Actual source code: ls.c
1: #include <../src/snes/impls/ls/lsimpl.h>
3: /*
4: This file implements a truncated Newton method with a line search,
5: for solving a system of nonlinear equations, using the KSP, Vec,
6: and Mat interfaces for linear solvers, vectors, and matrices,
7: respectively.
9: The following basic routines are required for each nonlinear solver:
10: SNESCreate_XXX() - Creates a nonlinear solver context
11: SNESSetFromOptions_XXX() - Sets runtime options
12: SNESSolve_XXX() - Solves the nonlinear system
13: SNESDestroy_XXX() - Destroys the nonlinear solver context
14: The suffix "_XXX" denotes a particular implementation, in this case
15: we use _NEWTONLS (e.g., SNESCreate_NEWTONLS, SNESSolve_NEWTONLS) for solving
16: systems of nonlinear equations with a line search (LS) method.
17: These routines are actually called via the common user interface
18: routines SNESCreate(), SNESSetFromOptions(), SNESSolve(), and
19: SNESDestroy(), so the application code interface remains identical
20: for all nonlinear solvers.
22: Another key routine is:
23: SNESSetUp_XXX() - Prepares for the use of a nonlinear solver
24: by setting data structures and options. The interface routine SNESSetUp()
25: is not usually called directly by the user, but instead is called by
26: SNESSolve() if necessary.
28: Additional basic routines are:
29: SNESView_XXX() - Prints details of runtime options that
30: have actually been used.
31: These are called by application codes via the interface routines
32: SNESView().
34: The various types of solvers (preconditioners, Krylov subspace methods,
35: nonlinear solvers, timesteppers) are all organized similarly, so the
36: above description applies to these categories also.
38: */
40: /*
41: Checks if J^T F = 0 which implies we've found a local minimum of the norm of the function,
42: || F(u) ||_2 but not a zero, F(u) = 0. In the case when one cannot compute J^T F we use the fact that
43: 0 = (J^T F)^T W = F^T J W iff W not in the null space of J. Thanks for Jorge More
44: for this trick. One assumes that the probability that W is in the null space of J is very, very small.
45: */
46: static PetscErrorCode SNESNEWTONLSCheckLocalMin_Private(SNES snes, Mat A, Vec F, PetscReal fnorm, PetscBool *ismin)
47: {
48: PetscReal a1;
49: PetscBool hastranspose;
50: Vec W;
51: PetscErrorCode (*objective)(SNES, Vec, PetscReal *, void *);
53: PetscFunctionBegin;
54: *ismin = PETSC_FALSE;
55: PetscCall(SNESGetObjective(snes, &objective, NULL));
56: if (!objective) {
57: PetscCall(MatHasOperation(A, MATOP_MULT_TRANSPOSE, &hastranspose));
58: PetscCall(VecDuplicate(F, &W));
59: if (hastranspose) {
60: /* Compute || J^T F|| */
61: PetscCall(MatMultTranspose(A, F, W));
62: PetscCall(VecNorm(W, NORM_2, &a1));
63: PetscCall(PetscInfo(snes, "|| J^T F|| %14.12e near zero implies found a local minimum\n", (double)(a1 / fnorm)));
64: if (a1 / fnorm < 1.e-4) *ismin = PETSC_TRUE;
65: } else {
66: Vec work;
67: PetscScalar result;
68: PetscReal wnorm;
70: PetscCall(VecSetRandom(W, NULL));
71: PetscCall(VecNorm(W, NORM_2, &wnorm));
72: PetscCall(VecDuplicate(W, &work));
73: PetscCall(MatMult(A, W, work));
74: PetscCall(VecDot(F, work, &result));
75: PetscCall(VecDestroy(&work));
76: a1 = PetscAbsScalar(result) / (fnorm * wnorm);
77: PetscCall(PetscInfo(snes, "(F^T J random)/(|| F ||*||random|| %14.12e near zero implies found a local minimum\n", (double)a1));
78: if (a1 < 1.e-4) *ismin = PETSC_TRUE;
79: }
80: PetscCall(VecDestroy(&W));
81: }
82: PetscFunctionReturn(PETSC_SUCCESS);
83: }
85: /*
86: Checks if J^T(F - J*X) = 0
87: */
88: static PetscErrorCode SNESNEWTONLSCheckResidual_Private(SNES snes, Mat A, Vec F, Vec X)
89: {
90: PetscReal a1, a2;
91: PetscBool hastranspose;
