xref: /petsc/src/snes/impls/vi/vi.c (revision a63bb30eff8b1dff6ddce5531d6230e04f6fd10b)

#include <../include/private/snesimpl.h> /*I "petscsnes.h" I*/
#include <../include/private/kspimpl.h>
#include <../include/private/matimpl.h>
#include <../include/private/dmimpl.h>

#undef __FUNCT__
#define __FUNCT__ "SNESVISetComputeVariableBounds"
/*@C
   SNESVISetComputeVariableBounds - Sets a function  that is called to compute the variable bounds

   Input parameter
+  snes - the SNES context
-  compute - computes the bounds

   Level: advanced

@*/
PetscErrorCode SNESVISetComputeVariableBounds(SNES snes, PetscErrorCode (*compute)(SNES,Vec,Vec))
{
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = SNESSetType(snes,SNESVIRS);CHKERRQ(ierr);
  snes->ops->computevariablebounds = compute;
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "SNESVIComputeInactiveSetIS"
/*
   SNESVIComputeInactiveSetIS - Gets the global indices for the bogus inactive set variables

   Input parameter
.  snes - the SNES context
.  X    - the snes solution vector

   Output parameter
.  ISact - active set index set

 */
PetscErrorCode SNESVIComputeInactiveSetIS(Vec upper,Vec lower,Vec X,Vec F,IS* inact)
{
  PetscErrorCode    ierr;
  const PetscScalar *x,*xl,*xu,*f;
  PetscInt          *idx_act,i,nlocal,nloc_isact=0,ilow,ihigh,i1=0;

  PetscFunctionBegin;
  ierr = VecGetLocalSize(X,&nlocal);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(X,&ilow,&ihigh);CHKERRQ(ierr);
  ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
  ierr = VecGetArrayRead(lower,&xl);CHKERRQ(ierr);
  ierr = VecGetArrayRead(upper,&xu);CHKERRQ(ierr);
  ierr = VecGetArrayRead(F,&f);CHKERRQ(ierr);
  /* Compute inactive set size */
  for (i=0; i < nlocal;i++) {
    if (((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + 1.e-8 || (PetscRealPart(f[i]) < 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - 1.e-8) || PetscRealPart(f[i]) > 0.0))) nloc_isact++;
  }

  ierr = PetscMalloc(nloc_isact*sizeof(PetscInt),&idx_act);CHKERRQ(ierr);

  /* Set inactive set indices */
  for(i=0; i < nlocal; i++) {
    if (((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + 1.e-8 || (PetscRealPart(f[i]) < 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - 1.e-8) || PetscRealPart(f[i]) > 0.0))) idx_act[i1++] = ilow+i;
  }

   /* Create inactive set IS */
  ierr = ISCreateGeneral(((PetscObject)upper)->comm,nloc_isact,idx_act,PETSC_OWN_POINTER,inact);CHKERRQ(ierr);

  ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(lower,&xl);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(upper,&xu);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(F,&f);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* --------------------------------------------------------------------------------------------------------*/

#undef __FUNCT__
#define __FUNCT__ "SNESMonitorVI"
PetscErrorCode  SNESMonitorVI(SNES snes,PetscInt its,PetscReal fgnorm,void *dummy)
{
  PetscErrorCode    ierr;
  PetscViewer        viewer = dummy ? (PetscViewer) dummy : PETSC_VIEWER_STDOUT_(((PetscObject)snes)->comm);
  const PetscScalar  *x,*xl,*xu,*f;
  PetscInt           i,n,act[2] = {0,0},fact[2],N;
  /* Number of components that actually hit the bounds (c.f. active variables) */
  PetscInt           act_bound[2] = {0,0},fact_bound[2];
  PetscReal          rnorm,fnorm;

  PetscFunctionBegin;
  ierr = VecGetLocalSize(snes->vec_sol,&n);CHKERRQ(ierr);
  ierr = VecGetSize(snes->vec_sol,&N);CHKERRQ(ierr);
  ierr = VecGetArrayRead(snes->xl,&xl);CHKERRQ(ierr);
  ierr = VecGetArrayRead(snes->xu,&xu);CHKERRQ(ierr);
  ierr = VecGetArrayRead(snes->vec_sol,&x);CHKERRQ(ierr);
  ierr = VecGetArrayRead(snes->vec_func,&f);CHKERRQ(ierr);

  rnorm = 0.0;
  for (i=0; i<n; i++) {
    if (((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + 1.e-8 || (PetscRealPart(f[i]) < 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - 1.e-8) || PetscRealPart(f[i]) > 0.0))) rnorm += PetscRealPart(PetscConj(f[i])*f[i]);
    else if (PetscRealPart(x[i]) <= PetscRealPart(xl[i]) + 1.e-8 && PetscRealPart(f[i]) >= 0.0) act[0]++;
    else if (PetscRealPart(x[i]) >= PetscRealPart(xu[i]) - 1.e-8 && PetscRealPart(f[i]) <= 0.0) act[1]++;
    else SETERRQ(((PetscObject)snes)->comm,PETSC_ERR_PLIB,"Can never get here");
  }

