xref: /petsc/src/mat/impls/baij/seq/baij.c (revision d8a51d2aac522cef49bfbd84fd4cf473dc3fa6ee)

/*
    Defines the basic matrix operations for the BAIJ (compressed row)
  matrix storage format.
*/
#include <../src/mat/impls/baij/seq/baij.h> /*I   "petscmat.h"  I*/
#include <petscblaslapack.h>
#include <petsc/private/kernels/blockinvert.h>
#include <petsc/private/kernels/blockmatmult.h>

/* defines MatSetValues_Seq_Hash(), MatAssemblyEnd_Seq_Hash(), MatSetUp_Seq_Hash() */
#define TYPE BAIJ
#define TYPE_BS
#include "../src/mat/impls/aij/seq/seqhashmatsetvalues.h"
#undef TYPE_BS
#define TYPE_BS _BS
#define TYPE_BS_ON
#include "../src/mat/impls/aij/seq/seqhashmatsetvalues.h"
#undef TYPE_BS
#include "../src/mat/impls/aij/seq/seqhashmat.h"
#undef TYPE
#undef TYPE_BS_ON

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

#if defined(PETSC_HAVE_MKL_SPARSE_OPTIMIZE)
PETSC_INTERN PetscErrorCode MatConvert_SeqBAIJ_SeqBAIJMKL(Mat, MatType, MatReuse, Mat *);
#endif
PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);

static PetscErrorCode MatGetColumnReductions_SeqBAIJ(Mat A, PetscInt type, PetscReal *reductions)
{
  Mat_SeqBAIJ *a_aij = (Mat_SeqBAIJ *)A->data;
  PetscInt     m, n, ib, jb, bs = A->rmap->bs;
  MatScalar   *a_val = a_aij->a;

  PetscFunctionBegin;
  PetscCall(MatGetSize(A, &m, &n));
  PetscCall(PetscArrayzero(reductions, n));
  if (type == NORM_2) {
    for (PetscInt i = a_aij->i[0]; i < a_aij->i[A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          reductions[A->cmap->rstart + a_aij->j[i] * bs + jb] += PetscAbsScalar(*a_val * *a_val);
          a_val++;
        }
      }
    }
  } else if (type == NORM_1) {
    for (PetscInt i = a_aij->i[0]; i < a_aij->i[A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          reductions[A->cmap->rstart + a_aij->j[i] * bs + jb] += PetscAbsScalar(*a_val);
          a_val++;
        }
      }
    }
  } else if (type == NORM_INFINITY) {
    for (PetscInt i = a_aij->i[0]; i < a_aij->i[A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          int col         = A->cmap->rstart + a_aij->j[i] * bs + jb;
          reductions[col] = PetscMax(PetscAbsScalar(*a_val), reductions[col]);
          a_val++;
        }
      }
    }
  } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
    for (PetscInt i = a_aij->i[0]; i < a_aij->i[A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          reductions[A->cmap->rstart + a_aij->j[i] * bs + jb] += PetscRealPart(*a_val);
          a_val++;
        }
      }
    }
  } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    for (PetscInt i = a_aij->i[0]; i < a_aij->i[A->rmap->n / bs]; i++) {
      for (jb = 0; jb < bs; jb++) {
        for (ib = 0; ib < bs; ib++) {
          reductions[A->cmap->rstart + a_aij->j[i] * bs + jb] += PetscImaginaryPart(*a_val);
          a_val++;
        }
      }
    }
  } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unknown reduction type");
  if (type == NORM_2) {
    for (PetscInt i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
  } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    for (PetscInt i = 0; i < n; i++) reductions[i] /= m;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatInvertBlockDiagonal_SeqBAIJ(Mat A, const PetscScalar **values)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt    *diag_offset, i, bs = A->rmap->bs, mbs = a->mbs, ipvt[5], bs2 = bs * bs, *v_pivots;
  MatScalar   *v     = a->a, *odiag, *diag, work[25], *v_work;
  PetscReal    shift = 0.0;
  PetscBool    allowzeropivot, zeropivotdetected = PETSC_FALSE;

  PetscFunctionBegin;
  allowzeropivot = PetscNot(A->erroriffailure);

  if (a->idiagvalid) {
    if (values) *values = a->idiag;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(MatMarkDiagonal_SeqBAIJ(A));
  diag_offset = a->diag;
  if (!a->idiag) { PetscCall(PetscMalloc1(bs2 * mbs, &a->idiag)); }
  diag = a->idiag;
  if (values) *values = a->idiag;
  /* factor and invert each block */
  switch (bs) {
  case 1:
    for (i = 0; i < mbs; i++) {
      odiag   = v + 1 * diag_offset[i];
      diag[0] = odiag[0];

