Actual source code: linesearchnleqerr.c
petsc-3.7.5 2017-01-01
1: #include <petsc/private/linesearchimpl.h> /*I "petscsnes.h" I*/
2: #include <petsc/private/snesimpl.h>
4: typedef struct {
5: PetscReal norm_delta_x_prev; /* norm of previous update */
6: PetscReal norm_bar_delta_x_prev; /* norm of previous bar update */
7: PetscReal mu_curr; /* current local Lipschitz estimate */
8: PetscReal lambda_prev; /* previous step length: for some reason SNESLineSearchGetLambda returns 1 instead of the previous step length */
9: } SNESLineSearch_NLEQERR;
11: static PetscBool NLEQERR_cited = PETSC_FALSE;
12: static const char NLEQERR_citation[] = "@book{deuflhard2011,\n"
13: " title = {Newton Methods for Nonlinear Problems},\n"
14: " author = {Peter Deuflhard},\n"
15: " volume = 35,\n"
16: " year = 2011,\n"
17: " isbn = {978-3-642-23898-7},\n"
18: " doi = {10.1007/978-3-642-23899-4},\n"
19: " publisher = {Springer-Verlag},\n"
20: " address = {Berlin, Heidelberg}\n}\n";
24: static PetscErrorCode SNESLineSearchReset_NLEQERR(SNESLineSearch linesearch)
25: {
26: SNESLineSearch_NLEQERR *nleqerr = (SNESLineSearch_NLEQERR*)linesearch->data;
29: nleqerr->mu_curr = 0.0;
30: nleqerr->norm_delta_x_prev = -1.0;
31: nleqerr->norm_bar_delta_x_prev = -1.0;
32: return(0);
33: }
37: static PetscErrorCode SNESLineSearchApply_NLEQERR(SNESLineSearch linesearch)
38: {
39: PetscBool changed_y,changed_w;
40: PetscErrorCode ierr;
41: Vec X,F,Y,W,G;
42: SNES snes;
43: PetscReal fnorm, xnorm, ynorm, gnorm, wnorm;
44: PetscReal lambda, minlambda, stol;
45: PetscViewer monitor;
46: PetscInt max_its, count, snes_iteration;
47: PetscReal theta, mudash, lambdadash;
48: SNESLineSearch_NLEQERR *nleqerr = (SNESLineSearch_NLEQERR*)linesearch->data;
49: KSPConvergedReason kspreason;
52: PetscCitationsRegister(NLEQERR_citation, &NLEQERR_cited);
54: SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, &G);
55: SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
56: SNESLineSearchGetLambda(linesearch, &lambda);
57: SNESLineSearchGetSNES(linesearch, &snes);
58: SNESLineSearchGetDefaultMonitor(linesearch, &monitor);
59: SNESLineSearchGetTolerances(linesearch,&minlambda,NULL,NULL,NULL,NULL,&max_its);
60: SNESGetTolerances(snes,NULL,NULL,&stol,NULL,NULL);
62: /* reset the state of the Lipschitz estimates */
63: SNESGetIterationNumber(snes, &snes_iteration);
64: if (!snes_iteration) {
65: SNESLineSearchReset_NLEQERR(linesearch);
66: }
68: /* precheck */
69: SNESLineSearchPreCheck(linesearch,X,Y,&changed_y);
70: SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED);
72: VecNormBegin(Y, NORM_2, &ynorm);
73: VecNormBegin(X, NORM_2, &xnorm);
74: VecNormEnd(Y, NORM_2, &ynorm);
75: VecNormEnd(X, NORM_2, &xnorm);
77: /* Note: Y is *minus* the Newton step. For whatever reason PETSc doesn't solve with the minus on the RHS. */
79: if (ynorm == 0.0) {
80: if (monitor) {
81: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
82: PetscViewerASCIIPrintf(monitor," Line search: Initial direction and size is 0\n");
83: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
84: }
85: VecCopy(X,W);
86: VecCopy(F,G);
87: SNESLineSearchSetNorms(linesearch,xnorm,fnorm,ynorm);
88: SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
89: return(0);
90: }
92: /* At this point, we've solved the Newton system for delta_x, and we assume that
93: its norm is greater than the solution tolerance (otherwise we wouldn't be in
94: here). So let's go ahead and estimate the Lipschitz constant.
