Actual source code: snesncg.c

      1: #include <../src/snes/impls/ncg/snesncgimpl.h>
      2: const char *const SNESNCGTypes[] = {"FR", "PRP", "HS", "DY", "CD", "SNESNCGType", "SNES_NCG_", NULL};

      4: static PetscErrorCode SNESDestroy_NCG(SNES snes)
      5: {
      6:   PetscFunctionBegin;
      7:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", NULL));
      8:   PetscCall(PetscFree(snes->data));
      9:   PetscFunctionReturn(PETSC_SUCCESS);
     10: }

     12: static PetscErrorCode SNESSetUp_NCG(SNES snes)
     13: {
     14:   PetscFunctionBegin;
     15:   PetscCall(SNESSetWorkVecs(snes, 2));
     16:   PetscCheck(snes->npcside != PC_RIGHT, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNESNCG only supports left preconditioning");
     17:   if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED;
     18:   PetscFunctionReturn(PETSC_SUCCESS);
     19: }

     21: static PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch)
     22: {
     23:   PetscScalar alpha, ptAp;
     24:   Vec         X, Y, F, W;
     25:   SNES        snes;
     26:   PetscReal  *fnorm, *xnorm, *ynorm;

     28:   PetscFunctionBegin;
     29:   PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
     30:   X     = linesearch->vec_sol;
     31:   W     = linesearch->vec_sol_new;
     32:   F     = linesearch->vec_func;
     33:   Y     = linesearch->vec_update;
     34:   fnorm = &linesearch->fnorm;
     35:   xnorm = &linesearch->xnorm;
     36:   ynorm = &linesearch->ynorm;

     38:   if (!snes->jacobian) PetscCall(SNESSetUpMatrices(snes));

     40:   /*
     41:    The exact step size for unpreconditioned linear CG is just:
     42:    alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy)
     43:    */
     44:   PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre));
     45:   SNESLineSearchCheckJacobianDomainError(snes, linesearch);

     47:   PetscCall(VecDot(F, F, &alpha));
     48:   PetscCall(MatMult(snes->jacobian, Y, W));
     49:   PetscCall(VecDot(Y, W, &ptAp));
     50:   alpha = alpha / ptAp;
     51:   PetscCall(VecAXPY(X, -alpha, Y));
     52:   PetscCall(SNESComputeFunction(snes, X, F));

     54:   PetscCall(VecNorm(F, NORM_2, fnorm));
     55:   SNESLineSearchCheckFunctionDomainError(snes, linesearch, *fnorm);
     56:   PetscCall(VecNorm(X, NORM_2, xnorm));
     57:   PetscCall(VecNorm(Y, NORM_2, ynorm));
     58:   PetscFunctionReturn(PETSC_SUCCESS);
     59: }

     61: /*MC
     62:    SNESLINESEARCHNCGLINEAR - Special line search only for the nonlinear CG solver `SNESNCG`

     64:    This line search uses the length "as if" the problem is linear (that is what is computed by the linear CG method) using the Jacobian of the function.
     65:    alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy) where r (f) is the current residual (function value), p (y) is the current search direction.

     67:    Level: advanced

     69:    Notes:
     70:    This requires a Jacobian-vector product but does not require the solution of a linear system with the Jacobian

     72:    This is a "odd-ball" line search, we don't know if it is in the literature or used in practice by anyone.

     74: .seealso: [](ch_snes), `SNES`, `SNESNCG`, `SNESLineSearchCreate()`, `SNESLineSearchSetType()`
     75: M*/

     77: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch)
     78: {
     79:   PetscFunctionBegin;
     80:   linesearch->ops->apply          = SNESLineSearchApply_NCGLinear;
     81:   linesearch->ops->destroy        = NULL;
     82:   linesearch->ops->setfromoptions = NULL;
     83:   linesearch->ops->reset          = NULL;
     84:   linesearch->ops->view           = NULL;
     85:   linesearch->ops->setup          = NULL;
     86:   PetscFunctionReturn(PETSC_SUCCESS);
     87: }

     89: static PetscErrorCode SNESSetFromOptions_NCG(SNES snes, PetscOptionItems PetscOptionsObject)
     90: {
     91:   SNES_NCG      *ncg     = (SNES_NCG *)snes->data;
     92:   PetscBool      debug   = PETSC_FALSE;
     93:   SNESNCGType    ncgtype = ncg->type;
     94:   SNESLineSearch linesearch;

