xref: /petsc/src/tao/bound/utils/isutil.c (revision 53506e15f4c198475be287552ae23f63a4890445)

#include "tao.h" /*I "tao.h" I*/
#include "petsc-private/matimpl.h"
#include "../src/tao/matrix/submatfree.h"
#include "tao_util.h" /*I "tao_util.h" I*/


#undef __FUNCT__
#define __FUNCT__ "VecWhichEqual"
/*@
  VecWhichEqual - Creates an index set containing the indices
             where the vectors Vec1 and Vec2 have identical elements.

  Collective on Vec

  Input Parameters:
. Vec1, Vec2 - the two vectors to compare

  OutputParameter:
. S - The index set containing the indices i where vec1[i] == vec2[i]

  Level: advanced
@*/
PetscErrorCode VecWhichEqual(Vec Vec1, Vec Vec2, IS * S)
{
  PetscErrorCode  ierr;
  PetscInt        i,n_same = 0;
  PetscInt        n,low,high,low2,high2;
  PetscInt        *same = NULL;
  PetscReal       *v1,*v2;
  MPI_Comm        comm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(Vec1,VEC_CLASSID,1);
  PetscValidHeaderSpecific(Vec2,VEC_CLASSID,2);
  PetscCheckSameComm(Vec1,1,Vec2,2);

  ierr = VecGetOwnershipRange(Vec1, &low, &high);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(Vec2, &low2, &high2);CHKERRQ(ierr);
  if ( low != low2 || high != high2 ) SETERRQ(PETSC_COMM_SELF,1,"Vectors must have identical layout");

  ierr = VecGetLocalSize(Vec1,&n);CHKERRQ(ierr);
  if (n>0){
    if (Vec1 == Vec2){
      ierr = VecGetArray(Vec1,&v1);CHKERRQ(ierr);
      v2=v1;
    } else {
      ierr = VecGetArray(Vec1,&v1);CHKERRQ(ierr);
      ierr = VecGetArray(Vec2,&v2);CHKERRQ(ierr);
    }

    ierr = PetscMalloc( n*sizeof(PetscInt),&same );CHKERRQ(ierr);

    for (i=0; i<n; i++){
      if (v1[i] == v2[i]) {same[n_same]=low+i; n_same++;}
    }

    if (Vec1 == Vec2){
      ierr = VecRestoreArray(Vec1,&v1);CHKERRQ(ierr);
    } else {
      ierr = VecRestoreArray(Vec1,&v1);CHKERRQ(ierr);
      ierr = VecRestoreArray(Vec2,&v2);CHKERRQ(ierr);
    }
  }
  ierr = PetscObjectGetComm((PetscObject)Vec1,&comm);CHKERRQ(ierr);
  ierr = ISCreateGeneral(comm,n_same,same,PETSC_OWN_POINTER,S);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecWhichLessThan"
/*@
  VecWhichLessThan - Creates an index set containing the indices
  where the vectors Vec1 < Vec2

  Collective on S

  Input Parameters:
. Vec1, Vec2 - the two vectors to compare

  OutputParameter:
. S - The index set containing the indices i where vec1[i] < vec2[i]

  Level: advanced
@*/
PetscErrorCode VecWhichLessThan(Vec Vec1, Vec Vec2, IS * S)
{
  PetscErrorCode ierr;
  PetscInt       i;
  PetscInt       n,low,high,low2,high2,n_lt=0;
  PetscInt       *lt = NULL;
  PetscReal      *v1,*v2;
  MPI_Comm       comm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(Vec1,VEC_CLASSID,1);
  PetscValidHeaderSpecific(Vec2,VEC_CLASSID,2);
  PetscCheckSameComm(Vec1,1,Vec2,2);

  ierr = VecGetOwnershipRange(Vec1, &low, &high);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(Vec2, &low2, &high2);CHKERRQ(ierr);
  if ( low != low2 || high != high2 ) SETERRQ(PETSC_COMM_SELF,1,"Vectors must haveidentical layout");

  ierr = VecGetLocalSize(Vec1,&n);CHKERRQ(ierr);
  if (n>0){
    if (Vec1 == Vec2){
      ierr = VecGetArray(Vec1,&v1);CHKERRQ(ierr);
      v2=v1;
    } else {
      ierr = VecGetArray(Vec1,&v1);CHKERRQ(ierr);
      ierr = VecGetArray(Vec2,&v2);CHKERRQ(ierr);
    }
    ierr = PetscMalloc( n*sizeof(PetscInt),&lt );CHKERRQ(ierr);

