Date: 2015-10-02T22:30:11+00:00

Actual source code: lmvm.c
petsc-3.6.2 2015-10-02
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      1: #include <petsctaolinesearch.h>
      2: #include <../src/tao/matrix/lmvmmat.h>
      3: #include <../src/tao/unconstrained/impls/lmvm/lmvm.h>

      5: #define LMVM_BFGS                0
      6: #define LMVM_SCALED_GRADIENT     1
      7: #define LMVM_GRADIENT            2

     11: static PetscErrorCode TaoSolve_LMVM(Tao tao)
     12: {
     13:   TAO_LMVM                     *lmP = (TAO_LMVM *)tao->data;
     14:   PetscReal                    f, fold, gdx, gnorm;
     15:   PetscReal                    step = 1.0;
     16:   PetscReal                    delta;
     17:   PetscErrorCode               ierr;
     18:   PetscInt                     stepType;
     19:   TaoConvergedReason           reason = TAO_CONTINUE_ITERATING;
     20:   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

     24:   if (tao->XL || tao->XU || tao->ops->computebounds) {
     25:     PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by lmvm algorithm\n");
     26:   }

     28:   /*  Check convergence criteria */
     29:   TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);
     30:   VecNorm(tao->gradient,NORM_2,&gnorm);
     31:   if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");

     33:   TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step, &reason);
     34:   if (reason != TAO_CONTINUE_ITERATING) return(0);

     36:   /*  Set initial scaling for the function */
     37:   if (f != 0.0) {
     38:     delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
     39:   } else {
     40:     delta = 2.0 / (gnorm*gnorm);
     41:   }
     42:   MatLMVMSetDelta(lmP->M,delta);

     44:   /*  Set counter for gradient/reset steps */
     45:   lmP->bfgs = 0;
     46:   lmP->sgrad = 0;
     47:   lmP->grad = 0;

     49:   /*  Have not converged; continue with Newton method */
     50:   while (reason == TAO_CONTINUE_ITERATING) {
     51:     /*  Compute direction */
     52:     MatLMVMUpdate(lmP->M,tao->solution,tao->gradient);
     53:     MatLMVMSolve(lmP->M, tao->gradient, lmP->D);
     54:     ++lmP->bfgs;

     56:     /*  Check for success (descent direction) */
     57:     VecDot(lmP->D, tao->gradient, &gdx);
     58:     if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
     59:       /* Step is not descent or direction produced not a number
     60:          We can assert bfgsUpdates > 1 in this case because
     61:          the first solve produces the scaled gradient direction,
     62:          which is guaranteed to be descent

     64:          Use steepest descent direction (scaled)
     65:       */

     67:       ++lmP->grad;

     69:       if (f != 0.0) {
     70:         delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
     71:       } else {
     72:         delta = 2.0 / (gnorm*gnorm);
     73:       }
     74:       MatLMVMSetDelta(lmP->M, delta);
     75:       MatLMVMReset(lmP->M);
     76:       MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);
     77:       MatLMVMSolve(lmP->M,tao->gradient, lmP->D);

     79:       /* On a reset, the direction cannot be not a number; it is a
     80:          scaled gradient step.  No need to check for this condition. */

     82:       lmP->bfgs = 1;
     83:       ++lmP->sgrad;
     84:       stepType = LMVM_SCALED_GRADIENT;
     85:     } else {
     86:       if (1 == lmP->bfgs) {
     87:         /*  The first BFGS direction is always the scaled gradient */
     88:         ++lmP->sgrad;
     89:         stepType = LMVM_SCALED_GRADIENT;
     90:       } else {
     91:         ++lmP->bfgs;
     92:         stepType = LMVM_BFGS;
     93:       }
     94:     }
     95:     VecScale(lmP->D, -1.0);

     97:     /*  Perform the linesearch */
     98:     fold = f;
     99:     VecCopy(tao->solution, lmP->Xold);
    100:     VecCopy(tao->gradient, lmP->Gold);

    102:     TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step,&ls_status);
    103:     TaoAddLineSearchCounts(tao);

