Date: 2015-10-02T22:23:52+00:00

Actual source code: viss.c
petsc-3.6.2 2015-10-02
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      2: #include <../src/snes/impls/vi/ss/vissimpl.h> /*I "petscsnes.h" I*/
      3: #include <../include/petsc/private/kspimpl.h>
      4: #include <../include/petsc/private/matimpl.h>
      5: #include <../include/petsc/private/dmimpl.h>

      8: /*
      9:   SNESVIComputeMeritFunction - Evaluates the merit function for the mixed complementarity problem.

     11:   Input Parameter:
     12: . phi - the semismooth function

     14:   Output Parameter:
     15: . merit - the merit function
     16: . phinorm - ||phi||

     18:   Notes:
     19:   The merit function for the mixed complementarity problem is defined as
     20:      merit = 0.5*phi^T*phi
     21: */
     24: static PetscErrorCode SNESVIComputeMeritFunction(Vec phi, PetscReal *merit,PetscReal *phinorm)
     25: {

     29:   VecNormBegin(phi,NORM_2,phinorm);
     30:   VecNormEnd(phi,NORM_2,phinorm);

     32:   *merit = 0.5*(*phinorm)*(*phinorm);
     33:   return(0);
     34: }

     36: PETSC_STATIC_INLINE PetscScalar Phi(PetscScalar a,PetscScalar b)
     37: {
     38:   return a + b - PetscSqrtScalar(a*a + b*b);
     39: }

     41: PETSC_STATIC_INLINE PetscScalar DPhi(PetscScalar a,PetscScalar b)
     42: {
     43:   if ((PetscAbsScalar(a) >= 1.e-6) || (PetscAbsScalar(b) >= 1.e-6)) return 1.0 - a/ PetscSqrtScalar(a*a + b*b);
     44:   else return .5;
     45: }

     47: /*
     48:    SNESVIComputeFunction - Reformulates a system of nonlinear equations in mixed complementarity form to a system of nonlinear equations in semismooth form.

     50:    Input Parameters:
     51: .  snes - the SNES context
     52: .  X - current iterate
     53: .  functx - user defined function context

     55:    Output Parameters:
     56: .  phi - Semismooth function

     58: */
     61: static PetscErrorCode SNESVIComputeFunction(SNES snes,Vec X,Vec phi,void *functx)
     62: {
     63:   PetscErrorCode    ierr;
     64:   SNES_VINEWTONSSLS *vi = (SNES_VINEWTONSSLS*)snes->data;
     65:   Vec               Xl  = snes->xl,Xu = snes->xu,F = snes->vec_func;
     66:   PetscScalar       *phi_arr,*f_arr,*l,*u;
     67:   const PetscScalar *x_arr;
     68:   PetscInt          i,nlocal;

     71:   (*vi->computeuserfunction)(snes,X,F,functx);
     72:   VecGetLocalSize(X,&nlocal);
     73:   VecGetArrayRead(X,&x_arr);
     74:   VecGetArray(F,&f_arr);
     75:   VecGetArray(Xl,&l);
     76:   VecGetArray(Xu,&u);
     77:   VecGetArray(phi,&phi_arr);

     79:   for (i=0; i < nlocal; i++) {
     80:     if ((PetscRealPart(l[i]) <= PETSC_NINFINITY) && (PetscRealPart(u[i]) >= PETSC_INFINITY)) { /* no constraints on variable */
     81:       phi_arr[i] = f_arr[i];
     82:     } else if (PetscRealPart(l[i]) <= PETSC_NINFINITY) {                      /* upper bound on variable only */
     83:       phi_arr[i] = -Phi(u[i] - x_arr[i],-f_arr[i]);
     84:     } else if (PetscRealPart(u[i]) >= PETSC_INFINITY) {                       /* lower bound on variable only */
     85:       phi_arr[i] = Phi(x_arr[i] - l[i],f_arr[i]);
     86:     } else if (l[i] == u[i]) {
     87:       phi_arr[i] = l[i] - x_arr[i];
     88:     } else {                                                /* both bounds on variable */
     89:       phi_arr[i] = Phi(x_arr[i] - l[i],-Phi(u[i] - x_arr[i],-f_arr[i]));
     90:     }
     91:   }

     93:   VecRestoreArrayRead(X,&x_arr);
     94:   VecRestoreArray(F,&f_arr);
     95:   VecRestoreArray(Xl,&l);
     96:   VecRestoreArray(Xu,&u);
     97:   VecRestoreArray(phi,&phi_arr);
     98:   return(0);
     99: }

