Actual source code: linesearchnleqerr.c
1: #include <petsc/private/linesearchimpl.h>
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";
22: static PetscErrorCode SNESLineSearchReset_NLEQERR(SNESLineSearch linesearch)
23: {
24: SNESLineSearch_NLEQERR *nleqerr = (SNESLineSearch_NLEQERR*)linesearch->data;
26: nleqerr->mu_curr = 0.0;
27: nleqerr->norm_delta_x_prev = -1.0;
28: nleqerr->norm_bar_delta_x_prev = -1.0;
29: return 0;
30: }
32: static PetscErrorCode SNESLineSearchApply_NLEQERR(SNESLineSearch linesearch)
33: {
34: PetscBool changed_y,changed_w;
35: Vec X,F,Y,W,G;
36: SNES snes;
37: PetscReal fnorm, xnorm, ynorm, gnorm, wnorm;
38: PetscReal lambda, minlambda, stol;
39: PetscViewer monitor;
40: PetscInt max_its, count, snes_iteration;
41: PetscReal theta, mudash, lambdadash;
42: SNESLineSearch_NLEQERR *nleqerr = (SNESLineSearch_NLEQERR*)linesearch->data;
43: KSPConvergedReason kspreason;
45: PetscCitationsRegister(NLEQERR_citation, &NLEQERR_cited);
47: SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, &G);
48: SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
49: SNESLineSearchGetLambda(linesearch, &lambda);
50: SNESLineSearchGetSNES(linesearch, &snes);
51: SNESLineSearchGetDefaultMonitor(linesearch, &monitor);
52: SNESLineSearchGetTolerances(linesearch,&minlambda,NULL,NULL,NULL,NULL,&max_its);
53: SNESGetTolerances(snes,NULL,NULL,&stol,NULL,NULL);
55: /* reset the state of the Lipschitz estimates */
56: SNESGetIterationNumber(snes, &snes_iteration);
57: if (!snes_iteration) {
58: SNESLineSearchReset_NLEQERR(linesearch);
59: }
61: /* precheck */
62: SNESLineSearchPreCheck(linesearch,X,Y,&changed_y);
63: SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED);
65: VecNormBegin(Y, NORM_2, &ynorm);
66: VecNormBegin(X, NORM_2, &xnorm);
67: VecNormEnd(Y, NORM_2, &ynorm);
68: VecNormEnd(X, NORM_2, &xnorm);
70: /* Note: Y is *minus* the Newton step. For whatever reason PETSc doesn't solve with the minus on the RHS. */
72: if (ynorm == 0.0) {
73: if (monitor) {
74: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
75: PetscViewerASCIIPrintf(monitor," Line search: Initial direction and size is 0\n");
76: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
77: }
78: VecCopy(X,W);
79: VecCopy(F,G);
80: SNESLineSearchSetNorms(linesearch,xnorm,fnorm,ynorm);
81: SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
82: return 0;
83: }
85: /* At this point, we've solved the Newton system for delta_x, and we assume that
86: its norm is greater than the solution tolerance (otherwise we wouldn't be in
87: here). So let's go ahead and estimate the Lipschitz constant.
89: W contains bar_delta_x_prev at this point. */
91: if (monitor) {
92: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
93: PetscViewerASCIIPrintf(monitor," Line search: norm of Newton step: %14.12e\n", (double) ynorm);
94: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
95: }
97: /* this needs information from a previous iteration, so can't do it on the first one */
98: if (nleqerr->norm_delta_x_prev > 0 && nleqerr->norm_bar_delta_x_prev > 0) {
99: VecWAXPY(G, +1.0, Y, W); /* bar_delta_x - delta_x; +1 because Y is -delta_x */
100: VecNormBegin(G, NORM_2, &gnorm);
101: VecNormEnd(G, NORM_2, &gnorm);
103: nleqerr->mu_curr = nleqerr->lambda_prev * (nleqerr->norm_delta_x_prev * nleqerr->norm_bar_delta_x_prev) / (gnorm * ynorm);
104: lambda = PetscMin(1.0, nleqerr->mu_curr);
106: if (monitor) {
107: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
108: PetscViewerASCIIPrintf(monitor," Line search: Lipschitz estimate: %14.12e; lambda: %14.12e\n", (double) nleqerr->mu_curr, (double) lambda);
109: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
110: }
111: } else {
112: lambda = linesearch->damping;
113: }
115: /* The main while loop of the algorithm.
