Actual source code: ntr.c

petsc-3.7.7 2017-09-25
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  1: #include <../src/tao/matrix/lmvmmat.h>
  2: #include <../src/tao/unconstrained/impls/ntr/ntr.h>

  4: #include <petscksp.h>
  5: #include <petscpc.h>
  6: #include <petsc/private/kspimpl.h>
  7: #include <petsc/private/pcimpl.h>

  9: #define NTR_KSP_NASH    0
 10: #define NTR_KSP_STCG    1
 11: #define NTR_KSP_GLTR    2
 12: #define NTR_KSP_TYPES   3

 14: #define NTR_PC_NONE     0
 15: #define NTR_PC_AHESS    1
 16: #define NTR_PC_BFGS     2
 17: #define NTR_PC_PETSC    3
 18: #define NTR_PC_TYPES    4

 20: #define BFGS_SCALE_AHESS   0
 21: #define BFGS_SCALE_BFGS    1
 22: #define BFGS_SCALE_TYPES   2

 24: #define NTR_INIT_CONSTANT         0
 25: #define NTR_INIT_DIRECTION        1
 26: #define NTR_INIT_INTERPOLATION    2
 27: #define NTR_INIT_TYPES            3

 29: #define NTR_UPDATE_REDUCTION      0
 30: #define NTR_UPDATE_INTERPOLATION  1
 31: #define NTR_UPDATE_TYPES          2

 33: static const char *NTR_KSP[64] = {  "nash", "stcg", "gltr"};

 35: static const char *NTR_PC[64] = {  "none", "ahess", "bfgs", "petsc"};

 37: static const char *BFGS_SCALE[64] = {  "ahess", "bfgs"};

 39: static const char *NTR_INIT[64] = {  "constant", "direction", "interpolation"};

 41: static const char *NTR_UPDATE[64] = {  "reduction", "interpolation"};

 43: /*  Routine for BFGS preconditioner */
 44: static PetscErrorCode MatLMVMSolveShell(PC pc, Vec xin, Vec xout);

 46: /*
 47:    TaoSolve_NTR - Implements Newton's Method with a trust region approach
 48:    for solving unconstrained minimization problems.

 50:    The basic algorithm is taken from MINPACK-2 (dstrn).

 52:    TaoSolve_NTR computes a local minimizer of a twice differentiable function
 53:    f by applying a trust region variant of Newton's method.  At each stage
 54:    of the algorithm, we use the prconditioned conjugate gradient method to
 55:    determine an approximate minimizer of the quadratic equation

 57:         q(s) = <s, Hs + g>

 59:    subject to the trust region constraint

 61:         || s ||_M <= radius,

 63:    where radius is the trust region radius and M is a symmetric positive
 64:    definite matrix (the preconditioner).  Here g is the gradient and H
 65:    is the Hessian matrix.

 67:    Note:  TaoSolve_NTR MUST use the iterative solver KSPNASH, KSPSTCG,
 68:           or KSPGLTR.  Thus, we set KSPNASH, KSPSTCG, or KSPGLTR in this
 69:           routine regardless of what the user may have previously specified.
 70: */
 73: static PetscErrorCode TaoSolve_NTR(Tao tao)
 74: {
 75:   TAO_NTR            *tr = (TAO_NTR *)tao->data;
 76:   PC                 pc;
 77:   KSPConvergedReason ksp_reason;
 78:   TaoConvergedReason reason;
 79:   PetscReal          fmin, ftrial, prered, actred, kappa, sigma, beta;
 80:   PetscReal          tau, tau_1, tau_2, tau_max, tau_min, max_radius;
 81:   PetscReal          f, gnorm;

 83:   PetscReal          delta;
 84:   PetscReal          norm_d;
 85:   PetscErrorCode     ierr;
 86:   PetscInt           bfgsUpdates = 0;
 87:   PetscInt           needH;

 89:   PetscInt           i_max = 5;
 90:   PetscInt           j_max = 1;
 91:   PetscInt           i, j, N, n, its;

 94:   if (tao->XL || tao->XU || tao->ops->computebounds) {
 95:     PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by ntr algorithm\n");
 96:   }

 98:   tao->trust = tao->trust0;

100:   /* Modify the radius if it is too large or small */
101:   tao->trust = PetscMax(tao->trust, tr->min_radius);
102:   tao->trust = PetscMin(tao->trust, tr->max_radius);


105:   if (NTR_PC_BFGS == tr->pc_type && !tr->M) {
106:     VecGetLocalSize(tao->solution,&n);
107:     VecGetSize(tao->solution,&N);
108:     MatCreateLMVM(((PetscObject)tao)->comm,n,N,&tr->M);
109:     MatLMVMAllocateVectors(tr->M,tao->solution);
110:   }

