예제 #1
0
파일: bntr.c 프로젝트: petsc/petsc
PetscErrorCode TaoSolve_BNTR(Tao tao)
{
  PetscErrorCode               ierr;
  TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
  KSPConvergedReason           ksp_reason;

  PetscReal                    oldTrust, prered, actred, steplen, resnorm;
  PetscBool                    cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
  PetscInt                     stepType, nDiff;
  
  PetscFunctionBegin;
  /* Initialize the preconditioner, KSP solver and trust radius/line search */
  tao->reason = TAO_CONTINUE_ITERATING;
  ierr = TaoBNKInitialize(tao, bnk->init_type, &needH);CHKERRQ(ierr);
  if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);

  /* Have not converged; continue with Newton method */
  while (tao->reason == TAO_CONTINUE_ITERATING) {
    /* Call general purpose update function */
    if (tao->ops->update) {
      ierr = (*tao->ops->update)(tao, tao->niter, tao->user_update);CHKERRQ(ierr);
    }
    ++tao->niter;
    
    if (needH && bnk->inactive_idx) { 
      /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
      ierr = TaoBNKTakeCGSteps(tao, &cgTerminate);CHKERRQ(ierr);
      if (cgTerminate) {
        tao->reason = bnk->bncg->reason;
        PetscFunctionReturn(0);
      }
      /* Compute the hessian and update the BFGS preconditioner at the new iterate */
      ierr = (*bnk->computehessian)(tao);CHKERRQ(ierr);
      needH = PETSC_FALSE;
    }
    
    /* Store current solution before it changes */
    bnk->fold = bnk->f;
    ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr);
    ierr = VecCopy(tao->gradient, bnk->Gold);CHKERRQ(ierr);
    ierr = VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);CHKERRQ(ierr);
    
    /* Enter into trust region loops */
    stepAccepted = PETSC_FALSE;
    while (!stepAccepted && tao->reason == TAO_CONTINUE_ITERATING) {
      tao->ksp_its=0;
      
      /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
      ierr = (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);CHKERRQ(ierr);

      /* Temporarily accept the step and project it into the bounds */
      ierr = VecAXPY(tao->solution, 1.0, tao->stepdirection);CHKERRQ(ierr);
      ierr = TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);CHKERRQ(ierr);

      /* Check if the projection changed the step direction */
      if (nDiff > 0) {
        /* Projection changed the step, so we have to recompute the step and 
           the predicted reduction. Leave the trust radius unchanged. */
        ierr = VecCopy(tao->solution, tao->stepdirection);CHKERRQ(ierr);
        ierr = VecAXPY(tao->stepdirection, -1.0, bnk->Xold);CHKERRQ(ierr);
        ierr = TaoBNKRecomputePred(tao, tao->stepdirection, &prered);CHKERRQ(ierr);
      } else {
        /* Step did not change, so we can just recover the pre-computed prediction */
        ierr = KSPCGGetObjFcn(tao->ksp, &prered);CHKERRQ(ierr);
      }
      prered = -prered;

      /* Compute the actual reduction and update the trust radius */
      ierr = TaoComputeObjective(tao, tao->solution, &bnk->f);CHKERRQ(ierr);
      if (PetscIsInfOrNanReal(bnk->f)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
      actred = bnk->fold - bnk->f;
      oldTrust = tao->trust;
      ierr = TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);CHKERRQ(ierr);

      if (stepAccepted) {
        /* Step is good, evaluate the gradient and flip the need-Hessian switch */
        steplen = 1.0;
        needH = PETSC_TRUE;
        ++bnk->newt;
        ierr = TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
        ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);CHKERRQ(ierr);
        ierr = VecCopy(bnk->unprojected_gradient, tao->gradient);CHKERRQ(ierr);
        ierr = VecISSet(tao->gradient, bnk->active_idx, 0.0);CHKERRQ(ierr);
        ierr = TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);CHKERRQ(ierr);
      } else {
        /* Step is bad, revert old solution and re-solve with new radius*/
        steplen = 0.0;
        needH = PETSC_FALSE;
        bnk->f = bnk->fold;
        ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
        ierr = VecCopy(bnk->Gold, tao->gradient);CHKERRQ(ierr);
        ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr);
        if (oldTrust == tao->trust) {
          /* Can't change the radius anymore so just terminate */
          tao->reason = TAO_DIVERGED_TR_REDUCTION;
        }
      }

