xref: /petsc/src/mat/impls/baij/mpi/mpibaij.c (revision e91c04dfc8a52dee1965211bb1cc8e5bf775178f)

#include <../src/mat/impls/baij/mpi/mpibaij.h> /*I  "petscmat.h"  I*/

#include <petsc/private/hashseti.h>
#include <petscblaslapack.h>
#include <petscsf.h>

static PetscErrorCode MatDestroy_MPIBAIJ(Mat mat)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;

  PetscFunctionBegin;
  PetscCall(PetscLogObjectState((PetscObject)mat, "Rows=%" PetscInt_FMT ",Cols=%" PetscInt_FMT, mat->rmap->N, mat->cmap->N));
  PetscCall(MatStashDestroy_Private(&mat->stash));
  PetscCall(MatStashDestroy_Private(&mat->bstash));
  PetscCall(MatDestroy(&baij->A));
  PetscCall(MatDestroy(&baij->B));
#if defined(PETSC_USE_CTABLE)
  PetscCall(PetscHMapIDestroy(&baij->colmap));
#else
  PetscCall(PetscFree(baij->colmap));
#endif
  PetscCall(PetscFree(baij->garray));
  PetscCall(VecDestroy(&baij->lvec));
  PetscCall(VecScatterDestroy(&baij->Mvctx));
  PetscCall(PetscFree2(baij->rowvalues, baij->rowindices));
  PetscCall(PetscFree(baij->barray));
  PetscCall(PetscFree2(baij->hd, baij->ht));
  PetscCall(PetscFree(baij->rangebs));
  PetscCall(PetscFree(mat->data));

  PetscCall(PetscObjectChangeTypeName((PetscObject)mat, NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatStoreValues_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatRetrieveValues_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIBAIJSetPreallocation_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIBAIJSetPreallocationCSR_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDiagonalScaleLocal_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetHashTableFactor_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpibaij_mpisbaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpibaij_mpiadj_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpibaij_mpiaij_C", NULL));
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpibaij_hypre_C", NULL));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpibaij_is_C", NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* defines MatSetValues_MPI_Hash(), MatAssemblyBegin_MPI_Hash(), and  MatAssemblyEnd_MPI_Hash() */
#define TYPE BAIJ
#include "../src/mat/impls/aij/mpi/mpihashmat.h"
#undef TYPE

#if defined(PETSC_HAVE_HYPRE)
PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat, MatType, MatReuse, Mat *);
#endif

static PetscErrorCode MatGetRowMaxAbs_MPIBAIJ(Mat A, Vec v, PetscInt idx[])
{
  Mat_MPIBAIJ       *a = (Mat_MPIBAIJ *)A->data;
  PetscInt           i, *idxb = NULL, m = A->rmap->n, bs = A->cmap->bs;
  PetscScalar       *va, *vv;
  Vec                vB, vA;
  const PetscScalar *vb;

  PetscFunctionBegin;
  PetscCall(MatCreateVecs(a->A, NULL, &vA));
  PetscCall(MatGetRowMaxAbs(a->A, vA, idx));

  PetscCall(VecGetArrayWrite(vA, &va));
  if (idx) {
    for (i = 0; i < m; i++) {
      if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
    }
  }

  PetscCall(MatCreateVecs(a->B, NULL, &vB));
  PetscCall(PetscMalloc1(m, &idxb));
  PetscCall(MatGetRowMaxAbs(a->B, vB, idxb));

  PetscCall(VecGetArrayWrite(v, &vv));
  PetscCall(VecGetArrayRead(vB, &vb));
  for (i = 0; i < m; i++) {
    if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
      vv[i] = vb[i];
      if (idx) idx[i] = bs * a->garray[idxb[i] / bs] + (idxb[i] % bs);
    } else {
      vv[i] = va[i];
      if (idx && PetscAbsScalar(va[i]) == PetscAbsScalar(vb[i]) && idxb[i] != -1 && idx[i] > bs * a->garray[idxb[i] / bs] + (idxb[i] % bs)) idx[i] = bs * a->garray[idxb[i] / bs] + (idxb[i] % bs);
    }
  }
  PetscCall(VecRestoreArrayWrite(vA, &vv));
  PetscCall(VecRestoreArrayWrite(vA, &va));
  PetscCall(VecRestoreArrayRead(vB, &vb));
  PetscCall(PetscFree(idxb));
  PetscCall(VecDestroy(&vA));
  PetscCall(VecDestroy(&vB));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetRowSumAbs_MPIBAIJ(Mat A, Vec v)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;
  Vec          vB, vA;

  PetscFunctionBegin;
  PetscCall(MatCreateVecs(a->A, NULL, &vA));
  PetscCall(MatGetRowSumAbs(a->A, vA));
  PetscCall(MatCreateVecs(a->B, NULL, &vB));
  PetscCall(MatGetRowSumAbs(a->B, vB));
  PetscCall(VecAXPY(vA, 1.0, vB));
  PetscCall(VecDestroy(&vB));
  PetscCall(VecCopy(vA, v));
  PetscCall(VecDestroy(&vA));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatStoreValues_MPIBAIJ(Mat mat)
{
  Mat_MPIBAIJ *aij = (Mat_MPIBAIJ *)mat->data;

  PetscFunctionBegin;
  PetscCall(MatStoreValues(aij->A));
  PetscCall(MatStoreValues(aij->B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatRetrieveValues_MPIBAIJ(Mat mat)
{
  Mat_MPIBAIJ *aij = (Mat_MPIBAIJ *)mat->data;

  PetscFunctionBegin;
  PetscCall(MatRetrieveValues(aij->A));
  PetscCall(MatRetrieveValues(aij->B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
     Local utility routine that creates a mapping from the global column
   number to the local number in the off-diagonal part of the local
   storage of the matrix.  This is done in a non scalable way since the
   length of colmap equals the global matrix length.
*/
PetscErrorCode MatCreateColmap_MPIBAIJ_Private(Mat mat)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  Mat_SeqBAIJ *B    = (Mat_SeqBAIJ *)baij->B->data;
  PetscInt     nbs = B->nbs, i, bs = mat->rmap->bs;

  PetscFunctionBegin;
#if defined(PETSC_USE_CTABLE)
  PetscCall(PetscHMapICreateWithSize(baij->nbs, &baij->colmap));
  for (i = 0; i < nbs; i++) PetscCall(PetscHMapISet(baij->colmap, baij->garray[i] + 1, i * bs + 1));
#else
  PetscCall(PetscCalloc1(baij->Nbs + 1, &baij->colmap));
  for (i = 0; i < nbs; i++) baij->colmap[baij->garray[i]] = i * bs + 1;
#endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

#define MatSetValues_SeqBAIJ_A_Private(row, col, value, addv, orow, ocol) \
  do { \
    brow = row / bs; \
    rp   = PetscSafePointerPlusOffset(aj, ai[brow]); \
    ap   = PetscSafePointerPlusOffset(aa, bs2 * ai[brow]); \
    rmax = aimax[brow]; \
    nrow = ailen[brow]; \
    bcol = col / bs; \
    ridx = row % bs; \
    cidx = col % bs; \
    low  = 0; \
    high = nrow; \
    while (high - low > 3) { \
      t = (low + high) / 2; \
      if (rp[t] > bcol) high = t; \
      else low = t; \
    } \
    for (_i = low; _i < high; _i++) { \
      if (rp[_i] > bcol) break; \
      if (rp[_i] == bcol) { \
        bap = ap + bs2 * _i + bs * cidx + ridx; \
        if (addv == ADD_VALUES) *bap += value; \
        else *bap = value; \
        goto a_noinsert; \
      } \
    } \
    if (a->nonew == 1) goto a_noinsert; \
    PetscCheck(a->nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", orow, ocol); \
    MatSeqXAIJReallocateAIJ(A, a->mbs, bs2, nrow, brow, bcol, rmax, aa, ai, aj, rp, ap, aimax, a->nonew, MatScalar); \
    N = nrow++ - 1; \
    /* shift up all the later entries in this row */ \
    PetscCall(PetscArraymove(rp + _i + 1, rp + _i, N - _i + 1)); \
    PetscCall(PetscArraymove(ap + bs2 * (_i + 1), ap + bs2 * _i, bs2 * (N - _i + 1))); \
    PetscCall(PetscArrayzero(ap + bs2 * _i, bs2)); \
    rp[_i]                          = bcol; \
    ap[bs2 * _i + bs * cidx + ridx] = value; \
  a_noinsert:; \
    ailen[brow] = nrow; \
  } while (0)

#define MatSetValues_SeqBAIJ_B_Private(row, col, value, addv, orow, ocol) \
  do { \
    brow = row / bs; \
    rp   = PetscSafePointerPlusOffset(bj, bi[brow]); \
    ap   = PetscSafePointerPlusOffset(ba, bs2 * bi[brow]); \
    rmax = bimax[brow]; \
    nrow = bilen[brow]; \
    bcol = col / bs; \
    ridx = row % bs; \
    cidx = col % bs; \
    low  = 0; \
    high = nrow; \
    while (high - low > 3) { \
      t = (low + high) / 2; \
      if (rp[t] > bcol) high = t; \
      else low = t; \
    } \
    for (_i = low; _i < high; _i++) { \
      if (rp[_i] > bcol) break; \
      if (rp[_i] == bcol) { \
        bap = ap + bs2 * _i + bs * cidx + ridx; \
        if (addv == ADD_VALUES) *bap += value; \
        else *bap = value; \
        goto b_noinsert; \
      } \
    } \
    if (b->nonew == 1) goto b_noinsert; \
    PetscCheck(b->nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at global row/column  (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", orow, ocol); \
    MatSeqXAIJReallocateAIJ(B, b->mbs, bs2, nrow, brow, bcol, rmax, ba, bi, bj, rp, ap, bimax, b->nonew, MatScalar); \
    N = nrow++ - 1; \
    /* shift up all the later entries in this row */ \
    PetscCall(PetscArraymove(rp + _i + 1, rp + _i, N - _i + 1)); \
    PetscCall(PetscArraymove(ap + bs2 * (_i + 1), ap + bs2 * _i, bs2 * (N - _i + 1))); \
    PetscCall(PetscArrayzero(ap + bs2 * _i, bs2)); \
    rp[_i]                          = bcol; \
    ap[bs2 * _i + bs * cidx + ridx] = value; \
  b_noinsert:; \
    bilen[brow] = nrow; \
  } while (0)

PetscErrorCode MatSetValues_MPIBAIJ(Mat mat, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode addv)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  MatScalar    value;
  PetscBool    roworiented = baij->roworiented;
  PetscInt     i, j, row, col;
  PetscInt     rstart_orig = mat->rmap->rstart;
  PetscInt     rend_orig = mat->rmap->rend, cstart_orig = mat->cmap->rstart;
  PetscInt     cend_orig = mat->cmap->rend, bs = mat->rmap->bs;

  /* Some Variables required in the macro */
  Mat          A     = baij->A;
  Mat_SeqBAIJ *a     = (Mat_SeqBAIJ *)A->data;
  PetscInt    *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
  MatScalar   *aa = a->a;

  Mat          B     = baij->B;
  Mat_SeqBAIJ *b     = (Mat_SeqBAIJ *)B->data;
  PetscInt    *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j;
  MatScalar   *ba = b->a;

  PetscInt  *rp, ii, nrow, _i, rmax, N, brow, bcol;
  PetscInt   low, high, t, ridx, cidx, bs2 = a->bs2;
  MatScalar *ap, *bap;

  PetscFunctionBegin;
  for (i = 0; i < m; i++) {
    if (im[i] < 0) continue;
    PetscCheck(im[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, im[i], mat->rmap->N - 1);
    if (im[i] >= rstart_orig && im[i] < rend_orig) {
      row = im[i] - rstart_orig;
      for (j = 0; j < n; j++) {
        if (in[j] >= cstart_orig && in[j] < cend_orig) {
          col = in[j] - cstart_orig;
          if (roworiented) value = v[i * n + j];
          else value = v[i + j * m];
          MatSetValues_SeqBAIJ_A_Private(row, col, value, addv, im[i], in[j]);
        } else if (in[j] < 0) {
          continue;
        } else {
          PetscCheck(in[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
          if (mat->was_assembled) {
            if (!baij->colmap) PetscCall(MatCreateColmap_MPIBAIJ_Private(mat));
#if defined(PETSC_USE_CTABLE)
            PetscCall(PetscHMapIGetWithDefault(baij->colmap, in[j] / bs + 1, 0, &col));
            col = col - 1;
#else
            col = baij->colmap[in[j] / bs] - 1;
#endif
            if (col < 0 && !((Mat_SeqBAIJ *)baij->B->data)->nonew) {
              PetscCall(MatDisAssemble_MPIBAIJ(mat));
              col = in[j];
              /* Reinitialize the variables required by MatSetValues_SeqBAIJ_B_Private() */
              B     = baij->B;
              b     = (Mat_SeqBAIJ *)B->data;
              bimax = b->imax;
              bi    = b->i;
              bilen = b->ilen;
              bj    = b->j;
              ba    = b->a;
            } else {
              PetscCheck(col >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", im[i], in[j]);
              col += in[j] % bs;
            }
          } else col = in[j];
          if (roworiented) value = v[i * n + j];
          else value = v[i + j * m];
          MatSetValues_SeqBAIJ_B_Private(row, col, value, addv, im[i], in[j]);
          /* PetscCall(MatSetValues_SeqBAIJ(baij->B,1,&row,1,&col,&value,addv)); */
        }
      }
    } else {
      PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Setting off process row %" PetscInt_FMT " even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set", im[i]);
      if (!baij->donotstash) {
        mat->assembled = PETSC_FALSE;
        if (roworiented) {
          PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, v + i * n, PETSC_FALSE));
        } else {
          PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, v + i, m, PETSC_FALSE));
        }
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode MatSetValuesBlocked_SeqBAIJ_Inlined(Mat A, PetscInt row, PetscInt col, const PetscScalar v[], InsertMode is, PetscInt orow, PetscInt ocol)
{
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  PetscInt          *rp, low, high, t, ii, jj, nrow, i, rmax, N;
  PetscInt          *imax = a->imax, *ai = a->i, *ailen = a->ilen;
  PetscInt          *aj = a->j, nonew = a->nonew, bs2 = a->bs2, bs = A->rmap->bs;
  PetscBool          roworiented = a->roworiented;
  const PetscScalar *value       = v;
  MatScalar         *ap, *aa = a->a, *bap;

  PetscFunctionBegin;
  rp    = aj + ai[row];
  ap    = aa + bs2 * ai[row];
  rmax  = imax[row];
  nrow  = ailen[row];
  value = v;
  low   = 0;
  high  = nrow;
  while (high - low > 7) {
    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) {
      bap = ap + bs2 * i;
      if (roworiented) {
        if (is == ADD_VALUES) {
          for (ii = 0; ii < bs; ii++) {
            for (jj = ii; jj < bs2; jj += bs) bap[jj] += *value++;
          }
        } else {
          for (ii = 0; ii < bs; ii++) {
            for (jj = ii; jj < bs2; jj += bs) bap[jj] = *value++;
          }
        }
      } else {
        if (is == ADD_VALUES) {
          for (ii = 0; ii < bs; ii++, value += bs) {
            for (jj = 0; jj < bs; jj++) bap[jj] += value[jj];
            bap += bs;
          }
        } else {
          for (ii = 0; ii < bs; ii++, value += bs) {
            for (jj = 0; jj < bs; jj++) bap[jj] = value[jj];
            bap += bs;
          }
        }
      }
      goto noinsert2;
    }
  }
  if (nonew == 1) goto noinsert2;
  PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new global block indexed nonzero block (%" PetscInt_FMT ", %" PetscInt_FMT ") in the matrix", orow, ocol);
  MatSeqXAIJReallocateAIJ(A, a->mbs, bs2, nrow, row, col, rmax, aa, ai, aj, rp, ap, imax, nonew, MatScalar);
  N = nrow++ - 1;
  high++;
  /* shift up all the later entries in this row */
  PetscCall(PetscArraymove(rp + i + 1, rp + i, N - i + 1));
  PetscCall(PetscArraymove(ap + bs2 * (i + 1), ap + bs2 * i, bs2 * (N - i + 1)));
  rp[i] = col;
  bap   = ap + bs2 * i;
  if (roworiented) {
    for (ii = 0; ii < bs; ii++) {
      for (jj = ii; jj < bs2; jj += bs) bap[jj] = *value++;
    }
  } else {
    for (ii = 0; ii < bs; ii++) {
      for (jj = 0; jj < bs; jj++) *bap++ = *value++;
    }
  }
noinsert2:;
  ailen[row] = nrow;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
    This routine should be optimized so that the block copy at ** Here a copy is required ** below is not needed
    by passing additional stride information into the MatSetValuesBlocked_SeqBAIJ_Inlined() routine
*/
static PetscErrorCode MatSetValuesBlocked_MPIBAIJ(Mat mat, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode addv)
{
  Mat_MPIBAIJ       *baij = (Mat_MPIBAIJ *)mat->data;
  const PetscScalar *value;
  MatScalar         *barray      = baij->barray;
  PetscBool          roworiented = baij->roworiented;
  PetscInt           i, j, ii, jj, row, col, rstart = baij->rstartbs;
  PetscInt           rend = baij->rendbs, cstart = baij->cstartbs, stepval;
  PetscInt           cend = baij->cendbs, bs = mat->rmap->bs, bs2 = baij->bs2;

  PetscFunctionBegin;
  if (!barray) {
    PetscCall(PetscMalloc1(bs2, &barray));
    baij->barray = barray;
  }

  if (roworiented) stepval = (n - 1) * bs;
  else stepval = (m - 1) * bs;

  for (i = 0; i < m; i++) {
    if (im[i] < 0) continue;
    PetscCheck(im[i] < baij->Mbs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Block indexed row too large %" PetscInt_FMT " max %" PetscInt_FMT, im[i], baij->Mbs - 1);
    if (im[i] >= rstart && im[i] < rend) {
      row = im[i] - rstart;
      for (j = 0; j < n; j++) {
        /* If NumCol = 1 then a copy is not required */
        if ((roworiented) && (n == 1)) {
          barray = (MatScalar *)v + i * bs2;
        } else if ((!roworiented) && (m == 1)) {
          barray = (MatScalar *)v + j * bs2;
        } else { /* Here a copy is required */
          if (roworiented) {
            value = v + (i * (stepval + bs) + j) * bs;
          } else {
            value = v + (j * (stepval + bs) + i) * bs;
          }
          for (ii = 0; ii < bs; ii++, value += bs + stepval) {
            for (jj = 0; jj < bs; jj++) barray[jj] = value[jj];
            barray += bs;
          }
          barray -= bs2;
        }

        if (in[j] >= cstart && in[j] < cend) {
          col = in[j] - cstart;
          PetscCall(MatSetValuesBlocked_SeqBAIJ_Inlined(baij->A, row, col, barray, addv, im[i], in[j]));
        } else if (in[j] < 0) {
          continue;
        } else {
          PetscCheck(in[j] < baij->Nbs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Block indexed column too large %" PetscInt_FMT " max %" PetscInt_FMT, in[j], baij->Nbs - 1);
          if (mat->was_assembled) {
            if (!baij->colmap) PetscCall(MatCreateColmap_MPIBAIJ_Private(mat));