    for (i=0; i<n; i++){
      if (v1[i] < v2[i]) {lt[n_lt]=low+i; n_lt++;}
    }

    if (Vec1 == Vec2){
      ierr = VecRestoreArray(Vec1,&v1);CHKERRQ(ierr);
    } else {
      ierr = VecRestoreArray(Vec1,&v1);CHKERRQ(ierr);
      ierr = VecRestoreArray(Vec2,&v2);CHKERRQ(ierr);
    }
  }
  ierr = PetscObjectGetComm((PetscObject)Vec1,&comm);CHKERRQ(ierr);
  ierr = ISCreateGeneral(comm,n_lt,lt,PETSC_OWN_POINTER,S);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecWhichGreaterThan"
/*@
  VecWhichGreaterThan - Creates an index set containing the indices
  where the vectors Vec1 > Vec2

  Collective on S

  Input Parameters:
. Vec1, Vec2 - the two vectors to compare

  OutputParameter:
. S - The index set containing the indices i where vec1[i] > vec2[i]

  Level: advanced
@*/
PetscErrorCode VecWhichGreaterThan(Vec Vec1, Vec Vec2, IS * S)
{
  PetscErrorCode ierr;
  PetscInt       n,low,high,low2,high2,n_gt=0,i;
  PetscInt       *gt=NULL;
  PetscReal      *v1,*v2;
  MPI_Comm       comm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(Vec1,VEC_CLASSID,1);
  PetscValidHeaderSpecific(Vec2,VEC_CLASSID,2);
  PetscCheckSameComm(Vec1,1,Vec2,2);

  ierr = VecGetOwnershipRange(Vec1, &low, &high);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(Vec2, &low2, &high2);CHKERRQ(ierr);
  if ( low != low2 || high != high2 ) SETERRQ(PETSC_COMM_SELF,1,"Vectors must be have identical layout");

  ierr = VecGetLocalSize(Vec1,&n);CHKERRQ(ierr);

  if (n>0){

    if (Vec1 == Vec2){
      ierr = VecGetArray(Vec1,&v1);CHKERRQ(ierr);
      v2=v1;
    } else {
      ierr = VecGetArray(Vec1,&v1);CHKERRQ(ierr);
      ierr = VecGetArray(Vec2,&v2);CHKERRQ(ierr);
    }

    ierr = PetscMalloc( n*sizeof(PetscInt), &gt );CHKERRQ(ierr);

    for (i=0; i<n; i++){
      if (v1[i] > v2[i]) {gt[n_gt]=low+i; n_gt++;}
    }

    if (Vec1 == Vec2){
      ierr = VecRestoreArray(Vec1,&v1);CHKERRQ(ierr);
    } else {
      ierr = VecRestoreArray(Vec1,&v1);CHKERRQ(ierr);
      ierr = VecRestoreArray(Vec2,&v2);CHKERRQ(ierr);
    }
  }
  ierr = PetscObjectGetComm((PetscObject)Vec1,&comm);CHKERRQ(ierr);
  ierr = ISCreateGeneral(comm,n_gt,gt,PETSC_OWN_POINTER,S);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecWhichBetween"
/*@
  VecWhichBetween - Creates an index set containing the indices
               where  VecLow < V < VecHigh

  Collective on S

  Input Parameters:
+ VecLow - lower bound
. V - Vector to compare
- VecHigh - higher bound

  OutputParameter:
. S - The index set containing the indices i where veclow[i] < v[i] < vechigh[i]

  Level: advanced
@*/
PetscErrorCode VecWhichBetween(Vec VecLow, Vec V, Vec VecHigh, IS *S)
{

  PetscErrorCode ierr;
  PetscInt       n,low,high,low2,high2,low3,high3,n_vm=0;
  PetscInt       *vm,i;
  PetscReal      *v1,*v2,*vmiddle;
  MPI_Comm       comm;

