xref: /petsc/src/mat/impls/aij/seq/inode.c (revision 32603206efff945aaef677fd0dad12e9aa894f1f)

/*
  This file provides high performance routines for the Inode format (compressed sparse row)
  by taking advantage of rows with identical nonzero structure (I-nodes).
*/
#include <../src/mat/impls/aij/seq/aij.h>
#if defined(PETSC_HAVE_XMMINTRIN_H)
  #include <xmmintrin.h>
#endif

static PetscErrorCode MatCreateColInode_Private(Mat A, PetscInt *size, PetscInt **ns)
{
  Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
  PetscInt    i, count, m, n, min_mn, *ns_row, *ns_col;

  PetscFunctionBegin;
  n = A->cmap->n;
  m = A->rmap->n;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  ns_row = a->inode.size;

  min_mn = (m < n) ? m : n;
  if (!ns) {
    for (count = 0, i = 0; count < min_mn; count += ns_row[i], i++);
    for (; count + 1 < n; count++, i++);
    if (count < n) i++;
    *size = i;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(PetscMalloc1(n + 1, &ns_col));

  /* Use the same row structure wherever feasible. */
  for (count = 0, i = 0; count < min_mn; count += ns_row[i], i++) ns_col[i] = ns_row[i];

  /* if m < n; pad up the remainder with inode_limit */
  for (; count + 1 < n; count++, i++) ns_col[i] = 1;
  /* The last node is the odd ball. pad it up with the remaining rows; */
  if (count < n) {
    ns_col[i] = n - count;
    i++;
  } else if (count > n) {
    /* Adjust for the over estimation */
    ns_col[i - 1] += n - count;
  }
  *size = i;
  *ns   = ns_col;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
      This builds symmetric version of nonzero structure,
*/
static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode_Symmetric(Mat A, const PetscInt *iia[], const PetscInt *jja[], PetscInt ishift, PetscInt oshift)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
  PetscInt       *work, *ia, *ja, nz, nslim_row, nslim_col, m, row, col, n;
  PetscInt       *tns, *tvc, *ns_row = a->inode.size, *ns_col, nsz, i1, i2;
  const PetscInt *j, *jmax, *ai = a->i, *aj = a->j;

  PetscFunctionBegin;
  nslim_row = a->inode.node_count;
  m         = A->rmap->n;
  n         = A->cmap->n;
  PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatGetRowIJ_SeqAIJ_Inode_Symmetric: Matrix should be square");
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");

  /* Use the row_inode as column_inode */
  nslim_col = nslim_row;
  ns_col    = ns_row;

  /* allocate space for reformatted inode structure */
  PetscCall(PetscMalloc2(nslim_col + 1, &tns, n + 1, &tvc));
  for (i1 = 0, tns[0] = 0; i1 < nslim_col; ++i1) tns[i1 + 1] = tns[i1] + ns_row[i1];

  for (i1 = 0, col = 0; i1 < nslim_col; ++i1) {
    nsz = ns_col[i1];
    for (i2 = 0; i2 < nsz; ++i2, ++col) tvc[col] = i1;
  }
  /* allocate space for row pointers */
  PetscCall(PetscCalloc1(nslim_row + 1, &ia));
  *iia = ia;
  PetscCall(PetscMalloc1(nslim_row + 1, &work));

  /* determine the number of columns in each row */
  ia[0] = oshift;
  for (i1 = 0, row = 0; i1 < nslim_row; row += ns_row[i1], i1++) {
    j    = aj + ai[row] + ishift;
    jmax = aj + ai[row + 1] + ishift;
    if (j == jmax) continue; /* empty row */
    col = *j++ + ishift;
    i2  = tvc[col];
    while (i2 < i1 && j < jmax) { /* 1.[-xx-d-xx--] 2.[-xx-------],off-diagonal elements */
      ia[i1 + 1]++;
      ia[i2 + 1]++;
      i2++; /* Start col of next node */
      while ((j < jmax) && ((col = *j + ishift) < tns[i2])) ++j;
      i2 = tvc[col];
    }
    if (i2 == i1) ia[i2 + 1]++; /* now the diagonal element */
  }

  /* shift ia[i] to point to next row */
  for (i1 = 1; i1 < nslim_row + 1; i1++) {
    row = ia[i1 - 1];
    ia[i1] += row;
    work[i1 - 1] = row - oshift;
  }

  /* allocate space for column pointers */
  nz = ia[nslim_row] + (!ishift);
  PetscCall(PetscMalloc1(nz, &ja));
  *jja = ja;

  /* loop over lower triangular part putting into ja */
  for (i1 = 0, row = 0; i1 < nslim_row; row += ns_row[i1], i1++) {
    j    = aj + ai[row] + ishift;
    jmax = aj + ai[row + 1] + ishift;
    if (j == jmax) continue; /* empty row */
    col = *j++ + ishift;
    i2  = tvc[col];
    while (i2 < i1 && j < jmax) {
      ja[work[i2]++] = i1 + oshift;
      ja[work[i1]++] = i2 + oshift;
      ++i2;
      while ((j < jmax) && ((col = *j + ishift) < tns[i2])) ++j; /* Skip rest col indices in this node */
      i2 = tvc[col];
    }
    if (i2 == i1) ja[work[i1]++] = i2 + oshift;
  }
  PetscCall(PetscFree(work));
  PetscCall(PetscFree2(tns, tvc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
      This builds nonsymmetric version of nonzero structure,
*/
static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode_Nonsymmetric(Mat A, const PetscInt *iia[], const PetscInt *jja[], PetscInt ishift, PetscInt oshift)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
  PetscInt       *work, *ia, *ja, nz, nslim_row, n, row, col, *ns_col, nslim_col;
  PetscInt       *tns, *tvc, nsz, i1, i2;
  const PetscInt *j, *ai = a->i, *aj = a->j, *ns_row = a->inode.size;

  PetscFunctionBegin;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  nslim_row = a->inode.node_count;
  n         = A->cmap->n;

  /* Create The column_inode for this matrix */
  PetscCall(MatCreateColInode_Private(A, &nslim_col, &ns_col));

  /* allocate space for reformatted column_inode structure */
  PetscCall(PetscMalloc2(nslim_col + 1, &tns, n + 1, &tvc));
  for (i1 = 0, tns[0] = 0; i1 < nslim_col; ++i1) tns[i1 + 1] = tns[i1] + ns_col[i1];

  for (i1 = 0, col = 0; i1 < nslim_col; ++i1) {
    nsz = ns_col[i1];
    for (i2 = 0; i2 < nsz; ++i2, ++col) tvc[col] = i1;
  }
  /* allocate space for row pointers */
  PetscCall(PetscCalloc1(nslim_row + 1, &ia));
  *iia = ia;
  PetscCall(PetscMalloc1(nslim_row + 1, &work));

  /* determine the number of columns in each row */
  ia[0] = oshift;
  for (i1 = 0, row = 0; i1 < nslim_row; row += ns_row[i1], i1++) {
    j  = aj + ai[row] + ishift;
    nz = ai[row + 1] - ai[row];
    if (!nz) continue; /* empty row */
    col = *j++ + ishift;
    i2  = tvc[col];
    while (nz-- > 0) { /* off-diagonal elements */
      ia[i1 + 1]++;
      i2++; /* Start col of next node */
      while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
      if (nz > 0) i2 = tvc[col];
    }
  }

  /* shift ia[i] to point to next row */
  for (i1 = 1; i1 < nslim_row + 1; i1++) {
    row = ia[i1 - 1];
    ia[i1] += row;
    work[i1 - 1] = row - oshift;
  }

  /* allocate space for column pointers */
  nz = ia[nslim_row] + (!ishift);
  PetscCall(PetscMalloc1(nz, &ja));
  *jja = ja;

  /* loop over matrix putting into ja */
  for (i1 = 0, row = 0; i1 < nslim_row; row += ns_row[i1], i1++) {
    j  = aj + ai[row] + ishift;
    nz = ai[row + 1] - ai[row];
    if (!nz) continue; /* empty row */
    col = *j++ + ishift;
    i2  = tvc[col];
    while (nz-- > 0) {
      ja[work[i1]++] = i2 + oshift;
      ++i2;
      while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
      if (nz > 0) i2 = tvc[col];
    }
  }
  PetscCall(PetscFree(ns_col));
  PetscCall(PetscFree(work));
  PetscCall(PetscFree2(tns, tvc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
{
  Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

  PetscFunctionBegin;
  if (n) *n = a->inode.node_count;
  if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
  if (!blockcompressed) {
    PetscCall(MatGetRowIJ_SeqAIJ(A, oshift, symmetric, blockcompressed, n, ia, ja, done));
  } else if (symmetric) {
    PetscCall(MatGetRowIJ_SeqAIJ_Inode_Symmetric(A, ia, ja, 0, oshift));
  } else {
    PetscCall(MatGetRowIJ_SeqAIJ_Inode_Nonsymmetric(A, ia, ja, 0, oshift));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatRestoreRowIJ_SeqAIJ_Inode(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
{
  PetscFunctionBegin;
  if (!ia) PetscFunctionReturn(PETSC_SUCCESS);

  if (!blockcompressed) {
    PetscCall(MatRestoreRowIJ_SeqAIJ(A, oshift, symmetric, blockcompressed, n, ia, ja, done));
  } else {
    PetscCall(PetscFree(*ia));
    PetscCall(PetscFree(*ja));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetColumnIJ_SeqAIJ_Inode_Nonsymmetric(Mat A, const PetscInt *iia[], const PetscInt *jja[], PetscInt ishift, PetscInt oshift)
{
  Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
  PetscInt   *work, *ia, *ja, *j, nz, nslim_row, n, row, col, *ns_col, nslim_col;
  PetscInt   *tns, *tvc, *ns_row = a->inode.size, nsz, i1, i2, *ai = a->i, *aj = a->j;

  PetscFunctionBegin;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  nslim_row = a->inode.node_count;
  n         = A->cmap->n;

  /* Create The column_inode for this matrix */
  PetscCall(MatCreateColInode_Private(A, &nslim_col, &ns_col));

  /* allocate space for reformatted column_inode structure */
  PetscCall(PetscMalloc2(nslim_col + 1, &tns, n + 1, &tvc));
  for (i1 = 0, tns[0] = 0; i1 < nslim_col; ++i1) tns[i1 + 1] = tns[i1] + ns_col[i1];

  for (i1 = 0, col = 0; i1 < nslim_col; ++i1) {
    nsz = ns_col[i1];
    for (i2 = 0; i2 < nsz; ++i2, ++col) tvc[col] = i1;
  }
  /* allocate space for column pointers */
  PetscCall(PetscCalloc1(nslim_col + 1, &ia));
  *iia = ia;
  PetscCall(PetscMalloc1(nslim_col + 1, &work));

  /* determine the number of columns in each row */
  ia[0] = oshift;
  for (i1 = 0, row = 0; i1 < nslim_row; row += ns_row[i1], i1++) {
    j   = aj + ai[row] + ishift;
    col = *j++ + ishift;
    i2  = tvc[col];
    nz  = ai[row + 1] - ai[row];
    while (nz-- > 0) { /* off-diagonal elements */
      /* ia[i1+1]++; */
      ia[i2 + 1]++;
      i2++;
      while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
      if (nz > 0) i2 = tvc[col];
    }
  }

  /* shift ia[i] to point to next col */
  for (i1 = 1; i1 < nslim_col + 1; i1++) {
    col = ia[i1 - 1];
    ia[i1] += col;
    work[i1 - 1] = col - oshift;
  }

  /* allocate space for column pointers */
  nz = ia[nslim_col] + (!ishift);
  PetscCall(PetscMalloc1(nz, &ja));
  *jja = ja;

  /* loop over matrix putting into ja */
  for (i1 = 0, row = 0; i1 < nslim_row; row += ns_row[i1], i1++) {
    j   = aj + ai[row] + ishift;
    col = *j++ + ishift;
    i2  = tvc[col];
    nz  = ai[row + 1] - ai[row];
    while (nz-- > 0) {
      /* ja[work[i1]++] = i2 + oshift; */
      ja[work[i2]++] = i1 + oshift;
      i2++;
      while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
      if (nz > 0) i2 = tvc[col];
    }
  }
  PetscCall(PetscFree(ns_col));
  PetscCall(PetscFree(work));
  PetscCall(PetscFree2(tns, tvc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetColumnIJ_SeqAIJ_Inode(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
{
  PetscFunctionBegin;
  PetscCall(MatCreateColInode_Private(A, n, NULL));
  if (!ia) PetscFunctionReturn(PETSC_SUCCESS);

  if (!blockcompressed) {
    PetscCall(MatGetColumnIJ_SeqAIJ(A, oshift, symmetric, blockcompressed, n, ia, ja, done));
  } else if (symmetric) {
    /* Since the indices are symmetric it doesn't matter */
    PetscCall(MatGetRowIJ_SeqAIJ_Inode_Symmetric(A, ia, ja, 0, oshift));
  } else {
    PetscCall(MatGetColumnIJ_SeqAIJ_Inode_Nonsymmetric(A, ia, ja, 0, oshift));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Inode(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
{
  PetscFunctionBegin;
  if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
  if (!blockcompressed) {
    PetscCall(MatRestoreColumnIJ_SeqAIJ(A, oshift, symmetric, blockcompressed, n, ia, ja, done));
  } else {
    PetscCall(PetscFree(*ia));
    PetscCall(PetscFree(*ja));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatMult_SeqAIJ_Inode(Mat A, Vec xx, Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
  PetscScalar        sum1, sum2, sum3, sum4, sum5, tmp0, tmp1;
  PetscScalar       *y;
  const PetscScalar *x;
  const MatScalar   *v1, *v2, *v3, *v4, *v5;
  PetscInt           i1, i2, n, i, row, node_max, nsz, sz, nonzerorow = 0;
  const PetscInt    *idx, *ns, *ii;

#if defined(PETSC_HAVE_PRAGMA_DISJOINT)
  #pragma disjoint(*x, *y, *v1, *v2, *v3, *v4, *v5)
#endif

  PetscFunctionBegin;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  node_max = a->inode.node_count;
  ns       = a->inode.size; /* Node Size array */
  PetscCall(VecGetArrayRead(xx, &x));
  PetscCall(VecGetArray(yy, &y));
  idx = a->j;
  v1  = a->a;
  ii  = a->i;

  for (i = 0, row = 0; i < node_max; ++i) {
    nsz = ns[i];
    n   = ii[1] - ii[0];
    nonzerorow += (n > 0) * nsz;
    ii += nsz;
    PetscPrefetchBlock(idx + nsz * n, n, 0, PETSC_PREFETCH_HINT_NTA);      /* Prefetch the indices for the block row after the current one */
    PetscPrefetchBlock(v1 + nsz * n, nsz * n, 0, PETSC_PREFETCH_HINT_NTA); /* Prefetch the values for the block row after the current one  */
    sz = n;                                                                /* No of non zeros in this row */
                                                                           /* Switch on the size of Node */
    switch (nsz) {                                                         /* Each loop in 'case' is unrolled */
    case 1:
      sum1 = 0.;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0]; /* The instructions are ordered to */
        i2 = idx[1]; /* make the compiler's job easy */
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
      }

      if (n == sz - 1) { /* Take care of the last nonzero  */
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
      }
      y[row++] = sum1;
      break;
    case 2:
      sum1 = 0.;
      sum2 = 0.;
      v2   = v1 + n;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0];
        i2 = idx[1];
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 += v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
      }
      if (n == sz - 1) {
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
        sum2 += *v2++ * tmp0;
      }
      y[row++] = sum1;
      y[row++] = sum2;
      v1       = v2; /* Since the next block to be processed starts there*/
      idx += sz;
      break;
    case 3:
      sum1 = 0.;
      sum2 = 0.;
      sum3 = 0.;
      v2   = v1 + n;
      v3   = v2 + n;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0];
        i2 = idx[1];
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 += v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 += v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
      }
      if (n == sz - 1) {
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
        sum2 += *v2++ * tmp0;
        sum3 += *v3++ * tmp0;
      }
      y[row++] = sum1;
      y[row++] = sum2;
      y[row++] = sum3;
      v1       = v3; /* Since the next block to be processed starts there*/
      idx += 2 * sz;
      break;
    case 4:
      sum1 = 0.;
      sum2 = 0.;
      sum3 = 0.;
      sum4 = 0.;
      v2   = v1 + n;
      v3   = v2 + n;
      v4   = v3 + n;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0];
        i2 = idx[1];
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 += v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 += v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
        sum4 += v4[0] * tmp0 + v4[1] * tmp1;
        v4 += 2;
      }
      if (n == sz - 1) {
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
        sum2 += *v2++ * tmp0;
        sum3 += *v3++ * tmp0;
        sum4 += *v4++ * tmp0;
      }
      y[row++] = sum1;
      y[row++] = sum2;
      y[row++] = sum3;
      y[row++] = sum4;
      v1       = v4; /* Since the next block to be processed starts there*/
      idx += 3 * sz;
      break;
    case 5:
      sum1 = 0.;
      sum2 = 0.;
      sum3 = 0.;
      sum4 = 0.;
      sum5 = 0.;
      v2   = v1 + n;
      v3   = v2 + n;
      v4   = v3 + n;
      v5   = v4 + n;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0];
        i2 = idx[1];
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 += v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 += v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
        sum4 += v4[0] * tmp0 + v4[1] * tmp1;
        v4 += 2;
        sum5 += v5[0] * tmp0 + v5[1] * tmp1;
        v5 += 2;
      }
      if (n == sz - 1) {
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
        sum2 += *v2++ * tmp0;
        sum3 += *v3++ * tmp0;
        sum4 += *v4++ * tmp0;
        sum5 += *v5++ * tmp0;
      }
      y[row++] = sum1;
      y[row++] = sum2;
      y[row++] = sum3;
      y[row++] = sum4;
      y[row++] = sum5;
      v1       = v5; /* Since the next block to be processed starts there */
      idx += 4 * sz;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported");
    }
  }
  PetscCall(VecRestoreArrayRead(xx, &x));
  PetscCall(VecRestoreArray(yy, &y));
  PetscCall(PetscLogFlops(2.0 * a->nz - nonzerorow));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Almost same code as the MatMult_SeqAIJ_Inode() */
PetscErrorCode MatMultAdd_SeqAIJ_Inode(Mat A, Vec xx, Vec zz, Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
  PetscScalar        sum1, sum2, sum3, sum4, sum5, tmp0, tmp1;
  const MatScalar   *v1, *v2, *v3, *v4, *v5;
  const PetscScalar *x;
  PetscScalar       *y, *z, *zt;
  PetscInt           i1, i2, n, i, row, node_max, nsz, sz;
  const PetscInt    *idx, *ns, *ii;

  PetscFunctionBegin;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  node_max = a->inode.node_count;
  ns       = a->inode.size; /* Node Size array */

