Actual source code: vi.c

petsc-3.7.4 2016-10-02
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  1: #include <petsc/private/snesimpl.h>  /*I "petscsnes.h" I*/
  2: #include <petscdm.h>

  6: /*@C
  7:    SNESVISetComputeVariableBounds - Sets a function that is called to compute the variable bounds

  9:    Input parameter
 10: +  snes - the SNES context
 11: -  compute - computes the bounds

 13:    Level: advanced

 15: .seealso:   SNESVISetVariableBounds()

 17: @*/
 18: PetscErrorCode SNESVISetComputeVariableBounds(SNES snes, PetscErrorCode (*compute)(SNES,Vec,Vec))
 19: {
 20:   PetscErrorCode ierr,(*f)(SNES,PetscErrorCode (*)(SNES,Vec,Vec));

 24:   PetscObjectQueryFunction((PetscObject)snes,"SNESVISetComputeVariableBounds_C",&f);
 25:   if (!f) {
 26:     SNESVISetComputeVariableBounds_VI(snes,compute);
 27:   } else {
 28:     PetscUseMethod(snes,"SNESVISetComputeVariableBounds_C",(SNES,PetscErrorCode (*)(SNES,Vec,Vec)),(snes,compute));
 29:   }
 30:   return(0);
 31: }

 35: PetscErrorCode SNESVISetComputeVariableBounds_VI(SNES snes,SNESVIComputeVariableBoundsFunction compute)
 36: {
 38:   snes->ops->computevariablebounds = compute;
 39:   return(0);
 40: }

 42: /* --------------------------------------------------------------------------------------------------------*/

 46: PetscErrorCode  SNESVIMonitorResidual(SNES snes,PetscInt its,PetscReal fgnorm,void *dummy)
 47: {
 49:   Vec            X, F, Finactive;
 50:   IS             isactive;
 51:   PetscViewer    viewer = (PetscViewer) dummy;

 54:   SNESGetFunction(snes,&F,0,0);
 55:   SNESGetSolution(snes,&X);
 56:   SNESVIGetActiveSetIS(snes,X,F,&isactive);
 57:   VecDuplicate(F,&Finactive);
 58:   VecCopy(F,Finactive);
 59:   VecISSet(Finactive,isactive,0.0);
 60:   ISDestroy(&isactive);
 61:   VecView(Finactive,viewer);
 62:   VecDestroy(&Finactive);
 63:   return(0);
 64: }

 68: PetscErrorCode  SNESMonitorVI(SNES snes,PetscInt its,PetscReal fgnorm,void *dummy)
 69: {
 70:   PetscErrorCode    ierr;
 71:   PetscViewer       viewer = (PetscViewer) dummy;
 72:   const PetscScalar *x,*xl,*xu,*f;
 73:   PetscInt          i,n,act[2] = {0,0},fact[2],N;
 74:   /* Number of components that actually hit the bounds (c.f. active variables) */
 75:   PetscInt          act_bound[2] = {0,0},fact_bound[2];
 76:   PetscReal         rnorm,fnorm,zerotolerance = snes->vizerotolerance;
 77:   double            tmp;

 81:   VecGetLocalSize(snes->vec_sol,&n);
 82:   VecGetSize(snes->vec_sol,&N);
 83:   VecGetArrayRead(snes->xl,&xl);
 84:   VecGetArrayRead(snes->xu,&xu);
 85:   VecGetArrayRead(snes->vec_sol,&x);
 86:   VecGetArrayRead(snes->vec_func,&f);

 88:   rnorm = 0.0;
 89:   for (i=0; i<n; i++) {
 90:     if (((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + zerotolerance || (PetscRealPart(f[i]) <= 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - zerotolerance) || PetscRealPart(f[i]) >= 0.0))) rnorm += PetscRealPart(PetscConj(f[i])*f[i]);
 91:     else if (PetscRealPart(x[i]) <= PetscRealPart(xl[i]) + zerotolerance && PetscRealPart(f[i]) > 0.0) act[0]++;
 92:     else if (PetscRealPart(x[i]) >= PetscRealPart(xu[i]) - zerotolerance && PetscRealPart(f[i]) < 0.0) act[1]++;
 93:     else SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_PLIB,"Can never get here");
 94:   }