112:   /* Check convergence criteria */
113:   TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);
114:   TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);
115:   if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
116:   needH = 1;

118:   TaoMonitor(tao, tao->niter, f, gnorm, 0.0, 1.0, &reason);
119:   if (reason != TAO_CONTINUE_ITERATING) return(0);

121:   /* Create vectors for the limited memory preconditioner */
122:   if ((NTR_PC_BFGS == tr->pc_type) &&
123:       (BFGS_SCALE_BFGS != tr->bfgs_scale_type)) {
124:     if (!tr->Diag) {
125:         VecDuplicate(tao->solution, &tr->Diag);
126:     }
127:   }

129:   switch(tr->ksp_type) {
130:   case NTR_KSP_NASH:
131:     KSPSetType(tao->ksp, KSPNASH);
132:     KSPSetFromOptions(tao->ksp);
133:     break;

135:   case NTR_KSP_STCG:
136:     KSPSetType(tao->ksp, KSPSTCG);
137:     KSPSetFromOptions(tao->ksp);
138:     break;

140:   default:
141:     KSPSetType(tao->ksp, KSPGLTR);
142:     KSPSetFromOptions(tao->ksp);
143:     break;
144:   }

146:   /*  Modify the preconditioner to use the bfgs approximation */
147:   KSPGetPC(tao->ksp, &pc);
148:   switch(tr->pc_type) {
149:   case NTR_PC_NONE:
150:     PCSetType(pc, PCNONE);
151:     PCSetFromOptions(pc);
152:     break;

154:   case NTR_PC_AHESS:
155:     PCSetType(pc, PCJACOBI);
156:     PCSetFromOptions(pc);
157:     PCJacobiSetUseAbs(pc,PETSC_TRUE);
158:     break;

160:   case NTR_PC_BFGS:
161:     PCSetType(pc, PCSHELL);
162:     PCSetFromOptions(pc);
163:     PCShellSetName(pc, "bfgs");
164:     PCShellSetContext(pc, tr->M);
165:     PCShellSetApply(pc, MatLMVMSolveShell);
166:     break;

168:   default:
169:     /*  Use the pc method set by pc_type */
170:     break;
171:   }

173:   /*  Initialize trust-region radius */
174:   switch(tr->init_type) {
175:   case NTR_INIT_CONSTANT:
176:     /*  Use the initial radius specified */
177:     break;

179:   case NTR_INIT_INTERPOLATION:
180:     /*  Use the initial radius specified */
181:     max_radius = 0.0;

183:     for (j = 0; j < j_max; ++j) {
184:       fmin = f;
185:       sigma = 0.0;

187:       if (needH) {
188:         TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
189:         needH = 0;
190:       }

192:       for (i = 0; i < i_max; ++i) {

194:         VecCopy(tao->solution, tr->W);
195:         VecAXPY(tr->W, -tao->trust/gnorm, tao->gradient);
196:         TaoComputeObjective(tao, tr->W, &ftrial);

198:         if (PetscIsInfOrNanReal(ftrial)) {
199:           tau = tr->gamma1_i;
200:         }
201:         else {
202:           if (ftrial < fmin) {
203:             fmin = ftrial;
204:             sigma = -tao->trust / gnorm;
205:           }

207:           MatMult(tao->hessian, tao->gradient, tao->stepdirection);
208:           VecDot(tao->gradient, tao->stepdirection, &prered);

210:           prered = tao->trust * (gnorm - 0.5 * tao->trust * prered / (gnorm * gnorm));
211:           actred = f - ftrial;
212:           if ((PetscAbsScalar(actred) <= tr->epsilon) &&
213:               (PetscAbsScalar(prered) <= tr->epsilon)) {
214:             kappa = 1.0;
215:           }
216:           else {
217:             kappa = actred / prered;
218:           }

220:           tau_1 = tr->theta_i * gnorm * tao->trust / (tr->theta_i * gnorm * tao->trust + (1.0 - tr->theta_i) * prered - actred);
221:           tau_2 = tr->theta_i * gnorm * tao->trust / (tr->theta_i * gnorm * tao->trust - (1.0 + tr->theta_i) * prered + actred);
222:           tau_min = PetscMin(tau_1, tau_2);
223:           tau_max = PetscMax(tau_1, tau_2);

225:           if (PetscAbsScalar(kappa - 1.0) <= tr->mu1_i) {
226:             /*  Great agreement */
227:             max_radius = PetscMax(max_radius, tao->trust);

