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 SNESLSCheckLocalMin_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,PETSC_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 SNESLSCheckResidual_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 _LS (e.g., SNESCreate_LS, SNESSolve_LS) 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_LS - 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_LS(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;
139: KSPConvergedReason kspreason;
140: PetscBool domainerror;
141: SNESLineSearch linesearch;
144: snes->numFailures = 0;
145: snes->numLinearSolveFailures = 0;
146: snes->reason = SNES_CONVERGED_ITERATING;
148: maxits = snes->max_its; /* maximum number of iterations */
149: X = snes->vec_sol; /* solution vector */
150: F = snes->vec_func; /* residual vector */
151: Y = snes->vec_sol_update; /* newton step */
152: G = snes->work[0];
153: W = snes->work[1];
155: PetscObjectTakeAccess(snes);
156: snes->iter = 0;
157: snes->norm = 0.0;
158: PetscObjectGrantAccess(snes);
159: SNESGetSNESLineSearch(snes, &linesearch);
160: if (!snes->vec_func_init_set) {
161: SNESComputeFunction(snes,X,F);
162: SNESGetFunctionDomainError(snes, &domainerror);
163: if (domainerror) {
164: snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
165: return(0);
166: }
167: } else {
168: snes->vec_func_init_set = PETSC_FALSE;
169: }
170: if (!snes->norm_init_set) {
171: VecNormBegin(F,NORM_2,&fnorm); /* fnorm <- ||F|| */
172: VecNormEnd(F,NORM_2,&fnorm);
173: if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
174: } else {
175: fnorm = snes->norm_init;
176: snes->norm_init_set = PETSC_FALSE;
177: }
178: PetscObjectTakeAccess(snes);
179: snes->norm = fnorm;
180: PetscObjectGrantAccess(snes);
181: SNESLogConvHistory(snes,fnorm,0);
182: SNESMonitor(snes,0,fnorm);
184: /* set parameter for default relative tolerance convergence test */
185: snes->ttol = fnorm*snes->rtol;
186: /* test convergence */
187: (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
188: if (snes->reason) return(0);
190: for (i=0; i<maxits; i++) {
192: /* Call general purpose update function */
193: if (snes->ops->update) {
194: (*snes->ops->update)(snes, snes->iter);
195: }
197: /* Solve J Y = F, where J is Jacobian matrix */
198: SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);
199: KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);
200: SNES_KSPSolve(snes,snes->ksp,F,Y);
201: KSPGetConvergedReason(snes->ksp,&kspreason);
202: if (kspreason < 0) {
203: if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
204: PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);
205: snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
206: break;
207: }
208: }
209: KSPGetIterationNumber(snes->ksp,&lits);
210: snes->linear_its += lits;
211: PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);
213: if (PetscLogPrintInfo){
214: SNESLSCheckResidual_Private(snes,snes->jacobian,F,Y,G,W);
215: }
217: /* Compute a (scaled) negative update in the line search routine:
218: X <- X - lambda*Y
219: and evaluate F = function(X) (depends on the line search).
220: */
221: gnorm = fnorm;
222: SNESLineSearchApply(linesearch, X, F, &fnorm, Y);
223: SNESLineSearchGetSuccess(linesearch, &lssucceed);
224: SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
225: PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",(double)gnorm,(double)fnorm,(double)ynorm,(int)lssucceed);
226: if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
227: SNESGetFunctionDomainError(snes, &domainerror);
228: if (domainerror) {
229: snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
230: return(0);
231: }
232: if (!lssucceed) {
233: if (++snes->numFailures >= snes->maxFailures) {
234: PetscBool ismin;
235: snes->reason = SNES_DIVERGED_LINE_SEARCH;
236: SNESLSCheckLocalMin_Private(snes,snes->jacobian,F,W,fnorm,&ismin);
237: if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
238: break;
239: }
240: }
241: /* Monitor convergence */
242: PetscObjectTakeAccess(snes);
243: snes->iter = i+1;
244: snes->norm = fnorm;
245: PetscObjectGrantAccess(snes);
246: SNESLogConvHistory(snes,snes->norm,lits);
247: SNESMonitor(snes,snes->iter,snes->norm);
248: /* Test for convergence */
249: (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
250: if (snes->reason) break;
251: }
252: if (i == maxits) {
253: PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);
254: if(!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
255: }
256: return(0);
257: }
258: /* -------------------------------------------------------------------------- */
259: /*
260: SNESSetUp_LS - Sets up the internal data structures for the later use
261: of the SNESLS nonlinear solver.
