aij/seq/matptap.c

/*
  Defines projective product routines where A is a SeqAIJ matrix
          C = P^T * A * P
*/

#include "src/mat/impls/aij/seq/aij.h"
#include "src/mat/utils/freespace.h"

int MatSeqAIJPtAP(Mat,Mat,Mat*);
int MatSeqAIJPtAPSymbolic(Mat,Mat,Mat*);
int MatSeqAIJPtAPNumeric(Mat,Mat,Mat);

static int MATSeqAIJ_PtAP         = 0;
static int MATSeqAIJ_PtAPSymbolic = 0;
static int MATSeqAIJ_PtAPNumeric  = 0;

/*
     MatSeqAIJPtAP - Creates the SeqAIJ matrix product, C,
           of SeqAIJ matrix A and matrix P:
                 C = P^T * A * P;

     Note: C is assumed to be uncreated.
           If this is not the case, Destroy C before calling this routine.
*/
#undef __FUNCT__
#define __FUNCT__ "MatSeqAIJPtAP"
int MatSeqAIJPtAP(Mat A,Mat P,Mat *C) {
  int ierr;
  char funct[80];

  PetscFunctionBegin;

  ierr = PetscLogEventBegin(MATSeqAIJ_PtAP,A,P,0,0);CHKERRQ(ierr);

  ierr = MatSeqAIJPtAPSymbolic(A,P,C);CHKERRQ(ierr);

  /* Avoid additional error checking included in */
/*   ierr = MatSeqAIJApplyPtAPNumeric(A,P,*C);CHKERRQ(ierr); */

  /* Query A for ApplyPtAPNumeric implementation based on types of P */
  ierr = PetscStrcpy(funct,"MatApplyPtAPNumeric_seqaij_");CHKERRQ(ierr);
  ierr = PetscStrcat(funct,P->type_name);CHKERRQ(ierr);
  ierr = PetscTryMethod(A,funct,(Mat,Mat,Mat),(A,P,*C));CHKERRQ(ierr);

  ierr = PetscLogEventEnd(MATSeqAIJ_PtAP,A,P,0,0);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

/*
     MatSeqAIJPtAPSymbolic - Creates the (i,j) structure of the SeqAIJ matrix product, C,
           of SeqAIJ matrix A and matrix P, according to:
                 C = P^T * A * P;

     Note: C is assumed to be uncreated.
           If this is not the case, Destroy C before calling this routine.
*/
#undef __FUNCT__
#define __FUNCT__ "MatSeqAIJPtAPSymbolic"
int MatSeqAIJPtAPSymbolic(Mat A,Mat P,Mat *C) {
  int ierr;
  char funct[80];

  PetscFunctionBegin;

  PetscValidPointer(C);

  PetscValidHeaderSpecific(A,MAT_COOKIE);
  PetscValidType(A);
  MatPreallocated(A);
  if (!A->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  PetscValidHeaderSpecific(P,MAT_COOKIE);
  PetscValidType(P);
  MatPreallocated(P);
  if (!P->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (P->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  if (P->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",P->M,A->N);
  if (A->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %d != %d",A->M,A->N);

  /* Query A for ApplyPtAP implementation based on types of P */
  ierr = PetscStrcpy(funct,"MatApplyPtAPSymbolic_seqaij_");CHKERRQ(ierr);
  ierr = PetscStrcat(funct,P->type_name);CHKERRQ(ierr);
  ierr = PetscTryMethod(A,funct,(Mat,Mat,Mat*),(A,P,C));CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatApplyPtAPSymbolic_SeqAIJ_SeqAIJ"
int MatApplyPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat *C) {
  int            ierr;
  FreeSpaceList  free_space=PETSC_NULL,current_space=PETSC_NULL;
  Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*p=(Mat_SeqAIJ*)P->data,*c;
  int            aishift=a->indexshift,pishift=p->indexshift;
  int            *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
  int            *ci,*cj,*denserow,*sparserow,*ptadenserow,*ptasparserow,*ptaj;
  int            an=A->N,am=A->M,pn=P->N,pm=P->M;
  int            i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi;
  MatScalar      *ca;

  PetscFunctionBegin;

  /* some error checking which could be moved into interface layer */
  if (aishift || pishift) SETERRQ(PETSC_ERR_SUP,"Shifted matrix indices are not supported.");