    101: /*
    102:    SNESVIComputeBsubdifferentialVectors - Computes the diagonal shift (Da) and row scaling (Db) vectors needed for the
    103:                                           the semismooth jacobian.
    104: */
    107: PetscErrorCode SNESVIComputeBsubdifferentialVectors(SNES snes,Vec X,Vec F,Mat jac,Vec Da,Vec Db)
    108: {
    110:   PetscScalar    *l,*u,*x,*f,*da,*db,da1,da2,db1,db2;
    111:   PetscInt       i,nlocal;

    114:   VecGetArray(X,&x);
    115:   VecGetArray(F,&f);
    116:   VecGetArray(snes->xl,&l);
    117:   VecGetArray(snes->xu,&u);
    118:   VecGetArray(Da,&da);
    119:   VecGetArray(Db,&db);
    120:   VecGetLocalSize(X,&nlocal);

    122:   for (i=0; i< nlocal; i++) {
    123:     if ((PetscRealPart(l[i]) <= PETSC_NINFINITY) && (PetscRealPart(u[i]) >= PETSC_INFINITY)) { /* no constraints on variable */
    124:       da[i] = 0;
    125:       db[i] = 1;
    126:     } else if (PetscRealPart(l[i]) <= PETSC_NINFINITY) {                     /* upper bound on variable only */
    127:       da[i] = DPhi(u[i] - x[i], -f[i]);
    128:       db[i] = DPhi(-f[i],u[i] - x[i]);
    129:     } else if (PetscRealPart(u[i]) >= PETSC_INFINITY) {                      /* lower bound on variable only */
    130:       da[i] = DPhi(x[i] - l[i], f[i]);
    131:       db[i] = DPhi(f[i],x[i] - l[i]);
    132:     } else if (l[i] == u[i]) {                              /* fixed variable */
    133:       da[i] = 1;
    134:       db[i] = 0;
    135:     } else {                                                /* upper and lower bounds on variable */
    136:       da1   = DPhi(x[i] - l[i], -Phi(u[i] - x[i], -f[i]));
    137:       db1   = DPhi(-Phi(u[i] - x[i], -f[i]),x[i] - l[i]);
    138:       da2   = DPhi(u[i] - x[i], -f[i]);
    139:       db2   = DPhi(-f[i],u[i] - x[i]);
    140:       da[i] = da1 + db1*da2;
    141:       db[i] = db1*db2;
    142:     }
    143:   }

    145:   VecRestoreArray(X,&x);
    146:   VecRestoreArray(F,&f);
    147:   VecRestoreArray(snes->xl,&l);
    148:   VecRestoreArray(snes->xu,&u);
    149:   VecRestoreArray(Da,&da);
    150:   VecRestoreArray(Db,&db);
    151:   return(0);
    152: }

    154: /*
    155:    SNESVIComputeJacobian - Computes the jacobian of the semismooth function.The Jacobian for the semismooth function is an element of the B-subdifferential of the Fischer-Burmeister function for complementarity problems.

    157:    Input Parameters:
    158: .  Da       - Diagonal shift vector for the semismooth jacobian.
    159: .  Db       - Row scaling vector for the semismooth jacobian.

    161:    Output Parameters:
    162: .  jac      - semismooth jacobian
    163: .  jac_pre  - optional preconditioning matrix

    165:    Notes:
    166:    The semismooth jacobian matrix is given by
    167:    jac = Da + Db*jacfun
    168:    where Db is the row scaling matrix stored as a vector,
    169:          Da is the diagonal perturbation matrix stored as a vector
    170:    and   jacfun is the jacobian of the original nonlinear function.
    171: */
    174: PetscErrorCode SNESVIComputeJacobian(Mat jac, Mat jac_pre,Vec Da, Vec Db)
    175: {

    178:   /* Do row scaling  and add diagonal perturbation */
    179:   MatDiagonalScale(jac,Db,NULL);
    180:   MatDiagonalSet(jac,Da,ADD_VALUES);
    181:   if (jac != jac_pre) { /* If jac and jac_pre are different */
    182:     MatDiagonalScale(jac_pre,Db,NULL);
    183:     MatDiagonalSet(jac_pre,Da,ADD_VALUES);
    184:   }
    185:   return(0);
    186: }

    188: /*
    189:    SNESVIComputeMeritFunctionGradient - Computes the gradient of the merit function psi.