 96:   for (i=0; i<n; i++) {
 97:     if (PetscRealPart(x[i]) <= PetscRealPart(xl[i]) + zerotolerance) act_bound[0]++;
 98:     else if (PetscRealPart(x[i]) >= PetscRealPart(xu[i]) - zerotolerance) act_bound[1]++;
 99:   }
100:   VecRestoreArrayRead(snes->vec_func,&f);
101:   VecRestoreArrayRead(snes->xl,&xl);
102:   VecRestoreArrayRead(snes->xu,&xu);
103:   VecRestoreArrayRead(snes->vec_sol,&x);
104:   MPIU_Allreduce(&rnorm,&fnorm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)snes));
105:   MPIU_Allreduce(act,fact,2,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)snes));
106:   MPIU_Allreduce(act_bound,fact_bound,2,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)snes));
107:   fnorm = PetscSqrtReal(fnorm);

109:   PetscViewerASCIIAddTab(viewer,((PetscObject)snes)->tablevel);
110:   if (snes->ntruebounds) tmp = ((double)(fact[0]+fact[1]))/((double)snes->ntruebounds);
111:   else tmp = 0.0;
112:   PetscViewerASCIIPrintf(viewer,"%3D SNES VI Function norm %g Active lower constraints %D/%D upper constraints %D/%D Percent of total %g Percent of bounded %g\n",its,(double)fnorm,fact[0],fact_bound[0],fact[1],fact_bound[1],((double)(fact[0]+fact[1]))/((double)N),tmp);

114:   PetscViewerASCIISubtractTab(viewer,((PetscObject)snes)->tablevel);
115:   return(0);
116: }

118: /*
119:      Checks if J^T F = 0 which implies we've found a local minimum of the norm of the function,
120:     || F(u) ||_2 but not a zero, F(u) = 0. In the case when one cannot compute J^T F we use the fact that
121:     0 = (J^T F)^T W = F^T J W iff W not in the null space of J. Thanks for Jorge More
122:     for this trick. One assumes that the probability that W is in the null space of J is very, very small.
123: */
126: PetscErrorCode SNESVICheckLocalMin_Private(SNES snes,Mat A,Vec F,Vec W,PetscReal fnorm,PetscBool *ismin)
127: {
128:   PetscReal      a1;
130:   PetscBool      hastranspose;

133:   *ismin = PETSC_FALSE;
134:   MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);
135:   if (hastranspose) {
136:     /* Compute || J^T F|| */
137:     MatMultTranspose(A,F,W);
138:     VecNorm(W,NORM_2,&a1);
139:     PetscInfo1(snes,"|| J^T F|| %g near zero implies found a local minimum\n",(double)(a1/fnorm));
140:     if (a1/fnorm < 1.e-4) *ismin = PETSC_TRUE;
141:   } else {
142:     Vec         work;
143:     PetscScalar result;
144:     PetscReal   wnorm;

146:     VecSetRandom(W,NULL);
147:     VecNorm(W,NORM_2,&wnorm);
148:     VecDuplicate(W,&work);
149:     MatMult(A,W,work);
150:     VecDot(F,work,&result);
151:     VecDestroy(&work);
152:     a1   = PetscAbsScalar(result)/(fnorm*wnorm);
153:     PetscInfo1(snes,"(F^T J random)/(|| F ||*||random|| %g near zero implies found a local minimum\n",(double)a1);
154:     if (a1 < 1.e-4) *ismin = PETSC_TRUE;
155:   }
156:   return(0);
157: }

159: /*
160:      Checks if J^T(F - J*X) = 0
161: */
164: PetscErrorCode SNESVICheckResidual_Private(SNES snes,Mat A,Vec F,Vec X,Vec W1,Vec W2)
165: {
166:   PetscReal      a1,a2;
168:   PetscBool      hastranspose;