116: At the end of this while loop, G should have the accepted new X in it. */
118: count = 0;
119: while (PETSC_TRUE) {
120: if (monitor) {
121: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
122: PetscViewerASCIIPrintf(monitor," Line search: entering iteration with lambda: %14.12e\n", lambda);
123: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
124: }
126: /* Check that we haven't performed too many iterations */
127: count += 1;
128: if (count >= max_its) {
129: if (monitor) {
130: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
131: PetscViewerASCIIPrintf(monitor," Line search: maximum iterations reached\n");
132: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
133: }
134: SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
135: return 0;
136: }
138: /* Now comes the Regularity Test. */
139: if (lambda <= minlambda) {
140: /* This isn't what is suggested by Deuflhard, but it works better in my experience */
141: if (monitor) {
142: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
143: PetscViewerASCIIPrintf(monitor," Line search: lambda has reached lambdamin, taking full Newton step\n");
144: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
145: }
146: lambda = 1.0;
147: VecWAXPY(G, -lambda, Y, X);
149: /* and clean up the state for next time */
150: SNESLineSearchReset_NLEQERR(linesearch);
151: /*
152: The clang static analyzer detected a problem here; once the loop is broken the values
153: nleqerr->norm_delta_x_prev = ynorm;
154: nleqerr->norm_bar_delta_x_prev = wnorm;
155: are set, but wnorm has not even been computed.
156: I don't know if this is the correct fix but by setting ynorm and wnorm to -1.0 at
157: least the linesearch object is kept in the state set by the SNESLineSearchReset_NLEQERR() call above
158: */
159: ynorm = wnorm = -1.0;
160: break;
161: }
163: /* Compute new trial iterate */
164: VecWAXPY(W, -lambda, Y, X);
165: SNESComputeFunction(snes, W, G);
167: /* 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 */
168: KSPSolve(snes->ksp, G, W);
169: KSPGetConvergedReason(snes->ksp, &kspreason);
170: if (kspreason < 0) {
171: PetscInfo(snes,"Solution for \\bar{delta x}^{k+1} failed.");
172: }
174: /* W now contains -bar_delta_x_curr. */
176: VecNorm(W, NORM_2, &wnorm);
177: if (monitor) {
178: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
179: PetscViewerASCIIPrintf(monitor," Line search: norm of simplified Newton update: %14.12e\n", (double) wnorm);
180: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
181: }
183: /* compute the monitoring quantities theta and mudash. */
185: theta = wnorm / ynorm;
187: VecWAXPY(G, -(1.0 - lambda), Y, W);
188: VecNorm(G, NORM_2, &gnorm);
190: mudash = (0.5 * ynorm * lambda * lambda) / gnorm;
192: /* Check for termination of the linesearch */
193: if (theta >= 1.0) {
194: /* need to go around again with smaller lambda */
195: if (monitor) {
196: PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
197: PetscViewerASCIIPrintf(monitor," Line search: monotonicity check failed, ratio: %14.12e\n", (double) theta);
198: PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
199: }
200: lambda = PetscMin(mudash, 0.5 * lambda);
201: lambda = PetscMax(lambda, minlambda);
202: /* continue through the loop, i.e. go back to regularity test */
203: } else {
204: /* linesearch terminated */
205: lambdadash = PetscMin(1.0, mudash);
207: if (lambdadash == 1.0 && lambda == 1.0 && wnorm <= stol) {
208: /* store the updated state, X - Y - W, in G:
209: I need to keep W for the next linesearch */
210: VecCopy(X, G);
211: VecAXPY(G, -1.0, Y);
212: VecAXPY(G, -1.0, W);
213: break;
214: }
216: /* Deuflhard suggests to add the following:
217: else if (lambdadash >= 4.0 * lambda) {
218: lambda = lambdadash;
219: }
220: to continue through the loop, i.e. go back to regularity test.