92: PetscErrorCode (*objective)(SNES, Vec, PetscReal *, void *);
94: PetscFunctionBegin;
95: PetscCall(MatHasOperation(A, MATOP_MULT_TRANSPOSE, &hastranspose));
96: PetscCall(SNESGetObjective(snes, &objective, NULL));
97: if (hastranspose && !objective) {
98: Vec W1, W2;
100: PetscCall(VecDuplicate(F, &W1));
101: PetscCall(VecDuplicate(F, &W2));
102: PetscCall(MatMult(A, X, W1));
103: PetscCall(VecAXPY(W1, -1.0, F));
105: /* Compute || J^T W|| */
106: PetscCall(MatMultTranspose(A, W1, W2));
107: PetscCall(VecNorm(W1, NORM_2, &a1));
108: PetscCall(VecNorm(W2, NORM_2, &a2));
109: if (a1 != 0.0) PetscCall(PetscInfo(snes, "||J^T(F-Ax)||/||F-AX|| %14.12e near zero implies inconsistent rhs\n", (double)(a2 / a1)));
110: PetscCall(VecDestroy(&W1));
111: PetscCall(VecDestroy(&W2));
112: }
113: PetscFunctionReturn(PETSC_SUCCESS);
114: }
116: // PetscClangLinter pragma disable: -fdoc-sowing-chars
117: /*
118: SNESSolve_NEWTONLS - Solves a nonlinear system with a truncated Newton
119: method with a line search.
121: Input Parameter:
122: . snes - the SNES context
124: */
125: static PetscErrorCode SNESSolve_NEWTONLS(SNES snes)
126: {
127: PetscInt maxits, i, lits;
128: SNESLineSearchReason lssucceed;
129: PetscReal fnorm, xnorm, ynorm;
130: Vec Y, X, F;
131: SNESLineSearch linesearch;
132: SNESConvergedReason reason;
133: #if defined(PETSC_USE_INFO)
134: PetscReal gnorm;
135: #endif
137: PetscFunctionBegin;
138: 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);
140: snes->numFailures = 0;
141: snes->numLinearSolveFailures = 0;
142: snes->reason = SNES_CONVERGED_ITERATING;
144: maxits = snes->max_its; /* maximum number of iterations */
145: X = snes->vec_sol; /* solution vector */
146: F = snes->vec_func; /* residual vector */
147: Y = snes->vec_sol_update; /* newton step */
149: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
150: snes->iter = 0;
151: snes->norm = 0.0;
152: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
153: PetscCall(SNESGetLineSearch(snes, &linesearch));
155: /* compute the preconditioned function first in the case of left preconditioning with preconditioned function */
156: if (snes->npc && snes->npcside == PC_LEFT && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
157: PetscCall(SNESApplyNPC(snes, X, NULL, F));
158: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
159: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT && reason != SNES_DIVERGED_TR_DELTA) {
160: PetscCall(SNESSetConvergedReason(snes, SNES_DIVERGED_INNER));
161: PetscFunctionReturn(PETSC_SUCCESS);
162: }
164: PetscCall(VecNormBegin(F, NORM_2, &fnorm));
165: PetscCall(VecNormEnd(F, NORM_2, &fnorm));
166: } else {
167: if (!snes->vec_func_init_set) {
168: PetscCall(SNESComputeFunction(snes, X, F));
169: } else snes->vec_func_init_set = PETSC_FALSE;
170: }
172: PetscCall(VecNorm(F, NORM_2, &fnorm)); /* fnorm <- ||F|| */
173: SNESCheckFunctionNorm(snes, fnorm);
174: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
175: snes->norm = fnorm;
176: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
177: PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));
179: /* test convergence */
180: PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm));
181: PetscCall(SNESMonitor(snes, 0, fnorm));
182: if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);
184: for (i = 0; i < maxits; i++) {
185: /* Call general purpose update function */
186: PetscTryTypeMethod(snes, update, snes->iter);
188: /* apply the nonlinear preconditioner */
189: if (snes->npc) {
190: if (snes->npcside == PC_RIGHT) {
191: PetscCall(SNESSetInitialFunction(snes->npc, F));
192: PetscCall(PetscLogEventBegin(SNES_NPCSolve, snes->npc, X, snes->vec_rhs, 0));
193: PetscCall(SNESSolve(snes->npc, snes->vec_rhs, X));