171:   MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);
172:   if (hastranspose) {
173:     MatMult(A,X,W1);
174:     VecAXPY(W1,-1.0,F);

176:     /* Compute || J^T W|| */
177:     MatMultTranspose(A,W1,W2);
178:     VecNorm(W1,NORM_2,&a1);
179:     VecNorm(W2,NORM_2,&a2);
180:     if (a1 != 0.0) {
181:       PetscInfo1(snes,"||J^T(F-Ax)||/||F-AX|| %g near zero implies inconsistent rhs\n",(double)(a2/a1));
182:     }
183:   }
184:   return(0);
185: }

187: /*
188:   SNESConvergedDefault_VI - Checks the convergence of the semismooth newton algorithm.

190:   Notes:
191:   The convergence criterion currently implemented is
192:   merit < abstol
193:   merit < rtol*merit_initial
194: */
197: PetscErrorCode SNESConvergedDefault_VI(SNES snes,PetscInt it,PetscReal xnorm,PetscReal gradnorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
198: {


205:   *reason = SNES_CONVERGED_ITERATING;

207:   if (!it) {
208:     /* set parameter for default relative tolerance convergence test */
209:     snes->ttol = fnorm*snes->rtol;
210:   }
211:   if (fnorm != fnorm) {
212:     PetscInfo(snes,"Failed to converged, function norm is NaN\n");
213:     *reason = SNES_DIVERGED_FNORM_NAN;
214:   } else if (fnorm < snes->abstol) {
215:     PetscInfo2(snes,"Converged due to function norm %g < %g\n",(double)fnorm,(double)snes->abstol);
216:     *reason = SNES_CONVERGED_FNORM_ABS;
217:   } else if (snes->nfuncs >= snes->max_funcs) {
218:     PetscInfo2(snes,"Exceeded maximum number of function evaluations: %D > %D\n",snes->nfuncs,snes->max_funcs);
219:     *reason = SNES_DIVERGED_FUNCTION_COUNT;
220:   }

222:   if (it && !*reason) {
223:     if (fnorm < snes->ttol) {
224:       PetscInfo2(snes,"Converged due to function norm %g < %g (relative tolerance)\n",(double)fnorm,(double)snes->ttol);
225:       *reason = SNES_CONVERGED_FNORM_RELATIVE;
226:     }
227:   }
228:   return(0);
229: }


232: /* -------------------------------------------------------------------------- */
233: /*
234:    SNESVIProjectOntoBounds - Projects X onto the feasible region so that Xl[i] <= X[i] <= Xu[i] for i = 1...n.

236:    Input Parameters:
237: .  SNES - nonlinear solver context

239:    Output Parameters:
240: .  X - Bound projected X

242: */

246: PetscErrorCode SNESVIProjectOntoBounds(SNES snes,Vec X)
247: {
248:   PetscErrorCode    ierr;
249:   const PetscScalar *xl,*xu;
250:   PetscScalar       *x;
251:   PetscInt          i,n;

254:   VecGetLocalSize(X,&n);
255:   VecGetArray(X,&x);
256:   VecGetArrayRead(snes->xl,&xl);
257:   VecGetArrayRead(snes->xu,&xu);

259:   for (i = 0; i<n; i++) {
260:     if (PetscRealPart(x[i]) < PetscRealPart(xl[i])) x[i] = xl[i];
261:     else if (PetscRealPart(x[i]) > PetscRealPart(xu[i])) x[i] = xu[i];
262:   }
263:   VecRestoreArray(X,&x);
264:   VecRestoreArrayRead(snes->xl,&xl);
265:   VecRestoreArrayRead(snes->xu,&xu);
266:   return(0);
267: }


272: /*
273:    SNESVIGetActiveSetIndices - Gets the global indices for the active set variables

275:    Input parameter
276: .  snes - the SNES context
277: .  X    - the snes solution vector
278: .  F    - the nonlinear function vector