#if defined(PETSC_USE_CTABLE)
            PetscCall(PetscHMapIGetWithDefault(baij->colmap, in[j] + 1, 0, &col));
            col = col < 1 ? -1 : (col - 1) / bs;
#else
            col = baij->colmap[in[j]] < 1 ? -1 : (baij->colmap[in[j]] - 1) / bs;
#endif
            if (col < 0 && !((Mat_SeqBAIJ *)baij->B->data)->nonew) {
              PetscCall(MatDisAssemble_MPIBAIJ(mat));
              col = in[j];
            } else PetscCheck(col >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new blocked indexed nonzero block (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", im[i], in[j]);
          } else col = in[j];
          PetscCall(MatSetValuesBlocked_SeqBAIJ_Inlined(baij->B, row, col, barray, addv, im[i], in[j]));
        }
      }
    } else {
      PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Setting off process block indexed row %" PetscInt_FMT " even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set", im[i]);
      if (!baij->donotstash) {
        if (roworiented) {
          PetscCall(MatStashValuesRowBlocked_Private(&mat->bstash, im[i], n, in, v, m, n, i));
        } else {
          PetscCall(MatStashValuesColBlocked_Private(&mat->bstash, im[i], n, in, v, m, n, i));
        }
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

#define HASH_KEY             0.6180339887
#define HASH(size, key, tmp) (tmp = (key) * HASH_KEY, (PetscInt)((size) * (tmp - (PetscInt)tmp)))
/* #define HASH(size,key) ((PetscInt)((size)*fmod(((key)*HASH_KEY),1))) */
/* #define HASH(size,key,tmp) ((PetscInt)((size)*fmod(((key)*HASH_KEY),1))) */
static PetscErrorCode MatSetValues_MPIBAIJ_HT(Mat mat, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode addv)
{
  Mat_MPIBAIJ *baij        = (Mat_MPIBAIJ *)mat->data;
  PetscBool    roworiented = baij->roworiented;
  PetscInt     i, j, row, col;
  PetscInt     rstart_orig = mat->rmap->rstart;
  PetscInt     rend_orig = mat->rmap->rend, Nbs = baij->Nbs;
  PetscInt     h1, key, size = baij->ht_size, bs = mat->rmap->bs, *HT = baij->ht, idx;
  PetscReal    tmp;
  MatScalar  **HD       = baij->hd, value;
  PetscInt     total_ct = baij->ht_total_ct, insert_ct = baij->ht_insert_ct;

  PetscFunctionBegin;
  for (i = 0; i < m; i++) {
    if (PetscDefined(USE_DEBUG)) {
      PetscCheck(im[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative row");
      PetscCheck(im[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, im[i], mat->rmap->N - 1);
    }
    row = im[i];
    if (row >= rstart_orig && row < rend_orig) {
      for (j = 0; j < n; j++) {
        col = in[j];
        if (roworiented) value = v[i * n + j];
        else value = v[i + j * m];
        /* Look up PetscInto the Hash Table */
        key = (row / bs) * Nbs + (col / bs) + 1;
        h1  = HASH(size, key, tmp);

        idx = h1;
        if (PetscDefined(USE_DEBUG)) {
          insert_ct++;
          total_ct++;
          if (HT[idx] != key) {
            for (idx = h1; (idx < size) && (HT[idx] != key); idx++, total_ct++);
            if (idx == size) {
              for (idx = 0; (idx < h1) && (HT[idx] != key); idx++, total_ct++);
              PetscCheck(idx != h1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "(%" PetscInt_FMT ",%" PetscInt_FMT ") has no entry in the hash table", row, col);
            }
          }
        } else if (HT[idx] != key) {
          for (idx = h1; (idx < size) && (HT[idx] != key); idx++);
          if (idx == size) {
            for (idx = 0; (idx < h1) && (HT[idx] != key); idx++);
            PetscCheck(idx != h1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "(%" PetscInt_FMT ",%" PetscInt_FMT ") has no entry in the hash table", row, col);
          }
        }
        /* A HASH table entry is found, so insert the values at the correct address */
        if (addv == ADD_VALUES) *(HD[idx] + (col % bs) * bs + (row % bs)) += value;
        else *(HD[idx] + (col % bs) * bs + (row % bs)) = value;
      }
    } else if (!baij->donotstash) {
      if (roworiented) {
        PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, v + i * n, PETSC_FALSE));
      } else {
        PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, v + i, m, PETSC_FALSE));
      }
    }
  }
  if (PetscDefined(USE_DEBUG)) {
    baij->ht_total_ct += total_ct;
    baij->ht_insert_ct += insert_ct;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValuesBlocked_MPIBAIJ_HT(Mat mat, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode addv)
{
  Mat_MPIBAIJ       *baij        = (Mat_MPIBAIJ *)mat->data;
  PetscBool          roworiented = baij->roworiented;
  PetscInt           i, j, ii, jj, row, col;
  PetscInt           rstart = baij->rstartbs;
  PetscInt           rend = mat->rmap->rend, stepval, bs = mat->rmap->bs, bs2 = baij->bs2, nbs2 = n * bs2;
  PetscInt           h1, key, size = baij->ht_size, idx, *HT = baij->ht, Nbs = baij->Nbs;
  PetscReal          tmp;
  MatScalar        **HD = baij->hd, *baij_a;
  const PetscScalar *v_t, *value;
  PetscInt           total_ct = baij->ht_total_ct, insert_ct = baij->ht_insert_ct;

  PetscFunctionBegin;
  if (roworiented) stepval = (n - 1) * bs;
  else stepval = (m - 1) * bs;

  for (i = 0; i < m; i++) {
    if (PetscDefined(USE_DEBUG)) {
      PetscCheck(im[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative row: %" PetscInt_FMT, im[i]);
      PetscCheck(im[i] < baij->Mbs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, im[i], baij->Mbs - 1);
    }
    row = im[i];
    v_t = v + i * nbs2;
    if (row >= rstart && row < rend) {
      for (j = 0; j < n; j++) {
        col = in[j];

        /* Look up into the Hash Table */
        key = row * Nbs + col + 1;
        h1  = HASH(size, key, tmp);

        idx = h1;
        if (PetscDefined(USE_DEBUG)) {
          total_ct++;
          insert_ct++;
          if (HT[idx] != key) {
            for (idx = h1; (idx < size) && (HT[idx] != key); idx++, total_ct++);
            if (idx == size) {
              for (idx = 0; (idx < h1) && (HT[idx] != key); idx++, total_ct++);
              PetscCheck(idx != h1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "(%" PetscInt_FMT ",%" PetscInt_FMT ") has no entry in the hash table", row, col);
            }
          }
        } else if (HT[idx] != key) {
          for (idx = h1; (idx < size) && (HT[idx] != key); idx++);
          if (idx == size) {
            for (idx = 0; (idx < h1) && (HT[idx] != key); idx++);
            PetscCheck(idx != h1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "(%" PetscInt_FMT ",%" PetscInt_FMT ") has no entry in the hash table", row, col);
          }
        }
        baij_a = HD[idx];
        if (roworiented) {
          /*value = v + i*(stepval+bs)*bs + j*bs;*/
          /* value = v + (i*(stepval+bs)+j)*bs; */
          value = v_t;
          v_t += bs;
          if (addv == ADD_VALUES) {
            for (ii = 0; ii < bs; ii++, value += stepval) {
              for (jj = ii; jj < bs2; jj += bs) baij_a[jj] += *value++;
            }
          } else {
            for (ii = 0; ii < bs; ii++, value += stepval) {
              for (jj = ii; jj < bs2; jj += bs) baij_a[jj] = *value++;
            }
          }
        } else {
          value = v + j * (stepval + bs) * bs + i * bs;
          if (addv == ADD_VALUES) {
            for (ii = 0; ii < bs; ii++, value += stepval, baij_a += bs) {
              for (jj = 0; jj < bs; jj++) baij_a[jj] += *value++;
            }
          } else {
            for (ii = 0; ii < bs; ii++, value += stepval, baij_a += bs) {
              for (jj = 0; jj < bs; jj++) baij_a[jj] = *value++;
            }
          }
        }
      }
    } else {
      if (!baij->donotstash) {
        if (roworiented) {
          PetscCall(MatStashValuesRowBlocked_Private(&mat->bstash, im[i], n, in, v, m, n, i));
        } else {
          PetscCall(MatStashValuesColBlocked_Private(&mat->bstash, im[i], n, in, v, m, n, i));
        }
      }
    }
  }
  if (PetscDefined(USE_DEBUG)) {
    baij->ht_total_ct += total_ct;
    baij->ht_insert_ct += insert_ct;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetValues_MPIBAIJ(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], PetscScalar v[])
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  PetscInt     bs = mat->rmap->bs, i, j, bsrstart = mat->rmap->rstart, bsrend = mat->rmap->rend;
  PetscInt     bscstart = mat->cmap->rstart, bscend = mat->cmap->rend, row, col, data;

  PetscFunctionBegin;
  for (i = 0; i < m; i++) {
    if (idxm[i] < 0) continue; /* negative row */
    PetscCheck(idxm[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, idxm[i], mat->rmap->N - 1);
    if (idxm[i] >= bsrstart && idxm[i] < bsrend) {
      row = idxm[i] - bsrstart;
      for (j = 0; j < n; j++) {
        if (idxn[j] < 0) continue; /* negative column */
        PetscCheck(idxn[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, idxn[j], mat->cmap->N - 1);
        if (idxn[j] >= bscstart && idxn[j] < bscend) {
          col = idxn[j] - bscstart;
          PetscCall(MatGetValues_SeqBAIJ(baij->A, 1, &row, 1, &col, v + i * n + j));
        } else {
          if (!baij->colmap) PetscCall(MatCreateColmap_MPIBAIJ_Private(mat));
#if defined(PETSC_USE_CTABLE)
          PetscCall(PetscHMapIGetWithDefault(baij->colmap, idxn[j] / bs + 1, 0, &data));
          data--;
#else
          data = baij->colmap[idxn[j] / bs] - 1;
#endif
          if ((data < 0) || (baij->garray[data / bs] != idxn[j] / bs)) *(v + i * n + j) = 0.0;
          else {
            col = data + idxn[j] % bs;
            PetscCall(MatGetValues_SeqBAIJ(baij->B, 1, &row, 1, &col, v + i * n + j));
          }
        }
      }
    } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Only local values currently supported");
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatNorm_MPIBAIJ(Mat mat, NormType type, PetscReal *nrm)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  Mat_SeqBAIJ *amat = (Mat_SeqBAIJ *)baij->A->data, *bmat = (Mat_SeqBAIJ *)baij->B->data;
  PetscInt     i, j, bs2 = baij->bs2, bs = baij->A->rmap->bs, nz, row, col;
  PetscReal    sum = 0.0;
  MatScalar   *v;

  PetscFunctionBegin;
  if (baij->size == 1) {
    PetscCall(MatNorm(baij->A, type, nrm));
  } else {
    if (type == NORM_FROBENIUS) {
      v  = amat->a;
      nz = amat->nz * bs2;
      for (i = 0; i < nz; i++) {
        sum += PetscRealPart(PetscConj(*v) * (*v));
        v++;
      }
      v  = bmat->a;
      nz = bmat->nz * bs2;
      for (i = 0; i < nz; i++) {
        sum += PetscRealPart(PetscConj(*v) * (*v));
        v++;
      }
      PetscCallMPI(MPIU_Allreduce(&sum, nrm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
      *nrm = PetscSqrtReal(*nrm);
    } else if (type == NORM_1) { /* max column sum */
      PetscReal *tmp;
      PetscInt  *jj, *garray = baij->garray, cstart = baij->rstartbs;

      PetscCall(PetscCalloc1(mat->cmap->N, &tmp));
      v  = amat->a;
      jj = amat->j;
      for (i = 0; i < amat->nz; i++) {
        for (j = 0; j < bs; j++) {
          col = bs * (cstart + *jj) + j; /* column index */
          for (row = 0; row < bs; row++) {
            tmp[col] += PetscAbsScalar(*v);
            v++;
          }
        }
        jj++;
      }
      v  = bmat->a;
      jj = bmat->j;
      for (i = 0; i < bmat->nz; i++) {
        for (j = 0; j < bs; j++) {
          col = bs * garray[*jj] + j;
          for (row = 0; row < bs; row++) {
            tmp[col] += PetscAbsScalar(*v);
            v++;
          }
        }
        jj++;
      }
      PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, tmp, mat->cmap->N, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
      *nrm = 0.0;
      for (j = 0; j < mat->cmap->N; j++) {
        if (tmp[j] > *nrm) *nrm = tmp[j];
      }
      PetscCall(PetscFree(tmp));
    } else if (type == NORM_INFINITY) { /* max row sum */
      PetscReal *sums;
      PetscCall(PetscMalloc1(bs, &sums));
      sum = 0.0;
      for (j = 0; j < amat->mbs; j++) {
        for (row = 0; row < bs; row++) sums[row] = 0.0;
        v  = amat->a + bs2 * amat->i[j];
        nz = amat->i[j + 1] - amat->i[j];
        for (i = 0; i < nz; i++) {
          for (col = 0; col < bs; col++) {
            for (row = 0; row < bs; row++) {
              sums[row] += PetscAbsScalar(*v);
              v++;
            }
          }
        }
        v  = bmat->a + bs2 * bmat->i[j];
        nz = bmat->i[j + 1] - bmat->i[j];
        for (i = 0; i < nz; i++) {
          for (col = 0; col < bs; col++) {
            for (row = 0; row < bs; row++) {
              sums[row] += PetscAbsScalar(*v);
              v++;
            }
          }
        }
        for (row = 0; row < bs; row++) {
          if (sums[row] > sum) sum = sums[row];
        }
      }
      PetscCallMPI(MPIU_Allreduce(&sum, nrm, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)mat)));
      PetscCall(PetscFree(sums));
    } else SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "No support for this norm yet");
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Creates the hash table, and sets the table
  This table is created only once.
  If new entried need to be added to the matrix
  then the hash table has to be destroyed and
  recreated.
*/
static PetscErrorCode MatCreateHashTable_MPIBAIJ_Private(Mat mat, PetscReal factor)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  Mat          A = baij->A, B = baij->B;
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)B->data;
  PetscInt     i, j, k, nz = a->nz + b->nz, h1, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
  PetscInt     ht_size, bs2 = baij->bs2, rstart = baij->rstartbs;
  PetscInt     cstart = baij->cstartbs, *garray = baij->garray, row, col, Nbs = baij->Nbs;
  PetscInt    *HT, key;
  MatScalar  **HD;
  PetscReal    tmp;
#if defined(PETSC_USE_INFO)
  PetscInt ct = 0, max = 0;
#endif

  PetscFunctionBegin;
  if (baij->ht) PetscFunctionReturn(PETSC_SUCCESS);

  baij->ht_size = (PetscInt)(factor * nz);
  ht_size       = baij->ht_size;

  /* Allocate Memory for Hash Table */
  PetscCall(PetscCalloc2(ht_size, &baij->hd, ht_size, &baij->ht));
  HD = baij->hd;
  HT = baij->ht;

  /* Loop Over A */
  for (i = 0; i < a->mbs; i++) {
    for (j = ai[i]; j < ai[i + 1]; j++) {
      row = i + rstart;
      col = aj[j] + cstart;

      key = row * Nbs + col + 1;
      h1  = HASH(ht_size, key, tmp);
      for (k = 0; k < ht_size; k++) {
        if (!HT[(h1 + k) % ht_size]) {
          HT[(h1 + k) % ht_size] = key;
          HD[(h1 + k) % ht_size] = a->a + j * bs2;
          break;
#if defined(PETSC_USE_INFO)
        } else {
          ct++;
#endif
        }
      }
#if defined(PETSC_USE_INFO)
      if (k > max) max = k;
#endif
    }
  }
  /* Loop Over B */
  for (i = 0; i < b->mbs; i++) {
    for (j = bi[i]; j < bi[i + 1]; j++) {
      row = i + rstart;
      col = garray[bj[j]];
      key = row * Nbs + col + 1;
      h1  = HASH(ht_size, key, tmp);
      for (k = 0; k < ht_size; k++) {
        if (!HT[(h1 + k) % ht_size]) {
          HT[(h1 + k) % ht_size] = key;
          HD[(h1 + k) % ht_size] = b->a + j * bs2;
          break;
#if defined(PETSC_USE_INFO)
        } else {
          ct++;
#endif
        }
      }
#if defined(PETSC_USE_INFO)
      if (k > max) max = k;
#endif
    }
  }

  /* Print Summary */
#if defined(PETSC_USE_INFO)
  for (i = 0, j = 0; i < ht_size; i++) {
    if (HT[i]) j++;
  }
  PetscCall(PetscInfo(mat, "Average Search = %5.2g,max search = %" PetscInt_FMT "\n", (!j) ? 0.0 : (double)(((PetscReal)(ct + j)) / j), max));
#endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAssemblyBegin_MPIBAIJ(Mat mat, MatAssemblyType mode)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  PetscInt     nstash, reallocs;

  PetscFunctionBegin;
  if (baij->donotstash || mat->nooffprocentries) PetscFunctionReturn(PETSC_SUCCESS);

  PetscCall(MatStashScatterBegin_Private(mat, &mat->stash, mat->rmap->range));
  PetscCall(MatStashScatterBegin_Private(mat, &mat->bstash, baij->rangebs));
  PetscCall(MatStashGetInfo_Private(&mat->stash, &nstash, &reallocs));
  PetscCall(PetscInfo(mat, "Stash has %" PetscInt_FMT " entries,uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
  PetscCall(MatStashGetInfo_Private(&mat->bstash, &nstash, &reallocs));
  PetscCall(PetscInfo(mat, "Block-Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAssemblyEnd_MPIBAIJ(Mat mat, MatAssemblyType mode)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  Mat_SeqBAIJ *a    = (Mat_SeqBAIJ *)baij->A->data;
  PetscInt     i, j, rstart, ncols, flg, bs2 = baij->bs2;
  PetscInt    *row, *col;
  PetscBool    r1, r2, r3, other_disassembled;
  MatScalar   *val;
  PetscMPIInt  n;