229:             if (tau_max < 1.0) {
230:               tau = tr->gamma3_i;
231:             }
232:             else if (tau_max > tr->gamma4_i) {
233:               tau = tr->gamma4_i;
234:             }
235:             else {
236:               tau = tau_max;
237:             }
238:           }
239:           else if (PetscAbsScalar(kappa - 1.0) <= tr->mu2_i) {
240:             /*  Good agreement */
241:             max_radius = PetscMax(max_radius, tao->trust);

243:             if (tau_max < tr->gamma2_i) {
244:               tau = tr->gamma2_i;
245:             }
246:             else if (tau_max > tr->gamma3_i) {
247:               tau = tr->gamma3_i;
248:             }
249:             else {
250:               tau = tau_max;
251:             }
252:           }
253:           else {
254:             /*  Not good agreement */
255:             if (tau_min > 1.0) {
256:               tau = tr->gamma2_i;
257:             }
258:             else if (tau_max < tr->gamma1_i) {
259:               tau = tr->gamma1_i;
260:             }
261:             else if ((tau_min < tr->gamma1_i) && (tau_max >= 1.0)) {
262:               tau = tr->gamma1_i;
263:             }
264:             else if ((tau_1 >= tr->gamma1_i) && (tau_1 < 1.0) &&
265:                      ((tau_2 < tr->gamma1_i) || (tau_2 >= 1.0))) {
266:               tau = tau_1;
267:             }
268:             else if ((tau_2 >= tr->gamma1_i) && (tau_2 < 1.0) &&
269:                      ((tau_1 < tr->gamma1_i) || (tau_2 >= 1.0))) {
270:               tau = tau_2;
271:             }
272:             else {
273:               tau = tau_max;
274:             }
275:           }
276:         }
277:         tao->trust = tau * tao->trust;
278:       }

280:       if (fmin < f) {
281:         f = fmin;
282:         VecAXPY(tao->solution, sigma, tao->gradient);
283:         TaoComputeGradient(tao,tao->solution, tao->gradient);

285:         TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);

287:         if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
288:         needH = 1;

290:         TaoMonitor(tao, tao->niter, f, gnorm, 0.0, 1.0, &reason);
291:         if (reason != TAO_CONTINUE_ITERATING) {
292:           return(0);
293:         }
294:       }
295:     }
296:     tao->trust = PetscMax(tao->trust, max_radius);

298:     /*  Modify the radius if it is too large or small */
299:     tao->trust = PetscMax(tao->trust, tr->min_radius);
300:     tao->trust = PetscMin(tao->trust, tr->max_radius);
301:     break;

303:   default:
304:     /*  Norm of the first direction will initialize radius */
305:     tao->trust = 0.0;
306:     break;
307:   }

309:   /* Set initial scaling for the BFGS preconditioner
310:      This step is done after computing the initial trust-region radius
311:      since the function value may have decreased */
312:   if (NTR_PC_BFGS == tr->pc_type) {
313:     if (f != 0.0) {
314:       delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
315:     }
316:     else {
317:       delta = 2.0 / (gnorm*gnorm);
318:     }
319:     MatLMVMSetDelta(tr->M,delta);
320:   }

322:   /* Have not converged; continue with Newton method */
323:   while (reason == TAO_CONTINUE_ITERATING) {
324:     ++tao->niter;
325:     tao->ksp_its=0;
326:     /* Compute the Hessian */
327:     if (needH) {
328:       TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
329:       needH = 0;
330:     }

332:     if (NTR_PC_BFGS == tr->pc_type) {
333:       if (BFGS_SCALE_AHESS == tr->bfgs_scale_type) {
334:         /* Obtain diagonal for the bfgs preconditioner */
335:         MatGetDiagonal(tao->hessian, tr->Diag);
336:         VecAbs(tr->Diag);
337:         VecReciprocal(tr->Diag);
338:         MatLMVMSetScale(tr->M,tr->Diag);
339:       }

341:       /* Update the limited memory preconditioner */
342:       MatLMVMUpdate(tr->M, tao->solution, tao->gradient);
343:       ++bfgsUpdates;
344:     }

346:     while (reason == TAO_CONTINUE_ITERATING) {
347:       KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre);