280:    Output parameter
281: .  ISact - active set index set
282:  */
283: PetscErrorCode SNESVIGetActiveSetIS(SNES snes,Vec X,Vec F,IS *ISact)
284: {
285:   PetscErrorCode    ierr;
286:   Vec               Xl=snes->xl,Xu=snes->xu;
287:   const PetscScalar *x,*f,*xl,*xu;
288:   PetscInt          *idx_act,i,nlocal,nloc_isact=0,ilow,ihigh,i1=0;
289:   PetscReal         zerotolerance = snes->vizerotolerance;
290: 
292:   VecGetLocalSize(X,&nlocal);
293:   VecGetOwnershipRange(X,&ilow,&ihigh);
294:   VecGetArrayRead(X,&x);
295:   VecGetArrayRead(Xl,&xl);
296:   VecGetArrayRead(Xu,&xu);
297:   VecGetArrayRead(F,&f);
298:   /* Compute active set size */
299:   for (i=0; i < nlocal;i++) {
300:     if (!((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + zerotolerance || (PetscRealPart(f[i]) <= 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - zerotolerance) || PetscRealPart(f[i]) >= 0.0))) nloc_isact++;
301:   }

303:   PetscMalloc1(nloc_isact,&idx_act);

305:   /* Set active set indices */
306:   for (i=0; i < nlocal; i++) {
307:     if (!((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + zerotolerance || (PetscRealPart(f[i]) <= 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - zerotolerance) || PetscRealPart(f[i]) >= 0.0))) idx_act[i1++] = ilow+i;
308:   }

310:   /* Create active set IS */
311:   ISCreateGeneral(PetscObjectComm((PetscObject)snes),nloc_isact,idx_act,PETSC_OWN_POINTER,ISact);

313:   VecRestoreArrayRead(X,&x);
314:   VecRestoreArrayRead(Xl,&xl);
315:   VecRestoreArrayRead(Xu,&xu);
316:   VecRestoreArrayRead(F,&f);
317:   return(0);
318: }

322: PetscErrorCode SNESVICreateIndexSets_RS(SNES snes,Vec X,Vec F,IS *ISact,IS *ISinact)
323: {
325:   PetscInt       rstart,rend;

328:   SNESVIGetActiveSetIS(snes,X,F,ISact);
329:   VecGetOwnershipRange(X,&rstart,&rend);
330:   ISComplement(*ISact,rstart,rend,ISinact);
331:   return(0);
332: }

336: PetscErrorCode SNESVIComputeInactiveSetFnorm(SNES snes,Vec F,Vec X, PetscReal *fnorm)
337: {
338:   PetscErrorCode    ierr;
339:   const PetscScalar *x,*xl,*xu,*f;
340:   PetscInt          i,n;
341:   PetscReal         rnorm,zerotolerance = snes->vizerotolerance;;

344:   VecGetLocalSize(X,&n);
345:   VecGetArrayRead(snes->xl,&xl);
346:   VecGetArrayRead(snes->xu,&xu);
347:   VecGetArrayRead(X,&x);
348:   VecGetArrayRead(F,&f);
349:   rnorm = 0.0;
350:   for (i=0; i<n; i++) {
351:     if (((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + zerotolerance || (PetscRealPart(f[i]) <= 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - zerotolerance) || PetscRealPart(f[i]) >= 0.0))) rnorm += PetscRealPart(PetscConj(f[i])*f[i]);
352:   }
353:   VecRestoreArrayRead(F,&f);
354:   VecRestoreArrayRead(snes->xl,&xl);
355:   VecRestoreArrayRead(snes->xu,&xu);
356:   VecRestoreArrayRead(X,&x);
357:   MPIU_Allreduce(&rnorm,fnorm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)snes));
358:   *fnorm = PetscSqrtReal(*fnorm);
359:   return(0);
360: }

364: PetscErrorCode SNESVIDMComputeVariableBounds(SNES snes,Vec xl, Vec xu)
365: {

369:   DMComputeVariableBounds(snes->dm, xl, xu);
370:   return(0);
371: }


374: /* -------------------------------------------------------------------------- */
375: /*
376:    SNESSetUp_VI - Does setup common to all VI solvers -- basically makes sure bounds have been properly set up
377:    of the SNESVI nonlinear solver.

