xref: /petsc/src/mat/impls/aij/seq/aij.c (revision c2e3fba1fe1cda7e6350bbca19c4ed35ce95940a)

/*
    Defines the basic matrix operations for the AIJ (compressed row)
  matrix storage format.
*/

#include <../src/mat/impls/aij/seq/aij.h>          /*I "petscmat.h" I*/
#include <petscblaslapack.h>
#include <petscbt.h>
#include <petsc/private/kernels/blocktranspose.h>

PetscErrorCode MatSeqAIJSetTypeFromOptions(Mat A)
{
  PetscBool            flg;
  char                 type[256];

  PetscFunctionBegin;
  PetscObjectOptionsBegin((PetscObject)A);
  PetscCall(PetscOptionsFList("-mat_seqaij_type","Matrix SeqAIJ type","MatSeqAIJSetType",MatSeqAIJList,"seqaij",type,256,&flg));
  if (flg) PetscCall(MatSeqAIJSetType(A,type));
  PetscOptionsEnd();
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetColumnReductions_SeqAIJ(Mat A,PetscInt type,PetscReal *reductions)
{
  PetscInt       i,m,n;
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  PetscCall(MatGetSize(A,&m,&n));
  PetscCall(PetscArrayzero(reductions,n));
  if (type == NORM_2) {
    for (i=0; i<aij->i[m]; i++) {
      reductions[aij->j[i]] += PetscAbsScalar(aij->a[i]*aij->a[i]);
    }
  } else if (type == NORM_1) {
    for (i=0; i<aij->i[m]; i++) {
      reductions[aij->j[i]] += PetscAbsScalar(aij->a[i]);
    }
  } else if (type == NORM_INFINITY) {
    for (i=0; i<aij->i[m]; i++) {
      reductions[aij->j[i]] = PetscMax(PetscAbsScalar(aij->a[i]),reductions[aij->j[i]]);
    }
  } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
    for (i=0; i<aij->i[m]; i++) {
      reductions[aij->j[i]] += PetscRealPart(aij->a[i]);
    }
  } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    for (i=0; i<aij->i[m]; i++) {
      reductions[aij->j[i]] += PetscImaginaryPart(aij->a[i]);
    }
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown reduction type");

  if (type == NORM_2) {
    for (i=0; i<n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
  } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    for (i=0; i<n; i++) reductions[i] /= m;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatFindOffBlockDiagonalEntries_SeqAIJ(Mat A,IS *is)
{
  Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
  PetscInt        i,m=A->rmap->n,cnt = 0, bs = A->rmap->bs;
  const PetscInt  *jj = a->j,*ii = a->i;
  PetscInt        *rows;

  PetscFunctionBegin;
  for (i=0; i<m; i++) {
    if ((ii[i] != ii[i+1]) && ((jj[ii[i]] < bs*(i/bs)) || (jj[ii[i+1]-1] > bs*((i+bs)/bs)-1))) {
      cnt++;
    }
  }
  PetscCall(PetscMalloc1(cnt,&rows));
  cnt  = 0;
  for (i=0; i<m; i++) {
    if ((ii[i] != ii[i+1]) && ((jj[ii[i]] < bs*(i/bs)) || (jj[ii[i+1]-1] > bs*((i+bs)/bs)-1))) {
      rows[cnt] = i;
      cnt++;
    }
  }
  PetscCall(ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,is));
  PetscFunctionReturn(0);
}

PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat A,PetscInt *nrows,PetscInt **zrows)
{
  Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
  const MatScalar *aa;
  PetscInt        i,m=A->rmap->n,cnt = 0;
  const PetscInt  *ii = a->i,*jj = a->j,*diag;
  PetscInt        *rows;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArrayRead(A,&aa));
  PetscCall(MatMarkDiagonal_SeqAIJ(A));
  diag = a->diag;
  for (i=0; i<m; i++) {
    if ((diag[i] >= ii[i+1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
      cnt++;
    }
  }
  PetscCall(PetscMalloc1(cnt,&rows));
  cnt  = 0;
  for (i=0; i<m; i++) {
    if ((diag[i] >= ii[i+1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
      rows[cnt++] = i;
    }
  }
  *nrows = cnt;
  *zrows = rows;
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscFunctionReturn(0);
}

PetscErrorCode MatFindZeroDiagonals_SeqAIJ(Mat A,IS *zrows)
{
  PetscInt       nrows,*rows;

  PetscFunctionBegin;
  *zrows = NULL;
  PetscCall(MatFindZeroDiagonals_SeqAIJ_Private(A,&nrows,&rows));
  PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A),nrows,rows,PETSC_OWN_POINTER,zrows));
  PetscFunctionReturn(0);
}

PetscErrorCode MatFindNonzeroRows_SeqAIJ(Mat A,IS *keptrows)
{
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
  const MatScalar *aa;
  PetscInt        m=A->rmap->n,cnt = 0;
  const PetscInt  *ii;
  PetscInt        n,i,j,*rows;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArrayRead(A,&aa));
  *keptrows = NULL;
  ii        = a->i;
  for (i=0; i<m; i++) {
    n = ii[i+1] - ii[i];
    if (!n) {
      cnt++;
      goto ok1;
    }
    for (j=ii[i]; j<ii[i+1]; j++) {
      if (aa[j] != 0.0) goto ok1;
    }
    cnt++;
ok1:;
  }
  if (!cnt) {
    PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
    PetscFunctionReturn(0);
  }
  PetscCall(PetscMalloc1(A->rmap->n-cnt,&rows));
  cnt  = 0;
  for (i=0; i<m; i++) {
    n = ii[i+1] - ii[i];
    if (!n) continue;
    for (j=ii[i]; j<ii[i+1]; j++) {
      if (aa[j] != 0.0) {
        rows[cnt++] = i;
        break;
      }
    }
  }
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscCall(ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,keptrows));
  PetscFunctionReturn(0);
}

PetscErrorCode  MatDiagonalSet_SeqAIJ(Mat Y,Vec D,InsertMode is)
{
  Mat_SeqAIJ        *aij = (Mat_SeqAIJ*) Y->data;
  PetscInt          i,m = Y->rmap->n;
  const PetscInt    *diag;
  MatScalar         *aa;
  const PetscScalar *v;
  PetscBool         missing;

  PetscFunctionBegin;
  if (Y->assembled) {
    PetscCall(MatMissingDiagonal_SeqAIJ(Y,&missing,NULL));
    if (!missing) {
      diag = aij->diag;
      PetscCall(VecGetArrayRead(D,&v));
      PetscCall(MatSeqAIJGetArray(Y,&aa));
      if (is == INSERT_VALUES) {
        for (i=0; i<m; i++) {
          aa[diag[i]] = v[i];
        }
      } else {
        for (i=0; i<m; i++) {
          aa[diag[i]] += v[i];
        }
      }
      PetscCall(MatSeqAIJRestoreArray(Y,&aa));
      PetscCall(VecRestoreArrayRead(D,&v));
      PetscFunctionReturn(0);
    }
    PetscCall(MatSeqAIJInvalidateDiagonal(Y));
  }
  PetscCall(MatDiagonalSet_Default(Y,D,is));
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *m,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       i,ishift;

  PetscFunctionBegin;
  *m = A->rmap->n;
  if (!ia) PetscFunctionReturn(0);
  ishift = 0;
  if (symmetric && !A->structurally_symmetric) {
    PetscCall(MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,PETSC_TRUE,ishift,oshift,(PetscInt**)ia,(PetscInt**)ja));
  } else if (oshift == 1) {
    PetscInt *tia;
    PetscInt nz = a->i[A->rmap->n];
    /* malloc space and  add 1 to i and j indices */
    PetscCall(PetscMalloc1(A->rmap->n+1,&tia));
    for (i=0; i<A->rmap->n+1; i++) tia[i] = a->i[i] + 1;
    *ia = tia;
    if (ja) {
      PetscInt *tja;
      PetscCall(PetscMalloc1(nz+1,&tja));
      for (i=0; i<nz; i++) tja[i] = a->j[i] + 1;
      *ja = tja;
    }
  } else {
    *ia = a->i;
    if (ja) *ja = a->j;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
{
  PetscFunctionBegin;
  if (!ia) PetscFunctionReturn(0);
  if ((symmetric && !A->structurally_symmetric) || oshift == 1) {
    PetscCall(PetscFree(*ia));
    if (ja) PetscCall(PetscFree(*ja));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
  PetscInt       nz = a->i[m],row,*jj,mr,col;

  PetscFunctionBegin;
  *nn = n;
  if (!ia) PetscFunctionReturn(0);
  if (symmetric) {
    PetscCall(MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,PETSC_TRUE,0,oshift,(PetscInt**)ia,(PetscInt**)ja));
  } else {
    PetscCall(PetscCalloc1(n,&collengths));
    PetscCall(PetscMalloc1(n+1,&cia));
    PetscCall(PetscMalloc1(nz,&cja));
    jj   = a->j;
    for (i=0; i<nz; i++) {
      collengths[jj[i]]++;
    }
    cia[0] = oshift;
    for (i=0; i<n; i++) {
      cia[i+1] = cia[i] + collengths[i];
    }
    PetscCall(PetscArrayzero(collengths,n));
    jj   = a->j;
    for (row=0; row<m; row++) {
      mr = a->i[row+1] - a->i[row];
      for (i=0; i<mr; i++) {
        col = *jj++;

        cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
      }
    }
    PetscCall(PetscFree(collengths));
    *ia  = cia; *ja = cja;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
{
  PetscFunctionBegin;
  if (!ia) PetscFunctionReturn(0);

  PetscCall(PetscFree(*ia));
  PetscCall(PetscFree(*ja));
  PetscFunctionReturn(0);
}

/*
 MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
 MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
 spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ() and MatFDColoringCreate_SeqXAIJ()
*/
PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
  PetscInt       nz = a->i[m],row,mr,col,tmp;
  PetscInt       *cspidx;
  const PetscInt *jj;

  PetscFunctionBegin;
  *nn = n;
  if (!ia) PetscFunctionReturn(0);

  PetscCall(PetscCalloc1(n,&collengths));
  PetscCall(PetscMalloc1(n+1,&cia));
  PetscCall(PetscMalloc1(nz,&cja));
  PetscCall(PetscMalloc1(nz,&cspidx));
  jj   = a->j;
  for (i=0; i<nz; i++) {
    collengths[jj[i]]++;
  }
  cia[0] = oshift;
  for (i=0; i<n; i++) {
    cia[i+1] = cia[i] + collengths[i];
  }
  PetscCall(PetscArrayzero(collengths,n));
  jj   = a->j;
  for (row=0; row<m; row++) {
    mr = a->i[row+1] - a->i[row];
    for (i=0; i<mr; i++) {
      col         = *jj++;
      tmp         = cia[col] + collengths[col]++ - oshift;
      cspidx[tmp] = a->i[row] + i; /* index of a->j */
      cja[tmp]    = row + oshift;
    }
  }
  PetscCall(PetscFree(collengths));
  *ia    = cia;
  *ja    = cja;
  *spidx = cspidx;
  PetscFunctionReturn(0);
}

PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
{
  PetscFunctionBegin;
  PetscCall(MatRestoreColumnIJ_SeqAIJ(A,oshift,symmetric,inodecompressed,n,ia,ja,done));
  PetscCall(PetscFree(*spidx));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetValuesRow_SeqAIJ(Mat A,PetscInt row,const PetscScalar v[])
{
  Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
  PetscInt       *ai = a->i;
  PetscScalar    *aa;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(A,&aa));
  PetscCall(PetscArraycpy(aa+ai[row],v,ai[row+1]-ai[row]));
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscFunctionReturn(0);
}

/*
    MatSeqAIJSetValuesLocalFast - An optimized version of MatSetValuesLocal() for SeqAIJ matrices with several assumptions

      -   a single row of values is set with each call
      -   no row or column indices are negative or (in error) larger than the number of rows or columns
      -   the values are always added to the matrix, not set
      -   no new locations are introduced in the nonzero structure of the matrix

     This does NOT assume the global column indices are sorted

*/

#include <petsc/private/isimpl.h>
PetscErrorCode MatSeqAIJSetValuesLocalFast(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       low,high,t,row,nrow,i,col,l;
  const PetscInt *rp,*ai = a->i,*ailen = a->ilen,*aj = a->j;
  PetscInt       lastcol = -1;
  MatScalar      *ap,value,*aa;
  const PetscInt *ridx = A->rmap->mapping->indices,*cidx = A->cmap->mapping->indices;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(A,&aa));
  row  = ridx[im[0]];
  rp   = aj + ai[row];
  ap   = aa + ai[row];
  nrow = ailen[row];
  low  = 0;
  high = nrow;
  for (l=0; l<n; l++) { /* loop over added columns */
    col = cidx[in[l]];
    value = v[l];

    if (col <= lastcol) low = 0;
    else high = nrow;
    lastcol = col;
    while (high-low > 5) {
      t = (low+high)/2;
      if (rp[t] > col) high = t;
      else low = t;
    }
    for (i=low; i<high; i++) {
      if (rp[i] == col) {
        ap[i] += value;
        low = i + 1;
        break;
      }
    }
  }
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  return 0;
}

PetscErrorCode MatSetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
  PetscInt       *imax = a->imax,*ai = a->i,*ailen = a->ilen;
  PetscInt       *aj = a->j,nonew = a->nonew,lastcol = -1;
  MatScalar      *ap=NULL,value=0.0,*aa;
  PetscBool      ignorezeroentries = a->ignorezeroentries;
  PetscBool      roworiented       = a->roworiented;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(A,&aa));
  for (k=0; k<m; k++) { /* loop over added rows */
    row = im[k];
    if (row < 0) continue;
    PetscCheck(row < A->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT,row,A->rmap->n-1);
    rp   = aj + ai[row];
    if (!A->structure_only) ap = aa + ai[row];
    rmax = imax[row]; nrow = ailen[row];
    low  = 0;
    high = nrow;
    for (l=0; l<n; l++) { /* loop over added columns */
      if (in[l] < 0) continue;
      PetscCheck(in[l] < A->cmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT,in[l],A->cmap->n-1);
      col = in[l];
      if (v && !A->structure_only) value = roworiented ? v[l + k*n] : v[k + l*m];
      if (!A->structure_only && value == 0.0 && ignorezeroentries && is == ADD_VALUES && row != col) continue;

      if (col <= lastcol) low = 0;
      else high = nrow;
      lastcol = col;
      while (high-low > 5) {
        t = (low+high)/2;
        if (rp[t] > col) high = t;
        else low = t;
      }
      for (i=low; i<high; i++) {
        if (rp[i] > col) break;
        if (rp[i] == col) {
          if (!A->structure_only) {
            if (is == ADD_VALUES) {
              ap[i] += value;
              (void)PetscLogFlops(1.0);
            }
            else ap[i] = value;
          }
          low = i + 1;
          goto noinsert;
        }
      }
      if (value == 0.0 && ignorezeroentries && row != col) goto noinsert;
      if (nonew == 1) goto noinsert;
      PetscCheck(nonew != -1,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at (%" PetscInt_FMT ",%" PetscInt_FMT ") in the matrix",row,col);
      if (A->structure_only) {
        MatSeqXAIJReallocateAIJ_structure_only(A,A->rmap->n,1,nrow,row,col,rmax,ai,aj,rp,imax,nonew,MatScalar);
      } else {
        MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
      }
      N = nrow++ - 1; a->nz++; high++;
      /* shift up all the later entries in this row */
      PetscCall(PetscArraymove(rp+i+1,rp+i,N-i+1));
      rp[i] = col;
      if (!A->structure_only) {
        PetscCall(PetscArraymove(ap+i+1,ap+i,N-i+1));
        ap[i] = value;
      }
      low = i + 1;
      A->nonzerostate++;
noinsert:;
    }
    ailen[row] = nrow;
  }
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetValues_SeqAIJ_SortedFullNoPreallocation(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       *rp,k,row;
  PetscInt       *ai = a->i;
  PetscInt       *aj = a->j;
  MatScalar      *aa,*ap;

  PetscFunctionBegin;
  PetscCheck(!A->was_assembled,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot call on assembled matrix.");
  PetscCheck(m*n+a->nz <= a->maxnz,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of entries in matrix will be larger than maximum nonzeros allocated for %" PetscInt_FMT " in MatSeqAIJSetTotalPreallocation()",a->maxnz);

  PetscCall(MatSeqAIJGetArray(A,&aa));
  for (k=0; k<m; k++) { /* loop over added rows */
    row  = im[k];
    rp   = aj + ai[row];
    ap   = aa + ai[row];

    PetscCall(PetscMemcpy(rp,in,n*sizeof(PetscInt)));
    if (!A->structure_only) {
      if (v) {
        PetscCall(PetscMemcpy(ap,v,n*sizeof(PetscScalar)));
        v   += n;
      } else {
        PetscCall(PetscMemzero(ap,n*sizeof(PetscScalar)));
      }
    }
    a->ilen[row] = n;
    a->imax[row] = n;
    a->i[row+1]  = a->i[row]+n;
    a->nz       += n;
  }
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscFunctionReturn(0);
}

/*@
    MatSeqAIJSetTotalPreallocation - Sets an upper bound on the total number of expected nonzeros in the matrix.

  Input Parameters:
+  A - the SeqAIJ matrix
-  nztotal - bound on the number of nonzeros

  Level: advanced

  Notes:
    This can be called if you will be provided the matrix row by row (from row zero) with sorted column indices for each row.
    Simply call MatSetValues() after this call to provide the matrix entries in the usual manner. This matrix may be used
    as always with multiple matrix assemblies.

.seealso: `MatSetOption()`, `MAT_SORTED_FULL`, `MatSetValues()`, `MatSeqAIJSetPreallocation()`
@*/

PetscErrorCode MatSeqAIJSetTotalPreallocation(Mat A,PetscInt nztotal)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  PetscCall(PetscLayoutSetUp(A->rmap));
  PetscCall(PetscLayoutSetUp(A->cmap));
  a->maxnz  = nztotal;
  if (!a->imax) {
    PetscCall(PetscMalloc1(A->rmap->n,&a->imax));
    PetscCall(PetscLogObjectMemory((PetscObject)A,A->rmap->n*sizeof(PetscInt)));
  }
  if (!a->ilen) {
    PetscCall(PetscMalloc1(A->rmap->n,&a->ilen));
    PetscCall(PetscLogObjectMemory((PetscObject)A,A->rmap->n*sizeof(PetscInt)));
  } else {
    PetscCall(PetscMemzero(a->ilen,A->rmap->n*sizeof(PetscInt)));
  }

  /* allocate the matrix space */
  if (A->structure_only) {
    PetscCall(PetscMalloc1(nztotal,&a->j));
    PetscCall(PetscMalloc1(A->rmap->n+1,&a->i));
    PetscCall(PetscLogObjectMemory((PetscObject)A,(A->rmap->n+1)*sizeof(PetscInt)+nztotal*sizeof(PetscInt)));
  } else {
    PetscCall(PetscMalloc3(nztotal,&a->a,nztotal,&a->j,A->rmap->n+1,&a->i));
    PetscCall(PetscLogObjectMemory((PetscObject)A,(A->rmap->n+1)*sizeof(PetscInt)+nztotal*(sizeof(PetscScalar)+sizeof(PetscInt))));
  }
  a->i[0] = 0;
  if (A->structure_only) {
    a->singlemalloc = PETSC_FALSE;
    a->free_a       = PETSC_FALSE;
  } else {
    a->singlemalloc = PETSC_TRUE;
    a->free_a       = PETSC_TRUE;
  }
  a->free_ij        = PETSC_TRUE;
  A->ops->setvalues = MatSetValues_SeqAIJ_SortedFullNoPreallocation;
  A->preallocated   = PETSC_TRUE;
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetValues_SeqAIJ_SortedFull(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       *rp,k,row;
  PetscInt       *ai = a->i,*ailen = a->ilen;
  PetscInt       *aj = a->j;
  MatScalar      *aa,*ap;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(A,&aa));
  for (k=0; k<m; k++) { /* loop over added rows */
    row  = im[k];
    PetscCheck(n <= a->imax[row],PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Preallocation for row %" PetscInt_FMT " does not match number of columns provided",n);
    rp   = aj + ai[row];
    ap   = aa + ai[row];
    if (!A->was_assembled) {
      PetscCall(PetscMemcpy(rp,in,n*sizeof(PetscInt)));
    }
    if (!A->structure_only) {
      if (v) {
        PetscCall(PetscMemcpy(ap,v,n*sizeof(PetscScalar)));
        v   += n;
      } else {
        PetscCall(PetscMemzero(ap,n*sizeof(PetscScalar)));
      }
    }
    ailen[row] = n;
    a->nz      += n;
  }
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],PetscScalar v[])
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       *rp,k,low,high,t,row,nrow,i,col,l,*aj = a->j;
  PetscInt       *ai = a->i,*ailen = a->ilen;
  MatScalar      *ap,*aa;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(A,&aa));
  for (k=0; k<m; k++) { /* loop over rows */
    row = im[k];
    if (row < 0) {v += n; continue;} /* negative row */
    PetscCheck(row < A->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT,row,A->rmap->n-1);
    rp   = aj + ai[row]; ap = aa + ai[row];
    nrow = ailen[row];
    for (l=0; l<n; l++) { /* loop over columns */
      if (in[l] < 0) {v++; continue;} /* negative column */
      PetscCheck(in[l] < A->cmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT,in[l],A->cmap->n-1);
      col  = in[l];
      high = nrow; low = 0; /* assume unsorted */
      while (high-low > 5) {
        t = (low+high)/2;
        if (rp[t] > col) high = t;
        else low = t;
      }
      for (i=low; i<high; i++) {
        if (rp[i] > col) break;
        if (rp[i] == col) {
          *v++ = ap[i];
          goto finished;
        }
      }
      *v++ = 0.0;
finished:;
    }
  }
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscFunctionReturn(0);
}

PetscErrorCode MatView_SeqAIJ_Binary(Mat mat,PetscViewer viewer)
{
  Mat_SeqAIJ        *A = (Mat_SeqAIJ*)mat->data;
  const PetscScalar *av;
  PetscInt          header[4],M,N,m,nz,i;
  PetscInt          *rowlens;

  PetscFunctionBegin;
  PetscCall(PetscViewerSetUp(viewer));

  M  = mat->rmap->N;
  N  = mat->cmap->N;
  m  = mat->rmap->n;
  nz = A->nz;

  /* write matrix header */
  header[0] = MAT_FILE_CLASSID;
  header[1] = M; header[2] = N; header[3] = nz;
  PetscCall(PetscViewerBinaryWrite(viewer,header,4,PETSC_INT));

  /* fill in and store row lengths */
  PetscCall(PetscMalloc1(m,&rowlens));
  for (i=0; i<m; i++) rowlens[i] = A->i[i+1] - A->i[i];
  PetscCall(PetscViewerBinaryWrite(viewer,rowlens,m,PETSC_INT));
  PetscCall(PetscFree(rowlens));
  /* store column indices */
  PetscCall(PetscViewerBinaryWrite(viewer,A->j,nz,PETSC_INT));
  /* store nonzero values */
  PetscCall(MatSeqAIJGetArrayRead(mat,&av));
  PetscCall(PetscViewerBinaryWrite(viewer,av,nz,PETSC_SCALAR));
  PetscCall(MatSeqAIJRestoreArrayRead(mat,&av));