194: PetscCall(PetscLogEventEnd(SNES_NPCSolve, snes->npc, X, snes->vec_rhs, 0));
195: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
196: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT && reason != SNES_DIVERGED_TR_DELTA) {
197: PetscCall(SNESSetConvergedReason(snes, SNES_DIVERGED_INNER));
198: PetscFunctionReturn(PETSC_SUCCESS);
199: }
200: PetscCall(SNESGetNPCFunction(snes, F, &fnorm));
201: } else if (snes->npcside == PC_LEFT && snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
202: PetscCall(SNESApplyNPC(snes, X, F, F));
203: PetscCall(SNESGetConvergedReason(snes->npc, &reason));
204: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT && reason != SNES_DIVERGED_TR_DELTA) {
205: PetscCall(SNESSetConvergedReason(snes, SNES_DIVERGED_INNER));
206: PetscFunctionReturn(PETSC_SUCCESS);
207: }
208: }
209: }
211: /* Solve J Y = F, where J is Jacobian matrix */
212: PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre));
213: SNESCheckJacobianDomainerror(snes);
214: PetscCall(KSPSetOperators(snes->ksp, snes->jacobian, snes->jacobian_pre));
215: PetscCall(KSPSolve(snes->ksp, F, Y));
216: SNESCheckKSPSolve(snes);
217: PetscCall(KSPGetIterationNumber(snes->ksp, &lits));
218: PetscCall(PetscInfo(snes, "iter=%" PetscInt_FMT ", linear solve iterations=%" PetscInt_FMT "\n", snes->iter, lits));
220: if (PetscLogPrintInfo) PetscCall(SNESNEWTONLSCheckResidual_Private(snes, snes->jacobian, F, Y));
222: #if defined(PETSC_USE_INFO)
223: gnorm = fnorm;
224: #endif
225: /* Compute a (scaled) negative update in the line search routine:
226: X <- X - lambda*Y
227: and evaluate F = function(X) (depends on the line search).
228: */
229: PetscCall(SNESLineSearchApply(linesearch, X, F, &fnorm, Y));
230: PetscCall(SNESLineSearchGetReason(linesearch, &lssucceed));
231: PetscCall(SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm));
232: PetscCall(PetscInfo(snes, "fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n", (double)gnorm, (double)fnorm, (double)ynorm, (int)lssucceed));
233: if (snes->reason) break;
234: SNESCheckFunctionNorm(snes, fnorm);
235: if (lssucceed) {
236: if (snes->stol * xnorm > ynorm) {
237: snes->reason = SNES_CONVERGED_SNORM_RELATIVE;
238: PetscFunctionReturn(PETSC_SUCCESS);
239: }
240: if (++snes->numFailures >= snes->maxFailures) {
241: PetscBool ismin;
242: snes->reason = SNES_DIVERGED_LINE_SEARCH;
243: PetscCall(SNESNEWTONLSCheckLocalMin_Private(snes, snes->jacobian, F, fnorm, &ismin));
244: if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
245: if (snes->errorifnotconverged && snes->reason) {
246: PetscViewer monitor;
247: PetscCall(SNESLineSearchGetDefaultMonitor(linesearch, &monitor));
248: PetscCheck(monitor, PetscObjectComm((PetscObject)snes), PETSC_ERR_NOT_CONVERGED, "SNESSolve has not converged due to %s. Suggest running with -snes_linesearch_monitor", SNESConvergedReasons[snes->reason]);
249: SETERRQ(PetscObjectComm((PetscObject)snes), PETSC_ERR_NOT_CONVERGED, "SNESSolve has not converged due %s.", SNESConvergedReasons[snes->reason]);
250: }
251: break;
252: }
253: }
254: /* Monitor convergence */
255: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
256: snes->iter = i + 1;
257: snes->norm = fnorm;
258: snes->ynorm = ynorm;
259: snes->xnorm = xnorm;
260: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
261: PetscCall(SNESLogConvergenceHistory(snes, snes->norm, lits));
262: /* Test for convergence */
263: PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
264: PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
265: if (snes->reason) break;
266: }
267: PetscFunctionReturn(PETSC_SUCCESS);
268: }
270: /*
271: SNESSetUp_NEWTONLS - Sets up the internal data structures for the later use
272: of the SNESNEWTONLS nonlinear solver.