  PetscCall(VecGetArrayRead(xx, &x));
  PetscCall(VecGetArrayPair(zz, yy, &z, &y));
  zt = z;

  idx = a->j;
  v1  = a->a;
  ii  = a->i;

  for (i = 0, row = 0; i < node_max; ++i) {
    nsz = ns[i];
    n   = ii[1] - ii[0];
    ii += nsz;
    sz = n;        /* No of non zeros in this row */
                   /* Switch on the size of Node */
    switch (nsz) { /* Each loop in 'case' is unrolled */
    case 1:
      sum1 = *zt++;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0]; /* The instructions are ordered to */
        i2 = idx[1]; /* make the compiler's job easy */
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
      }

      if (n == sz - 1) { /* Take care of the last nonzero  */
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
      }
      y[row++] = sum1;
      break;
    case 2:
      sum1 = *zt++;
      sum2 = *zt++;
      v2   = v1 + n;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0];
        i2 = idx[1];
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 += v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
      }
      if (n == sz - 1) {
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
        sum2 += *v2++ * tmp0;
      }
      y[row++] = sum1;
      y[row++] = sum2;
      v1       = v2; /* Since the next block to be processed starts there*/
      idx += sz;
      break;
    case 3:
      sum1 = *zt++;
      sum2 = *zt++;
      sum3 = *zt++;
      v2   = v1 + n;
      v3   = v2 + n;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0];
        i2 = idx[1];
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 += v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 += v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
      }
      if (n == sz - 1) {
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
        sum2 += *v2++ * tmp0;
        sum3 += *v3++ * tmp0;
      }
      y[row++] = sum1;
      y[row++] = sum2;
      y[row++] = sum3;
      v1       = v3; /* Since the next block to be processed starts there*/
      idx += 2 * sz;
      break;
    case 4:
      sum1 = *zt++;
      sum2 = *zt++;
      sum3 = *zt++;
      sum4 = *zt++;
      v2   = v1 + n;
      v3   = v2 + n;
      v4   = v3 + n;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0];
        i2 = idx[1];
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 += v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 += v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
        sum4 += v4[0] * tmp0 + v4[1] * tmp1;
        v4 += 2;
      }
      if (n == sz - 1) {
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
        sum2 += *v2++ * tmp0;
        sum3 += *v3++ * tmp0;
        sum4 += *v4++ * tmp0;
      }
      y[row++] = sum1;
      y[row++] = sum2;
      y[row++] = sum3;
      y[row++] = sum4;
      v1       = v4; /* Since the next block to be processed starts there*/
      idx += 3 * sz;
      break;
    case 5:
      sum1 = *zt++;
      sum2 = *zt++;
      sum3 = *zt++;
      sum4 = *zt++;
      sum5 = *zt++;
      v2   = v1 + n;
      v3   = v2 + n;
      v4   = v3 + n;
      v5   = v4 + n;

      for (n = 0; n < sz - 1; n += 2) {
        i1 = idx[0];
        i2 = idx[1];
        idx += 2;
        tmp0 = x[i1];
        tmp1 = x[i2];
        sum1 += v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 += v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 += v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
        sum4 += v4[0] * tmp0 + v4[1] * tmp1;
        v4 += 2;
        sum5 += v5[0] * tmp0 + v5[1] * tmp1;
        v5 += 2;
      }
      if (n == sz - 1) {
        tmp0 = x[*idx++];
        sum1 += *v1++ * tmp0;
        sum2 += *v2++ * tmp0;
        sum3 += *v3++ * tmp0;
        sum4 += *v4++ * tmp0;
        sum5 += *v5++ * tmp0;
      }
      y[row++] = sum1;
      y[row++] = sum2;
      y[row++] = sum3;
      y[row++] = sum4;
      y[row++] = sum5;
      v1       = v5; /* Since the next block to be processed starts there */
      idx += 4 * sz;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported");
    }
  }
  PetscCall(VecRestoreArrayRead(xx, &x));
  PetscCall(VecRestoreArrayPair(zz, yy, &z, &y));
  PetscCall(PetscLogFlops(2.0 * a->nz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSolve_SeqAIJ_Inode_inplace(Mat A, Vec bb, Vec xx)
{
  Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
  IS                 iscol = a->col, isrow = a->row;
  const PetscInt    *r, *c, *rout, *cout;
  PetscInt           i, j, n = A->rmap->n, nz;
  PetscInt           node_max, *ns, row, nsz, aii, i0, i1;
  const PetscInt    *ai = a->i, *a_j = a->j, *vi, *ad, *aj;
  PetscScalar       *x, *tmp, *tmps, tmp0, tmp1;
  PetscScalar        sum1, sum2, sum3, sum4, sum5;
  const MatScalar   *v1, *v2, *v3, *v4, *v5, *a_a = a->a, *aa;
  const PetscScalar *b;

  PetscFunctionBegin;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  node_max = a->inode.node_count;
  ns       = a->inode.size; /* Node Size array */

  PetscCall(VecGetArrayRead(bb, &b));
  PetscCall(VecGetArrayWrite(xx, &x));
  tmp = a->solve_work;

  PetscCall(ISGetIndices(isrow, &rout));
  r = rout;
  PetscCall(ISGetIndices(iscol, &cout));
  c = cout + (n - 1);

  /* forward solve the lower triangular */
  tmps = tmp;
  aa   = a_a;
  aj   = a_j;
  ad   = a->diag;

  for (i = 0, row = 0; i < node_max; ++i) {
    nsz = ns[i];
    aii = ai[row];
    v1  = aa + aii;
    vi  = aj + aii;
    nz  = ad[row] - aii;
    if (i < node_max - 1) {
      /* Prefetch the block after the current one, the prefetch itself can't cause a memory error,
      * but our indexing to determine its size could. */
      PetscPrefetchBlock(aj + ai[row + nsz], ad[row + nsz] - ai[row + nsz], 0, PETSC_PREFETCH_HINT_NTA); /* indices */
      /* In my tests, it seems to be better to fetch entire rows instead of just the lower-triangular part */
      PetscPrefetchBlock(aa + ai[row + nsz], ad[row + nsz + ns[i + 1] - 1] - ai[row + nsz], 0, PETSC_PREFETCH_HINT_NTA);
      /* for (j=0; j<ns[i+1]; j++) PetscPrefetchBlock(aa+ai[row+nsz+j],ad[row+nsz+j]-ai[row+nsz+j],0,0); */
    }

    switch (nsz) { /* Each loop in 'case' is unrolled */
    case 1:
      sum1 = b[*r++];
      for (j = 0; j < nz - 1; j += 2) {
        i0 = vi[0];
        i1 = vi[1];
        vi += 2;
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
      }
      if (j == nz - 1) {
        tmp0 = tmps[*vi++];
        sum1 -= *v1++ * tmp0;
      }
      tmp[row++] = sum1;
      break;
    case 2:
      sum1 = b[*r++];
      sum2 = b[*r++];
      v2   = aa + ai[row + 1];

      for (j = 0; j < nz - 1; j += 2) {
        i0 = vi[0];
        i1 = vi[1];
        vi += 2;
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
      }
      if (j == nz - 1) {
        tmp0 = tmps[*vi++];
        sum1 -= *v1++ * tmp0;
        sum2 -= *v2++ * tmp0;
      }
      sum2 -= *v2++ * sum1;
      tmp[row++] = sum1;
      tmp[row++] = sum2;
      break;
    case 3:
      sum1 = b[*r++];
      sum2 = b[*r++];
      sum3 = b[*r++];
      v2   = aa + ai[row + 1];
      v3   = aa + ai[row + 2];

      for (j = 0; j < nz - 1; j += 2) {
        i0 = vi[0];
        i1 = vi[1];
        vi += 2;
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
      }
      if (j == nz - 1) {
        tmp0 = tmps[*vi++];
        sum1 -= *v1++ * tmp0;
        sum2 -= *v2++ * tmp0;
        sum3 -= *v3++ * tmp0;
      }
      sum2 -= *v2++ * sum1;
      sum3 -= *v3++ * sum1;
      sum3 -= *v3++ * sum2;

      tmp[row++] = sum1;
      tmp[row++] = sum2;
      tmp[row++] = sum3;
      break;

    case 4:
      sum1 = b[*r++];
      sum2 = b[*r++];
      sum3 = b[*r++];
      sum4 = b[*r++];
      v2   = aa + ai[row + 1];
      v3   = aa + ai[row + 2];
      v4   = aa + ai[row + 3];

      for (j = 0; j < nz - 1; j += 2) {
        i0 = vi[0];
        i1 = vi[1];
        vi += 2;
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
        sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
        v4 += 2;
      }
      if (j == nz - 1) {
        tmp0 = tmps[*vi++];
        sum1 -= *v1++ * tmp0;
        sum2 -= *v2++ * tmp0;
        sum3 -= *v3++ * tmp0;
        sum4 -= *v4++ * tmp0;
      }
      sum2 -= *v2++ * sum1;
      sum3 -= *v3++ * sum1;
      sum4 -= *v4++ * sum1;
      sum3 -= *v3++ * sum2;
      sum4 -= *v4++ * sum2;
      sum4 -= *v4++ * sum3;

      tmp[row++] = sum1;
      tmp[row++] = sum2;
      tmp[row++] = sum3;
      tmp[row++] = sum4;
      break;
    case 5:
      sum1 = b[*r++];
      sum2 = b[*r++];
      sum3 = b[*r++];
      sum4 = b[*r++];
      sum5 = b[*r++];
      v2   = aa + ai[row + 1];
      v3   = aa + ai[row + 2];
      v4   = aa + ai[row + 3];
      v5   = aa + ai[row + 4];

      for (j = 0; j < nz - 1; j += 2) {
        i0 = vi[0];
        i1 = vi[1];
        vi += 2;
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
        v1 += 2;
        sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
        v2 += 2;
        sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
        v3 += 2;
        sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
        v4 += 2;
        sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
        v5 += 2;
      }
      if (j == nz - 1) {
        tmp0 = tmps[*vi++];
        sum1 -= *v1++ * tmp0;
        sum2 -= *v2++ * tmp0;
        sum3 -= *v3++ * tmp0;
        sum4 -= *v4++ * tmp0;
        sum5 -= *v5++ * tmp0;
      }

      sum2 -= *v2++ * sum1;
      sum3 -= *v3++ * sum1;
      sum4 -= *v4++ * sum1;
      sum5 -= *v5++ * sum1;
      sum3 -= *v3++ * sum2;
      sum4 -= *v4++ * sum2;
      sum5 -= *v5++ * sum2;
      sum4 -= *v4++ * sum3;
      sum5 -= *v5++ * sum3;
      sum5 -= *v5++ * sum4;

      tmp[row++] = sum1;
      tmp[row++] = sum2;
      tmp[row++] = sum3;
      tmp[row++] = sum4;
      tmp[row++] = sum5;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported ");
    }
  }
  /* backward solve the upper triangular */
  for (i = node_max - 1, row = n - 1; i >= 0; i--) {
    nsz = ns[i];
    aii = ai[row + 1] - 1;
    v1  = aa + aii;
    vi  = aj + aii;
    nz  = aii - ad[row];
    switch (nsz) { /* Each loop in 'case' is unrolled */
    case 1:
      sum1 = tmp[row];

      for (j = nz; j > 1; j -= 2) {
        vi -= 2;
        i0   = vi[2];
        i1   = vi[1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        v1 -= 2;
        sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
      }
      if (j == 1) {
        tmp0 = tmps[*vi--];
        sum1 -= *v1-- * tmp0;
      }
      x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
      row--;
      break;
    case 2:
      sum1 = tmp[row];
      sum2 = tmp[row - 1];
      v2   = aa + ai[row] - 1;
      for (j = nz; j > 1; j -= 2) {
        vi -= 2;
        i0   = vi[2];
        i1   = vi[1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        v1 -= 2;
        v2 -= 2;
        sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
        sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
      }
      if (j == 1) {
        tmp0 = tmps[*vi--];
        sum1 -= *v1-- * tmp0;
        sum2 -= *v2-- * tmp0;
      }

      tmp0 = x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
      row--;
      sum2 -= *v2-- * tmp0;
      x[*c--] = tmp[row] = sum2 * a_a[ad[row]];
      row--;
      break;
    case 3:
      sum1 = tmp[row];
      sum2 = tmp[row - 1];
      sum3 = tmp[row - 2];
      v2   = aa + ai[row] - 1;
      v3   = aa + ai[row - 1] - 1;
      for (j = nz; j > 1; j -= 2) {
        vi -= 2;
        i0   = vi[2];
        i1   = vi[1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        v1 -= 2;
        v2 -= 2;
        v3 -= 2;
        sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
        sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
        sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
      }
      if (j == 1) {
        tmp0 = tmps[*vi--];
        sum1 -= *v1-- * tmp0;
        sum2 -= *v2-- * tmp0;
        sum3 -= *v3-- * tmp0;
      }
      tmp0 = x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
      row--;
      sum2 -= *v2-- * tmp0;
      sum3 -= *v3-- * tmp0;
      tmp0 = x[*c--] = tmp[row] = sum2 * a_a[ad[row]];
      row--;
      sum3 -= *v3-- * tmp0;
      x[*c--] = tmp[row] = sum3 * a_a[ad[row]];
      row--;

      break;
    case 4:
      sum1 = tmp[row];
      sum2 = tmp[row - 1];
      sum3 = tmp[row - 2];
      sum4 = tmp[row - 3];
      v2   = aa + ai[row] - 1;
      v3   = aa + ai[row - 1] - 1;
      v4   = aa + ai[row - 2] - 1;

      for (j = nz; j > 1; j -= 2) {
        vi -= 2;
        i0   = vi[2];
        i1   = vi[1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        v1 -= 2;
        v2 -= 2;
        v3 -= 2;
        v4 -= 2;
        sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
        sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
        sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
        sum4 -= v4[2] * tmp0 + v4[1] * tmp1;
      }
      if (j == 1) {
        tmp0 = tmps[*vi--];
        sum1 -= *v1-- * tmp0;
        sum2 -= *v2-- * tmp0;
        sum3 -= *v3-- * tmp0;
        sum4 -= *v4-- * tmp0;
      }

      tmp0 = x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
      row--;
      sum2 -= *v2-- * tmp0;
      sum3 -= *v3-- * tmp0;
      sum4 -= *v4-- * tmp0;
      tmp0 = x[*c--] = tmp[row] = sum2 * a_a[ad[row]];
      row--;
      sum3 -= *v3-- * tmp0;
      sum4 -= *v4-- * tmp0;
      tmp0 = x[*c--] = tmp[row] = sum3 * a_a[ad[row]];
      row--;
      sum4 -= *v4-- * tmp0;
      x[*c--] = tmp[row] = sum4 * a_a[ad[row]];
      row--;
      break;
    case 5:
      sum1 = tmp[row];
      sum2 = tmp[row - 1];
      sum3 = tmp[row - 2];
      sum4 = tmp[row - 3];
      sum5 = tmp[row - 4];
      v2   = aa + ai[row] - 1;
      v3   = aa + ai[row - 1] - 1;
      v4   = aa + ai[row - 2] - 1;
      v5   = aa + ai[row - 3] - 1;
      for (j = nz; j > 1; j -= 2) {
        vi -= 2;
        i0   = vi[2];
        i1   = vi[1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        v1 -= 2;
        v2 -= 2;
        v3 -= 2;
        v4 -= 2;
        v5 -= 2;
        sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
        sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
        sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
        sum4 -= v4[2] * tmp0 + v4[1] * tmp1;
        sum5 -= v5[2] * tmp0 + v5[1] * tmp1;
      }
      if (j == 1) {
        tmp0 = tmps[*vi--];
        sum1 -= *v1-- * tmp0;
        sum2 -= *v2-- * tmp0;
        sum3 -= *v3-- * tmp0;
        sum4 -= *v4-- * tmp0;
        sum5 -= *v5-- * tmp0;
      }

      tmp0 = x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
      row--;
      sum2 -= *v2-- * tmp0;
      sum3 -= *v3-- * tmp0;
      sum4 -= *v4-- * tmp0;
      sum5 -= *v5-- * tmp0;
      tmp0 = x[*c--] = tmp[row] = sum2 * a_a[ad[row]];
      row--;
      sum3 -= *v3-- * tmp0;
      sum4 -= *v4-- * tmp0;
      sum5 -= *v5-- * tmp0;
      tmp0 = x[*c--] = tmp[row] = sum3 * a_a[ad[row]];
      row--;
      sum4 -= *v4-- * tmp0;
      sum5 -= *v5-- * tmp0;
      tmp0 = x[*c--] = tmp[row] = sum4 * a_a[ad[row]];
      row--;
      sum5 -= *v5-- * tmp0;
      x[*c--] = tmp[row] = sum5 * a_a[ad[row]];
      row--;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported ");
    }
  }
  PetscCall(ISRestoreIndices(isrow, &rout));
  PetscCall(ISRestoreIndices(iscol, &cout));
  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArrayWrite(xx, &x));
  PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatLUFactorNumeric_SeqAIJ_Inode(Mat B, Mat A, const MatFactorInfo *info)
{
  Mat              C = B;
  Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)C->data;
  IS               isrow = b->row, isicol = b->icol;
  const PetscInt  *r, *ic, *ics;
  const PetscInt   n = A->rmap->n, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bdiag = b->diag;
  PetscInt         i, j, k, nz, nzL, row, *pj;
  const PetscInt  *ajtmp, *bjtmp;
  MatScalar       *pc, *pc1, *pc2, *pc3, *pc4, mul1, mul2, mul3, mul4, *pv, *rtmp1, *rtmp2, *rtmp3, *rtmp4;
  const MatScalar *aa = a->a, *v, *v1, *v2, *v3, *v4;
  FactorShiftCtx   sctx;
  const PetscInt  *ddiag;
  PetscReal        rs;
  MatScalar        d;
  PetscInt         inod, nodesz, node_max, col;
  const PetscInt  *ns;
  PetscInt        *tmp_vec1, *tmp_vec2, *nsmap;

  PetscFunctionBegin;
  /* MatPivotSetUp(): initialize shift context sctx */
  PetscCall(PetscMemzero(&sctx, sizeof(FactorShiftCtx)));

  if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
    ddiag          = a->diag;
    sctx.shift_top = info->zeropivot;
    for (i = 0; i < n; i++) {
      /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
      d  = (aa)[ddiag[i]];
      rs = -PetscAbsScalar(d) - PetscRealPart(d);
      v  = aa + ai[i];
      nz = ai[i + 1] - ai[i];
      for (j = 0; j < nz; j++) rs += PetscAbsScalar(v[j]);
      if (rs > sctx.shift_top) sctx.shift_top = rs;
    }
    sctx.shift_top *= 1.1;
    sctx.nshift_max = 5;
    sctx.shift_lo   = 0.;
    sctx.shift_hi   = 1.;
  }

  PetscCall(ISGetIndices(isrow, &r));
  PetscCall(ISGetIndices(isicol, &ic));

  PetscCall(PetscCalloc4(n, &rtmp1, n, &rtmp2, n, &rtmp3, n, &rtmp4));
  ics = ic;

  node_max = a->inode.node_count;
  ns       = a->inode.size;
  PetscCheck(ns, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Matrix without inode information");

  /* If max inode size > 4, split it into two inodes.*/
  /* also map the inode sizes according to the ordering */
  PetscCall(PetscMalloc1(n + 1, &tmp_vec1));
  for (i = 0, j = 0; i < node_max; ++i, ++j) {
    if (ns[i] > 4) {
      tmp_vec1[j] = 4;
      ++j;
      tmp_vec1[j] = ns[i] - tmp_vec1[j - 1];
    } else {
      tmp_vec1[j] = ns[i];
    }
  }
  /* Use the correct node_max */
  node_max = j;

