Actual source code: linesearchnleqerr.c

petsc-3.6.4 2016-04-12
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  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;

 28:   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;
 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:   SNESLineSearchGetMonitor(linesearch, &monitor);
 59:   SNESLineSearchGetTolerances(linesearch,&minlambda,NULL,NULL,NULL,NULL,&max_its);
 60:   SNESGetTolerances(snes,NULL,NULL,&stol,NULL,NULL);
 61:   nleqerr   = (SNESLineSearch_NLEQERR*)linesearch->data;

 63:   /* reset the state of the Lipschitz estimates */
 64:   SNESGetIterationNumber(snes, &snes_iteration);
 65:   if (snes_iteration == 0) {
 66:     SNESLineSearchReset_NLEQERR(linesearch);
 67:   }

 69:   /* precheck */
 70:   SNESLineSearchPreCheck(linesearch,X,Y,&changed_y);
 71:   SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED);

 73:   VecNormBegin(Y, NORM_2, &ynorm);
 74:   VecNormBegin(X, NORM_2, &xnorm);
 75:   VecNormEnd(Y, NORM_2, &ynorm);
 76:   VecNormEnd(X, NORM_2, &xnorm);

 78:   /* Note: Y is *minus* the Newton step. For whatever reason PETSc doesn't solve with the minus on
 79:      the RHS. */

 81:   if (ynorm == 0.0) {
 82:     if (monitor) {
 83:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
 84:       PetscViewerASCIIPrintf(monitor,"    Line search: Initial direction and size is 0\n");
 85:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
 86:     }
 87:     VecCopy(X,W);
 88:     VecCopy(F,G);
 89:     SNESLineSearchSetNorms(linesearch,xnorm,fnorm,ynorm);
 90:     SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
 91:     return(0);
 92:   }

 94:   /* At this point, we've solved the Newton system for delta_x, and we assume that
 95:      its norm is greater than the solution tolerance (otherwise we wouldn't be in
 96:      here). So let's go ahead and estimate the Lipschitz constant. 

 98:      W contains bar_delta_x_prev at this point. */

100:   if (monitor) {
101:     PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
102:     PetscViewerASCIIPrintf(monitor,"    Line search: norm of Newton step: %14.12e\n", (double) ynorm);
103:     PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
104:   }

106:   /* this needs information from a previous iteration, so can't do it on the first one */
107:   if (nleqerr->norm_delta_x_prev > 0 && nleqerr->norm_bar_delta_x_prev > 0) {
108:     VecWAXPY(G, +1.0, Y, W); /* bar_delta_x - delta_x; +1 because Y is -delta_x */
109:     VecNormBegin(G, NORM_2, &gnorm);
110:     VecNormEnd(G, NORM_2, &gnorm);

112:     nleqerr->mu_curr = nleqerr->lambda_prev * (nleqerr->norm_delta_x_prev * nleqerr->norm_bar_delta_x_prev) / (gnorm * ynorm);
113:     lambda = PetscMin(1.0, nleqerr->mu_curr);

115:     if (monitor) {
116:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
117:       PetscViewerASCIIPrintf(monitor,"    Line search: Lipschitz estimate: %14.12e; lambda: %14.12e\n", (double) nleqerr->mu_curr, (double) lambda);
118:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
119:     }
120:   } else {
121:     lambda = linesearch->damping;
122:   }

124:   /* The main while loop of the algorithm. 
125:      At the end of this while loop, G should have the accepted new X in it. */

127:   count = 0;
128:   while (PETSC_TRUE) {
129:     if (monitor) {
130:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
131:       PetscViewerASCIIPrintf(monitor,"    Line search: entering iteration with lambda: %14.12e\n", lambda);
132:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
133:     }

135:     /* Check that we haven't performed too many iterations */
136:     count += 1;
137:     if (count >= max_its) {
138:       if (monitor) {
139:         PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
140:         PetscViewerASCIIPrintf(monitor,"    Line search: maximum iterations reached\n");
141:         PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
142:       }
143:       SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
144:       return(0);
145:     }