  /* write block size option to the viewer's .info file */
  PetscCall(MatView_Binary_BlockSizes(mat,viewer));
  PetscFunctionReturn(0);
}

static PetscErrorCode MatView_SeqAIJ_ASCII_structonly(Mat A,PetscViewer viewer)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       i,k,m=A->rmap->N;

  PetscFunctionBegin;
  PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
  for (i=0; i<m; i++) {
    PetscCall(PetscViewerASCIIPrintf(viewer,"row %" PetscInt_FMT ":",i));
    for (k=a->i[i]; k<a->i[i+1]; k++) {
      PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ") ",a->j[k]));
    }
    PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
  }
  PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
  PetscFunctionReturn(0);
}

extern PetscErrorCode MatSeqAIJFactorInfo_Matlab(Mat,PetscViewer);

PetscErrorCode MatView_SeqAIJ_ASCII(Mat A,PetscViewer viewer)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const PetscScalar *av;
  PetscInt          i,j,m = A->rmap->n;
  const char        *name;
  PetscViewerFormat format;

  PetscFunctionBegin;
  if (A->structure_only) {
    PetscCall(MatView_SeqAIJ_ASCII_structonly(A,viewer));
    PetscFunctionReturn(0);
  }

  PetscCall(PetscViewerGetFormat(viewer,&format));
  if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(0);

  /* trigger copy to CPU if needed */
  PetscCall(MatSeqAIJGetArrayRead(A,&av));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&av));
  if (format == PETSC_VIEWER_ASCII_MATLAB) {
    PetscInt nofinalvalue = 0;
    if (m && ((a->i[m] == a->i[m-1]) || (a->j[a->nz-1] != A->cmap->n-1))) {
      /* Need a dummy value to ensure the dimension of the matrix. */
      nofinalvalue = 1;
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
    PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT " \n",m,A->cmap->n));
    PetscCall(PetscViewerASCIIPrintf(viewer,"%% Nonzeros = %" PetscInt_FMT " \n",a->nz));
#if defined(PETSC_USE_COMPLEX)
    PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",4);\n",a->nz+nofinalvalue));
#else
    PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",a->nz+nofinalvalue));
#endif
    PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = [\n"));

    for (i=0; i<m; i++) {
      for (j=a->i[i]; j<a->i[i+1]; j++) {
#if defined(PETSC_USE_COMPLEX)
        PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e %18.16e\n",i+1,a->j[j]+1,(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j])));
#else
        PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",i+1,a->j[j]+1,(double)a->a[j]));
#endif
      }
    }
    if (nofinalvalue) {
#if defined(PETSC_USE_COMPLEX)
      PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e %18.16e\n",m,A->cmap->n,0.,0.));
#else
      PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",m,A->cmap->n,0.0));
#endif
    }
    PetscCall(PetscObjectGetName((PetscObject)A,&name));
    PetscCall(PetscViewerASCIIPrintf(viewer,"];\n %s = spconvert(zzz);\n",name));
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
  } else if (format == PETSC_VIEWER_ASCII_COMMON) {
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
    for (i=0; i<m; i++) {
      PetscCall(PetscViewerASCIIPrintf(viewer,"row %" PetscInt_FMT ":",i));
      for (j=a->i[i]; j<a->i[i+1]; j++) {
#if defined(PETSC_USE_COMPLEX)
        if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j])));
        } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j])));
        } else if (PetscRealPart(a->a[j]) != 0.0) {
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)PetscRealPart(a->a[j])));
        }
#else
        if (a->a[j] != 0.0) PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)a->a[j]));
#endif
      }
      PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
  } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
    PetscInt nzd=0,fshift=1,*sptr;
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
    PetscCall(PetscMalloc1(m+1,&sptr));
    for (i=0; i<m; i++) {
      sptr[i] = nzd+1;
      for (j=a->i[i]; j<a->i[i+1]; j++) {
        if (a->j[j] >= i) {
#if defined(PETSC_USE_COMPLEX)
          if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
#else
          if (a->a[j] != 0.0) nzd++;
#endif
        }
      }
    }
    sptr[m] = nzd+1;
    PetscCall(PetscViewerASCIIPrintf(viewer," %" PetscInt_FMT " %" PetscInt_FMT "\n\n",m,nzd));
    for (i=0; i<m+1; i+=6) {
      if (i+4<m) {
        PetscCall(PetscViewerASCIIPrintf(viewer," %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3],sptr[i+4],sptr[i+5]));
      } else if (i+3<m) {
        PetscCall(PetscViewerASCIIPrintf(viewer," %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3],sptr[i+4]));
      } else if (i+2<m) {
        PetscCall(PetscViewerASCIIPrintf(viewer," %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3]));
      } else if (i+1<m) {
        PetscCall(PetscViewerASCIIPrintf(viewer," %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n",sptr[i],sptr[i+1],sptr[i+2]));
      } else if (i<m) {
        PetscCall(PetscViewerASCIIPrintf(viewer," %" PetscInt_FMT " %" PetscInt_FMT "\n",sptr[i],sptr[i+1]));
      } else {
        PetscCall(PetscViewerASCIIPrintf(viewer," %" PetscInt_FMT "\n",sptr[i]));
      }
    }
    PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
    PetscCall(PetscFree(sptr));
    for (i=0; i<m; i++) {
      for (j=a->i[i]; j<a->i[i+1]; j++) {
        if (a->j[j] >= i) PetscCall(PetscViewerASCIIPrintf(viewer," %" PetscInt_FMT " ",a->j[j]+fshift));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
    }
    PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
    for (i=0; i<m; i++) {
      for (j=a->i[i]; j<a->i[i+1]; j++) {
        if (a->j[j] >= i) {
#if defined(PETSC_USE_COMPLEX)
          if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) {
            PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e %18.16e ",(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j])));
          }
#else
          if (a->a[j] != 0.0) PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e ",(double)a->a[j]));
#endif
        }
      }
      PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
  } else if (format == PETSC_VIEWER_ASCII_DENSE) {
    PetscInt    cnt = 0,jcnt;
    PetscScalar value;
#if defined(PETSC_USE_COMPLEX)
    PetscBool   realonly = PETSC_TRUE;

    for (i=0; i<a->i[m]; i++) {
      if (PetscImaginaryPart(a->a[i]) != 0.0) {
        realonly = PETSC_FALSE;
        break;
      }
    }
#endif

    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
    for (i=0; i<m; i++) {
      jcnt = 0;
      for (j=0; j<A->cmap->n; j++) {
        if (jcnt < a->i[i+1]-a->i[i] && j == a->j[cnt]) {
          value = a->a[cnt++];
          jcnt++;
        } else {
          value = 0.0;
        }
#if defined(PETSC_USE_COMPLEX)
        if (realonly) {
          PetscCall(PetscViewerASCIIPrintf(viewer," %7.5e ",(double)PetscRealPart(value)));
        } else {
          PetscCall(PetscViewerASCIIPrintf(viewer," %7.5e+%7.5e i ",(double)PetscRealPart(value),(double)PetscImaginaryPart(value)));
        }
#else
        PetscCall(PetscViewerASCIIPrintf(viewer," %7.5e ",(double)value));
#endif
      }
      PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
  } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
    PetscInt fshift=1;
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
#if defined(PETSC_USE_COMPLEX)
    PetscCall(PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate complex general\n"));
#else
    PetscCall(PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate real general\n"));
#endif
    PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", m, A->cmap->n, a->nz));
    for (i=0; i<m; i++) {
      for (j=a->i[i]; j<a->i[i+1]; j++) {
#if defined(PETSC_USE_COMPLEX)
        PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %g %g\n", i+fshift,a->j[j]+fshift,(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j])));
#else
        PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %g\n", i+fshift, a->j[j]+fshift, (double)a->a[j]));
#endif
      }
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
  } else {
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
    if (A->factortype) {
      for (i=0; i<m; i++) {
        PetscCall(PetscViewerASCIIPrintf(viewer,"row %" PetscInt_FMT ":",i));
        /* L part */
        for (j=a->i[i]; j<a->i[i+1]; j++) {
#if defined(PETSC_USE_COMPLEX)
          if (PetscImaginaryPart(a->a[j]) > 0.0) {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j])));
          } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j]))));
          } else {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)PetscRealPart(a->a[j])));
          }
#else
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)a->a[j]));
#endif
        }
        /* diagonal */
        j = a->diag[i];
#if defined(PETSC_USE_COMPLEX)
        if (PetscImaginaryPart(a->a[j]) > 0.0) {
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->j[j],(double)PetscRealPart(1.0/a->a[j]),(double)PetscImaginaryPart(1.0/a->a[j])));
        } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->j[j],(double)PetscRealPart(1.0/a->a[j]),(double)(-PetscImaginaryPart(1.0/a->a[j]))));
        } else {
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)PetscRealPart(1.0/a->a[j])));
        }
#else
        PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)(1.0/a->a[j])));
#endif

        /* U part */
        for (j=a->diag[i+1]+1; j<a->diag[i]; j++) {
#if defined(PETSC_USE_COMPLEX)
          if (PetscImaginaryPart(a->a[j]) > 0.0) {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j])));
          } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j]))));
          } else {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)PetscRealPart(a->a[j])));
          }
#else
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)a->a[j]));
#endif
        }
        PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
      }
    } else {
      for (i=0; i<m; i++) {
        PetscCall(PetscViewerASCIIPrintf(viewer,"row %" PetscInt_FMT ":",i));
        for (j=a->i[i]; j<a->i[i+1]; j++) {
#if defined(PETSC_USE_COMPLEX)
          if (PetscImaginaryPart(a->a[j]) > 0.0) {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j])));
          } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j])));
          } else {
            PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)PetscRealPart(a->a[j])));
          }
#else
          PetscCall(PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->j[j],(double)a->a[j]));
#endif
        }
        PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
      }
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
  }
  PetscCall(PetscViewerFlush(viewer));
  PetscFunctionReturn(0);
}

#include <petscdraw.h>
PetscErrorCode MatView_SeqAIJ_Draw_Zoom(PetscDraw draw,void *Aa)
{
  Mat               A  = (Mat) Aa;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscInt          i,j,m = A->rmap->n;
  int               color;
  PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r;
  PetscViewer       viewer;
  PetscViewerFormat format;
  const PetscScalar *aa;

  PetscFunctionBegin;
  PetscCall(PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer));
  PetscCall(PetscViewerGetFormat(viewer,&format));
  PetscCall(PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr));

  /* loop over matrix elements drawing boxes */
  PetscCall(MatSeqAIJGetArrayRead(A,&aa));
  if (format != PETSC_VIEWER_DRAW_CONTOUR) {
    PetscDrawCollectiveBegin(draw);
    /* Blue for negative, Cyan for zero and  Red for positive */
    color = PETSC_DRAW_BLUE;
    for (i=0; i<m; i++) {
      y_l = m - i - 1.0; y_r = y_l + 1.0;
      for (j=a->i[i]; j<a->i[i+1]; j++) {
        x_l = a->j[j]; x_r = x_l + 1.0;
        if (PetscRealPart(aa[j]) >=  0.) continue;
        PetscCall(PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color));
      }
    }
    color = PETSC_DRAW_CYAN;
    for (i=0; i<m; i++) {
      y_l = m - i - 1.0; y_r = y_l + 1.0;
      for (j=a->i[i]; j<a->i[i+1]; j++) {
        x_l = a->j[j]; x_r = x_l + 1.0;
        if (aa[j] !=  0.) continue;
        PetscCall(PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color));
      }
    }
    color = PETSC_DRAW_RED;
    for (i=0; i<m; i++) {
      y_l = m - i - 1.0; y_r = y_l + 1.0;
      for (j=a->i[i]; j<a->i[i+1]; j++) {
        x_l = a->j[j]; x_r = x_l + 1.0;
        if (PetscRealPart(aa[j]) <=  0.) continue;
        PetscCall(PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color));
      }
    }
    PetscDrawCollectiveEnd(draw);
  } else {
    /* use contour shading to indicate magnitude of values */
    /* first determine max of all nonzero values */
    PetscReal      minv = 0.0, maxv = 0.0;
    PetscInt       nz   = a->nz, count = 0;
    PetscDraw      popup;

    for (i=0; i<nz; i++) {
      if (PetscAbsScalar(aa[i]) > maxv) maxv = PetscAbsScalar(aa[i]);
    }
    if (minv >= maxv) maxv = minv + PETSC_SMALL;
    PetscCall(PetscDrawGetPopup(draw,&popup));
    PetscCall(PetscDrawScalePopup(popup,minv,maxv));

    PetscDrawCollectiveBegin(draw);
    for (i=0; i<m; i++) {
      y_l = m - i - 1.0;
      y_r = y_l + 1.0;
      for (j=a->i[i]; j<a->i[i+1]; j++) {
        x_l = a->j[j];
        x_r = x_l + 1.0;
        color = PetscDrawRealToColor(PetscAbsScalar(aa[count]),minv,maxv);
        PetscCall(PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color));
        count++;
      }
    }
    PetscDrawCollectiveEnd(draw);
  }
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscFunctionReturn(0);
}

#include <petscdraw.h>
PetscErrorCode MatView_SeqAIJ_Draw(Mat A,PetscViewer viewer)
{
  PetscDraw      draw;
  PetscReal      xr,yr,xl,yl,h,w;
  PetscBool      isnull;

  PetscFunctionBegin;
  PetscCall(PetscViewerDrawGetDraw(viewer,0,&draw));
  PetscCall(PetscDrawIsNull(draw,&isnull));
  if (isnull) PetscFunctionReturn(0);

  xr   = A->cmap->n; yr  = A->rmap->n; h = yr/10.0; w = xr/10.0;
  xr  += w;          yr += h;         xl = -w;     yl = -h;
  PetscCall(PetscDrawSetCoordinates(draw,xl,yl,xr,yr));
  PetscCall(PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer));
  PetscCall(PetscDrawZoom(draw,MatView_SeqAIJ_Draw_Zoom,A));
  PetscCall(PetscObjectCompose((PetscObject)A,"Zoomviewer",NULL));
  PetscCall(PetscDrawSave(draw));
  PetscFunctionReturn(0);
}

PetscErrorCode MatView_SeqAIJ(Mat A,PetscViewer viewer)
{
  PetscBool      iascii,isbinary,isdraw;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw));
  if (iascii) {
    PetscCall(MatView_SeqAIJ_ASCII(A,viewer));
  } else if (isbinary) {
    PetscCall(MatView_SeqAIJ_Binary(A,viewer));
  } else if (isdraw) {
    PetscCall(MatView_SeqAIJ_Draw(A,viewer));
  }
  PetscCall(MatView_SeqAIJ_Inode(A,viewer));
  PetscFunctionReturn(0);
}

PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat A,MatAssemblyType mode)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       fshift = 0,i,*ai = a->i,*aj = a->j,*imax = a->imax;
  PetscInt       m      = A->rmap->n,*ip,N,*ailen = a->ilen,rmax = 0;
  MatScalar      *aa    = a->a,*ap;
  PetscReal      ratio  = 0.6;

  PetscFunctionBegin;
  if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  if (A->was_assembled && A->ass_nonzerostate == A->nonzerostate) {
    /* we need to respect users asking to use or not the inodes routine in between matrix assemblies */
    PetscCall(MatAssemblyEnd_SeqAIJ_Inode(A,mode));
    PetscFunctionReturn(0);
  }

  if (m) rmax = ailen[0]; /* determine row with most nonzeros */
  for (i=1; i<m; i++) {
    /* move each row back by the amount of empty slots (fshift) before it*/
    fshift += imax[i-1] - ailen[i-1];
    rmax    = PetscMax(rmax,ailen[i]);
    if (fshift) {
      ip = aj + ai[i];
      ap = aa + ai[i];
      N  = ailen[i];
      PetscCall(PetscArraymove(ip-fshift,ip,N));
      if (!A->structure_only) {
        PetscCall(PetscArraymove(ap-fshift,ap,N));
      }
    }
    ai[i] = ai[i-1] + ailen[i-1];
  }
  if (m) {
    fshift += imax[m-1] - ailen[m-1];
    ai[m]   = ai[m-1] + ailen[m-1];
  }

  /* reset ilen and imax for each row */
  a->nonzerorowcnt = 0;
  if (A->structure_only) {
    PetscCall(PetscFree(a->imax));
    PetscCall(PetscFree(a->ilen));
  } else { /* !A->structure_only */
    for (i=0; i<m; i++) {
      ailen[i] = imax[i] = ai[i+1] - ai[i];
      a->nonzerorowcnt += ((ai[i+1] - ai[i]) > 0);
    }
  }
  a->nz = ai[m];
  PetscCheck(!fshift || a->nounused != -1,PETSC_COMM_SELF,PETSC_ERR_PLIB, "Unused space detected in matrix: %" PetscInt_FMT " X %" PetscInt_FMT ", %" PetscInt_FMT " unneeded", m, A->cmap->n, fshift);

  PetscCall(MatMarkDiagonal_SeqAIJ(A));
  PetscCall(PetscInfo(A,"Matrix size: %" PetscInt_FMT " X %" PetscInt_FMT "; storage space: %" PetscInt_FMT " unneeded,%" PetscInt_FMT " used\n",m,A->cmap->n,fshift,a->nz));
  PetscCall(PetscInfo(A,"Number of mallocs during MatSetValues() is %" PetscInt_FMT "\n",a->reallocs));
  PetscCall(PetscInfo(A,"Maximum nonzeros in any row is %" PetscInt_FMT "\n",rmax));

  A->info.mallocs    += a->reallocs;
  a->reallocs         = 0;
  A->info.nz_unneeded = (PetscReal)fshift;
  a->rmax             = rmax;

  if (!A->structure_only) {
    PetscCall(MatCheckCompressedRow(A,a->nonzerorowcnt,&a->compressedrow,a->i,m,ratio));
  }
  PetscCall(MatAssemblyEnd_SeqAIJ_Inode(A,mode));
  PetscFunctionReturn(0);
}

PetscErrorCode MatRealPart_SeqAIJ(Mat A)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       i,nz = a->nz;
  MatScalar      *aa;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(A,&aa));
  for (i=0; i<nz; i++) aa[i] = PetscRealPart(aa[i]);
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscFunctionReturn(0);
}

PetscErrorCode MatImaginaryPart_SeqAIJ(Mat A)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       i,nz = a->nz;
  MatScalar      *aa;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(A,&aa));
  for (i=0; i<nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscFunctionReturn(0);
}

PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  MatScalar      *aa;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArrayWrite(A,&aa));
  PetscCall(PetscArrayzero(aa,a->i[A->rmap->n]));
  PetscCall(MatSeqAIJRestoreArrayWrite(A,&aa));
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatResetPreallocationCOO_SeqAIJ(Mat A)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  PetscCall(PetscFree(a->perm));
  PetscCall(PetscFree(a->jmap));
  PetscFunctionReturn(0);
}

PetscErrorCode MatDestroy_SeqAIJ(Mat A)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
#if defined(PETSC_USE_LOG)
  PetscLogObjectState((PetscObject)A,"Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT ", NZ=%" PetscInt_FMT,A->rmap->n,A->cmap->n,a->nz);
#endif
  PetscCall(MatSeqXAIJFreeAIJ(A,&a->a,&a->j,&a->i));
  PetscCall(MatResetPreallocationCOO_SeqAIJ(A));
  PetscCall(ISDestroy(&a->row));
  PetscCall(ISDestroy(&a->col));
  PetscCall(PetscFree(a->diag));
  PetscCall(PetscFree(a->ibdiag));
  PetscCall(PetscFree(a->imax));
  PetscCall(PetscFree(a->ilen));
  PetscCall(PetscFree(a->ipre));
  PetscCall(PetscFree3(a->idiag,a->mdiag,a->ssor_work));
  PetscCall(PetscFree(a->solve_work));
  PetscCall(ISDestroy(&a->icol));
  PetscCall(PetscFree(a->saved_values));
  PetscCall(PetscFree2(a->compressedrow.i,a->compressedrow.rindex));
  PetscCall(MatDestroy_SeqAIJ_Inode(A));
  PetscCall(PetscFree(A->data));

  /* MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted may allocate this.
     That function is so heavily used (sometimes in an hidden way through multnumeric function pointers)
     that is hard to properly add this data to the MatProduct data. We free it here to avoid
     users reusing the matrix object with different data to incur in obscure segmentation faults
     due to different matrix sizes */
  PetscCall(PetscObjectCompose((PetscObject)A,"__PETSc__ab_dense",NULL));

  PetscCall(PetscObjectChangeTypeName((PetscObject)A,NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetColumnIndices_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatStoreValues_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatRetrieveValues_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsbaij_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqbaij_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijperm_C",NULL));
#if defined(PETSC_HAVE_CUDA)
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijcusparse_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaijcusparse_seqaij_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaij_seqaijcusparse_C",NULL));
#endif
#if defined(PETSC_HAVE_KOKKOS_KERNELS)
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijkokkos_C",NULL));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijcrl_C",NULL));
#if defined(PETSC_HAVE_ELEMENTAL)
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_elemental_C",NULL));
#endif
#if defined(PETSC_HAVE_SCALAPACK)
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_scalapack_C",NULL));
#endif
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_hypre_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_transpose_seqaij_seqaij_C",NULL));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqdense_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsell_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_is_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatIsTranspose_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocation_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatResetPreallocation_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocationCSR_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatReorderForNonzeroDiagonal_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_is_seqaij_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqdense_seqaij_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaij_seqaij_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJKron_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatSetPreallocationCOO_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A,"MatSetValuesCOO_C",NULL));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetOption_SeqAIJ(Mat A,MatOption op,PetscBool flg)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  switch (op) {
  case MAT_ROW_ORIENTED:
    a->roworiented = flg;
    break;
  case MAT_KEEP_NONZERO_PATTERN:
    a->keepnonzeropattern = flg;
    break;
  case MAT_NEW_NONZERO_LOCATIONS:
    a->nonew = (flg ? 0 : 1);
    break;
  case MAT_NEW_NONZERO_LOCATION_ERR:
    a->nonew = (flg ? -1 : 0);
    break;
  case MAT_NEW_NONZERO_ALLOCATION_ERR:
    a->nonew = (flg ? -2 : 0);
    break;
  case MAT_UNUSED_NONZERO_LOCATION_ERR:
    a->nounused = (flg ? -1 : 0);
    break;
  case MAT_IGNORE_ZERO_ENTRIES:
    a->ignorezeroentries = flg;
    break;
  case MAT_SPD:
  case MAT_SYMMETRIC:
  case MAT_STRUCTURALLY_SYMMETRIC:
  case MAT_HERMITIAN:
  case MAT_SYMMETRY_ETERNAL:
  case MAT_STRUCTURE_ONLY:
    /* These options are handled directly by MatSetOption() */
    break;
  case MAT_FORCE_DIAGONAL_ENTRIES:
  case MAT_IGNORE_OFF_PROC_ENTRIES:
  case MAT_USE_HASH_TABLE:
    PetscCall(PetscInfo(A,"Option %s ignored\n",MatOptions[op]));
    break;
  case MAT_USE_INODES:
    PetscCall(MatSetOption_SeqAIJ_Inode(A,MAT_USE_INODES,flg));
    break;
  case MAT_SUBMAT_SINGLEIS:
    A->submat_singleis = flg;
    break;
  case MAT_SORTED_FULL:
    if (flg) A->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
    else     A->ops->setvalues = MatSetValues_SeqAIJ;
    break;
  case MAT_FORM_EXPLICIT_TRANSPOSE:
    A->form_explicit_transpose = flg;
    break;
  default:
    SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetDiagonal_SeqAIJ(Mat A,Vec v)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscInt          i,j,n,*ai=a->i,*aj=a->j;
  PetscScalar       *x;
  const PetscScalar *aa;