  PetscFunctionBegin;
  /* do not use 'b=(Mat_SeqBAIJ*)baij->B->data' as B can be reset in disassembly */
  if (!baij->donotstash && !mat->nooffprocentries) {
    while (1) {
      PetscCall(MatStashScatterGetMesg_Private(&mat->stash, &n, &row, &col, &val, &flg));
      if (!flg) break;

      for (i = 0; i < n;) {
        /* Now identify the consecutive vals belonging to the same row */
        for (j = i, rstart = row[j]; j < n; j++) {
          if (row[j] != rstart) break;
        }
        if (j < n) ncols = j - i;
        else ncols = n - i;
        /* Now assemble all these values with a single function call */
        PetscCall(MatSetValues_MPIBAIJ(mat, 1, row + i, ncols, col + i, val + i, mat->insertmode));
        i = j;
      }
    }
    PetscCall(MatStashScatterEnd_Private(&mat->stash));
    /* Now process the block-stash. Since the values are stashed column-oriented,
       set the row-oriented flag to column-oriented, and after MatSetValues()
       restore the original flags */
    r1 = baij->roworiented;
    r2 = a->roworiented;
    r3 = ((Mat_SeqBAIJ *)baij->B->data)->roworiented;

    baij->roworiented                           = PETSC_FALSE;
    a->roworiented                              = PETSC_FALSE;
    ((Mat_SeqBAIJ *)baij->B->data)->roworiented = PETSC_FALSE;
    while (1) {
      PetscCall(MatStashScatterGetMesg_Private(&mat->bstash, &n, &row, &col, &val, &flg));
      if (!flg) break;

      for (i = 0; i < n;) {
        /* Now identify the consecutive vals belonging to the same row */
        for (j = i, rstart = row[j]; j < n; j++) {
          if (row[j] != rstart) break;
        }
        if (j < n) ncols = j - i;
        else ncols = n - i;
        PetscCall(MatSetValuesBlocked_MPIBAIJ(mat, 1, row + i, ncols, col + i, val + i * bs2, mat->insertmode));
        i = j;
      }
    }
    PetscCall(MatStashScatterEnd_Private(&mat->bstash));

    baij->roworiented                           = r1;
    a->roworiented                              = r2;
    ((Mat_SeqBAIJ *)baij->B->data)->roworiented = r3;
  }

  PetscCall(MatAssemblyBegin(baij->A, mode));
  PetscCall(MatAssemblyEnd(baij->A, mode));

  /* determine if any processor has disassembled, if so we must
     also disassemble ourselves, in order that we may reassemble. */
  /*
     if nonzero structure of submatrix B cannot change then we know that
     no processor disassembled thus we can skip this stuff
  */
  if (!((Mat_SeqBAIJ *)baij->B->data)->nonew) {
    PetscCallMPI(MPIU_Allreduce(&mat->was_assembled, &other_disassembled, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    if (mat->was_assembled && !other_disassembled) PetscCall(MatDisAssemble_MPIBAIJ(mat));
  }

  if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) PetscCall(MatSetUpMultiply_MPIBAIJ(mat));
  PetscCall(MatAssemblyBegin(baij->B, mode));
  PetscCall(MatAssemblyEnd(baij->B, mode));

#if defined(PETSC_USE_INFO)
  if (baij->ht && mode == MAT_FINAL_ASSEMBLY) {
    PetscCall(PetscInfo(mat, "Average Hash Table Search in MatSetValues = %5.2f\n", (double)((PetscReal)baij->ht_total_ct) / baij->ht_insert_ct));

    baij->ht_total_ct  = 0;
    baij->ht_insert_ct = 0;
  }
#endif
  if (baij->ht_flag && !baij->ht && mode == MAT_FINAL_ASSEMBLY) {
    PetscCall(MatCreateHashTable_MPIBAIJ_Private(mat, baij->ht_fact));

    mat->ops->setvalues        = MatSetValues_MPIBAIJ_HT;
    mat->ops->setvaluesblocked = MatSetValuesBlocked_MPIBAIJ_HT;
  }

  PetscCall(PetscFree2(baij->rowvalues, baij->rowindices));

  baij->rowvalues = NULL;

  /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
  if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqBAIJ *)baij->A->data)->nonew) {
    PetscObjectState state = baij->A->nonzerostate + baij->B->nonzerostate;
    PetscCallMPI(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

extern PetscErrorCode MatView_SeqBAIJ(Mat, PetscViewer);
#include <petscdraw.h>
static PetscErrorCode MatView_MPIBAIJ_ASCIIorDraworSocket(Mat mat, PetscViewer viewer)
{
  Mat_MPIBAIJ      *baij = (Mat_MPIBAIJ *)mat->data;
  PetscMPIInt       rank = baij->rank;
  PetscInt          bs   = mat->rmap->bs;
  PetscBool         iascii, isdraw;
  PetscViewer       sviewer;
  PetscViewerFormat format;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
  if (iascii) {
    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
      MatInfo info;
      PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
      PetscCall(MatGetInfo(mat, MAT_LOCAL, &info));
      PetscCall(PetscViewerASCIIPushSynchronized(viewer));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] Local rows %" PetscInt_FMT " nz %" PetscInt_FMT " nz alloced %" PetscInt_FMT " bs %" PetscInt_FMT " mem %g\n", rank, mat->rmap->n, (PetscInt)info.nz_used, (PetscInt)info.nz_allocated,
                                                   mat->rmap->bs, info.memory));
      PetscCall(MatGetInfo(baij->A, MAT_LOCAL, &info));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] on-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
      PetscCall(MatGetInfo(baij->B, MAT_LOCAL, &info));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] off-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
      PetscCall(PetscViewerFlush(viewer));
      PetscCall(PetscViewerASCIIPopSynchronized(viewer));
      PetscCall(PetscViewerASCIIPrintf(viewer, "Information on VecScatter used in matrix-vector product: \n"));
      PetscCall(VecScatterView(baij->Mvctx, viewer));
      PetscFunctionReturn(PETSC_SUCCESS);
    } else if (format == PETSC_VIEWER_ASCII_INFO) {
      PetscCall(PetscViewerASCIIPrintf(viewer, "  block size is %" PetscInt_FMT "\n", bs));
      PetscFunctionReturn(PETSC_SUCCESS);
    } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
      PetscFunctionReturn(PETSC_SUCCESS);
    }
  }

  if (isdraw) {
    PetscDraw draw;
    PetscBool isnull;
    PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
    PetscCall(PetscDrawIsNull(draw, &isnull));
    if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
  }

  {
    /* assemble the entire matrix onto first processor. */
    Mat          A;
    Mat_SeqBAIJ *Aloc;
    PetscInt     M = mat->rmap->N, N = mat->cmap->N, *ai, *aj, col, i, j, k, *rvals, mbs = baij->mbs;
    MatScalar   *a;
    const char  *matname;

    /* Here we are creating a temporary matrix, so will assume MPIBAIJ is acceptable */
    /* Perhaps this should be the type of mat? */
    PetscCall(MatCreate(PetscObjectComm((PetscObject)mat), &A));
    if (rank == 0) {
      PetscCall(MatSetSizes(A, M, N, M, N));
    } else {
      PetscCall(MatSetSizes(A, 0, 0, M, N));
    }
    PetscCall(MatSetType(A, MATMPIBAIJ));
    PetscCall(MatMPIBAIJSetPreallocation(A, mat->rmap->bs, 0, NULL, 0, NULL));
    PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));

    /* copy over the A part */
    Aloc = (Mat_SeqBAIJ *)baij->A->data;
    ai   = Aloc->i;
    aj   = Aloc->j;
    a    = Aloc->a;
    PetscCall(PetscMalloc1(bs, &rvals));

    for (i = 0; i < mbs; i++) {
      rvals[0] = bs * (baij->rstartbs + i);
      for (j = 1; j < bs; j++) rvals[j] = rvals[j - 1] + 1;
      for (j = ai[i]; j < ai[i + 1]; j++) {
        col = (baij->cstartbs + aj[j]) * bs;
        for (k = 0; k < bs; k++) {
          PetscCall(MatSetValues_MPIBAIJ(A, bs, rvals, 1, &col, a, INSERT_VALUES));
          col++;
          a += bs;
        }
      }
    }
    /* copy over the B part */
    Aloc = (Mat_SeqBAIJ *)baij->B->data;
    ai   = Aloc->i;
    aj   = Aloc->j;
    a    = Aloc->a;
    for (i = 0; i < mbs; i++) {
      rvals[0] = bs * (baij->rstartbs + i);
      for (j = 1; j < bs; j++) rvals[j] = rvals[j - 1] + 1;
      for (j = ai[i]; j < ai[i + 1]; j++) {
        col = baij->garray[aj[j]] * bs;
        for (k = 0; k < bs; k++) {
          PetscCall(MatSetValues_MPIBAIJ(A, bs, rvals, 1, &col, a, INSERT_VALUES));
          col++;
          a += bs;
        }
      }
    }
    PetscCall(PetscFree(rvals));
    PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
    /*
       Everyone has to call to draw the matrix since the graphics waits are
       synchronized across all processors that share the PetscDraw object
    */
    PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    if (((PetscObject)mat)->name) PetscCall(PetscObjectGetName((PetscObject)mat, &matname));
    if (rank == 0) {
      if (((PetscObject)mat)->name) PetscCall(PetscObjectSetName((PetscObject)((Mat_MPIBAIJ *)A->data)->A, matname));
      PetscCall(MatView_SeqBAIJ(((Mat_MPIBAIJ *)A->data)->A, sviewer));
    }
    PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    PetscCall(MatDestroy(&A));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Used for both MPIBAIJ and MPISBAIJ matrices */
PetscErrorCode MatView_MPIBAIJ_Binary(Mat mat, PetscViewer viewer)
{
  Mat_MPIBAIJ    *aij    = (Mat_MPIBAIJ *)mat->data;
  Mat_SeqBAIJ    *A      = (Mat_SeqBAIJ *)aij->A->data;
  Mat_SeqBAIJ    *B      = (Mat_SeqBAIJ *)aij->B->data;
  const PetscInt *garray = aij->garray;
  PetscInt        header[4], M, N, m, rs, cs, bs, cnt, i, j, ja, jb, k, l;
  PetscCount      nz, hnz;
  PetscInt       *rowlens, *colidxs;
  PetscScalar    *matvals;
  PetscMPIInt     rank;

  PetscFunctionBegin;
  PetscCall(PetscViewerSetUp(viewer));

  M  = mat->rmap->N;
  N  = mat->cmap->N;
  m  = mat->rmap->n;
  rs = mat->rmap->rstart;
  cs = mat->cmap->rstart;
  bs = mat->rmap->bs;
  nz = bs * bs * (A->nz + B->nz);

  /* write matrix header */
  header[0] = MAT_FILE_CLASSID;
  header[1] = M;
  header[2] = N;
  PetscCallMPI(MPI_Reduce(&nz, &hnz, 1, MPIU_COUNT, MPI_SUM, 0, PetscObjectComm((PetscObject)mat)));
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
  if (rank == 0) PetscCall(PetscIntCast(hnz, &header[3]));
  PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));

  /* fill in and store row lengths */
  PetscCall(PetscMalloc1(m, &rowlens));
  for (cnt = 0, i = 0; i < A->mbs; i++)
    for (j = 0; j < bs; j++) rowlens[cnt++] = bs * (A->i[i + 1] - A->i[i] + B->i[i + 1] - B->i[i]);
  PetscCall(PetscViewerBinaryWriteAll(viewer, rowlens, m, rs, M, PETSC_INT));
  PetscCall(PetscFree(rowlens));

  /* fill in and store column indices */
  PetscCall(PetscMalloc1(nz, &colidxs));
  for (cnt = 0, i = 0; i < A->mbs; i++) {
    for (k = 0; k < bs; k++) {
      for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
        if (garray[B->j[jb]] > cs / bs) break;
        for (l = 0; l < bs; l++) colidxs[cnt++] = bs * garray[B->j[jb]] + l;
      }
      for (ja = A->i[i]; ja < A->i[i + 1]; ja++)
        for (l = 0; l < bs; l++) colidxs[cnt++] = bs * A->j[ja] + l + cs;
      for (; jb < B->i[i + 1]; jb++)
        for (l = 0; l < bs; l++) colidxs[cnt++] = bs * garray[B->j[jb]] + l;
    }
  }
  PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_LIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscCount_FMT, cnt, nz);
  PetscCall(PetscViewerBinaryWriteAll(viewer, colidxs, nz, PETSC_DECIDE, PETSC_DECIDE, PETSC_INT));
  PetscCall(PetscFree(colidxs));

  /* fill in and store nonzero values */
  PetscCall(PetscMalloc1(nz, &matvals));
  for (cnt = 0, i = 0; i < A->mbs; i++) {
    for (k = 0; k < bs; k++) {
      for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
        if (garray[B->j[jb]] > cs / bs) break;
        for (l = 0; l < bs; l++) matvals[cnt++] = B->a[bs * (bs * jb + l) + k];
      }
      for (ja = A->i[i]; ja < A->i[i + 1]; ja++)
        for (l = 0; l < bs; l++) matvals[cnt++] = A->a[bs * (bs * ja + l) + k];
      for (; jb < B->i[i + 1]; jb++)
        for (l = 0; l < bs; l++) matvals[cnt++] = B->a[bs * (bs * jb + l) + k];
    }
  }
  PetscCall(PetscViewerBinaryWriteAll(viewer, matvals, nz, PETSC_DECIDE, PETSC_DECIDE, PETSC_SCALAR));
  PetscCall(PetscFree(matvals));

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

PetscErrorCode MatView_MPIBAIJ(Mat mat, PetscViewer viewer)
{
  PetscBool iascii, isdraw, issocket, isbinary;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSOCKET, &issocket));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
  if (iascii || isdraw || issocket) {
    PetscCall(MatView_MPIBAIJ_ASCIIorDraworSocket(mat, viewer));
  } else if (isbinary) PetscCall(MatView_MPIBAIJ_Binary(mat, viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMult_MPIBAIJ(Mat A, Vec xx, Vec yy)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;
  PetscInt     nt;

  PetscFunctionBegin;
  PetscCall(VecGetLocalSize(xx, &nt));
  PetscCheck(nt == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible partition of A and xx");
  PetscCall(VecGetLocalSize(yy, &nt));
  PetscCheck(nt == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible partition of A and yy");
  PetscCall(VecScatterBegin(a->Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall((*a->A->ops->mult)(a->A, xx, yy));
  PetscCall(VecScatterEnd(a->Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall((*a->B->ops->multadd)(a->B, a->lvec, yy, yy));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultAdd_MPIBAIJ(Mat A, Vec xx, Vec yy, Vec zz)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(VecScatterBegin(a->Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall((*a->A->ops->multadd)(a->A, xx, yy, zz));
  PetscCall(VecScatterEnd(a->Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall((*a->B->ops->multadd)(a->B, a->lvec, zz, zz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTranspose_MPIBAIJ(Mat A, Vec xx, Vec yy)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  /* do nondiagonal part */
  PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
  /* do local part */
  PetscCall((*a->A->ops->multtranspose)(a->A, xx, yy));
  /* add partial results together */
  PetscCall(VecScatterBegin(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTransposeAdd_MPIBAIJ(Mat A, Vec xx, Vec yy, Vec zz)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  /* do nondiagonal part */
  PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
  /* do local part */
  PetscCall((*a->A->ops->multtransposeadd)(a->A, xx, yy, zz));
  /* add partial results together */
  PetscCall(VecScatterBegin(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  This only works correctly for square matrices where the subblock A->A is the
   diagonal block
*/
static PetscErrorCode MatGetDiagonal_MPIBAIJ(Mat A, Vec v)
{
  PetscFunctionBegin;
  PetscCheck(A->rmap->N == A->cmap->N, PETSC_COMM_SELF, PETSC_ERR_SUP, "Supports only square matrix where A->A is diag block");
  PetscCall(MatGetDiagonal(((Mat_MPIBAIJ *)A->data)->A, v));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatScale_MPIBAIJ(Mat A, PetscScalar aa)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(MatScale(a->A, aa));
  PetscCall(MatScale(a->B, aa));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatGetRow_MPIBAIJ(Mat matin, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
{
  Mat_MPIBAIJ *mat = (Mat_MPIBAIJ *)matin->data;
  PetscScalar *vworkA, *vworkB, **pvA, **pvB, *v_p;
  PetscInt     bs = matin->rmap->bs, bs2 = mat->bs2, i, *cworkA, *cworkB, **pcA, **pcB;
  PetscInt     nztot, nzA, nzB, lrow, brstart = matin->rmap->rstart, brend = matin->rmap->rend;
  PetscInt    *cmap, *idx_p, cstart = mat->cstartbs;

  PetscFunctionBegin;
  PetscCheck(row >= brstart && row < brend, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only local rows");
  PetscCheck(!mat->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Already active");
  mat->getrowactive = PETSC_TRUE;

  if (!mat->rowvalues && (idx || v)) {
    /*
        allocate enough space to hold information from the longest row.
    */
    Mat_SeqBAIJ *Aa = (Mat_SeqBAIJ *)mat->A->data, *Ba = (Mat_SeqBAIJ *)mat->B->data;
    PetscInt     max = 1, mbs = mat->mbs, tmp;
    for (i = 0; i < mbs; i++) {
      tmp = Aa->i[i + 1] - Aa->i[i] + Ba->i[i + 1] - Ba->i[i];
      if (max < tmp) max = tmp;
    }
    PetscCall(PetscMalloc2(max * bs2, &mat->rowvalues, max * bs2, &mat->rowindices));
  }
  lrow = row - brstart;

  pvA = &vworkA;
  pcA = &cworkA;
  pvB = &vworkB;
  pcB = &cworkB;
  if (!v) {
    pvA = NULL;
    pvB = NULL;
  }
  if (!idx) {
    pcA = NULL;
    if (!v) pcB = NULL;
  }
  PetscCall((*mat->A->ops->getrow)(mat->A, lrow, &nzA, pcA, pvA));
  PetscCall((*mat->B->ops->getrow)(mat->B, lrow, &nzB, pcB, pvB));
  nztot = nzA + nzB;

  cmap = mat->garray;
  if (v || idx) {
    if (nztot) {
      /* Sort by increasing column numbers, assuming A and B already sorted */
      PetscInt imark = -1;
      if (v) {
        *v = v_p = mat->rowvalues;
        for (i = 0; i < nzB; i++) {
          if (cmap[cworkB[i] / bs] < cstart) v_p[i] = vworkB[i];
          else break;
        }
        imark = i;
        for (i = 0; i < nzA; i++) v_p[imark + i] = vworkA[i];
        for (i = imark; i < nzB; i++) v_p[nzA + i] = vworkB[i];
      }
      if (idx) {
        *idx = idx_p = mat->rowindices;
        if (imark > -1) {
          for (i = 0; i < imark; i++) idx_p[i] = cmap[cworkB[i] / bs] * bs + cworkB[i] % bs;
        } else {
          for (i = 0; i < nzB; i++) {
            if (cmap[cworkB[i] / bs] < cstart) idx_p[i] = cmap[cworkB[i] / bs] * bs + cworkB[i] % bs;
            else break;
          }
          imark = i;
        }
        for (i = 0; i < nzA; i++) idx_p[imark + i] = cstart * bs + cworkA[i];
        for (i = imark; i < nzB; i++) idx_p[nzA + i] = cmap[cworkB[i] / bs] * bs + cworkB[i] % bs;
      }
    } else {
      if (idx) *idx = NULL;
      if (v) *v = NULL;
    }
  }
  *nz = nztot;
  PetscCall((*mat->A->ops->restorerow)(mat->A, lrow, &nzA, pcA, pvA));
  PetscCall((*mat->B->ops->restorerow)(mat->B, lrow, &nzB, pcB, pvB));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatRestoreRow_MPIBAIJ(Mat mat, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;