379:    Input Parameter:
380: .  snes - the SNES context

382:    Application Interface Routine: SNESSetUp()

384:    Notes:
385:    For basic use of the SNES solvers, the user need not explicitly call
386:    SNESSetUp(), since these actions will automatically occur during
387:    the call to SNESSolve().
388:  */
391: PetscErrorCode SNESSetUp_VI(SNES snes)
392: {
394:   PetscInt       i_start[3],i_end[3];

397:   SNESSetWorkVecs(snes,1);
398:   SNESSetUpMatrices(snes);

400:   if (!snes->ops->computevariablebounds && snes->dm) {
401:     PetscBool flag;
402:     DMHasVariableBounds(snes->dm, &flag);
403:     if (flag) {
404:       snes->ops->computevariablebounds = SNESVIDMComputeVariableBounds;
405:     }
406:   }
407:   if (!snes->usersetbounds) {
408:     if (snes->ops->computevariablebounds) {
409:       if (!snes->xl) {VecDuplicate(snes->vec_sol,&snes->xl);}
410:       if (!snes->xu) {VecDuplicate(snes->vec_sol,&snes->xu);}
411:       (*snes->ops->computevariablebounds)(snes,snes->xl,snes->xu);
412:     } else if (!snes->xl && !snes->xu) {
413:       /* If the lower and upper bound on variables are not set, set it to -Inf and Inf */
414:       VecDuplicate(snes->vec_sol, &snes->xl);
415:       VecSet(snes->xl,PETSC_NINFINITY);
416:       VecDuplicate(snes->vec_sol, &snes->xu);
417:       VecSet(snes->xu,PETSC_INFINITY);
418:     } else {
419:       /* Check if lower bound, upper bound and solution vector distribution across the processors is identical */
420:       VecGetOwnershipRange(snes->vec_sol,i_start,i_end);
421:       VecGetOwnershipRange(snes->xl,i_start+1,i_end+1);
422:       VecGetOwnershipRange(snes->xu,i_start+2,i_end+2);
423:       if ((i_start[0] != i_start[1]) || (i_start[0] != i_start[2]) || (i_end[0] != i_end[1]) || (i_end[0] != i_end[2]))
424:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Distribution of lower bound, upper bound and the solution vector should be identical across all the processors.");
425:     }
426:   }
427:   return(0);
428: }
429: /* -------------------------------------------------------------------------- */
432: PetscErrorCode SNESReset_VI(SNES snes)
433: {

437:   VecDestroy(&snes->xl);
438:   VecDestroy(&snes->xu);
439:   snes->usersetbounds = PETSC_FALSE;
440:   return(0);
441: }

443: /*
444:    SNESDestroy_VI - Destroys the private SNES_VI context that was created
445:    with SNESCreate_VI().

447:    Input Parameter:
448: .  snes - the SNES context

450:    Application Interface Routine: SNESDestroy()
451:  */
454: PetscErrorCode SNESDestroy_VI(SNES snes)
455: {

459:   PetscFree(snes->data);

461:   /* clear composed functions */
462:   PetscObjectComposeFunction((PetscObject)snes,"SNESLineSearchSet_C",NULL);
463:   PetscObjectComposeFunction((PetscObject)snes,"SNESLineSearchSetDefaultMonitor_C",NULL);
464:   return(0);
465: }

469: /*@
470:    SNESVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu.

472:    Input Parameters:
473: .  snes - the SNES context.
474: .  xl   - lower bound.
475: .  xu   - upper bound.

477:    Notes:
478:    If this routine is not called then the lower and upper bounds are set to
479:    PETSC_NINFINITY and PETSC_INFINITY respectively during SNESSetUp().

