Actual source code: ls.c
petsc-3.4.5 2014-06-29
2: #include <../src/snes/impls/ls/lsimpl.h>
4: /*
5: Checks if J^T F = 0 which implies we've found a local minimum of the norm of the function,
6: || 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
7: 0 = (J^T F)^T W = F^T J W iff W not in the null space of J. Thanks for Jorge More
8: for this trick. One assumes that the probability that W is in the null space of J is very, very small.
9: */
12: PetscErrorCode SNESNEWTONLSCheckLocalMin_Private(SNES snes,Mat A,Vec F,Vec W,PetscReal fnorm,PetscBool *ismin)
13: {
14: PetscReal a1;
16: PetscBool hastranspose;
19: *ismin = PETSC_FALSE;
20: MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);
21: if (hastranspose) {
22: /* Compute || J^T F|| */
23: MatMultTranspose(A,F,W);
24: VecNorm(W,NORM_2,&a1);
25: PetscInfo1(snes,"|| J^T F|| %14.12e near zero implies found a local minimum\n",(double)(a1/fnorm));
26: if (a1/fnorm < 1.e-4) *ismin = PETSC_TRUE;
27: } else {
28: Vec work;
29: PetscScalar result;
30: PetscReal wnorm;
32: VecSetRandom(W,NULL);
33: VecNorm(W,NORM_2,&wnorm);
34: VecDuplicate(W,&work);
35: MatMult(A,W,work);
36: VecDot(F,work,&result);
37: VecDestroy(&work);
38: a1 = PetscAbsScalar(result)/(fnorm*wnorm);
39: PetscInfo1(snes,"(F^T J random)/(|| F ||*||random|| %14.12e near zero implies found a local minimum\n",(double)a1);
40: if (a1 < 1.e-4) *ismin = PETSC_TRUE;
41: }
42: return(0);
43: }
45: /*
46: Checks if J^T(F - J*X) = 0
47: */
50: PetscErrorCode SNESNEWTONLSCheckResidual_Private(SNES snes,Mat A,Vec F,Vec X,Vec W1,Vec W2)
51: {
52: PetscReal a1,a2;
54: PetscBool hastranspose;
57: MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);
58: if (hastranspose) {
59: MatMult(A,X,W1);
60: VecAXPY(W1,-1.0,F);
62: /* Compute || J^T W|| */
63: MatMultTranspose(A,W1,W2);
64: VecNorm(W1,NORM_2,&a1);
65: VecNorm(W2,NORM_2,&a2);
66: if (a1 != 0.0) {
67: PetscInfo1(snes,"||J^T(F-Ax)||/||F-AX|| %14.12e near zero implies inconsistent rhs\n",(double)(a2/a1));
68: }
69: }
70: return(0);
71: }
73: /* --------------------------------------------------------------------
75: This file implements a truncated Newton method with a line search,
76: for solving a system of nonlinear equations, using the KSP, Vec,
77: and Mat interfaces for linear solvers, vectors, and matrices,
78: respectively.
80: The following basic routines are required for each nonlinear solver:
81: SNESCreate_XXX() - Creates a nonlinear solver context
82: SNESSetFromOptions_XXX() - Sets runtime options
83: SNESSolve_XXX() - Solves the nonlinear system
84: SNESDestroy_XXX() - Destroys the nonlinear solver context
85: The suffix "_XXX" denotes a particular implementation, in this case
86: we use _NEWTONLS (e.g., SNESCreate_NEWTONLS, SNESSolve_NEWTONLS) for solving
87: systems of nonlinear equations with a line search (LS) method.
88: These routines are actually called via the common user interface
89: routines SNESCreate(), SNESSetFromOptions(), SNESSolve(), and
90: SNESDestroy(), so the application code interface remains identical
91: for all nonlinear solvers.