      /*  Check for termination */
      ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);CHKERRQ(ierr);
      ierr = VecNorm(bnk->W, NORM_2, &resnorm);CHKERRQ(ierr);
      if (PetscIsInfOrNanReal(resnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
      ierr = TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);CHKERRQ(ierr);
      ierr = TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);CHKERRQ(ierr);
      ierr = (*tao->ops->convergencetest)(tao, tao->cnvP);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}
예제 #2
0
/*
   TaoSolve_NTR - Implements Newton's Method with a trust region approach
   for solving unconstrained minimization problems.

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

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

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

   subject to the trust region constraint

        || s ||_M <= radius,

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

   Note:  TaoSolve_NTR MUST use the iterative solver KSPCGNASH, KSPCGSTCG,
          or KSPCGGLTR.  Thus, we set KSPCGNASH, KSPCGSTCG, or KSPCGGLTR in this
          routine regardless of what the user may have previously specified.
*/
static PetscErrorCode TaoSolve_NTR(Tao tao)
{
  TAO_NTR            *tr = (TAO_NTR *)tao->data;
  KSPType            ksp_type;
  PetscBool          is_nash,is_stcg,is_gltr;
  KSPConvergedReason ksp_reason;
  PC                 pc;
  TaoConvergedReason reason;
  PetscReal          fmin, ftrial, prered, actred, kappa, sigma, beta;
  PetscReal          tau, tau_1, tau_2, tau_max, tau_min, max_radius;
  PetscReal          f, gnorm;

  PetscReal          delta;
  PetscReal          norm_d;
  PetscErrorCode     ierr;
  PetscInt           bfgsUpdates = 0;
  PetscInt           needH;

  PetscInt           i_max = 5;
  PetscInt           j_max = 1;
  PetscInt           i, j, N, n, its;

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

  ierr = KSPGetType(tao->ksp,&ksp_type);CHKERRQ(ierr);
  ierr = PetscStrcmp(ksp_type,KSPCGNASH,&is_nash);CHKERRQ(ierr);
  ierr = PetscStrcmp(ksp_type,KSPCGSTCG,&is_stcg);CHKERRQ(ierr);
  ierr = PetscStrcmp(ksp_type,KSPCGGLTR,&is_gltr);CHKERRQ(ierr);
  if (!is_nash && !is_stcg && !is_gltr) {
    SETERRQ(PETSC_COMM_SELF,1,"TAO_NTR requires nash, stcg, or gltr for the KSP");
  }

  /* Initialize the radius and modify if it is too large or small */
  tao->trust = tao->trust0;
  tao->trust = PetscMax(tao->trust, tr->min_radius);
  tao->trust = PetscMin(tao->trust, tr->max_radius);

  if (NTR_PC_BFGS == tr->pc_type && !tr->M) {
    ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr);
    ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr);
    ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&tr->M);CHKERRQ(ierr);
    ierr = MatLMVMAllocateVectors(tr->M,tao->solution);CHKERRQ(ierr);
  }

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

  ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, 1.0, &reason);CHKERRQ(ierr);
  if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);

  /* Create vectors for the limited memory preconditioner */
  if ((NTR_PC_BFGS == tr->pc_type) && (BFGS_SCALE_BFGS != tr->bfgs_scale_type)) {
    if (!tr->Diag) {
        ierr = VecDuplicate(tao->solution, &tr->Diag);CHKERRQ(ierr);
    }
  }