481:    Level: advanced

483: @*/
484: PetscErrorCode SNESVISetVariableBounds(SNES snes, Vec xl, Vec xu)
485: {
486:   PetscErrorCode ierr,(*f)(SNES,Vec,Vec);

492:   PetscObjectQueryFunction((PetscObject)snes,"SNESVISetVariableBounds_C",&f);
493:   if (!f) {
494:     SNESVISetVariableBounds_VI(snes, xl, xu);
495:   } else {
496:     PetscUseMethod(snes,"SNESVISetVariableBounds_C",(SNES,Vec,Vec),(snes,xl,xu));
497:   }
498:   snes->usersetbounds = PETSC_TRUE;
499:   return(0);
500: }

504: PetscErrorCode SNESVISetVariableBounds_VI(SNES snes,Vec xl,Vec xu)
505: {
506:   PetscErrorCode    ierr;
507:   const PetscScalar *xxl,*xxu;
508:   PetscInt          i,n, cnt = 0;

511:   SNESGetFunction(snes,&snes->vec_func,NULL,NULL);
512:   if (!snes->vec_func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call SNESSetFunction() or SNESSetDM() first");
513:   {
514:     PetscInt xlN,xuN,N;
515:     VecGetSize(xl,&xlN);
516:     VecGetSize(xu,&xuN);
517:     VecGetSize(snes->vec_func,&N);
518:     if (xlN != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incompatible vector lengths lower bound = %D solution vector = %D",xlN,N);
519:     if (xuN != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incompatible vector lengths: upper bound = %D solution vector = %D",xuN,N);
520:   }
521:   PetscObjectReference((PetscObject)xl);
522:   PetscObjectReference((PetscObject)xu);
523:   VecDestroy(&snes->xl);
524:   VecDestroy(&snes->xu);
525:   snes->xl = xl;
526:   snes->xu = xu;
527:   VecGetLocalSize(xl,&n);
528:   VecGetArrayRead(xl,&xxl);
529:   VecGetArrayRead(xu,&xxu);
530:   for (i=0; i<n; i++) cnt += ((xxl[i] != PETSC_NINFINITY) || (xxu[i] != PETSC_INFINITY));

532:   MPIU_Allreduce(&cnt,&snes->ntruebounds,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)snes));
533:   VecRestoreArrayRead(xl,&xxl);
534:   VecRestoreArrayRead(xu,&xxu);
535:   return(0);
536: }

540: PetscErrorCode SNESSetFromOptions_VI(PetscOptionItems *PetscOptionsObject,SNES snes)
541: {
543:   PetscBool      flg = PETSC_FALSE;
544:   SNESLineSearch linesearch;

547:   PetscOptionsHead(PetscOptionsObject,"SNES VI options");
548:   PetscOptionsReal("-snes_vi_zero_tolerance","Tolerance for considering x[] value to be on a bound","None",snes->vizerotolerance,&snes->vizerotolerance,NULL);
549:   PetscOptionsBool("-snes_vi_monitor","Monitor all non-active variables","SNESMonitorResidual",flg,&flg,NULL);
550:   if (flg) {
551:     SNESMonitorSet(snes,SNESMonitorVI,PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes)),NULL);
552:   }
553:   flg = PETSC_FALSE;
554:   PetscOptionsBool("-snes_vi_monitor_residual","Monitor residual all non-active variables; using zero for active constraints","SNESMonitorVIResidual",flg,&flg,NULL);
555:   if (flg) {
556:     SNESMonitorSet(snes,SNESVIMonitorResidual,PETSC_VIEWER_DRAW_(PetscObjectComm((PetscObject)snes)),NULL);
557:   }
558:   if (!snes->linesearch) {
559:     SNESGetLineSearch(snes, &linesearch);
560:     SNESLineSearchSetType(linesearch, SNESLINESEARCHBT);
561:     SNESLineSearchBTSetAlpha(linesearch, 0.0);
562:   }
563:   PetscOptionsTail();
564:   return(0);
565: }