  PetscFunctionBegin;
  PetscCall(VecGetLocalSize(v,&n));
  PetscCheck(n == A->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
  PetscCall(MatSeqAIJGetArrayRead(A,&aa));
  if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
    PetscInt *diag=a->diag;
    PetscCall(VecGetArrayWrite(v,&x));
    for (i=0; i<n; i++) x[i] = 1.0/aa[diag[i]];
    PetscCall(VecRestoreArrayWrite(v,&x));
    PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
    PetscFunctionReturn(0);
  }

  PetscCall(VecGetArrayWrite(v,&x));
  for (i=0; i<n; i++) {
    x[i] = 0.0;
    for (j=ai[i]; j<ai[i+1]; j++) {
      if (aj[j] == i) {
        x[i] = aa[j];
        break;
      }
    }
  }
  PetscCall(VecRestoreArrayWrite(v,&x));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscFunctionReturn(0);
}

#include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat A,Vec xx,Vec zz,Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const MatScalar   *aa;
  PetscScalar       *y;
  const PetscScalar *x;
  PetscInt          m = A->rmap->n;
#if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
  const MatScalar   *v;
  PetscScalar       alpha;
  PetscInt          n,i,j;
  const PetscInt    *idx,*ii,*ridx=NULL;
  Mat_CompressedRow cprow    = a->compressedrow;
  PetscBool         usecprow = cprow.use;
#endif

  PetscFunctionBegin;
  if (zz != yy) PetscCall(VecCopy(zz,yy));
  PetscCall(VecGetArrayRead(xx,&x));
  PetscCall(VecGetArray(yy,&y));
  PetscCall(MatSeqAIJGetArrayRead(A,&aa));

#if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
  fortranmulttransposeaddaij_(&m,x,a->i,a->j,aa,y);
#else
  if (usecprow) {
    m    = cprow.nrows;
    ii   = cprow.i;
    ridx = cprow.rindex;
  } else {
    ii = a->i;
  }
  for (i=0; i<m; i++) {
    idx = a->j + ii[i];
    v   = aa + ii[i];
    n   = ii[i+1] - ii[i];
    if (usecprow) {
      alpha = x[ridx[i]];
    } else {
      alpha = x[i];
    }
    for (j=0; j<n; j++) y[idx[j]] += alpha*v[j];
  }
#endif
  PetscCall(PetscLogFlops(2.0*a->nz));
  PetscCall(VecRestoreArrayRead(xx,&x));
  PetscCall(VecRestoreArray(yy,&y));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqAIJ(Mat A,Vec xx,Vec yy)
{
  PetscFunctionBegin;
  PetscCall(VecSet(yy,0.0));
  PetscCall(MatMultTransposeAdd_SeqAIJ(A,xx,yy,yy));
  PetscFunctionReturn(0);
}

#include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>

PetscErrorCode MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscScalar       *y;
  const PetscScalar *x;
  const MatScalar   *aa,*a_a;
  PetscInt          m=A->rmap->n;
  const PetscInt    *aj,*ii,*ridx=NULL;
  PetscInt          n,i;
  PetscScalar       sum;
  PetscBool         usecprow=a->compressedrow.use;

#if defined(PETSC_HAVE_PRAGMA_DISJOINT)
#pragma disjoint(*x,*y,*aa)
#endif

  PetscFunctionBegin;
  if (a->inode.use && a->inode.checked) {
    PetscCall(MatMult_SeqAIJ_Inode(A,xx,yy));
    PetscFunctionReturn(0);
  }
  PetscCall(MatSeqAIJGetArrayRead(A,&a_a));
  PetscCall(VecGetArrayRead(xx,&x));
  PetscCall(VecGetArray(yy,&y));
  ii   = a->i;
  if (usecprow) { /* use compressed row format */
    PetscCall(PetscArrayzero(y,m));
    m    = a->compressedrow.nrows;
    ii   = a->compressedrow.i;
    ridx = a->compressedrow.rindex;
    for (i=0; i<m; i++) {
      n           = ii[i+1] - ii[i];
      aj          = a->j + ii[i];
      aa          = a_a + ii[i];
      sum         = 0.0;
      PetscSparseDensePlusDot(sum,x,aa,aj,n);
      /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
      y[*ridx++] = sum;
    }
  } else { /* do not use compressed row format */
#if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
    aj   = a->j;
    aa   = a_a;
    fortranmultaij_(&m,x,ii,aj,aa,y);
#else
    for (i=0; i<m; i++) {
      n           = ii[i+1] - ii[i];
      aj          = a->j + ii[i];
      aa          = a_a + ii[i];
      sum         = 0.0;
      PetscSparseDensePlusDot(sum,x,aa,aj,n);
      y[i] = sum;
    }
#endif
  }
  PetscCall(PetscLogFlops(2.0*a->nz - a->nonzerorowcnt));
  PetscCall(VecRestoreArrayRead(xx,&x));
  PetscCall(VecRestoreArray(yy,&y));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&a_a));
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultMax_SeqAIJ(Mat A,Vec xx,Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscScalar       *y;
  const PetscScalar *x;
  const MatScalar   *aa,*a_a;
  PetscInt          m=A->rmap->n;
  const PetscInt    *aj,*ii,*ridx=NULL;
  PetscInt          n,i,nonzerorow=0;
  PetscScalar       sum;
  PetscBool         usecprow=a->compressedrow.use;

#if defined(PETSC_HAVE_PRAGMA_DISJOINT)
#pragma disjoint(*x,*y,*aa)
#endif

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArrayRead(A,&a_a));
  PetscCall(VecGetArrayRead(xx,&x));
  PetscCall(VecGetArray(yy,&y));
  if (usecprow) { /* use compressed row format */
    m    = a->compressedrow.nrows;
    ii   = a->compressedrow.i;
    ridx = a->compressedrow.rindex;
    for (i=0; i<m; i++) {
      n           = ii[i+1] - ii[i];
      aj          = a->j + ii[i];
      aa          = a_a + ii[i];
      sum         = 0.0;
      nonzerorow += (n>0);
      PetscSparseDenseMaxDot(sum,x,aa,aj,n);
      /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
      y[*ridx++] = sum;
    }
  } else { /* do not use compressed row format */
    ii = a->i;
    for (i=0; i<m; i++) {
      n           = ii[i+1] - ii[i];
      aj          = a->j + ii[i];
      aa          = a_a + ii[i];
      sum         = 0.0;
      nonzerorow += (n>0);
      PetscSparseDenseMaxDot(sum,x,aa,aj,n);
      y[i] = sum;
    }
  }
  PetscCall(PetscLogFlops(2.0*a->nz - nonzerorow));
  PetscCall(VecRestoreArrayRead(xx,&x));
  PetscCall(VecRestoreArray(yy,&y));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&a_a));
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAddMax_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscScalar       *y,*z;
  const PetscScalar *x;
  const MatScalar   *aa,*a_a;
  PetscInt          m = A->rmap->n,*aj,*ii;
  PetscInt          n,i,*ridx=NULL;
  PetscScalar       sum;
  PetscBool         usecprow=a->compressedrow.use;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArrayRead(A,&a_a));
  PetscCall(VecGetArrayRead(xx,&x));
  PetscCall(VecGetArrayPair(yy,zz,&y,&z));
  if (usecprow) { /* use compressed row format */
    if (zz != yy) {
      PetscCall(PetscArraycpy(z,y,m));
    }
    m    = a->compressedrow.nrows;
    ii   = a->compressedrow.i;
    ridx = a->compressedrow.rindex;
    for (i=0; i<m; i++) {
      n   = ii[i+1] - ii[i];
      aj  = a->j + ii[i];
      aa  = a_a + ii[i];
      sum = y[*ridx];
      PetscSparseDenseMaxDot(sum,x,aa,aj,n);
      z[*ridx++] = sum;
    }
  } else { /* do not use compressed row format */
    ii = a->i;
    for (i=0; i<m; i++) {
      n   = ii[i+1] - ii[i];
      aj  = a->j + ii[i];
      aa  = a_a + ii[i];
      sum = y[i];
      PetscSparseDenseMaxDot(sum,x,aa,aj,n);
      z[i] = sum;
    }
  }
  PetscCall(PetscLogFlops(2.0*a->nz));
  PetscCall(VecRestoreArrayRead(xx,&x));
  PetscCall(VecRestoreArrayPair(yy,zz,&y,&z));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&a_a));
  PetscFunctionReturn(0);
}

#include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
PetscErrorCode MatMultAdd_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscScalar       *y,*z;
  const PetscScalar *x;
  const MatScalar   *aa,*a_a;
  const PetscInt    *aj,*ii,*ridx=NULL;
  PetscInt          m = A->rmap->n,n,i;
  PetscScalar       sum;
  PetscBool         usecprow=a->compressedrow.use;

  PetscFunctionBegin;
  if (a->inode.use && a->inode.checked) {
    PetscCall(MatMultAdd_SeqAIJ_Inode(A,xx,yy,zz));
    PetscFunctionReturn(0);
  }
  PetscCall(MatSeqAIJGetArrayRead(A,&a_a));
  PetscCall(VecGetArrayRead(xx,&x));
  PetscCall(VecGetArrayPair(yy,zz,&y,&z));
  if (usecprow) { /* use compressed row format */
    if (zz != yy) {
      PetscCall(PetscArraycpy(z,y,m));
    }
    m    = a->compressedrow.nrows;
    ii   = a->compressedrow.i;
    ridx = a->compressedrow.rindex;
    for (i=0; i<m; i++) {
      n   = ii[i+1] - ii[i];
      aj  = a->j + ii[i];
      aa  = a_a + ii[i];
      sum = y[*ridx];
      PetscSparseDensePlusDot(sum,x,aa,aj,n);
      z[*ridx++] = sum;
    }
  } else { /* do not use compressed row format */
    ii = a->i;
#if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
    aj = a->j;
    aa = a_a;
    fortranmultaddaij_(&m,x,ii,aj,aa,y,z);
#else
    for (i=0; i<m; i++) {
      n   = ii[i+1] - ii[i];
      aj  = a->j + ii[i];
      aa  = a_a + ii[i];
      sum = y[i];
      PetscSparseDensePlusDot(sum,x,aa,aj,n);
      z[i] = sum;
    }
#endif
  }
  PetscCall(PetscLogFlops(2.0*a->nz));
  PetscCall(VecRestoreArrayRead(xx,&x));
  PetscCall(VecRestoreArrayPair(yy,zz,&y,&z));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&a_a));
  PetscFunctionReturn(0);
}

/*
     Adds diagonal pointers to sparse matrix structure.
*/
PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat A)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       i,j,m = A->rmap->n;
  PetscBool      alreadySet = PETSC_TRUE;

  PetscFunctionBegin;
  if (!a->diag) {
    PetscCall(PetscMalloc1(m,&a->diag));
    PetscCall(PetscLogObjectMemory((PetscObject)A, m*sizeof(PetscInt)));
    alreadySet = PETSC_FALSE;
  }
  for (i=0; i<A->rmap->n; i++) {
    /* If A's diagonal is already correctly set, this fast track enables cheap and repeated MatMarkDiagonal_SeqAIJ() calls */
    if (alreadySet) {
      PetscInt pos = a->diag[i];
      if (pos >= a->i[i] && pos < a->i[i+1] && a->j[pos] == i) continue;
    }

    a->diag[i] = a->i[i+1];
    for (j=a->i[i]; j<a->i[i+1]; j++) {
      if (a->j[j] == i) {
        a->diag[i] = j;
        break;
      }
    }
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatShift_SeqAIJ(Mat A,PetscScalar v)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const PetscInt    *diag = (const PetscInt*)a->diag;
  const PetscInt    *ii = (const PetscInt*) a->i;
  PetscInt          i,*mdiag = NULL;
  PetscInt          cnt = 0; /* how many diagonals are missing */

  PetscFunctionBegin;
  if (!A->preallocated || !a->nz) {
    PetscCall(MatSeqAIJSetPreallocation(A,1,NULL));
    PetscCall(MatShift_Basic(A,v));
    PetscFunctionReturn(0);
  }

  if (a->diagonaldense) {
    cnt = 0;
  } else {
    PetscCall(PetscCalloc1(A->rmap->n,&mdiag));
    for (i=0; i<A->rmap->n; i++) {
      if (diag[i] >= ii[i+1]) {
        cnt++;
        mdiag[i] = 1;
      }
    }
  }
  if (!cnt) {
    PetscCall(MatShift_Basic(A,v));
  } else {
    PetscScalar *olda = a->a;  /* preserve pointers to current matrix nonzeros structure and values */
    PetscInt    *oldj = a->j, *oldi = a->i;
    PetscBool   singlemalloc = a->singlemalloc,free_a = a->free_a,free_ij = a->free_ij;

    a->a = NULL;
    a->j = NULL;
    a->i = NULL;
    /* increase the values in imax for each row where a diagonal is being inserted then reallocate the matrix data structures */
    for (i=0; i<A->rmap->n; i++) {
      a->imax[i] += mdiag[i];
      a->imax[i] = PetscMin(a->imax[i],A->cmap->n);
    }
    PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(A,0,a->imax));

    /* copy old values into new matrix data structure */
    for (i=0; i<A->rmap->n; i++) {
      PetscCall(MatSetValues(A,1,&i,a->imax[i] - mdiag[i],&oldj[oldi[i]],&olda[oldi[i]],ADD_VALUES));
      if (i < A->cmap->n) {
        PetscCall(MatSetValue(A,i,i,v,ADD_VALUES));
      }
    }
    PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
    if (singlemalloc) {
      PetscCall(PetscFree3(olda,oldj,oldi));
    } else {
      if (free_a)  PetscCall(PetscFree(olda));
      if (free_ij) PetscCall(PetscFree(oldj));
      if (free_ij) PetscCall(PetscFree(oldi));
    }
  }
  PetscCall(PetscFree(mdiag));
  a->diagonaldense = PETSC_TRUE;
  PetscFunctionReturn(0);
}

/*
     Checks for missing diagonals
*/
PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A,PetscBool  *missing,PetscInt *d)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       *diag,*ii = a->i,i;

  PetscFunctionBegin;
  *missing = PETSC_FALSE;
  if (A->rmap->n > 0 && !ii) {
    *missing = PETSC_TRUE;
    if (d) *d = 0;
    PetscCall(PetscInfo(A,"Matrix has no entries therefore is missing diagonal\n"));
  } else {
    PetscInt n;
    n = PetscMin(A->rmap->n, A->cmap->n);
    diag = a->diag;
    for (i=0; i<n; i++) {
      if (diag[i] >= ii[i+1]) {
        *missing = PETSC_TRUE;
        if (d) *d = i;
        PetscCall(PetscInfo(A,"Matrix is missing diagonal number %" PetscInt_FMT "\n",i));
        break;
      }
    }
  }
  PetscFunctionReturn(0);
}

#include <petscblaslapack.h>
#include <petsc/private/kernels/blockinvert.h>

/*
    Note that values is allocated externally by the PC and then passed into this routine
*/
PetscErrorCode MatInvertVariableBlockDiagonal_SeqAIJ(Mat A,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *diag)
{
  PetscInt        n = A->rmap->n, i, ncnt = 0, *indx,j,bsizemax = 0,*v_pivots;
  PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
  const PetscReal shift = 0.0;
  PetscInt        ipvt[5];
  PetscScalar     work[25],*v_work;

  PetscFunctionBegin;
  allowzeropivot = PetscNot(A->erroriffailure);
  for (i=0; i<nblocks; i++) ncnt += bsizes[i];
  PetscCheck(ncnt == n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Total blocksizes %" PetscInt_FMT " doesn't match number matrix rows %" PetscInt_FMT,ncnt,n);
  for (i=0; i<nblocks; i++) {
    bsizemax = PetscMax(bsizemax,bsizes[i]);
  }
  PetscCall(PetscMalloc1(bsizemax,&indx));
  if (bsizemax > 7) {
    PetscCall(PetscMalloc2(bsizemax,&v_work,bsizemax,&v_pivots));
  }
  ncnt = 0;
  for (i=0; i<nblocks; i++) {
    for (j=0; j<bsizes[i]; j++) indx[j] = ncnt+j;
    PetscCall(MatGetValues(A,bsizes[i],indx,bsizes[i],indx,diag));
    switch (bsizes[i]) {
    case 1:
      *diag = 1.0/(*diag);
      break;
    case 2:
      PetscCall(PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_2(diag));
      break;
    case 3:
      PetscCall(PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_3(diag));
      break;
    case 4:
      PetscCall(PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_4(diag));
      break;
    case 5:
      PetscCall(PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_5(diag));
      break;
    case 6:
      PetscCall(PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_6(diag));
      break;
    case 7:
      PetscCall(PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_7(diag));
      break;
    default:
      PetscCall(PetscKernel_A_gets_inverse_A(bsizes[i],diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_N(diag,bsizes[i]));
    }
    ncnt   += bsizes[i];
    diag += bsizes[i]*bsizes[i];
  }
  if (bsizemax > 7) {
    PetscCall(PetscFree2(v_work,v_pivots));
  }
  PetscCall(PetscFree(indx));
  PetscFunctionReturn(0);
}

/*
   Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
*/
PetscErrorCode  MatInvertDiagonal_SeqAIJ(Mat A,PetscScalar omega,PetscScalar fshift)
{
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
  PetscInt        i,*diag,m = A->rmap->n;
  const MatScalar *v;
  PetscScalar     *idiag,*mdiag;

  PetscFunctionBegin;
  if (a->idiagvalid) PetscFunctionReturn(0);
  PetscCall(MatMarkDiagonal_SeqAIJ(A));
  diag = a->diag;
  if (!a->idiag) {
    PetscCall(PetscMalloc3(m,&a->idiag,m,&a->mdiag,m,&a->ssor_work));
    PetscCall(PetscLogObjectMemory((PetscObject)A,3*m*sizeof(PetscScalar)));
  }

  mdiag = a->mdiag;
  idiag = a->idiag;
  PetscCall(MatSeqAIJGetArrayRead(A,&v));
  if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
    for (i=0; i<m; i++) {
      mdiag[i] = v[diag[i]];
      if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
        if (PetscRealPart(fshift)) {
          PetscCall(PetscInfo(A,"Zero diagonal on row %" PetscInt_FMT "\n",i));
          A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
          A->factorerror_zeropivot_value = 0.0;
          A->factorerror_zeropivot_row   = i;
        } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %" PetscInt_FMT,i);
      }
      idiag[i] = 1.0/v[diag[i]];
    }
    PetscCall(PetscLogFlops(m));
  } else {
    for (i=0; i<m; i++) {
      mdiag[i] = v[diag[i]];
      idiag[i] = omega/(fshift + v[diag[i]]);
    }
    PetscCall(PetscLogFlops(2.0*m));
  }
  a->idiagvalid = PETSC_TRUE;
  PetscCall(MatSeqAIJRestoreArrayRead(A,&v));
  PetscFunctionReturn(0);
}

#include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
PetscErrorCode MatSOR_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscScalar       *x,d,sum,*t,scale;
  const MatScalar   *v,*idiag=NULL,*mdiag,*aa;
  const PetscScalar *b, *bs,*xb, *ts;
  PetscInt          n,m = A->rmap->n,i;
  const PetscInt    *idx,*diag;

  PetscFunctionBegin;
  if (a->inode.use && a->inode.checked && omega == 1.0 && fshift == 0.0) {
    PetscCall(MatSOR_SeqAIJ_Inode(A,bb,omega,flag,fshift,its,lits,xx));
    PetscFunctionReturn(0);
  }
  its = its*lits;

  if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
  if (!a->idiagvalid) PetscCall(MatInvertDiagonal_SeqAIJ(A,omega,fshift));
  a->fshift = fshift;
  a->omega  = omega;

  diag  = a->diag;
  t     = a->ssor_work;
  idiag = a->idiag;
  mdiag = a->mdiag;

  PetscCall(MatSeqAIJGetArrayRead(A,&aa));
  PetscCall(VecGetArray(xx,&x));
  PetscCall(VecGetArrayRead(bb,&b));
  /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
  if (flag == SOR_APPLY_UPPER) {
    /* apply (U + D/omega) to the vector */
    bs = b;
    for (i=0; i<m; i++) {
      d   = fshift + mdiag[i];
      n   = a->i[i+1] - diag[i] - 1;
      idx = a->j + diag[i] + 1;
      v   = aa + diag[i] + 1;
      sum = b[i]*d/omega;
      PetscSparseDensePlusDot(sum,bs,v,idx,n);
      x[i] = sum;
    }
    PetscCall(VecRestoreArray(xx,&x));
    PetscCall(VecRestoreArrayRead(bb,&b));
    PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
    PetscCall(PetscLogFlops(a->nz));
    PetscFunctionReturn(0);
  }

  PetscCheck(flag != SOR_APPLY_LOWER,PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
  else if (flag & SOR_EISENSTAT) {
    /* Let  A = L + U + D; where L is lower triangular,
    U is upper triangular, E = D/omega; This routine applies

            (L + E)^{-1} A (U + E)^{-1}

    to a vector efficiently using Eisenstat's trick.
    */
    scale = (2.0/omega) - 1.0;

    /*  x = (E + U)^{-1} b */
    for (i=m-1; i>=0; i--) {
      n   = a->i[i+1] - diag[i] - 1;
      idx = a->j + diag[i] + 1;
      v   = aa + diag[i] + 1;
      sum = b[i];
      PetscSparseDenseMinusDot(sum,x,v,idx,n);
      x[i] = sum*idiag[i];
    }

    /*  t = b - (2*E - D)x */
    v = aa;
    for (i=0; i<m; i++) t[i] = b[i] - scale*(v[*diag++])*x[i];

    /*  t = (E + L)^{-1}t */
    ts   = t;
    diag = a->diag;
    for (i=0; i<m; i++) {
      n   = diag[i] - a->i[i];
      idx = a->j + a->i[i];
      v   = aa + a->i[i];
      sum = t[i];
      PetscSparseDenseMinusDot(sum,ts,v,idx,n);
      t[i] = sum*idiag[i];
      /*  x = x + t */
      x[i] += t[i];
    }