  for (i=0; i<n; i++) {
    if (PetscRealPart(x[i]) <= PetscRealPart(xl[i]) + 1.e-8) act_bound[0]++;
    else if (PetscRealPart(x[i]) >= PetscRealPart(xu[i]) - 1.e-8) act_bound[1]++;
  }
  ierr = VecRestoreArrayRead(snes->vec_func,&f);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(snes->xl,&xl);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(snes->xu,&xu);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(snes->vec_sol,&x);CHKERRQ(ierr);
  ierr = MPI_Allreduce(&rnorm,&fnorm,1,MPIU_REAL,MPIU_SUM,((PetscObject)snes)->comm);CHKERRQ(ierr);
  ierr = MPI_Allreduce(act,fact,2,MPIU_INT,MPIU_SUM,((PetscObject)snes)->comm);CHKERRQ(ierr);
  ierr = MPI_Allreduce(act_bound,fact_bound,2,MPIU_INT,MPIU_SUM,((PetscObject)snes)->comm);CHKERRQ(ierr);
  fnorm = PetscSqrtReal(fnorm);

  ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES VI Function norm %14.12e Active lower constraints %D/%D upper constraints %D/%D Percent of total %g Percent of bounded %g\n",its,(double)fnorm,fact[0],fact_bound[0],fact[1],fact_bound[1],((double)(fact[0]+fact[1]))/((double)N),((double)(fact[0]+fact[1]))/((double)snes->ntruebounds));CHKERRQ(ierr);

  ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
     Checks if J^T F = 0 which implies we've found a local minimum of the norm of the function,
    || F(u) ||_2 but not a zero, F(u) = 0. In the case when one cannot compute J^T F we use the fact that
    0 = (J^T F)^T W = F^T J W iff W not in the null space of J. Thanks for Jorge More
    for this trick. One assumes that the probability that W is in the null space of J is very, very small.
*/
#undef __FUNCT__
#define __FUNCT__ "SNESVICheckLocalMin_Private"
PetscErrorCode SNESVICheckLocalMin_Private(SNES snes,Mat A,Vec F,Vec W,PetscReal fnorm,PetscBool *ismin)
{
  PetscReal      a1;
  PetscErrorCode ierr;
  PetscBool     hastranspose;

  PetscFunctionBegin;
  *ismin = PETSC_FALSE;
  ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr);
  if (hastranspose) {
    /* Compute || J^T F|| */
    ierr = MatMultTranspose(A,F,W);CHKERRQ(ierr);
    ierr = VecNorm(W,NORM_2,&a1);CHKERRQ(ierr);
    ierr = PetscInfo1(snes,"|| J^T F|| %g near zero implies found a local minimum\n",(double)(a1/fnorm));CHKERRQ(ierr);
    if (a1/fnorm < 1.e-4) *ismin = PETSC_TRUE;
  } else {
    Vec         work;
    PetscScalar result;
    PetscReal   wnorm;

    ierr = VecSetRandom(W,PETSC_NULL);CHKERRQ(ierr);
    ierr = VecNorm(W,NORM_2,&wnorm);CHKERRQ(ierr);
    ierr = VecDuplicate(W,&work);CHKERRQ(ierr);
    ierr = MatMult(A,W,work);CHKERRQ(ierr);
    ierr = VecDot(F,work,&result);CHKERRQ(ierr);
    ierr = VecDestroy(&work);CHKERRQ(ierr);
    a1   = PetscAbsScalar(result)/(fnorm*wnorm);
    ierr = PetscInfo1(snes,"(F^T J random)/(|| F ||*||random|| %g near zero implies found a local minimum\n",(double)a1);CHKERRQ(ierr);
    if (a1 < 1.e-4) *ismin = PETSC_TRUE;
  }
  PetscFunctionReturn(0);
}

/*
     Checks if J^T(F - J*X) = 0
*/
#undef __FUNCT__
#define __FUNCT__ "SNESVICheckResidual_Private"
PetscErrorCode SNESVICheckResidual_Private(SNES snes,Mat A,Vec F,Vec X,Vec W1,Vec W2)
{
  PetscReal      a1,a2;
  PetscErrorCode ierr;
  PetscBool     hastranspose;

  PetscFunctionBegin;
  ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr);
  if (hastranspose) {
    ierr = MatMult(A,X,W1);CHKERRQ(ierr);
    ierr = VecAXPY(W1,-1.0,F);CHKERRQ(ierr);

    /* Compute || J^T W|| */
    ierr = MatMultTranspose(A,W1,W2);CHKERRQ(ierr);
    ierr = VecNorm(W1,NORM_2,&a1);CHKERRQ(ierr);
    ierr = VecNorm(W2,NORM_2,&a2);CHKERRQ(ierr);
    if (a1 != 0.0) {
      ierr = PetscInfo1(snes,"||J^T(F-Ax)||/||F-AX|| %g near zero implies inconsistent rhs\n",(double)(a2/a1));CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

/*
  SNESDefaultConverged_VI - Checks the convergence of the semismooth newton algorithm.