96: W contains bar_delta_x_prev at this point. */
98: if (monitor) {
99: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
100: PetscViewerASCIIPrintf(monitor," Line search: norm of Newton step: %14.12e\n", (double) ynorm);
101: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
102: }
104: /* this needs information from a previous iteration, so can't do it on the first one */
105: if (nleqerr->norm_delta_x_prev > 0 && nleqerr->norm_bar_delta_x_prev > 0) {
106: VecWAXPY(G, +1.0, Y, W); /* bar_delta_x - delta_x; +1 because Y is -delta_x */
107: VecNormBegin(G, NORM_2, &gnorm);
108: VecNormEnd(G, NORM_2, &gnorm);
110: nleqerr->mu_curr = nleqerr->lambda_prev * (nleqerr->norm_delta_x_prev * nleqerr->norm_bar_delta_x_prev) / (gnorm * ynorm);
111: lambda = PetscMin(1.0, nleqerr->mu_curr);
113: if (monitor) {
114: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
115: PetscViewerASCIIPrintf(monitor," Line search: Lipschitz estimate: %14.12e; lambda: %14.12e\n", (double) nleqerr->mu_curr, (double) lambda);
116: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
117: }
118: } else {
119: lambda = linesearch->damping;
120: }
122: /* The main while loop of the algorithm.
123: At the end of this while loop, G should have the accepted new X in it. */
125: count = 0;
126: while (PETSC_TRUE) {
127: if (monitor) {
128: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
129: PetscViewerASCIIPrintf(monitor," Line search: entering iteration with lambda: %14.12e\n", lambda);
130: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
131: }
133: /* Check that we haven't performed too many iterations */
134: count += 1;
135: if (count >= max_its) {
136: if (monitor) {
137: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
138: PetscViewerASCIIPrintf(monitor," Line search: maximum iterations reached\n");
139: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
140: }
141: SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
142: return(0);
143: }
145: /* Now comes the Regularity Test. */
146: if (lambda <= minlambda) {
147: /* This isn't what is suggested by Deuflhard, but it works better in my experience */
148: if (monitor) {
149: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
150: PetscViewerASCIIPrintf(monitor," Line search: lambda has reached lambdamin, taking full Newton step\n");
151: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
152: }
153: lambda = 1.0;
154: VecWAXPY(G, -lambda, Y, X);
156: /* and clean up the state for next time */
157: SNESLineSearchReset_NLEQERR(linesearch);
158: /*
159: The clang static analyzer detected a problem here; once the loop is broken the values
160: nleqerr->norm_delta_x_prev = ynorm;
161: nleqerr->norm_bar_delta_x_prev = wnorm;
162: are set, but wnorm has not even been computed.
163: I don't know if this is the correct fix but by setting ynorm and wnorm to -1.0 at
164: least the linesearch object is kept in the state set by the SNESLineSearchReset_NLEQERR() call above
165: */
166: ynorm = wnorm = -1.0;
167: break;
168: }
170: /* Compute new trial iterate */
171: VecWAXPY(W, -lambda, Y, X);
172: SNESComputeFunction(snes, W, G);
174: /* Solve linear system for bar_delta_x_curr: old Jacobian, new RHS. Note absence of minus sign, compared to Deuflhard, in keeping with PETSc convention */
175: KSPSolve(snes->ksp, G, W);
176: KSPGetConvergedReason(snes->ksp, &kspreason);
177: if (kspreason < 0) {
178: PetscInfo(snes,"Solution for \\bar{delta x}^{k+1} failed.");
179: }
181: /* W now contains -bar_delta_x_curr. */
183: VecNorm(W, NORM_2, &wnorm);
184: if (monitor) {
185: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
186: PetscViewerASCIIPrintf(monitor," Line search: norm of simplified Newton update: %14.12e\n", (double) wnorm);
187: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
188: }
190: /* compute the monitoring quantities theta and mudash. */
192: theta = wnorm / ynorm;
194: VecWAXPY(G, -(1.0 - lambda), Y, W);
195: VecNorm(G, NORM_2, &gnorm);
197: mudash = (0.5 * ynorm * lambda * lambda) / gnorm;
199: /* Check for termination of the linesearch */
200: if (theta >= 1.0) {
201: /* need to go around again with smaller lambda */
202: if (monitor) {
203: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
204: PetscViewerASCIIPrintf(monitor," Line search: monotonicity check failed, ratio: %14.12e\n", (double) theta);
205: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
206: }
207: lambda = PetscMin(mudash, 0.5 * lambda);
208: lambda = PetscMax(lambda, minlambda);
209: /* continue through the loop, i.e. go back to regularity test */
210: } else {
211: /* linesearch terminated */
212: lambdadash = PetscMin(1.0, mudash);
214: if (lambdadash == 1.0 && lambda == 1.0 && wnorm <= stol) {
215: /* store the updated state, X - Y - W, in G:
216: I need to keep W for the next linesearch */
217: VecCopy(X, G);
218: VecAXPY(G, -1.0, Y);
219: VecAXPY(G, -1.0, W);
220: break;
221: }
223: /* Deuflhard suggests to add the following:
224: else if (lambdadash >= 4.0 * lambda) {
225: lambda = lambdadash;
226: }
227: to continue through the loop, i.e. go back to regularity test.