93: Another key routine is:
94: SNESSetUp_XXX() - Prepares for the use of a nonlinear solver
95: by setting data structures and options. The interface routine SNESSetUp()
96: is not usually called directly by the user, but instead is called by
97: SNESSolve() if necessary.
99: Additional basic routines are:
100: SNESView_XXX() - Prints details of runtime options that
101: have actually been used.
102: These are called by application codes via the interface routines
103: SNESView().
105: The various types of solvers (preconditioners, Krylov subspace methods,
106: nonlinear solvers, timesteppers) are all organized similarly, so the
107: above description applies to these categories also.
109: -------------------------------------------------------------------- */
110: /*
111: SNESSolve_NEWTONLS - Solves a nonlinear system with a truncated Newton
112: method with a line search.
114: Input Parameters:
115: . snes - the SNES context
117: Output Parameter:
118: . outits - number of iterations until termination
120: Application Interface Routine: SNESSolve()
122: Notes:
123: This implements essentially a truncated Newton method with a
124: line search. By default a cubic backtracking line search
125: is employed, as described in the text "Numerical Methods for
126: Unconstrained Optimization and Nonlinear Equations" by Dennis
127: and Schnabel.
128: */
131: PetscErrorCode SNESSolve_NEWTONLS(SNES snes)
132: {
133: PetscErrorCode ierr;
134: PetscInt maxits,i,lits;
135: PetscBool lssucceed;
136: MatStructure flg = DIFFERENT_NONZERO_PATTERN;
137: PetscReal fnorm,gnorm,xnorm,ynorm;
138: Vec Y,X,F,G,W,FPC;
139: KSPConvergedReason kspreason;
140: PetscBool domainerror;
141: SNESLineSearch linesearch;
142: SNESConvergedReason reason;
145: snes->numFailures = 0;
146: snes->numLinearSolveFailures = 0;
147: snes->reason = SNES_CONVERGED_ITERATING;
149: maxits = snes->max_its; /* maximum number of iterations */
150: X = snes->vec_sol; /* solution vector */
151: F = snes->vec_func; /* residual vector */
152: Y = snes->vec_sol_update; /* newton step */
153: G = snes->work[0];
154: W = snes->work[1];
156: PetscObjectAMSTakeAccess((PetscObject)snes);
157: snes->iter = 0;
158: snes->norm = 0.0;
159: PetscObjectAMSGrantAccess((PetscObject)snes);
160: SNESGetLineSearch(snes, &linesearch);
161: if (!snes->vec_func_init_set) {
162: SNESComputeFunction(snes,X,F);
163: SNESGetFunctionDomainError(snes, &domainerror);
164: if (domainerror) {
165: snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
166: return(0);
167: }
168: } else snes->vec_func_init_set = PETSC_FALSE;
170: if (!snes->norm_init_set) {
171: VecNormBegin(F,NORM_2,&fnorm); /* fnorm <- ||F|| */
172: VecNormEnd(F,NORM_2,&fnorm);
173: if (PetscIsInfOrNanReal(fnorm)) {
174: snes->reason = SNES_DIVERGED_FNORM_NAN;
175: return(0);
176: }
177: } else {
178: fnorm = snes->norm_init;
179: snes->norm_init_set = PETSC_FALSE;
180: }
181: PetscObjectAMSTakeAccess((PetscObject)snes);
182: snes->norm = fnorm;
183: PetscObjectAMSGrantAccess((PetscObject)snes);
184: SNESLogConvergenceHistory(snes,fnorm,0);
185: SNESMonitor(snes,0,fnorm);
187: /* set parameter for default relative tolerance convergence test */
188: snes->ttol = fnorm*snes->rtol;
189: /* test convergence */
190: (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
191: if (snes->reason) return(0);
193: for (i=0; i<maxits; i++) {
195: /* Call general purpose update function */
196: if (snes->ops->update) {
197: (*snes->ops->update)(snes, snes->iter);
198: }
200: /* apply the nonlinear preconditioner if it's right preconditioned */