349:       /* Solve the trust region subproblem */
350:       if (NTR_KSP_NASH == tr->ksp_type) {
351:         KSPNASHSetRadius(tao->ksp,tao->trust);
352:         KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
353:         KSPGetIterationNumber(tao->ksp,&its);
354:         tao->ksp_its+=its;
355:         tao->ksp_tot_its+=its;
356:         KSPNASHGetNormD(tao->ksp, &norm_d);
357:       } else if (NTR_KSP_STCG == tr->ksp_type) {
358:         KSPSTCGSetRadius(tao->ksp,tao->trust);
359:         KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
360:         KSPGetIterationNumber(tao->ksp,&its);
361:         tao->ksp_its+=its;
362:         tao->ksp_tot_its+=its;
363:         KSPSTCGGetNormD(tao->ksp, &norm_d);
364:       } else { /* NTR_KSP_GLTR */
365:         KSPGLTRSetRadius(tao->ksp,tao->trust);
366:         KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
367:         KSPGetIterationNumber(tao->ksp,&its);
368:         tao->ksp_its+=its;
369:         tao->ksp_tot_its+=its;
370:         KSPGLTRGetNormD(tao->ksp, &norm_d);
371:       }

373:       if (0.0 == tao->trust) {
374:         /* Radius was uninitialized; use the norm of the direction */
375:         if (norm_d > 0.0) {
376:           tao->trust = norm_d;

378:           /* Modify the radius if it is too large or small */
379:           tao->trust = PetscMax(tao->trust, tr->min_radius);
380:           tao->trust = PetscMin(tao->trust, tr->max_radius);
381:         }
382:         else {
383:           /* The direction was bad; set radius to default value and re-solve
384:              the trust-region subproblem to get a direction */
385:           tao->trust = tao->trust0;

387:           /* Modify the radius if it is too large or small */
388:           tao->trust = PetscMax(tao->trust, tr->min_radius);
389:           tao->trust = PetscMin(tao->trust, tr->max_radius);

391:           if (NTR_KSP_NASH == tr->ksp_type) {
392:             KSPNASHSetRadius(tao->ksp,tao->trust);
393:             KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
394:             KSPGetIterationNumber(tao->ksp,&its);
395:             tao->ksp_its+=its;
396:             tao->ksp_tot_its+=its;
397:             KSPNASHGetNormD(tao->ksp, &norm_d);
398:           } else if (NTR_KSP_STCG == tr->ksp_type) {
399:             KSPSTCGSetRadius(tao->ksp,tao->trust);
400:             KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
401:             KSPGetIterationNumber(tao->ksp,&its);
402:             tao->ksp_its+=its;
403:             tao->ksp_tot_its+=its;
404:             KSPSTCGGetNormD(tao->ksp, &norm_d);
405:           } else { /* NTR_KSP_GLTR */
406:             KSPGLTRSetRadius(tao->ksp,tao->trust);
407:             KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
408:             KSPGetIterationNumber(tao->ksp,&its);
409:             tao->ksp_its+=its;
410:             tao->ksp_tot_its+=its;
411:             KSPGLTRGetNormD(tao->ksp, &norm_d);
412:           }

414:           if (norm_d == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
415:         }
416:       }
417:       VecScale(tao->stepdirection, -1.0);
418:       KSPGetConvergedReason(tao->ksp, &ksp_reason);
419:       if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) &&
420:           (NTR_PC_BFGS == tr->pc_type) && (bfgsUpdates > 1)) {
421:         /* Preconditioner is numerically indefinite; reset the
422:            approximate if using BFGS preconditioning. */

424:         if (f != 0.0) {
425:           delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
426:         }
427:         else {
428:           delta = 2.0 / (gnorm*gnorm);
429:         }
430:         MatLMVMSetDelta(tr->M, delta);
431:         MatLMVMReset(tr->M);
432:         MatLMVMUpdate(tr->M, tao->solution, tao->gradient);
433:         bfgsUpdates = 1;
434:       }

436:       if (NTR_UPDATE_REDUCTION == tr->update_type) {
437:         /* Get predicted reduction */
438:         if (NTR_KSP_NASH == tr->ksp_type) {
439:           KSPNASHGetObjFcn(tao->ksp,&prered);
440:         } else if (NTR_KSP_STCG == tr->ksp_type) {
441:           KSPSTCGGetObjFcn(tao->ksp,&prered);
442:         } else { /* gltr */
443:           KSPGLTRGetObjFcn(tao->ksp,&prered);
444:         }

446:         if (prered >= 0.0) {
447:           /* The predicted reduction has the wrong sign.  This cannot
448:              happen in infinite precision arithmetic.  Step should
449:              be rejected! */
450:           tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
451:         }
452:         else {
453:           /* Compute trial step and function value */
454:           VecCopy(tao->solution,tr->W);
455:           VecAXPY(tr->W, 1.0, tao->stepdirection);
456:           TaoComputeObjective(tao, tr->W, &ftrial);

458:           if (PetscIsInfOrNanReal(ftrial)) {
459:             tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
460:           } else {
461:             /* Compute and actual reduction */
462:             actred = f - ftrial;
463:             prered = -prered;
464:             if ((PetscAbsScalar(actred) <= tr->epsilon) &&
465:                 (PetscAbsScalar(prered) <= tr->epsilon)) {
466:               kappa = 1.0;
467:             }
468:             else {
469:               kappa = actred / prered;
470:             }

