impls/vi/vi.c

#include <petsc/private/snesimpl.h> /*I "petscsnes.h" I*/
#include <petscdm.h>

/*@C
   SNESVISetComputeVariableBounds - Sets a function that is called to compute the bounds on variable for
   (differential) variable inequalities.

   Input parameter:
+  snes - the `SNES` context
-  compute - function that computes the bounds

 Calling Sequence of function:
  PetscErrorCode compute(SNES snes,Vec lower,Vec higher, void *ctx)

+ snes - the `SNES` context
. lower - vector to hold lower bounds
- higher - vector to hold upper bounds

   Level: advanced

   Notes:
   Problems with bound constraints can be solved with the reduced space, `SNESVINEWTONRSLS`, and semi-smooth `SNESVINEWTONSSLS` solvers.

   For entries with no bounds you can set `PETSC_NINFINITY` or `PETSC_INFINITY`

   You may use `SNESVISetVariableBounds()` to provide the bounds once if they will never change

   If you have associated a `DM` with the `SNES` and provided a function to the `DM` via `DMSetVariableBounds()` that will be used automatically
   to provide the bounds and you need not use this function.

.seealso: `SNESVISetVariableBounds()`, `DMSetVariableBounds()`, `SNESSetFunctionDomainError()`, `SNESSetJacobianDomainError()`, `SNESVINEWTONRSLS`, `SNESVINEWTONSSLS`,
          'SNESSetType()`
@*/
PetscErrorCode SNESVISetComputeVariableBounds(SNES snes, PetscErrorCode (*compute)(SNES, Vec, Vec))
{
  PetscErrorCode (*f)(SNES, PetscErrorCode(*)(SNES, Vec, Vec));

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes, SNES_CLASSID, 1);
  PetscCall(PetscObjectQueryFunction((PetscObject)snes, "SNESVISetComputeVariableBounds_C", &f));
  if (f) PetscUseMethod(snes, "SNESVISetComputeVariableBounds_C", (SNES, PetscErrorCode(*)(SNES, Vec, Vec)), (snes, compute));
  else PetscCall(SNESVISetComputeVariableBounds_VI(snes, compute));
  PetscFunctionReturn(0);
}

PetscErrorCode SNESVISetComputeVariableBounds_VI(SNES snes, SNESVIComputeVariableBoundsFunction compute)
{
  PetscFunctionBegin;
  snes->ops->computevariablebounds = compute;
  PetscFunctionReturn(0);
}

PetscErrorCode SNESVIMonitorResidual(SNES snes, PetscInt its, PetscReal fgnorm, void *dummy)
{
  Vec         X, F, Finactive;
  IS          isactive;
  PetscViewer viewer = (PetscViewer)dummy;

  PetscFunctionBegin;
  PetscCall(SNESGetFunction(snes, &F, NULL, NULL));
  PetscCall(SNESGetSolution(snes, &X));
  PetscCall(SNESVIGetActiveSetIS(snes, X, F, &isactive));
  PetscCall(VecDuplicate(F, &Finactive));
  PetscCall(VecCopy(F, Finactive));
  PetscCall(VecISSet(Finactive, isactive, 0.0));
  PetscCall(ISDestroy(&isactive));
  PetscCall(VecView(Finactive, viewer));
  PetscCall(VecDestroy(&Finactive));
  PetscFunctionReturn(0);
}

PetscErrorCode SNESMonitorVI(SNES snes, PetscInt its, PetscReal fgnorm, void *dummy)
{
  PetscViewer        viewer = (PetscViewer)dummy;
  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, zerotolerance = snes->vizerotolerance;
  double    tmp;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 4);
  PetscCall(VecGetLocalSize(snes->vec_sol, &n));
  PetscCall(VecGetSize(snes->vec_sol, &N));
  PetscCall(VecGetArrayRead(snes->xl, &xl));
  PetscCall(VecGetArrayRead(snes->xu, &xu));
  PetscCall(VecGetArrayRead(snes->vec_sol, &x));
  PetscCall(VecGetArrayRead(snes->vec_func, &f));