  PetscFunctionBegin;
  PetscCheck(baij->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "MatGetRow not called");
  baij->getrowactive = PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroEntries_MPIBAIJ(Mat A)
{
  Mat_MPIBAIJ *l = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(MatZeroEntries(l->A));
  PetscCall(MatZeroEntries(l->B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetInfo_MPIBAIJ(Mat matin, MatInfoType flag, MatInfo *info)
{
  Mat_MPIBAIJ   *a = (Mat_MPIBAIJ *)matin->data;
  Mat            A = a->A, B = a->B;
  PetscLogDouble isend[5], irecv[5];

  PetscFunctionBegin;
  info->block_size = (PetscReal)matin->rmap->bs;

  PetscCall(MatGetInfo(A, MAT_LOCAL, info));

  isend[0] = info->nz_used;
  isend[1] = info->nz_allocated;
  isend[2] = info->nz_unneeded;
  isend[3] = info->memory;
  isend[4] = info->mallocs;

  PetscCall(MatGetInfo(B, MAT_LOCAL, info));

  isend[0] += info->nz_used;
  isend[1] += info->nz_allocated;
  isend[2] += info->nz_unneeded;
  isend[3] += info->memory;
  isend[4] += info->mallocs;

  if (flag == MAT_LOCAL) {
    info->nz_used      = isend[0];
    info->nz_allocated = isend[1];
    info->nz_unneeded  = isend[2];
    info->memory       = isend[3];
    info->mallocs      = isend[4];
  } else if (flag == MAT_GLOBAL_MAX) {
    PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)matin)));

    info->nz_used      = irecv[0];
    info->nz_allocated = irecv[1];
    info->nz_unneeded  = irecv[2];
    info->memory       = irecv[3];
    info->mallocs      = irecv[4];
  } else if (flag == MAT_GLOBAL_SUM) {
    PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)matin)));

    info->nz_used      = irecv[0];
    info->nz_allocated = irecv[1];
    info->nz_unneeded  = irecv[2];
    info->memory       = irecv[3];
    info->mallocs      = irecv[4];
  } else SETERRQ(PetscObjectComm((PetscObject)matin), PETSC_ERR_ARG_WRONG, "Unknown MatInfoType argument %d", (int)flag);
  info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
  info->fill_ratio_needed = 0;
  info->factor_mallocs    = 0;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetOption_MPIBAIJ(Mat A, MatOption op, PetscBool flg)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  switch (op) {
  case MAT_NEW_NONZERO_LOCATIONS:
  case MAT_NEW_NONZERO_ALLOCATION_ERR:
  case MAT_UNUSED_NONZERO_LOCATION_ERR:
  case MAT_KEEP_NONZERO_PATTERN:
  case MAT_NEW_NONZERO_LOCATION_ERR:
    MatCheckPreallocated(A, 1);
    PetscCall(MatSetOption(a->A, op, flg));
    PetscCall(MatSetOption(a->B, op, flg));
    break;
  case MAT_ROW_ORIENTED:
    MatCheckPreallocated(A, 1);
    a->roworiented = flg;

    PetscCall(MatSetOption(a->A, op, flg));
    PetscCall(MatSetOption(a->B, op, flg));
    break;
  case MAT_FORCE_DIAGONAL_ENTRIES:
  case MAT_SORTED_FULL:
    PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
    break;
  case MAT_IGNORE_OFF_PROC_ENTRIES:
    a->donotstash = flg;
    break;
  case MAT_USE_HASH_TABLE:
    a->ht_flag = flg;
    a->ht_fact = 1.39;
    break;
  case MAT_SYMMETRIC:
  case MAT_STRUCTURALLY_SYMMETRIC:
  case MAT_HERMITIAN:
  case MAT_SUBMAT_SINGLEIS:
  case MAT_SYMMETRY_ETERNAL:
  case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
  case MAT_SPD_ETERNAL:
    /* if the diagonal matrix is square it inherits some of the properties above */
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "unknown option %d", op);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatTranspose_MPIBAIJ(Mat A, MatReuse reuse, Mat *matout)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)A->data;
  Mat_SeqBAIJ *Aloc;
  Mat          B;
  PetscInt     M = A->rmap->N, N = A->cmap->N, *ai, *aj, i, *rvals, j, k, col;
  PetscInt     bs = A->rmap->bs, mbs = baij->mbs;
  MatScalar   *a;

  PetscFunctionBegin;
  if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *matout));
  if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_INPLACE_MATRIX) {
    PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    PetscCall(MatSetSizes(B, A->cmap->n, A->rmap->n, N, M));
    PetscCall(MatSetType(B, ((PetscObject)A)->type_name));
    /* Do not know preallocation information, but must set block size */
    PetscCall(MatMPIBAIJSetPreallocation(B, A->rmap->bs, PETSC_DECIDE, NULL, PETSC_DECIDE, NULL));
  } else {
    B = *matout;
  }

  /* copy over the A part */
  Aloc = (Mat_SeqBAIJ *)baij->A->data;
  ai   = Aloc->i;
  aj   = Aloc->j;
  a    = Aloc->a;
  PetscCall(PetscMalloc1(bs, &rvals));

  for (i = 0; i < mbs; i++) {
    rvals[0] = bs * (baij->rstartbs + i);
    for (j = 1; j < bs; j++) rvals[j] = rvals[j - 1] + 1;
    for (j = ai[i]; j < ai[i + 1]; j++) {
      col = (baij->cstartbs + aj[j]) * bs;
      for (k = 0; k < bs; k++) {
        PetscCall(MatSetValues_MPIBAIJ(B, 1, &col, bs, rvals, a, INSERT_VALUES));

        col++;
        a += bs;
      }
    }
  }
  /* copy over the B part */
  Aloc = (Mat_SeqBAIJ *)baij->B->data;
  ai   = Aloc->i;
  aj   = Aloc->j;
  a    = Aloc->a;
  for (i = 0; i < mbs; i++) {
    rvals[0] = bs * (baij->rstartbs + i);
    for (j = 1; j < bs; j++) rvals[j] = rvals[j - 1] + 1;
    for (j = ai[i]; j < ai[i + 1]; j++) {
      col = baij->garray[aj[j]] * bs;
      for (k = 0; k < bs; k++) {
        PetscCall(MatSetValues_MPIBAIJ(B, 1, &col, bs, rvals, a, INSERT_VALUES));
        col++;
        a += bs;
      }
    }
  }
  PetscCall(PetscFree(rvals));
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));

  if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) *matout = B;
  else PetscCall(MatHeaderMerge(A, &B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDiagonalScale_MPIBAIJ(Mat mat, Vec ll, Vec rr)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  Mat          a = baij->A, b = baij->B;
  PetscInt     s1, s2, s3;

  PetscFunctionBegin;
  PetscCall(MatGetLocalSize(mat, &s2, &s3));
  if (rr) {
    PetscCall(VecGetLocalSize(rr, &s1));
    PetscCheck(s1 == s3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "right vector non-conforming local size");
    /* Overlap communication with computation. */
    PetscCall(VecScatterBegin(baij->Mvctx, rr, baij->lvec, INSERT_VALUES, SCATTER_FORWARD));
  }
  if (ll) {
    PetscCall(VecGetLocalSize(ll, &s1));
    PetscCheck(s1 == s2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "left vector non-conforming local size");
    PetscUseTypeMethod(b, diagonalscale, ll, NULL);
  }
  /* scale  the diagonal block */
  PetscUseTypeMethod(a, diagonalscale, ll, rr);

  if (rr) {
    /* Do a scatter end and then right scale the off-diagonal block */
    PetscCall(VecScatterEnd(baij->Mvctx, rr, baij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    PetscUseTypeMethod(b, diagonalscale, NULL, baij->lvec);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroRows_MPIBAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
{
  Mat_MPIBAIJ *l = (Mat_MPIBAIJ *)A->data;
  PetscInt    *lrows;
  PetscInt     r, len;
  PetscBool    cong;

  PetscFunctionBegin;
  /* get locally owned rows */
  PetscCall(MatZeroRowsMapLocal_Private(A, N, rows, &len, &lrows));
  /* fix right-hand side if needed */
  if (x && b) {
    const PetscScalar *xx;
    PetscScalar       *bb;

    PetscCall(VecGetArrayRead(x, &xx));
    PetscCall(VecGetArray(b, &bb));
    for (r = 0; r < len; ++r) bb[lrows[r]] = diag * xx[lrows[r]];
    PetscCall(VecRestoreArrayRead(x, &xx));
    PetscCall(VecRestoreArray(b, &bb));
  }

  /* actually zap the local rows */
  /*
        Zero the required rows. If the "diagonal block" of the matrix
     is square and the user wishes to set the diagonal we use separate
     code so that MatSetValues() is not called for each diagonal allocating
     new memory, thus calling lots of mallocs and slowing things down.

  */
  /* must zero l->B before l->A because the (diag) case below may put values into l->B*/
  PetscCall(MatZeroRows_SeqBAIJ(l->B, len, lrows, 0.0, NULL, NULL));
  PetscCall(MatHasCongruentLayouts(A, &cong));
  if ((diag != 0.0) && cong) {
    PetscCall(MatZeroRows_SeqBAIJ(l->A, len, lrows, diag, NULL, NULL));
  } else if (diag != 0.0) {
    PetscCall(MatZeroRows_SeqBAIJ(l->A, len, lrows, 0.0, NULL, NULL));
    PetscCheck(!((Mat_SeqBAIJ *)l->A->data)->nonew, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatZeroRows() on rectangular matrices cannot be used with the Mat options MAT_NEW_NONZERO_LOCATIONS, MAT_NEW_NONZERO_LOCATION_ERR, and MAT_NEW_NONZERO_ALLOCATION_ERR");
    for (r = 0; r < len; ++r) {
      const PetscInt row = lrows[r] + A->rmap->rstart;
      PetscCall(MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES));
    }
    PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  } else {
    PetscCall(MatZeroRows_SeqBAIJ(l->A, len, lrows, 0.0, NULL, NULL));
  }
  PetscCall(PetscFree(lrows));

  /* only change matrix nonzero state if pattern was allowed to be changed */
  if (!((Mat_SeqBAIJ *)l->A->data)->keepnonzeropattern || !((Mat_SeqBAIJ *)l->A->data)->nonew) {
    PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
    PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroRowsColumns_MPIBAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
{
  Mat_MPIBAIJ       *l = (Mat_MPIBAIJ *)A->data;
  PetscMPIInt        n, p = 0;
  PetscInt           i, j, k, r, len = 0, row, col, count;
  PetscInt          *lrows, *owners = A->rmap->range;
  PetscSFNode       *rrows;
  PetscSF            sf;
  const PetscScalar *xx;
  PetscScalar       *bb, *mask;
  Vec                xmask, lmask;
  Mat_SeqBAIJ       *baij = (Mat_SeqBAIJ *)l->B->data;
  PetscInt           bs = A->rmap->bs, bs2 = baij->bs2;
  PetscScalar       *aa;

  PetscFunctionBegin;
  PetscCall(PetscMPIIntCast(A->rmap->n, &n));
  /* Create SF where leaves are input rows and roots are owned rows */
  PetscCall(PetscMalloc1(n, &lrows));
  for (r = 0; r < n; ++r) lrows[r] = -1;
  PetscCall(PetscMalloc1(N, &rrows));
  for (r = 0; r < N; ++r) {
    const PetscInt idx = rows[r];
    PetscCheck(idx >= 0 && A->rmap->N > idx, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row %" PetscInt_FMT " out of range [0,%" PetscInt_FMT ")", idx, A->rmap->N);
    if (idx < owners[p] || owners[p + 1] <= idx) { /* short-circuit the search if the last p owns this row too */
      PetscCall(PetscLayoutFindOwner(A->rmap, idx, &p));
    }
    rrows[r].rank  = p;
    rrows[r].index = rows[r] - owners[p];
  }
  PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
  PetscCall(PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER));
  /* Collect flags for rows to be zeroed */
  PetscCall(PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *)rows, lrows, MPI_LOR));
  PetscCall(PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *)rows, lrows, MPI_LOR));
  PetscCall(PetscSFDestroy(&sf));
  /* Compress and put in row numbers */
  for (r = 0; r < n; ++r)
    if (lrows[r] >= 0) lrows[len++] = r;
  /* zero diagonal part of matrix */
  PetscCall(MatZeroRowsColumns(l->A, len, lrows, diag, x, b));
  /* handle off-diagonal part of matrix */
  PetscCall(MatCreateVecs(A, &xmask, NULL));
  PetscCall(VecDuplicate(l->lvec, &lmask));
  PetscCall(VecGetArray(xmask, &bb));
  for (i = 0; i < len; i++) bb[lrows[i]] = 1;
  PetscCall(VecRestoreArray(xmask, &bb));
  PetscCall(VecScatterBegin(l->Mvctx, xmask, lmask, ADD_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(l->Mvctx, xmask, lmask, ADD_VALUES, SCATTER_FORWARD));
  PetscCall(VecDestroy(&xmask));
  if (x) {
    PetscCall(VecScatterBegin(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecGetArrayRead(l->lvec, &xx));
    PetscCall(VecGetArray(b, &bb));
  }
  PetscCall(VecGetArray(lmask, &mask));
  /* remove zeroed rows of off-diagonal matrix */
  for (i = 0; i < len; ++i) {
    row   = lrows[i];
    count = (baij->i[row / bs + 1] - baij->i[row / bs]) * bs;
    aa    = baij->a + baij->i[row / bs] * bs2 + (row % bs);
    for (k = 0; k < count; ++k) {
      aa[0] = 0.0;
      aa += bs;
    }
  }
  /* loop over all elements of off process part of matrix zeroing removed columns*/
  for (i = 0; i < l->B->rmap->N; ++i) {
    row = i / bs;
    for (j = baij->i[row]; j < baij->i[row + 1]; ++j) {
      for (k = 0; k < bs; ++k) {
        col = bs * baij->j[j] + k;
        if (PetscAbsScalar(mask[col])) {
          aa = baij->a + j * bs2 + (i % bs) + bs * k;
          if (x) bb[i] -= aa[0] * xx[col];
          aa[0] = 0.0;
        }
      }
    }
  }
  if (x) {
    PetscCall(VecRestoreArray(b, &bb));
    PetscCall(VecRestoreArrayRead(l->lvec, &xx));
  }
  PetscCall(VecRestoreArray(lmask, &mask));
  PetscCall(VecDestroy(&lmask));
  PetscCall(PetscFree(lrows));

  /* only change matrix nonzero state if pattern was allowed to be changed */
  if (!((Mat_SeqBAIJ *)l->A->data)->nonew) {
    PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
    PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetUnfactored_MPIBAIJ(Mat A)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(MatSetUnfactored(a->A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDuplicate_MPIBAIJ(Mat, MatDuplicateOption, Mat *);

static PetscErrorCode MatEqual_MPIBAIJ(Mat A, Mat B, PetscBool *flag)
{
  Mat_MPIBAIJ *matB = (Mat_MPIBAIJ *)B->data, *matA = (Mat_MPIBAIJ *)A->data;
  Mat          a, b, c, d;
  PetscBool    flg;

  PetscFunctionBegin;
  a = matA->A;
  b = matA->B;
  c = matB->A;
  d = matB->B;

  PetscCall(MatEqual(a, c, &flg));
  if (flg) PetscCall(MatEqual(b, d, &flg));
  PetscCallMPI(MPIU_Allreduce(&flg, flag, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCopy_MPIBAIJ(Mat A, Mat B, MatStructure str)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;
  Mat_MPIBAIJ *b = (Mat_MPIBAIJ *)B->data;

  PetscFunctionBegin;
  /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
  if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
    PetscCall(MatCopy_Basic(A, B, str));
  } else {
    PetscCall(MatCopy(a->A, b->A, str));
    PetscCall(MatCopy(a->B, b->B, str));
  }
  PetscCall(PetscObjectStateIncrease((PetscObject)B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatAXPYGetPreallocation_MPIBAIJ(Mat Y, const PetscInt *yltog, Mat X, const PetscInt *xltog, PetscInt *nnz)
{
  PetscInt     bs = Y->rmap->bs, m = Y->rmap->N / bs;
  Mat_SeqBAIJ *x = (Mat_SeqBAIJ *)X->data;
  Mat_SeqBAIJ *y = (Mat_SeqBAIJ *)Y->data;

  PetscFunctionBegin;
  PetscCall(MatAXPYGetPreallocation_MPIX_private(m, x->i, x->j, xltog, y->i, y->j, yltog, nnz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAXPY_MPIBAIJ(Mat Y, PetscScalar a, Mat X, MatStructure str)
{
  Mat_MPIBAIJ *xx = (Mat_MPIBAIJ *)X->data, *yy = (Mat_MPIBAIJ *)Y->data;
  PetscBLASInt bnz, one                         = 1;
  Mat_SeqBAIJ *x, *y;
  PetscInt     bs2 = Y->rmap->bs * Y->rmap->bs;