472:             /* Accept or reject the step and update radius */
473:             if (kappa < tr->eta1) {
474:               /* Reject the step */
475:               tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
476:             }
477:             else {
478:               /* Accept the step */
479:               if (kappa < tr->eta2) {
480:                 /* Marginal bad step */
481:                 tao->trust = tr->alpha2 * PetscMin(tao->trust, norm_d);
482:               }
483:               else if (kappa < tr->eta3) {
484:                 /* Reasonable step */
485:                 tao->trust = tr->alpha3 * tao->trust;
486:               }
487:               else if (kappa < tr->eta4) {
488:                 /* Good step */
489:                 tao->trust = PetscMax(tr->alpha4 * norm_d, tao->trust);
490:               }
491:               else {
492:                 /* Very good step */
493:                 tao->trust = PetscMax(tr->alpha5 * norm_d, tao->trust);
494:               }
495:               break;
496:             }
497:           }
498:         }
499:       }
500:       else {
501:         /* Get predicted reduction */
502:         if (NTR_KSP_NASH == tr->ksp_type) {
503:           KSPNASHGetObjFcn(tao->ksp,&prered);
504:         } else if (NTR_KSP_STCG == tr->ksp_type) {
505:           KSPSTCGGetObjFcn(tao->ksp,&prered);
506:         } else { /* gltr */
507:           KSPGLTRGetObjFcn(tao->ksp,&prered);
508:         }

510:         if (prered >= 0.0) {
511:           /* The predicted reduction has the wrong sign.  This cannot
512:              happen in infinite precision arithmetic.  Step should
513:              be rejected! */
514:           tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
515:         }
516:         else {
517:           VecCopy(tao->solution, tr->W);
518:           VecAXPY(tr->W, 1.0, tao->stepdirection);
519:           TaoComputeObjective(tao, tr->W, &ftrial);
520:           if (PetscIsInfOrNanReal(ftrial)) {
521:             tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
522:           }
523:           else {
524:             VecDot(tao->gradient, tao->stepdirection, &beta);
525:             actred = f - ftrial;
526:             prered = -prered;
527:             if ((PetscAbsScalar(actred) <= tr->epsilon) &&
528:                 (PetscAbsScalar(prered) <= tr->epsilon)) {
529:               kappa = 1.0;
530:             }
531:             else {
532:               kappa = actred / prered;
533:             }

535:             tau_1 = tr->theta * beta / (tr->theta * beta - (1.0 - tr->theta) * prered + actred);
536:             tau_2 = tr->theta * beta / (tr->theta * beta + (1.0 + tr->theta) * prered - actred);
537:             tau_min = PetscMin(tau_1, tau_2);
538:             tau_max = PetscMax(tau_1, tau_2);

540:             if (kappa >= 1.0 - tr->mu1) {
541:               /* Great agreement; accept step and update radius */
542:               if (tau_max < 1.0) {
543:                 tao->trust = PetscMax(tao->trust, tr->gamma3 * norm_d);
544:               }
545:               else if (tau_max > tr->gamma4) {
546:                 tao->trust = PetscMax(tao->trust, tr->gamma4 * norm_d);
547:               }
548:               else {
549:                 tao->trust = PetscMax(tao->trust, tau_max * norm_d);
550:               }
551:               break;
552:             }
553:             else if (kappa >= 1.0 - tr->mu2) {
554:               /* Good agreement */

556:               if (tau_max < tr->gamma2) {
557:                 tao->trust = tr->gamma2 * PetscMin(tao->trust, norm_d);
558:               }
559:               else if (tau_max > tr->gamma3) {
560:                 tao->trust = PetscMax(tao->trust, tr->gamma3 * norm_d);
561:               }
562:               else if (tau_max < 1.0) {
563:                 tao->trust = tau_max * PetscMin(tao->trust, norm_d);
564:               }
565:               else {
566:                 tao->trust = PetscMax(tao->trust, tau_max * norm_d);
567:               }
568:               break;
569:             }
570:             else {
571:               /* Not good agreement */
572:               if (tau_min > 1.0) {
573:                 tao->trust = tr->gamma2 * PetscMin(tao->trust, norm_d);
574:               }
575:               else if (tau_max < tr->gamma1) {
576:                 tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
577:               }
578:               else if ((tau_min < tr->gamma1) && (tau_max >= 1.0)) {
579:                 tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
580:               }
581:               else if ((tau_1 >= tr->gamma1) && (tau_1 < 1.0) &&
582:                        ((tau_2 < tr->gamma1) || (tau_2 >= 1.0))) {
583:                 tao->trust = tau_1 * PetscMin(tao->trust, norm_d);
584:               }
585:               else if ((tau_2 >= tr->gamma1) && (tau_2 < 1.0) &&
586:                        ((tau_1 < tr->gamma1) || (tau_2 >= 1.0))) {
587:                 tao->trust = tau_2 * PetscMin(tao->trust, norm_d);
588:               }
589:               else {
590:                 tao->trust = tau_max * PetscMin(tao->trust, norm_d);
591:               }
592:             }
593:           }
594:         }
595:       }