    191:    Input Parameters:
    192:    phi - semismooth function.
    193:    H   - semismooth jacobian

    195:    Output Parameters:
    196:    dpsi - merit function gradient

    198:    Notes:
    199:   The merit function gradient is computed as follows
    200:         dpsi = H^T*phi
    201: */
    204: PetscErrorCode SNESVIComputeMeritFunctionGradient(Mat H, Vec phi, Vec dpsi)
    205: {

    209:   MatMultTranspose(H,phi,dpsi);
    210:   return(0);
    211: }

    215: /*
    216:    SNESSolve_VINEWTONSSLS - Solves the complementarity problem with a semismooth Newton
    217:    method using a line search.

    219:    Input Parameters:
    220: .  snes - the SNES context

    222:    Application Interface Routine: SNESSolve()

    224:    Notes:
    225:    This implements essentially a semismooth Newton method with a
    226:    line search. The default line search does not do any line search
    227:    but rather takes a full Newton step.

    229:    Developer Note: the code in this file should be slightly modified so that this routine need not exist and the SNESSolve_NEWTONLS() routine is called directly with the appropriate wrapped function and Jacobian evaluations

    231: */
    234: PetscErrorCode SNESSolve_VINEWTONSSLS(SNES snes)
    235: {
    236:   SNES_VINEWTONSSLS    *vi = (SNES_VINEWTONSSLS*)snes->data;
    237:   PetscErrorCode       ierr;
    238:   PetscInt             maxits,i,lits;
    239:   SNESLineSearchReason lssucceed;
    240:   PetscReal            gnorm,xnorm=0,ynorm;
    241:   Vec                  Y,X,F;
    242:   KSPConvergedReason   kspreason;
    243:   DM                   dm;
    244:   DMSNES               sdm;

    247:   SNESGetDM(snes,&dm);
    248:   DMGetDMSNES(dm,&sdm);

    250:   vi->computeuserfunction   = sdm->ops->computefunction;
    251:   sdm->ops->computefunction = SNESVIComputeFunction;

    253:   snes->numFailures            = 0;
    254:   snes->numLinearSolveFailures = 0;
    255:   snes->reason                 = SNES_CONVERGED_ITERATING;

    257:   maxits = snes->max_its;               /* maximum number of iterations */
    258:   X      = snes->vec_sol;               /* solution vector */
    259:   F      = snes->vec_func;              /* residual vector */
    260:   Y      = snes->work[0];               /* work vectors */

    262:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    263:   snes->iter = 0;
    264:   snes->norm = 0.0;
    265:   PetscObjectSAWsGrantAccess((PetscObject)snes);

    267:   SNESVIProjectOntoBounds(snes,X);
    268:   SNESComputeFunction(snes,X,vi->phi);
    269:   if (snes->domainerror) {
    270:     snes->reason              = SNES_DIVERGED_FUNCTION_DOMAIN;
    271:     sdm->ops->computefunction = vi->computeuserfunction;
    272:     return(0);
    273:   }
    274:   /* Compute Merit function */
    275:   SNESVIComputeMeritFunction(vi->phi,&vi->merit,&vi->phinorm);

    277:   VecNormBegin(X,NORM_2,&xnorm);        /* xnorm <- ||x||  */
    278:   VecNormEnd(X,NORM_2,&xnorm);
    279:   SNESCheckFunctionNorm(snes,vi->merit);

    281:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    282:   snes->norm = vi->phinorm;
    283:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    284:   SNESLogConvergenceHistory(snes,vi->phinorm,0);
    285:   SNESMonitor(snes,0,vi->phinorm);

    287:   /* test convergence */
    288:   (*snes->ops->converged)(snes,0,0.0,0.0,vi->phinorm,&snes->reason,snes->cnvP);
    289:   if (snes->reason) {
    290:     sdm->ops->computefunction = vi->computeuserfunction;
    291:     return(0);
    292:   }

    294:   for (i=0; i<maxits; i++) {

    296:     /* Call general purpose update function */
    297:     if (snes->ops->update) {
    298:       (*snes->ops->update)(snes, snes->iter);
    299:     }

    301:     /* Solve J Y = Phi, where J is the semismooth jacobian */

    303:     /* Get the jacobian -- note that the function must be the original function for snes_fd and snes_fd_color to work for this*/
    304:     sdm->ops->computefunction = vi->computeuserfunction;
    305:     SNESComputeJacobian(snes,X,snes->jacobian,snes->jacobian_pre);
    306:     sdm->ops->computefunction = SNESVIComputeFunction;

