Date: 2022-03-04T17:39:31+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;

     27:   nleqerr->mu_curr               = 0.0;
     28:   nleqerr->norm_delta_x_prev     = -1.0;
     29:   nleqerr->norm_bar_delta_x_prev = -1.0;
     30:   return(0);
     31: }

     33: static PetscErrorCode  SNESLineSearchApply_NLEQERR(SNESLineSearch linesearch)
     34: {
     35:   PetscBool              changed_y,changed_w;
     36:   PetscErrorCode         ierr;
     37:   Vec                    X,F,Y,W,G;
     38:   SNES                   snes;
     39:   PetscReal              fnorm, xnorm, ynorm, gnorm, wnorm;
     40:   PetscReal              lambda, minlambda, stol;
     41:   PetscViewer            monitor;
     42:   PetscInt               max_its, count, snes_iteration;
     43:   PetscReal              theta, mudash, lambdadash;
     44:   SNESLineSearch_NLEQERR *nleqerr = (SNESLineSearch_NLEQERR*)linesearch->data;
     45:   KSPConvergedReason     kspreason;

     48:   PetscCitationsRegister(NLEQERR_citation, &NLEQERR_cited);

     50:   SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, &G);
     51:   SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
     52:   SNESLineSearchGetLambda(linesearch, &lambda);
     53:   SNESLineSearchGetSNES(linesearch, &snes);
     54:   SNESLineSearchGetDefaultMonitor(linesearch, &monitor);
     55:   SNESLineSearchGetTolerances(linesearch,&minlambda,NULL,NULL,NULL,NULL,&max_its);
     56:   SNESGetTolerances(snes,NULL,NULL,&stol,NULL,NULL);

     58:   /* reset the state of the Lipschitz estimates */
     59:   SNESGetIterationNumber(snes, &snes_iteration);
     60:   if (!snes_iteration) {
     61:     SNESLineSearchReset_NLEQERR(linesearch);
     62:   }

     64:   /* precheck */
     65:   SNESLineSearchPreCheck(linesearch,X,Y,&changed_y);
     66:   SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED);

     68:   VecNormBegin(Y, NORM_2, &ynorm);
     69:   VecNormBegin(X, NORM_2, &xnorm);
     70:   VecNormEnd(Y, NORM_2, &ynorm);
     71:   VecNormEnd(X, NORM_2, &xnorm);

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

     75:   if (ynorm == 0.0) {
     76:     if (monitor) {
     77:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
     78:       PetscViewerASCIIPrintf(monitor,"    Line search: Initial direction and size is 0\n");
     79:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
     80:     }
     81:     VecCopy(X,W);
     82:     VecCopy(F,G);
     83:     SNESLineSearchSetNorms(linesearch,xnorm,fnorm,ynorm);
     84:     SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
     85:     return(0);
     86:   }

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

     92:      W contains bar_delta_x_prev at this point. */

     94:   if (monitor) {
     95:     PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
     96:     PetscViewerASCIIPrintf(monitor,"    Line search: norm of Newton step: %14.12e\n", (double) ynorm);
     97:     PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
     98:   }

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

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

    109:     if (monitor) {
    110:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
    111:       PetscViewerASCIIPrintf(monitor,"    Line search: Lipschitz estimate: %14.12e; lambda: %14.12e\n", (double) nleqerr->mu_curr, (double) lambda);
    112:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
    113:     }
    114:   } else {
    115:     lambda = linesearch->damping;
    116:   }

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

    121:   count = 0;
    122:   while (PETSC_TRUE) {
    123:     if (monitor) {
    124:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
    125:       PetscViewerASCIIPrintf(monitor,"    Line search: entering iteration with lambda: %14.12e\n", lambda);
    126:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
    127:     }

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

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

    152:       /* and clean up the state for next time */
    153:       SNESLineSearchReset_NLEQERR(linesearch);
    154:       /*
    155:          The clang static analyzer detected a problem here; once the loop is broken the values
    156:          nleqerr->norm_delta_x_prev     = ynorm;
    157:          nleqerr->norm_bar_delta_x_prev = wnorm;
    158:          are set, but wnorm has not even been computed.
    159:          I don't know if this is the correct fix but by setting ynorm and wnorm to -1.0 at
    160:          least the linesearch object is kept in the state set by the SNESLineSearchReset_NLEQERR() call above
    161:       */
    162:       ynorm = wnorm = -1.0;
    163:       break;
    164:     }

    166:     /* Compute new trial iterate */
    167:     VecWAXPY(W, -lambda, Y, X);
    168:     SNESComputeFunction(snes, W, G);

    170:     /* 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 */
    171:     KSPSolve(snes->ksp, G, W);
    172:     KSPGetConvergedReason(snes->ksp, &kspreason);
    173:     if (kspreason < 0) {
    174:       PetscInfo(snes,"Solution for \\bar{delta x}^{k+1} failed.");
    175:     }

    177:     /* W now contains -bar_delta_x_curr. */

    179:     VecNorm(W, NORM_2, &wnorm);
    180:     if (monitor) {
    181:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
    182:       PetscViewerASCIIPrintf(monitor,"    Line search: norm of simplified Newton update: %14.12e\n", (double) wnorm);
    183:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
    184:     }

