impls/redundant/redundant.c

/*
  This file defines a "solve the problem redundantly on each subgroup of processor" preconditioner.
*/
#include <petsc/private/pcimpl.h>
#include <petscksp.h>           /*I "petscksp.h" I*/

typedef struct {
  KSP          ksp;
  PC           pc;                   /* actual preconditioner used on each processor */
  Vec          xsub,ysub;            /* vectors of a subcommunicator to hold parallel vectors of PetscObjectComm((PetscObject)pc) */
  Vec          xdup,ydup;            /* parallel vector that congregates xsub or ysub facilitating vector scattering */
  Mat          pmats;                /* matrix and optional preconditioner matrix belong to a subcommunicator */
  VecScatter   scatterin,scatterout; /* scatter used to move all values to each processor group (subcommunicator) */
  PetscBool    useparallelmat;
  PetscSubcomm psubcomm;
  PetscInt     nsubcomm;           /* num of data structure PetscSubcomm */
} PC_Redundant;

#undef __FUNCT__
#define __FUNCT__ "PCView_Redundant"
static PetscErrorCode PCView_Redundant(PC pc,PetscViewer viewer)
{
  PC_Redundant   *red = (PC_Redundant*)pc->data;
  PetscErrorCode ierr;
  PetscBool      iascii,isstring;
  PetscViewer    subviewer;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);CHKERRQ(ierr);
  if (iascii) {
    if (!red->psubcomm) {
      ierr = PetscViewerASCIIPrintf(viewer,"  Redundant preconditioner: Not yet setup\n");CHKERRQ(ierr);
    } else {
      ierr = PetscViewerASCIIPrintf(viewer,"  Redundant preconditioner: First (color=0) of %D PCs follows\n",red->nsubcomm);CHKERRQ(ierr);
      ierr = PetscViewerGetSubViewer(viewer,((PetscObject)red->pc)->comm,&subviewer);CHKERRQ(ierr);
      if (!red->psubcomm->color) { /* only view first redundant pc */
        ierr = PetscViewerASCIIPushTab(subviewer);CHKERRQ(ierr);
        ierr = KSPView(red->ksp,subviewer);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPopTab(subviewer);CHKERRQ(ierr);
      }
      ierr = PetscViewerRestoreSubViewer(viewer,((PetscObject)red->pc)->comm,&subviewer);CHKERRQ(ierr);
    }
  } else if (isstring) {
    ierr = PetscViewerStringSPrintf(viewer," Redundant solver preconditioner");CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCSetUp_Redundant"
static PetscErrorCode PCSetUp_Redundant(PC pc)
{
  PC_Redundant   *red = (PC_Redundant*)pc->data;
  PetscErrorCode ierr;
  PetscInt       mstart,mend,mlocal,M;
  PetscMPIInt    size;
  MPI_Comm       comm,subcomm;
  Vec            x;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);

  /* if pmatrix set by user is sequential then we do not need to gather the parallel matrix */
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  if (size == 1) red->useparallelmat = PETSC_FALSE;

  if (!pc->setupcalled) {
    PetscInt mloc_sub;
    if (!red->psubcomm) { /* create red->psubcomm, new ksp and pc over subcomm */
      KSP ksp;
      ierr = PCRedundantGetKSP(pc,&ksp);CHKERRQ(ierr);
    }
    subcomm = PetscSubcommChild(red->psubcomm);

    if (red->useparallelmat) {
      /* grab the parallel matrix and put it into processors of a subcomminicator */
      ierr = MatCreateRedundantMatrix(pc->pmat,red->psubcomm->n,subcomm,MAT_INITIAL_MATRIX,&red->pmats);CHKERRQ(ierr);

      ierr = MPI_Comm_size(subcomm,&size);CHKERRQ(ierr);
      if (size > 1) {
        PetscBool foundpack;
        ierr = MatGetFactorAvailable(red->pmats,NULL,MAT_FACTOR_LU,&foundpack);CHKERRQ(ierr);
        if (!foundpack) { /* reset default ksp and pc */
          ierr = KSPSetType(red->ksp,KSPGMRES);CHKERRQ(ierr);
          ierr = PCSetType(red->pc,PCBJACOBI);CHKERRQ(ierr);
        }
      }

      ierr = KSPSetOperators(red->ksp,red->pmats,red->pmats);CHKERRQ(ierr);

      /* get working vectors xsub and ysub */
      ierr = MatCreateVecs(red->pmats,&red->xsub,&red->ysub);CHKERRQ(ierr);