597:       /* The step computed was not good and the radius was decreased.
598:          Monitor the radius to terminate. */
599:       TaoMonitor(tao, tao->niter, f, gnorm, 0.0, tao->trust, &reason);
600:     }

602:     /* The radius may have been increased; modify if it is too large */
603:     tao->trust = PetscMin(tao->trust, tr->max_radius);

605:     if (reason == TAO_CONTINUE_ITERATING) {
606:       VecCopy(tr->W, tao->solution);
607:       f = ftrial;
608:       TaoComputeGradient(tao, tao->solution, tao->gradient);
609:       TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);
610:       if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
611:       needH = 1;
612:       TaoMonitor(tao, tao->niter, f, gnorm, 0.0, tao->trust, &reason);
613:     }
614:   }
615:   return(0);
616: }

618: /*------------------------------------------------------------*/
621: static PetscErrorCode TaoSetUp_NTR(Tao tao)
622: {
623:   TAO_NTR *tr = (TAO_NTR *)tao->data;


628:   if (!tao->gradient) {VecDuplicate(tao->solution, &tao->gradient);}
629:   if (!tao->stepdirection) {VecDuplicate(tao->solution, &tao->stepdirection);}
630:   if (!tr->W) {VecDuplicate(tao->solution, &tr->W);}

632:   tr->Diag = 0;
633:   tr->M = 0;


636:   return(0);
637: }

639: /*------------------------------------------------------------*/
642: static PetscErrorCode TaoDestroy_NTR(Tao tao)
643: {
644:   TAO_NTR        *tr = (TAO_NTR *)tao->data;

648:   if (tao->setupcalled) {
649:     VecDestroy(&tr->W);
650:   }
651:   MatDestroy(&tr->M);
652:   VecDestroy(&tr->Diag);
653:   PetscFree(tao->data);
654:   return(0);
655: }

657: /*------------------------------------------------------------*/
660: static PetscErrorCode TaoSetFromOptions_NTR(PetscOptionItems *PetscOptionsObject,Tao tao)
661: {
662:   TAO_NTR        *tr = (TAO_NTR *)tao->data;

