Actual source code: viss.c

petsc-3.8.2 2017-11-09
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  2:  #include <../src/snes/impls/vi/ss/vissimpl.h>

  4: /*
  5:   SNESVIComputeMeritFunction - Evaluates the merit function for the mixed complementarity problem.

  7:   Input Parameter:
  8: . phi - the semismooth function

 10:   Output Parameter:
 11: . merit - the merit function
 12: . phinorm - ||phi||

 14:   Notes:
 15:   The merit function for the mixed complementarity problem is defined as
 16:      merit = 0.5*phi^T*phi
 17: */
 18: static PetscErrorCode SNESVIComputeMeritFunction(Vec phi, PetscReal *merit,PetscReal *phinorm)
 19: {

 23:   VecNormBegin(phi,NORM_2,phinorm);
 24:   VecNormEnd(phi,NORM_2,phinorm);

 26:   *merit = 0.5*(*phinorm)*(*phinorm);
 27:   return(0);
 28: }

 30: PETSC_STATIC_INLINE PetscScalar Phi(PetscScalar a,PetscScalar b)
 31: {
 32:   return a + b - PetscSqrtScalar(a*a + b*b);
 33: }

 35: PETSC_STATIC_INLINE PetscScalar DPhi(PetscScalar a,PetscScalar b)
 36: {
 37:   if ((PetscAbsScalar(a) >= 1.e-6) || (PetscAbsScalar(b) >= 1.e-6)) return 1.0 - a/ PetscSqrtScalar(a*a + b*b);
 38:   else return .5;
 39: }

 41: /*
 42:    SNESVIComputeFunction - Reformulates a system of nonlinear equations in mixed complementarity form to a system of nonlinear equations in semismooth form.

 44:    Input Parameters:
 45: .  snes - the SNES context
 46: .  X - current iterate
 47: .  functx - user defined function context

 49:    Output Parameters:
 50: .  phi - Semismooth function

 52: */
 53: static PetscErrorCode SNESVIComputeFunction(SNES snes,Vec X,Vec phi,void *functx)
 54: {
 55:   PetscErrorCode    ierr;
 56:   SNES_VINEWTONSSLS *vi = (SNES_VINEWTONSSLS*)snes->data;
 57:   Vec               Xl  = snes->xl,Xu = snes->xu,F = snes->vec_func;
 58:   PetscScalar       *phi_arr,*f_arr,*l,*u;
 59:   const PetscScalar *x_arr;
 60:   PetscInt          i,nlocal;

 63:   (*vi->computeuserfunction)(snes,X,F,functx);
 64:   VecGetLocalSize(X,&nlocal);
 65:   VecGetArrayRead(X,&x_arr);
 66:   VecGetArray(F,&f_arr);
 67:   VecGetArray(Xl,&l);
 68:   VecGetArray(Xu,&u);
 69:   VecGetArray(phi,&phi_arr);

 71:   for (i=0; i < nlocal; i++) {
 72:     if ((PetscRealPart(l[i]) <= PETSC_NINFINITY) && (PetscRealPart(u[i]) >= PETSC_INFINITY)) { /* no constraints on variable */
 73:       phi_arr[i] = f_arr[i];
 74:     } else if (PetscRealPart(l[i]) <= PETSC_NINFINITY) {                      /* upper bound on variable only */
 75:       phi_arr[i] = -Phi(u[i] - x_arr[i],-f_arr[i]);
 76:     } else if (PetscRealPart(u[i]) >= PETSC_INFINITY) {                       /* lower bound on variable only */
 77:       phi_arr[i] = Phi(x_arr[i] - l[i],f_arr[i]);
 78:     } else if (l[i] == u[i]) {
 79:       phi_arr[i] = l[i] - x_arr[i];
 80:     } else {                                                /* both bounds on variable */
 81:       phi_arr[i] = Phi(x_arr[i] - l[i],-Phi(u[i] - x_arr[i],-f_arr[i]));
 82:     }
 83:   }

 85:   VecRestoreArrayRead(X,&x_arr);
 86:   VecRestoreArray(F,&f_arr);
 87:   VecRestoreArray(Xl,&l);
 88:   VecRestoreArray(Xu,&u);
 89:   VecRestoreArray(phi,&phi_arr);
 90:   return(0);
 91: }