  /* Now reorder the inode info based on mat re-ordering info */
  /* First create a row -> inode_size_array_index map */
  PetscCall(PetscMalloc1(n + 1, &nsmap));
  PetscCall(PetscMalloc1(node_max + 1, &tmp_vec2));
  for (i = 0, row = 0; i < node_max; i++) {
    nodesz = tmp_vec1[i];
    for (j = 0; j < nodesz; j++, row++) nsmap[row] = i;
  }
  /* Using nsmap, create a reordered ns structure */
  for (i = 0, j = 0; i < node_max; i++) {
    nodesz      = tmp_vec1[nsmap[r[j]]]; /* here the reordered row_no is in r[] */
    tmp_vec2[i] = nodesz;
    j += nodesz;
  }
  PetscCall(PetscFree(nsmap));
  PetscCall(PetscFree(tmp_vec1));

  /* Now use the correct ns */
  ns = tmp_vec2;

  do {
    sctx.newshift = PETSC_FALSE;
    /* Now loop over each block-row, and do the factorization */
    for (inod = 0, i = 0; inod < node_max; inod++) { /* i: row index; inod: inode index */
      nodesz = ns[inod];

      switch (nodesz) {
      case 1:
        /* zero rtmp1 */
        /* L part */
        nz    = bi[i + 1] - bi[i];
        bjtmp = bj + bi[i];
        for (j = 0; j < nz; j++) rtmp1[bjtmp[j]] = 0.0;

        /* U part */
        nz    = bdiag[i] - bdiag[i + 1];
        bjtmp = bj + bdiag[i + 1] + 1;
        for (j = 0; j < nz; j++) rtmp1[bjtmp[j]] = 0.0;

        /* load in initial (unfactored row) */
        nz    = ai[r[i] + 1] - ai[r[i]];
        ajtmp = aj + ai[r[i]];
        v     = aa + ai[r[i]];
        for (j = 0; j < nz; j++) rtmp1[ics[ajtmp[j]]] = v[j];

        /* ZeropivotApply() */
        rtmp1[i] += sctx.shift_amount; /* shift the diagonal of the matrix */

        /* elimination */
        bjtmp = bj + bi[i];
        row   = *bjtmp++;
        nzL   = bi[i + 1] - bi[i];
        for (k = 0; k < nzL; k++) {
          pc = rtmp1 + row;
          if (*pc != 0.0) {
            pv   = b->a + bdiag[row];
            mul1 = *pc * (*pv);
            *pc  = mul1;
            pj   = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
            pv   = b->a + bdiag[row + 1] + 1;
            nz   = bdiag[row] - bdiag[row + 1] - 1; /* num of entries in U(row,:) excluding diag */
            for (j = 0; j < nz; j++) rtmp1[pj[j]] -= mul1 * pv[j];
            PetscCall(PetscLogFlops(1 + 2.0 * nz));
          }
          row = *bjtmp++;
        }

        /* finished row so stick it into b->a */
        rs = 0.0;
        /* L part */
        pv = b->a + bi[i];
        pj = b->j + bi[i];
        nz = bi[i + 1] - bi[i];
        for (j = 0; j < nz; j++) {
          pv[j] = rtmp1[pj[j]];
          rs += PetscAbsScalar(pv[j]);
        }

        /* U part */
        pv = b->a + bdiag[i + 1] + 1;
        pj = b->j + bdiag[i + 1] + 1;
        nz = bdiag[i] - bdiag[i + 1] - 1;
        for (j = 0; j < nz; j++) {
          pv[j] = rtmp1[pj[j]];
          rs += PetscAbsScalar(pv[j]);
        }

        /* Check zero pivot */
        sctx.rs = rs;
        sctx.pv = rtmp1[i];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i));
        if (sctx.newshift) break;

        /* Mark diagonal and invert diagonal for simpler triangular solves */
        pv  = b->a + bdiag[i];
        *pv = 1.0 / sctx.pv; /* sctx.pv = rtmp1[i]+shiftamount if shifttype==MAT_SHIFT_INBLOCKS */
        break;

      case 2:
        /* zero rtmp1 and rtmp2 */
        /* L part */
        nz    = bi[i + 1] - bi[i];
        bjtmp = bj + bi[i];
        for (j = 0; j < nz; j++) {
          col        = bjtmp[j];
          rtmp1[col] = 0.0;
          rtmp2[col] = 0.0;
        }

        /* U part */
        nz    = bdiag[i] - bdiag[i + 1];
        bjtmp = bj + bdiag[i + 1] + 1;
        for (j = 0; j < nz; j++) {
          col        = bjtmp[j];
          rtmp1[col] = 0.0;
          rtmp2[col] = 0.0;
        }

        /* load in initial (unfactored row) */
        nz    = ai[r[i] + 1] - ai[r[i]];
        ajtmp = aj + ai[r[i]];
        v1    = aa + ai[r[i]];
        v2    = aa + ai[r[i] + 1];
        for (j = 0; j < nz; j++) {
          col        = ics[ajtmp[j]];
          rtmp1[col] = v1[j];
          rtmp2[col] = v2[j];
        }
        /* ZeropivotApply(): shift the diagonal of the matrix  */
        rtmp1[i] += sctx.shift_amount;
        rtmp2[i + 1] += sctx.shift_amount;

        /* elimination */
        bjtmp = bj + bi[i];
        row   = *bjtmp++; /* pivot row */
        nzL   = bi[i + 1] - bi[i];
        for (k = 0; k < nzL; k++) {
          pc1 = rtmp1 + row;
          pc2 = rtmp2 + row;
          if (*pc1 != 0.0 || *pc2 != 0.0) {
            pv   = b->a + bdiag[row];
            mul1 = *pc1 * (*pv);
            mul2 = *pc2 * (*pv);
            *pc1 = mul1;
            *pc2 = mul2;

            pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
            pv = b->a + bdiag[row + 1] + 1;
            nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries in U(row,:) excluding diag */
            for (j = 0; j < nz; j++) {
              col = pj[j];
              rtmp1[col] -= mul1 * pv[j];
              rtmp2[col] -= mul2 * pv[j];
            }
            PetscCall(PetscLogFlops(2 + 4.0 * nz));
          }
          row = *bjtmp++;
        }

        /* finished row i; check zero pivot, then stick row i into b->a */
        rs = 0.0;
        /* L part */
        pc1 = b->a + bi[i];
        pj  = b->j + bi[i];
        nz  = bi[i + 1] - bi[i];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc1[j] = rtmp1[col];
          rs += PetscAbsScalar(pc1[j]);
        }
        /* U part */
        pc1 = b->a + bdiag[i + 1] + 1;
        pj  = b->j + bdiag[i + 1] + 1;
        nz  = bdiag[i] - bdiag[i + 1] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc1[j] = rtmp1[col];
          rs += PetscAbsScalar(pc1[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp1[i];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i));
        if (sctx.newshift) break;
        pc1  = b->a + bdiag[i]; /* Mark diagonal */
        *pc1 = 1.0 / sctx.pv;

        /* Now take care of diagonal 2x2 block. */
        pc2 = rtmp2 + i;
        if (*pc2 != 0.0) {
          mul1 = (*pc2) * (*pc1);             /* *pc1=diag[i] is inverted! */
          *pc2 = mul1;                        /* insert L entry */
          pj   = b->j + bdiag[i + 1] + 1;     /* beginning of U(i,:) */
          nz   = bdiag[i] - bdiag[i + 1] - 1; /* num of entries in U(i,:) excluding diag */
          for (j = 0; j < nz; j++) {
            col = pj[j];
            rtmp2[col] -= mul1 * rtmp1[col];
          }
          PetscCall(PetscLogFlops(1 + 2.0 * nz));
        }

        /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
        rs = 0.0;
        /* L part */
        pc2 = b->a + bi[i + 1];
        pj  = b->j + bi[i + 1];
        nz  = bi[i + 2] - bi[i + 1];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc2[j] = rtmp2[col];
          rs += PetscAbsScalar(pc2[j]);
        }
        /* U part */
        pc2 = b->a + bdiag[i + 2] + 1;
        pj  = b->j + bdiag[i + 2] + 1;
        nz  = bdiag[i + 1] - bdiag[i + 2] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc2[j] = rtmp2[col];
          rs += PetscAbsScalar(pc2[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp2[i + 1];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i + 1));
        if (sctx.newshift) break;
        pc2  = b->a + bdiag[i + 1];
        *pc2 = 1.0 / sctx.pv;
        break;

      case 3:
        /* zero rtmp */
        /* L part */
        nz    = bi[i + 1] - bi[i];
        bjtmp = bj + bi[i];
        for (j = 0; j < nz; j++) {
          col        = bjtmp[j];
          rtmp1[col] = 0.0;
          rtmp2[col] = 0.0;
          rtmp3[col] = 0.0;
        }

        /* U part */
        nz    = bdiag[i] - bdiag[i + 1];
        bjtmp = bj + bdiag[i + 1] + 1;
        for (j = 0; j < nz; j++) {
          col        = bjtmp[j];
          rtmp1[col] = 0.0;
          rtmp2[col] = 0.0;
          rtmp3[col] = 0.0;
        }

        /* load in initial (unfactored row) */
        nz    = ai[r[i] + 1] - ai[r[i]];
        ajtmp = aj + ai[r[i]];
        v1    = aa + ai[r[i]];
        v2    = aa + ai[r[i] + 1];
        v3    = aa + ai[r[i] + 2];
        for (j = 0; j < nz; j++) {
          col        = ics[ajtmp[j]];
          rtmp1[col] = v1[j];
          rtmp2[col] = v2[j];
          rtmp3[col] = v3[j];
        }
        /* ZeropivotApply(): shift the diagonal of the matrix  */
        rtmp1[i] += sctx.shift_amount;
        rtmp2[i + 1] += sctx.shift_amount;
        rtmp3[i + 2] += sctx.shift_amount;

        /* elimination */
        bjtmp = bj + bi[i];
        row   = *bjtmp++; /* pivot row */
        nzL   = bi[i + 1] - bi[i];
        for (k = 0; k < nzL; k++) {
          pc1 = rtmp1 + row;
          pc2 = rtmp2 + row;
          pc3 = rtmp3 + row;
          if (*pc1 != 0.0 || *pc2 != 0.0 || *pc3 != 0.0) {
            pv   = b->a + bdiag[row];
            mul1 = *pc1 * (*pv);
            mul2 = *pc2 * (*pv);
            mul3 = *pc3 * (*pv);
            *pc1 = mul1;
            *pc2 = mul2;
            *pc3 = mul3;

            pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
            pv = b->a + bdiag[row + 1] + 1;
            nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries in U(row,:) excluding diag */
            for (j = 0; j < nz; j++) {
              col = pj[j];
              rtmp1[col] -= mul1 * pv[j];
              rtmp2[col] -= mul2 * pv[j];
              rtmp3[col] -= mul3 * pv[j];
            }
            PetscCall(PetscLogFlops(3 + 6.0 * nz));
          }
          row = *bjtmp++;
        }

        /* finished row i; check zero pivot, then stick row i into b->a */
        rs = 0.0;
        /* L part */
        pc1 = b->a + bi[i];
        pj  = b->j + bi[i];
        nz  = bi[i + 1] - bi[i];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc1[j] = rtmp1[col];
          rs += PetscAbsScalar(pc1[j]);
        }
        /* U part */
        pc1 = b->a + bdiag[i + 1] + 1;
        pj  = b->j + bdiag[i + 1] + 1;
        nz  = bdiag[i] - bdiag[i + 1] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc1[j] = rtmp1[col];
          rs += PetscAbsScalar(pc1[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp1[i];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i));
        if (sctx.newshift) break;
        pc1  = b->a + bdiag[i]; /* Mark diag[i] */
        *pc1 = 1.0 / sctx.pv;

        /* Now take care of 1st column of diagonal 3x3 block. */
        pc2 = rtmp2 + i;
        pc3 = rtmp3 + i;
        if (*pc2 != 0.0 || *pc3 != 0.0) {
          mul2 = (*pc2) * (*pc1);
          *pc2 = mul2;
          mul3 = (*pc3) * (*pc1);
          *pc3 = mul3;
          pj   = b->j + bdiag[i + 1] + 1;     /* beginning of U(i,:) */
          nz   = bdiag[i] - bdiag[i + 1] - 1; /* num of entries in U(i,:) excluding diag */
          for (j = 0; j < nz; j++) {
            col = pj[j];
            rtmp2[col] -= mul2 * rtmp1[col];
            rtmp3[col] -= mul3 * rtmp1[col];
          }
          PetscCall(PetscLogFlops(2 + 4.0 * nz));
        }

        /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
        rs = 0.0;
        /* L part */
        pc2 = b->a + bi[i + 1];
        pj  = b->j + bi[i + 1];
        nz  = bi[i + 2] - bi[i + 1];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc2[j] = rtmp2[col];
          rs += PetscAbsScalar(pc2[j]);
        }
        /* U part */
        pc2 = b->a + bdiag[i + 2] + 1;
        pj  = b->j + bdiag[i + 2] + 1;
        nz  = bdiag[i + 1] - bdiag[i + 2] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc2[j] = rtmp2[col];
          rs += PetscAbsScalar(pc2[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp2[i + 1];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i + 1));
        if (sctx.newshift) break;
        pc2  = b->a + bdiag[i + 1];
        *pc2 = 1.0 / sctx.pv; /* Mark diag[i+1] */

        /* Now take care of 2nd column of diagonal 3x3 block. */
        pc3 = rtmp3 + i + 1;
        if (*pc3 != 0.0) {
          mul3 = (*pc3) * (*pc2);
          *pc3 = mul3;
          pj   = b->j + bdiag[i + 2] + 1;         /* beginning of U(i+1,:) */
          nz   = bdiag[i + 1] - bdiag[i + 2] - 1; /* num of entries in U(i+1,:) excluding diag */
          for (j = 0; j < nz; j++) {
            col = pj[j];
            rtmp3[col] -= mul3 * rtmp2[col];
          }
          PetscCall(PetscLogFlops(1 + 2.0 * nz));
        }

        /* finished i+2; check zero pivot, then stick row i+2 into b->a */
        rs = 0.0;
        /* L part */
        pc3 = b->a + bi[i + 2];
        pj  = b->j + bi[i + 2];
        nz  = bi[i + 3] - bi[i + 2];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc3[j] = rtmp3[col];
          rs += PetscAbsScalar(pc3[j]);
        }
        /* U part */
        pc3 = b->a + bdiag[i + 3] + 1;
        pj  = b->j + bdiag[i + 3] + 1;
        nz  = bdiag[i + 2] - bdiag[i + 3] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc3[j] = rtmp3[col];
          rs += PetscAbsScalar(pc3[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp3[i + 2];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i + 2));
        if (sctx.newshift) break;
        pc3  = b->a + bdiag[i + 2];
        *pc3 = 1.0 / sctx.pv; /* Mark diag[i+2] */
        break;
      case 4:
        /* zero rtmp */
        /* L part */
        nz    = bi[i + 1] - bi[i];
        bjtmp = bj + bi[i];
        for (j = 0; j < nz; j++) {
          col        = bjtmp[j];
          rtmp1[col] = 0.0;
          rtmp2[col] = 0.0;
          rtmp3[col] = 0.0;
          rtmp4[col] = 0.0;
        }

        /* U part */
        nz    = bdiag[i] - bdiag[i + 1];
        bjtmp = bj + bdiag[i + 1] + 1;
        for (j = 0; j < nz; j++) {
          col        = bjtmp[j];
          rtmp1[col] = 0.0;
          rtmp2[col] = 0.0;
          rtmp3[col] = 0.0;
          rtmp4[col] = 0.0;
        }

        /* load in initial (unfactored row) */
        nz    = ai[r[i] + 1] - ai[r[i]];
        ajtmp = aj + ai[r[i]];
        v1    = aa + ai[r[i]];
        v2    = aa + ai[r[i] + 1];
        v3    = aa + ai[r[i] + 2];
        v4    = aa + ai[r[i] + 3];
        for (j = 0; j < nz; j++) {
          col        = ics[ajtmp[j]];
          rtmp1[col] = v1[j];
          rtmp2[col] = v2[j];
          rtmp3[col] = v3[j];
          rtmp4[col] = v4[j];
        }
        /* ZeropivotApply(): shift the diagonal of the matrix  */
        rtmp1[i] += sctx.shift_amount;
        rtmp2[i + 1] += sctx.shift_amount;
        rtmp3[i + 2] += sctx.shift_amount;
        rtmp4[i + 3] += sctx.shift_amount;

        /* elimination */
        bjtmp = bj + bi[i];
        row   = *bjtmp++; /* pivot row */
        nzL   = bi[i + 1] - bi[i];
        for (k = 0; k < nzL; k++) {
          pc1 = rtmp1 + row;
          pc2 = rtmp2 + row;
          pc3 = rtmp3 + row;
          pc4 = rtmp4 + row;
          if (*pc1 != 0.0 || *pc2 != 0.0 || *pc3 != 0.0 || *pc4 != 0.0) {
            pv   = b->a + bdiag[row];
            mul1 = *pc1 * (*pv);
            mul2 = *pc2 * (*pv);
            mul3 = *pc3 * (*pv);
            mul4 = *pc4 * (*pv);
            *pc1 = mul1;
            *pc2 = mul2;
            *pc3 = mul3;
            *pc4 = mul4;

            pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
            pv = b->a + bdiag[row + 1] + 1;
            nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries in U(row,:) excluding diag */
            for (j = 0; j < nz; j++) {
              col = pj[j];
              rtmp1[col] -= mul1 * pv[j];
              rtmp2[col] -= mul2 * pv[j];
              rtmp3[col] -= mul3 * pv[j];
              rtmp4[col] -= mul4 * pv[j];
            }
            PetscCall(PetscLogFlops(4 + 8.0 * nz));
          }
          row = *bjtmp++;
        }

        /* finished row i; check zero pivot, then stick row i into b->a */
        rs = 0.0;
        /* L part */
        pc1 = b->a + bi[i];
        pj  = b->j + bi[i];
        nz  = bi[i + 1] - bi[i];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc1[j] = rtmp1[col];
          rs += PetscAbsScalar(pc1[j]);
        }
        /* U part */
        pc1 = b->a + bdiag[i + 1] + 1;
        pj  = b->j + bdiag[i + 1] + 1;
        nz  = bdiag[i] - bdiag[i + 1] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc1[j] = rtmp1[col];
          rs += PetscAbsScalar(pc1[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp1[i];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i));
        if (sctx.newshift) break;
        pc1  = b->a + bdiag[i]; /* Mark diag[i] */
        *pc1 = 1.0 / sctx.pv;

        /* Now take care of 1st column of diagonal 4x4 block. */
        pc2 = rtmp2 + i;
        pc3 = rtmp3 + i;
        pc4 = rtmp4 + i;
        if (*pc2 != 0.0 || *pc3 != 0.0 || *pc4 != 0.0) {
          mul2 = (*pc2) * (*pc1);
          *pc2 = mul2;
          mul3 = (*pc3) * (*pc1);
          *pc3 = mul3;
          mul4 = (*pc4) * (*pc1);
          *pc4 = mul4;
          pj   = b->j + bdiag[i + 1] + 1;     /* beginning of U(i,:) */
          nz   = bdiag[i] - bdiag[i + 1] - 1; /* num of entries in U(i,:) excluding diag */
          for (j = 0; j < nz; j++) {
            col = pj[j];
            rtmp2[col] -= mul2 * rtmp1[col];
            rtmp3[col] -= mul3 * rtmp1[col];
            rtmp4[col] -= mul4 * rtmp1[col];
          }
          PetscCall(PetscLogFlops(3 + 6.0 * nz));
        }