666:   PetscOptionsHead(PetscOptionsObject,"Newton trust region method for unconstrained optimization");
667:   PetscOptionsEList("-tao_ntr_ksp_type", "ksp type", "", NTR_KSP, NTR_KSP_TYPES, NTR_KSP[tr->ksp_type], &tr->ksp_type,NULL);
668:   PetscOptionsEList("-tao_ntr_pc_type", "pc type", "", NTR_PC, NTR_PC_TYPES, NTR_PC[tr->pc_type], &tr->pc_type,NULL);
669:   PetscOptionsEList("-tao_ntr_bfgs_scale_type", "bfgs scale type", "", BFGS_SCALE, BFGS_SCALE_TYPES, BFGS_SCALE[tr->bfgs_scale_type], &tr->bfgs_scale_type,NULL);
670:   PetscOptionsEList("-tao_ntr_init_type", "tao->trust initialization type", "", NTR_INIT, NTR_INIT_TYPES, NTR_INIT[tr->init_type], &tr->init_type,NULL);
671:   PetscOptionsEList("-tao_ntr_update_type", "radius update type", "", NTR_UPDATE, NTR_UPDATE_TYPES, NTR_UPDATE[tr->update_type], &tr->update_type,NULL);
672:   PetscOptionsReal("-tao_ntr_eta1", "step is unsuccessful if actual reduction < eta1 * predicted reduction", "", tr->eta1, &tr->eta1,NULL);
673:   PetscOptionsReal("-tao_ntr_eta2", "", "", tr->eta2, &tr->eta2,NULL);
674:   PetscOptionsReal("-tao_ntr_eta3", "", "", tr->eta3, &tr->eta3,NULL);
675:   PetscOptionsReal("-tao_ntr_eta4", "", "", tr->eta4, &tr->eta4,NULL);
676:   PetscOptionsReal("-tao_ntr_alpha1", "", "", tr->alpha1, &tr->alpha1,NULL);
677:   PetscOptionsReal("-tao_ntr_alpha2", "", "", tr->alpha2, &tr->alpha2,NULL);
678:   PetscOptionsReal("-tao_ntr_alpha3", "", "", tr->alpha3, &tr->alpha3,NULL);
679:   PetscOptionsReal("-tao_ntr_alpha4", "", "", tr->alpha4, &tr->alpha4,NULL);
680:   PetscOptionsReal("-tao_ntr_alpha5", "", "", tr->alpha5, &tr->alpha5,NULL);
681:   PetscOptionsReal("-tao_ntr_mu1", "", "", tr->mu1, &tr->mu1,NULL);
682:   PetscOptionsReal("-tao_ntr_mu2", "", "", tr->mu2, &tr->mu2,NULL);
683:   PetscOptionsReal("-tao_ntr_gamma1", "", "", tr->gamma1, &tr->gamma1,NULL);
684:   PetscOptionsReal("-tao_ntr_gamma2", "", "", tr->gamma2, &tr->gamma2,NULL);
685:   PetscOptionsReal("-tao_ntr_gamma3", "", "", tr->gamma3, &tr->gamma3,NULL);
686:   PetscOptionsReal("-tao_ntr_gamma4", "", "", tr->gamma4, &tr->gamma4,NULL);
687:   PetscOptionsReal("-tao_ntr_theta", "", "", tr->theta, &tr->theta,NULL);
688:   PetscOptionsReal("-tao_ntr_mu1_i", "", "", tr->mu1_i, &tr->mu1_i,NULL);
689:   PetscOptionsReal("-tao_ntr_mu2_i", "", "", tr->mu2_i, &tr->mu2_i,NULL);
690:   PetscOptionsReal("-tao_ntr_gamma1_i", "", "", tr->gamma1_i, &tr->gamma1_i,NULL);
691:   PetscOptionsReal("-tao_ntr_gamma2_i", "", "", tr->gamma2_i, &tr->gamma2_i,NULL);
692:   PetscOptionsReal("-tao_ntr_gamma3_i", "", "", tr->gamma3_i, &tr->gamma3_i,NULL);
693:   PetscOptionsReal("-tao_ntr_gamma4_i", "", "", tr->gamma4_i, &tr->gamma4_i,NULL);
694:   PetscOptionsReal("-tao_ntr_theta_i", "", "", tr->theta_i, &tr->theta_i,NULL);
695:   PetscOptionsReal("-tao_ntr_min_radius", "lower bound on initial trust-region radius", "", tr->min_radius, &tr->min_radius,NULL);
696:   PetscOptionsReal("-tao_ntr_max_radius", "upper bound on trust-region radius", "", tr->max_radius, &tr->max_radius,NULL);
697:   PetscOptionsReal("-tao_ntr_epsilon", "tolerance used when computing actual and predicted reduction", "", tr->epsilon, &tr->epsilon,NULL);
698:   PetscOptionsTail();
699:   KSPSetFromOptions(tao->ksp);
700:   return(0);
701: }

703: /*------------------------------------------------------------*/
706: static PetscErrorCode TaoView_NTR(Tao tao, PetscViewer viewer)
707: {
708:   TAO_NTR        *tr = (TAO_NTR *)tao->data;
710:   PetscInt       nrejects;
711:   PetscBool      isascii;

714:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
715:   if (isascii) {
716:     PetscViewerASCIIPushTab(viewer);
717:     if (NTR_PC_BFGS == tr->pc_type && tr->M) {
718:       MatLMVMGetRejects(tr->M, &nrejects);
719:       PetscViewerASCIIPrintf(viewer, "Rejected matrix updates: %D\n", nrejects);
720:     }
721:     PetscViewerASCIIPopTab(viewer);
722:   }
723:   return(0);
724: }

726: /*------------------------------------------------------------*/
727: /*MC
728:   TAONTR - Newton's method with trust region for unconstrained minimization.
729:   At each iteration, the Newton trust region method solves the system.
730:   NTR expects a KSP solver with a trust region radius.
731:             min_d  .5 dT Hk d + gkT d,  s.t.   ||d|| < Delta_k