201: if (snes->pc && snes->pcside == PC_RIGHT) {
202: SNESSetInitialFunction(snes->pc, F);
203: SNESSetInitialFunctionNorm(snes->pc, fnorm);
204: PetscLogEventBegin(SNES_NPCSolve,snes->pc,X,snes->vec_rhs,0);
205: SNESSolve(snes->pc, snes->vec_rhs, X);
206: PetscLogEventEnd(SNES_NPCSolve,snes->pc,X,snes->vec_rhs,0);
207: SNESGetConvergedReason(snes->pc,&reason);
208: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
209: snes->reason = SNES_DIVERGED_INNER;
210: return(0);
211: }
212: SNESGetFunction(snes->pc, &FPC, NULL, NULL);
213: VecCopy(FPC, F);
214: SNESGetFunctionNorm(snes->pc, &fnorm);
215: }
217: /* Solve J Y = F, where J is Jacobian matrix */
218: SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);
219: KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);
220: KSPSolve(snes->ksp,F,Y);
221: KSPGetConvergedReason(snes->ksp,&kspreason);
222: if (kspreason < 0) {
223: if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
224: PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);
225: snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
226: break;
227: }
228: }
229: KSPGetIterationNumber(snes->ksp,&lits);
230: snes->linear_its += lits;
231: PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);
233: if (PetscLogPrintInfo) {
234: SNESNEWTONLSCheckResidual_Private(snes,snes->jacobian,F,Y,G,W);
235: }
237: /* Compute a (scaled) negative update in the line search routine:
238: X <- X - lambda*Y
239: and evaluate F = function(X) (depends on the line search).
240: */
241: gnorm = fnorm;
242: SNESLineSearchApply(linesearch, X, F, &fnorm, Y);
243: SNESLineSearchGetSuccess(linesearch, &lssucceed);
244: SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
245: PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",(double)gnorm,(double)fnorm,(double)ynorm,(int)lssucceed);
246: if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
247: SNESGetFunctionDomainError(snes, &domainerror);
248: if (domainerror) {
249: snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
250: return(0);
251: }
252: if (!lssucceed) {
253: if (snes->stol*xnorm > ynorm) {
254: snes->reason = SNES_CONVERGED_SNORM_RELATIVE;
255: return(0);
256: }
257: if (++snes->numFailures >= snes->maxFailures) {
258: PetscBool ismin;
259: snes->reason = SNES_DIVERGED_LINE_SEARCH;
260: SNESNEWTONLSCheckLocalMin_Private(snes,snes->jacobian,F,W,fnorm,&ismin);
261: if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
262: break;
263: }
264: }
265: /* Monitor convergence */
266: PetscObjectAMSTakeAccess((PetscObject)snes);
267: snes->iter = i+1;
268: snes->norm = fnorm;
269: PetscObjectAMSGrantAccess((PetscObject)snes);
270: SNESLogConvergenceHistory(snes,snes->norm,lits);
271: SNESMonitor(snes,snes->iter,snes->norm);
272: /* Test for convergence */
273: (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
274: if (snes->reason) break;
275: }
276: if (i == maxits) {
277: PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);
278: if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
279: }
280: return(0);
281: }
282: /* -------------------------------------------------------------------------- */
283: /*
284: SNESSetUp_NEWTONLS - Sets up the internal data structures for the later use
285: of the SNESNEWTONLS nonlinear solver.
287: Input Parameter:
288: . snes - the SNES context
289: . x - the solution vector
291: Application Interface Routine: SNESSetUp()
293: Notes:
294: For basic use of the SNES solvers, the user need not explicitly call
295: SNESSetUp(), since these actions will automatically occur during
296: the call to SNESSolve().