  /*  Modify the preconditioner to use the bfgs approximation */
  ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr);
  switch(tr->pc_type) {
  case NTR_PC_NONE:
    ierr = PCSetType(pc, PCNONE);CHKERRQ(ierr);
    ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
    break;

  case NTR_PC_AHESS:
    ierr = PCSetType(pc, PCJACOBI);CHKERRQ(ierr);
    ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
    ierr = PCJacobiSetUseAbs(pc,PETSC_TRUE);CHKERRQ(ierr);
    break;

  case NTR_PC_BFGS:
    ierr = PCSetType(pc, PCSHELL);CHKERRQ(ierr);
    ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
    ierr = PCShellSetName(pc, "bfgs");CHKERRQ(ierr);
    ierr = PCShellSetContext(pc, tr->M);CHKERRQ(ierr);
    ierr = PCShellSetApply(pc, MatLMVMSolveShell);CHKERRQ(ierr);
    break;

  default:
    /*  Use the pc method set by pc_type */
    break;
  }

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

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

    for (j = 0; j < j_max; ++j) {
      fmin = f;
      sigma = 0.0;

      if (needH) {
        ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
        needH = 0;
      }

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

        ierr = VecCopy(tao->solution, tr->W);CHKERRQ(ierr);
        ierr = VecAXPY(tr->W, -tao->trust/gnorm, tao->gradient);CHKERRQ(ierr);
        ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr);

        if (PetscIsInfOrNanReal(ftrial)) {
          tau = tr->gamma1_i;
        }
        else {
          if (ftrial < fmin) {
            fmin = ftrial;
            sigma = -tao->trust / gnorm;
          }

          ierr = MatMult(tao->hessian, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
          ierr = VecDot(tao->gradient, tao->stepdirection, &prered);CHKERRQ(ierr);

          prered = tao->trust * (gnorm - 0.5 * tao->trust * prered / (gnorm * gnorm));
          actred = f - ftrial;
          if ((PetscAbsScalar(actred) <= tr->epsilon) &&
              (PetscAbsScalar(prered) <= tr->epsilon)) {
            kappa = 1.0;
          }
          else {
            kappa = actred / prered;
          }

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

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

            if (tau_max < 1.0) {
              tau = tr->gamma3_i;
            }
            else if (tau_max > tr->gamma4_i) {
              tau = tr->gamma4_i;
            }
            else {
              tau = tau_max;
            }
          }
          else if (PetscAbsScalar(kappa - 1.0) <= tr->mu2_i) {
            /*  Good agreement */
            max_radius = PetscMax(max_radius, tao->trust);

            if (tau_max < tr->gamma2_i) {
              tau = tr->gamma2_i;
            }
            else if (tau_max > tr->gamma3_i) {
              tau = tr->gamma3_i;
            }
            else {
              tau = tau_max;
            }
          }
          else {
            /*  Not good agreement */
            if (tau_min > 1.0) {
              tau = tr->gamma2_i;
            }
            else if (tau_max < tr->gamma1_i) {
              tau = tr->gamma1_i;
            }
            else if ((tau_min < tr->gamma1_i) && (tau_max >= 1.0)) {
              tau = tr->gamma1_i;
            }
            else if ((tau_1 >= tr->gamma1_i) && (tau_1 < 1.0) &&
                     ((tau_2 < tr->gamma1_i) || (tau_2 >= 1.0))) {
              tau = tau_1;
            }
            else if ((tau_2 >= tr->gamma1_i) && (tau_2 < 1.0) &&
                     ((tau_1 < tr->gamma1_i) || (tau_2 >= 1.0))) {
              tau = tau_2;
            }
            else {
              tau = tau_max;
            }
          }
        }
        tao->trust = tau * tao->trust;
      }

      if (fmin < f) {
        f = fmin;
        ierr = VecAXPY(tao->solution, sigma, tao->gradient);CHKERRQ(ierr);
        ierr = TaoComputeGradient(tao,tao->solution, tao->gradient);CHKERRQ(ierr);

        ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);

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

        ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, 1.0, &reason);CHKERRQ(ierr);
        if (reason != TAO_CONTINUE_ITERATING) {
          PetscFunctionReturn(0);
        }
      }
    }
    tao->trust = PetscMax(tao->trust, max_radius);