  PetscValidHeaderSpecific(V,VEC_CLASSID,2);
  PetscCheckSameComm(V,2,VecLow,1); PetscCheckSameComm(V,2,VecHigh,3);

  ierr = VecGetOwnershipRange(VecLow, &low, &high);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(VecHigh, &low2, &high2);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(V, &low3, &high3);CHKERRQ(ierr);
  if ( low!=low2 || high!=high2 || low!=low3 || high!=high3) SETERRQ(PETSC_COMM_SELF,1,"Vectors must have identical layout");

  ierr = VecGetLocalSize(VecLow,&n);CHKERRQ(ierr);
  if (n>0){
    ierr = VecGetArray(VecLow,&v1);CHKERRQ(ierr);
    if (VecLow != VecHigh){
      ierr = VecGetArray(VecHigh,&v2);CHKERRQ(ierr);
    } else {
      v2=v1;
    }
    if ( V != VecLow && V != VecHigh){
      ierr = VecGetArray(V,&vmiddle);CHKERRQ(ierr);
    } else if ( V==VecLow ){
      vmiddle=v1;
    } else {
      vmiddle =v2;
    }

    ierr = PetscMalloc( n*sizeof(PetscInt), &vm );CHKERRQ(ierr);

    for (i=0; i<n; i++){
      if (v1[i] < vmiddle[i] && vmiddle[i] < v2[i]) {vm[n_vm]=low+i; n_vm++;}
    }

    ierr = VecRestoreArray(VecLow,&v1);CHKERRQ(ierr);
    if (VecLow != VecHigh){
      ierr = VecRestoreArray(VecHigh,&v2);CHKERRQ(ierr);
    }
    if ( V != VecLow && V != VecHigh){
      ierr = VecRestoreArray(V,&vmiddle);CHKERRQ(ierr);
    }
  }
  ierr = PetscObjectGetComm((PetscObject)V,&comm);CHKERRQ(ierr);
  ierr = ISCreateGeneral(comm,n_vm,vm,PETSC_OWN_POINTER,S);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "VecWhichBetweenOrEqual"
/*@
  VecWhichBetweenOrEqual - Creates an index set containing the indices
  where  VecLow <= V <= VecHigh

  Collective on S

  Input Parameters:
+ VecLow - lower bound
. V - Vector to compare
- VecHigh - higher bound

  OutputParameter:
. S - The index set containing the indices i where veclow[i] <= v[i] <= vechigh[i]

  Level: advanced
@*/

PetscErrorCode VecWhichBetweenOrEqual(Vec VecLow, Vec V, Vec VecHigh, IS * S)
{
  PetscErrorCode ierr;
  PetscInt       n,low,high,low2,high2,low3,high3,n_vm=0,i;
  PetscInt       *vm = NULL;
  PetscReal      *v1,*v2,*vmiddle;
  MPI_Comm       comm;

  PetscValidHeaderSpecific(V,VEC_CLASSID,2);
  PetscCheckSameComm(V,2,VecLow,1); PetscCheckSameComm(V,2,VecHigh,3);

  ierr = VecGetOwnershipRange(VecLow, &low, &high);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(VecHigh, &low2, &high2);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(V, &low3, &high3);CHKERRQ(ierr);
  if ( low!=low2 || high!=high2 || low!=low3 || high!=high3 ) SETERRQ(PETSC_COMM_SELF,1,"Vectors must have identical layout");

  ierr = VecGetLocalSize(VecLow,&n);CHKERRQ(ierr);

  if (n>0){
    ierr = VecGetArray(VecLow,&v1);CHKERRQ(ierr);
    if (VecLow != VecHigh){
      ierr = VecGetArray(VecHigh,&v2);CHKERRQ(ierr);
    } else {
      v2=v1;
    }
    if ( V != VecLow && V != VecHigh){
      ierr = VecGetArray(V,&vmiddle);CHKERRQ(ierr);
    } else if ( V==VecLow ){
      vmiddle=v1;
    } else {
      vmiddle =v2;
    }

    ierr = PetscMalloc( n*sizeof(PetscInt), &vm );CHKERRQ(ierr);

    for (i=0; i<n; i++){
      if (v1[i] <= vmiddle[i] && vmiddle[i] <= v2[i]) {vm[n_vm]=low+i; n_vm++;}
    }

    ierr = VecRestoreArray(VecLow,&v1);CHKERRQ(ierr);
    if (VecLow != VecHigh){
      ierr = VecRestoreArray(VecHigh,&v2);CHKERRQ(ierr);
    }
    if ( V != VecLow && V != VecHigh){
      ierr = VecRestoreArray(V,&vmiddle);CHKERRQ(ierr);
    }
  }
  ierr = PetscObjectGetComm((PetscObject)V,&comm);CHKERRQ(ierr);
  ierr = ISCreateGeneral(comm,n_vm,vm,PETSC_OWN_POINTER,S);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "VecGetSubVec"
/*@
  VecGetSubVec - Gets a subvector using the IS