 93: /*
 94:    SNESVIComputeBsubdifferentialVectors - Computes the diagonal shift (Da) and row scaling (Db) vectors needed for the
 95:                                           the semismooth jacobian.
 96: */
 97: PetscErrorCode SNESVIComputeBsubdifferentialVectors(SNES snes,Vec X,Vec F,Mat jac,Vec Da,Vec Db)
 98: {
100:   PetscScalar    *l,*u,*x,*f,*da,*db,da1,da2,db1,db2;
101:   PetscInt       i,nlocal;

104:   VecGetArray(X,&x);
105:   VecGetArray(F,&f);
106:   VecGetArray(snes->xl,&l);
107:   VecGetArray(snes->xu,&u);
108:   VecGetArray(Da,&da);
109:   VecGetArray(Db,&db);
110:   VecGetLocalSize(X,&nlocal);

112:   for (i=0; i< nlocal; i++) {
113:     if ((PetscRealPart(l[i]) <= PETSC_NINFINITY) && (PetscRealPart(u[i]) >= PETSC_INFINITY)) { /* no constraints on variable */
114:       da[i] = 0;
115:       db[i] = 1;
116:     } else if (PetscRealPart(l[i]) <= PETSC_NINFINITY) {                     /* upper bound on variable only */
117:       da[i] = DPhi(u[i] - x[i], -f[i]);
118:       db[i] = DPhi(-f[i],u[i] - x[i]);
119:     } else if (PetscRealPart(u[i]) >= PETSC_INFINITY) {                      /* lower bound on variable only */
120:       da[i] = DPhi(x[i] - l[i], f[i]);
121:       db[i] = DPhi(f[i],x[i] - l[i]);
122:     } else if (l[i] == u[i]) {                              /* fixed variable */
123:       da[i] = 1;
124:       db[i] = 0;
125:     } else {                                                /* upper and lower bounds on variable */
126:       da1   = DPhi(x[i] - l[i], -Phi(u[i] - x[i], -f[i]));
127:       db1   = DPhi(-Phi(u[i] - x[i], -f[i]),x[i] - l[i]);
128:       da2   = DPhi(u[i] - x[i], -f[i]);
129:       db2   = DPhi(-f[i],u[i] - x[i]);
130:       da[i] = da1 + db1*da2;
131:       db[i] = db1*db2;
132:     }
133:   }

135:   VecRestoreArray(X,&x);
136:   VecRestoreArray(F,&f);
137:   VecRestoreArray(snes->xl,&l);
138:   VecRestoreArray(snes->xu,&u);
139:   VecRestoreArray(Da,&da);
140:   VecRestoreArray(Db,&db);
141:   return(0);
142: }

144: /*
145:    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.

147:    Input Parameters:
148: .  Da       - Diagonal shift vector for the semismooth jacobian.
149: .  Db       - Row scaling vector for the semismooth jacobian.

151:    Output Parameters:
152: .  jac      - semismooth jacobian
153: .  jac_pre  - optional preconditioning matrix

155:    Notes:
156:    The semismooth jacobian matrix is given by
157:    jac = Da + Db*jacfun
158:    where Db is the row scaling matrix stored as a vector,
159:          Da is the diagonal perturbation matrix stored as a vector
160:    and   jacfun is the jacobian of the original nonlinear function.
161: */
162: PetscErrorCode SNESVIComputeJacobian(Mat jac, Mat jac_pre,Vec Da, Vec Db)
163: {

166:   /* Do row scaling  and add diagonal perturbation */
167:   MatDiagonalScale(jac,Db,NULL);
168:   MatDiagonalSet(jac,Da,ADD_VALUES);
169:   if (jac != jac_pre) { /* If jac and jac_pre are different */
170:     MatDiagonalScale(jac_pre,Db,NULL);
171:     MatDiagonalSet(jac_pre,Da,ADD_VALUES);
172:   }
173:   return(0);
174: }

176: /*
177:    SNESVIComputeMeritFunctionGradient - Computes the gradient of the merit function psi.