    PetscCall(PetscLogFlops(6.0*m-1 + 2.0*a->nz));
    PetscCall(VecRestoreArray(xx,&x));
    PetscCall(VecRestoreArrayRead(bb,&b));
    PetscFunctionReturn(0);
  }
  if (flag & SOR_ZERO_INITIAL_GUESS) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
      for (i=0; i<m; i++) {
        n   = diag[i] - a->i[i];
        idx = a->j + a->i[i];
        v   = aa + a->i[i];
        sum = b[i];
        PetscSparseDenseMinusDot(sum,x,v,idx,n);
        t[i] = sum;
        x[i] = sum*idiag[i];
      }
      xb   = t;
      PetscCall(PetscLogFlops(a->nz));
    } else xb = b;
    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
      for (i=m-1; i>=0; i--) {
        n   = a->i[i+1] - diag[i] - 1;
        idx = a->j + diag[i] + 1;
        v   = aa + diag[i] + 1;
        sum = xb[i];
        PetscSparseDenseMinusDot(sum,x,v,idx,n);
        if (xb == b) {
          x[i] = sum*idiag[i];
        } else {
          x[i] = (1-omega)*x[i] + sum*idiag[i];  /* omega in idiag */
        }
      }
      PetscCall(PetscLogFlops(a->nz)); /* assumes 1/2 in upper */
    }
    its--;
  }
  while (its--) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
      for (i=0; i<m; i++) {
        /* lower */
        n   = diag[i] - a->i[i];
        idx = a->j + a->i[i];
        v   = aa + a->i[i];
        sum = b[i];
        PetscSparseDenseMinusDot(sum,x,v,idx,n);
        t[i] = sum;             /* save application of the lower-triangular part */
        /* upper */
        n   = a->i[i+1] - diag[i] - 1;
        idx = a->j + diag[i] + 1;
        v   = aa + diag[i] + 1;
        PetscSparseDenseMinusDot(sum,x,v,idx,n);
        x[i] = (1. - omega)*x[i] + sum*idiag[i]; /* omega in idiag */
      }
      xb   = t;
      PetscCall(PetscLogFlops(2.0*a->nz));
    } else xb = b;
    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
      for (i=m-1; i>=0; i--) {
        sum = xb[i];
        if (xb == b) {
          /* whole matrix (no checkpointing available) */
          n   = a->i[i+1] - a->i[i];
          idx = a->j + a->i[i];
          v   = aa + a->i[i];
          PetscSparseDenseMinusDot(sum,x,v,idx,n);
          x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
        } else { /* lower-triangular part has been saved, so only apply upper-triangular */
          n   = a->i[i+1] - diag[i] - 1;
          idx = a->j + diag[i] + 1;
          v   = aa + diag[i] + 1;
          PetscSparseDenseMinusDot(sum,x,v,idx,n);
          x[i] = (1. - omega)*x[i] + sum*idiag[i];  /* omega in idiag */
        }
      }
      if (xb == b) {
        PetscCall(PetscLogFlops(2.0*a->nz));
      } else {
        PetscCall(PetscLogFlops(a->nz)); /* assumes 1/2 in upper */
      }
    }
  }
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscCall(VecRestoreArray(xx,&x));
  PetscCall(VecRestoreArrayRead(bb,&b));
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
{
  Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  info->block_size   = 1.0;
  info->nz_allocated = a->maxnz;
  info->nz_used      = a->nz;
  info->nz_unneeded  = (a->maxnz - a->nz);
  info->assemblies   = A->num_ass;
  info->mallocs      = A->info.mallocs;
  info->memory       = ((PetscObject)A)->mem;
  if (A->factortype) {
    info->fill_ratio_given  = A->info.fill_ratio_given;
    info->fill_ratio_needed = A->info.fill_ratio_needed;
    info->factor_mallocs    = A->info.factor_mallocs;
  } else {
    info->fill_ratio_given  = 0;
    info->fill_ratio_needed = 0;
    info->factor_mallocs    = 0;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatZeroRows_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscInt          i,m = A->rmap->n - 1;
  const PetscScalar *xx;
  PetscScalar       *bb,*aa;
  PetscInt          d = 0;

  PetscFunctionBegin;
  if (x && b) {
    PetscCall(VecGetArrayRead(x,&xx));
    PetscCall(VecGetArray(b,&bb));
    for (i=0; i<N; i++) {
      PetscCheck(rows[i] >= 0 && rows[i] <= m,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %" PetscInt_FMT " out of range", rows[i]);
      if (rows[i] >= A->cmap->n) continue;
      bb[rows[i]] = diag*xx[rows[i]];
    }
    PetscCall(VecRestoreArrayRead(x,&xx));
    PetscCall(VecRestoreArray(b,&bb));
  }

  PetscCall(MatSeqAIJGetArray(A,&aa));
  if (a->keepnonzeropattern) {
    for (i=0; i<N; i++) {
      PetscCheck(rows[i] >= 0 && rows[i] <= m,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %" PetscInt_FMT " out of range", rows[i]);
      PetscCall(PetscArrayzero(&aa[a->i[rows[i]]],a->ilen[rows[i]]));
    }
    if (diag != 0.0) {
      for (i=0; i<N; i++) {
        d = rows[i];
        if (rows[i] >= A->cmap->n) continue;
        PetscCheck(a->diag[d] < a->i[d+1],PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in the zeroed row %" PetscInt_FMT,d);
      }
      for (i=0; i<N; i++) {
        if (rows[i] >= A->cmap->n) continue;
        aa[a->diag[rows[i]]] = diag;
      }
    }
  } else {
    if (diag != 0.0) {
      for (i=0; i<N; i++) {
        PetscCheck(rows[i] >= 0 && rows[i] <= m,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %" PetscInt_FMT " out of range", rows[i]);
        if (a->ilen[rows[i]] > 0) {
          if (rows[i] >= A->cmap->n) {
            a->ilen[rows[i]] = 0;
          } else {
            a->ilen[rows[i]]    = 1;
            aa[a->i[rows[i]]]   = diag;
            a->j[a->i[rows[i]]] = rows[i];
          }
        } else if (rows[i] < A->cmap->n) { /* in case row was completely empty */
          PetscCall(MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES));
        }
      }
    } else {
      for (i=0; i<N; i++) {
        PetscCheck(rows[i] >= 0 && rows[i] <= m,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %" PetscInt_FMT " out of range", rows[i]);
        a->ilen[rows[i]] = 0;
      }
    }
    A->nonzerostate++;
  }
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscCall((*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  PetscInt          i,j,m = A->rmap->n - 1,d = 0;
  PetscBool         missing,*zeroed,vecs = PETSC_FALSE;
  const PetscScalar *xx;
  PetscScalar       *bb,*aa;

  PetscFunctionBegin;
  if (!N) PetscFunctionReturn(0);
  PetscCall(MatSeqAIJGetArray(A,&aa));
  if (x && b) {
    PetscCall(VecGetArrayRead(x,&xx));
    PetscCall(VecGetArray(b,&bb));
    vecs = PETSC_TRUE;
  }
  PetscCall(PetscCalloc1(A->rmap->n,&zeroed));
  for (i=0; i<N; i++) {
    PetscCheck(rows[i] >= 0 && rows[i] <= m,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %" PetscInt_FMT " out of range", rows[i]);
    PetscCall(PetscArrayzero(&aa[a->i[rows[i]]],a->ilen[rows[i]]));

    zeroed[rows[i]] = PETSC_TRUE;
  }
  for (i=0; i<A->rmap->n; i++) {
    if (!zeroed[i]) {
      for (j=a->i[i]; j<a->i[i+1]; j++) {
        if (a->j[j] < A->rmap->n && zeroed[a->j[j]]) {
          if (vecs) bb[i] -= aa[j]*xx[a->j[j]];
          aa[j] = 0.0;
        }
      }
    } else if (vecs && i < A->cmap->N) bb[i] = diag*xx[i];
  }
  if (x && b) {
    PetscCall(VecRestoreArrayRead(x,&xx));
    PetscCall(VecRestoreArray(b,&bb));
  }
  PetscCall(PetscFree(zeroed));
  if (diag != 0.0) {
    PetscCall(MatMissingDiagonal_SeqAIJ(A,&missing,&d));
    if (missing) {
      for (i=0; i<N; i++) {
        if (rows[i] >= A->cmap->N) continue;
        PetscCheck(!a->nonew || rows[i] < d,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %" PetscInt_FMT " (%" PetscInt_FMT ")",d,rows[i]);
        PetscCall(MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES));
      }
    } else {
      for (i=0; i<N; i++) {
        aa[a->diag[rows[i]]] = diag;
      }
    }
  }
  PetscCall(MatSeqAIJRestoreArray(A,&aa));
  PetscCall((*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const PetscScalar *aa;
  PetscInt          *itmp;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArrayRead(A,&aa));
  *nz = a->i[row+1] - a->i[row];
  if (v) *v = (PetscScalar*)(aa + a->i[row]);
  if (idx) {
    itmp = a->j + a->i[row];
    if (*nz) *idx = itmp;
    else *idx = NULL;
  }
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscFunctionReturn(0);
}

PetscErrorCode MatRestoreRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
{
  PetscFunctionBegin;
  if (nz)  *nz = 0;
  if (idx) *idx = NULL;
  if (v)   *v = NULL;
  PetscFunctionReturn(0);
}

PetscErrorCode MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
{
  Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
  const MatScalar *v;
  PetscReal       sum = 0.0;
  PetscInt        i,j;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArrayRead(A,&v));
  if (type == NORM_FROBENIUS) {
#if defined(PETSC_USE_REAL___FP16)
    PetscBLASInt one = 1,nz = a->nz;
    PetscStackCallBLAS("BLASnrm2",*nrm = BLASnrm2_(&nz,v,&one));
#else
    for (i=0; i<a->nz; i++) {
      sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
    }
    *nrm = PetscSqrtReal(sum);
#endif
    PetscCall(PetscLogFlops(2.0*a->nz));
  } else if (type == NORM_1) {
    PetscReal *tmp;
    PetscInt  *jj = a->j;
    PetscCall(PetscCalloc1(A->cmap->n+1,&tmp));
    *nrm = 0.0;
    for (j=0; j<a->nz; j++) {
      tmp[*jj++] += PetscAbsScalar(*v);  v++;
    }
    for (j=0; j<A->cmap->n; j++) {
      if (tmp[j] > *nrm) *nrm = tmp[j];
    }
    PetscCall(PetscFree(tmp));
    PetscCall(PetscLogFlops(PetscMax(a->nz-1,0)));
  } else if (type == NORM_INFINITY) {
    *nrm = 0.0;
    for (j=0; j<A->rmap->n; j++) {
      const PetscScalar *v2 = v + a->i[j];
      sum = 0.0;
      for (i=0; i<a->i[j+1]-a->i[j]; i++) {
        sum += PetscAbsScalar(*v2); v2++;
      }
      if (sum > *nrm) *nrm = sum;
    }
    PetscCall(PetscLogFlops(PetscMax(a->nz-1,0)));
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for two norm");
  PetscCall(MatSeqAIJRestoreArrayRead(A,&v));
  PetscFunctionReturn(0);
}

/* Merged from MatGetSymbolicTranspose_SeqAIJ() - replace MatGetSymbolicTranspose_SeqAIJ()? */
PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat A,Mat *B)
{
  PetscInt       i,j,anzj;
  Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b;
  PetscInt       an=A->cmap->N,am=A->rmap->N;
  PetscInt       *ati,*atj,*atfill,*ai=a->i,*aj=a->j;

  PetscFunctionBegin;
  /* Allocate space for symbolic transpose info and work array */
  PetscCall(PetscCalloc1(an+1,&ati));
  PetscCall(PetscMalloc1(ai[am],&atj));
  PetscCall(PetscMalloc1(an,&atfill));

  /* Walk through aj and count ## of non-zeros in each row of A^T. */
  /* Note: offset by 1 for fast conversion into csr format. */
  for (i=0;i<ai[am];i++) ati[aj[i]+1] += 1;
  /* Form ati for csr format of A^T. */
  for (i=0;i<an;i++) ati[i+1] += ati[i];

  /* Copy ati into atfill so we have locations of the next free space in atj */
  PetscCall(PetscArraycpy(atfill,ati,an));

  /* Walk through A row-wise and mark nonzero entries of A^T. */
  for (i=0;i<am;i++) {
    anzj = ai[i+1] - ai[i];
    for (j=0;j<anzj;j++) {
      atj[atfill[*aj]] = i;
      atfill[*aj++]   += 1;
    }
  }

  /* Clean up temporary space and complete requests. */
  PetscCall(PetscFree(atfill));
  PetscCall(MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),an,am,ati,atj,NULL,B));
  PetscCall(MatSetBlockSizes(*B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs)));
  PetscCall(MatSetType(*B,((PetscObject)A)->type_name));

  b          = (Mat_SeqAIJ*)((*B)->data);
  b->free_a  = PETSC_FALSE;
  b->free_ij = PETSC_TRUE;
  b->nonew   = 0;
  PetscFunctionReturn(0);
}

PetscErrorCode  MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
{
  Mat_SeqAIJ      *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
  PetscInt        *adx,*bdx,*aii,*bii,*aptr,*bptr;
  const MatScalar *va,*vb;
  PetscInt        ma,na,mb,nb, i;

  PetscFunctionBegin;
  PetscCall(MatGetSize(A,&ma,&na));
  PetscCall(MatGetSize(B,&mb,&nb));
  if (ma!=nb || na!=mb) {
    *f = PETSC_FALSE;
    PetscFunctionReturn(0);
  }
  PetscCall(MatSeqAIJGetArrayRead(A,&va));
  PetscCall(MatSeqAIJGetArrayRead(B,&vb));
  aii  = aij->i; bii = bij->i;
  adx  = aij->j; bdx = bij->j;
  PetscCall(PetscMalloc1(ma,&aptr));
  PetscCall(PetscMalloc1(mb,&bptr));
  for (i=0; i<ma; i++) aptr[i] = aii[i];
  for (i=0; i<mb; i++) bptr[i] = bii[i];

  *f = PETSC_TRUE;
  for (i=0; i<ma; i++) {
    while (aptr[i]<aii[i+1]) {
      PetscInt    idc,idr;
      PetscScalar vc,vr;
      /* column/row index/value */
      idc = adx[aptr[i]];
      idr = bdx[bptr[idc]];
      vc  = va[aptr[i]];
      vr  = vb[bptr[idc]];
      if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
        *f = PETSC_FALSE;
        goto done;
      } else {
        aptr[i]++;
        if (B || i!=idc) bptr[idc]++;
      }
    }
  }
done:
  PetscCall(PetscFree(aptr));
  PetscCall(PetscFree(bptr));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&va));
  PetscCall(MatSeqAIJRestoreArrayRead(B,&vb));
  PetscFunctionReturn(0);
}

PetscErrorCode  MatIsHermitianTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
  PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
  MatScalar      *va,*vb;
  PetscInt       ma,na,mb,nb, i;

  PetscFunctionBegin;
  PetscCall(MatGetSize(A,&ma,&na));
  PetscCall(MatGetSize(B,&mb,&nb));
  if (ma!=nb || na!=mb) {
    *f = PETSC_FALSE;
    PetscFunctionReturn(0);
  }
  aii  = aij->i; bii = bij->i;
  adx  = aij->j; bdx = bij->j;
  va   = aij->a; vb = bij->a;
  PetscCall(PetscMalloc1(ma,&aptr));
  PetscCall(PetscMalloc1(mb,&bptr));
  for (i=0; i<ma; i++) aptr[i] = aii[i];
  for (i=0; i<mb; i++) bptr[i] = bii[i];

  *f = PETSC_TRUE;
  for (i=0; i<ma; i++) {
    while (aptr[i]<aii[i+1]) {
      PetscInt    idc,idr;
      PetscScalar vc,vr;
      /* column/row index/value */
      idc = adx[aptr[i]];
      idr = bdx[bptr[idc]];
      vc  = va[aptr[i]];
      vr  = vb[bptr[idc]];
      if (i!=idr || PetscAbsScalar(vc-PetscConj(vr)) > tol) {
        *f = PETSC_FALSE;
        goto done;
      } else {
        aptr[i]++;
        if (B || i!=idc) bptr[idc]++;
      }
    }
  }
done:
  PetscCall(PetscFree(aptr));
  PetscCall(PetscFree(bptr));
  PetscFunctionReturn(0);
}

PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
{
  PetscFunctionBegin;
  PetscCall(MatIsTranspose_SeqAIJ(A,A,tol,f));
  PetscFunctionReturn(0);
}

PetscErrorCode MatIsHermitian_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
{
  PetscFunctionBegin;
  PetscCall(MatIsHermitianTranspose_SeqAIJ(A,A,tol,f));
  PetscFunctionReturn(0);
}

PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const PetscScalar *l,*r;
  PetscScalar       x;
  MatScalar         *v;
  PetscInt          i,j,m = A->rmap->n,n = A->cmap->n,M,nz = a->nz;
  const PetscInt    *jj;

  PetscFunctionBegin;
  if (ll) {
    /* The local size is used so that VecMPI can be passed to this routine
       by MatDiagonalScale_MPIAIJ */
    PetscCall(VecGetLocalSize(ll,&m));
    PetscCheck(m == A->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
    PetscCall(VecGetArrayRead(ll,&l));
    PetscCall(MatSeqAIJGetArray(A,&v));
    for (i=0; i<m; i++) {
      x = l[i];
      M = a->i[i+1] - a->i[i];
      for (j=0; j<M; j++) (*v++) *= x;
    }
    PetscCall(VecRestoreArrayRead(ll,&l));
    PetscCall(PetscLogFlops(nz));
    PetscCall(MatSeqAIJRestoreArray(A,&v));
  }
  if (rr) {
    PetscCall(VecGetLocalSize(rr,&n));
    PetscCheck(n == A->cmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
    PetscCall(VecGetArrayRead(rr,&r));
    PetscCall(MatSeqAIJGetArray(A,&v));
    jj = a->j;
    for (i=0; i<nz; i++) (*v++) *= r[*jj++];
    PetscCall(MatSeqAIJRestoreArray(A,&v));
    PetscCall(VecRestoreArrayRead(rr,&r));
    PetscCall(PetscLogFlops(nz));
  }
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscFunctionReturn(0);
}

PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,PetscInt csize,MatReuse scall,Mat *B)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data,*c;
  PetscInt          *smap,i,k,kstart,kend,oldcols = A->cmap->n,*lens;
  PetscInt          row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
  const PetscInt    *irow,*icol;
  const PetscScalar *aa;
  PetscInt          nrows,ncols;
  PetscInt          *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
  MatScalar         *a_new,*mat_a;
  Mat               C;
  PetscBool         stride;

  PetscFunctionBegin;
  PetscCall(ISGetIndices(isrow,&irow));
  PetscCall(ISGetLocalSize(isrow,&nrows));
  PetscCall(ISGetLocalSize(iscol,&ncols));

  PetscCall(PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride));
  if (stride) {
    PetscCall(ISStrideGetInfo(iscol,&first,&step));
  } else {
    first = 0;
    step  = 0;
  }
  if (stride && step == 1) {
    /* special case of contiguous rows */
    PetscCall(PetscMalloc2(nrows,&lens,nrows,&starts));
    /* loop over new rows determining lens and starting points */
    for (i=0; i<nrows; i++) {
      kstart = ai[irow[i]];
      kend   = kstart + ailen[irow[i]];
      starts[i] = kstart;
      for (k=kstart; k<kend; k++) {
        if (aj[k] >= first) {
          starts[i] = k;
          break;
        }
      }
      sum = 0;
      while (k < kend) {
        if (aj[k++] >= first+ncols) break;
        sum++;
      }
      lens[i] = sum;
    }
    /* create submatrix */
    if (scall == MAT_REUSE_MATRIX) {
      PetscInt n_cols,n_rows;
      PetscCall(MatGetSize(*B,&n_rows,&n_cols));
      PetscCheck(n_rows == nrows && n_cols == ncols,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
      PetscCall(MatZeroEntries(*B));
      C    = *B;
    } else {
      PetscInt rbs,cbs;
      PetscCall(MatCreate(PetscObjectComm((PetscObject)A),&C));
      PetscCall(MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE));
      PetscCall(ISGetBlockSize(isrow,&rbs));
      PetscCall(ISGetBlockSize(iscol,&cbs));
      PetscCall(MatSetBlockSizes(C,rbs,cbs));
      PetscCall(MatSetType(C,((PetscObject)A)->type_name));
      PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens));
    }
    c = (Mat_SeqAIJ*)C->data;

    /* loop over rows inserting into submatrix */
    a_new = c->a;
    j_new = c->j;
    i_new = c->i;
    PetscCall(MatSeqAIJGetArrayRead(A,&aa));
    for (i=0; i<nrows; i++) {
      ii    = starts[i];
      lensi = lens[i];
      for (k=0; k<lensi; k++) {
        *j_new++ = aj[ii+k] - first;
      }
      PetscCall(PetscArraycpy(a_new,aa + starts[i],lensi));
      a_new     += lensi;
      i_new[i+1] = i_new[i] + lensi;
      c->ilen[i] = lensi;
    }
    PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
    PetscCall(PetscFree2(lens,starts));
  } else {
    PetscCall(ISGetIndices(iscol,&icol));
    PetscCall(PetscCalloc1(oldcols,&smap));
    PetscCall(PetscMalloc1(1+nrows,&lens));
    for (i=0; i<ncols; i++) {
      PetscCheck(icol[i] < oldcols,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Requesting column beyond largest column icol[%" PetscInt_FMT "] %" PetscInt_FMT " >= A->cmap->n %" PetscInt_FMT,i,icol[i],oldcols);
      smap[icol[i]] = i+1;
    }

    /* determine lens of each row */
    for (i=0; i<nrows; i++) {
      kstart  = ai[irow[i]];
      kend    = kstart + a->ilen[irow[i]];
      lens[i] = 0;
      for (k=kstart; k<kend; k++) {
        if (smap[aj[k]]) {
          lens[i]++;
        }
      }
    }
    /* Create and fill new matrix */
    if (scall == MAT_REUSE_MATRIX) {
      PetscBool equal;

      c = (Mat_SeqAIJ*)((*B)->data);
      PetscCheck((*B)->rmap->n  == nrows && (*B)->cmap->n == ncols,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
      PetscCall(PetscArraycmp(c->ilen,lens,(*B)->rmap->n,&equal));
      PetscCheck(equal,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
      PetscCall(PetscArrayzero(c->ilen,(*B)->rmap->n));
      C    = *B;
    } else {
      PetscInt rbs,cbs;
      PetscCall(MatCreate(PetscObjectComm((PetscObject)A),&C));
      PetscCall(MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE));
      PetscCall(ISGetBlockSize(isrow,&rbs));
      PetscCall(ISGetBlockSize(iscol,&cbs));
      PetscCall(MatSetBlockSizes(C,rbs,cbs));
      PetscCall(MatSetType(C,((PetscObject)A)->type_name));
      PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens));
    }
    PetscCall(MatSeqAIJGetArrayRead(A,&aa));
    c = (Mat_SeqAIJ*)(C->data);
    for (i=0; i<nrows; i++) {
      row      = irow[i];
      kstart   = ai[row];
      kend     = kstart + a->ilen[row];
      mat_i    = c->i[i];
      mat_j    = c->j + mat_i;
      mat_a    = c->a + mat_i;
      mat_ilen = c->ilen + i;
      for (k=kstart; k<kend; k++) {
        if ((tcol=smap[a->j[k]])) {
          *mat_j++ = tcol - 1;
          *mat_a++ = aa[k];
          (*mat_ilen)++;

        }
      }
    }
    PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
    /* Free work space */
    PetscCall(ISRestoreIndices(iscol,&icol));
    PetscCall(PetscFree(smap));
    PetscCall(PetscFree(lens));
    /* sort */
    for (i = 0; i < nrows; i++) {
      PetscInt ilen;

      mat_i = c->i[i];
      mat_j = c->j + mat_i;
      mat_a = c->a + mat_i;
      ilen  = c->ilen[i];
      PetscCall(PetscSortIntWithScalarArray(ilen,mat_j,mat_a));
    }
  }
#if defined(PETSC_HAVE_DEVICE)
  PetscCall(MatBindToCPU(C,A->boundtocpu));
#endif
  PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