733:   Options Database Keys:
734: + -tao_ntr_ksp_type - "nash","stcg","gltr"
735: . -tao_ntr_pc_type - "none","ahess","bfgs","petsc"
736: . -tao_ntr_bfgs_scale_type - type of scaling with bfgs pc, "ahess" or "bfgs"
737: . -tao_ntr_init_type - "constant","direction","interpolation"
738: . -tao_ntr_update_type - "reduction","interpolation"
739: . -tao_ntr_min_radius - lower bound on trust region radius
740: . -tao_ntr_max_radius - upper bound on trust region radius
741: . -tao_ntr_epsilon - tolerance for accepting actual / predicted reduction
742: . -tao_ntr_mu1_i - mu1 interpolation init factor
743: . -tao_ntr_mu2_i - mu2 interpolation init factor
744: . -tao_ntr_gamma1_i - gamma1 interpolation init factor
745: . -tao_ntr_gamma2_i - gamma2 interpolation init factor
746: . -tao_ntr_gamma3_i - gamma3 interpolation init factor
747: . -tao_ntr_gamma4_i - gamma4 interpolation init factor
748: . -tao_ntr_theta_i - thetha1 interpolation init factor
749: . -tao_ntr_eta1 - eta1 reduction update factor
750: . -tao_ntr_eta2 - eta2 reduction update factor
751: . -tao_ntr_eta3 - eta3 reduction update factor
752: . -tao_ntr_eta4 - eta4 reduction update factor
753: . -tao_ntr_alpha1 - alpha1 reduction update factor
754: . -tao_ntr_alpha2 - alpha2 reduction update factor
755: . -tao_ntr_alpha3 - alpha3 reduction update factor
756: . -tao_ntr_alpha4 - alpha4 reduction update factor
757: . -tao_ntr_alpha4 - alpha4 reduction update factor
758: . -tao_ntr_mu1 - mu1 interpolation update
759: . -tao_ntr_mu2 - mu2 interpolation update
760: . -tao_ntr_gamma1 - gamma1 interpolcation update
761: . -tao_ntr_gamma2 - gamma2 interpolcation update
762: . -tao_ntr_gamma3 - gamma3 interpolcation update
763: . -tao_ntr_gamma4 - gamma4 interpolation update
764: - -tao_ntr_theta - theta interpolation update

766:   Level: beginner
767: M*/

771: PETSC_EXTERN PetscErrorCode TaoCreate_NTR(Tao tao)
772: {
773:   TAO_NTR *tr;


778:   PetscNewLog(tao,&tr);

780:   tao->ops->setup = TaoSetUp_NTR;
781:   tao->ops->solve = TaoSolve_NTR;
782:   tao->ops->view = TaoView_NTR;
783:   tao->ops->setfromoptions = TaoSetFromOptions_NTR;
784:   tao->ops->destroy = TaoDestroy_NTR;

786:   /* Override default settings (unless already changed) */
787:   if (!tao->max_it_changed) tao->max_it = 50;
788:   if (!tao->trust0_changed) tao->trust0 = 100.0;
789:   tao->data = (void*)tr;

791:   /*  Standard trust region update parameters */
792:   tr->eta1 = 1.0e-4;
793:   tr->eta2 = 0.25;
794:   tr->eta3 = 0.50;
795:   tr->eta4 = 0.90;

797:   tr->alpha1 = 0.25;
798:   tr->alpha2 = 0.50;
799:   tr->alpha3 = 1.00;
800:   tr->alpha4 = 2.00;
801:   tr->alpha5 = 4.00;

803:   /*  Interpolation parameters */
804:   tr->mu1_i = 0.35;
805:   tr->mu2_i = 0.50;

807:   tr->gamma1_i = 0.0625;
808:   tr->gamma2_i = 0.50;
809:   tr->gamma3_i = 2.00;
810:   tr->gamma4_i = 5.00;

812:   tr->theta_i = 0.25;

814:   /*  Interpolation trust region update parameters */
815:   tr->mu1 = 0.10;
816:   tr->mu2 = 0.50;

818:   tr->gamma1 = 0.25;
819:   tr->gamma2 = 0.50;
820:   tr->gamma3 = 2.00;
821:   tr->gamma4 = 4.00;

823:   tr->theta = 0.05;

825:   tr->min_radius = 1.0e-10;
826:   tr->max_radius = 1.0e10;
827:   tr->epsilon = 1.0e-6;

829:   tr->ksp_type        = NTR_KSP_STCG;
830:   tr->pc_type         = NTR_PC_BFGS;
831:   tr->bfgs_scale_type = BFGS_SCALE_AHESS;
832:   tr->init_type       = NTR_INIT_INTERPOLATION;
833:   tr->update_type     = NTR_UPDATE_REDUCTION;


836:   /* Set linear solver to default for trust region */
837:   KSPCreate(((PetscObject)tao)->comm, &tao->ksp);
838:   KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
839:   return(0);
840: }


845: static PetscErrorCode MatLMVMSolveShell(PC pc, Vec b, Vec x)
846: {
848:     Mat M;
853:     PCShellGetContext(pc,(void**)&M);
854:     MatLMVMSolve(M, b, x);
855:     return(0);
856: }