    186:     /* compute the monitoring quantities theta and mudash. */

    188:     theta = wnorm / ynorm;

    190:     VecWAXPY(G, -(1.0 - lambda), Y, W);
    191:     VecNorm(G, NORM_2, &gnorm);

    193:     mudash = (0.5 * ynorm * lambda * lambda) / gnorm;

    195:     /* Check for termination of the linesearch */
    196:     if (theta >= 1.0) {
    197:       /* need to go around again with smaller lambda */
    198:       if (monitor) {
    199:         PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
    200:         PetscViewerASCIIPrintf(monitor,"    Line search: monotonicity check failed, ratio: %14.12e\n", (double) theta);
    201:         PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
    202:       }
    203:       lambda = PetscMin(mudash, 0.5 * lambda);
    204:       lambda = PetscMax(lambda, minlambda);
    205:       /* continue through the loop, i.e. go back to regularity test */
    206:     } else {
    207:       /* linesearch terminated */
    208:       lambdadash = PetscMin(1.0, mudash);

    210:       if (lambdadash == 1.0 && lambda == 1.0 && wnorm <= stol) {
    211:         /* store the updated state, X - Y - W, in G:
    212:            I need to keep W for the next linesearch */
    213:         VecCopy(X, G);
    214:         VecAXPY(G, -1.0, Y);
    215:         VecAXPY(G, -1.0, W);
    216:         break;
    217:       }

    219:       /* Deuflhard suggests to add the following:
    220:       else if (lambdadash >= 4.0 * lambda) {
    221:         lambda = lambdadash;
    222:       }
    223:       to continue through the loop, i.e. go back to regularity test.
    224:       I deliberately exclude this, as I have practical experience of this
    225:       getting stuck in infinite loops (on e.g. an Allen--Cahn problem). */

    227:       else {
    228:         /* accept iterate without adding on, i.e. don't use bar_delta_x;
    229:            again, I need to keep W for the next linesearch */
    230:         VecWAXPY(G, -lambda, Y, X);
    231:         break;
    232:       }
    233:     }
    234:   }

    236:   if (linesearch->ops->viproject) {
    237:     (*linesearch->ops->viproject)(snes, G);
    238:   }

    240:   /* W currently contains -bar_delta_u. Scale it so that it contains bar_delta_u. */
    241:   VecScale(W, -1.0);

    243:   /* postcheck */
    244:   SNESLineSearchPostCheck(linesearch,X,Y,G,&changed_y,&changed_w);
    245:   if (changed_y || changed_w) {
    246:     SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_USER);
    247:     PetscInfo(snes,"Changing the search direction here doesn't make sense.\n");
    248:     return(0);
    249:   }

    251:   /* copy the solution and information from this iteration over */
    252:   nleqerr->norm_delta_x_prev     = ynorm;
    253:   nleqerr->norm_bar_delta_x_prev = wnorm;
    254:   nleqerr->lambda_prev           = lambda;

    256:   VecCopy(G, X);
    257:   SNESComputeFunction(snes, X, F);
    258:   VecNorm(X, NORM_2, &xnorm);
    259:   VecNorm(F, NORM_2, &fnorm);
    260:   SNESLineSearchSetLambda(linesearch, lambda);
    261:   SNESLineSearchSetNorms(linesearch, xnorm, fnorm, (ynorm < 0 ? PETSC_INFINITY : ynorm));
    262:   return(0);
    263: }

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

    272:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    273:   nleqerr   = (SNESLineSearch_NLEQERR*)linesearch->data;
    274:   if (iascii) {
    275:     PetscViewerASCIIPrintf(viewer, "  NLEQ-ERR affine-covariant linesearch");
    276:     PetscViewerASCIIPrintf(viewer, "  current local Lipschitz estimate omega=%e\n", (double)nleqerr->mu_curr);
    277:   }
    278:   return(0);
    279: }

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

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

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

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

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

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

    309:    Pseudocode is given on page 148.

    311:    Options Database Keys:
    312: +  -snes_linesearch_damping<1.0> - initial step length
    313: -  -snes_linesearch_minlambda<1e-12> - minimum step length allowed

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

    317:    Level: advanced

    319: .seealso: SNESLineSearchCreate(), SNESLineSearchSetType()
    320: M*/
    321: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NLEQERR(SNESLineSearch linesearch)
    322: {
    323:   SNESLineSearch_NLEQERR *nleqerr;
    324:   PetscErrorCode         ierr;

    327:   linesearch->ops->apply          = SNESLineSearchApply_NLEQERR;
    328:   linesearch->ops->destroy        = SNESLineSearchDestroy_NLEQERR;
    329:   linesearch->ops->setfromoptions = NULL;
    330:   linesearch->ops->reset          = SNESLineSearchReset_NLEQERR;
    331:   linesearch->ops->view           = SNESLineSearchView_NLEQERR;
    332:   linesearch->ops->setup          = NULL;

    334:   PetscNewLog(linesearch,&nleqerr);

    336:   linesearch->data    = (void*)nleqerr;
    337:   linesearch->max_its = 40;
    338:   SNESLineSearchReset_NLEQERR(linesearch);
    339:   return(0);
    340: }