  Input Parameters:
+ vfull - the full matrix
. is - the index set for the subvector
. reduced_type - the method TAO is using for subsetting (TAO_SUBSET_SUBVEC, TAO_SUBSET_MASK,  TAO_SUBSET_MATRIXFREE)
- maskvalue - the value to set the unused vector elements to (for TAO_SUBSET_MASK or TAO_SUBSET_MATRIXFREE)

  Output Parameters:
. vreduced - the subvector

  Note:
  maskvalue should usually be 0.0, unless a pointwise divide will be used.
@*/
PetscErrorCode VecGetSubVec(Vec vfull, IS is, PetscInt reduced_type, PetscReal maskvalue, Vec *vreduced)
{
  PetscErrorCode ierr;
  PetscInt       nfull,nreduced,nreduced_local,rlow,rhigh,flow,fhigh;
  PetscInt       i,nlocal;
  PetscReal      *fv,*rv;
  const PetscInt *s;
  IS             ident;
  VecType        vtype;
  VecScatter     scatter;
  MPI_Comm       comm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(vfull,VEC_CLASSID,1);
  PetscValidHeaderSpecific(is,IS_CLASSID,2);

  ierr = VecGetSize(vfull, &nfull);CHKERRQ(ierr);
  ierr = ISGetSize(is, &nreduced);CHKERRQ(ierr);

  if (nreduced == nfull) {
    ierr = VecDestroy(vreduced);CHKERRQ(ierr);
    ierr = VecDuplicate(vfull,vreduced);CHKERRQ(ierr);
    ierr = VecCopy(vfull,*vreduced);CHKERRQ(ierr);
  } else {
    switch (reduced_type) {
    case TAO_SUBSET_SUBVEC:
      ierr = VecGetType(vfull,&vtype);CHKERRQ(ierr);
      ierr = VecGetOwnershipRange(vfull,&flow,&fhigh);CHKERRQ(ierr);
      ierr = ISGetLocalSize(is,&nreduced_local);CHKERRQ(ierr);
      ierr = PetscObjectGetComm((PetscObject)vfull,&comm);CHKERRQ(ierr);
      if (*vreduced) {
        ierr = VecDestroy(vreduced);CHKERRQ(ierr);
      }
      ierr = VecCreate(comm,vreduced);CHKERRQ(ierr);
      ierr = VecSetType(*vreduced,vtype);CHKERRQ(ierr);

      ierr = VecSetSizes(*vreduced,nreduced_local,nreduced);CHKERRQ(ierr);
      ierr = VecGetOwnershipRange(*vreduced,&rlow,&rhigh);CHKERRQ(ierr);
      ierr = ISCreateStride(comm,nreduced_local,rlow,1,&ident);CHKERRQ(ierr);
      ierr = VecScatterCreate(vfull,is,*vreduced,ident,&scatter);CHKERRQ(ierr);
      ierr = VecScatterBegin(scatter,vfull,*vreduced,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(scatter,vfull,*vreduced,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterDestroy(&scatter);CHKERRQ(ierr);
      ierr = ISDestroy(&ident);CHKERRQ(ierr);
      break;

    case TAO_SUBSET_MASK:
    case TAO_SUBSET_MATRIXFREE:
      /* vr[i] = vf[i]   if i in is
       vr[i] = 0       otherwise */
      if (*vreduced == NULL) {
        ierr = VecDuplicate(vfull,vreduced);CHKERRQ(ierr);
      }