  /* Start timer */
  ierr = PetscLogEventBegin(MATSeqAIJ_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);

  /* Get ij structure of P^T */
  ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
  ptJ=ptj;

  /* Allocate ci array, arrays for fill computation and */
  /* free space for accumulating nonzero column info */
  ierr = PetscMalloc((pn+1)*sizeof(int),&ci);CHKERRQ(ierr);
  ci[0] = 0;

  ierr = PetscMalloc((2*pn+2*an+1)*sizeof(int),&ptadenserow);CHKERRQ(ierr);
  ierr = PetscMemzero(ptadenserow,(2*pn+2*an+1)*sizeof(int));CHKERRQ(ierr);
  ptasparserow = ptadenserow  + an;
  denserow     = ptasparserow + an;
  sparserow    = denserow     + pn;

  /* Set initial free space to be nnz(A) scaled by aspect ratio of P. */
  /* This should be reasonable if sparsity of PtAP is similar to that of A. */
  ierr          = GetMoreSpace((ai[am]/pm)*pn,&free_space);
  current_space = free_space;

  /* Determine symbolic info for each row of C: */
  for (i=0;i<pn;i++) {
    ptnzi  = pti[i+1] - pti[i];
    ptanzi = 0;
    /* Determine symbolic row of PtA: */
    for (j=0;j<ptnzi;j++) {
      arow = *ptJ++;
      anzj = ai[arow+1] - ai[arow];
      ajj  = aj + ai[arow];
      for (k=0;k<anzj;k++) {
        if (!ptadenserow[ajj[k]]) {
          ptadenserow[ajj[k]]    = -1;
          ptasparserow[ptanzi++] = ajj[k];
        }
      }
    }
      /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
    ptaj = ptasparserow;
    cnzi   = 0;
    for (j=0;j<ptanzi;j++) {
      prow = *ptaj++;
      pnzj = pi[prow+1] - pi[prow];
      pjj  = pj + pi[prow];
      for (k=0;k<pnzj;k++) {
        if (!denserow[pjj[k]]) {
            denserow[pjj[k]]  = -1;
            sparserow[cnzi++] = pjj[k];
        }
      }
    }

    /* sort sparserow */
    ierr = PetscSortInt(cnzi,sparserow);CHKERRQ(ierr);

    /* If free space is not available, make more free space */
    /* Double the amount of total space in the list */
    if (current_space->local_remaining<cnzi) {
      ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
    }

    /* Copy data into free space, and zero out denserows */
    ierr = PetscMemcpy(current_space->array,sparserow,cnzi*sizeof(int));CHKERRQ(ierr);
    current_space->array           += cnzi;
    current_space->local_used      += cnzi;
    current_space->local_remaining -= cnzi;

    for (j=0;j<ptanzi;j++) {
      ptadenserow[ptasparserow[j]] = 0;
    }
    for (j=0;j<cnzi;j++) {
      denserow[sparserow[j]] = 0;
    }
      /* Aside: Perhaps we should save the pta info for the numerical factorization. */
      /*        For now, we will recompute what is needed. */
    ci[i+1] = ci[i] + cnzi;
  }
  /* nnz is now stored in ci[ptm], column indices are in the list of free space */
  /* Allocate space for cj, initialize cj, and */
  /* destroy list of free space and other temporary array(s) */
  ierr = PetscMalloc((ci[pn]+1)*sizeof(int),&cj);CHKERRQ(ierr);
  ierr = MakeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
  ierr = PetscFree(ptadenserow);CHKERRQ(ierr);

  /* Allocate space for ca */
  ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
  ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr);

  /* put together the new matrix */
  ierr = MatCreateSeqAIJWithArrays(A->comm,pn,pn,ci,cj,ca,C);CHKERRQ(ierr);

  /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
  /* Since these are PETSc arrays, change flags to free them as necessary. */
  c = (Mat_SeqAIJ *)((*C)->data);
  c->freedata = PETSC_TRUE;
  c->nonew    = 0;

  /* Clean up. */
  ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);

  ierr = PetscLogEventEnd(MATSeqAIJ_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
EXTERN_C_END