      /* create working vectors xdup and ydup.
       xdup concatenates all xsub's contigously to form a mpi vector over dupcomm  (see PetscSubcommCreate_interlaced())
       ydup concatenates all ysub and has empty local arrays because ysub's arrays will be place into it.
       Note: we use communicator dupcomm, not PetscObjectComm((PetscObject)pc)! */
      ierr = MatGetLocalSize(red->pmats,&mloc_sub,NULL);CHKERRQ(ierr);
      ierr = VecCreateMPI(PetscSubcommContiguousParent(red->psubcomm),mloc_sub,PETSC_DECIDE,&red->xdup);CHKERRQ(ierr);
      ierr = VecCreateMPIWithArray(PetscSubcommContiguousParent(red->psubcomm),1,mloc_sub,PETSC_DECIDE,NULL,&red->ydup);CHKERRQ(ierr);

      /* create vecscatters */
      if (!red->scatterin) { /* efficiency of scatterin is independent from psubcomm_type! */
        IS       is1,is2;
        PetscInt *idx1,*idx2,i,j,k;

        ierr = MatCreateVecs(pc->pmat,&x,0);CHKERRQ(ierr);
        ierr = VecGetSize(x,&M);CHKERRQ(ierr);
        ierr = VecGetOwnershipRange(x,&mstart,&mend);CHKERRQ(ierr);
        mlocal = mend - mstart;
        ierr = PetscMalloc2(red->psubcomm->n*mlocal,&idx1,red->psubcomm->n*mlocal,&idx2);CHKERRQ(ierr);
        j    = 0;
        for (k=0; k<red->psubcomm->n; k++) {
          for (i=mstart; i<mend; i++) {
            idx1[j]   = i;
            idx2[j++] = i + M*k;
          }
        }
        ierr = ISCreateGeneral(comm,red->psubcomm->n*mlocal,idx1,PETSC_COPY_VALUES,&is1);CHKERRQ(ierr);
        ierr = ISCreateGeneral(comm,red->psubcomm->n*mlocal,idx2,PETSC_COPY_VALUES,&is2);CHKERRQ(ierr);
        ierr = VecScatterCreate(x,is1,red->xdup,is2,&red->scatterin);CHKERRQ(ierr);
        ierr = ISDestroy(&is1);CHKERRQ(ierr);
        ierr = ISDestroy(&is2);CHKERRQ(ierr);

        /* Impl below is good for PETSC_SUBCOMM_INTERLACED (no inter-process communication) and PETSC_SUBCOMM_CONTIGUOUS (communication within subcomm) */
        ierr = ISCreateStride(comm,mlocal,mstart+ red->psubcomm->color*M,1,&is1);CHKERRQ(ierr);
        ierr = ISCreateStride(comm,mlocal,mstart,1,&is2);CHKERRQ(ierr);
        ierr = VecScatterCreate(red->xdup,is1,x,is2,&red->scatterout);CHKERRQ(ierr);
        ierr = ISDestroy(&is1);CHKERRQ(ierr);
        ierr = ISDestroy(&is2);CHKERRQ(ierr);
        ierr = PetscFree2(idx1,idx2);CHKERRQ(ierr);
        ierr = VecDestroy(&x);CHKERRQ(ierr);
      }
    } else { /* !red->useparallelmat */
      ierr = KSPSetOperators(red->ksp,pc->mat,pc->pmat);CHKERRQ(ierr);
    }
  } else { /* pc->setupcalled */
    if (red->useparallelmat) {
      MatReuse       reuse;
      /* grab the parallel matrix and put it into processors of a subcomminicator */
      /*--------------------------------------------------------------------------*/
      if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
        /* destroy old matrices */
        ierr  = MatDestroy(&red->pmats);CHKERRQ(ierr);
        reuse = MAT_INITIAL_MATRIX;
      } else {
        reuse = MAT_REUSE_MATRIX;
      }
      ierr = MatCreateRedundantMatrix(pc->pmat,red->psubcomm->n,PetscSubcommChild(red->psubcomm),reuse,&red->pmats);CHKERRQ(ierr);
      ierr = KSPSetOperators(red->ksp,red->pmats,red->pmats);CHKERRQ(ierr);
    } else { /* !red->useparallelmat */
      ierr = KSPSetOperators(red->ksp,pc->mat,pc->pmat);CHKERRQ(ierr);
    }
  }

  if (pc->setfromoptionscalled) {
    ierr = KSPSetFromOptions(red->ksp);CHKERRQ(ierr);
  }
  ierr = KSPSetUp(red->ksp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCApply_Redundant"
static PetscErrorCode PCApply_Redundant(PC pc,Vec x,Vec y)
{
  PC_Redundant   *red = (PC_Redundant*)pc->data;
  PetscErrorCode ierr;
  PetscScalar    *array;