     96:   PetscFunctionBegin;
     97:   PetscOptionsHeadBegin(PetscOptionsObject, "SNES NCG options");
     98:   PetscCall(PetscOptionsBool("-snes_ncg_monitor", "Monitor the beta values used in the NCG iterations", "SNES", ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL));
     99:   if (debug) ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
    100:   PetscCall(PetscOptionsEnum("-snes_ncg_type", "NCG Beta type used", "SNESNCGSetType", SNESNCGTypes, (PetscEnum)ncg->type, (PetscEnum *)&ncgtype, NULL));
    101:   PetscCall(SNESNCGSetType(snes, ncgtype));
    102:   PetscOptionsHeadEnd();
    103:   if (!snes->linesearch) {
    104:     PetscCall(SNESGetLineSearch(snes, &linesearch));
    105:     if (!((PetscObject)linesearch)->type_name) {
    106:       if (!snes->npc) {
    107:         PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHCP));
    108:       } else {
    109:         PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHSECANT));
    110:       }
    111:     }
    112:   }
    113:   PetscFunctionReturn(PETSC_SUCCESS);
    114: }

    116: static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer)
    117: {
    118:   SNES_NCG *ncg = (SNES_NCG *)snes->data;
    119:   PetscBool isascii;

    121:   PetscFunctionBegin;
    122:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    123:   if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer, "  type: %s\n", SNESNCGTypes[ncg->type]));
    124:   PetscFunctionReturn(PETSC_SUCCESS);
    125: }

    127: /*@
    128:   SNESNCGSetType - Sets the conjugate update type for nonlinear CG `SNESNCG`.

    130:   Logically Collective

    132:   Input Parameters:
    133: + snes  - the iterative context
    134: - btype - update type, see `SNESNCGType`

    136:   Options Database Key:
    137: . -snes_ncg_type (prp|fr|hs|dy|cd) - strategy for selecting algorithm for computing beta

    139:   Level: intermediate

    141:   Notes:
    142:   `SNES_NCG_PRP` is the default, and the only one that tolerates generalized search directions.

    144:   It is not clear what "generalized search directions" means, does it mean use with a nonlinear preconditioner,
    145:   that is using -npc_snes_type <type>, `SNESSetNPC()`, or `SNESGetNPC()`?

    147: .seealso: [](ch_snes), `SNES`, `SNESNCG`, `SNESNCGType`, `SNES_NCG_FR`, `SNES_NCG_PRP`, `SNES_NCG_HS`, `SNES_NCG_DY`, `SNES_NCG_CD`
    148: @*/
    149: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
    150: {
    151:   PetscFunctionBegin;
    153:   PetscTryMethod(snes, "SNESNCGSetType_C", (SNES, SNESNCGType), (snes, btype));
    154:   PetscFunctionReturn(PETSC_SUCCESS);
    155: }

    157: static PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
    158: {
    159:   SNES_NCG *ncg = (SNES_NCG *)snes->data;

    161:   PetscFunctionBegin;
    162:   ncg->type = btype;
    163:   PetscFunctionReturn(PETSC_SUCCESS);
    164: }

    166: /*
    167:   SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.

    169:   Input Parameter:
    170: . snes - the `SNES` context

    172:   Output Parameter:
    173: . outits - number of iterations until termination

    175:   Application Interface Routine: SNESSolve()
    176: */
    177: static PetscErrorCode SNESSolve_NCG(SNES snes)
    178: {
    179:   SNES_NCG           *ncg = (SNES_NCG *)snes->data;
    180:   Vec                 X, dX, lX, F, dXold;
    181:   PetscReal           fnorm, ynorm, xnorm, beta = 0.0;
    182:   PetscScalar         dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
    183:   PetscInt            maxits, i;
    184:   SNESLineSearch      linesearch;
    185:   SNESConvergedReason reason;

    187:   PetscFunctionBegin;
    188:   PetscCheck(!snes->xl && !snes->xu && !snes->ops->computevariablebounds, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

    190:   PetscCall(PetscCitationsRegister(SNESCitation, &SNEScite));
    191:   snes->reason = SNES_CONVERGED_ITERATING;

    193:   maxits = snes->max_its;        /* maximum number of iterations */
    194:   X      = snes->vec_sol;        /* X^n */
    195:   dXold  = snes->work[0];        /* The previous iterate of X */
    196:   dX     = snes->work[1];        /* the preconditioned direction */
    197:   lX     = snes->vec_sol_update; /* the conjugate direction */
    198:   F      = snes->vec_func;       /* residual vector */

    200:   PetscCall(SNESGetLineSearch(snes, &linesearch));