#include "src/mat/impls/maij/maij.h"
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatApplyPtAPSymbolic_SeqAIJ_SeqMAIJ"
int MatApplyPtAPSymbolic_SeqAIJ_SeqMAIJ(Mat A,Mat PP,Mat *C) {
  int            ierr;
  FreeSpaceList  free_space=PETSC_NULL,current_space=PETSC_NULL;
  Mat_SeqMAIJ    *pp=(Mat_SeqMAIJ*)PP->data;
  Mat            P=pp->AIJ;
  Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*p=(Mat_SeqAIJ*)P->data,*c;
  int            aishift=a->indexshift,pishift=p->indexshift;
  int            *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
  int            *ci,*cj,*denserow,*sparserow,*ptadenserow,*ptasparserow,*ptaj;
  int            an=A->N,am=A->M,pn=P->N,pm=P->M,ppdof=pp->dof;
  int            i,j,k,dof,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi;
  MatScalar      *ca;

  PetscFunctionBegin;

  /* some error checking which could be moved into interface layer */
  if (aishift || pishift) SETERRQ(PETSC_ERR_SUP,"Shifted matrix indices are not supported.");

  /* Start timer */
  ierr = PetscLogEventBegin(MATSeqAIJ_PtAPSymbolic,A,PP,0,0);CHKERRQ(ierr);

  /* Get ij structure of P^T */
  ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);

  /* Allocate ci array, arrays for fill computation and */
  /* free space for accumulating nonzero column info */
  ierr = PetscMalloc((pn+1)*sizeof(int),&ci);CHKERRQ(ierr);
  ci[0] = 0;

  ierr = PetscMalloc((2*pn+2*an+1)*sizeof(int),&ptadenserow);CHKERRQ(ierr);
  ierr = PetscMemzero(ptadenserow,(2*pn+2*an+1)*sizeof(int));CHKERRQ(ierr);
  ptasparserow = ptadenserow  + an;
  denserow     = ptasparserow + an;
  sparserow    = denserow     + pn;

  /* Set initial free space to be nnz(A) scaled by aspect ratio of P. */
  /* This should be reasonable if sparsity of PtAP is similar to that of A. */
  ierr          = GetMoreSpace((ai[am]/pm)*pn,&free_space);
  current_space = free_space;

  /* Determine symbolic info for each row of C: */
  for (i=0;i<pn/ppdof;i++) {
    ptnzi  = pti[i+1] - pti[i];
    ptanzi = 0;
    ptJ    = ptj + pti[i];
    for (dof=0;dof<ppdof;dof++) {
    /* Determine symbolic row of PtA: */
      for (j=0;j<ptnzi;j++) {
        arow = ptJ[j] + dof;
        anzj = ai[arow+1] - ai[arow];
        ajj  = aj + ai[arow];
        for (k=0;k<anzj;k++) {
          if (!ptadenserow[ajj[k]]) {
            ptadenserow[ajj[k]]    = -1;
            ptasparserow[ptanzi++] = ajj[k];
          }
        }
      }
      /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
      ptaj = ptasparserow;
      cnzi   = 0;
      for (j=0;j<ptanzi;j++) {
        prow = (*ptaj++)/dof;
        pnzj = pi[prow+1] - pi[prow];
        pjj  = pj + pi[prow];
        for (k=0;k<pnzj;k++) {
          if (!denserow[pjj[k]]) {
            denserow[pjj[k]]  = -1;
            sparserow[cnzi++] = pjj[k];
          }
        }
      }

      /* sort sparserow */
      ierr = PetscSortInt(cnzi,sparserow);CHKERRQ(ierr);

      /* If free space is not available, make more free space */
      /* Double the amount of total space in the list */
      if (current_space->local_remaining<cnzi) {
        ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
      }

      /* Copy data into free space, and zero out denserows */
      ierr = PetscMemcpy(current_space->array,sparserow,cnzi*sizeof(int));CHKERRQ(ierr);
      current_space->array           += cnzi;
      current_space->local_used      += cnzi;
      current_space->local_remaining -= cnzi;

      for (j=0;j<ptanzi;j++) {
        ptadenserow[ptasparserow[j]] = 0;
      }
      for (j=0;j<cnzi;j++) {
        denserow[sparserow[j]] = 0;
      }
      /* Aside: Perhaps we should save the pta info for the numerical factorization. */
      /*        For now, we will recompute what is needed. */
      ci[i+1+dof] = ci[i+dof] + cnzi;
    }
  }
  /* nnz is now stored in ci[ptm], column indices are in the list of free space */
  /* Allocate space for cj, initialize cj, and */
  /* destroy list of free space and other temporary array(s) */
  ierr = PetscMalloc((ci[pn]+1)*sizeof(int),&cj);CHKERRQ(ierr);
  ierr = MakeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
  ierr = PetscFree(ptadenserow);CHKERRQ(ierr);