  PetscFunctionBegin;
  if (!red->useparallelmat) {
    ierr = KSPSolve(red->ksp,x,y);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  /* scatter x to xdup */
  ierr = VecScatterBegin(red->scatterin,x,red->xdup,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecScatterEnd(red->scatterin,x,red->xdup,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);

  /* place xdup's local array into xsub */
  ierr = VecGetArray(red->xdup,&array);CHKERRQ(ierr);
  ierr = VecPlaceArray(red->xsub,(const PetscScalar*)array);CHKERRQ(ierr);

  /* apply preconditioner on each processor */
  ierr = KSPSolve(red->ksp,red->xsub,red->ysub);CHKERRQ(ierr);
  ierr = VecResetArray(red->xsub);CHKERRQ(ierr);
  ierr = VecRestoreArray(red->xdup,&array);CHKERRQ(ierr);

  /* place ysub's local array into ydup */
  ierr = VecGetArray(red->ysub,&array);CHKERRQ(ierr);
  ierr = VecPlaceArray(red->ydup,(const PetscScalar*)array);CHKERRQ(ierr);

  /* scatter ydup to y */
  ierr = VecScatterBegin(red->scatterout,red->ydup,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecScatterEnd(red->scatterout,red->ydup,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecResetArray(red->ydup);CHKERRQ(ierr);
  ierr = VecRestoreArray(red->ysub,&array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCApplyTranspose_Redundant"
static PetscErrorCode PCApplyTranspose_Redundant(PC pc,Vec x,Vec y)
{
  PC_Redundant   *red = (PC_Redundant*)pc->data;
  PetscErrorCode ierr;
  PetscScalar    *array;

  PetscFunctionBegin;
  if (!red->useparallelmat) {
    ierr = KSPSolveTranspose(red->ksp,x,y);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  /* scatter x to xdup */
  ierr = VecScatterBegin(red->scatterin,x,red->xdup,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecScatterEnd(red->scatterin,x,red->xdup,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);

  /* place xdup's local array into xsub */
  ierr = VecGetArray(red->xdup,&array);CHKERRQ(ierr);
  ierr = VecPlaceArray(red->xsub,(const PetscScalar*)array);CHKERRQ(ierr);

  /* apply preconditioner on each processor */
  ierr = KSPSolveTranspose(red->ksp,red->xsub,red->ysub);CHKERRQ(ierr);
  ierr = VecResetArray(red->xsub);CHKERRQ(ierr);
  ierr = VecRestoreArray(red->xdup,&array);CHKERRQ(ierr);

  /* place ysub's local array into ydup */
  ierr = VecGetArray(red->ysub,&array);CHKERRQ(ierr);
  ierr = VecPlaceArray(red->ydup,(const PetscScalar*)array);CHKERRQ(ierr);

  /* scatter ydup to y */
  ierr = VecScatterBegin(red->scatterout,red->ydup,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecScatterEnd(red->scatterout,red->ydup,y,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecResetArray(red->ydup);CHKERRQ(ierr);
  ierr = VecRestoreArray(red->ysub,&array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCReset_Redundant"
static PetscErrorCode PCReset_Redundant(PC pc)
{
  PC_Redundant   *red = (PC_Redundant*)pc->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (red->useparallelmat) {
    ierr = VecScatterDestroy(&red->scatterin);CHKERRQ(ierr);
    ierr = VecScatterDestroy(&red->scatterout);CHKERRQ(ierr);
    ierr = VecDestroy(&red->ysub);CHKERRQ(ierr);
    ierr = VecDestroy(&red->xsub);CHKERRQ(ierr);
    ierr = VecDestroy(&red->xdup);CHKERRQ(ierr);
    ierr = VecDestroy(&red->ydup);CHKERRQ(ierr);
  }
  ierr = MatDestroy(&red->pmats);CHKERRQ(ierr);
  ierr = KSPReset(red->ksp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCDestroy_Redundant"
static PetscErrorCode PCDestroy_Redundant(PC pc)
{
  PC_Redundant   *red = (PC_Redundant*)pc->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PCReset_Redundant(pc);CHKERRQ(ierr);
  ierr = KSPDestroy(&red->ksp);CHKERRQ(ierr);
  ierr = PetscSubcommDestroy(&red->psubcomm);CHKERRQ(ierr);
  ierr = PetscFree(pc->data);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCSetFromOptions_Redundant"
static PetscErrorCode PCSetFromOptions_Redundant(PetscOptionItems *PetscOptionsObject,PC pc)
{
  PetscErrorCode ierr;
  PC_Redundant   *red = (PC_Redundant*)pc->data;