        /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
        rs = 0.0;
        /* L part */
        pc2 = b->a + bi[i + 1];
        pj  = b->j + bi[i + 1];
        nz  = bi[i + 2] - bi[i + 1];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc2[j] = rtmp2[col];
          rs += PetscAbsScalar(pc2[j]);
        }
        /* U part */
        pc2 = b->a + bdiag[i + 2] + 1;
        pj  = b->j + bdiag[i + 2] + 1;
        nz  = bdiag[i + 1] - bdiag[i + 2] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc2[j] = rtmp2[col];
          rs += PetscAbsScalar(pc2[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp2[i + 1];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i + 1));
        if (sctx.newshift) break;
        pc2  = b->a + bdiag[i + 1];
        *pc2 = 1.0 / sctx.pv; /* Mark diag[i+1] */

        /* Now take care of 2nd column of diagonal 4x4 block. */
        pc3 = rtmp3 + i + 1;
        pc4 = rtmp4 + i + 1;
        if (*pc3 != 0.0 || *pc4 != 0.0) {
          mul3 = (*pc3) * (*pc2);
          *pc3 = mul3;
          mul4 = (*pc4) * (*pc2);
          *pc4 = mul4;
          pj   = b->j + bdiag[i + 2] + 1;         /* beginning of U(i+1,:) */
          nz   = bdiag[i + 1] - bdiag[i + 2] - 1; /* num of entries in U(i+1,:) excluding diag */
          for (j = 0; j < nz; j++) {
            col = pj[j];
            rtmp3[col] -= mul3 * rtmp2[col];
            rtmp4[col] -= mul4 * rtmp2[col];
          }
          PetscCall(PetscLogFlops(4.0 * nz));
        }

        /* finished i+2; check zero pivot, then stick row i+2 into b->a */
        rs = 0.0;
        /* L part */
        pc3 = b->a + bi[i + 2];
        pj  = b->j + bi[i + 2];
        nz  = bi[i + 3] - bi[i + 2];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc3[j] = rtmp3[col];
          rs += PetscAbsScalar(pc3[j]);
        }
        /* U part */
        pc3 = b->a + bdiag[i + 3] + 1;
        pj  = b->j + bdiag[i + 3] + 1;
        nz  = bdiag[i + 2] - bdiag[i + 3] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc3[j] = rtmp3[col];
          rs += PetscAbsScalar(pc3[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp3[i + 2];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i + 2));
        if (sctx.newshift) break;
        pc3  = b->a + bdiag[i + 2];
        *pc3 = 1.0 / sctx.pv; /* Mark diag[i+2] */

        /* Now take care of 3rd column of diagonal 4x4 block. */
        pc4 = rtmp4 + i + 2;
        if (*pc4 != 0.0) {
          mul4 = (*pc4) * (*pc3);
          *pc4 = mul4;
          pj   = b->j + bdiag[i + 3] + 1;         /* beginning of U(i+2,:) */
          nz   = bdiag[i + 2] - bdiag[i + 3] - 1; /* num of entries in U(i+2,:) excluding diag */
          for (j = 0; j < nz; j++) {
            col = pj[j];
            rtmp4[col] -= mul4 * rtmp3[col];
          }
          PetscCall(PetscLogFlops(1 + 2.0 * nz));
        }

        /* finished i+3; check zero pivot, then stick row i+3 into b->a */
        rs = 0.0;
        /* L part */
        pc4 = b->a + bi[i + 3];
        pj  = b->j + bi[i + 3];
        nz  = bi[i + 4] - bi[i + 3];
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc4[j] = rtmp4[col];
          rs += PetscAbsScalar(pc4[j]);
        }
        /* U part */
        pc4 = b->a + bdiag[i + 4] + 1;
        pj  = b->j + bdiag[i + 4] + 1;
        nz  = bdiag[i + 3] - bdiag[i + 4] - 1; /* exclude diagonal */
        for (j = 0; j < nz; j++) {
          col    = pj[j];
          pc4[j] = rtmp4[col];
          rs += PetscAbsScalar(pc4[j]);
        }

        sctx.rs = rs;
        sctx.pv = rtmp4[i + 3];
        PetscCall(MatPivotCheck(B, A, info, &sctx, i + 3));
        if (sctx.newshift) break;
        pc4  = b->a + bdiag[i + 3];
        *pc4 = 1.0 / sctx.pv; /* Mark diag[i+3] */
        break;

      default:
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Node size not yet supported ");
      }
      if (sctx.newshift) break; /* break for (inod=0,i=0; inod<node_max; inod++) */
      i += nodesz;              /* Update the row */
    }

    /* MatPivotRefine() */
    if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction > 0 && sctx.nshift < sctx.nshift_max) {
      /*
       * if no shift in this attempt & shifting & started shifting & can refine,
       * then try lower shift
       */
      sctx.shift_hi       = sctx.shift_fraction;
      sctx.shift_fraction = (sctx.shift_hi + sctx.shift_lo) / 2.;
      sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
      sctx.newshift       = PETSC_TRUE;
      sctx.nshift++;
    }
  } while (sctx.newshift);

  PetscCall(PetscFree4(rtmp1, rtmp2, rtmp3, rtmp4));
  PetscCall(PetscFree(tmp_vec2));
  PetscCall(ISRestoreIndices(isicol, &ic));
  PetscCall(ISRestoreIndices(isrow, &r));

  if (b->inode.size) {
    C->ops->solve = MatSolve_SeqAIJ_Inode;
  } else {
    C->ops->solve = MatSolve_SeqAIJ;
  }
  C->ops->solveadd          = MatSolveAdd_SeqAIJ;
  C->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
  C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
  C->ops->matsolve          = MatMatSolve_SeqAIJ;
  C->ops->matsolvetranspose = MatMatSolveTranspose_SeqAIJ;
  C->assembled              = PETSC_TRUE;
  C->preallocated           = PETSC_TRUE;

  PetscCall(PetscLogFlops(C->cmap->n));

  /* MatShiftView(A,info,&sctx) */
  if (sctx.nshift) {
    if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
      PetscCall(PetscInfo(A, "number of shift_pd tries %" PetscInt_FMT ", shift_amount %g, diagonal shifted up by %e fraction top_value %e\n", sctx.nshift, (double)sctx.shift_amount, (double)sctx.shift_fraction, (double)sctx.shift_top));
    } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
      PetscCall(PetscInfo(A, "number of shift_nz tries %" PetscInt_FMT ", shift_amount %g\n", sctx.nshift, (double)sctx.shift_amount));
    } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
      PetscCall(PetscInfo(A, "number of shift_inblocks applied %" PetscInt_FMT ", each shift_amount %g\n", sctx.nshift, (double)info->shiftamount));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if 0
// unused
static PetscErrorCode MatLUFactorNumeric_SeqAIJ_Inode_inplace(Mat B, Mat A, const MatFactorInfo *info)
{
  Mat              C = B;
  Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)C->data;
  IS               iscol = b->col, isrow = b->row, isicol = b->icol;
  const PetscInt  *r, *ic, *c, *ics;
  PetscInt         n = A->rmap->n, *bi = b->i;
  PetscInt        *bj = b->j, *nbj = b->j + 1, *ajtmp, *bjtmp, nz, nz_tmp, row, prow;
  PetscInt         i, j, idx, *bd = b->diag, node_max, nodesz;
  PetscInt        *ai = a->i, *aj = a->j;
  PetscInt        *ns, *tmp_vec1, *tmp_vec2, *nsmap, *pj;
  PetscScalar      mul1, mul2, mul3, tmp;
  MatScalar       *pc1, *pc2, *pc3, *ba = b->a, *pv, *rtmp11, *rtmp22, *rtmp33;
  const MatScalar *v1, *v2, *v3, *aa    = a->a, *rtmp1;
  PetscReal        rs = 0.0;
  FactorShiftCtx   sctx;

  PetscFunctionBegin;
  sctx.shift_top      = 0;
  sctx.nshift_max     = 0;
  sctx.shift_lo       = 0;
  sctx.shift_hi       = 0;
  sctx.shift_fraction = 0;

  /* if both shift schemes are chosen by user, only use info->shiftpd */
  if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
    sctx.shift_top = 0;
    for (i = 0; i < n; i++) {
      /* calculate rs = sum(|aij|)-RealPart(aii), amt of shift needed for this row */
      rs    = 0.0;
      ajtmp = aj + ai[i];
      rtmp1 = aa + ai[i];
      nz    = ai[i + 1] - ai[i];
      for (j = 0; j < nz; j++) {
        if (*ajtmp != i) {
          rs += PetscAbsScalar(*rtmp1++);
        } else {
          rs -= PetscRealPart(*rtmp1++);
        }
        ajtmp++;
      }
      if (rs > sctx.shift_top) sctx.shift_top = rs;
    }
    if (sctx.shift_top == 0.0) sctx.shift_top += 1.e-12;
    sctx.shift_top *= 1.1;
    sctx.nshift_max = 5;
    sctx.shift_lo   = 0.;
    sctx.shift_hi   = 1.;
  }
  sctx.shift_amount = 0;
  sctx.nshift       = 0;

  PetscCall(ISGetIndices(isrow, &r));
  PetscCall(ISGetIndices(iscol, &c));
  PetscCall(ISGetIndices(isicol, &ic));
  PetscCall(PetscCalloc3(n, &rtmp11, n, &rtmp22, n, &rtmp33));
  ics = ic;

  node_max = a->inode.node_count;
  ns       = a->inode.size;
  PetscCheck(ns, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Matrix without inode information");

  /* If max inode size > 3, split it into two inodes.*/
  /* also map the inode sizes according to the ordering */
  PetscCall(PetscMalloc1(n + 1, &tmp_vec1));
  for (i = 0, j = 0; i < node_max; ++i, ++j) {
    if (ns[i] > 3) {
      tmp_vec1[j] = ns[i] / 2; /* Assuming ns[i] < =5  */
      ++j;
      tmp_vec1[j] = ns[i] - tmp_vec1[j - 1];
    } else {
      tmp_vec1[j] = ns[i];
    }
  }
  /* Use the correct node_max */
  node_max = j;

  /* Now reorder the inode info based on mat re-ordering info */
  /* First create a row -> inode_size_array_index map */
  PetscCall(PetscMalloc2(n + 1, &nsmap, node_max + 1, &tmp_vec2));
  for (i = 0, row = 0; i < node_max; i++) {
    nodesz = tmp_vec1[i];
    for (j = 0; j < nodesz; j++, row++) nsmap[row] = i;
  }
  /* Using nsmap, create a reordered ns structure */
  for (i = 0, j = 0; i < node_max; i++) {
    nodesz      = tmp_vec1[nsmap[r[j]]]; /* here the reordered row_no is in r[] */
    tmp_vec2[i] = nodesz;
    j += nodesz;
  }
  PetscCall(PetscFree2(nsmap, tmp_vec1));
  /* Now use the correct ns */
  ns = tmp_vec2;

  do {
    sctx.newshift = PETSC_FALSE;
    /* Now loop over each block-row, and do the factorization */
    for (i = 0, row = 0; i < node_max; i++) {
      nodesz = ns[i];
      nz     = bi[row + 1] - bi[row];
      bjtmp  = bj + bi[row];

      switch (nodesz) {
      case 1:
        for (j = 0; j < nz; j++) {
          idx         = bjtmp[j];
          rtmp11[idx] = 0.0;
        }

        /* load in initial (unfactored row) */
        idx    = r[row];
        nz_tmp = ai[idx + 1] - ai[idx];
        ajtmp  = aj + ai[idx];
        v1     = aa + ai[idx];

        for (j = 0; j < nz_tmp; j++) {
          idx         = ics[ajtmp[j]];
          rtmp11[idx] = v1[j];
        }
        rtmp11[ics[r[row]]] += sctx.shift_amount;

        prow = *bjtmp++;
        while (prow < row) {
          pc1 = rtmp11 + prow;
          if (*pc1 != 0.0) {
            pv     = ba + bd[prow];
            pj     = nbj + bd[prow];
            mul1   = *pc1 * *pv++;
            *pc1   = mul1;
            nz_tmp = bi[prow + 1] - bd[prow] - 1;
            PetscCall(PetscLogFlops(1 + 2.0 * nz_tmp));
            for (j = 0; j < nz_tmp; j++) {
              tmp = pv[j];
              idx = pj[j];
              rtmp11[idx] -= mul1 * tmp;
            }
          }
          prow = *bjtmp++;
        }
        pj  = bj + bi[row];
        pc1 = ba + bi[row];

        sctx.pv     = rtmp11[row];
        rtmp11[row] = 1.0 / rtmp11[row]; /* invert diag */
        rs          = 0.0;
        for (j = 0; j < nz; j++) {
          idx    = pj[j];
          pc1[j] = rtmp11[idx]; /* rtmp11 -> ba */
          if (idx != row) rs += PetscAbsScalar(pc1[j]);
        }
        sctx.rs = rs;
        PetscCall(MatPivotCheck(B, A, info, &sctx, row));
        if (sctx.newshift) goto endofwhile;
        break;

      case 2:
        for (j = 0; j < nz; j++) {
          idx         = bjtmp[j];
          rtmp11[idx] = 0.0;
          rtmp22[idx] = 0.0;
        }

        /* load in initial (unfactored row) */
        idx    = r[row];
        nz_tmp = ai[idx + 1] - ai[idx];
        ajtmp  = aj + ai[idx];
        v1     = aa + ai[idx];
        v2     = aa + ai[idx + 1];
        for (j = 0; j < nz_tmp; j++) {
          idx         = ics[ajtmp[j]];
          rtmp11[idx] = v1[j];
          rtmp22[idx] = v2[j];
        }
        rtmp11[ics[r[row]]] += sctx.shift_amount;
        rtmp22[ics[r[row + 1]]] += sctx.shift_amount;

        prow = *bjtmp++;
        while (prow < row) {
          pc1 = rtmp11 + prow;
          pc2 = rtmp22 + prow;
          if (*pc1 != 0.0 || *pc2 != 0.0) {
            pv   = ba + bd[prow];
            pj   = nbj + bd[prow];
            mul1 = *pc1 * *pv;
            mul2 = *pc2 * *pv;
            ++pv;
            *pc1 = mul1;
            *pc2 = mul2;

            nz_tmp = bi[prow + 1] - bd[prow] - 1;
            for (j = 0; j < nz_tmp; j++) {
              tmp = pv[j];
              idx = pj[j];
              rtmp11[idx] -= mul1 * tmp;
              rtmp22[idx] -= mul2 * tmp;
            }
            PetscCall(PetscLogFlops(2 + 4.0 * nz_tmp));
          }
          prow = *bjtmp++;
        }

        /* Now take care of diagonal 2x2 block. Note: prow = row here */
        pc1 = rtmp11 + prow;
        pc2 = rtmp22 + prow;

        sctx.pv = *pc1;
        pj      = bj + bi[prow];
        rs      = 0.0;
        for (j = 0; j < nz; j++) {
          idx = pj[j];
          if (idx != prow) rs += PetscAbsScalar(rtmp11[idx]);
        }
        sctx.rs = rs;
        PetscCall(MatPivotCheck(B, A, info, &sctx, row));
        if (sctx.newshift) goto endofwhile;

        if (*pc2 != 0.0) {
          pj     = nbj + bd[prow];
          mul2   = (*pc2) / (*pc1); /* since diag is not yet inverted.*/
          *pc2   = mul2;
          nz_tmp = bi[prow + 1] - bd[prow] - 1;
          for (j = 0; j < nz_tmp; j++) {
            idx = pj[j];
            tmp = rtmp11[idx];
            rtmp22[idx] -= mul2 * tmp;
          }
          PetscCall(PetscLogFlops(1 + 2.0 * nz_tmp));
        }

        pj  = bj + bi[row];
        pc1 = ba + bi[row];
        pc2 = ba + bi[row + 1];

        sctx.pv         = rtmp22[row + 1];
        rs              = 0.0;
        rtmp11[row]     = 1.0 / rtmp11[row];
        rtmp22[row + 1] = 1.0 / rtmp22[row + 1];
        /* copy row entries from dense representation to sparse */
        for (j = 0; j < nz; j++) {
          idx    = pj[j];
          pc1[j] = rtmp11[idx];
          pc2[j] = rtmp22[idx];
          if (idx != row + 1) rs += PetscAbsScalar(pc2[j]);
        }
        sctx.rs = rs;
        PetscCall(MatPivotCheck(B, A, info, &sctx, row + 1));
        if (sctx.newshift) goto endofwhile;
        break;

      case 3:
        for (j = 0; j < nz; j++) {
          idx         = bjtmp[j];
          rtmp11[idx] = 0.0;
          rtmp22[idx] = 0.0;
          rtmp33[idx] = 0.0;
        }
        /* copy the nonzeros for the 3 rows from sparse representation to dense in rtmp*[] */
        idx    = r[row];
        nz_tmp = ai[idx + 1] - ai[idx];
        ajtmp  = aj + ai[idx];
        v1     = aa + ai[idx];
        v2     = aa + ai[idx + 1];
        v3     = aa + ai[idx + 2];
        for (j = 0; j < nz_tmp; j++) {
          idx         = ics[ajtmp[j]];
          rtmp11[idx] = v1[j];
          rtmp22[idx] = v2[j];
          rtmp33[idx] = v3[j];
        }
        rtmp11[ics[r[row]]] += sctx.shift_amount;
        rtmp22[ics[r[row + 1]]] += sctx.shift_amount;
        rtmp33[ics[r[row + 2]]] += sctx.shift_amount;

        /* loop over all pivot row blocks above this row block */
        prow = *bjtmp++;
        while (prow < row) {
          pc1 = rtmp11 + prow;
          pc2 = rtmp22 + prow;
          pc3 = rtmp33 + prow;
          if (*pc1 != 0.0 || *pc2 != 0.0 || *pc3 != 0.0) {
            pv   = ba + bd[prow];
            pj   = nbj + bd[prow];
            mul1 = *pc1 * *pv;
            mul2 = *pc2 * *pv;
            mul3 = *pc3 * *pv;
            ++pv;
            *pc1 = mul1;
            *pc2 = mul2;
            *pc3 = mul3;

            nz_tmp = bi[prow + 1] - bd[prow] - 1;
            /* update this row based on pivot row */
            for (j = 0; j < nz_tmp; j++) {
              tmp = pv[j];
              idx = pj[j];
              rtmp11[idx] -= mul1 * tmp;
              rtmp22[idx] -= mul2 * tmp;
              rtmp33[idx] -= mul3 * tmp;
            }
            PetscCall(PetscLogFlops(3 + 6.0 * nz_tmp));
          }
          prow = *bjtmp++;
        }