    105:     while (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER && (stepType != LMVM_GRADIENT)) {
    106:       /*  Linesearch failed */
    107:       /*  Reset factors and use scaled gradient step */
    108:       f = fold;
    109:       VecCopy(lmP->Xold, tao->solution);
    110:       VecCopy(lmP->Gold, tao->gradient);

    112:       switch(stepType) {
    113:       case LMVM_BFGS:
    114:         /*  Failed to obtain acceptable iterate with BFGS step */
    115:         /*  Attempt to use the scaled gradient direction */

    117:         if (f != 0.0) {
    118:           delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
    119:         } else {
    120:           delta = 2.0 / (gnorm*gnorm);
    121:         }
    122:         MatLMVMSetDelta(lmP->M, delta);
    123:         MatLMVMReset(lmP->M);
    124:         MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);
    125:         MatLMVMSolve(lmP->M, tao->gradient, lmP->D);

    127:         /* On a reset, the direction cannot be not a number; it is a
    128:            scaled gradient step.  No need to check for this condition. */

    130:         lmP->bfgs = 1;
    131:         ++lmP->sgrad;
    132:         stepType = LMVM_SCALED_GRADIENT;
    133:         break;

    135:       case LMVM_SCALED_GRADIENT:
    136:         /* The scaled gradient step did not produce a new iterate;
    137:            attempt to use the gradient direction.
    138:            Need to make sure we are not using a different diagonal scaling */
    139:         MatLMVMSetDelta(lmP->M, 1.0);
    140:         MatLMVMReset(lmP->M);
    141:         MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);
    142:         MatLMVMSolve(lmP->M, tao->gradient, lmP->D);

    144:         lmP->bfgs = 1;
    145:         ++lmP->grad;
    146:         stepType = LMVM_GRADIENT;
    147:         break;
    148:       }
    149:       VecScale(lmP->D, -1.0);

    151:       /*  Perform the linesearch */
    152:       TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status);
    153:       TaoAddLineSearchCounts(tao);
    154:     }

    156:     if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
    157:       /*  Failed to find an improving point */
    158:       f = fold;
    159:       VecCopy(lmP->Xold, tao->solution);
    160:       VecCopy(lmP->Gold, tao->gradient);
    161:       step = 0.0;
    162:       reason = TAO_DIVERGED_LS_FAILURE;
    163:       tao->reason = TAO_DIVERGED_LS_FAILURE;
    164:     }
    165:     /*  Check for termination */
    166:     VecNorm(tao->gradient, NORM_2, &gnorm);
    167:     tao->niter++;
    168:     TaoMonitor(tao,tao->niter,f,gnorm,0.0,step,&reason);
    169:   }
    170:   return(0);
    171: }

    175: static PetscErrorCode TaoSetUp_LMVM(Tao tao)
    176: {
    177:   TAO_LMVM       *lmP = (TAO_LMVM *)tao->data;
    178:   PetscInt       n,N;

    182:   /* Existence of tao->solution checked in TaoSetUp() */
    183:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
    184:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
    185:   if (!lmP->D) {VecDuplicate(tao->solution,&lmP->D);  }
    186:   if (!lmP->Xold) {VecDuplicate(tao->solution,&lmP->Xold);  }
    187:   if (!lmP->Gold) {VecDuplicate(tao->solution,&lmP->Gold);  }

    189:   /*  Create matrix for the limited memory approximation */
    190:   VecGetLocalSize(tao->solution,&n);
    191:   VecGetSize(tao->solution,&N);
    192:   MatCreateLMVM(((PetscObject)tao)->comm,n,N,&lmP->M);
    193:   MatLMVMAllocateVectors(lmP->M,tao->solution);
    194:   return(0);
    195: }

    197: /* ---------------------------------------------------------- */
    200: static PetscErrorCode TaoDestroy_LMVM(Tao tao)
    201: {
    202:   TAO_LMVM       *lmP = (TAO_LMVM *)tao->data;

    206:   if (tao->setupcalled) {
    207:     VecDestroy(&lmP->Xold);
    208:     VecDestroy(&lmP->Gold);
    209:     VecDestroy(&lmP->D);
    210:     MatDestroy(&lmP->M);
    211:   }
    212:   PetscFree(tao->data);
    213:   return(0);
    214: }