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

  for (i = 0; i < n; i++) {
    if (PetscRealPart(x[i]) <= PetscRealPart(xl[i]) + zerotolerance) act_bound[0]++;
    else if (PetscRealPart(x[i]) >= PetscRealPart(xu[i]) - zerotolerance) act_bound[1]++;
  }
  PetscCall(VecRestoreArrayRead(snes->vec_func, &f));
  PetscCall(VecRestoreArrayRead(snes->xl, &xl));
  PetscCall(VecRestoreArrayRead(snes->xu, &xu));
  PetscCall(VecRestoreArrayRead(snes->vec_sol, &x));
  PetscCall(MPIU_Allreduce(&rnorm, &fnorm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)snes)));
  PetscCall(MPIU_Allreduce(act, fact, 2, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)snes)));
  PetscCall(MPIU_Allreduce(act_bound, fact_bound, 2, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)snes)));
  fnorm = PetscSqrtReal(fnorm);

  PetscCall(PetscViewerASCIIAddTab(viewer, ((PetscObject)snes)->tablevel));
  if (snes->ntruebounds) tmp = ((double)(fact[0] + fact[1])) / ((double)snes->ntruebounds);
  else tmp = 0.0;
  PetscCall(PetscViewerASCIIPrintf(viewer, "%3" PetscInt_FMT " SNES VI Function norm %g Active lower constraints %" PetscInt_FMT "/%" PetscInt_FMT " upper constraints %" PetscInt_FMT "/%" PetscInt_FMT " 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), tmp));

  PetscCall(PetscViewerASCIISubtractTab(viewer, ((PetscObject)snes)->tablevel));
  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.
*/
PetscErrorCode SNESVICheckLocalMin_Private(SNES snes, Mat A, Vec F, Vec W, PetscReal fnorm, PetscBool *ismin)
{
  PetscReal a1;
  PetscBool hastranspose;

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

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

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

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

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

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

  Notes:
  The convergence criterion currently implemented is
  merit < abstol
  merit < rtol*merit_initial
*/
PetscErrorCode SNESConvergedDefault_VI(SNES snes, PetscInt it, PetscReal xnorm, PetscReal gradnorm, PetscReal fnorm, SNESConvergedReason *reason, void *dummy)
{
  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) {
    PetscCall(PetscInfo(snes, "Failed to converged, function norm is NaN\n"));
    *reason = SNES_DIVERGED_FNORM_NAN;
  } else if (fnorm < snes->abstol && (it || !snes->forceiteration)) {
    PetscCall(PetscInfo(snes, "Converged due to function norm %g < %g\n", (double)fnorm, (double)snes->abstol));
    *reason = SNES_CONVERGED_FNORM_ABS;
  } else if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
    PetscCall(PetscInfo(snes, "Exceeded maximum number of function evaluations: %" PetscInt_FMT " > %" PetscInt_FMT "\n", snes->nfuncs, snes->max_funcs));
    *reason = SNES_DIVERGED_FUNCTION_COUNT;
  }

  if (it && !*reason) {
    if (fnorm < snes->ttol) {
      PetscCall(PetscInfo(snes, "Converged due to function norm %g < %g (relative tolerance)\n", (double)fnorm, (double)snes->ttol));
      *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

*/

PetscErrorCode SNESVIProjectOntoBounds(SNES snes, Vec X)
{
  const PetscScalar *xl, *xu;
  PetscScalar       *x;
  PetscInt           i, n;

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

  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];
  }
  PetscCall(VecRestoreArray(X, &x));
  PetscCall(VecRestoreArrayRead(snes->xl, &xl));
  PetscCall(VecRestoreArrayRead(snes->xu, &xu));
  PetscFunctionReturn(0);
}

/*
   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)
{
  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;
  PetscReal          zerotolerance = snes->vizerotolerance;

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

  PetscCall(PetscMalloc1(nloc_isact, &idx_act));

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

  /* Create active set IS */
  PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)snes), nloc_isact, idx_act, PETSC_OWN_POINTER, ISact));

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

PetscErrorCode SNESVICreateIndexSets_RS(SNES snes, Vec X, Vec F, IS *ISact, IS *ISinact)
{
  PetscInt rstart, rend;

  PetscFunctionBegin;
  PetscCall(SNESVIGetActiveSetIS(snes, X, F, ISact));
  PetscCall(VecGetOwnershipRange(X, &rstart, &rend));
  PetscCall(ISComplement(*ISact, rstart, rend, ISinact));
  PetscFunctionReturn(0);
}