  /* Allocate space for ca */
  ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
  ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr);

  /* put together the new matrix */
  ierr = MatCreateSeqAIJWithArrays(A->comm,pn,pn,ci,cj,ca,C);CHKERRQ(ierr);

  /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
  /* Since these are PETSc arrays, change flags to free them as necessary. */
  c = (Mat_SeqAIJ *)((*C)->data);
  c->freedata = PETSC_TRUE;
  c->nonew    = 0;

  /* Clean up. */
  ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);

  ierr = PetscLogEventEnd(MATSeqAIJ_PtAPSymbolic,A,PP,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
EXTERN_C_END

#include "src/mat/impls/maij/maij.h"
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatApplyPtAPSymbolic_SeqAIJ_SeqMAIJ"
int MatApplyPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat PP,Mat *C) {
  int            ierr;
  FreeSpaceList  free_space=PETSC_NULL,current_space=PETSC_NULL;
  Mat_SeqMAIJ    *pp=(Mat_SeqMAIJ*)PP->data;
  Mat             P=pp->AIJ;
  Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*p=(Mat_SeqAIJ*)P->data,*c;
  int            aishift=a->indexshift,pishift=p->indexshift;
  int            *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
  int            *ci,*cj,*denserow,*sparserow,*ptadenserow,*ptasparserow,*ptaj;
  int            an=A->N,am=A->M,pn=P->N,pm=P->M;
  int            i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi;
  MatScalar      *ca;

  PetscFunctionBegin;

  /* some error checking which could be moved into interface layer */
  if (aishift || pishift) SETERRQ(PETSC_ERR_SUP,"Shifted matrix indices are not supported.");

  /* Start timer */
  ierr = PetscLogEventBegin(MATSeqAIJ_PtAPSymbolic,A,PP,0,0);CHKERRQ(ierr);

  /* Get ij structure of P^T */
  ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
  ptJ=ptj;

  /* Allocate ci array, arrays for fill computation and */
  /* free space for accumulating nonzero column info */
  ierr = PetscMalloc(((pn+1)*1)*sizeof(int),&ci);CHKERRQ(ierr);
  ci[0] = 0;

  ierr = PetscMalloc((2*pn+2*an+1)*sizeof(int),&ptadenserow);CHKERRQ(ierr);
  ierr = PetscMemzero(ptadenserow,(2*pn+2*an+1)*sizeof(int));CHKERRQ(ierr);
  ptasparserow = ptadenserow  + an;
  denserow     = ptasparserow + an;
  sparserow    = denserow     + pn;

  /* Set initial free space to be nnz(A) scaled by aspect ratio of P. */
  /* This should be reasonable if sparsity of PtAP is similar to that of A. */
  ierr          = GetMoreSpace((ai[am]/pm)*pn,&free_space);
  current_space = free_space;

  /* Determine symbolic info for each row of C: */
  for (i=0;i<pn;i++) {
    ptnzi  = pti[i+1] - pti[i];
    ptanzi = 0;
    /* Determine symbolic row of PtA: */
    for (j=0;j<ptnzi;j++) {
      arow = *ptJ++;
      anzj = ai[arow+1] - ai[arow];
      ajj  = aj + ai[arow];
      for (k=0;k<anzj;k++) {
        if (!ptadenserow[ajj[k]]) {
          ptadenserow[ajj[k]]    = -1;
          ptasparserow[ptanzi++] = ajj[k];
        }
      }
    }
    /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
    ptaj = ptasparserow;
    cnzi   = 0;
    for (j=0;j<ptanzi;j++) {
      prow = *ptaj++;
      pnzj = pi[prow+1] - pi[prow];
      pjj  = pj + pi[prow];
      for (k=0;k<pnzj;k++) {
        if (!denserow[pjj[k]]) {
          denserow[pjj[k]]  = -1;
          sparserow[cnzi++] = pjj[k];
        }
      }
    }