  PetscCall(ISRestoreIndices(isrow,&irow));
  *B   = C;
  PetscFunctionReturn(0);
}

PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
{
  Mat            B;

  PetscFunctionBegin;
  if (scall == MAT_INITIAL_MATRIX) {
    PetscCall(MatCreate(subComm,&B));
    PetscCall(MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n));
    PetscCall(MatSetBlockSizesFromMats(B,mat,mat));
    PetscCall(MatSetType(B,MATSEQAIJ));
    PetscCall(MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE));
    *subMat = B;
  } else {
    PetscCall(MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
  Mat            outA;
  PetscBool      row_identity,col_identity;

  PetscFunctionBegin;
  PetscCheck(info->levels == 0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");

  PetscCall(ISIdentity(row,&row_identity));
  PetscCall(ISIdentity(col,&col_identity));

  outA             = inA;
  outA->factortype = MAT_FACTOR_LU;
  PetscCall(PetscFree(inA->solvertype));
  PetscCall(PetscStrallocpy(MATSOLVERPETSC,&inA->solvertype));

  PetscCall(PetscObjectReference((PetscObject)row));
  PetscCall(ISDestroy(&a->row));

  a->row = row;

  PetscCall(PetscObjectReference((PetscObject)col));
  PetscCall(ISDestroy(&a->col));

  a->col = col;

  /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
  PetscCall(ISDestroy(&a->icol));
  PetscCall(ISInvertPermutation(col,PETSC_DECIDE,&a->icol));
  PetscCall(PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol));

  if (!a->solve_work) { /* this matrix may have been factored before */
    PetscCall(PetscMalloc1(inA->rmap->n+1,&a->solve_work));
    PetscCall(PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar)));
  }

  PetscCall(MatMarkDiagonal_SeqAIJ(inA));
  if (row_identity && col_identity) {
    PetscCall(MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info));
  } else {
    PetscCall(MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
  PetscScalar    *v;
  PetscBLASInt   one = 1,bnz;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(inA,&v));
  PetscCall(PetscBLASIntCast(a->nz,&bnz));
  PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&alpha,v,&one));
  PetscCall(PetscLogFlops(a->nz));
  PetscCall(MatSeqAIJRestoreArray(inA,&v));
  PetscCall(MatSeqAIJInvalidateDiagonal(inA));
  PetscFunctionReturn(0);
}

PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
{
  PetscInt       i;

  PetscFunctionBegin;
  if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
    PetscCall(PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr));

    for (i=0; i<submatj->nrqr; ++i) {
      PetscCall(PetscFree(submatj->sbuf2[i]));
    }
    PetscCall(PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1));

    if (submatj->rbuf1) {
      PetscCall(PetscFree(submatj->rbuf1[0]));
      PetscCall(PetscFree(submatj->rbuf1));
    }

    for (i=0; i<submatj->nrqs; ++i) {
      PetscCall(PetscFree(submatj->rbuf3[i]));
    }
    PetscCall(PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3));
    PetscCall(PetscFree(submatj->pa));
  }

#if defined(PETSC_USE_CTABLE)
  PetscCall(PetscTableDestroy((PetscTable*)&submatj->rmap));
  if (submatj->cmap_loc) PetscCall(PetscFree(submatj->cmap_loc));
  PetscCall(PetscFree(submatj->rmap_loc));
#else
  PetscCall(PetscFree(submatj->rmap));
#endif

  if (!submatj->allcolumns) {
#if defined(PETSC_USE_CTABLE)
    PetscCall(PetscTableDestroy((PetscTable*)&submatj->cmap));
#else
    PetscCall(PetscFree(submatj->cmap));
#endif
  }
  PetscCall(PetscFree(submatj->row2proc));

  PetscCall(PetscFree(submatj));
  PetscFunctionReturn(0);
}

PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
{
  Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
  Mat_SubSppt    *submatj = c->submatis1;

  PetscFunctionBegin;
  PetscCall((*submatj->destroy)(C));
  PetscCall(MatDestroySubMatrix_Private(submatj));
  PetscFunctionReturn(0);
}

PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n,Mat *mat[])
{
  PetscInt       i;
  Mat            C;
  Mat_SeqAIJ     *c;
  Mat_SubSppt    *submatj;

  PetscFunctionBegin;
  for (i=0; i<n; i++) {
    C       = (*mat)[i];
    c       = (Mat_SeqAIJ*)C->data;
    submatj = c->submatis1;
    if (submatj) {
      if (--((PetscObject)C)->refct <= 0) {
        PetscCall((*submatj->destroy)(C));
        PetscCall(MatDestroySubMatrix_Private(submatj));
        PetscCall(PetscFree(C->defaultvectype));
        PetscCall(PetscLayoutDestroy(&C->rmap));
        PetscCall(PetscLayoutDestroy(&C->cmap));
        PetscCall(PetscHeaderDestroy(&C));
      }
    } else {
      PetscCall(MatDestroy(&C));
    }
  }

  /* Destroy Dummy submatrices created for reuse */
  PetscCall(MatDestroySubMatrices_Dummy(n,mat));

  PetscCall(PetscFree(*mat));
  PetscFunctionReturn(0);
}

PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
{
  PetscInt       i;

  PetscFunctionBegin;
  if (scall == MAT_INITIAL_MATRIX) {
    PetscCall(PetscCalloc1(n+1,B));
  }

  for (i=0; i<n; i++) {
    PetscCall(MatCreateSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
  const PetscInt *idx;
  PetscInt       start,end,*ai,*aj;
  PetscBT        table;

  PetscFunctionBegin;
  m  = A->rmap->n;
  ai = a->i;
  aj = a->j;

  PetscCheck(ov >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");

  PetscCall(PetscMalloc1(m+1,&nidx));
  PetscCall(PetscBTCreate(m,&table));

  for (i=0; i<is_max; i++) {
    /* Initialize the two local arrays */
    isz  = 0;
    PetscCall(PetscBTMemzero(m,table));

    /* Extract the indices, assume there can be duplicate entries */
    PetscCall(ISGetIndices(is[i],&idx));
    PetscCall(ISGetLocalSize(is[i],&n));

    /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
    for (j=0; j<n; ++j) {
      if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
    }
    PetscCall(ISRestoreIndices(is[i],&idx));
    PetscCall(ISDestroy(&is[i]));

    k = 0;
    for (j=0; j<ov; j++) { /* for each overlap */
      n = isz;
      for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
        row   = nidx[k];
        start = ai[row];
        end   = ai[row+1];
        for (l = start; l<end; l++) {
          val = aj[l];
          if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
        }
      }
    }
    PetscCall(ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i)));
  }
  PetscCall(PetscBTDestroy(&table));
  PetscCall(PetscFree(nidx));
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------- */
PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
  const PetscInt *row,*col;
  PetscInt       *cnew,j,*lens;
  IS             icolp,irowp;
  PetscInt       *cwork = NULL;
  PetscScalar    *vwork = NULL;

  PetscFunctionBegin;
  PetscCall(ISInvertPermutation(rowp,PETSC_DECIDE,&irowp));
  PetscCall(ISGetIndices(irowp,&row));
  PetscCall(ISInvertPermutation(colp,PETSC_DECIDE,&icolp));
  PetscCall(ISGetIndices(icolp,&col));

  /* determine lengths of permuted rows */
  PetscCall(PetscMalloc1(m+1,&lens));
  for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
  PetscCall(MatCreate(PetscObjectComm((PetscObject)A),B));
  PetscCall(MatSetSizes(*B,m,n,m,n));
  PetscCall(MatSetBlockSizesFromMats(*B,A,A));
  PetscCall(MatSetType(*B,((PetscObject)A)->type_name));
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens));
  PetscCall(PetscFree(lens));

  PetscCall(PetscMalloc1(n,&cnew));
  for (i=0; i<m; i++) {
    PetscCall(MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork));
    for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
    PetscCall(MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES));
    PetscCall(MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork));
  }
  PetscCall(PetscFree(cnew));

  (*B)->assembled = PETSC_FALSE;

#if defined(PETSC_HAVE_DEVICE)
  PetscCall(MatBindToCPU(*B,A->boundtocpu));
#endif
  PetscCall(MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY));
  PetscCall(ISRestoreIndices(irowp,&row));
  PetscCall(ISRestoreIndices(icolp,&col));
  PetscCall(ISDestroy(&irowp));
  PetscCall(ISDestroy(&icolp));
  if (rowp == colp) {
    PetscCall(MatPropagateSymmetryOptions(A,*B));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
{
  PetscFunctionBegin;
  /* If the two matrices have the same copy implementation, use fast copy. */
  if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
    Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
    Mat_SeqAIJ        *b = (Mat_SeqAIJ*)B->data;
    const PetscScalar *aa;

    PetscCall(MatSeqAIJGetArrayRead(A,&aa));
    PetscCheck(a->i[A->rmap->n] == b->i[B->rmap->n],PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Number of nonzeros in two matrices are different %" PetscInt_FMT " != %" PetscInt_FMT,a->i[A->rmap->n],b->i[B->rmap->n]);
    PetscCall(PetscArraycpy(b->a,aa,a->i[A->rmap->n]));
    PetscCall(PetscObjectStateIncrease((PetscObject)B));
    PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  } else {
    PetscCall(MatCopy_Basic(A,B,str));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetUp_SeqAIJ(Mat A)
{
  PetscFunctionBegin;
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,NULL));
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
{
  Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  *array = a->a;
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
{
  PetscFunctionBegin;
  *array = NULL;
  PetscFunctionReturn(0);
}

/*
   Computes the number of nonzeros per row needed for preallocation when X and Y
   have different nonzero structure.
*/
PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *yi,const PetscInt *yj,PetscInt *nnz)
{
  PetscInt       i,j,k,nzx,nzy;

  PetscFunctionBegin;
  /* Set the number of nonzeros in the new matrix */
  for (i=0; i<m; i++) {
    const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
    nzx = xi[i+1] - xi[i];
    nzy = yi[i+1] - yi[i];
    nnz[i] = 0;
    for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
      for (; k<nzy && yjj[k]<xjj[j]; k++) nnz[i]++; /* Catch up to X */
      if (k<nzy && yjj[k]==xjj[j]) k++;             /* Skip duplicate */
      nnz[i]++;
    }
    for (; k<nzy; k++) nnz[i]++;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
{
  PetscInt       m = Y->rmap->N;
  Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
  Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;

  PetscFunctionBegin;
  /* Set the number of nonzeros in the new matrix */
  PetscCall(MatAXPYGetPreallocation_SeqX_private(m,x->i,x->j,y->i,y->j,nnz));
  PetscFunctionReturn(0);
}

PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
{
  Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;

  PetscFunctionBegin;
  if (str == UNKNOWN_NONZERO_PATTERN || (PetscDefined(USE_DEBUG) && str == SAME_NONZERO_PATTERN)) {
    PetscBool e = x->nz == y->nz ? PETSC_TRUE : PETSC_FALSE;
    if (e) {
      PetscCall(PetscArraycmp(x->i,y->i,Y->rmap->n+1,&e));
      if (e) {
        PetscCall(PetscArraycmp(x->j,y->j,y->nz,&e));
        if (e) str = SAME_NONZERO_PATTERN;
      }
    }
    if (!e) PetscCheck(str != SAME_NONZERO_PATTERN,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"MatStructure is not SAME_NONZERO_PATTERN");
  }
  if (str == SAME_NONZERO_PATTERN) {
    const PetscScalar *xa;
    PetscScalar       *ya,alpha = a;
    PetscBLASInt      one = 1,bnz;

    PetscCall(PetscBLASIntCast(x->nz,&bnz));
    PetscCall(MatSeqAIJGetArray(Y,&ya));
    PetscCall(MatSeqAIJGetArrayRead(X,&xa));
    PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,xa,&one,ya,&one));
    PetscCall(MatSeqAIJRestoreArrayRead(X,&xa));
    PetscCall(MatSeqAIJRestoreArray(Y,&ya));
    PetscCall(PetscLogFlops(2.0*bnz));
    PetscCall(MatSeqAIJInvalidateDiagonal(Y));
    PetscCall(PetscObjectStateIncrease((PetscObject)Y));
  } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
    PetscCall(MatAXPY_Basic(Y,a,X,str));
  } else {
    Mat      B;
    PetscInt *nnz;
    PetscCall(PetscMalloc1(Y->rmap->N,&nnz));
    PetscCall(MatCreate(PetscObjectComm((PetscObject)Y),&B));
    PetscCall(PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name));
    PetscCall(MatSetLayouts(B,Y->rmap,Y->cmap));
    PetscCall(MatSetType(B,((PetscObject)Y)->type_name));
    PetscCall(MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz));
    PetscCall(MatSeqAIJSetPreallocation(B,0,nnz));
    PetscCall(MatAXPY_BasicWithPreallocation(B,Y,a,X,str));
    PetscCall(MatHeaderMerge(Y,&B));
    PetscCall(PetscFree(nnz));
  }
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat mat)
{
#if defined(PETSC_USE_COMPLEX)
  Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
  PetscInt     i,nz;
  PetscScalar *a;

  PetscFunctionBegin;
  nz = aij->nz;
  PetscCall(MatSeqAIJGetArray(mat,&a));
  for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
  PetscCall(MatSeqAIJRestoreArray(mat,&a));
#else
  PetscFunctionBegin;
#endif
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
{
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
  PetscInt        i,j,m = A->rmap->n,*ai,*aj,ncols,n;
  PetscReal       atmp;
  PetscScalar     *x;
  const MatScalar *aa,*av;

  PetscFunctionBegin;
  PetscCheck(!A->factortype,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscCall(MatSeqAIJGetArrayRead(A,&av));
  aa = av;
  ai = a->i;
  aj = a->j;

  PetscCall(VecSet(v,0.0));
  PetscCall(VecGetArrayWrite(v,&x));
  PetscCall(VecGetLocalSize(v,&n));
  PetscCheck(n == A->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
  for (i=0; i<m; i++) {
    ncols = ai[1] - ai[0]; ai++;
    for (j=0; j<ncols; j++) {
      atmp = PetscAbsScalar(*aa);
      if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
      aa++; aj++;
    }
  }
  PetscCall(VecRestoreArrayWrite(v,&x));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&av));
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
{
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
  PetscInt        i,j,m = A->rmap->n,*ai,*aj,ncols,n;
  PetscScalar     *x;
  const MatScalar *aa,*av;

  PetscFunctionBegin;
  PetscCheck(!A->factortype,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscCall(MatSeqAIJGetArrayRead(A,&av));
  aa = av;
  ai = a->i;
  aj = a->j;

  PetscCall(VecSet(v,0.0));
  PetscCall(VecGetArrayWrite(v,&x));
  PetscCall(VecGetLocalSize(v,&n));
  PetscCheck(n == A->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
  for (i=0; i<m; i++) {
    ncols = ai[1] - ai[0]; ai++;
    if (ncols == A->cmap->n) { /* row is dense */
      x[i] = *aa; if (idx) idx[i] = 0;
    } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
      x[i] = 0.0;
      if (idx) {
        for (j=0; j<ncols; j++) { /* find first implicit 0.0 in the row */
          if (aj[j] > j) {
            idx[i] = j;
            break;
          }
        }
        /* in case first implicit 0.0 in the row occurs at ncols-th column */
        if (j==ncols && j < A->cmap->n) idx[i] = j;
      }
    }
    for (j=0; j<ncols; j++) {
      if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
      aa++; aj++;
    }
  }
  PetscCall(VecRestoreArrayWrite(v,&x));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&av));
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
{
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
  PetscInt        i,j,m = A->rmap->n,*ai,*aj,ncols,n;
  PetscScalar     *x;
  const MatScalar *aa,*av;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArrayRead(A,&av));
  aa = av;
  ai = a->i;
  aj = a->j;

  PetscCall(VecSet(v,0.0));
  PetscCall(VecGetArrayWrite(v,&x));
  PetscCall(VecGetLocalSize(v,&n));
  PetscCheck(n == m,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector, %" PetscInt_FMT " vs. %" PetscInt_FMT " rows", m, n);
  for (i=0; i<m; i++) {
    ncols = ai[1] - ai[0]; ai++;
    if (ncols == A->cmap->n) { /* row is dense */
      x[i] = *aa; if (idx) idx[i] = 0;
    } else {  /* row is sparse so already KNOW minimum is 0.0 or higher */
      x[i] = 0.0;
      if (idx) {   /* find first implicit 0.0 in the row */
        for (j=0; j<ncols; j++) {
          if (aj[j] > j) {
            idx[i] = j;
            break;
          }
        }
        /* in case first implicit 0.0 in the row occurs at ncols-th column */
        if (j==ncols && j < A->cmap->n) idx[i] = j;
      }
    }
    for (j=0; j<ncols; j++) {
      if (PetscAbsScalar(x[i]) > PetscAbsScalar(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
      aa++; aj++;
    }
  }
  PetscCall(VecRestoreArrayWrite(v,&x));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&av));
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
{
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
  PetscInt        i,j,m = A->rmap->n,ncols,n;
  const PetscInt  *ai,*aj;
  PetscScalar     *x;
  const MatScalar *aa,*av;

  PetscFunctionBegin;
  PetscCheck(!A->factortype,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscCall(MatSeqAIJGetArrayRead(A,&av));
  aa = av;
  ai = a->i;
  aj = a->j;

  PetscCall(VecSet(v,0.0));
  PetscCall(VecGetArrayWrite(v,&x));
  PetscCall(VecGetLocalSize(v,&n));
  PetscCheck(n == m,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
  for (i=0; i<m; i++) {
    ncols = ai[1] - ai[0]; ai++;
    if (ncols == A->cmap->n) { /* row is dense */
      x[i] = *aa; if (idx) idx[i] = 0;
    } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
      x[i] = 0.0;
      if (idx) {   /* find first implicit 0.0 in the row */
        for (j=0; j<ncols; j++) {
          if (aj[j] > j) {
            idx[i] = j;
            break;
          }
        }
        /* in case first implicit 0.0 in the row occurs at ncols-th column */
        if (j==ncols && j < A->cmap->n) idx[i] = j;
      }
    }
    for (j=0; j<ncols; j++) {
      if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
      aa++; aj++;
    }
  }
  PetscCall(VecRestoreArrayWrite(v,&x));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&av));
  PetscFunctionReturn(0);
}

PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
{
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
  PetscInt        i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
  MatScalar       *diag,work[25],*v_work;
  const PetscReal shift = 0.0;
  PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;

  PetscFunctionBegin;
  allowzeropivot = PetscNot(A->erroriffailure);
  if (a->ibdiagvalid) {
    if (values) *values = a->ibdiag;
    PetscFunctionReturn(0);
  }
  PetscCall(MatMarkDiagonal_SeqAIJ(A));
  if (!a->ibdiag) {
    PetscCall(PetscMalloc1(bs2*mbs,&a->ibdiag));
    PetscCall(PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar)));
  }
  diag = a->ibdiag;
  if (values) *values = a->ibdiag;
  /* factor and invert each block */
  switch (bs) {
  case 1:
    for (i=0; i<mbs; i++) {
      PetscCall(MatGetValues(A,1,&i,1,&i,diag+i));
      if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
        if (allowzeropivot) {
          A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
          A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
          A->factorerror_zeropivot_row   = i;
          PetscCall(PetscInfo(A,"Zero pivot, row %" PetscInt_FMT " pivot %g tolerance %g\n",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON));
        } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %" PetscInt_FMT " pivot %g tolerance %g",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);
      }
      diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
    }
    break;
  case 2:
    for (i=0; i<mbs; i++) {
      ij[0] = 2*i; ij[1] = 2*i + 1;
      PetscCall(MatGetValues(A,2,ij,2,ij,diag));
      PetscCall(PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_2(diag));
      diag += 4;
    }
    break;
  case 3:
    for (i=0; i<mbs; i++) {
      ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
      PetscCall(MatGetValues(A,3,ij,3,ij,diag));
      PetscCall(PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_3(diag));
      diag += 9;
    }
    break;
  case 4:
    for (i=0; i<mbs; i++) {
      ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
      PetscCall(MatGetValues(A,4,ij,4,ij,diag));
      PetscCall(PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_4(diag));
      diag += 16;
    }
    break;
  case 5:
    for (i=0; i<mbs; i++) {
      ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
      PetscCall(MatGetValues(A,5,ij,5,ij,diag));
      PetscCall(PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_5(diag));
      diag += 25;
    }
    break;
  case 6:
    for (i=0; i<mbs; i++) {
      ij[0] = 6*i; ij[1] = 6*i + 1; ij[2] = 6*i + 2; ij[3] = 6*i + 3; ij[4] = 6*i + 4; ij[5] = 6*i + 5;
      PetscCall(MatGetValues(A,6,ij,6,ij,diag));
      PetscCall(PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_6(diag));
      diag += 36;
    }
    break;
  case 7:
    for (i=0; i<mbs; i++) {
      ij[0] = 7*i; ij[1] = 7*i + 1; ij[2] = 7*i + 2; ij[3] = 7*i + 3; ij[4] = 7*i + 4; ij[5] = 7*i + 5; ij[5] = 7*i + 6;
      PetscCall(MatGetValues(A,7,ij,7,ij,diag));
      PetscCall(PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_7(diag));
      diag += 49;
    }
    break;
  default:
    PetscCall(PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ));
    for (i=0; i<mbs; i++) {
      for (j=0; j<bs; j++) {
        IJ[j] = bs*i + j;
      }
      PetscCall(MatGetValues(A,bs,IJ,bs,IJ,diag));
      PetscCall(PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      PetscCall(PetscKernel_A_gets_transpose_A_N(diag,bs));
      diag += bs2;
    }
    PetscCall(PetscFree3(v_work,v_pivots,IJ));
  }
  a->ibdiagvalid = PETSC_TRUE;
  PetscFunctionReturn(0);
}

static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
  PetscScalar    a,*aa;
  PetscInt       m,n,i,j,col;

  PetscFunctionBegin;
  if (!x->assembled) {
    PetscCall(MatGetSize(x,&m,&n));
    for (i=0; i<m; i++) {
      for (j=0; j<aij->imax[i]; j++) {
        PetscCall(PetscRandomGetValue(rctx,&a));
        col  = (PetscInt)(n*PetscRealPart(a));
        PetscCall(MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES));
      }
    }
  } else {
    PetscCall(MatSeqAIJGetArrayWrite(x,&aa));
    for (i=0; i<aij->nz; i++) PetscCall(PetscRandomGetValue(rctx,aa+i));
    PetscCall(MatSeqAIJRestoreArrayWrite(x,&aa));
  }
  PetscCall(MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

/* Like MatSetRandom_SeqAIJ, but do not set values on columns in range of [low, high) */
PetscErrorCode  MatSetRandomSkipColumnRange_SeqAIJ_Private(Mat x,PetscInt low,PetscInt high,PetscRandom rctx)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
  PetscScalar    a;
  PetscInt       m,n,i,j,col,nskip;