    202:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
    203:   snes->iter = 0;
    204:   snes->norm = 0.;
    205:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));

    207:   /* compute the initial function and preconditioned update dX */

    209:   if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
    210:     PetscCall(SNESApplyNPC(snes, X, NULL, dX));
    211:     PetscCall(SNESGetConvergedReason(snes->npc, &reason));
    212:     if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    213:       snes->reason = SNES_DIVERGED_INNER;
    214:       PetscFunctionReturn(PETSC_SUCCESS);
    215:     }
    216:     PetscCall(VecCopy(dX, F));
    217:     PetscCall(VecNorm(F, NORM_2, &fnorm));
    218:   } else {
    219:     if (!snes->vec_func_init_set) PetscCall(SNESComputeFunction(snes, X, F));
    220:     else snes->vec_func_init_set = PETSC_FALSE;

    222:     /* convergence test */
    223:     PetscCall(VecNorm(F, NORM_2, &fnorm));
    224:     SNESCheckFunctionDomainError(snes, fnorm);
    225:     PetscCall(VecCopy(F, dX));
    226:   }
    227:   if (snes->npc) {
    228:     if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
    229:       PetscCall(SNESApplyNPC(snes, X, F, dX));
    230:       PetscCall(SNESGetConvergedReason(snes->npc, &reason));
    231:       if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    232:         snes->reason = SNES_DIVERGED_INNER;
    233:         PetscFunctionReturn(PETSC_SUCCESS);
    234:       }
    235:     }
    236:   }
    237:   PetscCall(VecCopy(dX, lX));
    238:   PetscCall(VecDot(dX, dX, &dXdotdX));

    240:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
    241:   snes->norm = fnorm;
    242:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
    243:   PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));

    245:   /* test convergence */
    246:   PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm));
    247:   PetscCall(SNESMonitor(snes, 0, fnorm));
    248:   if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

    250:   /* Call general purpose update function */
    251:   PetscTryTypeMethod(snes, update, snes->iter);

    253:   /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */

    255:   for (i = 1; i < maxits + 1; i++) {
    256:     /* some update types require the old update direction or conjugate direction */
    257:     if (ncg->type != SNES_NCG_FR) PetscCall(VecCopy(dX, dXold));
    258:     PetscCall(SNESLineSearchApply(linesearch, X, F, &fnorm, lX));
    259:     if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);
    260:     PetscCall(SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm));
    261:     SNESCheckLineSearchFailure(snes);
    262:     if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
    263:       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
    264:       PetscFunctionReturn(PETSC_SUCCESS);
    265:     }
    266:     /* Monitor convergence */
    267:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
    268:     snes->iter  = i;
    269:     snes->norm  = fnorm;
    270:     snes->xnorm = xnorm;
    271:     snes->ynorm = ynorm;
    272:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
    273:     PetscCall(SNESLogConvergenceHistory(snes, snes->norm, 0));

    275:     /* Test for convergence */
    276:     PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
    277:     PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
    278:     if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

    280:     /* Call general purpose update function */
    281:     PetscTryTypeMethod(snes, update, snes->iter);
    282:     if (snes->npc) {
    283:       if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
    284:         PetscCall(SNESApplyNPC(snes, X, NULL, dX));
    285:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
    286:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    287:           snes->reason = SNES_DIVERGED_INNER;
    288:           PetscFunctionReturn(PETSC_SUCCESS);
    289:         }
    290:         PetscCall(VecCopy(dX, F));
    291:       } else {
    292:         PetscCall(SNESApplyNPC(snes, X, F, dX));
    293:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
    294:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    295:           snes->reason = SNES_DIVERGED_INNER;
    296:           PetscFunctionReturn(PETSC_SUCCESS);
    297:         }
    298:       }
    299:     } else {
    300:       PetscCall(VecCopy(F, dX));
    301:     }