    216: /*------------------------------------------------------------*/
    219: static PetscErrorCode TaoSetFromOptions_LMVM(PetscOptions *PetscOptionsObject,Tao tao)
    220: {

    224:   PetscOptionsHead(PetscOptionsObject,"Limited-memory variable-metric method for unconstrained optimization");
    225:   TaoLineSearchSetFromOptions(tao->linesearch);
    226:   PetscOptionsTail();
    227:   return(0);
    228: }

    230: /*------------------------------------------------------------*/
    233: static PetscErrorCode TaoView_LMVM(Tao tao, PetscViewer viewer)
    234: {
    235:   TAO_LMVM       *lm = (TAO_LMVM *)tao->data;
    236:   PetscBool      isascii;

    240:   PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);
    241:   if (isascii) {
    242:     PetscViewerASCIIPushTab(viewer);
    243:     PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", lm->bfgs);
    244:     PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", lm->sgrad);
    245:     PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", lm->grad);
    246:     PetscViewerASCIIPopTab(viewer);
    247:   }
    248:   return(0);
    249: }

    251: /* ---------------------------------------------------------- */

    253: /*MC
    254:      TAOLMVM - Limited Memory Variable Metric method is a quasi-Newton
    255:      optimization solver for unconstrained minimization. It solves
    256:      the Newton step
    257:               Hkdk = - gk

    259:      using an approximation Bk in place of Hk, where Bk is composed using
    260:      the BFGS update formula. A More-Thuente line search is then used
    261:      to computed the steplength in the dk direction
    262:   Options Database Keys:
    263: +     -tao_lmm_vectors - number of vectors to use for approximation
    264: .     -tao_lmm_scale_type - "none","scalar","broyden"
    265: .     -tao_lmm_limit_type - "none","average","relative","absolute"
    266: .     -tao_lmm_rescale_type - "none","scalar","gl"
    267: .     -tao_lmm_limit_mu - mu limiting factor
    268: .     -tao_lmm_limit_nu - nu limiting factor
    269: .     -tao_lmm_delta_min - minimum delta value
    270: .     -tao_lmm_delta_max - maximum delta value
    271: .     -tao_lmm_broyden_phi - phi factor for Broyden scaling
    272: .     -tao_lmm_scalar_alpha - alpha factor for scalar scaling
    273: .     -tao_lmm_rescale_alpha - alpha factor for rescaling diagonal
    274: .     -tao_lmm_rescale_beta - beta factor for rescaling diagonal
    275: .     -tao_lmm_scalar_history - amount of history for scalar scaling
    276: .     -tao_lmm_rescale_history - amount of history for rescaling diagonal
    277: -     -tao_lmm_eps - rejection tolerance

    279:   Level: beginner
    280: M*/

    284: PETSC_EXTERN PetscErrorCode TaoCreate_LMVM(Tao tao)
    285: {
    286:   TAO_LMVM       *lmP;
    287:   const char     *morethuente_type = TAOLINESEARCHMT;

    291:   tao->ops->setup = TaoSetUp_LMVM;
    292:   tao->ops->solve = TaoSolve_LMVM;
    293:   tao->ops->view = TaoView_LMVM;
    294:   tao->ops->setfromoptions = TaoSetFromOptions_LMVM;
    295:   tao->ops->destroy = TaoDestroy_LMVM;

    297:   PetscNewLog(tao,&lmP);
    298:   lmP->D = 0;
    299:   lmP->M = 0;
    300:   lmP->Xold = 0;
    301:   lmP->Gold = 0;

    303:   tao->data = (void*)lmP;
    304:   /* Override default settings (unless already changed) */
    305:   if (!tao->max_it_changed) tao->max_it = 2000;
    306:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
    307:   if (!tao->fatol_changed) tao->fatol = 1.0e-4;
    308:   if (!tao->frtol_changed) tao->frtol = 1.0e-4;

    310:   TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);
    311:   TaoLineSearchSetType(tao->linesearch,morethuente_type);
    312:   TaoLineSearchUseTaoRoutines(tao->linesearch,tao);
    313:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
    314:   return(0);
    315: }