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

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

  /* Set initial scaling for the BFGS preconditioner
     This step is done after computing the initial trust-region radius
     since the function value may have decreased */
  if (NTR_PC_BFGS == tr->pc_type) {
    if (f != 0.0) {
      delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
    }
    else {
      delta = 2.0 / (gnorm*gnorm);
    }
    ierr = MatLMVMSetDelta(tr->M,delta);CHKERRQ(ierr);
  }

  /* Have not converged; continue with Newton method */
  while (reason == TAO_CONTINUE_ITERATING) {
    ++tao->niter;
    tao->ksp_its=0;
    /* Compute the Hessian */
    if (needH) {
      ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
      needH = 0;
    }

    if (NTR_PC_BFGS == tr->pc_type) {
      if (BFGS_SCALE_AHESS == tr->bfgs_scale_type) {
        /* Obtain diagonal for the bfgs preconditioner */
        ierr = MatGetDiagonal(tao->hessian, tr->Diag);CHKERRQ(ierr);
        ierr = VecAbs(tr->Diag);CHKERRQ(ierr);
        ierr = VecReciprocal(tr->Diag);CHKERRQ(ierr);
        ierr = MatLMVMSetScale(tr->M,tr->Diag);CHKERRQ(ierr);
      }

      /* Update the limited memory preconditioner */
      ierr = MatLMVMUpdate(tr->M, tao->solution, tao->gradient);CHKERRQ(ierr);
      ++bfgsUpdates;
    }

    while (reason == TAO_CONTINUE_ITERATING) {
      ierr = KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre);CHKERRQ(ierr);

      /* Solve the trust region subproblem */
      ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
      ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
      ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
      tao->ksp_its+=its;
      tao->ksp_tot_its+=its;
      ierr = KSPCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);

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

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

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

          ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
          ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
          ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
          tao->ksp_its+=its;
          tao->ksp_tot_its+=its;
          ierr = KSPCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);

          if (norm_d == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
        }
      }
      ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
      ierr = KSPGetConvergedReason(tao->ksp, &ksp_reason);CHKERRQ(ierr);
      if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) &&
          (NTR_PC_BFGS == tr->pc_type) && (bfgsUpdates > 1)) {
        /* Preconditioner is numerically indefinite; reset the
           approximate if using BFGS preconditioning. */

        if (f != 0.0) {
          delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
        }
        else {
          delta = 2.0 / (gnorm*gnorm);
        }
        ierr = MatLMVMSetDelta(tr->M, delta);CHKERRQ(ierr);
        ierr = MatLMVMReset(tr->M);CHKERRQ(ierr);
        ierr = MatLMVMUpdate(tr->M, tao->solution, tao->gradient);CHKERRQ(ierr);
        bfgsUpdates = 1;
      }

      if (NTR_UPDATE_REDUCTION == tr->update_type) {
        /* Get predicted reduction */
        ierr = KSPCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
        if (prered >= 0.0) {
          /* The predicted reduction has the wrong sign.  This cannot
             happen in infinite precision arithmetic.  Step should
             be rejected! */
          tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
        }
        else {
          /* Compute trial step and function value */
          ierr = VecCopy(tao->solution,tr->W);CHKERRQ(ierr);
          ierr = VecAXPY(tr->W, 1.0, tao->stepdirection);CHKERRQ(ierr);
          ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr);

          if (PetscIsInfOrNanReal(ftrial)) {
            tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
          } else {
            /* Compute and actual reduction */
            actred = f - ftrial;
            prered = -prered;
            if ((PetscAbsScalar(actred) <= tr->epsilon) &&
                (PetscAbsScalar(prered) <= tr->epsilon)) {
              kappa = 1.0;
            }
            else {
              kappa = actred / prered;
            }