      ierr = VecSet(*vreduced,maskvalue);CHKERRQ(ierr);
      ierr = ISGetLocalSize(is,&nlocal);CHKERRQ(ierr);
      ierr = VecGetOwnershipRange(vfull,&flow,&fhigh);CHKERRQ(ierr);
      ierr = VecGetArray(vfull,&fv);CHKERRQ(ierr);
      ierr = VecGetArray(*vreduced,&rv);CHKERRQ(ierr);
      ierr = ISGetIndices(is,&s);CHKERRQ(ierr);
      if (nlocal > (fhigh-flow)) SETERRQ2(PETSC_COMM_WORLD,1,"IS local size %d > Vec local size %d",nlocal,fhigh-flow);
      for (i=0;i<nlocal;i++) {
        rv[s[i]-flow] = fv[s[i]-flow];
      }
      ierr = ISRestoreIndices(is,&s);CHKERRQ(ierr);
      ierr = VecRestoreArray(vfull,&fv);CHKERRQ(ierr);
      ierr = VecRestoreArray(*vreduced,&rv);CHKERRQ(ierr);
      break;
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecReducedXPY"
/*@
  VecReducedXPY - Adds a reduced vector to the appropriate elements of a full-space vector.

  Input Parameters:
+ vfull - the full-space vector
. vreduced - the reduced-space vector
- is - the index set for the reduced space

  Output Parameters:
. vfull - the sum of the full-space vector and reduced-space vector
@*/
PetscErrorCode VecReducedXPY(Vec vfull, Vec vreduced, IS is)
{
  VecScatter     scatter;
  IS             ident;
  PetscInt       nfull,nreduced,rlow,rhigh;
  MPI_Comm       comm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(vfull,VEC_CLASSID,1);
  PetscValidHeaderSpecific(vreduced,VEC_CLASSID,2);
  PetscValidHeaderSpecific(is,IS_CLASSID,3);
  ierr = VecGetSize(vfull,&nfull);CHKERRQ(ierr);
  ierr = VecGetSize(vreduced,&nreduced);CHKERRQ(ierr);

  if (nfull == nreduced) { /* Also takes care of masked vectors */
    ierr = VecAXPY(vfull,1.0,vreduced);CHKERRQ(ierr);
  } else {
    ierr = PetscObjectGetComm((PetscObject)vfull,&comm);CHKERRQ(ierr);
    ierr = VecGetOwnershipRange(vreduced,&rlow,&rhigh);CHKERRQ(ierr);
    ierr = ISCreateStride(comm,rhigh-rlow,rlow,1,&ident);CHKERRQ(ierr);
    ierr = VecScatterCreate(vreduced,ident,vfull,is,&scatter);CHKERRQ(ierr);
    ierr = VecScatterBegin(scatter,vreduced,vfull,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(scatter,vreduced,vfull,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterDestroy(&scatter);CHKERRQ(ierr);
    ierr = ISDestroy(&ident);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "ISCreateComplement"
/*@
   ISCreateComplement - Creates the complement of the the index set

   Collective on IS

   Input Parameter:
+  S -  a PETSc IS
-  V - the reference vector space

   Output Parameter:
.  T -  the complement of S


.seealso ISCreateGeneral()

   Level: advanced
@*/
PetscErrorCode ISCreateComplement(IS S, Vec V, IS *T)
{
  PetscErrorCode ierr;
  PetscInt       i,nis,nloc,high,low,n=0;
  const PetscInt *s;
  PetscInt       *tt,*ss;
  MPI_Comm       comm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(S,IS_CLASSID,1);
  PetscValidHeaderSpecific(V,VEC_CLASSID,2);

  ierr = VecGetOwnershipRange(V,&low,&high);CHKERRQ(ierr);
  ierr = VecGetLocalSize(V,&nloc);CHKERRQ(ierr);
  ierr = ISGetLocalSize(S,&nis);CHKERRQ(ierr);
  ierr = PetscMalloc( nloc*sizeof(PetscInt),&tt );CHKERRQ(ierr);
  ierr = PetscMalloc( nloc*sizeof(PetscInt),&ss );CHKERRQ(ierr);

  ierr = ISGetIndices(S, &s);CHKERRQ(ierr);
  for (i=low; i<high; i++){ tt[i-low]=i; }
  for (i=0; i<nis; i++){ tt[s[i]-low] = -2; }

  for (i=0; i<nloc; i++){
    if (tt[i]>-1){ ss[n]=tt[i]; n++; }
  }
  ierr = ISRestoreIndices(S, &s);CHKERRQ(ierr);

  ierr = PetscObjectGetComm((PetscObject)S,&comm);CHKERRQ(ierr);
  ierr = ISCreateGeneral(comm,n,ss,PETSC_COPY_VALUES,T);CHKERRQ(ierr);
  ierr = PetscFree(tt);CHKERRQ(ierr);
  ierr = PetscFree(ss);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecISSetToConstant"
/*@
   VecISSetToConstant - Sets the elements of a vector, specified by an index set, to a constant

