Actual source code: viss.c

petsc-3.6.0 2015-06-09
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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: }