            /* Accept or reject the step and update radius */
            if (kappa < tr->eta1) {
              /* Reject the step */
              tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
            }
            else {
              /* Accept the step */
              if (kappa < tr->eta2) {
                /* Marginal bad step */
                tao->trust = tr->alpha2 * PetscMin(tao->trust, norm_d);
              }
              else if (kappa < tr->eta3) {
                /* Reasonable step */
                tao->trust = tr->alpha3 * tao->trust;
              }
              else if (kappa < tr->eta4) {
                /* Good step */
                tao->trust = PetscMax(tr->alpha4 * norm_d, tao->trust);
              }
              else {
                /* Very good step */
                tao->trust = PetscMax(tr->alpha5 * norm_d, tao->trust);
              }
              break;
            }
          }
        }
      }
      else {
        /* Get predicted reduction */
        ierr = KSPCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
        if (prered >= 0.0) {
          /* The predicted reduction has the wrong sign.  This cannot
             happen in infinite precision arithmetic.  Step should
             be rejected! */
          tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
        }
        else {
          ierr = VecCopy(tao->solution, tr->W);CHKERRQ(ierr);
          ierr = VecAXPY(tr->W, 1.0, tao->stepdirection);CHKERRQ(ierr);
          ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr);
          if (PetscIsInfOrNanReal(ftrial)) {
            tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
          }
          else {
            ierr = VecDot(tao->gradient, tao->stepdirection, &beta);CHKERRQ(ierr);
            actred = f - ftrial;
            prered = -prered;
            if ((PetscAbsScalar(actred) <= tr->epsilon) &&
                (PetscAbsScalar(prered) <= tr->epsilon)) {
              kappa = 1.0;
            }
            else {
              kappa = actred / prered;
            }

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

            if (kappa >= 1.0 - tr->mu1) {
              /* Great agreement; accept step and update radius */
              if (tau_max < 1.0) {
                tao->trust = PetscMax(tao->trust, tr->gamma3 * norm_d);
              }
              else if (tau_max > tr->gamma4) {
                tao->trust = PetscMax(tao->trust, tr->gamma4 * norm_d);
              }
              else {
                tao->trust = PetscMax(tao->trust, tau_max * norm_d);
              }
              break;
            }
            else if (kappa >= 1.0 - tr->mu2) {
              /* Good agreement */

              if (tau_max < tr->gamma2) {
                tao->trust = tr->gamma2 * PetscMin(tao->trust, norm_d);
              }
              else if (tau_max > tr->gamma3) {
                tao->trust = PetscMax(tao->trust, tr->gamma3 * norm_d);
              }
              else if (tau_max < 1.0) {
                tao->trust = tau_max * PetscMin(tao->trust, norm_d);
              }
              else {
                tao->trust = PetscMax(tao->trust, tau_max * norm_d);
              }
              break;
            }
            else {
              /* Not good agreement */
              if (tau_min > 1.0) {
                tao->trust = tr->gamma2 * PetscMin(tao->trust, norm_d);
              }
              else if (tau_max < tr->gamma1) {
                tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
              }
              else if ((tau_min < tr->gamma1) && (tau_max >= 1.0)) {
                tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
              }
              else if ((tau_1 >= tr->gamma1) && (tau_1 < 1.0) &&
                       ((tau_2 < tr->gamma1) || (tau_2 >= 1.0))) {
                tao->trust = tau_1 * PetscMin(tao->trust, norm_d);
              }
              else if ((tau_2 >= tr->gamma1) && (tau_2 < 1.0) &&
                       ((tau_1 < tr->gamma1) || (tau_2 >= 1.0))) {
                tao->trust = tau_2 * PetscMin(tao->trust, norm_d);
              }
              else {
                tao->trust = tau_max * PetscMin(tao->trust, norm_d);
              }
            }
          }
        }
      }

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

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

    if (reason == TAO_CONTINUE_ITERATING) {
      ierr = VecCopy(tr->W, tao->solution);CHKERRQ(ierr);
      f = ftrial;
      ierr = TaoComputeGradient(tao, tao->solution, tao->gradient);CHKERRQ(ierr);
      ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
      if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
      needH = 1;
      ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, tao->trust, &reason);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}
예제 #3
0
static PetscErrorCode TaoSolve_BLMVM(Tao tao)
{
  PetscErrorCode               ierr;
  TAO_BLMVM                    *blmP = (TAO_BLMVM *)tao->data;
  TaoConvergedReason           reason = TAO_CONTINUE_ITERATING;
  TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;
  PetscReal                    f, fold, gdx, gnorm;
  PetscReal                    stepsize = 1.0,delta;