    308:     /* Get the diagonal shift and row scaling vectors */
    309:     SNESVIComputeBsubdifferentialVectors(snes,X,F,snes->jacobian,vi->Da,vi->Db);
    310:     /* Compute the semismooth jacobian */
    311:     SNESVIComputeJacobian(snes->jacobian,snes->jacobian_pre,vi->Da,vi->Db);
    312:     /* Compute the merit function gradient */
    313:     SNESVIComputeMeritFunctionGradient(snes->jacobian,vi->phi,vi->dpsi);
    314:     KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre);
    315:     KSPSolve(snes->ksp,vi->phi,Y);
    316:     KSPGetConvergedReason(snes->ksp,&kspreason);

    318:     if (kspreason < 0) {
    319:       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
    320:         PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);
    321:         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
    322:         break;
    323:       }
    324:     }
    325:     KSPGetIterationNumber(snes->ksp,&lits);
    326:     snes->linear_its += lits;
    327:     PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);
    328:     /*
    329:     if (snes->ops->precheck) {
    330:       PetscBool changed_y = PETSC_FALSE;
    331:       (*snes->ops->precheck)(snes,X,Y,snes->precheck,&changed_y);
    332:     }

    334:     if (PetscLogPrintInfo) {
    335:       SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);
    336:     }
    337:     */
    338:     /* Compute a (scaled) negative update in the line search routine:
    339:          Y <- X - lambda*Y
    340:        and evaluate G = function(Y) (depends on the line search).
    341:     */
    342:     VecCopy(Y,snes->vec_sol_update);
    343:     ynorm = 1; gnorm = vi->phinorm;
    344:     SNESLineSearchApply(snes->linesearch, X, vi->phi, &gnorm, Y);
    345:     SNESLineSearchGetReason(snes->linesearch, &lssucceed);
    346:     SNESLineSearchGetNorms(snes->linesearch, &xnorm, &gnorm, &ynorm);
    347:     PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",(double)vi->phinorm,(double)gnorm,(double)ynorm,(int)lssucceed);
    348:     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
    349:     if (snes->domainerror) {
    350:       snes->reason              = SNES_DIVERGED_FUNCTION_DOMAIN;
    351:       sdm->ops->computefunction = vi->computeuserfunction;
    352:       return(0);
    353:     }
    354:     if (lssucceed) {
    355:       if (++snes->numFailures >= snes->maxFailures) {
    356:         PetscBool ismin;
    357:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
    358:         SNESVICheckLocalMin_Private(snes,snes->jacobian,vi->phi,X,gnorm,&ismin);
    359:         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
    360:         break;
    361:       }
    362:     }
    363:     /* Update function and solution vectors */
    364:     vi->phinorm = gnorm;
    365:     vi->merit   = 0.5*vi->phinorm*vi->phinorm;
    366:     /* Monitor convergence */
    367:     PetscObjectSAWsTakeAccess((PetscObject)snes);
    368:     snes->iter = i+1;
    369:     snes->norm = vi->phinorm;
    370:     PetscObjectSAWsGrantAccess((PetscObject)snes);
    371:     SNESLogConvergenceHistory(snes,snes->norm,lits);
    372:     SNESMonitor(snes,snes->iter,snes->norm);
    373:     /* Test for convergence, xnorm = || X || */
    374:     if (snes->ops->converged != SNESConvergedSkip) { VecNorm(X,NORM_2,&xnorm); }
    375:     (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,vi->phinorm,&snes->reason,snes->cnvP);
    376:     if (snes->reason) break;
    377:   }
    378:   if (i == maxits) {
    379:     PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);
    380:     if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
    381:   }
    382:   sdm->ops->computefunction = vi->computeuserfunction;
    383:   return(0);
    384: }

    386: /* -------------------------------------------------------------------------- */
    387: /*
    388:    SNESSetUp_VINEWTONSSLS - Sets up the internal data structures for the later use
    389:    of the SNES nonlinear solver.

    391:    Input Parameter:
    392: .  snes - the SNES context

    394:    Application Interface Routine: SNESSetUp()

    396:    Notes:
    397:    For basic use of the SNES solvers, the user need not explicitly call
    398:    SNESSetUp(), since these actions will automatically occur during
    399:    the call to SNESSolve().
    400:  */
    403: PetscErrorCode SNESSetUp_VINEWTONSSLS(SNES snes)
    404: {
    405:   PetscErrorCode    ierr;
    406:   SNES_VINEWTONSSLS *vi = (SNES_VINEWTONSSLS*) snes->data;