   Input Parameter:
+  S -  a PETSc IS
.  c - the constant
-  V - a Vec

.seealso VecSet()

   Level: advanced
@*/
PetscErrorCode VecISSetToConstant(IS S, PetscReal c, Vec V)
{
  PetscErrorCode ierr;
  PetscInt       nloc,low,high,i;
  const PetscInt *s;
  PetscReal      *v;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(V,VEC_CLASSID,3);
  PetscValidHeaderSpecific(S,IS_CLASSID,1);
  PetscValidType(V,3);
  PetscCheckSameComm(V,3,S,1);

  ierr = VecGetOwnershipRange(V, &low, &high);CHKERRQ(ierr);
  ierr = ISGetLocalSize(S,&nloc);CHKERRQ(ierr);
  ierr = ISGetIndices(S, &s);CHKERRQ(ierr);
  ierr = VecGetArray(V,&v);CHKERRQ(ierr);
  for (i=0; i<nloc; i++){
    v[s[i]-low] = c;
  }
  ierr = ISRestoreIndices(S, &s);CHKERRQ(ierr);
  ierr = VecRestoreArray(V,&v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetSubMat"
/*@
  MatGetSubMat - Gets a submatrix using the IS

  Input Parameters:
+ M - the full matrix (n x n)
. is - the index set for the submatrix (both row and column index sets need to be the same)
. v1 - work vector of dimension n, needed for TAO_SUBSET_MASK option
- subset_type - the method TAO is using for subsetting (TAO_SUBSET_SUBVEC, TAO_SUBSET_MASK,
  TAO_SUBSET_MATRIXFREE)

  Output Parameters:
. Msub - the submatrix
@*/
PetscErrorCode MatGetSubMat(Mat M, IS is, Vec v1, TaoSubsetType subset_type, Mat *Msub)
{
  PetscErrorCode ierr;
  IS             iscomp;
  PetscBool      flg;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(M,MAT_CLASSID,1);
  PetscValidHeaderSpecific(is,IS_CLASSID,2);
  ierr = MatDestroy(Msub);CHKERRQ(ierr);
  switch (subset_type) {
  case TAO_SUBSET_SUBVEC:
    ierr = MatGetSubMatrix(M, is, is, MAT_INITIAL_MATRIX, Msub);CHKERRQ(ierr);
    break;

  case TAO_SUBSET_MASK:
    /* Get Reduced Hessian
     Msub[i,j] = M[i,j] if i,j in Free_Local or i==j
     Msub[i,j] = 0      if i!=j and i or j not in Free_Local
     */
    ierr = PetscOptionsBool("-different_submatrix","use separate hessian matrix when computing submatrices","TaoSubsetType",PETSC_FALSE,&flg,NULL);
    if (flg == PETSC_TRUE) {
      ierr = MatDuplicate(M, MAT_COPY_VALUES, Msub);CHKERRQ(ierr);
    } else {
      /* Act on hessian directly (default) */
      ierr = PetscObjectReference((PetscObject)M);CHKERRQ(ierr);
      *Msub = M;
    }
    /* Save the diagonal to temporary vector */
    ierr = MatGetDiagonal(*Msub,v1);CHKERRQ(ierr);

    /* Zero out rows and columns */
    ierr = ISCreateComplement(is,v1,&iscomp);CHKERRQ(ierr);

    /* Use v1 instead of 0 here because of PETSc bug */
    ierr = MatZeroRowsColumnsIS(*Msub,iscomp,1.0,v1,v1);CHKERRQ(ierr);

    ierr = ISDestroy(&iscomp);CHKERRQ(ierr);
    break;
  case TAO_SUBSET_MATRIXFREE:
    ierr = ISCreateComplement(is,v1,&iscomp);CHKERRQ(ierr);
    ierr = MatCreateSubMatrixFree(M,iscomp,iscomp,Msub);CHKERRQ(ierr);
    ierr = ISDestroy(&iscomp);CHKERRQ(ierr);
    break;
  }
  PetscFunctionReturn(0);
}