    303:     /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
    304:     switch (ncg->type) {
    305:     case SNES_NCG_FR: /* Fletcher-Reeves */
    306:       dXolddotdXold = dXdotdX;
    307:       PetscCall(VecDot(dX, dX, &dXdotdX));
    308:       beta = PetscRealPart(dXdotdX / dXolddotdXold);
    309:       break;
    310:     case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
    311:       dXolddotdXold = dXdotdX;
    312:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
    313:       PetscCall(VecDotBegin(dXold, dX, &dXdotdXold));
    314:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
    315:       PetscCall(VecDotEnd(dXold, dX, &dXdotdXold));
    316:       beta = PetscRealPart((dXdotdX - dXdotdXold) / dXolddotdXold);
    317:       if (beta < 0.0) beta = 0.0; /* restart */
    318:       break;
    319:     case SNES_NCG_HS: /* Hestenes-Stiefel */
    320:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
    321:       PetscCall(VecDotBegin(dX, dXold, &dXdotdXold));
    322:       PetscCall(VecDotBegin(lX, dX, &lXdotdX));
    323:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
    324:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
    325:       PetscCall(VecDotEnd(dX, dXold, &dXdotdXold));
    326:       PetscCall(VecDotEnd(lX, dX, &lXdotdX));
    327:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
    328:       beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
    329:       break;
    330:     case SNES_NCG_DY: /* Dai-Yuan */
    331:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
    332:       PetscCall(VecDotBegin(lX, dX, &lXdotdX));
    333:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
    334:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
    335:       PetscCall(VecDotEnd(lX, dX, &lXdotdX));
    336:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
    337:       beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
    338:       break;
    339:     case SNES_NCG_CD: /* Conjugate Descent */
    340:       PetscCall(VecDotBegin(dX, dX, &dXdotdX));
    341:       PetscCall(VecDotBegin(lX, dXold, &lXdotdXold));
    342:       PetscCall(VecDotEnd(dX, dX, &dXdotdX));
    343:       PetscCall(VecDotEnd(lX, dXold, &lXdotdXold));
    344:       beta = PetscRealPart(dXdotdX / lXdotdXold);
    345:       break;
    346:     }
    347:     if (ncg->monitor) PetscCall(PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta));
    348:     PetscCall(VecAYPX(lX, beta, dX));
    349:   }
    350:   PetscFunctionReturn(PETSC_SUCCESS);
    351: }

    353: /*MC
    354:   SNESNCG - Nonlinear Conjugate-Gradient method for the solution of nonlinear systems {cite}`bruneknepleysmithtu15`.

    356:   Level: beginner

    358:   Options Database Keys:
    359: +   -snes_ncg_type (fr|prp|dy|hs|cd)    - Choice of conjugate-gradient update parameter, default is `prp`.
    360: .   -snes_linesearch_type (cp|l2|basic) - Line search type.
    361: -   -snes_ncg_monitor                   - Print the beta values nonlinear Conjugate-Gradient used in the  iteration, .

    363:    Notes:
    364:    This solves the nonlinear system of equations $ F(x) = 0 $ using the nonlinear generalization of the conjugate
    365:    gradient method.  This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise
    366:    chooses the initial search direction as $ F(x) $ for the initial guess $x$.

    368:    Only supports left non-linear preconditioning.

    370:    Default line search is `SNESLINESEARCHCP`, unless a nonlinear preconditioner is used with `-npc_snes_type` <type>, `SNESSetNPC()`, or `SNESGetNPC()` then
    371:    `SNESLINESEARCHSECANT` is used. Also supports the special-purpose line search `SNESLINESEARCHNCGLINEAR`

    373: .seealso: [](ch_snes), `SNES`, `SNESNCG`, `SNESCreate()`, `SNESType`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNEWTONTR`, `SNESNGMRES`, `SNESQN`, `SNESLINESEARCHNCGLINEAR`, `SNESNCGSetType()`, `SNESLineSearchSetType()`
    374: M*/
    375: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
    376: {
    377:   SNES_NCG *neP;

    379:   PetscFunctionBegin;
    380:   snes->ops->destroy        = SNESDestroy_NCG;
    381:   snes->ops->setup          = SNESSetUp_NCG;
    382:   snes->ops->setfromoptions = SNESSetFromOptions_NCG;
    383:   snes->ops->view           = SNESView_NCG;
    384:   snes->ops->solve          = SNESSolve_NCG;

    386:   snes->usesksp = PETSC_FALSE;
    387:   snes->usesnpc = PETSC_TRUE;
    388:   snes->npcside = PC_LEFT;

    390:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

    392:   PetscCall(SNESParametersInitialize(snes));
    393:   PetscObjectParameterSetDefault(snes, max_funcs, 30000);
    394:   PetscObjectParameterSetDefault(snes, max_its, 10000);
    395:   PetscObjectParameterSetDefault(snes, stol, 1e-20);

    397:   PetscCall(PetscNew(&neP));
    398:   snes->data   = (void *)neP;
    399:   neP->monitor = NULL;
    400:   neP->type    = SNES_NCG_PRP;
    401:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNCGSetType_C", SNESNCGSetType_NCG));
    402:   PetscFunctionReturn(PETSC_SUCCESS);
    403: }