221: I deliberately exclude this, as I have practical experience of this
222: getting stuck in infinite loops (on e.g. an Allen--Cahn problem). */
224: else {
225: /* accept iterate without adding on, i.e. don't use bar_delta_x;
226: again, I need to keep W for the next linesearch */
227: VecWAXPY(G, -lambda, Y, X);
228: break;
229: }
230: }
231: }
233: if (linesearch->ops->viproject) {
234: (*linesearch->ops->viproject)(snes, G);
235: }
237: /* W currently contains -bar_delta_u. Scale it so that it contains bar_delta_u. */
238: VecScale(W, -1.0);
240: /* postcheck */
241: SNESLineSearchPostCheck(linesearch,X,Y,G,&changed_y,&changed_w);
242: if (changed_y || changed_w) {
243: SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_USER);
244: PetscInfo(snes,"Changing the search direction here doesn't make sense.\n");
245: return 0;
246: }
248: /* copy the solution and information from this iteration over */
249: nleqerr->norm_delta_x_prev = ynorm;
250: nleqerr->norm_bar_delta_x_prev = wnorm;
251: nleqerr->lambda_prev = lambda;
253: VecCopy(G, X);
254: SNESComputeFunction(snes, X, F);
255: VecNorm(X, NORM_2, &xnorm);
256: VecNorm(F, NORM_2, &fnorm);
257: SNESLineSearchSetLambda(linesearch, lambda);
258: SNESLineSearchSetNorms(linesearch, xnorm, fnorm, (ynorm < 0 ? PETSC_INFINITY : ynorm));
259: return 0;
260: }
262: PetscErrorCode SNESLineSearchView_NLEQERR(SNESLineSearch linesearch, PetscViewer viewer)
263: {
264: PetscBool iascii;
265: SNESLineSearch_NLEQERR *nleqerr;
267: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
268: nleqerr = (SNESLineSearch_NLEQERR*)linesearch->data;
269: if (iascii) {
270: PetscViewerASCIIPrintf(viewer, " NLEQ-ERR affine-covariant linesearch");
271: PetscViewerASCIIPrintf(viewer, " current local Lipschitz estimate omega=%e\n", (double)nleqerr->mu_curr);
272: }
273: return 0;
274: }
276: static PetscErrorCode SNESLineSearchDestroy_NLEQERR(SNESLineSearch linesearch)
277: {
278: PetscFree(linesearch->data);
279: return 0;
280: }
282: /*MC
283: SNESLINESEARCHNLEQERR - Error-oriented affine-covariant globalised Newton algorithm of Deuflhard (2011).
285: This linesearch is intended for Newton-type methods which are affine covariant. Affine covariance
286: means that Newton's method will give the same iterations for F(x) = 0 and AF(x) = 0 for a nonsingular
287: matrix A. This is a fundamental property; the philosophy of this linesearch is that globalisations
288: of Newton's method should carefully preserve it.
290: For a discussion of the theory behind this algorithm, see
292: @book{deuflhard2011,
293: title={Newton Methods for Nonlinear Problems},
294: author={Deuflhard, P.},
295: volume={35},
296: year={2011},
297: publisher={Springer-Verlag},
298: address={Berlin, Heidelberg}
299: }
301: Pseudocode is given on page 148.
303: Options Database Keys:
304: + -snes_linesearch_damping<1.0> - initial step length
305: - -snes_linesearch_minlambda<1e-12> - minimum step length allowed
307: Contributed by Patrick Farrell <patrick.farrell@maths.ox.ac.uk>
309: Level: advanced
311: .seealso: SNESLineSearchCreate(), SNESLineSearchSetType()
312: M*/
313: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NLEQERR(SNESLineSearch linesearch)
314: {
315: SNESLineSearch_NLEQERR *nleqerr;
317: linesearch->ops->apply = SNESLineSearchApply_NLEQERR;
318: linesearch->ops->destroy = SNESLineSearchDestroy_NLEQERR;
319: linesearch->ops->setfromoptions = NULL;
320: linesearch->ops->reset = SNESLineSearchReset_NLEQERR;
321: linesearch->ops->view = SNESLineSearchView_NLEQERR;
322: linesearch->ops->setup = NULL;
324: PetscNewLog(linesearch,&nleqerr);
326: linesearch->data = (void*)nleqerr;
327: linesearch->max_its = 40;
328: SNESLineSearchReset_NLEQERR(linesearch);
329: return 0;
330: }