    /* sort sparserow */
    ierr = PetscSortInt(cnzi,sparserow);CHKERRQ(ierr);

    /* If free space is not available, make more free space */
    /* Double the amount of total space in the list */
    if (current_space->local_remaining<cnzi) {
      ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
    }

    /* Copy data into free space, and zero out denserows */
    ierr = PetscMemcpy(current_space->array,sparserow,cnzi*sizeof(int));CHKERRQ(ierr);
    current_space->array           += cnzi;
    current_space->local_used      += cnzi;
    current_space->local_remaining -= cnzi;

    for (j=0;j<ptanzi;j++) {
      ptadenserow[ptasparserow[j]] = 0;
    }
    for (j=0;j<cnzi;j++) {
      denserow[sparserow[j]] = 0;
    }
    /* Aside: Perhaps we should save the pta info for the numerical factorization. */
    /*        For now, we will recompute what is needed. */
    ci[i+1] = ci[i] + cnzi;
  }
  /* nnz is now stored in ci[ptm], column indices are in the list of free space */
  /* Allocate space for cj, initialize cj, and */
  /* destroy list of free space and other temporary array(s) */
  ierr = PetscMalloc((ci[pn]+1)*sizeof(int),&cj);CHKERRQ(ierr);
  ierr = MakeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
  ierr = PetscFree(ptadenserow);CHKERRQ(ierr);

  /* Allocate space for ca */
  ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
  ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr);

  /* put together the new matrix */
  ierr = MatCreateSeqAIJWithArrays(A->comm,pn,pn,ci,cj,ca,C);CHKERRQ(ierr);

  /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
  /* Since these are PETSc arrays, change flags to free them as necessary. */
  c = (Mat_SeqAIJ *)((*C)->data);
  c->freedata = PETSC_TRUE;
  c->nonew    = 0;

  /* Clean up. */
  ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);

  ierr = PetscLogEventEnd(MATSeqAIJ_PtAPSymbolic,A,PP,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
EXTERN_C_END

/*
     MatSeqAIJPtAPNumeric - Computes the SeqAIJ matrix product, C,
           of SeqAIJ matrix A and matrix P, according to:
                 C = P^T * A * P
     Note: C must have been created by calling MatSeqAIJApplyPtAPSymbolic.
*/
#undef __FUNCT__
#define __FUNCT__ "MatSeqAIJPtAPNumeric"
int MatSeqAIJPtAPNumeric(Mat A,Mat P,Mat C) {
  int ierr;
  char funct[80];

  PetscFunctionBegin;

  PetscValidHeaderSpecific(A,MAT_COOKIE);
  PetscValidType(A);
  MatPreallocated(A);
  if (!A->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  PetscValidHeaderSpecific(P,MAT_COOKIE);
  PetscValidType(P);
  MatPreallocated(P);
  if (!P->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (P->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  PetscValidHeaderSpecific(C,MAT_COOKIE);
  PetscValidType(C);
  MatPreallocated(C);
  if (!C->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (C->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  if (P->N!=C->M) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",P->N,C->M);
  if (P->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",P->M,A->N);
  if (A->M!=A->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %d != %d",A->M,A->N);
  if (P->N!=C->N) SETERRQ2(PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %d != %d",P->N,C->N);

  /* Query A for ApplyPtAP implementation based on types of P */
  ierr = PetscStrcpy(funct,"MatApplyPtAPNumeric_seqaij_");CHKERRQ(ierr);
  ierr = PetscStrcat(funct,P->type_name);CHKERRQ(ierr);
  ierr = PetscTryMethod(A,funct,(Mat,Mat,Mat),(A,P,C));CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatApplyPtAPNumeric_SeqAIJ_SeqAIJ"
int MatApplyPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) {
  int        ierr,flops=0;
  Mat_SeqAIJ *a  = (Mat_SeqAIJ *) A->data;
  Mat_SeqAIJ *p  = (Mat_SeqAIJ *) P->data;
  Mat_SeqAIJ *c  = (Mat_SeqAIJ *) C->data;
  int        aishift=a->indexshift,pishift=p->indexshift,cishift=c->indexshift;
  int        *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
  int        *ci=c->i,*cj=c->j,*cjj;
  int        am=A->M,cn=C->N,cm=C->M;
  int        i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
  MatScalar  *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;