  PetscFunctionBegin;
  /*  Project initial point onto bounds */
  ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
  ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
  ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);


  /* Check convergence criteria */
  ierr = TaoComputeObjectiveAndGradient(tao, tao->solution,&f,blmP->unprojected_gradient);CHKERRQ(ierr);
  ierr = VecBoundGradientProjection(blmP->unprojected_gradient,tao->solution, tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);

  ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
  if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf pr NaN");

  ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, stepsize, &reason);CHKERRQ(ierr);
  if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);

  /* Set initial scaling for the function */
  if (f != 0.0) {
    delta = 2.0*PetscAbsScalar(f) / (gnorm*gnorm);
  } else {
    delta = 2.0 / (gnorm*gnorm);
  }
  ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);

  /* Set counter for gradient/reset steps */
  blmP->grad = 0;
  blmP->reset = 0;

  /* Have not converged; continue with Newton method */
  while (reason == TAO_CONTINUE_ITERATING) {
    /* Compute direction */
    ierr = MatLMVMUpdate(blmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
    ierr = MatLMVMSolve(blmP->M, blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
    ierr = VecBoundGradientProjection(tao->stepdirection,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);

    /* Check for success (descent direction) */
    ierr = VecDot(blmP->unprojected_gradient, tao->gradient, &gdx);CHKERRQ(ierr);
    if (gdx <= 0) {
      /* Step is not descent or solve was not successful
         Use steepest descent direction (scaled) */
      ++blmP->grad;

      if (f != 0.0) {
        delta = 2.0*PetscAbsScalar(f) / (gnorm*gnorm);
      } else {
        delta = 2.0 / (gnorm*gnorm);
      }
      ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);
      ierr = MatLMVMReset(blmP->M);CHKERRQ(ierr);
      ierr = MatLMVMUpdate(blmP->M, tao->solution, blmP->unprojected_gradient);CHKERRQ(ierr);
      ierr = MatLMVMSolve(blmP->M,blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
    }
    ierr = VecScale(tao->stepdirection,-1.0);CHKERRQ(ierr);

    /* Perform the linesearch */
    fold = f;
    ierr = VecCopy(tao->solution, blmP->Xold);CHKERRQ(ierr);
    ierr = VecCopy(blmP->unprojected_gradient, blmP->Gold);CHKERRQ(ierr);
    ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
    ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, blmP->unprojected_gradient, tao->stepdirection, &stepsize, &ls_status);CHKERRQ(ierr);
    ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);

    if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
      /* Linesearch failed
         Reset factors and use scaled (projected) gradient step */
      ++blmP->reset;

      f = fold;
      ierr = VecCopy(blmP->Xold, tao->solution);CHKERRQ(ierr);
      ierr = VecCopy(blmP->Gold, blmP->unprojected_gradient);CHKERRQ(ierr);

      if (f != 0.0) {
        delta = 2.0* PetscAbsScalar(f) / (gnorm*gnorm);
      } else {
        delta = 2.0/ (gnorm*gnorm);
      }
      ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);
      ierr = MatLMVMReset(blmP->M);CHKERRQ(ierr);
      ierr = MatLMVMUpdate(blmP->M, tao->solution, blmP->unprojected_gradient);CHKERRQ(ierr);
      ierr = MatLMVMSolve(blmP->M, blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
      ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);

      /* This may be incorrect; linesearch has values fo stepmax and stepmin
         that should be reset. */
      ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
      ierr = TaoLineSearchApply(tao->linesearch,tao->solution,&f, blmP->unprojected_gradient, tao->stepdirection,  &stepsize, &ls_status);CHKERRQ(ierr);
      ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);

      if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
        tao->reason = TAO_DIVERGED_LS_FAILURE;
        break;
      }
    }

    /* Check for converged */
    ierr = VecBoundGradientProjection(blmP->unprojected_gradient, tao->solution, tao->XL, tao->XU, tao->gradient);CHKERRQ(ierr);
    ierr = TaoGradientNorm(tao, tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr);


    if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Not-a-Number");
    tao->niter++;
    ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, stepsize, &reason);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}