  PetscFunctionBegin;
  if (str == SAME_NONZERO_PATTERN) {
    PetscScalar alpha = a;
    x                 = (Mat_SeqBAIJ *)xx->A->data;
    y                 = (Mat_SeqBAIJ *)yy->A->data;
    PetscCall(PetscBLASIntCast(x->nz * bs2, &bnz));
    PetscCallBLAS("BLASaxpy", BLASaxpy_(&bnz, &alpha, x->a, &one, y->a, &one));
    x = (Mat_SeqBAIJ *)xx->B->data;
    y = (Mat_SeqBAIJ *)yy->B->data;
    PetscCall(PetscBLASIntCast(x->nz * bs2, &bnz));
    PetscCallBLAS("BLASaxpy", BLASaxpy_(&bnz, &alpha, x->a, &one, y->a, &one));
    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_d, *nnz_o, bs = Y->rmap->bs;
    PetscCall(PetscMalloc1(yy->A->rmap->N, &nnz_d));
    PetscCall(PetscMalloc1(yy->B->rmap->N, &nnz_o));
    PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
    PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
    PetscCall(MatSetSizes(B, Y->rmap->n, Y->cmap->n, Y->rmap->N, Y->cmap->N));
    PetscCall(MatSetBlockSizesFromMats(B, Y, Y));
    PetscCall(MatSetType(B, MATMPIBAIJ));
    PetscCall(MatAXPYGetPreallocation_SeqBAIJ(yy->A, xx->A, nnz_d));
    PetscCall(MatAXPYGetPreallocation_MPIBAIJ(yy->B, yy->garray, xx->B, xx->garray, nnz_o));
    PetscCall(MatMPIBAIJSetPreallocation(B, bs, 0, nnz_d, 0, nnz_o));
    /* MatAXPY_BasicWithPreallocation() for BAIJ matrix is much slower than AIJ, even for bs=1 ! */
    PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
    PetscCall(MatHeaderMerge(Y, &B));
    PetscCall(PetscFree(nnz_d));
    PetscCall(PetscFree(nnz_o));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatConjugate_MPIBAIJ(Mat mat)
{
  PetscFunctionBegin;
  if (PetscDefined(USE_COMPLEX)) {
    Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)mat->data;

    PetscCall(MatConjugate_SeqBAIJ(a->A));
    PetscCall(MatConjugate_SeqBAIJ(a->B));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatRealPart_MPIBAIJ(Mat A)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(MatRealPart(a->A));
  PetscCall(MatRealPart(a->B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatImaginaryPart_MPIBAIJ(Mat A)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(MatImaginaryPart(a->A));
  PetscCall(MatImaginaryPart(a->B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCreateSubMatrix_MPIBAIJ(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *newmat)
{
  IS       iscol_local;
  PetscInt csize;

  PetscFunctionBegin;
  PetscCall(ISGetLocalSize(iscol, &csize));
  if (call == MAT_REUSE_MATRIX) {
    PetscCall(PetscObjectQuery((PetscObject)*newmat, "ISAllGather", (PetscObject *)&iscol_local));
    PetscCheck(iscol_local, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
  } else {
    PetscCall(ISAllGather(iscol, &iscol_local));
  }
  PetscCall(MatCreateSubMatrix_MPIBAIJ_Private(mat, isrow, iscol_local, csize, call, newmat, PETSC_FALSE));
  if (call == MAT_INITIAL_MATRIX) {
    PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    PetscCall(ISDestroy(&iscol_local));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Not great since it makes two copies of the submatrix, first an SeqBAIJ
  in local and then by concatenating the local matrices the end result.
  Writing it directly would be much like MatCreateSubMatrices_MPIBAIJ().
  This routine is used for BAIJ and SBAIJ matrices (unfortunate dependency).
*/
PetscErrorCode MatCreateSubMatrix_MPIBAIJ_Private(Mat mat, IS isrow, IS iscol, PetscInt csize, MatReuse call, Mat *newmat, PetscBool sym)
{
  PetscMPIInt  rank, size;
  PetscInt     i, m, n, rstart, row, rend, nz, *cwork, j, bs;
  PetscInt    *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
  Mat          M, Mreuse;
  MatScalar   *vwork, *aa;
  MPI_Comm     comm;
  IS           isrow_new, iscol_new;
  Mat_SeqBAIJ *aij;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
  PetscCallMPI(MPI_Comm_rank(comm, &rank));
  PetscCallMPI(MPI_Comm_size(comm, &size));
  /* The compression and expansion should be avoided. Doesn't point
     out errors, might change the indices, hence buggey */
  PetscCall(ISCompressIndicesGeneral(mat->rmap->N, mat->rmap->n, mat->rmap->bs, 1, &isrow, &isrow_new));
  if (isrow == iscol) {
    iscol_new = isrow_new;
    PetscCall(PetscObjectReference((PetscObject)iscol_new));
  } else PetscCall(ISCompressIndicesGeneral(mat->cmap->N, mat->cmap->n, mat->cmap->bs, 1, &iscol, &iscol_new));

  if (call == MAT_REUSE_MATRIX) {
    PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Mreuse));
    PetscCheck(Mreuse, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    PetscCall(MatCreateSubMatrices_MPIBAIJ_local(mat, 1, &isrow_new, &iscol_new, MAT_REUSE_MATRIX, &Mreuse, sym));
  } else {
    PetscCall(MatCreateSubMatrices_MPIBAIJ_local(mat, 1, &isrow_new, &iscol_new, MAT_INITIAL_MATRIX, &Mreuse, sym));
  }
  PetscCall(ISDestroy(&isrow_new));
  PetscCall(ISDestroy(&iscol_new));
  /*
      m - number of local rows
      n - number of columns (same on all processors)
      rstart - first row in new global matrix generated
  */
  PetscCall(MatGetBlockSize(mat, &bs));
  PetscCall(MatGetSize(Mreuse, &m, &n));
  m = m / bs;
  n = n / bs;

  if (call == MAT_INITIAL_MATRIX) {
    aij = (Mat_SeqBAIJ *)Mreuse->data;
    ii  = aij->i;
    jj  = aij->j;

    /*
        Determine the number of non-zeros in the diagonal and off-diagonal
        portions of the matrix in order to do correct preallocation
    */

    /* first get start and end of "diagonal" columns */
    if (csize == PETSC_DECIDE) {
      PetscCall(ISGetSize(isrow, &mglobal));
      if (mglobal == n * bs) { /* square matrix */
        nlocal = m;
      } else {
        nlocal = n / size + ((n % size) > rank);
      }
    } else {
      nlocal = csize / bs;
    }
    PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    rstart = rend - nlocal;
    PetscCheck(rank != size - 1 || rend == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local column sizes %" PetscInt_FMT " do not add up to total number of columns %" PetscInt_FMT, rend, n);

    /* next, compute all the lengths */
    PetscCall(PetscMalloc2(m + 1, &dlens, m + 1, &olens));
    for (i = 0; i < m; i++) {
      jend = ii[i + 1] - ii[i];
      olen = 0;
      dlen = 0;
      for (j = 0; j < jend; j++) {
        if (*jj < rstart || *jj >= rend) olen++;
        else dlen++;
        jj++;
      }
      olens[i] = olen;
      dlens[i] = dlen;
    }
    PetscCall(MatCreate(comm, &M));
    PetscCall(MatSetSizes(M, bs * m, bs * nlocal, PETSC_DECIDE, bs * n));
    PetscCall(MatSetType(M, sym ? ((PetscObject)mat)->type_name : MATMPIBAIJ));
    PetscCall(MatMPIBAIJSetPreallocation(M, bs, 0, dlens, 0, olens));
    PetscCall(MatMPISBAIJSetPreallocation(M, bs, 0, dlens, 0, olens));
    PetscCall(PetscFree2(dlens, olens));
  } else {
    PetscInt ml, nl;

    M = *newmat;
    PetscCall(MatGetLocalSize(M, &ml, &nl));
    PetscCheck(ml == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    PetscCall(MatZeroEntries(M));
    /*
         The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
       rather than the slower MatSetValues().
    */
    M->was_assembled = PETSC_TRUE;
    M->assembled     = PETSC_FALSE;
  }
  PetscCall(MatSetOption(M, MAT_ROW_ORIENTED, PETSC_FALSE));
  PetscCall(MatGetOwnershipRange(M, &rstart, &rend));
  aij = (Mat_SeqBAIJ *)Mreuse->data;
  ii  = aij->i;
  jj  = aij->j;
  aa  = aij->a;
  for (i = 0; i < m; i++) {
    row   = rstart / bs + i;
    nz    = ii[i + 1] - ii[i];
    cwork = jj;
    jj    = PetscSafePointerPlusOffset(jj, nz);
    vwork = aa;
    aa    = PetscSafePointerPlusOffset(aa, nz * bs * bs);
    PetscCall(MatSetValuesBlocked_MPIBAIJ(M, 1, &row, nz, cwork, vwork, INSERT_VALUES));
  }

  PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
  *newmat = M;

  /* save submatrix used in processor for next request */
  if (call == MAT_INITIAL_MATRIX) {
    PetscCall(PetscObjectCompose((PetscObject)M, "SubMatrix", (PetscObject)Mreuse));
    PetscCall(PetscObjectDereference((PetscObject)Mreuse));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatPermute_MPIBAIJ(Mat A, IS rowp, IS colp, Mat *B)
{
  MPI_Comm        comm, pcomm;
  PetscInt        clocal_size, nrows;
  const PetscInt *rows;
  PetscMPIInt     size;
  IS              crowp, lcolp;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
  /* make a collective version of 'rowp' */
  PetscCall(PetscObjectGetComm((PetscObject)rowp, &pcomm));
  if (pcomm == comm) {
    crowp = rowp;
  } else {
    PetscCall(ISGetSize(rowp, &nrows));
    PetscCall(ISGetIndices(rowp, &rows));
    PetscCall(ISCreateGeneral(comm, nrows, rows, PETSC_COPY_VALUES, &crowp));
    PetscCall(ISRestoreIndices(rowp, &rows));
  }
  PetscCall(ISSetPermutation(crowp));
  /* make a local version of 'colp' */
  PetscCall(PetscObjectGetComm((PetscObject)colp, &pcomm));
  PetscCallMPI(MPI_Comm_size(pcomm, &size));
  if (size == 1) {
    lcolp = colp;
  } else {
    PetscCall(ISAllGather(colp, &lcolp));
  }
  PetscCall(ISSetPermutation(lcolp));
  /* now we just get the submatrix */
  PetscCall(MatGetLocalSize(A, NULL, &clocal_size));
  PetscCall(MatCreateSubMatrix_MPIBAIJ_Private(A, crowp, lcolp, clocal_size, MAT_INITIAL_MATRIX, B, PETSC_FALSE));
  /* clean up */
  if (pcomm != comm) PetscCall(ISDestroy(&crowp));
  if (size > 1) PetscCall(ISDestroy(&lcolp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetGhosts_MPIBAIJ(Mat mat, PetscInt *nghosts, const PetscInt *ghosts[])
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *)mat->data;
  Mat_SeqBAIJ *B    = (Mat_SeqBAIJ *)baij->B->data;

  PetscFunctionBegin;
  if (nghosts) *nghosts = B->nbs;
  if (ghosts) *ghosts = baij->garray;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetSeqNonzeroStructure_MPIBAIJ(Mat A, Mat *newmat)
{
  Mat          B;
  Mat_MPIBAIJ *a  = (Mat_MPIBAIJ *)A->data;
  Mat_SeqBAIJ *ad = (Mat_SeqBAIJ *)a->A->data, *bd = (Mat_SeqBAIJ *)a->B->data;
  Mat_SeqAIJ  *b;
  PetscMPIInt  size, rank, *recvcounts = NULL, *displs = NULL;
  PetscInt     sendcount, i, *rstarts = A->rmap->range, n, cnt, j, bs = A->rmap->bs;
  PetscInt     m, *garray = a->garray, *lens, *jsendbuf, *a_jsendbuf, *b_jsendbuf;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));

  /*   Tell every processor the number of nonzeros per row  */
  PetscCall(PetscMalloc1(A->rmap->N / bs, &lens));
  for (i = A->rmap->rstart / bs; i < A->rmap->rend / bs; i++) lens[i] = ad->i[i - A->rmap->rstart / bs + 1] - ad->i[i - A->rmap->rstart / bs] + bd->i[i - A->rmap->rstart / bs + 1] - bd->i[i - A->rmap->rstart / bs];
  PetscCall(PetscMalloc1(2 * size, &recvcounts));
  displs = recvcounts + size;
  for (i = 0; i < size; i++) {
    PetscCall(PetscMPIIntCast(A->rmap->range[i + 1] / bs - A->rmap->range[i] / bs, &recvcounts[i]));
    PetscCall(PetscMPIIntCast(A->rmap->range[i] / bs, &displs[i]));
  }
  PetscCallMPI(MPI_Allgatherv(MPI_IN_PLACE, 0, MPI_DATATYPE_NULL, lens, recvcounts, displs, MPIU_INT, PetscObjectComm((PetscObject)A)));
  /* Create the sequential matrix of the same type as the local block diagonal  */
  PetscCall(MatCreate(PETSC_COMM_SELF, &B));
  PetscCall(MatSetSizes(B, A->rmap->N / bs, A->cmap->N / bs, PETSC_DETERMINE, PETSC_DETERMINE));
  PetscCall(MatSetType(B, MATSEQAIJ));
  PetscCall(MatSeqAIJSetPreallocation(B, 0, lens));
  b = (Mat_SeqAIJ *)B->data;

  /*     Copy my part of matrix column indices over  */
  sendcount  = ad->nz + bd->nz;
  jsendbuf   = b->j + b->i[rstarts[rank] / bs];
  a_jsendbuf = ad->j;
  b_jsendbuf = bd->j;
  n          = A->rmap->rend / bs - A->rmap->rstart / bs;
  cnt        = 0;
  for (i = 0; i < n; i++) {
    /* put in lower diagonal portion */
    m = bd->i[i + 1] - bd->i[i];
    while (m > 0) {
      /* is it above diagonal (in bd (compressed) numbering) */
      if (garray[*b_jsendbuf] > A->rmap->rstart / bs + i) break;
      jsendbuf[cnt++] = garray[*b_jsendbuf++];
      m--;
    }

    /* put in diagonal portion */
    for (j = ad->i[i]; j < ad->i[i + 1]; j++) jsendbuf[cnt++] = A->rmap->rstart / bs + *a_jsendbuf++;

    /* put in upper diagonal portion */
    while (m-- > 0) jsendbuf[cnt++] = garray[*b_jsendbuf++];
  }
  PetscCheck(cnt == sendcount, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Corrupted PETSc matrix: nz given %" PetscInt_FMT " actual nz %" PetscInt_FMT, sendcount, cnt);

  /*  Gather all column indices to all processors  */
  for (i = 0; i < size; i++) {
    recvcounts[i] = 0;
    for (j = A->rmap->range[i] / bs; j < A->rmap->range[i + 1] / bs; j++) recvcounts[i] += lens[j];
  }
  displs[0] = 0;
  for (i = 1; i < size; i++) displs[i] = displs[i - 1] + recvcounts[i - 1];
  PetscCallMPI(MPI_Allgatherv(MPI_IN_PLACE, 0, MPI_DATATYPE_NULL, b->j, recvcounts, displs, MPIU_INT, PetscObjectComm((PetscObject)A)));
  /*  Assemble the matrix into usable form (note numerical values not yet set)  */
  /* set the b->ilen (length of each row) values */
  PetscCall(PetscArraycpy(b->ilen, lens, A->rmap->N / bs));
  /* set the b->i indices */
  b->i[0] = 0;
  for (i = 1; i <= A->rmap->N / bs; i++) b->i[i] = b->i[i - 1] + lens[i - 1];
  PetscCall(PetscFree(lens));
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  PetscCall(PetscFree(recvcounts));

  PetscCall(MatPropagateSymmetryOptions(A, B));
  *newmat = B;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSOR_MPIBAIJ(Mat matin, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
{
  Mat_MPIBAIJ *mat = (Mat_MPIBAIJ *)matin->data;
  Vec          bb1 = NULL;

  PetscFunctionBegin;
  if (flag == SOR_APPLY_UPPER) {
    PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS) PetscCall(VecDuplicate(bb, &bb1));

  if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
      its--;
    }

    while (its--) {
      PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

      /* update rhs: bb1 = bb - B*x */
      PetscCall(VecScale(mat->lvec, -1.0));
      PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

      /* local sweep */
      PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_SYMMETRIC_SWEEP, fshift, lits, 1, xx));
    }
  } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
      its--;
    }
    while (its--) {
      PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

      /* update rhs: bb1 = bb - B*x */
      PetscCall(VecScale(mat->lvec, -1.0));
      PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

      /* local sweep */
      PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_FORWARD_SWEEP, fshift, lits, 1, xx));
    }
  } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
      its--;
    }
    while (its--) {
      PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

      /* update rhs: bb1 = bb - B*x */
      PetscCall(VecScale(mat->lvec, -1.0));
      PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

      /* local sweep */
      PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_BACKWARD_SWEEP, fshift, lits, 1, xx));
    }
  } else SETERRQ(PetscObjectComm((PetscObject)matin), PETSC_ERR_SUP, "Parallel version of SOR requested not supported");

  PetscCall(VecDestroy(&bb1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetColumnReductions_MPIBAIJ(Mat A, PetscInt type, PetscReal *reductions)
{
  Mat_MPIBAIJ *aij = (Mat_MPIBAIJ *)A->data;
  PetscInt     m, N, i, *garray = aij->garray;
  PetscInt     ib, jb, bs = A->rmap->bs;
  Mat_SeqBAIJ *a_aij = (Mat_SeqBAIJ *)aij->A->data;
  MatScalar   *a_val = a_aij->a;
  Mat_SeqBAIJ *b_aij = (Mat_SeqBAIJ *)aij->B->data;
  MatScalar   *b_val = b_aij->a;
  PetscReal   *work;