  Notes:
  The convergence criterion currently implemented is
  merit < abstol
  merit < rtol*merit_initial
*/
#undef __FUNCT__
#define __FUNCT__ "SNESDefaultConverged_VI"
PetscErrorCode SNESDefaultConverged_VI(SNES snes,PetscInt it,PetscReal xnorm,PetscReal gradnorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
  PetscValidPointer(reason,6);

  *reason = SNES_CONVERGED_ITERATING;

  if (!it) {
    /* set parameter for default relative tolerance convergence test */
    snes->ttol = fnorm*snes->rtol;
  }
  if (fnorm != fnorm) {
    ierr = PetscInfo(snes,"Failed to converged, function norm is NaN\n");CHKERRQ(ierr);
    *reason = SNES_DIVERGED_FNORM_NAN;
  } else if (fnorm < snes->abstol) {
    ierr = PetscInfo2(snes,"Converged due to function norm %g < %g\n",(double)fnorm,(double)snes->abstol);CHKERRQ(ierr);
    *reason = SNES_CONVERGED_FNORM_ABS;
  } else if (snes->nfuncs >= snes->max_funcs) {
    ierr = PetscInfo2(snes,"Exceeded maximum number of function evaluations: %D > %D\n",snes->nfuncs,snes->max_funcs);CHKERRQ(ierr);
    *reason = SNES_DIVERGED_FUNCTION_COUNT;
  }

  if (it && !*reason) {
    if (fnorm < snes->ttol) {
      ierr = PetscInfo2(snes,"Converged due to function norm %g < %g (relative tolerance)\n",(double)fnorm,(double)snes->ttol);CHKERRQ(ierr);
      *reason = SNES_CONVERGED_FNORM_RELATIVE;
    }
  }
  PetscFunctionReturn(0);
}


/* -------------------------------------------------------------------------- */
/*
   SNESVIProjectOntoBounds - Projects X onto the feasible region so that Xl[i] <= X[i] <= Xu[i] for i = 1...n.

   Input Parameters:
.  SNES - nonlinear solver context

   Output Parameters:
.  X - Bound projected X

*/

#undef __FUNCT__
#define __FUNCT__ "SNESVIProjectOntoBounds"
PetscErrorCode SNESVIProjectOntoBounds(SNES snes,Vec X)
{
  PetscErrorCode    ierr;
  const PetscScalar *xl,*xu;
  PetscScalar       *x;
  PetscInt          i,n;

  PetscFunctionBegin;
  ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
  ierr = VecGetArray(X,&x);CHKERRQ(ierr);
  ierr = VecGetArrayRead(snes->xl,&xl);CHKERRQ(ierr);
  ierr = VecGetArrayRead(snes->xu,&xu);CHKERRQ(ierr);

  for(i = 0;i<n;i++) {
    if (PetscRealPart(x[i]) < PetscRealPart(xl[i])) x[i] = xl[i];
    else if (PetscRealPart(x[i]) > PetscRealPart(xu[i])) x[i] = xu[i];
  }
  ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(snes->xl,&xl);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(snes->xu,&xu);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "SNESVIGetActiveSetIS"
/*
   SNESVIGetActiveSetIndices - Gets the global indices for the active set variables

   Input parameter
.  snes - the SNES context
.  X    - the snes solution vector
.  F    - the nonlinear function vector

   Output parameter
.  ISact - active set index set
 */
PetscErrorCode SNESVIGetActiveSetIS(SNES snes,Vec X,Vec F,IS* ISact)
{
  PetscErrorCode   ierr;
  Vec               Xl=snes->xl,Xu=snes->xu;
  const PetscScalar *x,*f,*xl,*xu;
  PetscInt          *idx_act,i,nlocal,nloc_isact=0,ilow,ihigh,i1=0;

  PetscFunctionBegin;
  ierr = VecGetLocalSize(X,&nlocal);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(X,&ilow,&ihigh);CHKERRQ(ierr);
  ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
  ierr = VecGetArrayRead(Xl,&xl);CHKERRQ(ierr);
  ierr = VecGetArrayRead(Xu,&xu);CHKERRQ(ierr);
  ierr = VecGetArrayRead(F,&f);CHKERRQ(ierr);
  /* Compute active set size */
  for (i=0; i < nlocal;i++) {
    if (!((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + 1.e-8 || (PetscRealPart(f[i]) < 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - 1.e-8) || PetscRealPart(f[i]) > 0.0))) nloc_isact++;
  }

  ierr = PetscMalloc(nloc_isact*sizeof(PetscInt),&idx_act);CHKERRQ(ierr);

  /* Set active set indices */
  for(i=0; i < nlocal; i++) {
    if (!((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + 1.e-8 || (PetscRealPart(f[i]) < 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - 1.e-8) || PetscRealPart(f[i]) > 0.0))) idx_act[i1++] = ilow+i;
  }