  PetscFunctionBegin;
  nskip = high - low;
  PetscCall(MatGetSize(x,&m,&n));
  n    -= nskip; /* shrink number of columns where nonzeros can be set */
  for (i=0; i<m; i++) {
    for (j=0; j<aij->imax[i]; j++) {
      PetscCall(PetscRandomGetValue(rctx,&a));
      col  = (PetscInt)(n*PetscRealPart(a));
      if (col >= low) col += nskip; /* shift col rightward to skip the hole */
      PetscCall(MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES));
    }
  }
  PetscCall(MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------*/
static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
                                        MatGetRow_SeqAIJ,
                                        MatRestoreRow_SeqAIJ,
                                        MatMult_SeqAIJ,
                                /*  4*/ MatMultAdd_SeqAIJ,
                                        MatMultTranspose_SeqAIJ,
                                        MatMultTransposeAdd_SeqAIJ,
                                        NULL,
                                        NULL,
                                        NULL,
                                /* 10*/ NULL,
                                        MatLUFactor_SeqAIJ,
                                        NULL,
                                        MatSOR_SeqAIJ,
                                        MatTranspose_SeqAIJ,
                                /*1 5*/ MatGetInfo_SeqAIJ,
                                        MatEqual_SeqAIJ,
                                        MatGetDiagonal_SeqAIJ,
                                        MatDiagonalScale_SeqAIJ,
                                        MatNorm_SeqAIJ,
                                /* 20*/ NULL,
                                        MatAssemblyEnd_SeqAIJ,
                                        MatSetOption_SeqAIJ,
                                        MatZeroEntries_SeqAIJ,
                                /* 24*/ MatZeroRows_SeqAIJ,
                                        NULL,
                                        NULL,
                                        NULL,
                                        NULL,
                                /* 29*/ MatSetUp_SeqAIJ,
                                        NULL,
                                        NULL,
                                        NULL,
                                        NULL,
                                /* 34*/ MatDuplicate_SeqAIJ,
                                        NULL,
                                        NULL,
                                        MatILUFactor_SeqAIJ,
                                        NULL,
                                /* 39*/ MatAXPY_SeqAIJ,
                                        MatCreateSubMatrices_SeqAIJ,
                                        MatIncreaseOverlap_SeqAIJ,
                                        MatGetValues_SeqAIJ,
                                        MatCopy_SeqAIJ,
                                /* 44*/ MatGetRowMax_SeqAIJ,
                                        MatScale_SeqAIJ,
                                        MatShift_SeqAIJ,
                                        MatDiagonalSet_SeqAIJ,
                                        MatZeroRowsColumns_SeqAIJ,
                                /* 49*/ MatSetRandom_SeqAIJ,
                                        MatGetRowIJ_SeqAIJ,
                                        MatRestoreRowIJ_SeqAIJ,
                                        MatGetColumnIJ_SeqAIJ,
                                        MatRestoreColumnIJ_SeqAIJ,
                                /* 54*/ MatFDColoringCreate_SeqXAIJ,
                                        NULL,
                                        NULL,
                                        MatPermute_SeqAIJ,
                                        NULL,
                                /* 59*/ NULL,
                                        MatDestroy_SeqAIJ,
                                        MatView_SeqAIJ,
                                        NULL,
                                        NULL,
                                /* 64*/ NULL,
                                        MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
                                        NULL,
                                        NULL,
                                        NULL,
                                /* 69*/ MatGetRowMaxAbs_SeqAIJ,
                                        MatGetRowMinAbs_SeqAIJ,
                                        NULL,
                                        NULL,
                                        NULL,
                                /* 74*/ NULL,
                                        MatFDColoringApply_AIJ,
                                        NULL,
                                        NULL,
                                        NULL,
                                /* 79*/ MatFindZeroDiagonals_SeqAIJ,
                                        NULL,
                                        NULL,
                                        NULL,
                                        MatLoad_SeqAIJ,
                                /* 84*/ MatIsSymmetric_SeqAIJ,
                                        MatIsHermitian_SeqAIJ,
                                        NULL,
                                        NULL,
                                        NULL,
                                /* 89*/ NULL,
                                        NULL,
                                        MatMatMultNumeric_SeqAIJ_SeqAIJ,
                                        NULL,
                                        NULL,
                                /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
                                        NULL,
                                        NULL,
                                        MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
                                        NULL,
                                /* 99*/ MatProductSetFromOptions_SeqAIJ,
                                        NULL,
                                        NULL,
                                        MatConjugate_SeqAIJ,
                                        NULL,
                                /*104*/ MatSetValuesRow_SeqAIJ,
                                        MatRealPart_SeqAIJ,
                                        MatImaginaryPart_SeqAIJ,
                                        NULL,
                                        NULL,
                                /*109*/ MatMatSolve_SeqAIJ,
                                        NULL,
                                        MatGetRowMin_SeqAIJ,
                                        NULL,
                                        MatMissingDiagonal_SeqAIJ,
                                /*114*/ NULL,
                                        NULL,
                                        NULL,
                                        NULL,
                                        NULL,
                                /*119*/ NULL,
                                        NULL,
                                        NULL,
                                        NULL,
                                        MatGetMultiProcBlock_SeqAIJ,
                                /*124*/ MatFindNonzeroRows_SeqAIJ,
                                        MatGetColumnReductions_SeqAIJ,
                                        MatInvertBlockDiagonal_SeqAIJ,
                                        MatInvertVariableBlockDiagonal_SeqAIJ,
                                        NULL,
                                /*129*/ NULL,
                                        NULL,
                                        NULL,
                                        MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
                                        MatTransposeColoringCreate_SeqAIJ,
                                /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
                                        MatTransColoringApplyDenToSp_SeqAIJ,
                                        NULL,
                                        NULL,
                                        MatRARtNumeric_SeqAIJ_SeqAIJ,
                                 /*139*/NULL,
                                        NULL,
                                        NULL,
                                        MatFDColoringSetUp_SeqXAIJ,
                                        MatFindOffBlockDiagonalEntries_SeqAIJ,
                                        MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
                                 /*145*/MatDestroySubMatrices_SeqAIJ,
                                        NULL,
                                        NULL
};

PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
{
  Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
  PetscInt   i,nz,n;

  PetscFunctionBegin;
  nz = aij->maxnz;
  n  = mat->rmap->n;
  for (i=0; i<nz; i++) {
    aij->j[i] = indices[i];
  }
  aij->nz = nz;
  for (i=0; i<n; i++) {
    aij->ilen[i] = aij->imax[i];
  }
  PetscFunctionReturn(0);
}

/*
 * Given a sparse matrix with global column indices, compact it by using a local column space.
 * The result matrix helps saving memory in other algorithms, such as MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable()
 */
PetscErrorCode  MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat mat, ISLocalToGlobalMapping *mapping)
{
  Mat_SeqAIJ         *aij = (Mat_SeqAIJ*)mat->data;
  PetscTable         gid1_lid1;
  PetscTablePosition tpos;
  PetscInt           gid,lid,i,ec,nz = aij->nz;
  PetscInt           *garray,*jj = aij->j;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidPointer(mapping,2);
  /* use a table */
  PetscCall(PetscTableCreate(mat->rmap->n,mat->cmap->N+1,&gid1_lid1));
  ec = 0;
  for (i=0; i<nz; i++) {
    PetscInt data,gid1 = jj[i] + 1;
    PetscCall(PetscTableFind(gid1_lid1,gid1,&data));
    if (!data) {
      /* one based table */
      PetscCall(PetscTableAdd(gid1_lid1,gid1,++ec,INSERT_VALUES));
    }
  }
  /* form array of columns we need */
  PetscCall(PetscMalloc1(ec,&garray));
  PetscCall(PetscTableGetHeadPosition(gid1_lid1,&tpos));
  while (tpos) {
    PetscCall(PetscTableGetNext(gid1_lid1,&tpos,&gid,&lid));
    gid--;
    lid--;
    garray[lid] = gid;
  }
  PetscCall(PetscSortInt(ec,garray)); /* sort, and rebuild */
  PetscCall(PetscTableRemoveAll(gid1_lid1));
  for (i=0; i<ec; i++) {
    PetscCall(PetscTableAdd(gid1_lid1,garray[i]+1,i+1,INSERT_VALUES));
  }
  /* compact out the extra columns in B */
  for (i=0; i<nz; i++) {
    PetscInt gid1 = jj[i] + 1;
    PetscCall(PetscTableFind(gid1_lid1,gid1,&lid));
    lid--;
    jj[i] = lid;
  }
  PetscCall(PetscLayoutDestroy(&mat->cmap));
  PetscCall(PetscTableDestroy(&gid1_lid1));
  PetscCall(PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)mat),ec,ec,1,&mat->cmap));
  PetscCall(ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,mat->cmap->bs,mat->cmap->n,garray,PETSC_OWN_POINTER,mapping));
  PetscCall(ISLocalToGlobalMappingSetType(*mapping,ISLOCALTOGLOBALMAPPINGHASH));
  PetscFunctionReturn(0);
}

/*@
    MatSeqAIJSetColumnIndices - Set the column indices for all the rows
       in the matrix.

  Input Parameters:
+  mat - the SeqAIJ matrix
-  indices - the column indices

  Level: advanced

  Notes:
    This can be called if you have precomputed the nonzero structure of the
  matrix and want to provide it to the matrix object to improve the performance
  of the MatSetValues() operation.

    You MUST have set the correct numbers of nonzeros per row in the call to
  MatCreateSeqAIJ(), and the columns indices MUST be sorted.

    MUST be called before any calls to MatSetValues();

    The indices should start with zero, not one.

@*/
PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidIntPointer(indices,2);
  PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));
  PetscFunctionReturn(0);
}

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

PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
  size_t         nz = aij->i[mat->rmap->n];

  PetscFunctionBegin;
  PetscCheck(aij->nonew,PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");

  /* allocate space for values if not already there */
  if (!aij->saved_values) {
    PetscCall(PetscMalloc1(nz+1,&aij->saved_values));
    PetscCall(PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar)));
  }

  /* copy values over */
  PetscCall(PetscArraycpy(aij->saved_values,aij->a,nz));
  PetscFunctionReturn(0);
}

/*@
    MatStoreValues - Stashes a copy of the matrix values; this allows, for
       example, reuse of the linear part of a Jacobian, while recomputing the
       nonlinear portion.

   Collect on Mat

  Input Parameters:
.  mat - the matrix (currently only AIJ matrices support this option)

  Level: advanced

  Common Usage, with SNESSolve():
$    Create Jacobian matrix
$    Set linear terms into matrix
$    Apply boundary conditions to matrix, at this time matrix must have
$      final nonzero structure (i.e. setting the nonlinear terms and applying
$      boundary conditions again will not change the nonzero structure
$    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
$    ierr = MatStoreValues(mat);
$    Call SNESSetJacobian() with matrix
$    In your Jacobian routine
$      ierr = MatRetrieveValues(mat);
$      Set nonlinear terms in matrix

  Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
$    // build linear portion of Jacobian
$    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
$    ierr = MatStoreValues(mat);
$    loop over nonlinear iterations
$       ierr = MatRetrieveValues(mat);
$       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
$       // call MatAssemblyBegin/End() on matrix
$       Solve linear system with Jacobian
$    endloop

  Notes:
    Matrix must already be assemblied before calling this routine
    Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
    calling this routine.

    When this is called multiple times it overwrites the previous set of stored values
    and does not allocated additional space.

.seealso: `MatRetrieveValues()`

@*/
PetscErrorCode  MatStoreValues(Mat mat)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscCheck(mat->assembled,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  PetscCheck(!mat->factortype,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));
  PetscFunctionReturn(0);
}

PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
  PetscInt       nz = aij->i[mat->rmap->n];

  PetscFunctionBegin;
  PetscCheck(aij->nonew,PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
  PetscCheck(aij->saved_values,PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
  /* copy values over */
  PetscCall(PetscArraycpy(aij->a,aij->saved_values,nz));
  PetscFunctionReturn(0);
}

/*@
    MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
       example, reuse of the linear part of a Jacobian, while recomputing the
       nonlinear portion.

   Collect on Mat

  Input Parameters:
.  mat - the matrix (currently only AIJ matrices support this option)

  Level: advanced

.seealso: `MatStoreValues()`

@*/
PetscErrorCode  MatRetrieveValues(Mat mat)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscCheck(mat->assembled,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  PetscCheck(!mat->factortype,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));
  PetscFunctionReturn(0);
}

/* --------------------------------------------------------------------------------*/
/*@C
   MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
   (the default parallel PETSc format).  For good matrix assembly performance
   the user should preallocate the matrix storage by setting the parameter nz
   (or the array nnz).  By setting these parameters accurately, performance
   during matrix assembly can be increased by more than a factor of 50.

   Collective

   Input Parameters:
+  comm - MPI communicator, set to PETSC_COMM_SELF
.  m - number of rows
.  n - number of columns
.  nz - number of nonzeros per row (same for all rows)
-  nnz - array containing the number of nonzeros in the various rows
         (possibly different for each row) or NULL

   Output Parameter:
.  A - the matrix

   It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
   MatXXXXSetPreallocation() paradigm instead of this routine directly.
   [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]

   Notes:
   If nnz is given then nz is ignored

   The AIJ format (also called the Yale sparse matrix format or
   compressed row storage), is fully compatible with standard Fortran 77
   storage.  That is, the stored row and column indices can begin at
   either one (as in Fortran) or zero.  See the users' manual for details.

   Specify the preallocated storage with either nz or nnz (not both).
   Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
   allocation.  For large problems you MUST preallocate memory or you
   will get TERRIBLE performance, see the users' manual chapter on matrices.

   By default, this format uses inodes (identical nodes) when possible, to
   improve numerical efficiency of matrix-vector products and solves. We
   search for consecutive rows with the same nonzero structure, thereby
   reusing matrix information to achieve increased efficiency.

   Options Database Keys:
+  -mat_no_inode  - Do not use inodes
-  -mat_inode_limit <limit> - Sets inode limit (max limit=5)

   Level: intermediate

.seealso: `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`

@*/
PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
{
  PetscFunctionBegin;
  PetscCall(MatCreate(comm,A));
  PetscCall(MatSetSizes(*A,m,n,m,n));
  PetscCall(MatSetType(*A,MATSEQAIJ));
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz));
  PetscFunctionReturn(0);
}

/*@C
   MatSeqAIJSetPreallocation - For good matrix assembly performance
   the user should preallocate the matrix storage by setting the parameter nz
   (or the array nnz).  By setting these parameters accurately, performance
   during matrix assembly can be increased by more than a factor of 50.

   Collective

   Input Parameters:
+  B - The matrix
.  nz - number of nonzeros per row (same for all rows)
-  nnz - array containing the number of nonzeros in the various rows
         (possibly different for each row) or NULL

   Notes:
     If nnz is given then nz is ignored

    The AIJ format (also called the Yale sparse matrix format or
   compressed row storage), is fully compatible with standard Fortran 77
   storage.  That is, the stored row and column indices can begin at
   either one (as in Fortran) or zero.  See the users' manual for details.

   Specify the preallocated storage with either nz or nnz (not both).
   Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
   allocation.  For large problems you MUST preallocate memory or you
   will get TERRIBLE performance, see the users' manual chapter on matrices.

   You can call MatGetInfo() to get information on how effective the preallocation was;
   for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
   You can also run with the option -info and look for messages with the string
   malloc in them to see if additional memory allocation was needed.

   Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
   entries or columns indices

   By default, this format uses inodes (identical nodes) when possible, to
   improve numerical efficiency of matrix-vector products and solves. We
   search for consecutive rows with the same nonzero structure, thereby
   reusing matrix information to achieve increased efficiency.

   Options Database Keys:
+  -mat_no_inode  - Do not use inodes
-  -mat_inode_limit <limit> - Sets inode limit (max limit=5)

   Level: intermediate

.seealso: `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`, `MatGetInfo()`,
          `MatSeqAIJSetTotalPreallocation()`

@*/
PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(B,MAT_CLASSID,1);
  PetscValidType(B,1);
  PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));
  PetscFunctionReturn(0);
}

PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
{
  Mat_SeqAIJ     *b;
  PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
  PetscInt       i;

  PetscFunctionBegin;
  if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
  if (nz == MAT_SKIP_ALLOCATION) {
    skipallocation = PETSC_TRUE;
    nz             = 0;
  }
  PetscCall(PetscLayoutSetUp(B->rmap));
  PetscCall(PetscLayoutSetUp(B->cmap));

  if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
  PetscCheck(nz >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %" PetscInt_FMT,nz);
  if (PetscUnlikelyDebug(nnz)) {
    for (i=0; i<B->rmap->n; i++) {
      PetscCheck(nnz[i] >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be less than 0: local row %" PetscInt_FMT " value %" PetscInt_FMT,i,nnz[i]);
      PetscCheck(nnz[i] <= B->cmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be greater than row length: local row %" PetscInt_FMT " value %" PetscInt_FMT " rowlength %" PetscInt_FMT,i,nnz[i],B->cmap->n);
    }
  }

  B->preallocated = PETSC_TRUE;

  b = (Mat_SeqAIJ*)B->data;

  if (!skipallocation) {
    if (!b->imax) {
      PetscCall(PetscMalloc1(B->rmap->n,&b->imax));
      PetscCall(PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt)));
    }
    if (!b->ilen) {
      /* b->ilen will count nonzeros in each row so far. */
      PetscCall(PetscCalloc1(B->rmap->n,&b->ilen));
      PetscCall(PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt)));
    } else {
      PetscCall(PetscMemzero(b->ilen,B->rmap->n*sizeof(PetscInt)));
    }
    if (!b->ipre) {
      PetscCall(PetscMalloc1(B->rmap->n,&b->ipre));
      PetscCall(PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt)));
    }
    if (!nnz) {
      if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
      else if (nz < 0) nz = 1;
      nz = PetscMin(nz,B->cmap->n);
      for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
      nz = nz*B->rmap->n;
    } else {
      PetscInt64 nz64 = 0;
      for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz64 += nnz[i];}
      PetscCall(PetscIntCast(nz64,&nz));
    }

    /* allocate the matrix space */
    /* FIXME: should B's old memory be unlogged? */
    PetscCall(MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i));
    if (B->structure_only) {
      PetscCall(PetscMalloc1(nz,&b->j));
      PetscCall(PetscMalloc1(B->rmap->n+1,&b->i));
      PetscCall(PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*sizeof(PetscInt)));
    } else {
      PetscCall(PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i));
      PetscCall(PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt))));
    }
    b->i[0] = 0;
    for (i=1; i<B->rmap->n+1; i++) {
      b->i[i] = b->i[i-1] + b->imax[i-1];
    }
    if (B->structure_only) {
      b->singlemalloc = PETSC_FALSE;
      b->free_a       = PETSC_FALSE;
    } else {
      b->singlemalloc = PETSC_TRUE;
      b->free_a       = PETSC_TRUE;
    }
    b->free_ij      = PETSC_TRUE;
  } else {
    b->free_a  = PETSC_FALSE;
    b->free_ij = PETSC_FALSE;
  }

  if (b->ipre && nnz != b->ipre && b->imax) {
    /* reserve user-requested sparsity */
    PetscCall(PetscArraycpy(b->ipre,b->imax,B->rmap->n));
  }

  b->nz               = 0;
  b->maxnz            = nz;
  B->info.nz_unneeded = (double)b->maxnz;
  if (realalloc) {
    PetscCall(MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE));
  }
  B->was_assembled = PETSC_FALSE;
  B->assembled     = PETSC_FALSE;
  PetscFunctionReturn(0);
}

PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
{
  Mat_SeqAIJ     *a;
  PetscInt       i;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);

  /* Check local size. If zero, then return */
  if (!A->rmap->n) PetscFunctionReturn(0);

  a = (Mat_SeqAIJ*)A->data;
  /* if no saved info, we error out */
  PetscCheck(a->ipre,PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"No saved preallocation info ");

  PetscCheck(a->i && a->j && a->a && a->imax && a->ilen,PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"Memory info is incomplete, and can not reset preallocation ");

  PetscCall(PetscArraycpy(a->imax,a->ipre,A->rmap->n));
  PetscCall(PetscArrayzero(a->ilen,A->rmap->n));
  a->i[0] = 0;
  for (i=1; i<A->rmap->n+1; i++) {
    a->i[i] = a->i[i-1] + a->imax[i-1];
  }
  A->preallocated     = PETSC_TRUE;
  a->nz               = 0;
  a->maxnz            = a->i[A->rmap->n];
  A->info.nz_unneeded = (double)a->maxnz;
  A->was_assembled    = PETSC_FALSE;
  A->assembled        = PETSC_FALSE;
  PetscFunctionReturn(0);
}

/*@
   MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.

   Input Parameters:
+  B - the matrix
.  i - the indices into j for the start of each row (starts with zero)
.  j - the column indices for each row (starts with zero) these must be sorted for each row
-  v - optional values in the matrix

   Level: developer

   Notes:
      The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()

      This routine may be called multiple times with different nonzero patterns (or the same nonzero pattern). The nonzero
      structure will be the union of all the previous nonzero structures.

    Developer Notes:
      An optimization could be added to the implementation where it checks if the i, and j are identical to the current i and j and
      then just copies the v values directly with PetscMemcpy().

      This routine could also take a PetscCopyMode argument to allow sharing the values instead of always copying them.

.seealso: `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatSeqAIJSetPreallocation()`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MatResetPreallocation()`
@*/
PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(B,MAT_CLASSID,1);
  PetscValidType(B,1);
  PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));
  PetscFunctionReturn(0);
}

PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
{
  PetscInt       i;
  PetscInt       m,n;
  PetscInt       nz;
  PetscInt       *nnz;

  PetscFunctionBegin;
  PetscCheck(Ii[0] == 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %" PetscInt_FMT, Ii[0]);

  PetscCall(PetscLayoutSetUp(B->rmap));
  PetscCall(PetscLayoutSetUp(B->cmap));

  PetscCall(MatGetSize(B, &m, &n));
  PetscCall(PetscMalloc1(m+1, &nnz));
  for (i = 0; i < m; i++) {
    nz     = Ii[i+1]- Ii[i];
    PetscCheck(nz >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative number of columns %" PetscInt_FMT, i, nz);
    nnz[i] = nz;
  }
  PetscCall(MatSeqAIJSetPreallocation(B, 0, nnz));
  PetscCall(PetscFree(nnz));

  for (i = 0; i < m; i++) {
    PetscCall(MatSetValues_SeqAIJ(B, 1, &i, Ii[i+1] - Ii[i], J+Ii[i], v ? v + Ii[i] : NULL, INSERT_VALUES));
  }

  PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));

  PetscCall(MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
  PetscFunctionReturn(0);
}

/*@
   MatSeqAIJKron - Computes C, the Kronecker product of A and B.

   Input Parameters:
+  A - left-hand side matrix
.  B - right-hand side matrix
-  reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

   Output Parameter:
.  C - Kronecker product of A and B

   Level: intermediate

   Notes:
      MAT_REUSE_MATRIX can only be used when the nonzero structure of the product matrix has not changed from that last call to MatSeqAIJKron().