  PetscFunctionBegin;

  /* Currently not for shifted matrices! */
  if (aishift || pishift || cishift) SETERRQ(PETSC_ERR_SUP,"Shifted matrix indices are not supported.");

  ierr = PetscLogEventBegin(MATSeqAIJ_PtAPNumeric,A,P,C,0);CHKERRQ(ierr);

  /* Allocate temporary array for storage of one row of A*P */
  ierr = PetscMalloc(cn*(sizeof(MatScalar)+2*sizeof(int)),&apa);CHKERRQ(ierr);
  ierr = PetscMemzero(apa,cn*(sizeof(MatScalar)+2*sizeof(int)));CHKERRQ(ierr);

  apj      = (int *)(apa + cn);
  apjdense = apj + cn;

  /* Clear old values in C */
  ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);

  for (i=0;i<am;i++) {
    /* Form sparse row of A*P */
    anzi  = ai[i+1] - ai[i];
    apnzj = 0;
    for (j=0;j<anzi;j++) {
      prow = *aj++;
      pnzj = pi[prow+1] - pi[prow];
      pjj  = pj + pi[prow];
      paj  = pa + pi[prow];
      for (k=0;k<pnzj;k++) {
        if (!apjdense[pjj[k]]) {
          apjdense[pjj[k]] = -1;
          apj[apnzj++]     = pjj[k];
        }
        apa[pjj[k]] += (*aa)*paj[k];
      }
      flops += 2*pnzj;
      aa++;
    }

    /* Sort the j index array for quick sparse axpy. */
    ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr);

    /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
    pnzi = pi[i+1] - pi[i];
    for (j=0;j<pnzi;j++) {
      nextap = 0;
      crow   = *pJ++;
      cjj    = cj + ci[crow];
      caj    = ca + ci[crow];
      /* Perform sparse axpy operation.  Note cjj includes apj. */
      for (k=0;nextap<apnzj;k++) {
        if (cjj[k]==apj[nextap]) {
          caj[k] += (*pA)*apa[apj[nextap++]];
        }
      }
      flops += 2*apnzj;
      pA++;
    }

    /* Zero the current row info for A*P */
    for (j=0;j<apnzj;j++) {
      apa[apj[j]]      = 0.;
      apjdense[apj[j]] = 0;
    }
  }

  /* Assemble the final matrix and clean up */
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscFree(apa);CHKERRQ(ierr);
  ierr = PetscLogFlops(flops);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MATSeqAIJ_PtAPNumeric,A,P,C,0);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "RegisterApplyPtAPRoutines_Private"
int RegisterApplyPtAPRoutines_Private(Mat A) {
  int ierr;

  PetscFunctionBegin;

  if (!MATSeqAIJ_PtAP) {
    ierr = PetscLogEventRegister(&MATSeqAIJ_PtAP,"MatSeqAIJApplyPtAP",MAT_COOKIE);CHKERRQ(ierr);
  }

  if (!MATSeqAIJ_PtAPSymbolic) {
    ierr = PetscLogEventRegister(&MATSeqAIJ_PtAPSymbolic,"MatSeqAIJApplyPtAPSymbolic",MAT_COOKIE);CHKERRQ(ierr);
  }
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)A,"MatApplyPtAPSymbolic_seqaij_seqaij",
                                           "MatApplyPtAPSymbolic_SeqAIJ_SeqAIJ",
                                           MatApplyPtAPSymbolic_SeqAIJ_SeqAIJ);CHKERRQ(ierr);

  if (!MATSeqAIJ_PtAPNumeric) {
    ierr = PetscLogEventRegister(&MATSeqAIJ_PtAPNumeric,"MatSeqAIJApplyPtAPNumeric",MAT_COOKIE);CHKERRQ(ierr);
  }
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)A,"MatApplyPtAPNumeric_seqaij_seqaij",
                                           "MatApplyPtAPNumeric_SeqAIJ_SeqAIJ",
                                           MatApplyPtAPNumeric_SeqAIJ_SeqAIJ);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}