Date: 2015-10-02T22:26:23+00:00

Actual source code: linesearchnleqerr.c
petsc-3.6.2 2015-10-02
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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: }