.seealso: `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATKAIJ`, `MatReuse`
@*/
PetscErrorCode MatSeqAIJKron(Mat A,Mat B,MatReuse reuse,Mat *C)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidType(B,2);
  PetscValidPointer(C,4);
  if (reuse == MAT_REUSE_MATRIX) {
    PetscValidHeaderSpecific(*C,MAT_CLASSID,4);
    PetscValidType(*C,4);
  }
  PetscTryMethod(A,"MatSeqAIJKron_C",(Mat,Mat,MatReuse,Mat*),(A,B,reuse,C));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSeqAIJKron_SeqAIJ(Mat A,Mat B,MatReuse reuse,Mat *C)
{
  Mat                newmat;
  Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJ         *b = (Mat_SeqAIJ*)B->data;
  PetscScalar        *v;
  const PetscScalar  *aa,*ba;
  PetscInt           *i,*j,m,n,p,q,nnz = 0,am = A->rmap->n,bm = B->rmap->n,an = A->cmap->n, bn = B->cmap->n;
  PetscBool          flg;

  PetscFunctionBegin;
  PetscCheck(!A->factortype,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscCheck(A->assembled,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  PetscCheck(!B->factortype,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscCheck(B->assembled,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  PetscCall(PetscObjectTypeCompare((PetscObject)B,MATSEQAIJ,&flg));
  PetscCheck(flg,PETSC_COMM_SELF,PETSC_ERR_SUP,"MatType %s",((PetscObject)B)->type_name);
  PetscCheck(reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX,PETSC_COMM_SELF,PETSC_ERR_SUP,"MatReuse %d",(int)reuse);
  if (reuse == MAT_INITIAL_MATRIX) {
    PetscCall(PetscMalloc2(am*bm+1,&i,a->i[am]*b->i[bm],&j));
    PetscCall(MatCreate(PETSC_COMM_SELF,&newmat));
    PetscCall(MatSetSizes(newmat,am*bm,an*bn,am*bm,an*bn));
    PetscCall(MatSetType(newmat,MATAIJ));
    i[0] = 0;
    for (m = 0; m < am; ++m) {
      for (p = 0; p < bm; ++p) {
        i[m*bm + p + 1] = i[m*bm + p] + (a->i[m+1] - a->i[m]) * (b->i[p+1] - b->i[p]);
        for (n = a->i[m]; n < a->i[m+1]; ++n) {
          for (q = b->i[p]; q < b->i[p+1]; ++q) {
            j[nnz++] = a->j[n]*bn + b->j[q];
          }
        }
      }
    }
    PetscCall(MatSeqAIJSetPreallocationCSR(newmat,i,j,NULL));
    *C = newmat;
    PetscCall(PetscFree2(i,j));
    nnz = 0;
  }
  PetscCall(MatSeqAIJGetArray(*C,&v));
  PetscCall(MatSeqAIJGetArrayRead(A,&aa));
  PetscCall(MatSeqAIJGetArrayRead(B,&ba));
  for (m = 0; m < am; ++m) {
    for (p = 0; p < bm; ++p) {
      for (n = a->i[m]; n < a->i[m+1]; ++n) {
        for (q = b->i[p]; q < b->i[p+1]; ++q) {
          v[nnz++] = aa[n] * ba[q];
        }
      }
    }
  }
  PetscCall(MatSeqAIJRestoreArray(*C,&v));
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscCall(MatSeqAIJRestoreArrayRead(B,&ba));
  PetscFunctionReturn(0);
}

#include <../src/mat/impls/dense/seq/dense.h>
#include <petsc/private/kernels/petscaxpy.h>

/*
    Computes (B'*A')' since computing B*A directly is untenable

               n                       p                          p
        [             ]       [             ]         [                 ]
      m [      A      ]  *  n [       B     ]   =   m [         C       ]
        [             ]       [             ]         [                 ]

*/
PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
{
  Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
  Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
  Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
  PetscInt          i,j,n,m,q,p;
  const PetscInt    *ii,*idx;
  const PetscScalar *b,*a,*a_q;
  PetscScalar       *c,*c_q;
  PetscInt          clda = sub_c->lda;
  PetscInt          alda = sub_a->lda;

  PetscFunctionBegin;
  m    = A->rmap->n;
  n    = A->cmap->n;
  p    = B->cmap->n;
  a    = sub_a->v;
  b    = sub_b->a;
  c    = sub_c->v;
  if (clda == m) {
    PetscCall(PetscArrayzero(c,m*p));
  } else {
    for (j=0;j<p;j++)
      for (i=0;i<m;i++)
        c[j*clda + i] = 0.0;
  }
  ii  = sub_b->i;
  idx = sub_b->j;
  for (i=0; i<n; i++) {
    q = ii[i+1] - ii[i];
    while (q-->0) {
      c_q = c + clda*(*idx);
      a_q = a + alda*i;
      PetscKernelAXPY(c_q,*b,a_q,m);
      idx++;
      b++;
    }
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat C)
{
  PetscInt       m=A->rmap->n,n=B->cmap->n;
  PetscBool      cisdense;

  PetscFunctionBegin;
  PetscCheck(A->cmap->n == B->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"A->cmap->n %" PetscInt_FMT " != B->rmap->n %" PetscInt_FMT,A->cmap->n,B->rmap->n);
  PetscCall(MatSetSizes(C,m,n,m,n));
  PetscCall(MatSetBlockSizesFromMats(C,A,B));
  PetscCall(PetscObjectTypeCompareAny((PetscObject)C,&cisdense,MATSEQDENSE,MATSEQDENSECUDA,""));
  if (!cisdense) {
    PetscCall(MatSetType(C,MATDENSE));
  }
  PetscCall(MatSetUp(C));

  C->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------*/
/*MC
   MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
   based on compressed sparse row format.

   Options Database Keys:
. -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()

   Level: beginner

   Notes:
    MatSetValues() may be called for this matrix type with a NULL argument for the numerical values,
    in this case the values associated with the rows and columns one passes in are set to zero
    in the matrix

    MatSetOptions(,MAT_STRUCTURE_ONLY,PETSC_TRUE) may be called for this matrix type. In this no
    space is allocated for the nonzero entries and any entries passed with MatSetValues() are ignored

  Developer Notes:
    It would be nice if all matrix formats supported passing NULL in for the numerical values

.seealso: `MatCreateSeqAIJ()`, `MatSetFromOptions()`, `MatSetType()`, `MatCreate()`, `MatType`, `MATSELL`, `MATSEQSELL`, `MATMPISELL`
M*/

/*MC
   MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.

   This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
   and MATMPIAIJ otherwise.  As a result, for single process communicators,
   MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
   for communicators controlling multiple processes.  It is recommended that you call both of
   the above preallocation routines for simplicity.

   Options Database Keys:
. -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()

  Developer Notes:
    Subclasses include MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
   enough exist.

  Level: beginner

.seealso: `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATMPIAIJ`, `MATSELL`, `MATSEQSELL`, `MATMPISELL`
M*/

/*MC
   MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.

   This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
   and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
   MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
   for communicators controlling multiple processes.  It is recommended that you call both of
   the above preallocation routines for simplicity.

   Options Database Keys:
. -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()

  Level: beginner

.seealso: `MatCreateMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`
M*/

PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
#if defined(PETSC_HAVE_ELEMENTAL)
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
#endif
#if defined(PETSC_HAVE_SCALAPACK)
PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat,MatType,MatReuse,Mat*);
#endif
#if defined(PETSC_HAVE_HYPRE)
PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A,MatType,MatReuse,Mat*);
#endif

PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat,MatType,MatReuse,Mat*);
PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);

/*@C
   MatSeqAIJGetArray - gives read/write access to the array where the data for a MATSEQAIJ matrix is stored

   Not Collective

   Input Parameter:
.  mat - a MATSEQAIJ matrix

   Output Parameter:
.   array - pointer to the data

   Level: intermediate

.seealso: `MatSeqAIJRestoreArray()`, `MatSeqAIJGetArrayF90()`
@*/
PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  if (aij->ops->getarray) {
    PetscCall((*aij->ops->getarray)(A,array));
  } else {
    *array = aij->a;
  }
  PetscFunctionReturn(0);
}

/*@C
   MatSeqAIJRestoreArray - returns access to the array where the data for a MATSEQAIJ matrix is stored obtained by MatSeqAIJGetArray()

   Not Collective

   Input Parameters:
+  mat - a MATSEQAIJ matrix
-  array - pointer to the data

   Level: intermediate

.seealso: `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArrayF90()`
@*/
PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  if (aij->ops->restorearray) {
    PetscCall((*aij->ops->restorearray)(A,array));
  } else {
    *array = NULL;
  }
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscCall(PetscObjectStateIncrease((PetscObject)A));
  PetscFunctionReturn(0);
}

/*@C
   MatSeqAIJGetArrayRead - gives read-only access to the array where the data for a MATSEQAIJ matrix is stored

   Not Collective

   Input Parameter:
.  mat - a MATSEQAIJ matrix

   Output Parameter:
.   array - pointer to the data

   Level: intermediate

.seealso: `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArrayRead()`
@*/
PetscErrorCode  MatSeqAIJGetArrayRead(Mat A,const PetscScalar **array)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  if (aij->ops->getarrayread) {
    PetscCall((*aij->ops->getarrayread)(A,array));
  } else {
    *array = aij->a;
  }
  PetscFunctionReturn(0);
}

/*@C
   MatSeqAIJRestoreArrayRead - restore the read-only access array obtained from MatSeqAIJGetArrayRead

   Not Collective

   Input Parameter:
.  mat - a MATSEQAIJ matrix

   Output Parameter:
.   array - pointer to the data

   Level: intermediate

.seealso: `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
@*/
PetscErrorCode  MatSeqAIJRestoreArrayRead(Mat A,const PetscScalar **array)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  if (aij->ops->restorearrayread) {
    PetscCall((*aij->ops->restorearrayread)(A,array));
  } else {
    *array = NULL;
  }
  PetscFunctionReturn(0);
}

/*@C
   MatSeqAIJGetArrayWrite - gives write-only access to the array where the data for a MATSEQAIJ matrix is stored

   Not Collective

   Input Parameter:
.  mat - a MATSEQAIJ matrix

   Output Parameter:
.   array - pointer to the data

   Level: intermediate

.seealso: `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArrayRead()`
@*/
PetscErrorCode  MatSeqAIJGetArrayWrite(Mat A,PetscScalar **array)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  if (aij->ops->getarraywrite) {
    PetscCall((*aij->ops->getarraywrite)(A,array));
  } else {
    *array = aij->a;
  }
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscCall(PetscObjectStateIncrease((PetscObject)A));
  PetscFunctionReturn(0);
}

/*@C
   MatSeqAIJRestoreArrayWrite - restore the read-only access array obtained from MatSeqAIJGetArrayRead

   Not Collective

   Input Parameter:
.  mat - a MATSEQAIJ matrix

   Output Parameter:
.   array - pointer to the data

   Level: intermediate

.seealso: `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
@*/
PetscErrorCode  MatSeqAIJRestoreArrayWrite(Mat A,PetscScalar **array)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  if (aij->ops->restorearraywrite) {
    PetscCall((*aij->ops->restorearraywrite)(A,array));
  } else {
    *array = NULL;
  }
  PetscFunctionReturn(0);
}

/*@C
   MatSeqAIJGetCSRAndMemType - Get the CSR arrays and the memory type of the SEQAIJ matrix

   Not Collective

   Input Parameter:
.  mat - a matrix of type MATSEQAIJ or its subclasses

   Output Parameters:
+  i - row map array of the matrix
.  j - column index array of the matrix
.  a - data array of the matrix
-  memtype - memory type of the arrays

  Notes:
   Any of the output parameters can be NULL, in which case the corresponding value is not returned.
   If mat is a device matrix, the arrays are on the device. Otherwise, they are on the host.

   One can call this routine on a preallocated but not assembled matrix to just get the memory of the CSR underneath the matrix.
   If the matrix is assembled, the data array 'a' is guaranteed to have the latest values of the matrix.

   Level: Developer

.seealso: `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
@*/
PetscErrorCode MatSeqAIJGetCSRAndMemType(Mat mat,const PetscInt **i,const PetscInt **j,PetscScalar **a,PetscMemType *mtype)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;

  PetscFunctionBegin;
  PetscCheck(mat->preallocated,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"matrix is not preallocated");
  if (aij->ops->getcsrandmemtype) {
    PetscCall((*aij->ops->getcsrandmemtype)(mat,i,j,a,mtype));
  } else {
    if (i) *i = aij->i;
    if (j) *j = aij->j;
    if (a) *a = aij->a;
    if (mtype) *mtype = PETSC_MEMTYPE_HOST;
  }
  PetscFunctionReturn(0);
}

/*@C
   MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row

   Not Collective

   Input Parameter:
.  mat - a MATSEQAIJ matrix

   Output Parameter:
.   nz - the maximum number of nonzeros in any row

   Level: intermediate

.seealso: `MatSeqAIJRestoreArray()`, `MatSeqAIJGetArrayF90()`
@*/
PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
{
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  *nz = aij->rmax;
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetPreallocationCOO_SeqAIJ(Mat mat, PetscCount coo_n, const PetscInt coo_i[], const PetscInt coo_j[])
{
  MPI_Comm                  comm;
  PetscInt                  *i,*j;
  PetscInt                  M,N,row;
  PetscCount                k,p,q,nneg,nnz,start,end; /* Index the coo array, so use PetscCount as their type */
  PetscInt                  *Ai; /* Change to PetscCount once we use it for row pointers */
  PetscInt                  *Aj;
  PetscScalar               *Aa;
  Mat_SeqAIJ                *seqaij = (Mat_SeqAIJ*)(mat->data);
  MatType                   rtype;
  PetscCount                *perm,*jmap;

  PetscFunctionBegin;
  PetscCall(MatResetPreallocationCOO_SeqAIJ(mat));
  PetscCall(PetscObjectGetComm((PetscObject)mat,&comm));
  PetscCall(MatGetSize(mat,&M,&N));
  PetscCall(PetscMalloc2(coo_n,&i,coo_n,&j));
  PetscCall(PetscArraycpy(i,coo_i,coo_n)); /* Make a copy since we'll modify it */
  PetscCall(PetscArraycpy(j,coo_j,coo_n));
  PetscCall(PetscMalloc1(coo_n,&perm));
  for (k=0; k<coo_n; k++) { /* Ignore entries with negative row or col indices */
    if (j[k] < 0) i[k] = -1;
    perm[k] = k;
  }

  /* Sort by row */
  PetscCall(PetscSortIntWithIntCountArrayPair(coo_n,i,j,perm));
  for (k=0; k<coo_n; k++) {if (i[k] >= 0) break;} /* Advance k to the first row with a non-negative index */
  nneg = k;
  PetscCall(PetscMalloc1(coo_n-nneg+1,&jmap)); /* +1 to make a CSR-like data structure. jmap[i] originally is the number of repeats for i-th nonzero */
  nnz  = 0; /* Total number of unique nonzeros to be counted */
  jmap++; /* Inc jmap by 1 for convinience */

  PetscCall(PetscCalloc1(M+1,&Ai)); /* CSR of A */
  PetscCall(PetscMalloc1(coo_n-nneg,&Aj)); /* We have at most coo_n-nneg unique nonzeros */

  /* In each row, sort by column, then unique column indices to get row length */
  Ai++; /* Inc by 1 for convinience */
  q = 0; /* q-th unique nonzero, with q starting from 0 */
  while (k<coo_n) {
    row   = i[k];
    start = k; /* [start,end) indices for this row */
    while (k<coo_n && i[k] == row) k++;
    end   = k;
    PetscCall(PetscSortIntWithCountArray(end-start,j+start,perm+start));
    /* Find number of unique col entries in this row */
    Aj[q]   = j[start]; /* Log the first nonzero in this row */
    jmap[q] = 1; /* Number of repeats of this nozero entry */
    Ai[row] = 1;
    nnz++;

    for (p=start+1; p<end; p++) { /* Scan remaining nonzero in this row */
      if (j[p] != j[p-1]) { /* Meet a new nonzero */
        q++;
        jmap[q] = 1;
        Aj[q]   = j[p];
        Ai[row]++;
        nnz++;
      } else {
        jmap[q]++;
      }
    }
    q++; /* Move to next row and thus next unique nonzero */
  }
  PetscCall(PetscFree2(i,j));

  Ai--; /* Back to the beginning of Ai[] */
  for (k=0; k<M; k++) Ai[k+1] += Ai[k];
  jmap--; /* Back to the beginning of jmap[] */
  jmap[0] = 0;
  for (k=0; k<nnz; k++) jmap[k+1] += jmap[k];
  if (nnz < coo_n-nneg) { /* Realloc with actual number of unique nonzeros */
    PetscCount *jmap_new;
    PetscInt   *Aj_new;

    PetscCall(PetscMalloc1(nnz+1,&jmap_new));
    PetscCall(PetscArraycpy(jmap_new,jmap,nnz+1));
    PetscCall(PetscFree(jmap));
    jmap = jmap_new;

    PetscCall(PetscMalloc1(nnz,&Aj_new));
    PetscCall(PetscArraycpy(Aj_new,Aj,nnz));
    PetscCall(PetscFree(Aj));
    Aj   = Aj_new;
  }

  if (nneg) { /* Discard heading entries with negative indices in perm[], as we'll access it from index 0 in MatSetValuesCOO */
    PetscCount *perm_new;

    PetscCall(PetscMalloc1(coo_n-nneg,&perm_new));
    PetscCall(PetscArraycpy(perm_new,perm+nneg,coo_n-nneg));
    PetscCall(PetscFree(perm));
    perm = perm_new;
  }

  PetscCall(MatGetRootType_Private(mat,&rtype));
  PetscCall(PetscCalloc1(nnz,&Aa)); /* Zero the matrix */
  PetscCall(MatSetSeqAIJWithArrays_private(PETSC_COMM_SELF,M,N,Ai,Aj,Aa,rtype,mat));

  seqaij->singlemalloc = PETSC_FALSE; /* Ai, Aj and Aa are not allocated in one big malloc */
  seqaij->free_a       = seqaij->free_ij = PETSC_TRUE; /* Let newmat own Ai, Aj and Aa */
  /* Record COO fields */
  seqaij->coo_n        = coo_n;
  seqaij->Atot         = coo_n-nneg; /* Annz is seqaij->nz, so no need to record that again */
  seqaij->jmap         = jmap; /* of length nnz+1 */
  seqaij->perm         = perm;
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSetValuesCOO_SeqAIJ(Mat A,const PetscScalar v[],InsertMode imode)
{
  Mat_SeqAIJ                  *aseq = (Mat_SeqAIJ*)A->data;
  PetscCount                  i,j,Annz = aseq->nz;
  PetscCount                  *perm = aseq->perm,*jmap = aseq->jmap;
  PetscScalar                 *Aa;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetArray(A,&Aa));
  for (i=0; i<Annz; i++) {
    PetscScalar sum = 0.0;
    for (j=jmap[i]; j<jmap[i+1]; j++) sum += v[perm[j]];
    Aa[i] = (imode == INSERT_VALUES? 0.0 : Aa[i]) + sum;
  }
  PetscCall(MatSeqAIJRestoreArray(A,&Aa));
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_CUDA)
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat,MatType,MatReuse,Mat*);
#endif
#if defined(PETSC_HAVE_KOKKOS_KERNELS)
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJKokkos(Mat,MatType,MatReuse,Mat*);
#endif

PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
{
  Mat_SeqAIJ     *b;
  PetscMPIInt    size;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B),&size));
  PetscCheck(size <= 1,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");

  PetscCall(PetscNewLog(B,&b));

  B->data = (void*)b;

  PetscCall(PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps)));
  if (B->sortedfull) B->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;

  b->row                = NULL;
  b->col                = NULL;
  b->icol               = NULL;
  b->reallocs           = 0;
  b->ignorezeroentries  = PETSC_FALSE;
  b->roworiented        = PETSC_TRUE;
  b->nonew              = 0;
  b->diag               = NULL;
  b->solve_work         = NULL;
  B->spptr              = NULL;
  b->saved_values       = NULL;
  b->idiag              = NULL;
  b->mdiag              = NULL;
  b->ssor_work          = NULL;
  b->omega              = 1.0;
  b->fshift             = 0.0;
  b->idiagvalid         = PETSC_FALSE;
  b->ibdiagvalid        = PETSC_FALSE;
  b->keepnonzeropattern = PETSC_FALSE;

  PetscCall(PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ));

#if defined(PETSC_HAVE_MATLAB_ENGINE)
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ));
#endif

  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijsell_C",MatConvert_SeqAIJ_SeqAIJSELL));
#if defined(PETSC_HAVE_MKL_SPARSE)
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijmkl_C",MatConvert_SeqAIJ_SeqAIJMKL));
#endif
#if defined(PETSC_HAVE_CUDA)
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcusparse_C",MatConvert_SeqAIJ_SeqAIJCUSPARSE));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqaijcusparse_seqaij_C",MatProductSetFromOptions_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqaij_seqaijcusparse_C",MatProductSetFromOptions_SeqAIJ));
#endif
#if defined(PETSC_HAVE_KOKKOS_KERNELS)
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijkokkos_C",MatConvert_SeqAIJ_SeqAIJKokkos));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL));
#if defined(PETSC_HAVE_ELEMENTAL)
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_elemental_C",MatConvert_SeqAIJ_Elemental));
#endif
#if defined(PETSC_HAVE_SCALAPACK)
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_scalapack_C",MatConvert_AIJ_ScaLAPACK));
#endif
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_hypre_C",MatConvert_AIJ_HYPRE));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_transpose_seqaij_seqaij_C",MatProductSetFromOptions_Transpose_AIJ_AIJ));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqdense_C",MatConvert_SeqAIJ_SeqDense));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsell_C",MatConvert_SeqAIJ_SeqSELL));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_is_C",MatConvert_XAIJ_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_is_seqaij_C",MatProductSetFromOptions_IS_XAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqdense_seqaij_C",MatProductSetFromOptions_SeqDense_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqaij_seqaij_C",MatProductSetFromOptions_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJKron_C",MatSeqAIJKron_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatSetPreallocationCOO_C",MatSetPreallocationCOO_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatSetValuesCOO_C",MatSetValuesCOO_SeqAIJ));
  PetscCall(MatCreate_SeqAIJ_Inode(B));
  PetscCall(PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ));
  PetscCall(MatSeqAIJSetTypeFromOptions(B));  /* this allows changing the matrix subtype to say MATSEQAIJPERM */
  PetscFunctionReturn(0);
}

/*
    Given a matrix generated with MatGetFactor() duplicates all the information in A into B
*/
PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
{
  Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data,*a = (Mat_SeqAIJ*)A->data;
  PetscInt       m = A->rmap->n,i;

  PetscFunctionBegin;
  PetscCheck(A->assembled || cpvalues == MAT_DO_NOT_COPY_VALUES,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot duplicate unassembled matrix");

  C->factortype = A->factortype;
  c->row        = NULL;
  c->col        = NULL;
  c->icol       = NULL;
  c->reallocs   = 0;

  C->assembled    = A->assembled;
  C->preallocated = A->preallocated;

  if (A->preallocated) {
    PetscCall(PetscLayoutReference(A->rmap,&C->rmap));
    PetscCall(PetscLayoutReference(A->cmap,&C->cmap));

    PetscCall(PetscMalloc1(m,&c->imax));
    PetscCall(PetscMemcpy(c->imax,a->imax,m*sizeof(PetscInt)));
    PetscCall(PetscMalloc1(m,&c->ilen));
    PetscCall(PetscMemcpy(c->ilen,a->ilen,m*sizeof(PetscInt)));
    PetscCall(PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt)));

    /* allocate the matrix space */
    if (mallocmatspace) {
      PetscCall(PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i));
      PetscCall(PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt)));

      c->singlemalloc = PETSC_TRUE;

      PetscCall(PetscArraycpy(c->i,a->i,m+1));
      if (m > 0) {
        PetscCall(PetscArraycpy(c->j,a->j,a->i[m]));
        if (cpvalues == MAT_COPY_VALUES) {
          const PetscScalar *aa;