  PetscFunctionBegin;
  ierr = PetscOptionsHead(PetscOptionsObject,"Redundant options");CHKERRQ(ierr);
  ierr = PetscOptionsInt("-pc_redundant_number","Number of redundant pc","PCRedundantSetNumber",red->nsubcomm,&red->nsubcomm,0);CHKERRQ(ierr);
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCRedundantSetNumber_Redundant"
static PetscErrorCode PCRedundantSetNumber_Redundant(PC pc,PetscInt nreds)
{
  PC_Redundant *red = (PC_Redundant*)pc->data;

  PetscFunctionBegin;
  red->nsubcomm = nreds;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCRedundantSetNumber"
/*@
   PCRedundantSetNumber - Sets the number of redundant preconditioner contexts.

   Logically Collective on PC

   Input Parameters:
+  pc - the preconditioner context
-  nredundant - number of redundant preconditioner contexts; for example if you are using 64 MPI processes and
                              use an nredundant of 4 there will be 4 parallel solves each on 16 = 64/4 processes.

   Level: advanced

.keywords: PC, redundant solve
@*/
PetscErrorCode PCRedundantSetNumber(PC pc,PetscInt nredundant)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  if (nredundant <= 0) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG, "num of redundant pc %D must be positive",nredundant);
  ierr = PetscTryMethod(pc,"PCRedundantSetNumber_C",(PC,PetscInt),(pc,nredundant));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCRedundantSetScatter_Redundant"
static PetscErrorCode PCRedundantSetScatter_Redundant(PC pc,VecScatter in,VecScatter out)
{
  PC_Redundant   *red = (PC_Redundant*)pc->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectReference((PetscObject)in);CHKERRQ(ierr);
  ierr = VecScatterDestroy(&red->scatterin);CHKERRQ(ierr);

  red->scatterin  = in;

  ierr = PetscObjectReference((PetscObject)out);CHKERRQ(ierr);
  ierr = VecScatterDestroy(&red->scatterout);CHKERRQ(ierr);
  red->scatterout = out;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCRedundantSetScatter"
/*@
   PCRedundantSetScatter - Sets the scatter used to copy values into the
     redundant local solve and the scatter to move them back into the global
     vector.

   Logically Collective on PC

   Input Parameters:
+  pc - the preconditioner context
.  in - the scatter to move the values in
-  out - the scatter to move them out

   Level: advanced

.keywords: PC, redundant solve
@*/
PetscErrorCode PCRedundantSetScatter(PC pc,VecScatter in,VecScatter out)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscValidHeaderSpecific(in,VEC_SCATTER_CLASSID,2);
  PetscValidHeaderSpecific(out,VEC_SCATTER_CLASSID,3);
  ierr = PetscTryMethod(pc,"PCRedundantSetScatter_C",(PC,VecScatter,VecScatter),(pc,in,out));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCRedundantGetKSP_Redundant"
static PetscErrorCode PCRedundantGetKSP_Redundant(PC pc,KSP *innerksp)
{
  PetscErrorCode ierr;
  PC_Redundant   *red = (PC_Redundant*)pc->data;
  MPI_Comm       comm,subcomm;
  const char     *prefix;

  PetscFunctionBegin;
  if (!red->psubcomm) {
    ierr = PCGetOptionsPrefix(pc,&prefix);CHKERRQ(ierr);

    ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
    ierr = PetscSubcommCreate(comm,&red->psubcomm);CHKERRQ(ierr);
    ierr = PetscSubcommSetNumber(red->psubcomm,red->nsubcomm);CHKERRQ(ierr);
    ierr = PetscSubcommSetType(red->psubcomm,PETSC_SUBCOMM_CONTIGUOUS);CHKERRQ(ierr);

    ierr = PetscSubcommSetOptionsPrefix(red->psubcomm,prefix);CHKERRQ(ierr);
    ierr = PetscSubcommSetFromOptions(red->psubcomm);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory((PetscObject)pc,sizeof(PetscSubcomm));CHKERRQ(ierr);

