impls/tr/tr.c

#include "src/snes/impls/tr/tr.h"                /*I   "petscsnes.h"   I*/

/*
   This convergence test determines if the two norm of the
   solution lies outside the trust region, if so it halts.
*/
#undef __FUNCT__
#define __FUNCT__ "SNES_TR_KSPConverged_Private"
PetscErrorCode SNES_TR_KSPConverged_Private(KSP ksp,int n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
{
  SNES                snes = (SNES) ctx;
  SNES_KSP_EW_ConvCtx *kctx = (SNES_KSP_EW_ConvCtx*)snes->kspconvctx;
  SNES_TR             *neP = (SNES_TR*)snes->data;
  Vec                 x;
  PetscReal           nrm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (snes->ksp_ewconv) {
    if (!kctx) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Eisenstat-Walker onvergence context not created");
    if (!n) {ierr = SNES_KSP_EW_ComputeRelativeTolerance_Private(snes,ksp);CHKERRQ(ierr);}
    kctx->lresid_last = rnorm;
  }
  ierr = KSPDefaultConverged(ksp,n,rnorm,reason,ctx);CHKERRQ(ierr);
  if (*reason) {
    PetscLogInfo(snes,"SNES_TR_KSPConverged_Private: regular convergence test KSP iterations=%d, rnorm=%g\n",n,rnorm);
  }

  /* Determine norm of solution */
  ierr = KSPBuildSolution(ksp,0,&x);CHKERRQ(ierr);
  ierr = VecNorm(x,NORM_2,&nrm);CHKERRQ(ierr);
  if (nrm >= neP->delta) {
    PetscLogInfo(snes,"SNES_TR_KSPConverged_Private: KSP iterations=%d, rnorm=%g\n",n,rnorm);
    PetscLogInfo(snes,"SNES_TR_KSPConverged_Private: Ending linear iteration early, delta=%g, length=%g\n",neP->delta,nrm);
    *reason = KSP_CONVERGED_STEP_LENGTH;
  }
  PetscFunctionReturn(0);
}

/*
   SNESSolve_TR - Implements Newton's Method with a very simple trust
   region approach for solving systems of nonlinear equations.


*/
#undef __FUNCT__
#define __FUNCT__ "SNESSolve_TR"
static PetscErrorCode SNESSolve_TR(SNES snes)
{
  SNES_TR             *neP = (SNES_TR*)snes->data;
  Vec                 X,F,Y,G,TMP,Ytmp;
  PetscErrorCode ierr;
  int                 maxits,i,lits,breakout = 0;
  MatStructure        flg = DIFFERENT_NONZERO_PATTERN;
  PetscReal           rho,fnorm,gnorm,gpnorm,xnorm,delta,nrm,ynorm,norm1;
  PetscScalar         mone = -1.0,cnorm;
  KSP                 ksp;
  SNESConvergedReason reason;
  PetscTruth          conv;

  PetscFunctionBegin;
  maxits	= snes->max_its;	/* maximum number of iterations */
  X		= snes->vec_sol;	/* solution vector */
  F		= snes->vec_func;	/* residual vector */
  Y		= snes->work[0];	/* work vectors */
  G		= snes->work[1];
  Ytmp          = snes->work[2];

  ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
  snes->iter = 0;
  ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
  ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr);         /* xnorm = || X || */

  ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);          /* F(X) */
  ierr = VecNorm(F,NORM_2,&fnorm);CHKERRQ(ierr);             /* fnorm <- || F || */
  ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
  snes->norm = fnorm;
  ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
  delta = neP->delta0*fnorm;
  neP->delta = delta;
  SNESLogConvHistory(snes,fnorm,0);
  SNESMonitor(snes,0,fnorm);
  ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr);

 if (fnorm < snes->atol) {snes->reason = SNES_CONVERGED_FNORM_ABS; PetscFunctionReturn(0);}

  /* set parameter for default relative tolerance convergence test */
  snes->ttol = fnorm*snes->rtol;