   /* Create active set IS */
  ierr = ISCreateGeneral(((PetscObject)snes)->comm,nloc_isact,idx_act,PETSC_OWN_POINTER,ISact);CHKERRQ(ierr);

  ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(Xl,&xl);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(Xu,&xu);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(F,&f);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "SNESVICreateIndexSets_RS"
PetscErrorCode SNESVICreateIndexSets_RS(SNES snes,Vec X,Vec F,IS* ISact,IS* ISinact)
{
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = SNESVIGetActiveSetIS(snes,X,F,ISact);CHKERRQ(ierr);
  ierr = ISComplement(*ISact,X->map->rstart,X->map->rend,ISinact);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "SNESVIComputeInactiveSetFnorm"
PetscErrorCode SNESVIComputeInactiveSetFnorm(SNES snes,Vec F,Vec X,PetscReal *fnorm)
{
  PetscErrorCode    ierr;
  const PetscScalar *x,*xl,*xu,*f;
  PetscInt          i,n;
  PetscReal         rnorm;

  PetscFunctionBegin;
  ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
  ierr = VecGetArrayRead(snes->xl,&xl);CHKERRQ(ierr);
  ierr = VecGetArrayRead(snes->xu,&xu);CHKERRQ(ierr);
  ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
  ierr = VecGetArrayRead(F,&f);CHKERRQ(ierr);
  rnorm = 0.0;
  for (i=0; i<n; i++) {
    if (((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + 1.e-8 || (PetscRealPart(f[i]) < 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - 1.e-8) || PetscRealPart(f[i]) > 0.0))) rnorm += PetscRealPart(PetscConj(f[i])*f[i]);
  }
  ierr = VecRestoreArrayRead(F,&f);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(snes->xl,&xl);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(snes->xu,&xu);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
  ierr = MPI_Allreduce(&rnorm,fnorm,1,MPIU_REAL,MPIU_SUM,((PetscObject)snes)->comm);CHKERRQ(ierr);
  *fnorm = PetscSqrtReal(*fnorm);
  PetscFunctionReturn(0);
}


/* -------------------------------------------------------------------------- */
/*
   SNESSetUp_VI - Does setup common to all VI solvers -- basically makes sure bounds have been properly set up
   of the SNESVI nonlinear solver.

   Input Parameter:
.  snes - the SNES context
.  x - the solution vector

   Application Interface Routine: SNESSetUp()

   Notes:
   For basic use of the SNES solvers, the user need not explicitly call
   SNESSetUp(), since these actions will automatically occur during
   the call to SNESSolve().
 */
#undef __FUNCT__
#define __FUNCT__ "SNESSetUp_VI"
PetscErrorCode SNESSetUp_VI(SNES snes)
{
  PetscErrorCode ierr;
  PetscInt       i_start[3],i_end[3];

  PetscFunctionBegin;

  ierr = SNESDefaultGetWork(snes,3);CHKERRQ(ierr);

  if (snes->ops->computevariablebounds) {
    if (!snes->xl) {ierr = VecDuplicate(snes->vec_sol,&snes->xl);CHKERRQ(ierr);}
    if (!snes->xu) {ierr = VecDuplicate(snes->vec_sol,&snes->xu);CHKERRQ(ierr);}
    ierr = (*snes->ops->computevariablebounds)(snes,snes->xl,snes->xu);CHKERRQ(ierr);
  } else if (!snes->xl && !snes->xu) {
    /* If the lower and upper bound on variables are not set, set it to -Inf and Inf */
    ierr = VecDuplicate(snes->vec_sol, &snes->xl);CHKERRQ(ierr);
    ierr = VecSet(snes->xl,SNES_VI_NINF);CHKERRQ(ierr);
    ierr = VecDuplicate(snes->vec_sol, &snes->xu);CHKERRQ(ierr);
    ierr = VecSet(snes->xu,SNES_VI_INF);CHKERRQ(ierr);
  } else {
    /* Check if lower bound, upper bound and solution vector distribution across the processors is identical */
    ierr = VecGetOwnershipRange(snes->vec_sol,i_start,i_end);CHKERRQ(ierr);
    ierr = VecGetOwnershipRange(snes->xl,i_start+1,i_end+1);CHKERRQ(ierr);
    ierr = VecGetOwnershipRange(snes->xu,i_start+2,i_end+2);CHKERRQ(ierr);
    if ((i_start[0] != i_start[1]) || (i_start[0] != i_start[2]) || (i_end[0] != i_end[1]) || (i_end[0] != i_end[2]))
      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Distribution of lower bound, upper bound and the solution vector should be identical across all the processors.");
  }

  PetscFunctionReturn(0);
}
/* -------------------------------------------------------------------------- */
#undef __FUNCT__
#define __FUNCT__ "SNESReset_VI"
PetscErrorCode SNESReset_VI(SNES snes)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecDestroy(&snes->xl);CHKERRQ(ierr);
  ierr = VecDestroy(&snes->xu);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
   SNESDestroy_VI - Destroys the private SNES_VI context that was created
   with SNESCreate_VI().