    /* create a new PC that processors in each subcomm have copy of */
    subcomm = PetscSubcommChild(red->psubcomm);

    ierr = KSPCreate(subcomm,&red->ksp);CHKERRQ(ierr);
    ierr = KSPSetErrorIfNotConverged(red->ksp,pc->erroriffailure);CHKERRQ(ierr);
    ierr = PetscObjectIncrementTabLevel((PetscObject)red->ksp,(PetscObject)pc,1);CHKERRQ(ierr);
    ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)red->ksp);CHKERRQ(ierr);
    ierr = KSPSetType(red->ksp,KSPPREONLY);CHKERRQ(ierr);
    ierr = KSPGetPC(red->ksp,&red->pc);CHKERRQ(ierr);
    ierr = PCSetType(red->pc,PCLU);CHKERRQ(ierr);

    ierr = KSPSetOptionsPrefix(red->ksp,prefix);CHKERRQ(ierr);
    ierr = KSPAppendOptionsPrefix(red->ksp,"redundant_");CHKERRQ(ierr);
  }
  *innerksp = red->ksp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCRedundantGetKSP"
/*@
   PCRedundantGetKSP - Gets the less parallel KSP created by the redundant PC.

   Not Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  innerksp - the KSP on the smaller set of processes

   Level: advanced

.keywords: PC, redundant solve
@*/
PetscErrorCode PCRedundantGetKSP(PC pc,KSP *innerksp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscValidPointer(innerksp,2);
  ierr = PetscTryMethod(pc,"PCRedundantGetKSP_C",(PC,KSP*),(pc,innerksp));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCRedundantGetOperators_Redundant"
static PetscErrorCode PCRedundantGetOperators_Redundant(PC pc,Mat *mat,Mat *pmat)
{
  PC_Redundant *red = (PC_Redundant*)pc->data;

  PetscFunctionBegin;
  if (mat)  *mat  = red->pmats;
  if (pmat) *pmat = red->pmats;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCRedundantGetOperators"
/*@
   PCRedundantGetOperators - gets the sequential matrix and preconditioner matrix

   Not Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameters:
+  mat - the matrix
-  pmat - the (possibly different) preconditioner matrix

   Level: advanced

.keywords: PC, redundant solve
@*/
PetscErrorCode PCRedundantGetOperators(PC pc,Mat *mat,Mat *pmat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  if (mat)  PetscValidPointer(mat,2);
  if (pmat) PetscValidPointer(pmat,3);
  ierr = PetscTryMethod(pc,"PCRedundantGetOperators_C",(PC,Mat*,Mat*),(pc,mat,pmat));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------------------*/
/*MC
     PCREDUNDANT - Runs a KSP solver with preconditioner for the entire problem on subgroups of processors

     Options for the redundant preconditioners can be set with -redundant_pc_xxx for the redundant KSP with -redundant_ksp_xxx

  Options Database:
.  -pc_redundant_number <n> - number of redundant solves, for example if you are using 64 MPI processes and
                              use an n of 4 there will be 4 parallel solves each on 16 = 64/4 processes.

   Level: intermediate

   Notes: The default KSP is preonly and the default PC is LU.

   Developer Notes: Note that PCSetInitialGuessNonzero()  is not used by this class but likely should be.

.seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PCRedundantSetScatter(),
           PCRedundantGetKSP(), PCRedundantGetOperators(), PCRedundantSetNumber()
M*/

#undef __FUNCT__
#define __FUNCT__ "PCCreate_Redundant"
PETSC_EXTERN PetscErrorCode PCCreate_Redundant(PC pc)
{
  PetscErrorCode ierr;
  PC_Redundant   *red;
  PetscMPIInt    size;

  PetscFunctionBegin;
  ierr = PetscNewLog(pc,&red);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);

  red->nsubcomm       = size;
  red->useparallelmat = PETSC_TRUE;
  pc->data            = (void*)red;

  pc->ops->apply          = PCApply_Redundant;
  pc->ops->applytranspose = PCApplyTranspose_Redundant;
  pc->ops->setup          = PCSetUp_Redundant;
  pc->ops->destroy        = PCDestroy_Redundant;
  pc->ops->reset          = PCReset_Redundant;
  pc->ops->setfromoptions = PCSetFromOptions_Redundant;
  pc->ops->view           = PCView_Redundant;

  ierr = PetscObjectComposeFunction((PetscObject)pc,"PCRedundantSetScatter_C",PCRedundantSetScatter_Redundant);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)pc,"PCRedundantSetNumber_C",PCRedundantSetNumber_Redundant);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)pc,"PCRedundantGetKSP_C",PCRedundantGetKSP_Redundant);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)pc,"PCRedundantGetOperators_C",PCRedundantGetOperators_Redundant);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}