179:    Input Parameters:
180:    phi - semismooth function.
181:    H   - semismooth jacobian

183:    Output Parameters:
184:    dpsi - merit function gradient

186:    Notes:
187:   The merit function gradient is computed as follows
188:         dpsi = H^T*phi
189: */
190: PetscErrorCode SNESVIComputeMeritFunctionGradient(Mat H, Vec phi, Vec dpsi)
191: {

195:   MatMultTranspose(H,phi,dpsi);
196:   return(0);
197: }



201: /*
202:    SNESSolve_VINEWTONSSLS - Solves the complementarity problem with a semismooth Newton
203:    method using a line search.

205:    Input Parameters:
206: .  snes - the SNES context

208:    Application Interface Routine: SNESSolve()

210:    Notes:
211:    This implements essentially a semismooth Newton method with a
212:    line search. The default line search does not do any line search
213:    but rather takes a full Newton step.

215:    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

217: */
218: PetscErrorCode SNESSolve_VINEWTONSSLS(SNES snes)
219: {
220:   SNES_VINEWTONSSLS    *vi = (SNES_VINEWTONSSLS*)snes->data;
221:   PetscErrorCode       ierr;
222:   PetscInt             maxits,i,lits;
223:   SNESLineSearchReason lssucceed;
224:   PetscReal            gnorm,xnorm=0,ynorm;
225:   Vec                  Y,X,F;
226:   KSPConvergedReason   kspreason;
227:   DM                   dm;
228:   DMSNES               sdm;

231:   SNESGetDM(snes,&dm);
232:   DMGetDMSNES(dm,&sdm);

234:   vi->computeuserfunction   = sdm->ops->computefunction;
235:   sdm->ops->computefunction = SNESVIComputeFunction;

237:   snes->numFailures            = 0;
238:   snes->numLinearSolveFailures = 0;
239:   snes->reason                 = SNES_CONVERGED_ITERATING;

241:   maxits = snes->max_its;               /* maximum number of iterations */
242:   X      = snes->vec_sol;               /* solution vector */
243:   F      = snes->vec_func;              /* residual vector */
244:   Y      = snes->work[0];               /* work vectors */

246:   PetscObjectSAWsTakeAccess((PetscObject)snes);
247:   snes->iter = 0;
248:   snes->norm = 0.0;
249:   PetscObjectSAWsGrantAccess((PetscObject)snes);

251:   SNESVIProjectOntoBounds(snes,X);
252:   SNESComputeFunction(snes,X,vi->phi);
253:   if (snes->domainerror) {
254:     snes->reason              = SNES_DIVERGED_FUNCTION_DOMAIN;
255:     sdm->ops->computefunction = vi->computeuserfunction;
256:     return(0);
257:   }
258:   /* Compute Merit function */
259:   SNESVIComputeMeritFunction(vi->phi,&vi->merit,&vi->phinorm);

261:   VecNormBegin(X,NORM_2,&xnorm);        /* xnorm <- ||x||  */
262:   VecNormEnd(X,NORM_2,&xnorm);
263:   SNESCheckFunctionNorm(snes,vi->merit);

265:   PetscObjectSAWsTakeAccess((PetscObject)snes);
266:   snes->norm = vi->phinorm;
267:   PetscObjectSAWsGrantAccess((PetscObject)snes);
268:   SNESLogConvergenceHistory(snes,vi->phinorm,0);
269:   SNESMonitor(snes,0,vi->phinorm);

271:   /* test convergence */
272:   (*snes->ops->converged)(snes,0,0.0,0.0,vi->phinorm,&snes->reason,snes->cnvP);
273:   if (snes->reason) {
274:     sdm->ops->computefunction = vi->computeuserfunction;
275:     return(0);
276:   }

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

280:     /* Call general purpose update function */
281:     if (snes->ops->update) {
282:       (*snes->ops->update)(snes, snes->iter);
283:     }

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

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

292:     /* Get the diagonal shift and row scaling vectors */
293:     SNESVIComputeBsubdifferentialVectors(snes,X,F,snes->jacobian,vi->Da,vi->Db);
294:     /* Compute the semismooth jacobian */
295:     SNESVIComputeJacobian(snes->jacobian,snes->jacobian_pre,vi->Da,vi->Db);
296:     /* Compute the merit function gradient */
297:     SNESVIComputeMeritFunctionGradient(snes->jacobian,vi->phi,vi->dpsi);
298:     KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre);
299:     KSPSolve(snes->ksp,vi->phi,Y);
300:     KSPGetConvergedReason(snes->ksp,&kspreason);