   Input Parameter:
.  snes - the SNES context

   Application Interface Routine: SNESDestroy()
 */
#undef __FUNCT__
#define __FUNCT__ "SNESDestroy_VI"
PetscErrorCode SNESDestroy_VI(SNES snes)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscFree(snes->data);CHKERRQ(ierr);

  /* clear composed functions */
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSet_C","",PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetMonitor_C","",PETSC_NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */

/*

      These line searches are common for all the VI solvers
*/
extern PetscErrorCode SNESSolve_VISS(SNES);

#undef __FUNCT__
#define __FUNCT__ "SNESLineSearchNo_VI"

/*
  This routine does not actually do a line search but it takes a full newton
  step while ensuring that the new iterates remain within the constraints.

*/
PetscErrorCode SNESLineSearchNo_VI(SNES snes,void *lsctx,Vec x,Vec f,Vec y,PetscReal fnorm,PetscReal xnorm,Vec g,Vec w,PetscReal *ynorm,PetscReal *gnorm,PetscBool *flag)
{
  PetscErrorCode ierr;
  PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;

  PetscFunctionBegin;
  *flag = PETSC_TRUE;
  ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
  ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);         /* ynorm = || y || */
  ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
  ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
  if (snes->ops->postcheckstep) {
   ierr = (*snes->ops->postcheckstep)(snes,x,y,w,snes->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
  }
  if (changed_y) {
    ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
    ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
  }
  ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
  ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
  if (!snes->domainerror) {
    if (snes->ops->solve != SNESSolve_VISS) {
       ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
    } else {
      ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);  /* gnorm = || g || */
    }
    if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
  }
  if (snes->ls_monitor) {
    ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: Using full step: fnorm %g gnorm %g\n",(double)fnorm,(double)*gnorm);CHKERRQ(ierr);
    ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */
#undef __FUNCT__
#define __FUNCT__ "SNESLineSearchNoNorms_VI"

/*
  This routine is a copy of SNESLineSearchNoNorms in snes/impls/ls/ls.c
*/
PetscErrorCode SNESLineSearchNoNorms_VI(SNES snes,void *lsctx,Vec x,Vec f,Vec y,PetscReal fnorm,PetscReal xnorm,Vec g,Vec w,PetscReal *ynorm,PetscReal *gnorm,PetscBool *flag)
{
  PetscErrorCode ierr;
  PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;

  PetscFunctionBegin;
  *flag = PETSC_TRUE;
  ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
  ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y      */
  ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
  if (snes->ops->postcheckstep) {
   ierr = (*snes->ops->postcheckstep)(snes,x,y,w,snes->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
  }
  if (changed_y) {
    ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);            /* w <- x - y   */
    ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
  }

  /* don't evaluate function the last time through */
  if (snes->iter < snes->max_its-1) {
    ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */

#undef __FUNCT__
#define __FUNCT__ "SNESLineSearchCubic_VI"
/*
  This routine implements a cubic line search while doing a projection on the variable bounds
*/
PetscErrorCode SNESLineSearchCubic_VI(SNES snes,void *lsctx,Vec x,Vec f,Vec y,PetscReal fnorm,PetscReal xnorm,Vec g,Vec w,PetscReal *ynorm,PetscReal *gnorm,PetscBool *flag)
{
  PetscReal      initslope,lambdaprev,gnormprev,a,b,d,t1,t2,rellength;
  PetscReal      minlambda,lambda,lambdatemp;
#if defined(PETSC_USE_COMPLEX)
  PetscScalar    cinitslope;
#endif
  PetscErrorCode ierr;
  PetscInt       count;
  PetscBool      changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;
  MPI_Comm       comm;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
  ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
  *flag   = PETSC_TRUE;

  ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
  if (*ynorm == 0.0) {
    if (snes->ls_monitor) {
      ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: Initial direction and size is 0\n");CHKERRQ(ierr);
      ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
    }
    *gnorm = fnorm;
    ierr   = VecCopy(x,w);CHKERRQ(ierr);
    ierr   = VecCopy(f,g);CHKERRQ(ierr);
    *flag  = PETSC_FALSE;
    goto theend1;
  }
  if (*ynorm > snes->maxstep) {	/* Step too big, so scale back */
    if (snes->ls_monitor) {
      ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: Scaling step by %g old ynorm %g\n",(double)(snes->maxstep/(*ynorm)),(double)(*ynorm));CHKERRQ(ierr);
      ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
    }
    ierr = VecScale(y,snes->maxstep/(*ynorm));CHKERRQ(ierr);
    *ynorm = snes->maxstep;
  }
  ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
  minlambda = snes->steptol/rellength;
  ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
  ierr = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
  initslope = PetscRealPart(cinitslope);
#else
  ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
#endif
  if (initslope > 0.0)  initslope = -initslope;
  if (initslope == 0.0) initslope = -1.0;

  ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
  ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
  if (snes->nfuncs >= snes->max_funcs) {
    ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
    *flag = PETSC_FALSE;
    snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
    goto theend1;
  }
  ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
  if (snes->ops->solve != SNESSolve_VISS) {
    ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
  } else {
    ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
  }
  if (snes->domainerror) {
    ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
  ierr = PetscInfo4(snes,"Initial fnorm %g gnorm %g alpha %g initslope %g\n",(double)fnorm,(double)*gnorm,(double)snes->ls_alpha,(double)initslope);CHKERRQ(ierr);
  if ((*gnorm)*(*gnorm) <= (1.0 - snes->ls_alpha)*fnorm*fnorm ) { /* Sufficient reduction */
    if (snes->ls_monitor) {
      ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: Using full step: fnorm %g gnorm %g\n",(double)fnorm,(double)(*gnorm));CHKERRQ(ierr);
      ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
    }
    goto theend1;
  }

  /* Fit points with quadratic */
  lambda     = 1.0;
  lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
  lambdaprev = lambda;
  gnormprev  = *gnorm;
  if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
  if (lambdatemp <= .1*lambda) lambda = .1*lambda;
  else                         lambda = lambdatemp;

  ierr  = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
  ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
  if (snes->nfuncs >= snes->max_funcs) {
    ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while attempting quadratic backtracking! %D \n",snes->nfuncs);CHKERRQ(ierr);
    *flag = PETSC_FALSE;
    snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
    goto theend1;
  }
  ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
  if (snes->ops->solve != SNESSolve_VISS) {
    ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
  } else {
    ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
  }
  if (snes->domainerror) {
    ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
  if (snes->ls_monitor) {
    ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: gnorm after quadratic fit %g\n",(double)(*gnorm));CHKERRQ(ierr);
    ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  }
  if ((*gnorm)*(*gnorm) < (1.0 - snes->ls_alpha)*fnorm*fnorm ) { /* sufficient reduction */
    if (snes->ls_monitor) {
      ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: Quadratically determined step, lambda=%18.16e\n",(double)lambda);CHKERRQ(ierr);
      ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
    }
    goto theend1;
  }

  /* Fit points with cubic */
  count = 1;
  while (PETSC_TRUE) {
    if (lambda <= minlambda) {
      if (snes->ls_monitor) {
        ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
 	ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: unable to find good step length! After %D tries \n",count);CHKERRQ(ierr);
	ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, minlambda=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",(double)fnorm,(double)(*gnorm),(double)(*ynorm),(double)minlambda,(double)lambda,(double)initslope);CHKERRQ(ierr);
        ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      }
      *flag = PETSC_FALSE;
      break;
    }
    t1 = .5*((*gnorm)*(*gnorm) - fnorm*fnorm) - lambda*initslope;
    t2 = .5*(gnormprev*gnormprev  - fnorm*fnorm) - lambdaprev*initslope;
    a  = (t1/(lambda*lambda) - t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
    b  = (-lambdaprev*t1/(lambda*lambda) + lambda*t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
    d  = b*b - 3*a*initslope;
    if (d < 0.0) d = 0.0;
    if (a == 0.0) {
      lambdatemp = -initslope/(2.0*b);
    } else {
      lambdatemp = (-b + PetscSqrtReal(d))/(3.0*a);
    }
    lambdaprev = lambda;
    gnormprev  = *gnorm;
    if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
    if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
    else                         lambda     = lambdatemp;
    ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
    ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
    if (snes->nfuncs >= snes->max_funcs) {
      ierr = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
      ierr = PetscInfo5(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",(double)fnorm,(double)(*gnorm),(double)(*ynorm),(double)lambda,(double)initslope);CHKERRQ(ierr);
      *flag = PETSC_FALSE;
      snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
      break;
    }
    ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
    if (snes->ops->solve != SNESSolve_VISS) {
      ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
    } else {
      ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
    }
    if (snes->domainerror) {
      ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
      PetscFunctionReturn(0);
    }
    if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
    if ((*gnorm)*(*gnorm) < (1.0 - snes->ls_alpha)*fnorm*fnorm) { /* is reduction enough? */
      if (snes->ls_monitor) {
	ierr = PetscPrintf(comm,"    Line search: Cubically determined step, current gnorm %g lambda=%18.16e\n",(double)(*gnorm),(double)lambda);CHKERRQ(ierr);
      }
      break;
    } else {
      if (snes->ls_monitor) {
        ierr = PetscPrintf(comm,"    Line search: Cubic step no good, shrinking lambda, current gnorm %g lambda=%18.16e\n",(double)(*gnorm),(double)lambda);CHKERRQ(ierr);
      }
    }
    count++;
  }
  theend1:
  /* Optional user-defined check for line search step validity */
  if (snes->ops->postcheckstep && *flag) {
    ierr = (*snes->ops->postcheckstep)(snes,x,y,w,snes->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
    if (changed_y) {
      ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
      ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
    }
    if (changed_y || changed_w) { /* recompute the function if the step has changed */
      ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
      if (snes->ops->solve != SNESSolve_VISS) {
        ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
      } else {
        ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
      }
      if (snes->domainerror) {
        ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
        PetscFunctionReturn(0);
      }
      if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
      ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
      ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
    }
  }
  ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "SNESLineSearchQuadratic_VI"
/*
  This routine does a quadratic line search while keeping the iterates within the variable bounds
*/
PetscErrorCode SNESLineSearchQuadratic_VI(SNES snes,void *lsctx,Vec x,Vec f,Vec y,PetscReal fnorm,PetscReal xnorm,Vec g,Vec w,PetscReal *ynorm,PetscReal *gnorm,PetscBool *flag)
{
  /*
     Note that for line search purposes we work with with the related
     minimization problem:
        min  z(x):  R^n -> R,
     where z(x) = .5 * fnorm*fnorm,and fnorm = || f ||_2.
   */
  PetscReal      initslope,minlambda,lambda,lambdatemp,rellength;
#if defined(PETSC_USE_COMPLEX)
  PetscScalar    cinitslope;
#endif
  PetscErrorCode ierr;
  PetscInt       count;
  PetscBool     changed_w = PETSC_FALSE,changed_y = PETSC_FALSE;