274: Input Parameter:
275: . snes - the SNES context
276: . x - the solution vector
278: Application Interface Routine: SNESSetUp()
280: */
281: static PetscErrorCode SNESSetUp_NEWTONLS(SNES snes)
282: {
283: PetscFunctionBegin;
284: PetscCall(SNESSetUpMatrices(snes));
285: if (snes->npcside == PC_LEFT && snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_PRECONDITIONED;
286: PetscFunctionReturn(PETSC_SUCCESS);
287: }
289: static PetscErrorCode SNESReset_NEWTONLS(SNES snes)
290: {
291: PetscFunctionBegin;
292: PetscFunctionReturn(PETSC_SUCCESS);
293: }
295: /*
296: SNESDestroy_NEWTONLS - Destroys the private SNES_NEWTONLS context that was created
297: with SNESCreate_NEWTONLS().
299: Input Parameter:
300: . snes - the SNES context
302: Application Interface Routine: SNESDestroy()
303: */
304: static PetscErrorCode SNESDestroy_NEWTONLS(SNES snes)
305: {
306: PetscFunctionBegin;
307: PetscCall(SNESReset_NEWTONLS(snes));
308: PetscCall(PetscFree(snes->data));
309: PetscFunctionReturn(PETSC_SUCCESS);
310: }
312: /*
313: SNESView_NEWTONLS - Prints info from the SNESNEWTONLS data structure.
315: Input Parameters:
316: . SNES - the SNES context
317: . viewer - visualization context
319: Application Interface Routine: SNESView()
320: */
321: static PetscErrorCode SNESView_NEWTONLS(SNES snes, PetscViewer viewer)
322: {
323: PetscBool iascii;
325: PetscFunctionBegin;
326: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
327: if (iascii) { }
328: PetscFunctionReturn(PETSC_SUCCESS);
329: }
331: /*
332: SNESSetFromOptions_NEWTONLS - Sets various parameters for the SNESNEWTONLS method.
334: Input Parameter:
335: . snes - the SNES context
337: Application Interface Routine: SNESSetFromOptions()
338: */
339: static PetscErrorCode SNESSetFromOptions_NEWTONLS(SNES snes, PetscOptionItems *PetscOptionsObject)
340: {
341: PetscFunctionBegin;
342: PetscFunctionReturn(PETSC_SUCCESS);
343: }
345: /*MC
346: SNESNEWTONLS - Newton based nonlinear solver that uses a line search
348: Options Database Keys:
349: + -snes_linesearch_type <bt> - bt,basic. Select line search type
350: . -snes_linesearch_order <3> - 2, 3. Selects the order of the line search for bt
351: . -snes_linesearch_norms <true> - Turns on/off computation of the norms for basic linesearch (`SNESLineSearchSetComputeNorms()`)
352: . -snes_linesearch_alpha <alpha> - Sets alpha used in determining if reduction in function norm is sufficient
353: . -snes_linesearch_maxstep <maxstep> - Sets the maximum stepsize the line search will use (if the 2-norm(y) > maxstep then scale y to be y = (maxstep/2-norm(y)) *y)
354: . -snes_linesearch_minlambda <minlambda> - Sets the minimum lambda the line search will tolerate
355: . -snes_linesearch_monitor - print information about progress of line searches
356: - -snes_linesearch_damping - damping factor used for basic line search
358: Level: beginner
360: Note:
361: This is the default nonlinear solver in `SNES`
363: .seealso: [](ch_snes), `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONTR`, `SNESQN`, `SNESLineSearchSetType()`, `SNESLineSearchSetOrder()`
364: `SNESLineSearchSetPostCheck()`, `SNESLineSearchSetPreCheck()` `SNESLineSearchSetComputeNorms()`, `SNESGetLineSearch()`
365: M*/
366: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONLS(SNES snes)
367: {
368: SNES_NEWTONLS *neP;
369: SNESLineSearch linesearch;
371: PetscFunctionBegin;
372: snes->ops->setup = SNESSetUp_NEWTONLS;
373: snes->ops->solve = SNESSolve_NEWTONLS;
374: snes->ops->destroy = SNESDestroy_NEWTONLS;
375: snes->ops->setfromoptions = SNESSetFromOptions_NEWTONLS;
376: snes->ops->view = SNESView_NEWTONLS;
377: snes->ops->reset = SNESReset_NEWTONLS;
379: snes->npcside = PC_RIGHT;
380: snes->usesksp = PETSC_TRUE;
381: snes->usesnpc = PETSC_TRUE;
383: PetscCall(SNESGetLineSearch(snes, &linesearch));
384: if (!((PetscObject)linesearch)->type_name) PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHBT));
386: snes->alwayscomputesfinalresidual = PETSC_TRUE;
388: PetscCall(PetscNew(&neP));
389: snes->data = (void *)neP;
390: PetscFunctionReturn(PETSC_SUCCESS);
391: }