  PetscFunctionBegin;
  PetscCall(MatGetSize(A, &m, &N));
  PetscCall(PetscCalloc1(N, &work));
  if (type == NORM_2) {
    for (i = a_aij->i[0]; i < a_aij->i[aij->A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          work[A->cmap->rstart + a_aij->j[i] * bs + jb] += PetscAbsScalar(*a_val * *a_val);
          a_val++;
        }
      }
    }
    for (i = b_aij->i[0]; i < b_aij->i[aij->B->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          work[garray[b_aij->j[i]] * bs + jb] += PetscAbsScalar(*b_val * *b_val);
          b_val++;
        }
      }
    }
  } else if (type == NORM_1) {
    for (i = a_aij->i[0]; i < a_aij->i[aij->A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          work[A->cmap->rstart + a_aij->j[i] * bs + jb] += PetscAbsScalar(*a_val);
          a_val++;
        }
      }
    }
    for (i = b_aij->i[0]; i < b_aij->i[aij->B->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          work[garray[b_aij->j[i]] * bs + jb] += PetscAbsScalar(*b_val);
          b_val++;
        }
      }
    }
  } else if (type == NORM_INFINITY) {
    for (i = a_aij->i[0]; i < a_aij->i[aij->A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          PetscInt col = A->cmap->rstart + a_aij->j[i] * bs + jb;
          work[col]    = PetscMax(PetscAbsScalar(*a_val), work[col]);
          a_val++;
        }
      }
    }
    for (i = b_aij->i[0]; i < b_aij->i[aij->B->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          PetscInt col = garray[b_aij->j[i]] * bs + jb;
          work[col]    = PetscMax(PetscAbsScalar(*b_val), work[col]);
          b_val++;
        }
      }
    }
  } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
    for (i = a_aij->i[0]; i < a_aij->i[aij->A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          work[A->cmap->rstart + a_aij->j[i] * bs + jb] += PetscRealPart(*a_val);
          a_val++;
        }
      }
    }
    for (i = b_aij->i[0]; i < b_aij->i[aij->B->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          work[garray[b_aij->j[i]] * bs + jb] += PetscRealPart(*b_val);
          b_val++;
        }
      }
    }
  } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    for (i = a_aij->i[0]; i < a_aij->i[aij->A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          work[A->cmap->rstart + a_aij->j[i] * bs + jb] += PetscImaginaryPart(*a_val);
          a_val++;
        }
      }
    }
    for (i = b_aij->i[0]; i < b_aij->i[aij->B->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          work[garray[b_aij->j[i]] * bs + jb] += PetscImaginaryPart(*b_val);
          b_val++;
        }
      }
    }
  } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unknown reduction type");
  if (type == NORM_INFINITY) {
    PetscCallMPI(MPIU_Allreduce(work, reductions, N, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)A)));
  } else {
    PetscCallMPI(MPIU_Allreduce(work, reductions, N, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)A)));
  }
  PetscCall(PetscFree(work));
  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(PETSC_SUCCESS);
}

static PetscErrorCode MatInvertBlockDiagonal_MPIBAIJ(Mat A, const PetscScalar **values)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(MatInvertBlockDiagonal(a->A, values));
  A->factorerrortype             = a->A->factorerrortype;
  A->factorerror_zeropivot_value = a->A->factorerror_zeropivot_value;
  A->factorerror_zeropivot_row   = a->A->factorerror_zeropivot_row;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatShift_MPIBAIJ(Mat Y, PetscScalar a)
{
  Mat_MPIBAIJ *maij = (Mat_MPIBAIJ *)Y->data;
  Mat_SeqBAIJ *aij  = (Mat_SeqBAIJ *)maij->A->data;

  PetscFunctionBegin;
  if (!Y->preallocated) {
    PetscCall(MatMPIBAIJSetPreallocation(Y, Y->rmap->bs, 1, NULL, 0, NULL));
  } else if (!aij->nz) {
    PetscInt nonew = aij->nonew;
    PetscCall(MatSeqBAIJSetPreallocation(maij->A, Y->rmap->bs, 1, NULL));
    aij->nonew = nonew;
  }
  PetscCall(MatShift_Basic(Y, a));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMissingDiagonal_MPIBAIJ(Mat A, PetscBool *missing, PetscInt *d)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only works for square matrices");
  PetscCall(MatMissingDiagonal(a->A, missing, d));
  if (d) {
    PetscInt rstart;
    PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
    *d += rstart / A->rmap->bs;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetDiagonalBlock_MPIBAIJ(Mat A, Mat *a)
{
  PetscFunctionBegin;
  *a = ((Mat_MPIBAIJ *)A->data)->A;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatEliminateZeros_MPIBAIJ(Mat A, PetscBool keep)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(MatEliminateZeros_SeqBAIJ(a->A, keep));        // possibly keep zero diagonal coefficients
  PetscCall(MatEliminateZeros_SeqBAIJ(a->B, PETSC_FALSE)); // never keep zero diagonal coefficients
  PetscFunctionReturn(PETSC_SUCCESS);
}

static struct _MatOps MatOps_Values = {MatSetValues_MPIBAIJ,
                                       MatGetRow_MPIBAIJ,
                                       MatRestoreRow_MPIBAIJ,
                                       MatMult_MPIBAIJ,
                                       /* 4*/ MatMultAdd_MPIBAIJ,
                                       MatMultTranspose_MPIBAIJ,
                                       MatMultTransposeAdd_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*10*/ NULL,
                                       NULL,
                                       NULL,
                                       MatSOR_MPIBAIJ,
                                       MatTranspose_MPIBAIJ,
                                       /*15*/ MatGetInfo_MPIBAIJ,
                                       MatEqual_MPIBAIJ,
                                       MatGetDiagonal_MPIBAIJ,
                                       MatDiagonalScale_MPIBAIJ,
                                       MatNorm_MPIBAIJ,
                                       /*20*/ MatAssemblyBegin_MPIBAIJ,
                                       MatAssemblyEnd_MPIBAIJ,
                                       MatSetOption_MPIBAIJ,
                                       MatZeroEntries_MPIBAIJ,
                                       /*24*/ MatZeroRows_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*29*/ MatSetUp_MPI_Hash,
                                       NULL,
                                       NULL,
                                       MatGetDiagonalBlock_MPIBAIJ,
                                       NULL,
                                       /*34*/ MatDuplicate_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*39*/ MatAXPY_MPIBAIJ,
                                       MatCreateSubMatrices_MPIBAIJ,
                                       MatIncreaseOverlap_MPIBAIJ,
                                       MatGetValues_MPIBAIJ,
                                       MatCopy_MPIBAIJ,
                                       /*44*/ NULL,
                                       MatScale_MPIBAIJ,
                                       MatShift_MPIBAIJ,
                                       NULL,
                                       MatZeroRowsColumns_MPIBAIJ,
                                       /*49*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*54*/ MatFDColoringCreate_MPIXAIJ,
                                       NULL,
                                       MatSetUnfactored_MPIBAIJ,
                                       MatPermute_MPIBAIJ,
                                       MatSetValuesBlocked_MPIBAIJ,
                                       /*59*/ MatCreateSubMatrix_MPIBAIJ,
                                       MatDestroy_MPIBAIJ,
                                       MatView_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       /*64*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*69*/ MatGetRowMaxAbs_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*74*/ NULL,
                                       MatFDColoringApply_BAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*79*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       MatLoad_MPIBAIJ,
                                       /*84*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*89*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*94*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*99*/ NULL,
                                       NULL,
                                       NULL,
                                       MatConjugate_MPIBAIJ,
                                       NULL,
                                       /*104*/ NULL,
                                       MatRealPart_MPIBAIJ,
                                       MatImaginaryPart_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       /*109*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       MatMissingDiagonal_MPIBAIJ,
                                       /*114*/ MatGetSeqNonzeroStructure_MPIBAIJ,
                                       NULL,
                                       MatGetGhosts_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       /*119*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       MatGetMultiProcBlock_MPIBAIJ,
                                       /*124*/ NULL,
                                       MatGetColumnReductions_MPIBAIJ,
                                       MatInvertBlockDiagonal_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       /*129*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*134*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*139*/ MatSetBlockSizes_Default,
                                       NULL,
                                       NULL,
                                       MatFDColoringSetUp_MPIXAIJ,
                                       NULL,
                                       /*144*/ MatCreateMPIMatConcatenateSeqMat_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*150*/ NULL,
                                       MatEliminateZeros_MPIBAIJ,
                                       MatGetRowSumAbs_MPIBAIJ,
                                       NULL,
                                       NULL,
                                       /*155*/ NULL,
                                       MatCopyHashToXAIJ_MPI_Hash};

PETSC_INTERN PetscErrorCode MatConvert_MPIBAIJ_MPISBAIJ(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);

static PetscErrorCode MatMPIBAIJSetPreallocationCSR_MPIBAIJ(Mat B, PetscInt bs, const PetscInt ii[], const PetscInt jj[], const PetscScalar V[])
{
  PetscInt        m, rstart, cstart, cend;
  PetscInt        i, j, dlen, olen, nz, nz_max = 0, *d_nnz = NULL, *o_nnz = NULL;
  const PetscInt *JJ          = NULL;
  PetscScalar    *values      = NULL;
  PetscBool       roworiented = ((Mat_MPIBAIJ *)B->data)->roworiented;
  PetscBool       nooffprocentries;

  PetscFunctionBegin;
  PetscCall(PetscLayoutSetBlockSize(B->rmap, bs));
  PetscCall(PetscLayoutSetBlockSize(B->cmap, bs));
  PetscCall(PetscLayoutSetUp(B->rmap));
  PetscCall(PetscLayoutSetUp(B->cmap));
  PetscCall(PetscLayoutGetBlockSize(B->rmap, &bs));
  m      = B->rmap->n / bs;
  rstart = B->rmap->rstart / bs;
  cstart = B->cmap->rstart / bs;
  cend   = B->cmap->rend / bs;

  PetscCheck(!ii[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "ii[0] must be 0 but it is %" PetscInt_FMT, ii[0]);
  PetscCall(PetscMalloc2(m, &d_nnz, m, &o_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);
    nz_max = PetscMax(nz_max, nz);
    dlen   = 0;
    olen   = 0;
    JJ     = jj + ii[i];
    for (j = 0; j < nz; j++) {
      if (*JJ < cstart || *JJ >= cend) olen++;
      else dlen++;
      JJ++;
    }
    d_nnz[i] = dlen;
    o_nnz[i] = olen;
  }
  PetscCall(MatMPIBAIJSetPreallocation(B, bs, 0, d_nnz, 0, o_nnz));
  PetscCall(PetscFree2(d_nnz, o_nnz));

  values = (PetscScalar *)V;
  if (!values) PetscCall(PetscCalloc1(bs * bs * nz_max, &values));
  for (i = 0; i < m; i++) {
    PetscInt        row   = i + rstart;
    PetscInt        ncols = ii[i + 1] - ii[i];
    const PetscInt *icols = jj + ii[i];
    if (bs == 1 || !roworiented) { /* block ordering matches the non-nested layout of MatSetValues so we can insert entire rows */
      const PetscScalar *svals = values + (V ? (bs * bs * ii[i]) : 0);
      PetscCall(MatSetValuesBlocked_MPIBAIJ(B, 1, &row, ncols, icols, svals, INSERT_VALUES));
    } else { /* block ordering does not match so we can only insert one block at a time. */
      PetscInt j;
      for (j = 0; j < ncols; j++) {
        const PetscScalar *svals = values + (V ? (bs * bs * (ii[i] + j)) : 0);
        PetscCall(MatSetValuesBlocked_MPIBAIJ(B, 1, &row, 1, &icols[j], svals, INSERT_VALUES));
      }
    }
  }

  if (!V) PetscCall(PetscFree(values));
  nooffprocentries    = B->nooffprocentries;
  B->nooffprocentries = PETSC_TRUE;
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  B->nooffprocentries = nooffprocentries;

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

/*@C
  MatMPIBAIJSetPreallocationCSR - Creates a sparse parallel matrix in `MATBAIJ` format using the given nonzero structure and (optional) numerical values

  Collective

  Input Parameters:
+ B  - the matrix
. bs - the block size
. i  - the indices into `j` for the start of each local row (starts with zero)
. j  - the column indices for each local row (starts with zero) these must be sorted for each row
- v  - optional values in the matrix, use `NULL` if not provided

  Level: advanced

  Notes:
  The `i`, `j`, and `v` arrays ARE copied by this routine into the internal format used by PETSc;
  thus you CANNOT change the matrix entries by changing the values of `v` after you have
  called this routine.

  The order of the entries in values is specified by the `MatOption` `MAT_ROW_ORIENTED`.  For example, C programs
  may want to use the default `MAT_ROW_ORIENTED` with value `PETSC_TRUE` and use an array v[nnz][bs][bs] where the second index is
  over rows within a block and the last index is over columns within a block row.  Fortran programs will likely set
  `MAT_ROW_ORIENTED` with value `PETSC_FALSE` and use a Fortran array v(bs,bs,nnz) in which the first index is over rows within a
  block column and the second index is over columns within a block.

  Though this routine has Preallocation() in the name it also sets the exact nonzero locations of the matrix entries and usually the numerical values as well

.seealso: `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIBAIJSetPreallocation()`, `MatCreateAIJ()`, `MATMPIAIJ`, `MatCreateMPIBAIJWithArrays()`, `MATMPIBAIJ`
@*/
PetscErrorCode MatMPIBAIJSetPreallocationCSR(Mat B, PetscInt bs, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
  PetscValidType(B, 1);
  PetscValidLogicalCollectiveInt(B, bs, 2);
  PetscTryMethod(B, "MatMPIBAIJSetPreallocationCSR_C", (Mat, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, bs, i, j, v));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatMPIBAIJSetPreallocation_MPIBAIJ(Mat B, PetscInt bs, PetscInt d_nz, const PetscInt *d_nnz, PetscInt o_nz, const PetscInt *o_nnz)
{
  Mat_MPIBAIJ *b = (Mat_MPIBAIJ *)B->data;
  PetscInt     i;
  PetscMPIInt  size;

  PetscFunctionBegin;
  if (B->hash_active) {
    B->ops[0]      = b->cops;
    B->hash_active = PETSC_FALSE;
  }
  if (!B->preallocated) PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)B), bs, &B->bstash));
  PetscCall(MatSetBlockSize(B, PetscAbs(bs)));
  PetscCall(PetscLayoutSetUp(B->rmap));
  PetscCall(PetscLayoutSetUp(B->cmap));
  PetscCall(PetscLayoutGetBlockSize(B->rmap, &bs));

  if (d_nnz) {
    for (i = 0; i < B->rmap->n / bs; i++) PetscCheck(d_nnz[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "d_nnz cannot be less than -1: local row %" PetscInt_FMT " value %" PetscInt_FMT, i, d_nnz[i]);
  }
  if (o_nnz) {
    for (i = 0; i < B->rmap->n / bs; i++) PetscCheck(o_nnz[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "o_nnz cannot be less than -1: local row %" PetscInt_FMT " value %" PetscInt_FMT, i, o_nnz[i]);
  }

  b->bs2 = bs * bs;
  b->mbs = B->rmap->n / bs;
  b->nbs = B->cmap->n / bs;
  b->Mbs = B->rmap->N / bs;
  b->Nbs = B->cmap->N / bs;

  for (i = 0; i <= b->size; i++) b->rangebs[i] = B->rmap->range[i] / bs;
  b->rstartbs = B->rmap->rstart / bs;
  b->rendbs   = B->rmap->rend / bs;
  b->cstartbs = B->cmap->rstart / bs;
  b->cendbs   = B->cmap->rend / bs;

#if defined(PETSC_USE_CTABLE)
  PetscCall(PetscHMapIDestroy(&b->colmap));
#else
  PetscCall(PetscFree(b->colmap));
#endif
  PetscCall(PetscFree(b->garray));
  PetscCall(VecDestroy(&b->lvec));
  PetscCall(VecScatterDestroy(&b->Mvctx));

  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

  MatSeqXAIJGetOptions_Private(b->B);
  PetscCall(MatDestroy(&b->B));
  PetscCall(MatCreate(PETSC_COMM_SELF, &b->B));
  PetscCall(MatSetSizes(b->B, B->rmap->n, size > 1 ? B->cmap->N : 0, B->rmap->n, size > 1 ? B->cmap->N : 0));
  PetscCall(MatSetType(b->B, MATSEQBAIJ));
  MatSeqXAIJRestoreOptions_Private(b->B);

  MatSeqXAIJGetOptions_Private(b->A);
  PetscCall(MatDestroy(&b->A));
  PetscCall(MatCreate(PETSC_COMM_SELF, &b->A));
  PetscCall(MatSetSizes(b->A, B->rmap->n, B->cmap->n, B->rmap->n, B->cmap->n));
  PetscCall(MatSetType(b->A, MATSEQBAIJ));
  MatSeqXAIJRestoreOptions_Private(b->A);

  PetscCall(MatSeqBAIJSetPreallocation(b->A, bs, d_nz, d_nnz));
  PetscCall(MatSeqBAIJSetPreallocation(b->B, bs, o_nz, o_nnz));
  B->preallocated  = PETSC_TRUE;
  B->was_assembled = PETSC_FALSE;
  B->assembled     = PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

extern PetscErrorCode MatDiagonalScaleLocal_MPIBAIJ(Mat, Vec);
extern PetscErrorCode MatSetHashTableFactor_MPIBAIJ(Mat, PetscReal);

PETSC_INTERN PetscErrorCode MatConvert_MPIBAIJ_MPIAdj(Mat B, MatType newtype, MatReuse reuse, Mat *adj)
{
  Mat_MPIBAIJ    *b = (Mat_MPIBAIJ *)B->data;
  Mat_SeqBAIJ    *d = (Mat_SeqBAIJ *)b->A->data, *o = (Mat_SeqBAIJ *)b->B->data;
  PetscInt        M = B->rmap->n / B->rmap->bs, i, *ii, *jj, cnt, j, k, rstart = B->rmap->rstart / B->rmap->bs;
  const PetscInt *id = d->i, *jd = d->j, *io = o->i, *jo = o->j, *garray = b->garray;

  PetscFunctionBegin;
  PetscCall(PetscMalloc1(M + 1, &ii));
  ii[0] = 0;
  for (i = 0; i < M; i++) {
    PetscCheck((id[i + 1] - id[i]) >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Indices wrong %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT, i, id[i], id[i + 1]);
    PetscCheck((io[i + 1] - io[i]) >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Indices wrong %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT, i, io[i], io[i + 1]);
    ii[i + 1] = ii[i] + id[i + 1] - id[i] + io[i + 1] - io[i];
    /* remove one from count of matrix has diagonal */
    for (j = id[i]; j < id[i + 1]; j++) {
      if (jd[j] == i) {
        ii[i + 1]--;
        break;
      }
    }
  }
  PetscCall(PetscMalloc1(ii[M], &jj));
  cnt = 0;
  for (i = 0; i < M; i++) {
    for (j = io[i]; j < io[i + 1]; j++) {
      if (garray[jo[j]] > rstart) break;
      jj[cnt++] = garray[jo[j]];
    }
    for (k = id[i]; k < id[i + 1]; k++) {
      if (jd[k] != i) jj[cnt++] = rstart + jd[k];
    }
    for (; j < io[i + 1]; j++) jj[cnt++] = garray[jo[j]];
  }
  PetscCall(MatCreateMPIAdj(PetscObjectComm((PetscObject)B), M, B->cmap->N / B->rmap->bs, ii, jj, NULL, adj));
  PetscFunctionReturn(PETSC_SUCCESS);
}