297: */
300: PetscErrorCode SNESSetUp_NEWTONLS(SNES snes)
301: {
305: SNESSetWorkVecs(snes,2);
306: SNESSetUpMatrices(snes);
307: return(0);
308: }
309: /* -------------------------------------------------------------------------- */
313: PetscErrorCode SNESReset_NEWTONLS(SNES snes)
314: {
316: return(0);
317: }
319: /*
320: SNESDestroy_NEWTONLS - Destroys the private SNES_NEWTONLS context that was created
321: with SNESCreate_NEWTONLS().
323: Input Parameter:
324: . snes - the SNES context
326: Application Interface Routine: SNESDestroy()
327: */
330: PetscErrorCode SNESDestroy_NEWTONLS(SNES snes)
331: {
335: SNESReset_NEWTONLS(snes);
336: PetscFree(snes->data);
337: return(0);
338: }
339: /* -------------------------------------------------------------------------- */
341: /*
342: SNESView_NEWTONLS - Prints info from the SNESNEWTONLS data structure.
344: Input Parameters:
345: . SNES - the SNES context
346: . viewer - visualization context
348: Application Interface Routine: SNESView()
349: */
352: static PetscErrorCode SNESView_NEWTONLS(SNES snes,PetscViewer viewer)
353: {
355: PetscBool iascii;
358: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
359: if (iascii) {
360: }
361: return(0);
362: }
364: /* -------------------------------------------------------------------------- */
365: /*
366: SNESSetFromOptions_NEWTONLS - Sets various parameters for the SNESNEWTONLS method.
368: Input Parameter:
369: . snes - the SNES context
371: Application Interface Routine: SNESSetFromOptions()
372: */
375: static PetscErrorCode SNESSetFromOptions_NEWTONLS(SNES snes)
376: {
378: SNESLineSearch linesearch;
381: PetscOptionsHead("SNESNEWTONLS options");
382: PetscOptionsTail();
383: /* set the default line search type */
384: if (!snes->linesearch) {
385: SNESGetLineSearch(snes, &linesearch);
386: SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);
387: }
388: return(0);
389: }
391: /* -------------------------------------------------------------------------- */
392: /*MC
393: SNESNEWTONLS - Newton based nonlinear solver that uses a line search
395: Options Database:
396: + -snes_linesearch_type <bt> - bt,basic. Select line search type
397: . -snes_linesearch_order <3> - 2, 3. Selects the order of the line search for bt
398: . -snes_linesearch_norms <true> - Turns on/off computation of the norms for basic linesearch
399: . -snes_linesearch_alpha <alpha> - Sets alpha used in determining if reduction in function norm is sufficient
400: . -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)
401: . -snes_linesearch_minlambda <minlambda> - Sets the minimum lambda the line search will tolerate
402: . -snes_linesearch_monitor - print information about progress of line searches
403: - -snes_linesearch_damping - damping factor used for basic line search
405: Notes: This is the default nonlinear solver in SNES
407: Level: beginner
409: .seealso: SNESCreate(), SNES, SNESSetType(), SNESNEWTONTR, SNESQN, SNESLineSearchSetType(), SNESLineSearchSetOrder()
410: SNESLineSearchSetPostCheck(), SNESLineSearchSetPreCheck() SNESLineSearchSetComputeNorms()
412: M*/
415: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONLS(SNES snes)
416: {
418: SNES_NEWTONLS *neP;
421: snes->ops->setup = SNESSetUp_NEWTONLS;
422: snes->ops->solve = SNESSolve_NEWTONLS;
423: snes->ops->destroy = SNESDestroy_NEWTONLS;
424: snes->ops->setfromoptions = SNESSetFromOptions_NEWTONLS;
425: snes->ops->view = SNESView_NEWTONLS;
426: snes->ops->reset = SNESReset_NEWTONLS;
428: snes->usesksp = PETSC_TRUE;
429: snes->usespc = PETSC_TRUE;
430: PetscNewLog(snes,SNES_NEWTONLS,&neP);
431: snes->data = (void*)neP;
432: return(0);
433: }