        /* Now take care of diagonal 3x3 block in this set of rows */
        /* note: prow = row here */
        pc1 = rtmp11 + prow;
        pc2 = rtmp22 + prow;
        pc3 = rtmp33 + prow;

        sctx.pv = *pc1;
        pj      = bj + bi[prow];
        rs      = 0.0;
        for (j = 0; j < nz; j++) {
          idx = pj[j];
          if (idx != row) rs += PetscAbsScalar(rtmp11[idx]);
        }
        sctx.rs = rs;
        PetscCall(MatPivotCheck(B, A, info, &sctx, row));
        if (sctx.newshift) goto endofwhile;

        if (*pc2 != 0.0 || *pc3 != 0.0) {
          mul2   = (*pc2) / (*pc1);
          mul3   = (*pc3) / (*pc1);
          *pc2   = mul2;
          *pc3   = mul3;
          nz_tmp = bi[prow + 1] - bd[prow] - 1;
          pj     = nbj + bd[prow];
          for (j = 0; j < nz_tmp; j++) {
            idx = pj[j];
            tmp = rtmp11[idx];
            rtmp22[idx] -= mul2 * tmp;
            rtmp33[idx] -= mul3 * tmp;
          }
          PetscCall(PetscLogFlops(2 + 4.0 * nz_tmp));
        }
        ++prow;

        pc2     = rtmp22 + prow;
        pc3     = rtmp33 + prow;
        sctx.pv = *pc2;
        pj      = bj + bi[prow];
        rs      = 0.0;
        for (j = 0; j < nz; j++) {
          idx = pj[j];
          if (idx != prow) rs += PetscAbsScalar(rtmp22[idx]);
        }
        sctx.rs = rs;
        PetscCall(MatPivotCheck(B, A, info, &sctx, row + 1));
        if (sctx.newshift) goto endofwhile;

        if (*pc3 != 0.0) {
          mul3   = (*pc3) / (*pc2);
          *pc3   = mul3;
          pj     = nbj + bd[prow];
          nz_tmp = bi[prow + 1] - bd[prow] - 1;
          for (j = 0; j < nz_tmp; j++) {
            idx = pj[j];
            tmp = rtmp22[idx];
            rtmp33[idx] -= mul3 * tmp;
          }
          PetscCall(PetscLogFlops(1 + 2.0 * nz_tmp));
        }

        pj  = bj + bi[row];
        pc1 = ba + bi[row];
        pc2 = ba + bi[row + 1];
        pc3 = ba + bi[row + 2];

        sctx.pv         = rtmp33[row + 2];
        rs              = 0.0;
        rtmp11[row]     = 1.0 / rtmp11[row];
        rtmp22[row + 1] = 1.0 / rtmp22[row + 1];
        rtmp33[row + 2] = 1.0 / rtmp33[row + 2];
        /* copy row entries from dense representation to sparse */
        for (j = 0; j < nz; j++) {
          idx    = pj[j];
          pc1[j] = rtmp11[idx];
          pc2[j] = rtmp22[idx];
          pc3[j] = rtmp33[idx];
          if (idx != row + 2) rs += PetscAbsScalar(pc3[j]);
        }

        sctx.rs = rs;
        PetscCall(MatPivotCheck(B, A, info, &sctx, row + 2));
        if (sctx.newshift) goto endofwhile;
        break;

      default:
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Node size not yet supported ");
      }
      row += nodesz; /* Update the row */
    }
  endofwhile:;
  } while (sctx.newshift);
  PetscCall(PetscFree3(rtmp11, rtmp22, rtmp33));
  PetscCall(PetscFree(tmp_vec2));
  PetscCall(ISRestoreIndices(isicol, &ic));
  PetscCall(ISRestoreIndices(isrow, &r));
  PetscCall(ISRestoreIndices(iscol, &c));

  (B)->ops->solve = MatSolve_SeqAIJ_inplace;
  /* do not set solve add, since MatSolve_Inode + Add is faster */
  C->ops->solvetranspose    = MatSolveTranspose_SeqAIJ_inplace;
  C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
  C->assembled              = PETSC_TRUE;
  C->preallocated           = PETSC_TRUE;
  if (sctx.nshift) {
    if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
      PetscCall(PetscInfo(A, "number of shift_pd tries %" PetscInt_FMT ", shift_amount %g, diagonal shifted up by %e fraction top_value %e\n", sctx.nshift, (double)sctx.shift_amount, (double)sctx.shift_fraction, (double)sctx.shift_top));
    } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
      PetscCall(PetscInfo(A, "number of shift_nz tries %" PetscInt_FMT ", shift_amount %g\n", sctx.nshift, (double)sctx.shift_amount));
    }
  }
  PetscCall(PetscLogFlops(C->cmap->n));
  PetscCall(MatSeqAIJCheckInode(C));
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

PetscErrorCode MatSolve_SeqAIJ_Inode(Mat A, Vec bb, Vec xx)
{
  Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
  IS                 iscol = a->col, isrow = a->row;
  const PetscInt    *r, *c, *rout, *cout;
  PetscInt           i, j, n = A->rmap->n;
  PetscInt           node_max, row, nsz, aii, i0, i1, nz;
  const PetscInt    *ai = a->i, *a_j = a->j, *ns, *vi, *ad, *aj;
  PetscScalar       *x, *tmp, *tmps, tmp0, tmp1;
  PetscScalar        sum1, sum2, sum3, sum4, sum5;
  const MatScalar   *v1, *v2, *v3, *v4, *v5, *a_a = a->a, *aa;
  const PetscScalar *b;

  PetscFunctionBegin;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  node_max = a->inode.node_count;
  ns       = a->inode.size; /* Node Size array */

  PetscCall(VecGetArrayRead(bb, &b));
  PetscCall(VecGetArrayWrite(xx, &x));
  tmp = a->solve_work;

  PetscCall(ISGetIndices(isrow, &rout));
  r = rout;
  PetscCall(ISGetIndices(iscol, &cout));
  c = cout;

  /* forward solve the lower triangular */
  tmps = tmp;
  aa   = a_a;
  aj   = a_j;
  ad   = a->diag;

  for (i = 0, row = 0; i < node_max; ++i) {
    nsz = ns[i];
    aii = ai[row];
    v1  = aa + aii;
    vi  = aj + aii;
    nz  = ai[row + 1] - ai[row];

    if (i < node_max - 1) {
      /* Prefetch the indices for the next block */
      PetscPrefetchBlock(aj + ai[row + nsz], ai[row + nsz + 1] - ai[row + nsz], 0, PETSC_PREFETCH_HINT_NTA); /* indices */
      /* Prefetch the data for the next block */
      PetscPrefetchBlock(aa + ai[row + nsz], ai[row + nsz + ns[i + 1]] - ai[row + nsz], 0, PETSC_PREFETCH_HINT_NTA);
    }

    switch (nsz) { /* Each loop in 'case' is unrolled */
    case 1:
      sum1 = b[r[row]];
      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
      }
      tmp[row++] = sum1;
      break;
    case 2:
      sum1 = b[r[row]];
      sum2 = b[r[row + 1]];
      v2   = aa + ai[row + 1];

      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
        sum2 -= v2[j] * tmp0 + v2[j + 1] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
        sum2 -= v2[j] * tmp0;
      }
      sum2 -= v2[nz] * sum1;
      tmp[row++] = sum1;
      tmp[row++] = sum2;
      break;
    case 3:
      sum1 = b[r[row]];
      sum2 = b[r[row + 1]];
      sum3 = b[r[row + 2]];
      v2   = aa + ai[row + 1];
      v3   = aa + ai[row + 2];

      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
        sum2 -= v2[j] * tmp0 + v2[j + 1] * tmp1;
        sum3 -= v3[j] * tmp0 + v3[j + 1] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
        sum2 -= v2[j] * tmp0;
        sum3 -= v3[j] * tmp0;
      }
      sum2 -= v2[nz] * sum1;
      sum3 -= v3[nz] * sum1;
      sum3 -= v3[nz + 1] * sum2;
      tmp[row++] = sum1;
      tmp[row++] = sum2;
      tmp[row++] = sum3;
      break;

    case 4:
      sum1 = b[r[row]];
      sum2 = b[r[row + 1]];
      sum3 = b[r[row + 2]];
      sum4 = b[r[row + 3]];
      v2   = aa + ai[row + 1];
      v3   = aa + ai[row + 2];
      v4   = aa + ai[row + 3];

      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
        sum2 -= v2[j] * tmp0 + v2[j + 1] * tmp1;
        sum3 -= v3[j] * tmp0 + v3[j + 1] * tmp1;
        sum4 -= v4[j] * tmp0 + v4[j + 1] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
        sum2 -= v2[j] * tmp0;
        sum3 -= v3[j] * tmp0;
        sum4 -= v4[j] * tmp0;
      }
      sum2 -= v2[nz] * sum1;
      sum3 -= v3[nz] * sum1;
      sum4 -= v4[nz] * sum1;
      sum3 -= v3[nz + 1] * sum2;
      sum4 -= v4[nz + 1] * sum2;
      sum4 -= v4[nz + 2] * sum3;

      tmp[row++] = sum1;
      tmp[row++] = sum2;
      tmp[row++] = sum3;
      tmp[row++] = sum4;
      break;
    case 5:
      sum1 = b[r[row]];
      sum2 = b[r[row + 1]];
      sum3 = b[r[row + 2]];
      sum4 = b[r[row + 3]];
      sum5 = b[r[row + 4]];
      v2   = aa + ai[row + 1];
      v3   = aa + ai[row + 2];
      v4   = aa + ai[row + 3];
      v5   = aa + ai[row + 4];

      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
        sum2 -= v2[j] * tmp0 + v2[j + 1] * tmp1;
        sum3 -= v3[j] * tmp0 + v3[j + 1] * tmp1;
        sum4 -= v4[j] * tmp0 + v4[j + 1] * tmp1;
        sum5 -= v5[j] * tmp0 + v5[j + 1] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
        sum2 -= v2[j] * tmp0;
        sum3 -= v3[j] * tmp0;
        sum4 -= v4[j] * tmp0;
        sum5 -= v5[j] * tmp0;
      }

      sum2 -= v2[nz] * sum1;
      sum3 -= v3[nz] * sum1;
      sum4 -= v4[nz] * sum1;
      sum5 -= v5[nz] * sum1;
      sum3 -= v3[nz + 1] * sum2;
      sum4 -= v4[nz + 1] * sum2;
      sum5 -= v5[nz + 1] * sum2;
      sum4 -= v4[nz + 2] * sum3;
      sum5 -= v5[nz + 2] * sum3;
      sum5 -= v5[nz + 3] * sum4;

      tmp[row++] = sum1;
      tmp[row++] = sum2;
      tmp[row++] = sum3;
      tmp[row++] = sum4;
      tmp[row++] = sum5;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported ");
    }
  }
  /* backward solve the upper triangular */
  for (i = node_max - 1, row = n - 1; i >= 0; i--) {
    nsz = ns[i];
    aii = ad[row + 1] + 1;
    v1  = aa + aii;
    vi  = aj + aii;
    nz  = ad[row] - ad[row + 1] - 1;

    if (i > 0) {
      /* Prefetch the indices for the next block */
      PetscPrefetchBlock(aj + ad[row - nsz + 1] + 1, ad[row - nsz] - ad[row - nsz + 1], 0, PETSC_PREFETCH_HINT_NTA);
      /* Prefetch the data for the next block */
      PetscPrefetchBlock(aa + ad[row - nsz + 1] + 1, ad[row - nsz - ns[i - 1] + 1] - ad[row - nsz + 1], 0, PETSC_PREFETCH_HINT_NTA);
    }

    switch (nsz) { /* Each loop in 'case' is unrolled */
    case 1:
      sum1 = tmp[row];

      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
      }
      x[c[row]] = tmp[row] = sum1 * v1[nz];
      row--;
      break;
    case 2:
      sum1 = tmp[row];
      sum2 = tmp[row - 1];
      v2   = aa + ad[row] + 1;
      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
        sum2 -= v2[j + 1] * tmp0 + v2[j + 2] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
        sum2 -= v2[j + 1] * tmp0;
      }

      tmp0 = x[c[row]] = tmp[row] = sum1 * v1[nz];
      row--;
      sum2 -= v2[0] * tmp0;
      x[c[row]] = tmp[row] = sum2 * v2[nz + 1];
      row--;
      break;
    case 3:
      sum1 = tmp[row];
      sum2 = tmp[row - 1];
      sum3 = tmp[row - 2];
      v2   = aa + ad[row] + 1;
      v3   = aa + ad[row - 1] + 1;
      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
        sum2 -= v2[j + 1] * tmp0 + v2[j + 2] * tmp1;
        sum3 -= v3[j + 2] * tmp0 + v3[j + 3] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
        sum2 -= v2[j + 1] * tmp0;
        sum3 -= v3[j + 2] * tmp0;
      }
      tmp0 = x[c[row]] = tmp[row] = sum1 * v1[nz];
      row--;
      sum2 -= v2[0] * tmp0;
      sum3 -= v3[1] * tmp0;
      tmp0 = x[c[row]] = tmp[row] = sum2 * v2[nz + 1];
      row--;
      sum3 -= v3[0] * tmp0;
      x[c[row]] = tmp[row] = sum3 * v3[nz + 2];
      row--;

      break;
    case 4:
      sum1 = tmp[row];
      sum2 = tmp[row - 1];
      sum3 = tmp[row - 2];
      sum4 = tmp[row - 3];
      v2   = aa + ad[row] + 1;
      v3   = aa + ad[row - 1] + 1;
      v4   = aa + ad[row - 2] + 1;

      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
        sum2 -= v2[j + 1] * tmp0 + v2[j + 2] * tmp1;
        sum3 -= v3[j + 2] * tmp0 + v3[j + 3] * tmp1;
        sum4 -= v4[j + 3] * tmp0 + v4[j + 4] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
        sum2 -= v2[j + 1] * tmp0;
        sum3 -= v3[j + 2] * tmp0;
        sum4 -= v4[j + 3] * tmp0;
      }

      tmp0 = x[c[row]] = tmp[row] = sum1 * v1[nz];
      row--;
      sum2 -= v2[0] * tmp0;
      sum3 -= v3[1] * tmp0;
      sum4 -= v4[2] * tmp0;
      tmp0 = x[c[row]] = tmp[row] = sum2 * v2[nz + 1];
      row--;
      sum3 -= v3[0] * tmp0;
      sum4 -= v4[1] * tmp0;
      tmp0 = x[c[row]] = tmp[row] = sum3 * v3[nz + 2];
      row--;
      sum4 -= v4[0] * tmp0;
      x[c[row]] = tmp[row] = sum4 * v4[nz + 3];
      row--;
      break;
    case 5:
      sum1 = tmp[row];
      sum2 = tmp[row - 1];
      sum3 = tmp[row - 2];
      sum4 = tmp[row - 3];
      sum5 = tmp[row - 4];
      v2   = aa + ad[row] + 1;
      v3   = aa + ad[row - 1] + 1;
      v4   = aa + ad[row - 2] + 1;
      v5   = aa + ad[row - 3] + 1;
      for (j = 0; j < nz - 1; j += 2) {
        i0   = vi[j];
        i1   = vi[j + 1];
        tmp0 = tmps[i0];
        tmp1 = tmps[i1];
        sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
        sum2 -= v2[j + 1] * tmp0 + v2[j + 2] * tmp1;
        sum3 -= v3[j + 2] * tmp0 + v3[j + 3] * tmp1;
        sum4 -= v4[j + 3] * tmp0 + v4[j + 4] * tmp1;
        sum5 -= v5[j + 4] * tmp0 + v5[j + 5] * tmp1;
      }
      if (j == nz - 1) {
        tmp0 = tmps[vi[j]];
        sum1 -= v1[j] * tmp0;
        sum2 -= v2[j + 1] * tmp0;
        sum3 -= v3[j + 2] * tmp0;
        sum4 -= v4[j + 3] * tmp0;
        sum5 -= v5[j + 4] * tmp0;
      }

      tmp0 = x[c[row]] = tmp[row] = sum1 * v1[nz];
      row--;
      sum2 -= v2[0] * tmp0;
      sum3 -= v3[1] * tmp0;
      sum4 -= v4[2] * tmp0;
      sum5 -= v5[3] * tmp0;
      tmp0 = x[c[row]] = tmp[row] = sum2 * v2[nz + 1];
      row--;
      sum3 -= v3[0] * tmp0;
      sum4 -= v4[1] * tmp0;
      sum5 -= v5[2] * tmp0;
      tmp0 = x[c[row]] = tmp[row] = sum3 * v3[nz + 2];
      row--;
      sum4 -= v4[0] * tmp0;
      sum5 -= v5[1] * tmp0;
      tmp0 = x[c[row]] = tmp[row] = sum4 * v4[nz + 3];
      row--;
      sum5 -= v5[0] * tmp0;
      x[c[row]] = tmp[row] = sum5 * v5[nz + 4];
      row--;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported ");
    }
  }
  PetscCall(ISRestoreIndices(isrow, &rout));
  PetscCall(ISRestoreIndices(iscol, &cout));
  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArrayWrite(xx, &x));
  PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
     Makes a longer coloring[] array and calls the usual code with that
*/
static PetscErrorCode MatColoringPatch_SeqAIJ_Inode(Mat mat, PetscInt ncolors, PetscInt nin, ISColoringValue coloring[], ISColoring *iscoloring)
{
  Mat_SeqAIJ      *a = (Mat_SeqAIJ *)mat->data;
  PetscInt         n = mat->cmap->n, m = a->inode.node_count, j, *ns = a->inode.size, row;
  PetscInt        *colorused, i;
  ISColoringValue *newcolor;

  PetscFunctionBegin;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  PetscCall(PetscMalloc1(n + 1, &newcolor));
  /* loop over inodes, marking a color for each column*/
  row = 0;
  for (i = 0; i < m; i++) {
    for (j = 0; j < ns[i]; j++) PetscCall(ISColoringValueCast(coloring[i] + j * ncolors, newcolor + row++));
  }

  /* eliminate unneeded colors */
  PetscCall(PetscCalloc1(5 * ncolors, &colorused));
  for (i = 0; i < n; i++) colorused[newcolor[i]] = 1;

  for (i = 1; i < 5 * ncolors; i++) colorused[i] += colorused[i - 1];
  ncolors = colorused[5 * ncolors - 1];
  for (i = 0; i < n; i++) PetscCall(ISColoringValueCast(colorused[newcolor[i]] - 1, newcolor + i));
  PetscCall(PetscFree(colorused));
  PetscCall(ISColoringCreate(PetscObjectComm((PetscObject)mat), ncolors, n, newcolor, PETSC_OWN_POINTER, iscoloring));
  PetscCall(PetscFree(coloring));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

PetscErrorCode MatSOR_SeqAIJ_Inode(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
{
  Mat_SeqAIJ        *a    = (Mat_SeqAIJ *)A->data;
  PetscScalar        sum1 = 0.0, sum2 = 0.0, sum3 = 0.0, sum4 = 0.0, sum5 = 0.0, tmp0, tmp1, tmp2, tmp3;
  MatScalar         *ibdiag, *bdiag, work[25], *t;
  PetscScalar       *x, tmp4, tmp5, x1, x2, x3, x4, x5;
  const MatScalar   *v = a->a, *v1 = NULL, *v2 = NULL, *v3 = NULL, *v4 = NULL, *v5 = NULL;
  const PetscScalar *xb, *b;
  PetscReal          zeropivot = 100. * PETSC_MACHINE_EPSILON, shift = 0.0;
  PetscInt           n, m = a->inode.node_count, cnt = 0, i, j, row, i1, i2;
  PetscInt           sz, k, ipvt[5];
  PetscBool          allowzeropivot, zeropivotdetected;
  const PetscInt    *sizes = a->inode.size, *idx, *diag = a->diag, *ii = a->i;

  PetscFunctionBegin;
  allowzeropivot = PetscNot(A->erroriffailure);
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  PetscCheck(omega == 1.0, PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for omega != 1.0; use -mat_no_inode");
  PetscCheck(fshift == 0.0, PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for fshift != 0.0; use -mat_no_inode");

  if (!a->inode.ibdiagvalid) {
    if (!a->inode.ibdiag) {
      /* calculate space needed for diagonal blocks */
      for (i = 0; i < m; i++) cnt += sizes[i] * sizes[i];
      a->inode.bdiagsize = cnt;