#include <../src/mat/impls/aij/mpi/mpiaij.h>

PETSC_INTERN PetscErrorCode MatConvert_SeqBAIJ_SeqAIJ(Mat, MatType, MatReuse, Mat *);

PETSC_INTERN PetscErrorCode MatConvert_MPIBAIJ_MPIAIJ(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;
  Mat_MPIAIJ  *b;
  Mat          B;

  PetscFunctionBegin;
  PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Matrix must be assembled");

  if (reuse == MAT_REUSE_MATRIX) {
    B = *newmat;
  } else {
    PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    PetscCall(MatSetType(B, MATMPIAIJ));
    PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    PetscCall(MatSetBlockSizes(B, A->rmap->bs, A->cmap->bs));
    PetscCall(MatSeqAIJSetPreallocation(B, 0, NULL));
    PetscCall(MatMPIAIJSetPreallocation(B, 0, NULL, 0, NULL));
  }
  b = (Mat_MPIAIJ *)B->data;

  if (reuse == MAT_REUSE_MATRIX) {
    PetscCall(MatConvert_SeqBAIJ_SeqAIJ(a->A, MATSEQAIJ, MAT_REUSE_MATRIX, &b->A));
    PetscCall(MatConvert_SeqBAIJ_SeqAIJ(a->B, MATSEQAIJ, MAT_REUSE_MATRIX, &b->B));
  } else {
    PetscInt   *garray = a->garray;
    Mat_SeqAIJ *bB;
    PetscInt    bs, nnz;
    PetscCall(MatDestroy(&b->A));
    PetscCall(MatDestroy(&b->B));
    /* just clear out the data structure */
    PetscCall(MatDisAssemble_MPIAIJ(B, PETSC_FALSE));
    PetscCall(MatConvert_SeqBAIJ_SeqAIJ(a->A, MATSEQAIJ, MAT_INITIAL_MATRIX, &b->A));
    PetscCall(MatConvert_SeqBAIJ_SeqAIJ(a->B, MATSEQAIJ, MAT_INITIAL_MATRIX, &b->B));

    /* Global numbering for b->B columns */
    bB  = (Mat_SeqAIJ *)b->B->data;
    bs  = A->rmap->bs;
    nnz = bB->i[A->rmap->n];
    for (PetscInt k = 0; k < nnz; k++) {
      PetscInt bj = bB->j[k] / bs;
      PetscInt br = bB->j[k] % bs;
      bB->j[k]    = garray[bj] * bs + br;
    }
  }
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));

  if (reuse == MAT_INPLACE_MATRIX) {
    PetscCall(MatHeaderReplace(A, &B));
  } else {
    *newmat = B;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
   MATMPIBAIJ - MATMPIBAIJ = "mpibaij" - A matrix type to be used for distributed block sparse matrices.

   Options Database Keys:
+ -mat_type mpibaij - sets the matrix type to `MATMPIBAIJ` during a call to `MatSetFromOptions()`
. -mat_block_size <bs> - set the blocksize used to store the matrix
. -mat_baij_mult_version version - indicate the version of the matrix-vector product to use  (0 often indicates using BLAS)
- -mat_use_hash_table <fact> - set hash table factor

   Level: beginner

   Note:
    `MatSetOption(A, 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

.seealso: `Mat`, `MATBAIJ`, `MATSEQBAIJ`, `MatCreateBAIJ`
M*/

PETSC_INTERN PetscErrorCode MatConvert_MPIBAIJ_MPIBSTRM(Mat, MatType, MatReuse, Mat *);

PETSC_EXTERN PetscErrorCode MatCreate_MPIBAIJ(Mat B)
{
  Mat_MPIBAIJ *b;
  PetscBool    flg = PETSC_FALSE;

  PetscFunctionBegin;
  PetscCall(PetscNew(&b));
  B->data      = (void *)b;
  B->ops[0]    = MatOps_Values;
  B->assembled = PETSC_FALSE;

  B->insertmode = NOT_SET_VALUES;
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)B), &b->rank));
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &b->size));

  /* build local table of row and column ownerships */
  PetscCall(PetscMalloc1(b->size + 1, &b->rangebs));

  /* build cache for off array entries formed */
  PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)B), 1, &B->stash));

  b->donotstash  = PETSC_FALSE;
  b->colmap      = NULL;
  b->garray      = NULL;
  b->roworiented = PETSC_TRUE;

  /* stuff used in block assembly */
  b->barray = NULL;

  /* stuff used for matrix vector multiply */
  b->lvec  = NULL;
  b->Mvctx = NULL;

  /* stuff for MatGetRow() */
  b->rowindices   = NULL;
  b->rowvalues    = NULL;
  b->getrowactive = PETSC_FALSE;

  /* hash table stuff */
  b->ht           = NULL;
  b->hd           = NULL;
  b->ht_size      = 0;
  b->ht_flag      = PETSC_FALSE;
  b->ht_fact      = 0;
  b->ht_total_ct  = 0;
  b->ht_insert_ct = 0;

  /* stuff for MatCreateSubMatrices_MPIBAIJ_local() */
  b->ijonly = PETSC_FALSE;

  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpibaij_mpiadj_C", MatConvert_MPIBAIJ_MPIAdj));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpibaij_mpiaij_C", MatConvert_MPIBAIJ_MPIAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpibaij_mpisbaij_C", MatConvert_MPIBAIJ_MPISBAIJ));
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpibaij_hypre_C", MatConvert_AIJ_HYPRE));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_MPIBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_MPIBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIBAIJSetPreallocation_C", MatMPIBAIJSetPreallocation_MPIBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIBAIJSetPreallocationCSR_C", MatMPIBAIJSetPreallocationCSR_MPIBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDiagonalScaleLocal_C", MatDiagonalScaleLocal_MPIBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetHashTableFactor_C", MatSetHashTableFactor_MPIBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpibaij_is_C", MatConvert_XAIJ_IS));
  PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATMPIBAIJ));

  PetscOptionsBegin(PetscObjectComm((PetscObject)B), NULL, "Options for loading MPIBAIJ matrix 1", "Mat");
  PetscCall(PetscOptionsName("-mat_use_hash_table", "Use hash table to save time in constructing matrix", "MatSetOption", &flg));
  if (flg) {
    PetscReal fact = 1.39;
    PetscCall(MatSetOption(B, MAT_USE_HASH_TABLE, PETSC_TRUE));
    PetscCall(PetscOptionsReal("-mat_use_hash_table", "Use hash table factor", "MatMPIBAIJSetHashTableFactor", fact, &fact, NULL));
    if (fact <= 1.0) fact = 1.39;
    PetscCall(MatMPIBAIJSetHashTableFactor(B, fact));
    PetscCall(PetscInfo(B, "Hash table Factor used %5.2g\n", (double)fact));
  }
  PetscOptionsEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

// PetscClangLinter pragma disable: -fdoc-section-header-unknown
/*MC
   MATBAIJ - MATBAIJ = "baij" - A matrix type to be used for block sparse matrices.

   This matrix type is identical to `MATSEQBAIJ` when constructed with a single process communicator,
   and `MATMPIBAIJ` otherwise.

   Options Database Keys:
. -mat_type baij - sets the matrix type to `MATBAIJ` during a call to `MatSetFromOptions()`

  Level: beginner

.seealso: `Mat`, `MatCreateBAIJ()`, `MATSEQBAIJ`, `MATMPIBAIJ`, `MatMPIBAIJSetPreallocation()`, `MatMPIBAIJSetPreallocationCSR()`
M*/

/*@
  MatMPIBAIJSetPreallocation - Allocates memory for a sparse parallel matrix in `MATMPIBAIJ` format
  (block compressed row).

  Collective

  Input Parameters:
+ B     - the matrix
. bs    - size of block, the blocks are ALWAYS square. One can use `MatSetBlockSizes()` to set a different row and column blocksize but the row
          blocksize always defines the size of the blocks. The column blocksize sets the blocksize of the vectors obtained with `MatCreateVecs()`
. d_nz  - number of block nonzeros per block row in diagonal portion of local
           submatrix  (same for all local rows)
. d_nnz - array containing the number of block nonzeros in the various block rows
           of the in diagonal portion of the local (possibly different for each block
           row) or `NULL`.  If you plan to factor the matrix you must leave room for the diagonal entry and
           set it even if it is zero.
. o_nz  - number of block nonzeros per block row in the off-diagonal portion of local
           submatrix (same for all local rows).
- o_nnz - array containing the number of nonzeros in the various block rows of the
           off-diagonal portion of the local submatrix (possibly different for
           each block row) or `NULL`.

   If the *_nnz parameter is given then the *_nz parameter is ignored

  Options Database Keys:
+ -mat_block_size            - size of the blocks to use
- -mat_use_hash_table <fact> - set hash table factor

  Level: intermediate

  Notes:
  For good matrix assembly performance
  the user should preallocate the matrix storage by setting the parameters
  `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).  By setting these parameters accurately,
  performance can be increased by more than a factor of 50.

  If `PETSC_DECIDE` or  `PETSC_DETERMINE` is used for a particular argument on one processor
  than it must be used on all processors that share the object for that argument.

  Storage Information:
  For a square global matrix we define each processor's diagonal portion
  to be its local rows and the corresponding columns (a square submatrix);
  each processor's off-diagonal portion encompasses the remainder of the
  local matrix (a rectangular submatrix).

  The user can specify preallocated storage for the diagonal part of
  the local submatrix with either `d_nz` or `d_nnz` (not both).  Set
  `d_nz` = `PETSC_DEFAULT` and `d_nnz` = `NULL` for PETSc to control dynamic
  memory allocation.  Likewise, specify preallocated storage for the
  off-diagonal part of the local submatrix with `o_nz` or `o_nnz` (not both).

  Consider a processor that owns rows 3, 4 and 5 of a parallel matrix. In
  the figure below we depict these three local rows and all columns (0-11).

.vb
           0 1 2 3 4 5 6 7 8 9 10 11
          --------------------------
   row 3  |o o o d d d o o o o  o  o
   row 4  |o o o d d d o o o o  o  o
   row 5  |o o o d d d o o o o  o  o
          --------------------------
.ve

  Thus, any entries in the d locations are stored in the d (diagonal)
  submatrix, and any entries in the o locations are stored in the
  o (off-diagonal) submatrix.  Note that the d and the o submatrices are
  stored simply in the `MATSEQBAIJ` format for compressed row storage.

  Now `d_nz` should indicate the number of block nonzeros per row in the d matrix,
  and `o_nz` should indicate the number of block nonzeros per row in the o matrix.
  In general, for PDE problems in which most nonzeros are near the diagonal,
  one expects `d_nz` >> `o_nz`.

  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.

.seealso: `Mat`, `MATMPIBAIJ`, `MatCreate()`, `MatCreateSeqBAIJ()`, `MatSetValues()`, `MatCreateBAIJ()`, `MatMPIBAIJSetPreallocationCSR()`, `PetscSplitOwnership()`
@*/
PetscErrorCode MatMPIBAIJSetPreallocation(Mat B, PetscInt bs, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
  PetscValidType(B, 1);
  PetscValidLogicalCollectiveInt(B, bs, 2);
  PetscTryMethod(B, "MatMPIBAIJSetPreallocation_C", (Mat, PetscInt, PetscInt, const PetscInt[], PetscInt, const PetscInt[]), (B, bs, d_nz, d_nnz, o_nz, o_nnz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// PetscClangLinter pragma disable: -fdoc-section-header-unknown
/*@
  MatCreateBAIJ - Creates a sparse parallel matrix in `MATBAIJ` format
  (block compressed row).

  Collective

  Input Parameters:
+ comm  - MPI communicator
. bs    - size of block, the blocks are ALWAYS square. One can use `MatSetBlockSizes()` to set a different row and column blocksize but the row
          blocksize always defines the size of the blocks. The column blocksize sets the blocksize of the vectors obtained with `MatCreateVecs()`
. m     - number of local rows (or `PETSC_DECIDE` to have calculated if M is given)
          This value should be the same as the local size used in creating the
          y vector for the matrix-vector product y = Ax.
. n     - number of local columns (or `PETSC_DECIDE` to have calculated if N is given)
          This value should be the same as the local size used in creating the
          x vector for the matrix-vector product y = Ax.
. M     - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
. N     - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
. d_nz  - number of nonzero blocks per block row in diagonal portion of local
          submatrix  (same for all local rows)
. d_nnz - array containing the number of nonzero blocks in the various block rows
          of the in diagonal portion of the local (possibly different for each block
          row) or NULL.  If you plan to factor the matrix you must leave room for the diagonal entry
          and set it even if it is zero.
. o_nz  - number of nonzero blocks per block row in the off-diagonal portion of local
          submatrix (same for all local rows).
- o_nnz - array containing the number of nonzero blocks in the various block rows of the
          off-diagonal portion of the local submatrix (possibly different for
          each block row) or NULL.

  Output Parameter:
. A - the matrix

  Options Database Keys:
+ -mat_block_size            - size of the blocks to use
- -mat_use_hash_table <fact> - set hash table factor

  Level: intermediate

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

  For good matrix assembly performance
  the user should preallocate the matrix storage by setting the parameters
  `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).  By setting these parameters accurately,
  performance can be increased by more than a factor of 50.

  If the *_nnz parameter is given then the *_nz parameter is ignored

  A nonzero block is any block that as 1 or more nonzeros in it

  The user MUST specify either the local or global matrix dimensions
  (possibly both).

  If `PETSC_DECIDE` or  `PETSC_DETERMINE` is used for a particular argument on one processor
  than it must be used on all processors that share the object for that argument.

  If `m` and `n` are not `PETSC_DECIDE`, then the values determine the `PetscLayout` of the matrix and the ranges returned by
  `MatGetOwnershipRange()`,  `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`, and `MatGetOwnershipRangesColumn()`.

  Storage Information:
  For a square global matrix we define each processor's diagonal portion
  to be its local rows and the corresponding columns (a square submatrix);
  each processor's off-diagonal portion encompasses the remainder of the
  local matrix (a rectangular submatrix).

  The user can specify preallocated storage for the diagonal part of
  the local submatrix with either d_nz or d_nnz (not both).  Set
  `d_nz` = `PETSC_DEFAULT` and `d_nnz` = `NULL` for PETSc to control dynamic
  memory allocation.  Likewise, specify preallocated storage for the
  off-diagonal part of the local submatrix with `o_nz` or `o_nnz` (not both).

  Consider a processor that owns rows 3, 4 and 5 of a parallel matrix. In
  the figure below we depict these three local rows and all columns (0-11).

.vb
           0 1 2 3 4 5 6 7 8 9 10 11
          --------------------------
   row 3  |o o o d d d o o o o  o  o
   row 4  |o o o d d d o o o o  o  o
   row 5  |o o o d d d o o o o  o  o
          --------------------------
.ve

  Thus, any entries in the d locations are stored in the d (diagonal)
  submatrix, and any entries in the o locations are stored in the
  o (off-diagonal) submatrix.  Note that the d and the o submatrices are
  stored simply in the `MATSEQBAIJ` format for compressed row storage.

  Now `d_nz` should indicate the number of block nonzeros per row in the d matrix,
  and `o_nz` should indicate the number of block nonzeros per row in the o matrix.
  In general, for PDE problems in which most nonzeros are near the diagonal,
  one expects `d_nz` >> `o_nz`.

.seealso: `Mat`, `MatCreate()`, `MatCreateSeqBAIJ()`, `MatSetValues()`, `MatMPIBAIJSetPreallocation()`, `MatMPIBAIJSetPreallocationCSR()`,
          `MatGetOwnershipRange()`,  `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`, `MatGetOwnershipRangesColumn()`, `PetscLayout`
@*/
PetscErrorCode MatCreateBAIJ(MPI_Comm comm, PetscInt bs, PetscInt m, PetscInt n, PetscInt M, PetscInt N, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[], Mat *A)
{
  PetscMPIInt size;

  PetscFunctionBegin;
  PetscCall(MatCreate(comm, A));
  PetscCall(MatSetSizes(*A, m, n, M, N));
  PetscCallMPI(MPI_Comm_size(comm, &size));
  if (size > 1) {
    PetscCall(MatSetType(*A, MATMPIBAIJ));
    PetscCall(MatMPIBAIJSetPreallocation(*A, bs, d_nz, d_nnz, o_nz, o_nnz));
  } else {
    PetscCall(MatSetType(*A, MATSEQBAIJ));
    PetscCall(MatSeqBAIJSetPreallocation(*A, bs, d_nz, d_nnz));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDuplicate_MPIBAIJ(Mat matin, MatDuplicateOption cpvalues, Mat *newmat)
{
  Mat          mat;
  Mat_MPIBAIJ *a, *oldmat = (Mat_MPIBAIJ *)matin->data;
  PetscInt     len = 0;

  PetscFunctionBegin;
  *newmat = NULL;
  PetscCall(MatCreate(PetscObjectComm((PetscObject)matin), &mat));
  PetscCall(MatSetSizes(mat, matin->rmap->n, matin->cmap->n, matin->rmap->N, matin->cmap->N));
  PetscCall(MatSetType(mat, ((PetscObject)matin)->type_name));

  PetscCall(PetscLayoutReference(matin->rmap, &mat->rmap));
  PetscCall(PetscLayoutReference(matin->cmap, &mat->cmap));
  if (matin->hash_active) {
    PetscCall(MatSetUp(mat));
  } else {
    mat->factortype   = matin->factortype;
    mat->preallocated = PETSC_TRUE;
    mat->assembled    = PETSC_TRUE;
    mat->insertmode   = NOT_SET_VALUES;

    a             = (Mat_MPIBAIJ *)mat->data;
    mat->rmap->bs = matin->rmap->bs;
    a->bs2        = oldmat->bs2;
    a->mbs        = oldmat->mbs;
    a->nbs        = oldmat->nbs;
    a->Mbs        = oldmat->Mbs;
    a->Nbs        = oldmat->Nbs;

    a->size         = oldmat->size;
    a->rank         = oldmat->rank;
    a->donotstash   = oldmat->donotstash;
    a->roworiented  = oldmat->roworiented;
    a->rowindices   = NULL;
    a->rowvalues    = NULL;
    a->getrowactive = PETSC_FALSE;
    a->barray       = NULL;
    a->rstartbs     = oldmat->rstartbs;
    a->rendbs       = oldmat->rendbs;
    a->cstartbs     = oldmat->cstartbs;
    a->cendbs       = oldmat->cendbs;