147:     /* Now comes the Regularity Test. */
148:     if (lambda <= minlambda) {
149:       /* This isn't what is suggested by Deuflhard, but it works better in my experience */
150:       if (monitor) {
151:         PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
152:         PetscViewerASCIIPrintf(monitor,"    Line search: lambda has reached lambdamin, taking full Newton step\n");
153:         PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
154:       }
155:       lambda = 1.0;
156:       VecWAXPY(G, -lambda, Y, X);

158:       /* and clean up the state for next time */
159:       SNESLineSearchReset_NLEQERR(linesearch);
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);
259:   return(0);
260: }

264: PetscErrorCode SNESLineSearchView_NLEQERR(SNESLineSearch linesearch, PetscViewer viewer)
265: {
266:   PetscErrorCode          ierr;
267:   PetscBool               iascii;
268:   SNESLineSearch_NLEQERR *nleqerr;

271:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
272:   nleqerr   = (SNESLineSearch_NLEQERR*)linesearch->data;
273:   if (iascii) {
274:     PetscViewerASCIIPrintf(viewer, "  NLEQ-ERR affine-covariant linesearch");
275:     PetscViewerASCIIPrintf(viewer, "  current local Lipschitz estimate omega=%e\n", (double)nleqerr->mu_curr);
276:   }
277:   return(0);
278: }

282: static PetscErrorCode SNESLineSearchDestroy_NLEQERR(SNESLineSearch linesearch)
283: {

287:   PetscFree(linesearch->data);
288:   return(0);
289: }

293: /*MC
294:    SNESLINESEARCHNLEQERR - Error-oriented affine-covariant globalised Newton algorithm of Deuflhard (2011).

296:    This linesearch is intended for Newton-type methods which are affine covariant. Affine covariance
297:    means that Newton's method will give the same iterations for F(x) = 0 and AF(x) = 0 for a nonsingular
298:    matrix A. This is a fundamental property; the philosophy of this linesearch is that globalisations
299:    of Newton's method should carefully preserve it.

301:    For a discussion of the theory behind this algorithm, see

303:    @book{deuflhard2011,
304:      title={Newton Methods for Nonlinear Problems},
305:      author={Deuflhard, P.},
306:      volume={35},
307:      year={2011},
308:      publisher={Springer-Verlag},
309:      address={Berlin, Heidelberg}
310:    }

312:    Pseudocode is given on page 148.

314:    Options Database Keys:
315: +  -snes_linesearch_damping<1.0> - initial step length
316: -  -snes_linesearch_minlambda<1e-12> - minimum step length allowed

318:    Contributed by Patrick Farrell <patrick.farrell@maths.ox.ac.uk>

320:    Level: advanced

322: .keywords: SNES, SNESLineSearch, damping

324: .seealso: SNESLineSearchCreate(), SNESLineSearchSetType()
325: M*/
326: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NLEQERR(SNESLineSearch linesearch)
327: {

329:   SNESLineSearch_NLEQERR *nleqerr;
330:   PetscErrorCode    ierr;

333:   linesearch->ops->apply          = SNESLineSearchApply_NLEQERR;
334:   linesearch->ops->destroy        = SNESLineSearchDestroy_NLEQERR;
335:   linesearch->ops->setfromoptions = NULL;
336:   linesearch->ops->reset          = SNESLineSearchReset_NLEQERR;
337:   linesearch->ops->view           = SNESLineSearchView_NLEQERR;
338:   linesearch->ops->setup          = NULL;

340:   PetscNewLog(linesearch,&nleqerr);

342:   linesearch->data    = (void*)nleqerr;
343:   linesearch->max_its = 40;
344:   SNESLineSearchReset_NLEQERR(linesearch);
345:   return(0);
346: }