      PetscCall(PetscMalloc3(cnt, &a->inode.ibdiag, cnt, &a->inode.bdiag, A->rmap->n, &a->inode.ssor_work));
    }

    /* copy over the diagonal blocks and invert them */
    ibdiag = a->inode.ibdiag;
    bdiag  = a->inode.bdiag;
    cnt    = 0;
    for (i = 0, row = 0; i < m; i++) {
      for (j = 0; j < sizes[i]; j++) {
        for (k = 0; k < sizes[i]; k++) bdiag[cnt + k * sizes[i] + j] = v[diag[row + j] - j + k];
      }
      PetscCall(PetscArraycpy(ibdiag + cnt, bdiag + cnt, sizes[i] * sizes[i]));

      switch (sizes[i]) {
      case 1:
        /* Create matrix data structure */
        if (PetscAbsScalar(ibdiag[cnt]) < zeropivot) {
          if (allowzeropivot) {
            A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
            A->factorerror_zeropivot_value = PetscAbsScalar(ibdiag[cnt]);
            A->factorerror_zeropivot_row   = row;
            PetscCall(PetscInfo(A, "Zero pivot, row %" PetscInt_FMT "\n", row));
          } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot on row %" PetscInt_FMT, row);
        }
        ibdiag[cnt] = 1.0 / ibdiag[cnt];
        break;
      case 2:
        PetscCall(PetscKernel_A_gets_inverse_A_2(ibdiag + cnt, shift, allowzeropivot, &zeropivotdetected));
        if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
        break;
      case 3:
        PetscCall(PetscKernel_A_gets_inverse_A_3(ibdiag + cnt, shift, allowzeropivot, &zeropivotdetected));
        if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
        break;
      case 4:
        PetscCall(PetscKernel_A_gets_inverse_A_4(ibdiag + cnt, shift, allowzeropivot, &zeropivotdetected));
        if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
        break;
      case 5:
        PetscCall(PetscKernel_A_gets_inverse_A_5(ibdiag + cnt, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
        if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
        break;
      default:
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
      }
      cnt += sizes[i] * sizes[i];
      row += sizes[i];
    }
    a->inode.ibdiagvalid = PETSC_TRUE;
  }
  ibdiag = a->inode.ibdiag;
  bdiag  = a->inode.bdiag;
  t      = a->inode.ssor_work;

  PetscCall(VecGetArray(xx, &x));
  PetscCall(VecGetArrayRead(bb, &b));
  /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
  if (flag & SOR_ZERO_INITIAL_GUESS) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
      for (i = 0, row = 0; i < m; i++) {
        sz  = diag[row] - ii[row];
        v1  = a->a + ii[row];
        idx = a->j + ii[row];

        /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
        switch (sizes[i]) {
        case 1:

          sum1 = b[row];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= *v1 * tmp0;
          }
          t[row]   = sum1;
          x[row++] = sum1 * (*ibdiag++);
          break;
        case 2:
          v2   = a->a + ii[row + 1];
          sum1 = b[row];
          sum2 = b[row + 1];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
          }
          t[row]     = sum1;
          t[row + 1] = sum2;
          x[row++]   = sum1 * ibdiag[0] + sum2 * ibdiag[2];
          x[row++]   = sum1 * ibdiag[1] + sum2 * ibdiag[3];
          ibdiag += 4;
          break;
        case 3:
          v2   = a->a + ii[row + 1];
          v3   = a->a + ii[row + 2];
          sum1 = b[row];
          sum2 = b[row + 1];
          sum3 = b[row + 2];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
          }
          t[row]     = sum1;
          t[row + 1] = sum2;
          t[row + 2] = sum3;
          x[row++]   = sum1 * ibdiag[0] + sum2 * ibdiag[3] + sum3 * ibdiag[6];
          x[row++]   = sum1 * ibdiag[1] + sum2 * ibdiag[4] + sum3 * ibdiag[7];
          x[row++]   = sum1 * ibdiag[2] + sum2 * ibdiag[5] + sum3 * ibdiag[8];
          ibdiag += 9;
          break;
        case 4:
          v2   = a->a + ii[row + 1];
          v3   = a->a + ii[row + 2];
          v4   = a->a + ii[row + 3];
          sum1 = b[row];
          sum2 = b[row + 1];
          sum3 = b[row + 2];
          sum4 = b[row + 3];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
            sum4 -= v4[0] * tmp0;
          }
          t[row]     = sum1;
          t[row + 1] = sum2;
          t[row + 2] = sum3;
          t[row + 3] = sum4;
          x[row++]   = sum1 * ibdiag[0] + sum2 * ibdiag[4] + sum3 * ibdiag[8] + sum4 * ibdiag[12];
          x[row++]   = sum1 * ibdiag[1] + sum2 * ibdiag[5] + sum3 * ibdiag[9] + sum4 * ibdiag[13];
          x[row++]   = sum1 * ibdiag[2] + sum2 * ibdiag[6] + sum3 * ibdiag[10] + sum4 * ibdiag[14];
          x[row++]   = sum1 * ibdiag[3] + sum2 * ibdiag[7] + sum3 * ibdiag[11] + sum4 * ibdiag[15];
          ibdiag += 16;
          break;
        case 5:
          v2   = a->a + ii[row + 1];
          v3   = a->a + ii[row + 2];
          v4   = a->a + ii[row + 3];
          v5   = a->a + ii[row + 4];
          sum1 = b[row];
          sum2 = b[row + 1];
          sum3 = b[row + 2];
          sum4 = b[row + 3];
          sum5 = b[row + 4];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2;
            sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
            v5 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
            sum4 -= v4[0] * tmp0;
            sum5 -= v5[0] * tmp0;
          }
          t[row]     = sum1;
          t[row + 1] = sum2;
          t[row + 2] = sum3;
          t[row + 3] = sum4;
          t[row + 4] = sum5;
          x[row++]   = sum1 * ibdiag[0] + sum2 * ibdiag[5] + sum3 * ibdiag[10] + sum4 * ibdiag[15] + sum5 * ibdiag[20];
          x[row++]   = sum1 * ibdiag[1] + sum2 * ibdiag[6] + sum3 * ibdiag[11] + sum4 * ibdiag[16] + sum5 * ibdiag[21];
          x[row++]   = sum1 * ibdiag[2] + sum2 * ibdiag[7] + sum3 * ibdiag[12] + sum4 * ibdiag[17] + sum5 * ibdiag[22];
          x[row++]   = sum1 * ibdiag[3] + sum2 * ibdiag[8] + sum3 * ibdiag[13] + sum4 * ibdiag[18] + sum5 * ibdiag[23];
          x[row++]   = sum1 * ibdiag[4] + sum2 * ibdiag[9] + sum3 * ibdiag[14] + sum4 * ibdiag[19] + sum5 * ibdiag[24];
          ibdiag += 25;
          break;
        default:
          SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
        }
      }

      xb = t;
      PetscCall(PetscLogFlops(a->nz));
    } else xb = b;
    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
      ibdiag = a->inode.ibdiag + a->inode.bdiagsize;
      for (i = m - 1, row = A->rmap->n - 1; i >= 0; i--) {
        ibdiag -= sizes[i] * sizes[i];
        sz  = ii[row + 1] - diag[row] - 1;
        v1  = a->a + diag[row] + 1;
        idx = a->j + diag[row] + 1;

        /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
        switch (sizes[i]) {
        case 1:

          sum1 = xb[row];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= *v1 * tmp0;
          }
          x[row--] = sum1 * (*ibdiag);
          break;

        case 2:

          sum1 = xb[row];
          sum2 = xb[row - 1];
          /* note that sum1 is associated with the second of the two rows */
          v2 = a->a + diag[row - 1] + 2;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= *v1 * tmp0;
            sum2 -= *v2 * tmp0;
          }
          x[row--] = sum2 * ibdiag[1] + sum1 * ibdiag[3];
          x[row--] = sum2 * ibdiag[0] + sum1 * ibdiag[2];
          break;
        case 3:

          sum1 = xb[row];
          sum2 = xb[row - 1];
          sum3 = xb[row - 2];
          v2   = a->a + diag[row - 1] + 2;
          v3   = a->a + diag[row - 2] + 3;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= *v1 * tmp0;
            sum2 -= *v2 * tmp0;
            sum3 -= *v3 * tmp0;
          }
          x[row--] = sum3 * ibdiag[2] + sum2 * ibdiag[5] + sum1 * ibdiag[8];
          x[row--] = sum3 * ibdiag[1] + sum2 * ibdiag[4] + sum1 * ibdiag[7];
          x[row--] = sum3 * ibdiag[0] + sum2 * ibdiag[3] + sum1 * ibdiag[6];
          break;
        case 4:

          sum1 = xb[row];
          sum2 = xb[row - 1];
          sum3 = xb[row - 2];
          sum4 = xb[row - 3];
          v2   = a->a + diag[row - 1] + 2;
          v3   = a->a + diag[row - 2] + 3;
          v4   = a->a + diag[row - 3] + 4;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= *v1 * tmp0;
            sum2 -= *v2 * tmp0;
            sum3 -= *v3 * tmp0;
            sum4 -= *v4 * tmp0;
          }
          x[row--] = sum4 * ibdiag[3] + sum3 * ibdiag[7] + sum2 * ibdiag[11] + sum1 * ibdiag[15];
          x[row--] = sum4 * ibdiag[2] + sum3 * ibdiag[6] + sum2 * ibdiag[10] + sum1 * ibdiag[14];
          x[row--] = sum4 * ibdiag[1] + sum3 * ibdiag[5] + sum2 * ibdiag[9] + sum1 * ibdiag[13];
          x[row--] = sum4 * ibdiag[0] + sum3 * ibdiag[4] + sum2 * ibdiag[8] + sum1 * ibdiag[12];
          break;
        case 5:

          sum1 = xb[row];
          sum2 = xb[row - 1];
          sum3 = xb[row - 2];
          sum4 = xb[row - 3];
          sum5 = xb[row - 4];
          v2   = a->a + diag[row - 1] + 2;
          v3   = a->a + diag[row - 2] + 3;
          v4   = a->a + diag[row - 3] + 4;
          v5   = a->a + diag[row - 4] + 5;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2;
            sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
            v5 += 2;
          }

          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= *v1 * tmp0;
            sum2 -= *v2 * tmp0;
            sum3 -= *v3 * tmp0;
            sum4 -= *v4 * tmp0;
            sum5 -= *v5 * tmp0;
          }
          x[row--] = sum5 * ibdiag[4] + sum4 * ibdiag[9] + sum3 * ibdiag[14] + sum2 * ibdiag[19] + sum1 * ibdiag[24];
          x[row--] = sum5 * ibdiag[3] + sum4 * ibdiag[8] + sum3 * ibdiag[13] + sum2 * ibdiag[18] + sum1 * ibdiag[23];
          x[row--] = sum5 * ibdiag[2] + sum4 * ibdiag[7] + sum3 * ibdiag[12] + sum2 * ibdiag[17] + sum1 * ibdiag[22];
          x[row--] = sum5 * ibdiag[1] + sum4 * ibdiag[6] + sum3 * ibdiag[11] + sum2 * ibdiag[16] + sum1 * ibdiag[21];
          x[row--] = sum5 * ibdiag[0] + sum4 * ibdiag[5] + sum3 * ibdiag[10] + sum2 * ibdiag[15] + sum1 * ibdiag[20];
          break;
        default:
          SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
        }
      }

      PetscCall(PetscLogFlops(a->nz));
    }
    its--;
  }
  while (its--) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
      for (i = 0, row = 0, ibdiag = a->inode.ibdiag; i < m; row += sizes[i], ibdiag += sizes[i] * sizes[i], i++) {
        sz  = diag[row] - ii[row];
        v1  = a->a + ii[row];
        idx = a->j + ii[row];
        /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
        switch (sizes[i]) {
        case 1:
          sum1 = b[row];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx++];
            sum1 -= *v1 * tmp0;
            v1++;
          }
          t[row] = sum1;
          sz     = ii[row + 1] - diag[row] - 1;
          idx    = a->j + diag[row] + 1;
          v1 += 1;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx++];
            sum1 -= *v1 * tmp0;
          }
          /* in MatSOR_SeqAIJ this line would be
           *
           * x[row] = (1-omega)*x[row]+(sum1+(*bdiag++)*x[row])*(*ibdiag++);
           *
           * but omega == 1, so this becomes
           *
           * x[row] = sum1*(*ibdiag++);
           *
           */
          x[row] = sum1 * (*ibdiag);
          break;
        case 2:
          v2   = a->a + ii[row + 1];
          sum1 = b[row];
          sum2 = b[row + 1];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx++];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            v1++;
            v2++;
          }
          t[row]     = sum1;
          t[row + 1] = sum2;
          sz         = ii[row + 1] - diag[row] - 2;
          idx        = a->j + diag[row] + 2;
          v1 += 2;
          v2 += 2;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
          }
          x[row]     = sum1 * ibdiag[0] + sum2 * ibdiag[2];
          x[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[3];
          break;
        case 3:
          v2   = a->a + ii[row + 1];
          v3   = a->a + ii[row + 2];
          sum1 = b[row];
          sum2 = b[row + 1];
          sum3 = b[row + 2];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx++];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
            v1++;
            v2++;
            v3++;
          }
          t[row]     = sum1;
          t[row + 1] = sum2;
          t[row + 2] = sum3;
          sz         = ii[row + 1] - diag[row] - 3;
          idx        = a->j + diag[row] + 3;
          v1 += 3;
          v2 += 3;
          v3 += 3;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
          }
          x[row]     = sum1 * ibdiag[0] + sum2 * ibdiag[3] + sum3 * ibdiag[6];
          x[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[4] + sum3 * ibdiag[7];
          x[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[5] + sum3 * ibdiag[8];
          break;
        case 4:
          v2   = a->a + ii[row + 1];
          v3   = a->a + ii[row + 2];
          v4   = a->a + ii[row + 3];
          sum1 = b[row];
          sum2 = b[row + 1];
          sum3 = b[row + 2];
          sum4 = b[row + 3];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx++];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
            sum4 -= v4[0] * tmp0;
            v1++;
            v2++;
            v3++;
            v4++;
          }
          t[row]     = sum1;
          t[row + 1] = sum2;
          t[row + 2] = sum3;
          t[row + 3] = sum4;
          sz         = ii[row + 1] - diag[row] - 4;
          idx        = a->j + diag[row] + 4;
          v1 += 4;
          v2 += 4;
          v3 += 4;
          v4 += 4;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
            sum4 -= v4[0] * tmp0;
          }
          x[row]     = sum1 * ibdiag[0] + sum2 * ibdiag[4] + sum3 * ibdiag[8] + sum4 * ibdiag[12];
          x[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[5] + sum3 * ibdiag[9] + sum4 * ibdiag[13];
          x[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[6] + sum3 * ibdiag[10] + sum4 * ibdiag[14];
          x[row + 3] = sum1 * ibdiag[3] + sum2 * ibdiag[7] + sum3 * ibdiag[11] + sum4 * ibdiag[15];
          break;
        case 5:
          v2   = a->a + ii[row + 1];
          v3   = a->a + ii[row + 2];
          v4   = a->a + ii[row + 3];
          v5   = a->a + ii[row + 4];
          sum1 = b[row];
          sum2 = b[row + 1];
          sum3 = b[row + 2];
          sum4 = b[row + 3];
          sum5 = b[row + 4];
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2;
            sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
            v5 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx++];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
            sum4 -= v4[0] * tmp0;
            sum5 -= v5[0] * tmp0;
            v1++;
            v2++;
            v3++;
            v4++;
            v5++;
          }
          t[row]     = sum1;
          t[row + 1] = sum2;
          t[row + 2] = sum3;
          t[row + 3] = sum4;
          t[row + 4] = sum5;
          sz         = ii[row + 1] - diag[row] - 5;
          idx        = a->j + diag[row] + 5;
          v1 += 5;
          v2 += 5;
          v3 += 5;
          v4 += 5;
          v5 += 5;
          for (n = 0; n < sz - 1; n += 2) {
            i1 = idx[0];
            i2 = idx[1];
            idx += 2;
            tmp0 = x[i1];
            tmp1 = x[i2];
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2;
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2;
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2;
            sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
            v5 += 2;
          }
          if (n == sz - 1) {
            tmp0 = x[*idx];
            sum1 -= v1[0] * tmp0;
            sum2 -= v2[0] * tmp0;
            sum3 -= v3[0] * tmp0;
            sum4 -= v4[0] * tmp0;
            sum5 -= v5[0] * tmp0;
          }
          x[row]     = sum1 * ibdiag[0] + sum2 * ibdiag[5] + sum3 * ibdiag[10] + sum4 * ibdiag[15] + sum5 * ibdiag[20];
          x[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[6] + sum3 * ibdiag[11] + sum4 * ibdiag[16] + sum5 * ibdiag[21];
          x[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[7] + sum3 * ibdiag[12] + sum4 * ibdiag[17] + sum5 * ibdiag[22];
          x[row + 3] = sum1 * ibdiag[3] + sum2 * ibdiag[8] + sum3 * ibdiag[13] + sum4 * ibdiag[18] + sum5 * ibdiag[23];
          x[row + 4] = sum1 * ibdiag[4] + sum2 * ibdiag[9] + sum3 * ibdiag[14] + sum4 * ibdiag[19] + sum5 * ibdiag[24];
          break;
        default:
          SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
        }
      }
      xb = t;
      PetscCall(PetscLogFlops(2.0 * a->nz)); /* undercounts diag inverse */
    } else xb = b;

    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
      ibdiag = a->inode.ibdiag + a->inode.bdiagsize;
      for (i = m - 1, row = A->rmap->n - 1; i >= 0; i--) {
        ibdiag -= sizes[i] * sizes[i];