  PetscFunctionBegin;
  ierr    = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
  *flag   = PETSC_TRUE;

  ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr);
  if (*ynorm == 0.0) {
    if (snes->ls_monitor) {
      ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"Line search: Direction and size is 0\n");CHKERRQ(ierr);
      ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
    }
    *gnorm = fnorm;
    ierr   = VecCopy(x,w);CHKERRQ(ierr);
    ierr   = VecCopy(f,g);CHKERRQ(ierr);
    *flag  = PETSC_FALSE;
    goto theend2;
  }
  if (*ynorm > snes->maxstep) {	/* Step too big, so scale back */
    ierr   = VecScale(y,snes->maxstep/(*ynorm));CHKERRQ(ierr);
    *ynorm = snes->maxstep;
  }
  ierr      = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr);
  minlambda = snes->steptol/rellength;
  ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
  ierr      = VecDot(f,w,&cinitslope);CHKERRQ(ierr);
  initslope = PetscRealPart(cinitslope);
#else
  ierr = VecDot(f,w,&initslope);CHKERRQ(ierr);
#endif
  if (initslope > 0.0)  initslope = -initslope;
  if (initslope == 0.0) initslope = -1.0;
  ierr = PetscInfo1(snes,"Initslope %g \n",(double)initslope);CHKERRQ(ierr);

  ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
  ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
  if (snes->nfuncs >= snes->max_funcs) {
    ierr  = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
    *flag = PETSC_FALSE;
    snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
    goto theend2;
  }
  ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
  if (snes->ops->solve != SNESSolve_VISS) {
    ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
  } else {
    ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
  }
  if (snes->domainerror) {
    ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
  if ((*gnorm)*(*gnorm) <= (1.0 - snes->ls_alpha)*fnorm*fnorm) { /* Sufficient reduction */
    if (snes->ls_monitor) {
      ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line search: Using full step: fnorm %g gnorm %g\n",(double)fnorm,(double)(*gnorm));CHKERRQ(ierr);
      ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
    }
    goto theend2;
  }

  /* Fit points with quadratic */
  lambda = 1.0;
  count = 1;
  while (PETSC_TRUE) {
    if (lambda <= minlambda) { /* bad luck; use full step */
      if (snes->ls_monitor) {
        ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"Line search: Unable to find good step length! %D \n",count);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"Line search: fnorm=%g, gnorm=%g, ynorm=%g, lambda=%g, initial slope=%g\n",(double)fnorm,(double)(*gnorm),(double)(*ynorm),(double)lambda,(double)initslope);CHKERRQ(ierr);
        ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      }
      ierr = VecCopy(x,w);CHKERRQ(ierr);
      *flag = PETSC_FALSE;
      break;
    }
    lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
    if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
    if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
    else                         lambda     = lambdatemp;

    ierr = VecWAXPY(w,-lambda,y,x);CHKERRQ(ierr);
    ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
    if (snes->nfuncs >= snes->max_funcs) {
      ierr  = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
      ierr  = PetscInfo5(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",(double)fnorm,(double)(*gnorm),(double)(*ynorm),(double)lambda,(double)initslope);CHKERRQ(ierr);
      *flag = PETSC_FALSE;
      snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
      break;
    }
    ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr);
    if (snes->domainerror) {
      ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
      PetscFunctionReturn(0);
    }
    if (snes->ops->solve != SNESSolve_VISS) {
      ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
    } else {
      ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
    }
    if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
    if ((*gnorm)*(*gnorm) < (1.0 - snes->ls_alpha)*fnorm*fnorm) { /* sufficient reduction */
      if (snes->ls_monitor) {
        ierr = PetscViewerASCIIAddTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(snes->ls_monitor,"    Line Search: Quadratically determined step, lambda=%g\n",(double)lambda);CHKERRQ(ierr);
        ierr = PetscViewerASCIISubtractTab(snes->ls_monitor,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
      }
      break;
    }
    count++;
  }
  theend2:
  /* Optional user-defined check for line search step validity */
  if (snes->ops->postcheckstep) {
    ierr = (*snes->ops->postcheckstep)(snes,x,y,w,snes->postcheck,&changed_y,&changed_w);CHKERRQ(ierr);
    if (changed_y) {
      ierr = VecWAXPY(w,-1.0,y,x);CHKERRQ(ierr);
      ierr = SNESVIProjectOntoBounds(snes,w);CHKERRQ(ierr);
    }
    if (changed_y || changed_w) { /* recompute the function if the step has changed */
      ierr = SNESComputeFunction(snes,w,g);
      if (snes->domainerror) {
        ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
        PetscFunctionReturn(0);
      }
      if (snes->ops->solve != SNESSolve_VISS) {
        ierr = SNESVIComputeInactiveSetFnorm(snes,g,w,gnorm);CHKERRQ(ierr);
      } else {
        ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr);
      }

      ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr);
      ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr);
      if (PetscIsInfOrNanReal(*gnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"User provided compute function generated a Not-a-Number");
    }
  }
  ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "SNESVISetVariableBounds"
/*@
   SNESVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu.

   Input Parameters:
.  snes - the SNES context.
.  xl   - lower bound.
.  xu   - upper bound.

   Notes:
   If this routine is not called then the lower and upper bounds are set to
   SNES_VI_INF and SNES_VI_NINF respectively during SNESSetUp().

   Level: advanced

@*/
PetscErrorCode SNESVISetVariableBounds(SNES snes, Vec xl, Vec xu)
{
  PetscErrorCode    ierr;
  const PetscScalar *xxl,*xxu;
  PetscInt          i,n, cnt = 0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
  PetscValidHeaderSpecific(xl,VEC_CLASSID,2);
  PetscValidHeaderSpecific(xu,VEC_CLASSID,3);
  ierr = SNESGetFunction(snes,&snes->vec_func,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
  if (!snes->vec_func) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call SNESSetFunction() or SNESSetDM() first");
  if (xl->map->N != snes->vec_func->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incompatible vector lengths lower bound = %D solution vector = %D",xl->map->N,snes->vec_func->map->N);
  if (xu->map->N != snes->vec_func->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incompatible vector lengths: upper bound = %D solution vector = %D",xu->map->N,snes->vec_func->map->N);
  ierr = SNESSetType(snes,SNESVIRS);CHKERRQ(ierr);
  ierr = PetscObjectReference((PetscObject)xl);CHKERRQ(ierr);
  ierr = PetscObjectReference((PetscObject)xu);CHKERRQ(ierr);
  ierr = VecDestroy(&snes->xl);CHKERRQ(ierr);
  ierr = VecDestroy(&snes->xu);CHKERRQ(ierr);
  snes->xl = xl;
  snes->xu = xu;
  ierr = VecGetLocalSize(xl,&n);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xl,&xxl);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xu,&xxu);CHKERRQ(ierr);
  for (i=0; i<n; i++) {
    cnt += ((xxl[i] != SNES_VI_NINF) || (xxu[i] != SNES_VI_INF));
  }
  ierr = MPI_Allreduce(&cnt,&snes->ntruebounds,1,MPIU_INT,MPI_SUM,((PetscObject)snes)->comm);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xl,&xxl);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xu,&xxu);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "SNESLineSearchSetType_VI"
PetscErrorCode  SNESLineSearchSetType_VI(SNES snes, SNESLineSearchType type)
{
  PetscErrorCode ierr;
  PetscFunctionBegin;

  switch (type) {
  case SNES_LS_BASIC:
    ierr = SNESLineSearchSet(snes,SNESLineSearchNo_VI,PETSC_NULL);CHKERRQ(ierr);
    break;
  case SNES_LS_BASIC_NONORMS:
    ierr = SNESLineSearchSet(snes,SNESLineSearchNoNorms_VI,PETSC_NULL);CHKERRQ(ierr);
    break;
  case SNES_LS_QUADRATIC:
    ierr = SNESLineSearchSet(snes,SNESLineSearchQuadratic_VI,PETSC_NULL);CHKERRQ(ierr);
    break;
  case SNES_LS_CUBIC:
    ierr = SNESLineSearchSet(snes,SNESLineSearchCubic_VI,PETSC_NULL);CHKERRQ(ierr);
    break;
  default:
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP,"Unknown line search type");
    break;
  }
  snes->ls_type = type;
  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "SNESSetFromOptions_VI"
PetscErrorCode SNESSetFromOptions_VI(SNES snes)
{
  PetscErrorCode  ierr;
  PetscBool       flg;

  PetscFunctionBegin;
  ierr = PetscOptionsHead("SNES VI options");CHKERRQ(ierr);
  ierr = PetscOptionsBool("-snes_vi_monitor","Monitor all non-active variables","None",PETSC_FALSE,&flg,0);CHKERRQ(ierr);
  if (flg) {
    ierr = SNESMonitorSet(snes,SNESMonitorVI,0,0);CHKERRQ(ierr);
  }
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}