PetscErrorCode SNESVIComputeInactiveSetFnorm(SNES snes, Vec F, Vec X, PetscReal *fnorm)
{
  const PetscScalar *x, *xl, *xu, *f;
  PetscInt           i, n;
  PetscReal          rnorm, zerotolerance = snes->vizerotolerance;

  PetscFunctionBegin;
  PetscCall(VecGetLocalSize(X, &n));
  PetscCall(VecGetArrayRead(snes->xl, &xl));
  PetscCall(VecGetArrayRead(snes->xu, &xu));
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(VecGetArrayRead(F, &f));
  rnorm = 0.0;
  for (i = 0; i < n; i++) {
    if (((PetscRealPart(x[i]) > PetscRealPart(xl[i]) + zerotolerance || (PetscRealPart(f[i]) <= 0.0)) && ((PetscRealPart(x[i]) < PetscRealPart(xu[i]) - zerotolerance) || PetscRealPart(f[i]) >= 0.0))) rnorm += PetscRealPart(PetscConj(f[i]) * f[i]);
  }
  PetscCall(VecRestoreArrayRead(F, &f));
  PetscCall(VecRestoreArrayRead(snes->xl, &xl));
  PetscCall(VecRestoreArrayRead(snes->xu, &xu));
  PetscCall(VecRestoreArrayRead(X, &x));
  PetscCall(MPIU_Allreduce(&rnorm, fnorm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)snes)));
  *fnorm = PetscSqrtReal(*fnorm);
  PetscFunctionReturn(0);
}

PetscErrorCode SNESVIDMComputeVariableBounds(SNES snes, Vec xl, Vec xu)
{
  PetscFunctionBegin;
  PetscCall(DMComputeVariableBounds(snes->dm, xl, xu));
  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

   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().
 */
PetscErrorCode SNESSetUp_VI(SNES snes)
{
  PetscInt i_start[3], i_end[3];

  PetscFunctionBegin;
  PetscCall(SNESSetWorkVecs(snes, 1));
  PetscCall(SNESSetUpMatrices(snes));

  if (!snes->ops->computevariablebounds && snes->dm) {
    PetscBool flag;
    PetscCall(DMHasVariableBounds(snes->dm, &flag));
    if (flag) snes->ops->computevariablebounds = SNESVIDMComputeVariableBounds;
  }
  if (!snes->usersetbounds) {
    if (snes->ops->computevariablebounds) {
      if (!snes->xl) PetscCall(VecDuplicate(snes->vec_sol, &snes->xl));
      if (!snes->xu) PetscCall(VecDuplicate(snes->vec_sol, &snes->xu));
      PetscUseTypeMethod(snes, computevariablebounds, snes->xl, snes->xu);
    } else if (!snes->xl && !snes->xu) {
      /* If the lower and upper bound on variables are not set, set it to -Inf and Inf */
      PetscCall(VecDuplicate(snes->vec_sol, &snes->xl));
      PetscCall(VecSet(snes->xl, PETSC_NINFINITY));
      PetscCall(VecDuplicate(snes->vec_sol, &snes->xu));
      PetscCall(VecSet(snes->xu, PETSC_INFINITY));
    } else {
      /* Check if lower bound, upper bound and solution vector distribution across the processors is identical */
      PetscCall(VecGetOwnershipRange(snes->vec_sol, i_start, i_end));
      PetscCall(VecGetOwnershipRange(snes->xl, i_start + 1, i_end + 1));
      PetscCall(VecGetOwnershipRange(snes->xu, i_start + 2, i_end + 2));
      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);
}
PetscErrorCode SNESReset_VI(SNES snes)
{
  PetscFunctionBegin;
  PetscCall(VecDestroy(&snes->xl));
  PetscCall(VecDestroy(&snes->xu));
  snes->usersetbounds = PETSC_FALSE;
  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()
 */
PetscErrorCode SNESDestroy_VI(SNES snes)
{
  PetscFunctionBegin;
  PetscCall(PetscFree(snes->data));

  /* clear composed functions */
  PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESVISetVariableBounds_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESVISetComputeVariableBounds_C", NULL));
  PetscFunctionReturn(0);
}

/*@
   SNESVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu. This allows solving
   (differential) variable inequalities.

   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
   `PETSC_NINFINITY` and `PETSC_INFINITY` respectively during `SNESSetUp()`.

