Date: 2022-08-02T03:14:58+00:00

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: }