Date: 2015-10-02T22:30:22+00:00

Actual source code: ntr.c
petsc-3.6.2 2015-10-02
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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:   VecNorm(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:         VecNorm(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:       VecNorm(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(PetscOptions *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: #if defined(PETSC_USE_REAL_SINGLE)
    790:   if (!tao->fatol_changed) tao->fatol = 1.0e-5;
    791:   if (!tao->frtol_changed) tao->frtol = 1.0e-5;
    792: #else
    793:   if (!tao->fatol_changed) tao->fatol = 1.0e-10;
    794:   if (!tao->frtol_changed) tao->frtol = 1.0e-10;
    795: #endif
    796:   tao->data = (void*)tr;

    798:   /*  Standard trust region update parameters */
    799:   tr->eta1 = 1.0e-4;
    800:   tr->eta2 = 0.25;
    801:   tr->eta3 = 0.50;
    802:   tr->eta4 = 0.90;

    804:   tr->alpha1 = 0.25;
    805:   tr->alpha2 = 0.50;
    806:   tr->alpha3 = 1.00;
    807:   tr->alpha4 = 2.00;
    808:   tr->alpha5 = 4.00;

    810:   /*  Interpolation parameters */
    811:   tr->mu1_i = 0.35;
    812:   tr->mu2_i = 0.50;

    814:   tr->gamma1_i = 0.0625;
    815:   tr->gamma2_i = 0.50;
    816:   tr->gamma3_i = 2.00;
    817:   tr->gamma4_i = 5.00;

    819:   tr->theta_i = 0.25;

    821:   /*  Interpolation trust region update parameters */
    822:   tr->mu1 = 0.10;
    823:   tr->mu2 = 0.50;

    825:   tr->gamma1 = 0.25;
    826:   tr->gamma2 = 0.50;
    827:   tr->gamma3 = 2.00;
    828:   tr->gamma4 = 4.00;

    830:   tr->theta = 0.05;

    832:   tr->min_radius = 1.0e-10;
    833:   tr->max_radius = 1.0e10;
    834:   tr->epsilon = 1.0e-6;

    836:   tr->ksp_type        = NTR_KSP_STCG;
    837:   tr->pc_type         = NTR_PC_BFGS;
    838:   tr->bfgs_scale_type = BFGS_SCALE_AHESS;
    839:   tr->init_type       = NTR_INIT_INTERPOLATION;
    840:   tr->update_type     = NTR_UPDATE_REDUCTION;

    843:   /* Set linear solver to default for trust region */
    844:   KSPCreate(((PetscObject)tao)->comm, &tao->ksp);
    845:   KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
    846:   return(0);
    847: }

    852: static PetscErrorCode MatLMVMSolveShell(PC pc, Vec b, Vec x)
    853: {
    855:     Mat M;
    860:     PCShellGetContext(pc,(void**)&M);
    861:     MatLMVMSolve(M, b, x);
    862:     return(0);
    863: }