  /* Set the stopping criteria to use the More' trick. */
  ierr = PetscOptionsHasName(PETSC_NULL,"-snes_tr_ksp_regular_convergence_test",&conv);CHKERRQ(ierr);
  if (!conv) {
    ierr = KSPSetConvergenceTest(ksp,SNES_TR_KSPConverged_Private,(void*)snes);CHKERRQ(ierr);
    PetscLogInfo(snes,"SNESSolve_TR: Using Krylov convergence test SNES_TR_KSPConverged_Private\n");
  }

  for (i=0; i<maxits; i++) {
    ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr);
    ierr = KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre,flg);CHKERRQ(ierr);

    /* Solve J Y = F, where J is Jacobian matrix */
    ierr = KSPSolve(snes->ksp,F,Ytmp);CHKERRQ(ierr);
    ierr = KSPGetIterationNumber(ksp,&lits);CHKERRQ(ierr);
    snes->linear_its += lits;
    PetscLogInfo(snes,"SNESSolve_TR: iter=%d, linear solve iterations=%d\n",snes->iter,lits);
    ierr = VecNorm(Ytmp,NORM_2,&nrm);CHKERRQ(ierr);
    norm1 = nrm;
    while(1) {
      ierr = VecCopy(Ytmp,Y);CHKERRQ(ierr);
      nrm = norm1;

      /* Scale Y if need be and predict new value of F norm */
      if (nrm >= delta) {
        nrm = delta/nrm;
        gpnorm = (1.0 - nrm)*fnorm;
        cnorm = nrm;
        PetscLogInfo(snes,"SNESSolve_TR: Scaling direction by %g\n",nrm);
        ierr = VecScale(&cnorm,Y);CHKERRQ(ierr);
        nrm = gpnorm;
        ynorm = delta;
      } else {
        gpnorm = 0.0;
        PetscLogInfo(snes,"SNESSolve_TR: Direction is in Trust Region\n");
        ynorm = nrm;
      }
      ierr = VecAYPX(&mone,X,Y);CHKERRQ(ierr);            /* Y <- X - Y */
      ierr = VecCopy(X,snes->vec_sol_update_always);CHKERRQ(ierr);
      ierr = SNESComputeFunction(snes,Y,G);CHKERRQ(ierr); /*  F(X) */
      ierr = VecNorm(G,NORM_2,&gnorm);CHKERRQ(ierr);      /* gnorm <- || g || */
      if (fnorm == gpnorm) rho = 0.0;
      else rho = (fnorm*fnorm - gnorm*gnorm)/(fnorm*fnorm - gpnorm*gpnorm);

      /* Update size of trust region */
      if      (rho < neP->mu)  delta *= neP->delta1;
      else if (rho < neP->eta) delta *= neP->delta2;
      else                     delta *= neP->delta3;
      PetscLogInfo(snes,"SNESSolve_TR: fnorm=%g, gnorm=%g, ynorm=%g\n",fnorm,gnorm,ynorm);
      PetscLogInfo(snes,"SNESSolve_TR: gpred=%g, rho=%g, delta=%g\n",gpnorm,rho,delta);
      neP->delta = delta;
      if (rho > neP->sigma) break;
      PetscLogInfo(snes,"SNESSolve_TR: Trying again in smaller region\n");
      /* check to see if progress is hopeless */
      neP->itflag = 0;
      ierr = (*snes->converged)(snes,xnorm,ynorm,fnorm,&reason,snes->cnvP);CHKERRQ(ierr);
      if (reason) {
        /* We're not progressing, so return with the current iterate */
        SNESMonitor(snes,i+1,fnorm);
        breakout = 1;
        break;
      }
      snes->numFailures++;
    }
    if (!breakout) {
      fnorm = gnorm;
      ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
      snes->iter = i+1;
      snes->norm = fnorm;
      ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
      TMP = F; F = G; snes->vec_func_always = F; G = TMP;
      TMP = X; X = Y; snes->vec_sol_always  = X; Y = TMP;
      ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr);		/* xnorm = || X || */
      SNESLogConvHistory(snes,fnorm,lits);
      SNESMonitor(snes,i+1,fnorm);