   Problems with bound constraints can be solved with the reduced space, `SNESVINEWTONRSLS`, and semi-smooth `SNESVINEWTONSSLS` solvers.

   For particular components that have no bounds you can use `PETSC_NINFINITY` or `PETSC_INFINITY`

   `SNESVISetVariableBounds()` can be used to provide a function that computes the bounds. This should be used if you are using, for example, grid
   sequencing and need bounds set for a variety of vectors

   Level: advanced

.seealso: `SNESVISetComputeVariableBounds()`, `SNESSetFunctionDomainError()`, `SNESSetJacobianDomainError()`, SNESVINEWTONRSLS, SNESVINEWTONSSLS, 'SNESSetType()`
@*/
PetscErrorCode SNESVISetVariableBounds(SNES snes, Vec xl, Vec xu)
{
  PetscErrorCode (*f)(SNES, Vec, Vec);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes, SNES_CLASSID, 1);
  PetscValidHeaderSpecific(xl, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(xu, VEC_CLASSID, 3);
  PetscCall(PetscObjectQueryFunction((PetscObject)snes, "SNESVISetVariableBounds_C", &f));
  if (f) PetscUseMethod(snes, "SNESVISetVariableBounds_C", (SNES, Vec, Vec), (snes, xl, xu));
  else PetscCall(SNESVISetVariableBounds_VI(snes, xl, xu));
  snes->usersetbounds = PETSC_TRUE;
  PetscFunctionReturn(0);
}

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

  PetscFunctionBegin;
  PetscCall(SNESGetFunction(snes, &snes->vec_func, NULL, NULL));
  PetscCheck(snes->vec_func, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call SNESSetFunction() or SNESSetDM() first");
  {
    PetscInt xlN, xuN, N;
    PetscCall(VecGetSize(xl, &xlN));
    PetscCall(VecGetSize(xu, &xuN));
    PetscCall(VecGetSize(snes->vec_func, &N));
    PetscCheck(xlN == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Incompatible vector lengths lower bound = %" PetscInt_FMT " solution vector = %" PetscInt_FMT, xlN, N);
    PetscCheck(xuN == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Incompatible vector lengths: upper bound = %" PetscInt_FMT " solution vector = %" PetscInt_FMT, xuN, N);
  }
  PetscCall(PetscObjectReference((PetscObject)xl));
  PetscCall(PetscObjectReference((PetscObject)xu));
  PetscCall(VecDestroy(&snes->xl));
  PetscCall(VecDestroy(&snes->xu));
  snes->xl = xl;
  snes->xu = xu;
  PetscCall(VecGetLocalSize(xl, &n));
  PetscCall(VecGetArrayRead(xl, &xxl));
  PetscCall(VecGetArrayRead(xu, &xxu));
  for (i = 0; i < n; i++) cnt += ((xxl[i] != PETSC_NINFINITY) || (xxu[i] != PETSC_INFINITY));

  PetscCall(MPIU_Allreduce(&cnt, &snes->ntruebounds, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)snes)));
  PetscCall(VecRestoreArrayRead(xl, &xxl));
  PetscCall(VecRestoreArrayRead(xu, &xxu));
  PetscFunctionReturn(0);
}

PetscErrorCode SNESSetFromOptions_VI(SNES snes, PetscOptionItems *PetscOptionsObject)
{
  PetscBool flg = PETSC_FALSE;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "SNES VI options");
  PetscCall(PetscOptionsReal("-snes_vi_zero_tolerance", "Tolerance for considering x[] value to be on a bound", "None", snes->vizerotolerance, &snes->vizerotolerance, NULL));
  PetscCall(PetscOptionsBool("-snes_vi_monitor", "Monitor all non-active variables", "SNESMonitorResidual", flg, &flg, NULL));
  if (flg) PetscCall(SNESMonitorSet(snes, SNESMonitorVI, PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes)), NULL));
  flg = PETSC_FALSE;
  PetscCall(PetscOptionsBool("-snes_vi_monitor_residual", "Monitor residual all non-active variables; using zero for active constraints", "SNESMonitorVIResidual", flg, &flg, NULL));
  if (flg) PetscCall(SNESMonitorSet(snes, SNESVIMonitorResidual, PETSC_VIEWER_DRAW_(PetscObjectComm((PetscObject)snes)), NULL));
  PetscOptionsHeadEnd();
  PetscFunctionReturn(0);
}