    /* hash table stuff */
    a->ht           = NULL;
    a->hd           = NULL;
    a->ht_size      = 0;
    a->ht_flag      = oldmat->ht_flag;
    a->ht_fact      = oldmat->ht_fact;
    a->ht_total_ct  = 0;
    a->ht_insert_ct = 0;

    PetscCall(PetscArraycpy(a->rangebs, oldmat->rangebs, a->size + 1));
    if (oldmat->colmap) {
#if defined(PETSC_USE_CTABLE)
      PetscCall(PetscHMapIDuplicate(oldmat->colmap, &a->colmap));
#else
      PetscCall(PetscMalloc1(a->Nbs, &a->colmap));
      PetscCall(PetscArraycpy(a->colmap, oldmat->colmap, a->Nbs));
#endif
    } else a->colmap = NULL;

    if (oldmat->garray && (len = ((Mat_SeqBAIJ *)oldmat->B->data)->nbs)) {
      PetscCall(PetscMalloc1(len, &a->garray));
      PetscCall(PetscArraycpy(a->garray, oldmat->garray, len));
    } else a->garray = NULL;

    PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)matin), matin->rmap->bs, &mat->bstash));
    PetscCall(VecDuplicate(oldmat->lvec, &a->lvec));
    PetscCall(VecScatterCopy(oldmat->Mvctx, &a->Mvctx));

    PetscCall(MatDuplicate(oldmat->A, cpvalues, &a->A));
    PetscCall(MatDuplicate(oldmat->B, cpvalues, &a->B));
  }
  PetscCall(PetscFunctionListDuplicate(((PetscObject)matin)->qlist, &((PetscObject)mat)->qlist));
  *newmat = mat;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Used for both MPIBAIJ and MPISBAIJ matrices */
PetscErrorCode MatLoad_MPIBAIJ_Binary(Mat mat, PetscViewer viewer)
{
  PetscInt     header[4], M, N, nz, bs, m, n, mbs, nbs, rows, cols, sum, i, j, k;
  PetscInt    *rowidxs, *colidxs, rs, cs, ce;
  PetscScalar *matvals;

  PetscFunctionBegin;
  PetscCall(PetscViewerSetUp(viewer));

  /* read in matrix header */
  PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
  PetscCheck(header[0] == MAT_FILE_CLASSID, PetscObjectComm((PetscObject)viewer), 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 MPIBAIJ");

  /* set block sizes from the viewer's .info file */
  PetscCall(MatLoad_Binary_BlockSizes(mat, viewer));
  /* set local sizes if not set already */
  if (mat->rmap->n < 0 && M == N) mat->rmap->n = mat->cmap->n;
  if (mat->cmap->n < 0 && M == N) mat->cmap->n = mat->rmap->n;
  /* set global sizes if not set already */
  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);
  PetscCall(MatGetBlockSize(mat, &bs));
  PetscCall(MatGetLocalSize(mat, &m, &n));
  PetscCall(PetscLayoutGetRange(mat->rmap, &rs, NULL));
  PetscCall(PetscLayoutGetRange(mat->cmap, &cs, &ce));
  mbs = m / bs;
  nbs = n / bs;

  /* read in row lengths and build row indices */
  PetscCall(PetscMalloc1(m + 1, &rowidxs));
  PetscCall(PetscViewerBinaryReadAll(viewer, rowidxs + 1, m, PETSC_DECIDE, M, PETSC_INT));
  rowidxs[0] = 0;
  for (i = 0; i < m; i++) rowidxs[i + 1] += rowidxs[i];
  PetscCallMPI(MPIU_Allreduce(&rowidxs[m], &sum, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)viewer)));
  PetscCheck(sum == nz, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Inconsistent matrix data in file: nonzeros = %" PetscInt_FMT ", sum-row-lengths = %" PetscInt_FMT, nz, sum);

  /* read in column indices and matrix values */
  PetscCall(PetscMalloc2(rowidxs[m], &colidxs, rowidxs[m], &matvals));
  PetscCall(PetscViewerBinaryReadAll(viewer, colidxs, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
  PetscCall(PetscViewerBinaryReadAll(viewer, matvals, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));

  {                /* preallocate matrix storage */
    PetscBT    bt; /* helper bit set to count diagonal nonzeros */
    PetscHSetI ht; /* helper hash set to count off-diagonal nonzeros */
    PetscBool  sbaij, done;
    PetscInt  *d_nnz, *o_nnz;

    PetscCall(PetscBTCreate(nbs, &bt));
    PetscCall(PetscHSetICreate(&ht));
    PetscCall(PetscCalloc2(mbs, &d_nnz, mbs, &o_nnz));
    PetscCall(PetscObjectTypeCompare((PetscObject)mat, MATMPISBAIJ, &sbaij));
    for (i = 0; i < mbs; i++) {
      PetscCall(PetscBTMemzero(nbs, bt));
      PetscCall(PetscHSetIClear(ht));
      for (k = 0; k < bs; k++) {
        PetscInt row = bs * i + k;
        for (j = rowidxs[row]; j < rowidxs[row + 1]; j++) {
          PetscInt col = colidxs[j];
          if (!sbaij || col >= row) {
            if (col >= cs && col < ce) {
              if (!PetscBTLookupSet(bt, (col - cs) / bs)) d_nnz[i]++;
            } else {
              PetscCall(PetscHSetIQueryAdd(ht, col / bs, &done));
              if (done) o_nnz[i]++;
            }
          }
        }
      }
    }
    PetscCall(PetscBTDestroy(&bt));
    PetscCall(PetscHSetIDestroy(&ht));
    PetscCall(MatMPIBAIJSetPreallocation(mat, bs, 0, d_nnz, 0, o_nnz));
    PetscCall(MatMPISBAIJSetPreallocation(mat, bs, 0, d_nnz, 0, o_nnz));
    PetscCall(PetscFree2(d_nnz, o_nnz));
  }

  /* store matrix values */
  for (i = 0; i < m; i++) {
    PetscInt row = rs + i, s = rowidxs[i], e = rowidxs[i + 1];
    PetscUseTypeMethod(mat, setvalues, 1, &row, e - s, colidxs + s, matvals + s, INSERT_VALUES);
  }

  PetscCall(PetscFree(rowidxs));
  PetscCall(PetscFree2(colidxs, matvals));
  PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatLoad_MPIBAIJ(Mat mat, PetscViewer viewer)
{
  PetscBool isbinary;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
  PetscCheck(isbinary, PetscObjectComm((PetscObject)viewer), PETSC_ERR_SUP, "Viewer type %s not yet supported for reading %s matrices", ((PetscObject)viewer)->type_name, ((PetscObject)mat)->type_name);
  PetscCall(MatLoad_MPIBAIJ_Binary(mat, viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatMPIBAIJSetHashTableFactor - Sets the factor required to compute the size of the matrices hash table

  Input Parameters:
+ mat  - the matrix
- fact - factor

  Options Database Key:
. -mat_use_hash_table <fact> - provide the factor

  Level: advanced

.seealso: `Mat`, `MATMPIBAIJ`, `MatSetOption()`
@*/
PetscErrorCode MatMPIBAIJSetHashTableFactor(Mat mat, PetscReal fact)
{
  PetscFunctionBegin;
  PetscTryMethod(mat, "MatSetHashTableFactor_C", (Mat, PetscReal), (mat, fact));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSetHashTableFactor_MPIBAIJ(Mat mat, PetscReal fact)
{
  Mat_MPIBAIJ *baij;

  PetscFunctionBegin;
  baij          = (Mat_MPIBAIJ *)mat->data;
  baij->ht_fact = fact;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatMPIBAIJGetSeqBAIJ(Mat A, Mat *Ad, Mat *Ao, const PetscInt *colmap[])
{
  Mat_MPIBAIJ *a = (Mat_MPIBAIJ *)A->data;
  PetscBool    flg;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIBAIJ, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "This function requires a MATMPIBAIJ matrix as input");
  if (Ad) *Ad = a->A;
  if (Ao) *Ao = a->B;
  if (colmap) *colmap = a->garray;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
    Special version for direct calls from Fortran (to eliminate two function call overheads
*/
#if defined(PETSC_HAVE_FORTRAN_CAPS)
  #define matmpibaijsetvaluesblocked_ MATMPIBAIJSETVALUESBLOCKED
#elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
  #define matmpibaijsetvaluesblocked_ matmpibaijsetvaluesblocked
#endif

// PetscClangLinter pragma disable: -fdoc-synopsis-matching-symbol-name
/*@C
  MatMPIBAIJSetValuesBlocked - Direct Fortran call to replace call to `MatSetValuesBlocked()`

  Collective

  Input Parameters:
+ matin  - the matrix
. min    - number of input rows
. im     - input rows
. nin    - number of input columns
. in     - input columns
. v      - numerical values input
- addvin - `INSERT_VALUES` or `ADD_VALUES`

  Level: advanced

  Developer Notes:
  This has a complete copy of `MatSetValuesBlocked_MPIBAIJ()` which is terrible code un-reuse.

.seealso: `Mat`, `MatSetValuesBlocked()`
@*/
PETSC_EXTERN PetscErrorCode matmpibaijsetvaluesblocked_(Mat *matin, PetscInt *min, const PetscInt im[], PetscInt *nin, const PetscInt in[], const MatScalar v[], InsertMode *addvin)
{
  /* convert input arguments to C version */
  Mat        mat = *matin;
  PetscInt   m = *min, n = *nin;
  InsertMode addv = *addvin;

  Mat_MPIBAIJ     *baij = (Mat_MPIBAIJ *)mat->data;
  const MatScalar *value;
  MatScalar       *barray      = baij->barray;
  PetscBool        roworiented = baij->roworiented;
  PetscInt         i, j, ii, jj, row, col, rstart = baij->rstartbs;
  PetscInt         rend = baij->rendbs, cstart = baij->cstartbs, stepval;
  PetscInt         cend = baij->cendbs, bs = mat->rmap->bs, bs2 = baij->bs2;

  PetscFunctionBegin;
  /* tasks normally handled by MatSetValuesBlocked() */
  if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
  else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
  PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
  if (mat->assembled) {
    mat->was_assembled = PETSC_TRUE;
    mat->assembled     = PETSC_FALSE;
  }
  PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));

  if (!barray) {
    PetscCall(PetscMalloc1(bs2, &barray));
    baij->barray = barray;
  }

  if (roworiented) stepval = (n - 1) * bs;
  else stepval = (m - 1) * bs;

  for (i = 0; i < m; i++) {
    if (im[i] < 0) continue;
    PetscCheck(im[i] < baij->Mbs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large, row %" PetscInt_FMT " max %" PetscInt_FMT, im[i], baij->Mbs - 1);
    if (im[i] >= rstart && im[i] < rend) {
      row = im[i] - rstart;
      for (j = 0; j < n; j++) {
        /* If NumCol = 1 then a copy is not required */
        if ((roworiented) && (n == 1)) {
          barray = (MatScalar *)v + i * bs2;
        } else if ((!roworiented) && (m == 1)) {
          barray = (MatScalar *)v + j * bs2;
        } else { /* Here a copy is required */
          if (roworiented) {
            value = v + i * (stepval + bs) * bs + j * bs;
          } else {
            value = v + j * (stepval + bs) * bs + i * bs;
          }
          for (ii = 0; ii < bs; ii++, value += stepval) {
            for (jj = 0; jj < bs; jj++) *barray++ = *value++;
          }
          barray -= bs2;
        }

        if (in[j] >= cstart && in[j] < cend) {
          col = in[j] - cstart;
          PetscCall(MatSetValuesBlocked_SeqBAIJ_Inlined(baij->A, row, col, barray, addv, im[i], in[j]));
        } else if (in[j] < 0) {
          continue;
        } else {
          PetscCheck(in[j] < baij->Nbs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large, col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], baij->Nbs - 1);
          if (mat->was_assembled) {
            if (!baij->colmap) PetscCall(MatCreateColmap_MPIBAIJ_Private(mat));

#if defined(PETSC_USE_DEBUG)
  #if defined(PETSC_USE_CTABLE)
            {
              PetscInt data;
              PetscCall(PetscHMapIGetWithDefault(baij->colmap, in[j] + 1, 0, &data));
              PetscCheck((data - 1) % bs == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Incorrect colmap");
            }
  #else
            PetscCheck((baij->colmap[in[j]] - 1) % bs == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Incorrect colmap");
  #endif
#endif
#if defined(PETSC_USE_CTABLE)
            PetscCall(PetscHMapIGetWithDefault(baij->colmap, in[j] + 1, 0, &col));
            col = (col - 1) / bs;
#else
            col = (baij->colmap[in[j]] - 1) / bs;
#endif
            if (col < 0 && !((Mat_SeqBAIJ *)baij->A->data)->nonew) {
              PetscCall(MatDisAssemble_MPIBAIJ(mat));
              col = in[j];
            }
          } else col = in[j];
          PetscCall(MatSetValuesBlocked_SeqBAIJ_Inlined(baij->B, row, col, barray, addv, im[i], in[j]));
        }
      }
    } else {
      if (!baij->donotstash) {
        if (roworiented) {
          PetscCall(MatStashValuesRowBlocked_Private(&mat->bstash, im[i], n, in, v, m, n, i));
        } else {
          PetscCall(MatStashValuesColBlocked_Private(&mat->bstash, im[i], n, in, v, m, n, i));
        }
      }
    }
  }

  /* task normally handled by MatSetValuesBlocked() */
  PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatCreateMPIBAIJWithArrays - creates a `MATMPIBAIJ` matrix using arrays that contain in standard block CSR format for the local rows.

  Collective

  Input Parameters:
+ comm - MPI communicator
. bs   - the block size, only a block size of 1 is supported
. m    - number of local rows (Cannot be `PETSC_DECIDE`)
. n    - This value should be the same as the local size used in creating the
         x vector for the matrix-vector product $ y = Ax $. (or `PETSC_DECIDE` to have
         calculated if `N` is given) For square matrices `n` is almost always `m`.
. M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
. N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
. i    - row indices; that is i[0] = 0, i[row] = i[row-1] + number of block elements in that rowth block 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 copied by this routine into the internal format used by PETSc;
  thus you CANNOT change the matrix entries by changing the values of a[] after you have
  called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

  The order of the entries in values is the same as the block compressed sparse row storage format; that is, it is
  the same as a three dimensional array in Fortran values(bs,bs,nnz) that contains the first column of the first
  block, followed by the second column of the first block etc etc.  That is, the blocks are contiguous in memory
  with column-major ordering within blocks.

  The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

.seealso: `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
          `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`
@*/
PetscErrorCode MatCreateMPIBAIJWithArrays(MPI_Comm comm, PetscInt bs, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt i[], const PetscInt j[], const PetscScalar a[], Mat *mat)
{
  PetscFunctionBegin;
  PetscCheck(!i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
  PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
  PetscCall(MatCreate(comm, mat));
  PetscCall(MatSetSizes(*mat, m, n, M, N));
  PetscCall(MatSetType(*mat, MATMPIBAIJ));
  PetscCall(MatSetBlockSize(*mat, bs));
  PetscCall(MatSetUp(*mat));
  PetscCall(MatSetOption(*mat, MAT_ROW_ORIENTED, PETSC_FALSE));
  PetscCall(MatMPIBAIJSetPreallocationCSR(*mat, bs, i, j, a));
  PetscCall(MatSetOption(*mat, MAT_ROW_ORIENTED, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIBAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
{
  PetscInt     m, N, i, rstart, nnz, Ii, bs, cbs;
  PetscInt    *indx;
  PetscScalar *values;

  PetscFunctionBegin;
  PetscCall(MatGetSize(inmat, &m, &N));
  if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
    Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)inmat->data;
    PetscInt    *dnz, *onz, mbs, Nbs, nbs;
    PetscInt    *bindx, rmax = a->rmax, j;
    PetscMPIInt  rank, size;

    PetscCall(MatGetBlockSizes(inmat, &bs, &cbs));
    mbs = m / bs;
    Nbs = N / cbs;
    if (n == PETSC_DECIDE) PetscCall(PetscSplitOwnershipBlock(comm, cbs, &n, &N));
    nbs = n / cbs;

    PetscCall(PetscMalloc1(rmax, &bindx));
    MatPreallocateBegin(comm, mbs, nbs, dnz, onz); /* inline function, output __end and __rstart are used below */

    PetscCallMPI(MPI_Comm_rank(comm, &rank));
    PetscCallMPI(MPI_Comm_rank(comm, &size));
    if (rank == size - 1) {
      /* Check sum(nbs) = Nbs */
      PetscCheck(__end == Nbs, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Sum of local block columns %" PetscInt_FMT " != global block columns %" PetscInt_FMT, __end, Nbs);
    }

    rstart = __rstart; /* block rstart of *outmat; see inline function MatPreallocateBegin */
    for (i = 0; i < mbs; i++) {
      PetscCall(MatGetRow_SeqBAIJ(inmat, i * bs, &nnz, &indx, NULL)); /* non-blocked nnz and indx */
      nnz = nnz / bs;
      for (j = 0; j < nnz; j++) bindx[j] = indx[j * bs] / bs;
      PetscCall(MatPreallocateSet(i + rstart, nnz, bindx, dnz, onz));
      PetscCall(MatRestoreRow_SeqBAIJ(inmat, i * bs, &nnz, &indx, NULL));
    }
    PetscCall(PetscFree(bindx));

    PetscCall(MatCreate(comm, outmat));
    PetscCall(MatSetSizes(*outmat, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    PetscCall(MatSetBlockSizes(*outmat, bs, cbs));
    PetscCall(MatSetType(*outmat, MATBAIJ));
    PetscCall(MatSeqBAIJSetPreallocation(*outmat, bs, 0, dnz));
    PetscCall(MatMPIBAIJSetPreallocation(*outmat, bs, 0, dnz, 0, onz));
    MatPreallocateEnd(dnz, onz);
    PetscCall(MatSetOption(*outmat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
  }

  /* numeric phase */
  PetscCall(MatGetBlockSizes(inmat, &bs, &cbs));
  PetscCall(MatGetOwnershipRange(*outmat, &rstart, NULL));

  for (i = 0; i < m; i++) {
    PetscCall(MatGetRow_SeqBAIJ(inmat, i, &nnz, &indx, &values));
    Ii = i + rstart;
    PetscCall(MatSetValues(*outmat, 1, &Ii, nnz, indx, values, INSERT_VALUES));
    PetscCall(MatRestoreRow_SeqBAIJ(inmat, i, &nnz, &indx, &values));
  }
  PetscCall(MatAssemblyBegin(*outmat, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(*outmat, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}