302:     if (kspreason < 0) {
303:       if (++snes->numLinearSolveFailures >= snes->maxLinearSolveFailures) {
304:         PetscInfo2(snes,"iter=%D, number linear solve failures %D greater than current SNES allowed, stopping solve\n",snes->iter,snes->numLinearSolveFailures);
305:         snes->reason = SNES_DIVERGED_LINEAR_SOLVE;
306:         break;
307:       }
308:     }
309:     KSPGetIterationNumber(snes->ksp,&lits);
310:     snes->linear_its += lits;
311:     PetscInfo2(snes,"iter=%D, linear solve iterations=%D\n",snes->iter,lits);
312:     /*
313:     if (snes->ops->precheck) {
314:       PetscBool changed_y = PETSC_FALSE;
315:       (*snes->ops->precheck)(snes,X,Y,snes->precheck,&changed_y);
316:     }

318:     if (PetscLogPrintInfo) {
319:       SNESVICheckResidual_Private(snes,snes->jacobian,F,Y,G,W);
320:     }
321:     */
322:     /* Compute a (scaled) negative update in the line search routine:
323:          Y <- X - lambda*Y
324:        and evaluate G = function(Y) (depends on the line search).
325:     */
326:     VecCopy(Y,snes->vec_sol_update);
327:     ynorm = 1; gnorm = vi->phinorm;
328:     SNESLineSearchApply(snes->linesearch, X, vi->phi, &gnorm, Y);
329:     SNESLineSearchGetReason(snes->linesearch, &lssucceed);
330:     SNESLineSearchGetNorms(snes->linesearch, &xnorm, &gnorm, &ynorm);
331:     PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",(double)vi->phinorm,(double)gnorm,(double)ynorm,(int)lssucceed);
332:     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
333:     if (snes->domainerror) {
334:       snes->reason              = SNES_DIVERGED_FUNCTION_DOMAIN;
335:       sdm->ops->computefunction = vi->computeuserfunction;
336:       return(0);
337:     }
338:     if (lssucceed) {
339:       if (++snes->numFailures >= snes->maxFailures) {
340:         PetscBool ismin;
341:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
342:         SNESVICheckLocalMin_Private(snes,snes->jacobian,vi->phi,X,gnorm,&ismin);
343:         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
344:         break;
345:       }
346:     }
347:     /* Update function and solution vectors */
348:     vi->phinorm = gnorm;
349:     vi->merit   = 0.5*vi->phinorm*vi->phinorm;
350:     /* Monitor convergence */
351:     PetscObjectSAWsTakeAccess((PetscObject)snes);
352:     snes->iter = i+1;
353:     snes->norm = vi->phinorm;
354:     PetscObjectSAWsGrantAccess((PetscObject)snes);
355:     SNESLogConvergenceHistory(snes,snes->norm,lits);
356:     SNESMonitor(snes,snes->iter,snes->norm);
357:     /* Test for convergence, xnorm = || X || */
358:     if (snes->ops->converged != SNESConvergedSkip) { VecNorm(X,NORM_2,&xnorm); }
359:     (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,vi->phinorm,&snes->reason,snes->cnvP);
360:     if (snes->reason) break;
361:   }
362:   if (i == maxits) {
363:     PetscInfo1(snes,"Maximum number of iterations has been reached: %D\n",maxits);
364:     if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
365:   }
366:   sdm->ops->computefunction = vi->computeuserfunction;
367:   return(0);
368: }

370: /* -------------------------------------------------------------------------- */
371: /*
372:    SNESSetUp_VINEWTONSSLS - Sets up the internal data structures for the later use
373:    of the SNES nonlinear solver.

375:    Input Parameter:
376: .  snes - the SNES context

378:    Application Interface Routine: SNESSetUp()

380:    Notes:
381:    For basic use of the SNES solvers, the user need not explicitly call
382:    SNESSetUp(), since these actions will automatically occur during
383:    the call to SNESSolve().
384:  */
385: PetscErrorCode SNESSetUp_VINEWTONSSLS(SNES snes)
386: {
387:   PetscErrorCode    ierr;
388:   SNES_VINEWTONSSLS *vi = (SNES_VINEWTONSSLS*) snes->data;