    409:   SNESSetUp_VI(snes);
    410:   VecDuplicate(snes->vec_sol, &vi->dpsi);
    411:   VecDuplicate(snes->vec_sol, &vi->phi);
    412:   VecDuplicate(snes->vec_sol, &vi->Da);
    413:   VecDuplicate(snes->vec_sol, &vi->Db);
    414:   VecDuplicate(snes->vec_sol, &vi->z);
    415:   VecDuplicate(snes->vec_sol, &vi->t);
    416:   return(0);
    417: }
    418: /* -------------------------------------------------------------------------- */
    421: PetscErrorCode SNESReset_VINEWTONSSLS(SNES snes)
    422: {
    423:   SNES_VINEWTONSSLS *vi = (SNES_VINEWTONSSLS*) snes->data;
    424:   PetscErrorCode    ierr;

    427:   SNESReset_VI(snes);
    428:   VecDestroy(&vi->dpsi);
    429:   VecDestroy(&vi->phi);
    430:   VecDestroy(&vi->Da);
    431:   VecDestroy(&vi->Db);
    432:   VecDestroy(&vi->z);
    433:   VecDestroy(&vi->t);
    434:   return(0);
    435: }

    437: /* -------------------------------------------------------------------------- */
    438: /*
    439:    SNESSetFromOptions_VINEWTONSSLS - Sets various parameters for the SNESVI method.

    441:    Input Parameter:
    442: .  snes - the SNES context

    444:    Application Interface Routine: SNESSetFromOptions()
    445: */
    448: static PetscErrorCode SNESSetFromOptions_VINEWTONSSLS(PetscOptions *PetscOptionsObject,SNES snes)
    449: {
    451:   SNESLineSearch linesearch;

    454:   SNESSetFromOptions_VI(PetscOptionsObject,snes);
    455:   PetscOptionsHead(PetscOptionsObject,"SNES semismooth method options");
    456:   PetscOptionsTail();
    457:   /* set up the default line search */
    458:   if (!snes->linesearch) {
    459:     SNESGetLineSearch(snes, &linesearch);
    460:     SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);
    461:     SNESLineSearchBTSetAlpha(linesearch, 0.0);
    462:   }
    463:   return(0);
    464: }

    467: /* -------------------------------------------------------------------------- */
    468: /*MC
    469:       SNESVINEWTONSSLS - Semi-smooth solver for variational inequalities based on Newton's method

    471:    Options Database:
    472: +   -snes_type <vinewtonssls,vinewtonrsls> a semi-smooth solver, a reduced space active set method
    473: -   -snes_vi_monitor - prints the number of active constraints at each iteration.

    475:    Level: beginner

    477:    References:
    478:    - T. S. Munson, F. Facchinei, M. C. Ferris, A. Fischer, and C. Kanzow. The semismooth
    479:      algorithm for large scale complementarity problems. INFORMS Journal on Computing, 13 (2001).
    480:    - T. S. Munson, and S. Benson. Flexible Complementarity Solvers for Large-Scale
    481:      Applications, Optimization Methods and Software, 21 (2006).

    483: .seealso:  SNESVISetVariableBounds(), SNESVISetComputeVariableBounds(), SNESCreate(), SNES, SNESSetType(), SNESVINEWTONRSLS, SNESNEWTONTR, SNESLineSearchSet(),SNESLineSearchSetPostCheck(), SNESLineSearchSetPreCheck()

    485: M*/
    488: PETSC_EXTERN PetscErrorCode SNESCreate_VINEWTONSSLS(SNES snes)
    489: {
    490:   PetscErrorCode    ierr;
    491:   SNES_VINEWTONSSLS *vi;

    494:   snes->ops->reset          = SNESReset_VINEWTONSSLS;
    495:   snes->ops->setup          = SNESSetUp_VINEWTONSSLS;
    496:   snes->ops->solve          = SNESSolve_VINEWTONSSLS;
    497:   snes->ops->destroy        = SNESDestroy_VI;
    498:   snes->ops->setfromoptions = SNESSetFromOptions_VINEWTONSSLS;
    499:   snes->ops->view           = NULL;

    501:   snes->usesksp = PETSC_TRUE;
    502:   snes->usespc  = PETSC_FALSE;

    504:   PetscNewLog(snes,&vi);
    505:   snes->data = (void*)vi;

    507:   PetscObjectComposeFunction((PetscObject)snes,"SNESVISetVariableBounds_C",SNESVISetVariableBounds_VI);
    508:   PetscObjectComposeFunction((PetscObject)snes,"SNESVISetComputeVariableBounds_C",SNESVISetComputeVariableBounds_VI);
    509:   return(0);
    510: }