      /* Test for convergence */
      neP->itflag = 1;
      ierr = (*snes->converged)(snes,xnorm,ynorm,fnorm,&reason,snes->cnvP);CHKERRQ(ierr);
      if (reason) {
        break;
      }
    } else {
      break;
    }
  }
  /* Verify solution is in corect location */
  if (X != snes->vec_sol) {
    ierr = VecCopy(X,snes->vec_sol);CHKERRQ(ierr);
  }
  if (F != snes->vec_func) {
    ierr = VecCopy(F,snes->vec_func);CHKERRQ(ierr);
  }
  snes->vec_sol_always  = snes->vec_sol;
  snes->vec_func_always = snes->vec_func;
  if (i == maxits) {
    PetscLogInfo(snes,"SNESSolve_TR: Maximum number of iterations has been reached: %d\n",maxits);
    reason = SNES_DIVERGED_MAX_IT;
  }
  ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
  snes->reason = reason;
  ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/*------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "SNESSetUp_TR"
static PetscErrorCode SNESSetUp_TR(SNES snes)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  snes->nwork = 4;
  ierr = VecDuplicateVecs(snes->vec_sol,snes->nwork,&snes->work);CHKERRQ(ierr);
  PetscLogObjectParents(snes,snes->nwork,snes->work);
  snes->vec_sol_update_always = snes->work[3];
  PetscFunctionReturn(0);
}
/*------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "SNESDestroy_TR"
static PetscErrorCode SNESDestroy_TR(SNES snes)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (snes->nwork) {
    ierr = VecDestroyVecs(snes->work,snes->nwork);CHKERRQ(ierr);
  }
  ierr = PetscFree(snes->data);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/*------------------------------------------------------------*/

#undef __FUNCT__
#define __FUNCT__ "SNESSetFromOptions_TR"
static PetscErrorCode SNESSetFromOptions_TR(SNES snes)
{
  SNES_TR *ctx = (SNES_TR *)snes->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscOptionsHead("SNES trust region options for nonlinear equations");CHKERRQ(ierr);
    ierr = PetscOptionsReal("-snes_trtol","Trust region tolerance","SNESSetTrustRegionTolerance",snes->deltatol,&snes->deltatol,0);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-snes_tr_mu","mu","None",ctx->mu,&ctx->mu,0);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-snes_tr_eta","eta","None",ctx->eta,&ctx->eta,0);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-snes_tr_sigma","sigma","None",ctx->sigma,&ctx->sigma,0);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-snes_tr_delta0","delta0","None",ctx->delta0,&ctx->delta0,0);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-snes_tr_delta1","delta1","None",ctx->delta1,&ctx->delta1,0);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-snes_tr_delta2","delta2","None",ctx->delta2,&ctx->delta2,0);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-snes_tr_delta3","delta3","None",ctx->delta3,&ctx->delta3,0);CHKERRQ(ierr);
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "SNESView_TR"
static PetscErrorCode SNESView_TR(SNES snes,PetscViewer viewer)
{
  SNES_TR *tr = (SNES_TR *)snes->data;
  PetscErrorCode ierr;
  PetscTruth iascii;

  PetscFunctionBegin;
  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
  if (iascii) {
    ierr = PetscViewerASCIIPrintf(viewer,"  mu=%g, eta=%g, sigma=%g\n",tr->mu,tr->eta,tr->sigma);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  delta0=%g, delta1=%g, delta2=%g, delta3=%g\n",tr->delta0,tr->delta1,tr->delta2,tr->delta3);CHKERRQ(ierr);
  } else {
    SETERRQ1(1,"Viewer type %s not supported for SNES EQ TR",((PetscObject)viewer)->type_name);
  }
  PetscFunctionReturn(0);
}

/* ---------------------------------------------------------------- */
#undef __FUNCT__
#define __FUNCT__ "SNESConverged_TR"
/*@C
   SNESConverged_TR - Monitors the convergence of the trust region
   method SNESTR for solving systems of nonlinear equations (default).

   Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  xnorm - 2-norm of current iterate
.  pnorm - 2-norm of current step
.  fnorm - 2-norm of function
-  dummy - unused context

   Output Parameter:
.   reason - one of
$  SNES_CONVERGED_FNORM_ABS       - (fnorm < atol),
$  SNES_CONVERGED_PNORM_RELATIVE  - (pnorm < xtol*xnorm),
$  SNES_CONVERGED_FNORM_RELATIVE  - (fnorm < rtol*fnorm0),
$  SNES_DIVERGED_FUNCTION_COUNT   - (nfct > maxf),
$  SNES_DIVERGED_FNORM_NAN        - (fnorm == NaN),
$  SNES_CONVERGED_TR_DELTA        - (delta < xnorm*deltatol),
$  SNES_CONVERGED_ITERATING       - (otherwise)

   where
+    delta    - trust region paramenter
.    deltatol - trust region size tolerance,
                set with SNESSetTrustRegionTolerance()
.    maxf - maximum number of function evaluations,
            set with SNESSetTolerances()
.    nfct - number of function evaluations,
.    atol - absolute function norm tolerance,
            set with SNESSetTolerances()
-    xtol - relative function norm tolerance,
            set with SNESSetTolerances()

   Level: intermediate

.keywords: SNES, nonlinear, default, converged, convergence

.seealso: SNESSetConvergenceTest(), SNESEisenstatWalkerConverged()
@*/
PetscErrorCode SNESConverged_TR(SNES snes,PetscReal xnorm,PetscReal pnorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
{
  SNES_TR *neP = (SNES_TR *)snes->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (fnorm != fnorm) {
    PetscLogInfo(snes,"SNESConverged_TR:Failed to converged, function norm is NaN\n");
    *reason = SNES_DIVERGED_FNORM_NAN;
  } else if (neP->delta < xnorm * snes->deltatol) {
    PetscLogInfo(snes,"SNESConverged_TR: Converged due to trust region param %g<%g*%g\n",neP->delta,xnorm,snes->deltatol);
    *reason = SNES_CONVERGED_TR_DELTA;
  } else if (neP->itflag) {
    ierr = SNESConverged_LS(snes,xnorm,pnorm,fnorm,reason,dummy);CHKERRQ(ierr);
  } else if (snes->nfuncs > snes->max_funcs) {
    PetscLogInfo(snes,"SNESConverged_TR: Exceeded maximum number of function evaluations: %d > %d\n",snes->nfuncs,snes->max_funcs);
    *reason = SNES_DIVERGED_FUNCTION_COUNT;
  } else {
    *reason = SNES_CONVERGED_ITERATING;
  }
  PetscFunctionReturn(0);
}
/* ------------------------------------------------------------ */
/*MC
      SNESTR - Newton based nonlinear solver that uses a trust region

   Options Database:
+    -snes_trtol <tol> Trust region tolerance
.    -snes_tr_mu <mu>
.    -snes_tr_eta <eta>
.    -snes_tr_sigma <sigma>
.    -snes_tr_delta0 <delta0>
.    -snes_tr_delta1 <delta1>
.    -snes_tr_delta2 <delta2>
-    -snes_tr_delta3 <delta3>

   The basic algorithm is taken from "The Minpack Project", by More',
   Sorensen, Garbow, Hillstrom, pages 88-111 of "Sources and Development
   of Mathematical Software", Wayne Cowell, editor.

   This is intended as a model implementation, since it does not
   necessarily have many of the bells and whistles of other
   implementations.

   Level: intermediate

.seealso:  SNESCreate(), SNES, SNESSetType(), SNESLS, SNESSetTrustRegionTolerance()

M*/
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "SNESCreate_TR"
PetscErrorCode SNESCreate_TR(SNES snes)
{
  SNES_TR *neP;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  snes->setup		= SNESSetUp_TR;
  snes->solve		= SNESSolve_TR;
  snes->destroy		= SNESDestroy_TR;
  snes->converged	= SNESConverged_TR;
  snes->setfromoptions  = SNESSetFromOptions_TR;
  snes->view            = SNESView_TR;
  snes->nwork           = 0;

  ierr			= PetscNew(SNES_TR,&neP);CHKERRQ(ierr);
  PetscLogObjectMemory(snes,sizeof(SNES_TR));
  snes->data	        = (void*)neP;
  neP->mu		= 0.25;
  neP->eta		= 0.75;
  neP->delta		= 0.0;
  neP->delta0		= 0.2;
  neP->delta1		= 0.3;
  neP->delta2		= 0.75;
  neP->delta3		= 2.0;
  neP->sigma		= 0.0001;
  neP->itflag		= 0;
  neP->rnorm0		= 0;
  neP->ttol		= 0;
  PetscFunctionReturn(0);
}
EXTERN_C_END