          PetscCall(MatSeqAIJGetArrayRead(A,&aa));
          PetscCall(PetscArraycpy(c->a,aa,a->i[m]));
          PetscCall(MatSeqAIJGetArrayRead(A,&aa));
        } else {
          PetscCall(PetscArrayzero(c->a,a->i[m]));
        }
      }
    }

    c->ignorezeroentries = a->ignorezeroentries;
    c->roworiented       = a->roworiented;
    c->nonew             = a->nonew;
    if (a->diag) {
      PetscCall(PetscMalloc1(m+1,&c->diag));
      PetscCall(PetscMemcpy(c->diag,a->diag,m*sizeof(PetscInt)));
      PetscCall(PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt)));
    } else c->diag = NULL;

    c->solve_work         = NULL;
    c->saved_values       = NULL;
    c->idiag              = NULL;
    c->ssor_work          = NULL;
    c->keepnonzeropattern = a->keepnonzeropattern;
    c->free_a             = PETSC_TRUE;
    c->free_ij            = PETSC_TRUE;

    c->rmax         = a->rmax;
    c->nz           = a->nz;
    c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */

    c->compressedrow.use   = a->compressedrow.use;
    c->compressedrow.nrows = a->compressedrow.nrows;
    if (a->compressedrow.use) {
      i    = a->compressedrow.nrows;
      PetscCall(PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex));
      PetscCall(PetscArraycpy(c->compressedrow.i,a->compressedrow.i,i+1));
      PetscCall(PetscArraycpy(c->compressedrow.rindex,a->compressedrow.rindex,i));
    } else {
      c->compressedrow.use    = PETSC_FALSE;
      c->compressedrow.i      = NULL;
      c->compressedrow.rindex = NULL;
    }
    c->nonzerorowcnt = a->nonzerorowcnt;
    C->nonzerostate  = A->nonzerostate;

    PetscCall(MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C));
  }
  PetscCall(PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist));
  PetscFunctionReturn(0);
}

PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
{
  PetscFunctionBegin;
  PetscCall(MatCreate(PetscObjectComm((PetscObject)A),B));
  PetscCall(MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n));
  if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
    PetscCall(MatSetBlockSizesFromMats(*B,A,A));
  }
  PetscCall(MatSetType(*B,((PetscObject)A)->type_name));
  PetscCall(MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE));
  PetscFunctionReturn(0);
}

PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
{
  PetscBool      isbinary, ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
  /* force binary viewer to load .info file if it has not yet done so */
  PetscCall(PetscViewerSetUp(viewer));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5));
  if (isbinary) {
    PetscCall(MatLoad_SeqAIJ_Binary(newMat,viewer));
  } else if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(MatLoad_AIJ_HDF5(newMat,viewer));
#else
    SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else {
    SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"Viewer type %s not yet supported for reading %s matrices",((PetscObject)viewer)->type_name,((PetscObject)newMat)->type_name);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatLoad_SeqAIJ_Binary(Mat mat, PetscViewer viewer)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)mat->data;
  PetscInt       header[4],*rowlens,M,N,nz,sum,rows,cols,i;

  PetscFunctionBegin;
  PetscCall(PetscViewerSetUp(viewer));

  /* read in matrix header */
  PetscCall(PetscViewerBinaryRead(viewer,header,4,NULL,PETSC_INT));
  PetscCheck(header[0] == MAT_FILE_CLASSID,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Not a matrix object in file");
  M = header[1]; N = header[2]; nz = header[3];
  PetscCheck(M >= 0,PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix row size (%" PetscInt_FMT ") in file is negative",M);
  PetscCheck(N >= 0,PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix column size (%" PetscInt_FMT ") in file is negative",N);
  PetscCheck(nz >= 0,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk, cannot load as SeqAIJ");

  /* set block sizes from the viewer's .info file */
  PetscCall(MatLoad_Binary_BlockSizes(mat,viewer));
  /* set local and global sizes if not set already */
  if (mat->rmap->n < 0) mat->rmap->n = M;
  if (mat->cmap->n < 0) mat->cmap->n = N;
  if (mat->rmap->N < 0) mat->rmap->N = M;
  if (mat->cmap->N < 0) mat->cmap->N = N;
  PetscCall(PetscLayoutSetUp(mat->rmap));
  PetscCall(PetscLayoutSetUp(mat->cmap));

  /* check if the matrix sizes are correct */
  PetscCall(MatGetSize(mat,&rows,&cols));
  PetscCheck(M == rows && N == cols,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different sizes (%" PetscInt_FMT ", %" PetscInt_FMT ") than the input matrix (%" PetscInt_FMT ", %" PetscInt_FMT ")",M,N,rows,cols);

  /* read in row lengths */
  PetscCall(PetscMalloc1(M,&rowlens));
  PetscCall(PetscViewerBinaryRead(viewer,rowlens,M,NULL,PETSC_INT));
  /* check if sum(rowlens) is same as nz */
  sum = 0; for (i=0; i<M; i++) sum += rowlens[i];
  PetscCheck(sum == nz,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent matrix data in file: nonzeros = %" PetscInt_FMT ", sum-row-lengths = %" PetscInt_FMT,nz,sum);
  /* preallocate and check sizes */
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(mat,0,rowlens));
  PetscCall(MatGetSize(mat,&rows,&cols));
  PetscCheck(M == rows && N == cols,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different length (%" PetscInt_FMT ", %" PetscInt_FMT ") than the input matrix (%" PetscInt_FMT ", %" PetscInt_FMT ")",M,N,rows,cols);
  /* store row lengths */
  PetscCall(PetscArraycpy(a->ilen,rowlens,M));
  PetscCall(PetscFree(rowlens));

  /* fill in "i" row pointers */
  a->i[0] = 0; for (i=0; i<M; i++) a->i[i+1] = a->i[i] + a->ilen[i];
  /* read in "j" column indices */
  PetscCall(PetscViewerBinaryRead(viewer,a->j,nz,NULL,PETSC_INT));
  /* read in "a" nonzero values */
  PetscCall(PetscViewerBinaryRead(viewer,a->a,nz,NULL,PETSC_SCALAR));

  PetscCall(MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
  const PetscScalar *aa,*ba;
#if defined(PETSC_USE_COMPLEX)
  PetscInt k;
#endif

  PetscFunctionBegin;
  /* If the  matrix dimensions are not equal,or no of nonzeros */
  if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
    *flg = PETSC_FALSE;
    PetscFunctionReturn(0);
  }

  /* if the a->i are the same */
  PetscCall(PetscArraycmp(a->i,b->i,A->rmap->n+1,flg));
  if (!*flg) PetscFunctionReturn(0);

  /* if a->j are the same */
  PetscCall(PetscArraycmp(a->j,b->j,a->nz,flg));
  if (!*flg) PetscFunctionReturn(0);

  PetscCall(MatSeqAIJGetArrayRead(A,&aa));
  PetscCall(MatSeqAIJGetArrayRead(B,&ba));
  /* if a->a are the same */
#if defined(PETSC_USE_COMPLEX)
  for (k=0; k<a->nz; k++) {
    if (PetscRealPart(aa[k]) != PetscRealPart(ba[k]) || PetscImaginaryPart(aa[k]) != PetscImaginaryPart(ba[k])) {
      *flg = PETSC_FALSE;
      PetscFunctionReturn(0);
    }
  }
#else
  PetscCall(PetscArraycmp(aa,ba,a->nz,flg));
#endif
  PetscCall(MatSeqAIJRestoreArrayRead(A,&aa));
  PetscCall(MatSeqAIJRestoreArrayRead(B,&ba));
  PetscFunctionReturn(0);
}

/*@
     MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
              provided by the user.

      Collective

   Input Parameters:
+   comm - must be an MPI communicator of size 1
.   m - number of rows
.   n - number of columns
.   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
.   j - column indices
-   a - matrix values

   Output Parameter:
.   mat - the matrix

   Level: intermediate

   Notes:
       The i, j, and a arrays are not copied by this routine, the user must free these arrays
    once the matrix is destroyed and not before

       You cannot set new nonzero locations into this matrix, that will generate an error.

       The i and j indices are 0 based

       The format which is used for the sparse matrix input, is equivalent to a
    row-major ordering.. i.e for the following matrix, the input data expected is
    as shown

$        1 0 0
$        2 0 3
$        4 5 6
$
$        i =  {0,1,3,6}  [size = nrow+1  = 3+1]
$        j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
$        v =  {1,2,3,4,5,6}  [size = 6]

.seealso: `MatCreate()`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MatCreateMPIAIJWithArrays()`, `MatMPIAIJSetPreallocationCSR()`

@*/
PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat)
{
  PetscInt       ii;
  Mat_SeqAIJ     *aij;
  PetscInt jj;

  PetscFunctionBegin;
  PetscCheck(m <= 0 || i[0] == 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
  PetscCall(MatCreate(comm,mat));
  PetscCall(MatSetSizes(*mat,m,n,m,n));
  /* PetscCall(MatSetBlockSizes(*mat,,)); */
  PetscCall(MatSetType(*mat,MATSEQAIJ));
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,NULL));
  aij  = (Mat_SeqAIJ*)(*mat)->data;
  PetscCall(PetscMalloc1(m,&aij->imax));
  PetscCall(PetscMalloc1(m,&aij->ilen));

  aij->i            = i;
  aij->j            = j;
  aij->a            = a;
  aij->singlemalloc = PETSC_FALSE;
  aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
  aij->free_a       = PETSC_FALSE;
  aij->free_ij      = PETSC_FALSE;

  for (ii=0,aij->nonzerorowcnt=0,aij->rmax=0; ii<m; ii++) {
    aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
    if (PetscDefined(USE_DEBUG)) {
      PetscCheck(i[ii+1] - i[ii] >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row length in i (row indices) row = %" PetscInt_FMT " length = %" PetscInt_FMT,ii,i[ii+1] - i[ii]);
      for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
        PetscCheck(j[jj] >= j[jj-1],PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %" PetscInt_FMT " (actual column %" PetscInt_FMT ") in row %" PetscInt_FMT " is not sorted",jj-i[ii],j[jj],ii);
        PetscCheck(j[jj] != j[jj-1],PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %" PetscInt_FMT " (actual column %" PetscInt_FMT ") in row %" PetscInt_FMT " is identical to previous entry",jj-i[ii],j[jj],ii);
      }
    }
  }
  if (PetscDefined(USE_DEBUG)) {
    for (ii=0; ii<aij->i[m]; ii++) {
      PetscCheck(j[ii] >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %" PetscInt_FMT " index = %" PetscInt_FMT,ii,j[ii]);
      PetscCheck(j[ii] <= n - 1,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column index to large at location = %" PetscInt_FMT " index = %" PetscInt_FMT,ii,j[ii]);
    }
  }

  PetscCall(MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

/*@
     MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
              provided by the user.

      Collective

   Input Parameters:
+   comm - must be an MPI communicator of size 1
.   m   - number of rows
.   n   - number of columns
.   i   - row indices
.   j   - column indices
.   a   - matrix values
.   nz  - number of nonzeros
-   idx - if the i and j indices start with 1 use PETSC_TRUE otherwise use PETSC_FALSE

   Output Parameter:
.   mat - the matrix

   Level: intermediate

   Example:
       For the following matrix, the input data expected is as shown (using 0 based indexing)
.vb
        1 0 0
        2 0 3
        4 5 6

        i =  {0,1,1,2,2,2}
        j =  {0,0,2,0,1,2}
        v =  {1,2,3,4,5,6}
.ve

.seealso: `MatCreate()`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MatCreateSeqAIJWithArrays()`, `MatMPIAIJSetPreallocationCSR()`, `MatSetValuesCOO()`

@*/
PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat,PetscInt nz,PetscBool idx)
{
  PetscInt       ii, *nnz, one = 1,row,col;

  PetscFunctionBegin;
  PetscCall(PetscCalloc1(m,&nnz));
  for (ii = 0; ii < nz; ii++) {
    nnz[i[ii] - !!idx] += 1;
  }
  PetscCall(MatCreate(comm,mat));
  PetscCall(MatSetSizes(*mat,m,n,m,n));
  PetscCall(MatSetType(*mat,MATSEQAIJ));
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz));
  for (ii = 0; ii < nz; ii++) {
    if (idx) {
      row = i[ii] - 1;
      col = j[ii] - 1;
    } else {
      row = i[ii];
      col = j[ii];
    }
    PetscCall(MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES));
  }
  PetscCall(MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY));
  PetscCall(PetscFree(nnz));
  PetscFunctionReturn(0);
}

PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
{
  Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;

  PetscFunctionBegin;
  a->idiagvalid  = PETSC_FALSE;
  a->ibdiagvalid = PETSC_FALSE;

  PetscCall(MatSeqAIJInvalidateDiagonal_Inode(A));
  PetscFunctionReturn(0);
}

PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
{
  PetscMPIInt    size;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(comm,&size));
  if (size == 1) {
    if (scall == MAT_INITIAL_MATRIX) {
      PetscCall(MatDuplicate(inmat,MAT_COPY_VALUES,outmat));
    } else {
      PetscCall(MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN));
    }
  } else {
    PetscCall(MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm,inmat,n,scall,outmat));
  }
  PetscFunctionReturn(0);
}

/*
 Permute A into C's *local* index space using rowemb,colemb.
 The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
 of [0,m), colemb is in [0,n).
 If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
 */
PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C,IS rowemb,IS colemb,MatStructure pattern,Mat B)
{
  /* If making this function public, change the error returned in this function away from _PLIB. */
  Mat_SeqAIJ     *Baij;
  PetscBool      seqaij;
  PetscInt       m,n,*nz,i,j,count;
  PetscScalar    v;
  const PetscInt *rowindices,*colindices;

  PetscFunctionBegin;
  if (!B) PetscFunctionReturn(0);
  /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij));
  PetscCheck(seqaij,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is of wrong type");
  if (rowemb) {
    PetscCall(ISGetLocalSize(rowemb,&m));
    PetscCheck(m == B->rmap->n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Row IS of size %" PetscInt_FMT " is incompatible with matrix row size %" PetscInt_FMT,m,B->rmap->n);
  } else {
    PetscCheck(C->rmap->n == B->rmap->n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is row-incompatible with the target matrix");
  }
  if (colemb) {
    PetscCall(ISGetLocalSize(colemb,&n));
    PetscCheck(n == B->cmap->n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag col IS of size %" PetscInt_FMT " is incompatible with input matrix col size %" PetscInt_FMT,n,B->cmap->n);
  } else {
    PetscCheck(C->cmap->n == B->cmap->n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is col-incompatible with the target matrix");
  }

  Baij = (Mat_SeqAIJ*)(B->data);
  if (pattern == DIFFERENT_NONZERO_PATTERN) {
    PetscCall(PetscMalloc1(B->rmap->n,&nz));
    for (i=0; i<B->rmap->n; i++) {
      nz[i] = Baij->i[i+1] - Baij->i[i];
    }
    PetscCall(MatSeqAIJSetPreallocation(C,0,nz));
    PetscCall(PetscFree(nz));
  }
  if (pattern == SUBSET_NONZERO_PATTERN) {
    PetscCall(MatZeroEntries(C));
  }
  count = 0;
  rowindices = NULL;
  colindices = NULL;
  if (rowemb) {
    PetscCall(ISGetIndices(rowemb,&rowindices));
  }
  if (colemb) {
    PetscCall(ISGetIndices(colemb,&colindices));
  }
  for (i=0; i<B->rmap->n; i++) {
    PetscInt row;
    row = i;
    if (rowindices) row = rowindices[i];
    for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
      PetscInt col;
      col  = Baij->j[count];
      if (colindices) col = colindices[col];
      v    = Baij->a[count];
      PetscCall(MatSetValues(C,1,&row,1,&col,&v,INSERT_VALUES));
      ++count;
    }
  }
  /* FIXME: set C's nonzerostate correctly. */
  /* Assembly for C is necessary. */
  C->preallocated = PETSC_TRUE;
  C->assembled     = PETSC_TRUE;
  C->was_assembled = PETSC_FALSE;
  PetscFunctionReturn(0);
}

PetscFunctionList MatSeqAIJList = NULL;

/*@C
   MatSeqAIJSetType - Converts a MATSEQAIJ matrix to a subtype

   Collective on Mat

   Input Parameters:
+  mat      - the matrix object
-  matype   - matrix type

   Options Database Key:
.  -mat_seqai_type  <method> - for example seqaijcrl

  Level: intermediate

.seealso: `PCSetType()`, `VecSetType()`, `MatCreate()`, `MatType`, `Mat`
@*/
PetscErrorCode  MatSeqAIJSetType(Mat mat, MatType matype)
{
  PetscBool      sametype;
  PetscErrorCode (*r)(Mat,MatType,MatReuse,Mat*);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscCall(PetscObjectTypeCompare((PetscObject)mat,matype,&sametype));
  if (sametype) PetscFunctionReturn(0);

  PetscCall(PetscFunctionListFind(MatSeqAIJList,matype,&r));
  PetscCheck(r,PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown Mat type given: %s",matype);
  PetscCall((*r)(mat,matype,MAT_INPLACE_MATRIX,&mat));
  PetscFunctionReturn(0);
}

/*@C
  MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential AIJ matrices

   Not Collective

   Input Parameters:
+  name - name of a new user-defined matrix type, for example MATSEQAIJCRL
-  function - routine to convert to subtype

   Notes:
   MatSeqAIJRegister() may be called multiple times to add several user-defined solvers.

   Then, your matrix can be chosen with the procedural interface at runtime via the option
$     -mat_seqaij_type my_mat

   Level: advanced

.seealso: `MatSeqAIJRegisterAll()`

  Level: advanced
@*/
PetscErrorCode  MatSeqAIJRegister(const char sname[],PetscErrorCode (*function)(Mat,MatType,MatReuse,Mat *))
{
  PetscFunctionBegin;
  PetscCall(MatInitializePackage());
  PetscCall(PetscFunctionListAdd(&MatSeqAIJList,sname,function));
  PetscFunctionReturn(0);
}

PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;

/*@C
  MatSeqAIJRegisterAll - Registers all of the matrix subtypes of SeqAIJ

  Not Collective

  Level: advanced

.seealso: `MatRegisterAll()`, `MatSeqAIJRegister()`
@*/
PetscErrorCode  MatSeqAIJRegisterAll(void)
{
  PetscFunctionBegin;
  if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(0);
  MatSeqAIJRegisterAllCalled = PETSC_TRUE;

  PetscCall(MatSeqAIJRegister(MATSEQAIJCRL,      MatConvert_SeqAIJ_SeqAIJCRL));
  PetscCall(MatSeqAIJRegister(MATSEQAIJPERM,     MatConvert_SeqAIJ_SeqAIJPERM));
  PetscCall(MatSeqAIJRegister(MATSEQAIJSELL,     MatConvert_SeqAIJ_SeqAIJSELL));
#if defined(PETSC_HAVE_MKL_SPARSE)
  PetscCall(MatSeqAIJRegister(MATSEQAIJMKL,      MatConvert_SeqAIJ_SeqAIJMKL));
#endif
#if defined(PETSC_HAVE_CUDA)
  PetscCall(MatSeqAIJRegister(MATSEQAIJCUSPARSE, MatConvert_SeqAIJ_SeqAIJCUSPARSE));
#endif
#if defined(PETSC_HAVE_KOKKOS_KERNELS)
  PetscCall(MatSeqAIJRegister(MATSEQAIJKOKKOS,   MatConvert_SeqAIJ_SeqAIJKokkos));
#endif
#if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
  PetscCall(MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL));
#endif
  PetscFunctionReturn(0);
}

/*
    Special version for direct calls from Fortran
*/
#include <petsc/private/fortranimpl.h>
#if defined(PETSC_HAVE_FORTRAN_CAPS)
#define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
#elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
#define matsetvaluesseqaij_ matsetvaluesseqaij
#endif

/* Change these macros so can be used in void function */

/* Change these macros so can be used in void function */
/* Identical to PetscCallVoid, except it assigns to *_ierr */
#undef  PetscCall
#define PetscCall(...) do {                                                                    \
    PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__;                                              \
    if (PetscUnlikely(ierr_msv_mpiaij)) {                                                      \
      *_ierr = PetscError(PETSC_COMM_SELF,__LINE__,PETSC_FUNCTION_NAME,__FILE__,ierr_msv_mpiaij,PETSC_ERROR_REPEAT," "); \
      return;                                                                                  \
    }                                                                                          \
  } while (0)

#undef SETERRQ
#define SETERRQ(comm,ierr,...) do {                                                            \
    *_ierr = PetscError(comm,__LINE__,PETSC_FUNCTION_NAME,__FILE__,ierr,PETSC_ERROR_INITIAL,__VA_ARGS__); \
    return;                                                                                    \
  } while (0)

PETSC_EXTERN void matsetvaluesseqaij_(Mat *AA,PetscInt *mm,const PetscInt im[],PetscInt *nn,const PetscInt in[],const PetscScalar v[],InsertMode *isis, PetscErrorCode *_ierr)
{
  Mat            A  = *AA;
  PetscInt       m  = *mm, n = *nn;
  InsertMode     is = *isis;
  Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
  PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
  PetscInt       *imax,*ai,*ailen;
  PetscInt       *aj,nonew = a->nonew,lastcol = -1;
  MatScalar      *ap,value,*aa;
  PetscBool      ignorezeroentries = a->ignorezeroentries;
  PetscBool      roworiented       = a->roworiented;

  PetscFunctionBegin;
  MatCheckPreallocated(A,1);
  imax  = a->imax;
  ai    = a->i;
  ailen = a->ilen;
  aj    = a->j;
  aa    = a->a;

  for (k=0; k<m; k++) { /* loop over added rows */
    row = im[k];
    if (row < 0) continue;
    PetscCheck(row < A->rmap->n,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
    rp   = aj + ai[row]; ap = aa + ai[row];
    rmax = imax[row]; nrow = ailen[row];
    low  = 0;
    high = nrow;
    for (l=0; l<n; l++) { /* loop over added columns */
      if (in[l] < 0) continue;
      PetscCheck(in[l] < A->cmap->n,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
      col = in[l];
      if (roworiented) value = v[l + k*n];
      else value = v[k + l*m];

      if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;

      if (col <= lastcol) low = 0;
      else high = nrow;
      lastcol = col;
      while (high-low > 5) {
        t = (low+high)/2;
        if (rp[t] > col) high = t;
        else             low  = t;
      }
      for (i=low; i<high; i++) {
        if (rp[i] > col) break;
        if (rp[i] == col) {
          if (is == ADD_VALUES) ap[i] += value;
          else                  ap[i] = value;
          goto noinsert;
        }
      }
      if (value == 0.0 && ignorezeroentries) goto noinsert;
      if (nonew == 1) goto noinsert;
      PetscCheck(nonew != -1,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
      MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
      N = nrow++ - 1; a->nz++; high++;
      /* shift up all the later entries in this row */
      for (ii=N; ii>=i; ii--) {
        rp[ii+1] = rp[ii];
        ap[ii+1] = ap[ii];
      }
      rp[i] = col;
      ap[i] = value;
      A->nonzerostate++;
noinsert:;
      low = i + 1;
    }
    ailen[row] = nrow;
  }
  PetscFunctionReturnVoid();
}
/* Undefining these here since they were redefined from their original definition above! No
 * other PETSc functions should be defined past this point, as it is impossible to recover the
 * original definitions */
#undef PetscCall
#undef SETERRQ