391:   SNESSetUp_VI(snes);
392:   VecDuplicate(snes->vec_sol, &vi->dpsi);
393:   VecDuplicate(snes->vec_sol, &vi->phi);
394:   VecDuplicate(snes->vec_sol, &vi->Da);
395:   VecDuplicate(snes->vec_sol, &vi->Db);
396:   VecDuplicate(snes->vec_sol, &vi->z);
397:   VecDuplicate(snes->vec_sol, &vi->t);
398:   return(0);
399: }
400: /* -------------------------------------------------------------------------- */
401: PetscErrorCode SNESReset_VINEWTONSSLS(SNES snes)
402: {
403:   SNES_VINEWTONSSLS *vi = (SNES_VINEWTONSSLS*) snes->data;
404:   PetscErrorCode    ierr;

407:   SNESReset_VI(snes);
408:   VecDestroy(&vi->dpsi);
409:   VecDestroy(&vi->phi);
410:   VecDestroy(&vi->Da);
411:   VecDestroy(&vi->Db);
412:   VecDestroy(&vi->z);
413:   VecDestroy(&vi->t);
414:   return(0);
415: }

417: /* -------------------------------------------------------------------------- */
418: /*
419:    SNESSetFromOptions_VINEWTONSSLS - Sets various parameters for the SNESVI method.

421:    Input Parameter:
422: .  snes - the SNES context

424:    Application Interface Routine: SNESSetFromOptions()
425: */
426: static PetscErrorCode SNESSetFromOptions_VINEWTONSSLS(PetscOptionItems *PetscOptionsObject,SNES snes)
427: {
429:   SNESLineSearch linesearch;

432:   SNESSetFromOptions_VI(PetscOptionsObject,snes);
433:   PetscOptionsHead(PetscOptionsObject,"SNES semismooth method options");
434:   PetscOptionsTail();
435:   /* set up the default line search */
436:   if (!snes->linesearch) {
437:     SNESGetLineSearch(snes, &linesearch);
438:     SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);
439:     SNESLineSearchBTSetAlpha(linesearch, 0.0);
440:   }
441:   return(0);
442: }


445: /* -------------------------------------------------------------------------- */
446: /*MC
447:       SNESVINEWTONSSLS - Semi-smooth solver for variational inequalities based on Newton's method

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

453:    Level: beginner

455:    References:
456: +  1. -  T. S. Munson, F. Facchinei, M. C. Ferris, A. Fischer, and C. Kanzow. The semismooth
457:      algorithm for large scale complementarity problems. INFORMS Journal on Computing, 13 (2001).
458: -  2. -  T. S. Munson, and S. Benson. Flexible Complementarity Solvers for Large Scale
459:      Applications, Optimization Methods and Software, 21 (2006).

461: .seealso:  SNESVISetVariableBounds(), SNESVISetComputeVariableBounds(), SNESCreate(), SNES, SNESSetType(), SNESVINEWTONRSLS, SNESNEWTONTR, SNESLineSearchSetType(),SNESLineSearchSetPostCheck(), SNESLineSearchSetPreCheck()

463: M*/
464: PETSC_EXTERN PetscErrorCode SNESCreate_VINEWTONSSLS(SNES snes)
465: {
466:   PetscErrorCode    ierr;
467:   SNES_VINEWTONSSLS *vi;

470:   snes->ops->reset          = SNESReset_VINEWTONSSLS;
471:   snes->ops->setup          = SNESSetUp_VINEWTONSSLS;
472:   snes->ops->solve          = SNESSolve_VINEWTONSSLS;
473:   snes->ops->destroy        = SNESDestroy_VI;
474:   snes->ops->setfromoptions = SNESSetFromOptions_VINEWTONSSLS;
475:   snes->ops->view           = NULL;

477:   snes->usesksp = PETSC_TRUE;
478:   snes->usesnpc = PETSC_FALSE;

480:   snes->alwayscomputesfinalresidual = PETSC_FALSE;

482:   PetscNewLog(snes,&vi);
483:   snes->data = (void*)vi;

485:   PetscObjectComposeFunction((PetscObject)snes,"SNESVISetVariableBounds_C",SNESVISetVariableBounds_VI);
486:   PetscObjectComposeFunction((PetscObject)snes,"SNESVISetComputeVariableBounds_C",SNESVISetComputeVariableBounds_VI);
487:   return(0);
488: }