        /* set RHS */
        if (xb == b) {
          /* whole (old way) */
          sz  = ii[row + 1] - ii[row];
          idx = a->j + ii[row];
          switch (sizes[i]) {
          case 5:
            v5 = a->a + ii[row - 4]; /* fall through */
          case 4:
            v4 = a->a + ii[row - 3]; /* fall through */
          case 3:
            v3 = a->a + ii[row - 2]; /* fall through */
          case 2:
            v2 = a->a + ii[row - 1]; /* fall through */
          case 1:
            v1 = a->a + ii[row];
            break;
          default:
            SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
          }
        } else {
          /* upper, no diag */
          sz  = ii[row + 1] - diag[row] - 1;
          idx = a->j + diag[row] + 1;
          switch (sizes[i]) {
          case 5:
            v5 = a->a + diag[row - 4] + 5; /* fall through */
          case 4:
            v4 = a->a + diag[row - 3] + 4; /* fall through */
          case 3:
            v3 = a->a + diag[row - 2] + 3; /* fall through */
          case 2:
            v2 = a->a + diag[row - 1] + 2; /* fall through */
          case 1:
            v1 = a->a + diag[row] + 1;
          }
        }
        /* set sum */
        switch (sizes[i]) {
        case 5:
          sum5 = xb[row - 4]; /* fall through */
        case 4:
          sum4 = xb[row - 3]; /* fall through */
        case 3:
          sum3 = xb[row - 2]; /* fall through */
        case 2:
          sum2 = xb[row - 1]; /* fall through */
        case 1:
          /* note that sum1 is associated with the last row */
          sum1 = xb[row];
        }
        /* do sums */
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = x[i1];
          tmp1 = x[i2];
          switch (sizes[i]) {
          case 5:
            sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
            v5 += 2; /* fall through */
          case 4:
            sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
            v4 += 2; /* fall through */
          case 3:
            sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
            v3 += 2; /* fall through */
          case 2:
            sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
            v2 += 2; /* fall through */
          case 1:
            sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
            v1 += 2;
          }
        }
        /* ragged edge */
        if (n == sz - 1) {
          tmp0 = x[*idx];
          switch (sizes[i]) {
          case 5:
            sum5 -= *v5 * tmp0; /* fall through */
          case 4:
            sum4 -= *v4 * tmp0; /* fall through */
          case 3:
            sum3 -= *v3 * tmp0; /* fall through */
          case 2:
            sum2 -= *v2 * tmp0; /* fall through */
          case 1:
            sum1 -= *v1 * tmp0;
          }
        }
        /* update */
        if (xb == b) {
          /* whole (old way) w/ diag */
          switch (sizes[i]) {
          case 5:
            x[row--] += sum5 * ibdiag[4] + sum4 * ibdiag[9] + sum3 * ibdiag[14] + sum2 * ibdiag[19] + sum1 * ibdiag[24];
            x[row--] += sum5 * ibdiag[3] + sum4 * ibdiag[8] + sum3 * ibdiag[13] + sum2 * ibdiag[18] + sum1 * ibdiag[23];
            x[row--] += sum5 * ibdiag[2] + sum4 * ibdiag[7] + sum3 * ibdiag[12] + sum2 * ibdiag[17] + sum1 * ibdiag[22];
            x[row--] += sum5 * ibdiag[1] + sum4 * ibdiag[6] + sum3 * ibdiag[11] + sum2 * ibdiag[16] + sum1 * ibdiag[21];
            x[row--] += sum5 * ibdiag[0] + sum4 * ibdiag[5] + sum3 * ibdiag[10] + sum2 * ibdiag[15] + sum1 * ibdiag[20];
            break;
          case 4:
            x[row--] += sum4 * ibdiag[3] + sum3 * ibdiag[7] + sum2 * ibdiag[11] + sum1 * ibdiag[15];
            x[row--] += sum4 * ibdiag[2] + sum3 * ibdiag[6] + sum2 * ibdiag[10] + sum1 * ibdiag[14];
            x[row--] += sum4 * ibdiag[1] + sum3 * ibdiag[5] + sum2 * ibdiag[9] + sum1 * ibdiag[13];
            x[row--] += sum4 * ibdiag[0] + sum3 * ibdiag[4] + sum2 * ibdiag[8] + sum1 * ibdiag[12];
            break;
          case 3:
            x[row--] += sum3 * ibdiag[2] + sum2 * ibdiag[5] + sum1 * ibdiag[8];
            x[row--] += sum3 * ibdiag[1] + sum2 * ibdiag[4] + sum1 * ibdiag[7];
            x[row--] += sum3 * ibdiag[0] + sum2 * ibdiag[3] + sum1 * ibdiag[6];
            break;
          case 2:
            x[row--] += sum2 * ibdiag[1] + sum1 * ibdiag[3];
            x[row--] += sum2 * ibdiag[0] + sum1 * ibdiag[2];
            break;
          case 1:
            x[row--] += sum1 * (*ibdiag);
            break;
          }
        } else {
          /* no diag so set =  */
          switch (sizes[i]) {
          case 5:
            x[row--] = sum5 * ibdiag[4] + sum4 * ibdiag[9] + sum3 * ibdiag[14] + sum2 * ibdiag[19] + sum1 * ibdiag[24];
            x[row--] = sum5 * ibdiag[3] + sum4 * ibdiag[8] + sum3 * ibdiag[13] + sum2 * ibdiag[18] + sum1 * ibdiag[23];
            x[row--] = sum5 * ibdiag[2] + sum4 * ibdiag[7] + sum3 * ibdiag[12] + sum2 * ibdiag[17] + sum1 * ibdiag[22];
            x[row--] = sum5 * ibdiag[1] + sum4 * ibdiag[6] + sum3 * ibdiag[11] + sum2 * ibdiag[16] + sum1 * ibdiag[21];
            x[row--] = sum5 * ibdiag[0] + sum4 * ibdiag[5] + sum3 * ibdiag[10] + sum2 * ibdiag[15] + sum1 * ibdiag[20];
            break;
          case 4:
            x[row--] = sum4 * ibdiag[3] + sum3 * ibdiag[7] + sum2 * ibdiag[11] + sum1 * ibdiag[15];
            x[row--] = sum4 * ibdiag[2] + sum3 * ibdiag[6] + sum2 * ibdiag[10] + sum1 * ibdiag[14];
            x[row--] = sum4 * ibdiag[1] + sum3 * ibdiag[5] + sum2 * ibdiag[9] + sum1 * ibdiag[13];
            x[row--] = sum4 * ibdiag[0] + sum3 * ibdiag[4] + sum2 * ibdiag[8] + sum1 * ibdiag[12];
            break;
          case 3:
            x[row--] = sum3 * ibdiag[2] + sum2 * ibdiag[5] + sum1 * ibdiag[8];
            x[row--] = sum3 * ibdiag[1] + sum2 * ibdiag[4] + sum1 * ibdiag[7];
            x[row--] = sum3 * ibdiag[0] + sum2 * ibdiag[3] + sum1 * ibdiag[6];
            break;
          case 2:
            x[row--] = sum2 * ibdiag[1] + sum1 * ibdiag[3];
            x[row--] = sum2 * ibdiag[0] + sum1 * ibdiag[2];
            break;
          case 1:
            x[row--] = sum1 * (*ibdiag);
            break;
          }
        }
      }
      if (xb == b) {
        PetscCall(PetscLogFlops(2.0 * a->nz));
      } else {
        PetscCall(PetscLogFlops(a->nz)); /* assumes 1/2 in upper, undercounts diag inverse */
      }
    }
  }
  if (flag & SOR_EISENSTAT) {
    /*
          Apply  (U + D)^-1  where D is now the block diagonal
    */
    ibdiag = a->inode.ibdiag + a->inode.bdiagsize;
    for (i = m - 1, row = A->rmap->n - 1; i >= 0; i--) {
      ibdiag -= sizes[i] * sizes[i];
      sz  = ii[row + 1] - diag[row] - 1;
      v1  = a->a + diag[row] + 1;
      idx = a->j + diag[row] + 1;
      /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
      switch (sizes[i]) {
      case 1:

        sum1 = b[row];
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = x[i1];
          tmp1 = x[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
        }

        if (n == sz - 1) {
          tmp0 = x[*idx];
          sum1 -= *v1 * tmp0;
        }
        x[row] = sum1 * (*ibdiag);
        row--;
        break;

      case 2:

        sum1 = b[row];
        sum2 = b[row - 1];
        /* note that sum1 is associated with the second of the two rows */
        v2 = a->a + diag[row - 1] + 2;
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = x[i1];
          tmp1 = x[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
          sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
          v2 += 2;
        }

        if (n == sz - 1) {
          tmp0 = x[*idx];
          sum1 -= *v1 * tmp0;
          sum2 -= *v2 * tmp0;
        }
        x[row]     = sum2 * ibdiag[1] + sum1 * ibdiag[3];
        x[row - 1] = sum2 * ibdiag[0] + sum1 * ibdiag[2];
        row -= 2;
        break;
      case 3:

        sum1 = b[row];
        sum2 = b[row - 1];
        sum3 = b[row - 2];
        v2   = a->a + diag[row - 1] + 2;
        v3   = a->a + diag[row - 2] + 3;
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = x[i1];
          tmp1 = x[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
          sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
          v2 += 2;
          sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
          v3 += 2;
        }

        if (n == sz - 1) {
          tmp0 = x[*idx];
          sum1 -= *v1 * tmp0;
          sum2 -= *v2 * tmp0;
          sum3 -= *v3 * tmp0;
        }
        x[row]     = sum3 * ibdiag[2] + sum2 * ibdiag[5] + sum1 * ibdiag[8];
        x[row - 1] = sum3 * ibdiag[1] + sum2 * ibdiag[4] + sum1 * ibdiag[7];
        x[row - 2] = sum3 * ibdiag[0] + sum2 * ibdiag[3] + sum1 * ibdiag[6];
        row -= 3;
        break;
      case 4:

        sum1 = b[row];
        sum2 = b[row - 1];
        sum3 = b[row - 2];
        sum4 = b[row - 3];
        v2   = a->a + diag[row - 1] + 2;
        v3   = a->a + diag[row - 2] + 3;
        v4   = a->a + diag[row - 3] + 4;
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = x[i1];
          tmp1 = x[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
          sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
          v2 += 2;
          sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
          v3 += 2;
          sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
          v4 += 2;
        }

        if (n == sz - 1) {
          tmp0 = x[*idx];
          sum1 -= *v1 * tmp0;
          sum2 -= *v2 * tmp0;
          sum3 -= *v3 * tmp0;
          sum4 -= *v4 * tmp0;
        }
        x[row]     = sum4 * ibdiag[3] + sum3 * ibdiag[7] + sum2 * ibdiag[11] + sum1 * ibdiag[15];
        x[row - 1] = sum4 * ibdiag[2] + sum3 * ibdiag[6] + sum2 * ibdiag[10] + sum1 * ibdiag[14];
        x[row - 2] = sum4 * ibdiag[1] + sum3 * ibdiag[5] + sum2 * ibdiag[9] + sum1 * ibdiag[13];
        x[row - 3] = sum4 * ibdiag[0] + sum3 * ibdiag[4] + sum2 * ibdiag[8] + sum1 * ibdiag[12];
        row -= 4;
        break;
      case 5:

        sum1 = b[row];
        sum2 = b[row - 1];
        sum3 = b[row - 2];
        sum4 = b[row - 3];
        sum5 = b[row - 4];
        v2   = a->a + diag[row - 1] + 2;
        v3   = a->a + diag[row - 2] + 3;
        v4   = a->a + diag[row - 3] + 4;
        v5   = a->a + diag[row - 4] + 5;
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = x[i1];
          tmp1 = x[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
          sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
          v2 += 2;
          sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
          v3 += 2;
          sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
          v4 += 2;
          sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
          v5 += 2;
        }

        if (n == sz - 1) {
          tmp0 = x[*idx];
          sum1 -= *v1 * tmp0;
          sum2 -= *v2 * tmp0;
          sum3 -= *v3 * tmp0;
          sum4 -= *v4 * tmp0;
          sum5 -= *v5 * tmp0;
        }
        x[row]     = sum5 * ibdiag[4] + sum4 * ibdiag[9] + sum3 * ibdiag[14] + sum2 * ibdiag[19] + sum1 * ibdiag[24];
        x[row - 1] = sum5 * ibdiag[3] + sum4 * ibdiag[8] + sum3 * ibdiag[13] + sum2 * ibdiag[18] + sum1 * ibdiag[23];
        x[row - 2] = sum5 * ibdiag[2] + sum4 * ibdiag[7] + sum3 * ibdiag[12] + sum2 * ibdiag[17] + sum1 * ibdiag[22];
        x[row - 3] = sum5 * ibdiag[1] + sum4 * ibdiag[6] + sum3 * ibdiag[11] + sum2 * ibdiag[16] + sum1 * ibdiag[21];
        x[row - 4] = sum5 * ibdiag[0] + sum4 * ibdiag[5] + sum3 * ibdiag[10] + sum2 * ibdiag[15] + sum1 * ibdiag[20];
        row -= 5;
        break;
      default:
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
      }
    }
    PetscCall(PetscLogFlops(a->nz));

    /*
           t = b - D x    where D is the block diagonal
    */
    cnt = 0;
    for (i = 0, row = 0; i < m; i++) {
      switch (sizes[i]) {
      case 1:
        t[row] = b[row] - bdiag[cnt++] * x[row];
        row++;
        break;
      case 2:
        x1         = x[row];
        x2         = x[row + 1];
        tmp1       = x1 * bdiag[cnt] + x2 * bdiag[cnt + 2];
        tmp2       = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 3];
        t[row]     = b[row] - tmp1;
        t[row + 1] = b[row + 1] - tmp2;
        row += 2;
        cnt += 4;
        break;
      case 3:
        x1         = x[row];
        x2         = x[row + 1];
        x3         = x[row + 2];
        tmp1       = x1 * bdiag[cnt] + x2 * bdiag[cnt + 3] + x3 * bdiag[cnt + 6];
        tmp2       = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 4] + x3 * bdiag[cnt + 7];
        tmp3       = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 8];
        t[row]     = b[row] - tmp1;
        t[row + 1] = b[row + 1] - tmp2;
        t[row + 2] = b[row + 2] - tmp3;
        row += 3;
        cnt += 9;
        break;
      case 4:
        x1         = x[row];
        x2         = x[row + 1];
        x3         = x[row + 2];
        x4         = x[row + 3];
        tmp1       = x1 * bdiag[cnt] + x2 * bdiag[cnt + 4] + x3 * bdiag[cnt + 8] + x4 * bdiag[cnt + 12];
        tmp2       = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 9] + x4 * bdiag[cnt + 13];
        tmp3       = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 6] + x3 * bdiag[cnt + 10] + x4 * bdiag[cnt + 14];
        tmp4       = x1 * bdiag[cnt + 3] + x2 * bdiag[cnt + 7] + x3 * bdiag[cnt + 11] + x4 * bdiag[cnt + 15];
        t[row]     = b[row] - tmp1;
        t[row + 1] = b[row + 1] - tmp2;
        t[row + 2] = b[row + 2] - tmp3;
        t[row + 3] = b[row + 3] - tmp4;
        row += 4;
        cnt += 16;
        break;
      case 5:
        x1         = x[row];
        x2         = x[row + 1];
        x3         = x[row + 2];
        x4         = x[row + 3];
        x5         = x[row + 4];
        tmp1       = x1 * bdiag[cnt] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 10] + x4 * bdiag[cnt + 15] + x5 * bdiag[cnt + 20];
        tmp2       = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 6] + x3 * bdiag[cnt + 11] + x4 * bdiag[cnt + 16] + x5 * bdiag[cnt + 21];
        tmp3       = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 7] + x3 * bdiag[cnt + 12] + x4 * bdiag[cnt + 17] + x5 * bdiag[cnt + 22];
        tmp4       = x1 * bdiag[cnt + 3] + x2 * bdiag[cnt + 8] + x3 * bdiag[cnt + 13] + x4 * bdiag[cnt + 18] + x5 * bdiag[cnt + 23];
        tmp5       = x1 * bdiag[cnt + 4] + x2 * bdiag[cnt + 9] + x3 * bdiag[cnt + 14] + x4 * bdiag[cnt + 19] + x5 * bdiag[cnt + 24];
        t[row]     = b[row] - tmp1;
        t[row + 1] = b[row + 1] - tmp2;
        t[row + 2] = b[row + 2] - tmp3;
        t[row + 3] = b[row + 3] - tmp4;
        t[row + 4] = b[row + 4] - tmp5;
        row += 5;
        cnt += 25;
        break;
      default:
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
      }
    }
    PetscCall(PetscLogFlops(m));

    /*
          Apply (L + D)^-1 where D is the block diagonal
    */
    for (i = 0, row = 0; i < m; i++) {
      sz  = diag[row] - ii[row];
      v1  = a->a + ii[row];
      idx = a->j + ii[row];
      /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
      switch (sizes[i]) {
      case 1:

        sum1 = t[row];
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = t[i1];
          tmp1 = t[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
        }

        if (n == sz - 1) {
          tmp0 = t[*idx];
          sum1 -= *v1 * tmp0;
        }
        x[row] += t[row] = sum1 * (*ibdiag++);
        row++;
        break;
      case 2:
        v2   = a->a + ii[row + 1];
        sum1 = t[row];
        sum2 = t[row + 1];
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = t[i1];
          tmp1 = t[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
          sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
          v2 += 2;
        }

        if (n == sz - 1) {
          tmp0 = t[*idx];
          sum1 -= v1[0] * tmp0;
          sum2 -= v2[0] * tmp0;
        }
        x[row] += t[row]         = sum1 * ibdiag[0] + sum2 * ibdiag[2];
        x[row + 1] += t[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[3];
        ibdiag += 4;
        row += 2;
        break;
      case 3:
        v2   = a->a + ii[row + 1];
        v3   = a->a + ii[row + 2];
        sum1 = t[row];
        sum2 = t[row + 1];
        sum3 = t[row + 2];
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = t[i1];
          tmp1 = t[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
          sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
          v2 += 2;
          sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
          v3 += 2;
        }

        if (n == sz - 1) {
          tmp0 = t[*idx];
          sum1 -= v1[0] * tmp0;
          sum2 -= v2[0] * tmp0;
          sum3 -= v3[0] * tmp0;
        }
        x[row] += t[row]         = sum1 * ibdiag[0] + sum2 * ibdiag[3] + sum3 * ibdiag[6];
        x[row + 1] += t[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[4] + sum3 * ibdiag[7];
        x[row + 2] += t[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[5] + sum3 * ibdiag[8];
        ibdiag += 9;
        row += 3;
        break;
      case 4:
        v2   = a->a + ii[row + 1];
        v3   = a->a + ii[row + 2];
        v4   = a->a + ii[row + 3];
        sum1 = t[row];
        sum2 = t[row + 1];
        sum3 = t[row + 2];
        sum4 = t[row + 3];
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = t[i1];
          tmp1 = t[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
          sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
          v2 += 2;
          sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
          v3 += 2;
          sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
          v4 += 2;
        }

        if (n == sz - 1) {
          tmp0 = t[*idx];
          sum1 -= v1[0] * tmp0;
          sum2 -= v2[0] * tmp0;
          sum3 -= v3[0] * tmp0;
          sum4 -= v4[0] * tmp0;
        }
        x[row] += t[row]         = sum1 * ibdiag[0] + sum2 * ibdiag[4] + sum3 * ibdiag[8] + sum4 * ibdiag[12];
        x[row + 1] += t[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[5] + sum3 * ibdiag[9] + sum4 * ibdiag[13];
        x[row + 2] += t[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[6] + sum3 * ibdiag[10] + sum4 * ibdiag[14];
        x[row + 3] += t[row + 3] = sum1 * ibdiag[3] + sum2 * ibdiag[7] + sum3 * ibdiag[11] + sum4 * ibdiag[15];
        ibdiag += 16;
        row += 4;
        break;
      case 5:
        v2   = a->a + ii[row + 1];
        v3   = a->a + ii[row + 2];
        v4   = a->a + ii[row + 3];
        v5   = a->a + ii[row + 4];
        sum1 = t[row];
        sum2 = t[row + 1];
        sum3 = t[row + 2];
        sum4 = t[row + 3];
        sum5 = t[row + 4];
        for (n = 0; n < sz - 1; n += 2) {
          i1 = idx[0];
          i2 = idx[1];
          idx += 2;
          tmp0 = t[i1];
          tmp1 = t[i2];
          sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
          v1 += 2;
          sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
          v2 += 2;
          sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
          v3 += 2;
          sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
          v4 += 2;
          sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
          v5 += 2;
        }

        if (n == sz - 1) {
          tmp0 = t[*idx];
          sum1 -= v1[0] * tmp0;
          sum2 -= v2[0] * tmp0;
          sum3 -= v3[0] * tmp0;
          sum4 -= v4[0] * tmp0;
          sum5 -= v5[0] * tmp0;
        }
        x[row] += t[row]         = sum1 * ibdiag[0] + sum2 * ibdiag[5] + sum3 * ibdiag[10] + sum4 * ibdiag[15] + sum5 * ibdiag[20];
        x[row + 1] += t[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[6] + sum3 * ibdiag[11] + sum4 * ibdiag[16] + sum5 * ibdiag[21];
        x[row + 2] += t[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[7] + sum3 * ibdiag[12] + sum4 * ibdiag[17] + sum5 * ibdiag[22];
        x[row + 3] += t[row + 3] = sum1 * ibdiag[3] + sum2 * ibdiag[8] + sum3 * ibdiag[13] + sum4 * ibdiag[18] + sum5 * ibdiag[23];
        x[row + 4] += t[row + 4] = sum1 * ibdiag[4] + sum2 * ibdiag[9] + sum3 * ibdiag[14] + sum4 * ibdiag[19] + sum5 * ibdiag[24];
        ibdiag += 25;
        row += 5;
        break;
      default:
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
      }
    }
    PetscCall(PetscLogFlops(a->nz));
  }
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultDiagonalBlock_SeqAIJ_Inode(Mat A, Vec bb, Vec xx)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
  PetscScalar       *x, tmp1, tmp2, tmp3, tmp4, tmp5, x1, x2, x3, x4, x5;
  const MatScalar   *bdiag = a->inode.bdiag;
  const PetscScalar *b;
  PetscInt           m = a->inode.node_count, cnt = 0, i, row;
  const PetscInt    *sizes = a->inode.size;