263: Input Parameter:
264: . snes - the SNES context
265: . x - the solution vector
267: Application Interface Routine: SNESSetUp()
269: Notes:
270: For basic use of the SNES solvers, the user need not explicitly call
271: SNESSetUp(), since these actions will automatically occur during
272: the call to SNESSolve().
273: */
276: PetscErrorCode SNESSetUp_LS(SNES snes)277: {
281: SNESDefaultGetWork(snes,2);
282: SNESSetUpMatrices(snes);
284: return(0);
285: }
286: /* -------------------------------------------------------------------------- */
290: PetscErrorCode SNESReset_LS(SNES snes)291: {
293: return(0);
294: }
296: /*
297: SNESDestroy_LS - Destroys the private SNES_LS context that was created
298: with SNESCreate_LS().
300: Input Parameter:
301: . snes - the SNES context
303: Application Interface Routine: SNESDestroy()
304: */
307: PetscErrorCode SNESDestroy_LS(SNES snes)308: {
312: SNESReset_LS(snes);
313: PetscFree(snes->data);
314: return(0);
315: }
316: /* -------------------------------------------------------------------------- */
318: /*
319: SNESView_LS - Prints info from the SNESLS data structure.
321: Input Parameters:
322: . SNES - the SNES context
323: . viewer - visualization context
325: Application Interface Routine: SNESView()
326: */
329: static PetscErrorCode SNESView_LS(SNES snes,PetscViewer viewer)330: {
332: PetscBool iascii;
335: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
336: if (iascii) {
337: }
338: return(0);
339: }
341: /* -------------------------------------------------------------------------- */
342: /*
343: SNESSetFromOptions_LS - Sets various parameters for the SNESLS method.
345: Input Parameter:
346: . snes - the SNES context
348: Application Interface Routine: SNESSetFromOptions()
349: */
352: static PetscErrorCode SNESSetFromOptions_LS(SNES snes)353: {
355: SNESLineSearch linesearch;
358: PetscOptionsHead("SNESLS options");
359: PetscOptionsTail();
360: /* set the default line search type */
361: if (!snes->linesearch) {
362: SNESGetSNESLineSearch(snes, &linesearch);
363: SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);
364: }
365: return(0);
366: }
368: /* -------------------------------------------------------------------------- */
369: /*MC
370: SNESLS - Newton based nonlinear solver that uses a line search
372: Options Database:
373: + -snes_linesearch_type<bt> - bt,basic. Select line search type
374: . -snes_linesearch_order <3> - 2, 3. Selects the order of the line search for bt
375: . -snes_linesearch_norms<true> - Turns on/off computation of the norms for basic linesearch
376: . -snes_linesearch_alpha<alpha> - Sets alpha used in determining if reduction in function norm is sufficient
377: . -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)
378: . -snes_linesearch_minlambda<minlambda> - Sets the minimum lambda the line search will tolerate
379: . -snes_linesearch_monitor - print information about progress of line searches
380: - -snes_linesearch_damping - damping factor used for basic line search
382: Notes: This is the default nonlinear solver in SNES384: Level: beginner
386: .seealso: SNESCreate(), SNES, SNESSetType(), SNESTR, SNESQN, SNESLineSearchSetType(), SNESLineSearchSetOrder()
387: SNESLineSearchSetPostCheck(), SNESLineSearchSetPreCheck() SNESLineSearchSetComputeNorms()
389: M*/
390: EXTERN_C_BEGIN
393: PetscErrorCode SNESCreate_LS(SNES snes)394: {
396: SNES_LS *neP;
399: snes->ops->setup = SNESSetUp_LS;
400: snes->ops->solve = SNESSolve_LS;
401: snes->ops->destroy = SNESDestroy_LS;
402: snes->ops->setfromoptions = SNESSetFromOptions_LS;
403: snes->ops->view = SNESView_LS;
404: snes->ops->reset = SNESReset_LS;
406: snes->usesksp = PETSC_TRUE;
407: snes->usespc = PETSC_FALSE;
408: PetscNewLog(snes,SNES_LS,&neP);
409: snes->data = (void*)neP;
410: return(0);
411: }
412: EXTERN_C_END