES_NCG_PRP;
420: PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", SNESNCGSetType_NCG));
421: PetscFunctionReturn(PETSC_SUCCESS);
422: }