  PetscFunctionBegin;
  PetscCheck(a->inode.size, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
  PetscCall(VecGetArray(xx, &x));
  PetscCall(VecGetArrayRead(bb, &b));
  cnt = 0;
  for (i = 0, row = 0; i < m; i++) {
    switch (sizes[i]) {
    case 1:
      x[row] = b[row] * bdiag[cnt++];
      row++;
      break;
    case 2:
      x1       = b[row];
      x2       = b[row + 1];
      tmp1     = x1 * bdiag[cnt] + x2 * bdiag[cnt + 2];
      tmp2     = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 3];
      x[row++] = tmp1;
      x[row++] = tmp2;
      cnt += 4;
      break;
    case 3:
      x1       = b[row];
      x2       = b[row + 1];
      x3       = b[row + 2];
      tmp1     = x1 * bdiag[cnt] + x2 * bdiag[cnt + 3] + x3 * bdiag[cnt + 6];
      tmp2     = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 4] + x3 * bdiag[cnt + 7];
      tmp3     = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 8];
      x[row++] = tmp1;
      x[row++] = tmp2;
      x[row++] = tmp3;
      cnt += 9;
      break;
    case 4:
      x1       = b[row];
      x2       = b[row + 1];
      x3       = b[row + 2];
      x4       = b[row + 3];
      tmp1     = x1 * bdiag[cnt] + x2 * bdiag[cnt + 4] + x3 * bdiag[cnt + 8] + x4 * bdiag[cnt + 12];
      tmp2     = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 9] + x4 * bdiag[cnt + 13];
      tmp3     = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 6] + x3 * bdiag[cnt + 10] + x4 * bdiag[cnt + 14];
      tmp4     = x1 * bdiag[cnt + 3] + x2 * bdiag[cnt + 7] + x3 * bdiag[cnt + 11] + x4 * bdiag[cnt + 15];
      x[row++] = tmp1;
      x[row++] = tmp2;
      x[row++] = tmp3;
      x[row++] = tmp4;
      cnt += 16;
      break;
    case 5:
      x1       = b[row];
      x2       = b[row + 1];
      x3       = b[row + 2];
      x4       = b[row + 3];
      x5       = b[row + 4];
      tmp1     = x1 * bdiag[cnt] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 10] + x4 * bdiag[cnt + 15] + x5 * bdiag[cnt + 20];
      tmp2     = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 6] + x3 * bdiag[cnt + 11] + x4 * bdiag[cnt + 16] + x5 * bdiag[cnt + 21];
      tmp3     = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 7] + x3 * bdiag[cnt + 12] + x4 * bdiag[cnt + 17] + x5 * bdiag[cnt + 22];
      tmp4     = x1 * bdiag[cnt + 3] + x2 * bdiag[cnt + 8] + x3 * bdiag[cnt + 13] + x4 * bdiag[cnt + 18] + x5 * bdiag[cnt + 23];
      tmp5     = x1 * bdiag[cnt + 4] + x2 * bdiag[cnt + 9] + x3 * bdiag[cnt + 14] + x4 * bdiag[cnt + 19] + x5 * bdiag[cnt + 24];
      x[row++] = tmp1;
      x[row++] = tmp2;
      x[row++] = tmp3;
      x[row++] = tmp4;
      x[row++] = tmp5;
      cnt += 25;
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Inode size %" PetscInt_FMT " not supported", sizes[i]);
    }
  }
  PetscCall(PetscLogFlops(2.0 * cnt));
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  a->inode.node_count       = 0;
  a->inode.use              = PETSC_FALSE;
  a->inode.checked          = PETSC_FALSE;
  a->inode.mat_nonzerostate = -1;
  A->ops->getrowij          = MatGetRowIJ_SeqAIJ;
  A->ops->restorerowij      = MatRestoreRowIJ_SeqAIJ;
  A->ops->getcolumnij       = MatGetColumnIJ_SeqAIJ;
  A->ops->restorecolumnij   = MatRestoreColumnIJ_SeqAIJ;
  A->ops->coloringpatch     = NULL;
  A->ops->multdiagonalblock = NULL;
  if (A->factortype) A->ops->solve = MatSolve_SeqAIJ_inplace;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
    samestructure indicates that the matrix has not changed its nonzero structure so we
    do not need to recompute the inodes
*/
PetscErrorCode MatSeqAIJCheckInode(Mat A)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
  PetscInt        i, j, m, nzx, nzy, *ns, node_count, blk_size;
  PetscBool       flag;
  const PetscInt *idx, *idy, *ii;

  PetscFunctionBegin;
  if (!a->inode.use) {
    PetscCall(MatSeqAIJ_Inode_ResetOps(A));
    PetscCall(PetscFree(a->inode.size));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  if (a->inode.checked && A->nonzerostate == a->inode.mat_nonzerostate) PetscFunctionReturn(PETSC_SUCCESS);

  m = A->rmap->n;
  if (!a->inode.size) PetscCall(PetscMalloc1(m + 1, &a->inode.size));
  ns = a->inode.size;

  i          = 0;
  node_count = 0;
  idx        = a->j;
  ii         = a->i;
  if (idx) {
    while (i < m) {            /* For each row */
      nzx = ii[i + 1] - ii[i]; /* Number of nonzeros */
      /* Limits the number of elements in a node to 'a->inode.limit' */
      for (j = i + 1, idy = idx, blk_size = 1; j < m && blk_size < a->inode.limit; ++j, ++blk_size) {
        nzy = ii[j + 1] - ii[j]; /* Same number of nonzeros */
        if (nzy != nzx) break;
        idy += nzx; /* Same nonzero pattern */
        PetscCall(PetscArraycmp(idx, idy, nzx, &flag));
        if (!flag) break;
      }
      ns[node_count++] = blk_size;
      idx += blk_size * nzx;
      i = j;
    }
  }
  /* If not enough inodes found,, do not use inode version of the routines */
  if (!m || !idx || node_count > .8 * m) {
    PetscCall(MatSeqAIJ_Inode_ResetOps(A));
    PetscCall(PetscFree(a->inode.size));
    PetscCall(PetscInfo(A, "Found %" PetscInt_FMT " nodes out of %" PetscInt_FMT " rows. Not using Inode routines\n", node_count, m));
  } else {
    if (!A->factortype) {
      A->ops->multdiagonalblock = MatMultDiagonalBlock_SeqAIJ_Inode;
      if (A->rmap->n == A->cmap->n) {
        A->ops->getrowij        = MatGetRowIJ_SeqAIJ_Inode;
        A->ops->restorerowij    = MatRestoreRowIJ_SeqAIJ_Inode;
        A->ops->getcolumnij     = MatGetColumnIJ_SeqAIJ_Inode;
        A->ops->restorecolumnij = MatRestoreColumnIJ_SeqAIJ_Inode;
        A->ops->coloringpatch   = MatColoringPatch_SeqAIJ_Inode;
      }
    } else {
      A->ops->solve = MatSolve_SeqAIJ_Inode_inplace;
    }
    a->inode.node_count = node_count;
    PetscCall(PetscInfo(A, "Found %" PetscInt_FMT " nodes of %" PetscInt_FMT ". Limit used: %" PetscInt_FMT ". Using Inode routines\n", node_count, m, a->inode.limit));
  }
  a->inode.checked          = PETSC_TRUE;
  a->inode.mat_nonzerostate = A->nonzerostate;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatDuplicate_SeqAIJ_Inode(Mat A, MatDuplicateOption cpvalues, Mat *C)
{
  Mat         B = *C;
  Mat_SeqAIJ *c = (Mat_SeqAIJ *)B->data, *a = (Mat_SeqAIJ *)A->data;
  PetscInt    m = A->rmap->n;

  PetscFunctionBegin;
  c->inode.use              = a->inode.use;
  c->inode.limit            = a->inode.limit;
  c->inode.max_limit        = a->inode.max_limit;
  c->inode.checked          = PETSC_FALSE;
  c->inode.size             = NULL;
  c->inode.node_count       = 0;
  c->inode.ibdiagvalid      = PETSC_FALSE;
  c->inode.ibdiag           = NULL;
  c->inode.bdiag            = NULL;
  c->inode.mat_nonzerostate = -1;
  if (a->inode.use) {
    if (a->inode.checked && a->inode.size) {
      PetscCall(PetscMalloc1(m + 1, &c->inode.size));
      PetscCall(PetscArraycpy(c->inode.size, a->inode.size, m + 1));

      c->inode.checked          = PETSC_TRUE;
      c->inode.node_count       = a->inode.node_count;
      c->inode.mat_nonzerostate = (*C)->nonzerostate;
    }
    /* note the table of functions below should match that in MatSeqAIJCheckInode() */
    if (!B->factortype) {
      B->ops->getrowij          = MatGetRowIJ_SeqAIJ_Inode;
      B->ops->restorerowij      = MatRestoreRowIJ_SeqAIJ_Inode;
      B->ops->getcolumnij       = MatGetColumnIJ_SeqAIJ_Inode;
      B->ops->restorecolumnij   = MatRestoreColumnIJ_SeqAIJ_Inode;
      B->ops->coloringpatch     = MatColoringPatch_SeqAIJ_Inode;
      B->ops->multdiagonalblock = MatMultDiagonalBlock_SeqAIJ_Inode;
    } else {
      B->ops->solve = MatSolve_SeqAIJ_Inode_inplace;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode MatGetRow_FactoredLU(PetscInt *cols, PetscInt nzl, PetscInt nzu, PetscInt nz, const PetscInt *ai, const PetscInt *aj, const PetscInt *adiag, PetscInt row)
{
  PetscInt        k;
  const PetscInt *vi;

  PetscFunctionBegin;
  vi = aj + ai[row];
  for (k = 0; k < nzl; k++) cols[k] = vi[k];
  vi        = aj + adiag[row];
  cols[nzl] = vi[0];
  vi        = aj + adiag[row + 1] + 1;
  for (k = 0; k < nzu; k++) cols[nzl + 1 + k] = vi[k];
  PetscFunctionReturn(PETSC_SUCCESS);
}
/*
   MatSeqAIJCheckInode_FactorLU - Check Inode for factored seqaij matrix.
   Modified from MatSeqAIJCheckInode().

   Input Parameters:
.  Mat A - ILU or LU matrix factor

*/
PetscErrorCode MatSeqAIJCheckInode_FactorLU(Mat A)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
  PetscInt        i, j, m, nzl1, nzu1, nzl2, nzu2, nzx, nzy, node_count, blk_size;
  PetscInt       *cols1, *cols2, *ns;
  const PetscInt *ai = a->i, *aj = a->j, *adiag = a->diag;
  PetscBool       flag;

  PetscFunctionBegin;
  if (!a->inode.use) PetscFunctionReturn(PETSC_SUCCESS);
  if (a->inode.checked) PetscFunctionReturn(PETSC_SUCCESS);

  m = A->rmap->n;
  if (a->inode.size) ns = a->inode.size;
  else PetscCall(PetscMalloc1(m + 1, &ns));

  i          = 0;
  node_count = 0;
  PetscCall(PetscMalloc2(m, &cols1, m, &cols2));
  while (i < m) {                       /* For each row */
    nzl1 = ai[i + 1] - ai[i];           /* Number of nonzeros in L */
    nzu1 = adiag[i] - adiag[i + 1] - 1; /* Number of nonzeros in U excluding diagonal*/
    nzx  = nzl1 + nzu1 + 1;
    PetscCall(MatGetRow_FactoredLU(cols1, nzl1, nzu1, nzx, ai, aj, adiag, i));

    /* Limits the number of elements in a node to 'a->inode.limit' */
    for (j = i + 1, blk_size = 1; j < m && blk_size < a->inode.limit; ++j, ++blk_size) {
      nzl2 = ai[j + 1] - ai[j];
      nzu2 = adiag[j] - adiag[j + 1] - 1;
      nzy  = nzl2 + nzu2 + 1;
      if (nzy != nzx) break;
      PetscCall(MatGetRow_FactoredLU(cols2, nzl2, nzu2, nzy, ai, aj, adiag, j));
      PetscCall(PetscArraycmp(cols1, cols2, nzx, &flag));
      if (!flag) break;
    }
    ns[node_count++] = blk_size;
    i                = j;
  }
  PetscCall(PetscFree2(cols1, cols2));
  /* If not enough inodes found,, do not use inode version of the routines */
  if (!m || node_count > .8 * m) {
    PetscCall(PetscFree(ns));

    a->inode.node_count = 0;
    a->inode.size       = NULL;
    a->inode.use        = PETSC_FALSE;

    PetscCall(PetscInfo(A, "Found %" PetscInt_FMT " nodes out of %" PetscInt_FMT " rows. Not using Inode routines\n", node_count, m));
  } else {
    A->ops->mult              = NULL;
    A->ops->sor               = NULL;
    A->ops->multadd           = NULL;
    A->ops->getrowij          = NULL;
    A->ops->restorerowij      = NULL;
    A->ops->getcolumnij       = NULL;
    A->ops->restorecolumnij   = NULL;
    A->ops->coloringpatch     = NULL;
    A->ops->multdiagonalblock = NULL;
    a->inode.node_count       = node_count;
    a->inode.size             = ns;

    PetscCall(PetscInfo(A, "Found %" PetscInt_FMT " nodes of %" PetscInt_FMT ". Limit used: %" PetscInt_FMT ". Using Inode routines\n", node_count, m, a->inode.limit));
  }
  a->inode.checked = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  a->inode.ibdiagvalid = PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
     This is really ugly. if inodes are used this replaces the
  permutations with ones that correspond to rows/cols of the matrix
  rather than inode blocks
*/
PetscErrorCode MatInodeAdjustForInodes(Mat A, IS *rperm, IS *cperm)
{
  PetscFunctionBegin;
  PetscTryMethod(A, "MatInodeAdjustForInodes_C", (Mat, IS *, IS *), (A, rperm, cperm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatInodeAdjustForInodes_SeqAIJ_Inode(Mat A, IS *rperm, IS *cperm)
{
  Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
  PetscInt        m = A->rmap->n, n = A->cmap->n, i, j, nslim_row = a->inode.node_count;
  const PetscInt *ridx, *cidx;
  PetscInt        row, col, *permr, *permc, *ns_row = a->inode.size, *tns, start_val, end_val, indx;
  PetscInt        nslim_col, *ns_col;
  IS              ris = *rperm, cis = *cperm;

  PetscFunctionBegin;
  if (!a->inode.size) PetscFunctionReturn(PETSC_SUCCESS);           /* no inodes so return */
  if (a->inode.node_count == m) PetscFunctionReturn(PETSC_SUCCESS); /* all inodes are of size 1 */

  PetscCall(MatCreateColInode_Private(A, &nslim_col, &ns_col));
  PetscCall(PetscMalloc1(((nslim_row > nslim_col ? nslim_row : nslim_col) + 1), &tns));
  PetscCall(PetscMalloc2(m, &permr, n, &permc));

  PetscCall(ISGetIndices(ris, &ridx));
  PetscCall(ISGetIndices(cis, &cidx));

  /* Form the inode structure for the rows of permuted matrix using inv perm*/
  for (i = 0, tns[0] = 0; i < nslim_row; ++i) tns[i + 1] = tns[i] + ns_row[i];

  /* Construct the permutations for rows*/
  for (i = 0, row = 0; i < nslim_row; ++i) {
    indx      = ridx[i];
    start_val = tns[indx];
    end_val   = tns[indx + 1];
    for (j = start_val; j < end_val; ++j, ++row) permr[row] = j;
  }

  /* Form the inode structure for the columns of permuted matrix using inv perm*/
  for (i = 0, tns[0] = 0; i < nslim_col; ++i) tns[i + 1] = tns[i] + ns_col[i];

  /* Construct permutations for columns */
  for (i = 0, col = 0; i < nslim_col; ++i) {
    indx      = cidx[i];
    start_val = tns[indx];
    end_val   = tns[indx + 1];
    for (j = start_val; j < end_val; ++j, ++col) permc[col] = j;
  }

  PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, permr, PETSC_COPY_VALUES, rperm));
  PetscCall(ISSetPermutation(*rperm));
  PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, permc, PETSC_COPY_VALUES, cperm));
  PetscCall(ISSetPermutation(*cperm));

  PetscCall(ISRestoreIndices(ris, &ridx));
  PetscCall(ISRestoreIndices(cis, &cidx));

  PetscCall(PetscFree(ns_col));
  PetscCall(PetscFree2(permr, permc));
  PetscCall(ISDestroy(&cis));
  PetscCall(ISDestroy(&ris));
  PetscCall(PetscFree(tns));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatInodeGetInodeSizes - Returns the inode information of a matrix with inodes

  Not Collective

  Input Parameter:
. A - the Inode matrix or matrix derived from the Inode class -- e.g., `MATSEQAIJ`

  Output Parameters:
+ node_count - no of inodes present in the matrix.
. sizes      - an array of size `node_count`, with the sizes of each inode.
- limit      - the max size used to generate the inodes.

  Level: advanced

  Note:
  It should be called after the matrix is assembled.
  The contents of the sizes[] array should not be changed.
  `NULL` may be passed for information not needed

.seealso: [](ch_matrices), `Mat`, `MatGetInfo()`
@*/
PetscErrorCode MatInodeGetInodeSizes(Mat A, PetscInt *node_count, PetscInt *sizes[], PetscInt *limit)
{
  PetscErrorCode (*f)(Mat, PetscInt *, PetscInt **, PetscInt *);

  PetscFunctionBegin;
  PetscCheck(A->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
  PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatInodeGetInodeSizes_C", &f));
  if (f) PetscCall((*f)(A, node_count, sizes, limit));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatInodeGetInodeSizes_SeqAIJ_Inode(Mat A, PetscInt *node_count, PetscInt *sizes[], PetscInt *limit)
{
  Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

  PetscFunctionBegin;
  if (node_count) *node_count = a->inode.node_count;
  if (sizes) *sizes = a->inode.size;
  if (limit) *limit = a->inode.limit;
  PetscFunctionReturn(PETSC_SUCCESS);
}