228: I deliberately exclude this, as I have practical experience of this
229: getting stuck in infinite loops (on e.g. an Allen--Cahn problem). */
231: else {
232: /* accept iterate without adding on, i.e. don't use bar_delta_x;
233: again, I need to keep W for the next linesearch */
234: VecWAXPY(G, -lambda, Y, X);
235: break;
236: }
237: }
238: }
240: if (linesearch->ops->viproject) {
241: (*linesearch->ops->viproject)(snes, G);
242: }
244: /* W currently contains -bar_delta_u. Scale it so that it contains bar_delta_u. */
245: VecScale(W, -1.0);
247: /* postcheck */
248: SNESLineSearchPostCheck(linesearch,X,Y,G,&changed_y,&changed_w);
249: if (changed_y || changed_w) {
250: SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_USER);
251: PetscInfo(snes,"Changing the search direction here doesn't make sense.\n");
252: return(0);
253: }
255: /* copy the solution and information from this iteration over */
256: nleqerr->norm_delta_x_prev = ynorm;
257: nleqerr->norm_bar_delta_x_prev = wnorm;
258: nleqerr->lambda_prev = lambda;
260: VecCopy(G, X);
261: SNESComputeFunction(snes, X, F);
262: VecNorm(X, NORM_2, &xnorm);
263: VecNorm(F, NORM_2, &fnorm);
264: SNESLineSearchSetLambda(linesearch, lambda);
265: SNESLineSearchSetNorms(linesearch, xnorm, fnorm, ynorm);
266: return(0);
267: }
271: PetscErrorCode SNESLineSearchView_NLEQERR(SNESLineSearch linesearch, PetscViewer viewer)
272: {
273: PetscErrorCode ierr;
274: PetscBool iascii;
275: SNESLineSearch_NLEQERR *nleqerr;
278: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
279: nleqerr = (SNESLineSearch_NLEQERR*)linesearch->data;
280: if (iascii) {
281: PetscViewerASCIIPrintf(viewer, " NLEQ-ERR affine-covariant linesearch");
282: PetscViewerASCIIPrintf(viewer, " current local Lipschitz estimate omega=%e\n", (double)nleqerr->mu_curr);
283: }
284: return(0);
285: }
289: static PetscErrorCode SNESLineSearchDestroy_NLEQERR(SNESLineSearch linesearch)
290: {
294: PetscFree(linesearch->data);
295: return(0);
296: }
300: /*MC
301: SNESLINESEARCHNLEQERR - Error-oriented affine-covariant globalised Newton algorithm of Deuflhard (2011).
303: This linesearch is intended for Newton-type methods which are affine covariant. Affine covariance
304: means that Newton's method will give the same iterations for F(x) = 0 and AF(x) = 0 for a nonsingular
305: matrix A. This is a fundamental property; the philosophy of this linesearch is that globalisations
306: of Newton's method should carefully preserve it.
308: For a discussion of the theory behind this algorithm, see
310: @book{deuflhard2011,
311: title={Newton Methods for Nonlinear Problems},
312: author={Deuflhard, P.},
313: volume={35},
314: year={2011},
315: publisher={Springer-Verlag},
316: address={Berlin, Heidelberg}
317: }
319: Pseudocode is given on page 148.
321: Options Database Keys:
322: + -snes_linesearch_damping<1.0> - initial step length
323: - -snes_linesearch_minlambda<1e-12> - minimum step length allowed
325: Contributed by Patrick Farrell <patrick.farrell@maths.ox.ac.uk>
327: Level: advanced
329: .keywords: SNES, SNESLineSearch, damping
331: .seealso: SNESLineSearchCreate(), SNESLineSearchSetType()
332: M*/
333: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NLEQERR(SNESLineSearch linesearch)
334: {
336: SNESLineSearch_NLEQERR *nleqerr;
337: PetscErrorCode ierr;
340: linesearch->ops->apply = SNESLineSearchApply_NLEQERR;
341: linesearch->ops->destroy = SNESLineSearchDestroy_NLEQERR;
342: linesearch->ops->setfromoptions = NULL;
343: linesearch->ops->reset = SNESLineSearchReset_NLEQERR;
344: linesearch->ops->view = SNESLineSearchView_NLEQERR;
345: linesearch->ops->setup = NULL;
347: PetscNewLog(linesearch,&nleqerr);
349: linesearch->data = (void*)nleqerr;
350: linesearch->max_its = 40;
351: SNESLineSearchReset_NLEQERR(linesearch);
352: return(0);
353: }