      if (PetscAbsScalar(diag[0] + shift) < PETSC_MACHINE_EPSILON) {
        if (allowzeropivot) {
          A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
          A->factorerror_zeropivot_value = PetscAbsScalar(diag[0]);
          A->factorerror_zeropivot_row   = i;
          PetscCall(PetscInfo(A, "Zero pivot, row %" PetscInt_FMT "\n", i));
        } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT " pivot value %g tolerance %g", i, (double)PetscAbsScalar(diag[0]), (double)PETSC_MACHINE_EPSILON);
      }

      diag[0] = (PetscScalar)1.0 / (diag[0] + shift);
      diag += 1;
    }
    break;
  case 2:
    for (i = 0; i < mbs; i++) {
      odiag   = v + 4 * diag_offset[i];
      diag[0] = odiag[0];
      diag[1] = odiag[1];
      diag[2] = odiag[2];
      diag[3] = odiag[3];
      PetscCall(PetscKernel_A_gets_inverse_A_2(diag, shift, allowzeropivot, &zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      diag += 4;
    }
    break;
  case 3:
    for (i = 0; i < mbs; i++) {
      odiag   = v + 9 * diag_offset[i];
      diag[0] = odiag[0];
      diag[1] = odiag[1];
      diag[2] = odiag[2];
      diag[3] = odiag[3];
      diag[4] = odiag[4];
      diag[5] = odiag[5];
      diag[6] = odiag[6];
      diag[7] = odiag[7];
      diag[8] = odiag[8];
      PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      diag += 9;
    }
    break;
  case 4:
    for (i = 0; i < mbs; i++) {
      odiag = v + 16 * diag_offset[i];
      PetscCall(PetscArraycpy(diag, odiag, 16));
      PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      diag += 16;
    }
    break;
  case 5:
    for (i = 0; i < mbs; i++) {
      odiag = v + 25 * diag_offset[i];
      PetscCall(PetscArraycpy(diag, odiag, 25));
      PetscCall(PetscKernel_A_gets_inverse_A_5(diag, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      diag += 25;
    }
    break;
  case 6:
    for (i = 0; i < mbs; i++) {
      odiag = v + 36 * diag_offset[i];
      PetscCall(PetscArraycpy(diag, odiag, 36));
      PetscCall(PetscKernel_A_gets_inverse_A_6(diag, shift, allowzeropivot, &zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      diag += 36;
    }
    break;
  case 7:
    for (i = 0; i < mbs; i++) {
      odiag = v + 49 * diag_offset[i];
      PetscCall(PetscArraycpy(diag, odiag, 49));
      PetscCall(PetscKernel_A_gets_inverse_A_7(diag, shift, allowzeropivot, &zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      diag += 49;
    }
    break;
  default:
    PetscCall(PetscMalloc2(bs, &v_work, bs, &v_pivots));
    for (i = 0; i < mbs; i++) {
      odiag = v + bs2 * diag_offset[i];
      PetscCall(PetscArraycpy(diag, odiag, bs2));
      PetscCall(PetscKernel_A_gets_inverse_A(bs, diag, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
      if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
      diag += bs2;
    }
    PetscCall(PetscFree2(v_work, v_pivots));
  }
  a->idiagvalid = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSOR_SeqBAIJ(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
{
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  PetscScalar       *x, *work, *w, *workt, *t;
  const MatScalar   *v, *aa = a->a, *idiag;
  const PetscScalar *b, *xb;
  PetscScalar        s[7], xw[7] = {0}; /* avoid some compilers thinking xw is uninitialized */
  PetscInt           m = a->mbs, i, i2, nz, bs = A->rmap->bs, bs2 = bs * bs, k, j, idx, it;
  const PetscInt    *diag, *ai = a->i, *aj = a->j, *vi;

  PetscFunctionBegin;
  its = its * lits;
  PetscCheck(!(flag & SOR_EISENSTAT), PETSC_COMM_SELF, PETSC_ERR_SUP, "No support yet for Eisenstat");
  PetscCheck(its > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Relaxation requires global its %" PetscInt_FMT " and local its %" PetscInt_FMT " both positive", its, lits);
  PetscCheck(!fshift, PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for diagonal shift");
  PetscCheck(omega == 1.0, PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for non-trivial relaxation factor");
  PetscCheck(!(flag & SOR_APPLY_UPPER) && !(flag & SOR_APPLY_LOWER), PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for applying upper or lower triangular parts");

  if (!a->idiagvalid) PetscCall(MatInvertBlockDiagonal(A, NULL));

  if (!m) PetscFunctionReturn(PETSC_SUCCESS);
  diag  = a->diag;
  idiag = a->idiag;
  k     = PetscMax(A->rmap->n, A->cmap->n);
  if (!a->mult_work) PetscCall(PetscMalloc1(k + 1, &a->mult_work));
  if (!a->sor_workt) PetscCall(PetscMalloc1(k, &a->sor_workt));
  if (!a->sor_work) PetscCall(PetscMalloc1(bs, &a->sor_work));
  work = a->mult_work;
  t    = a->sor_workt;
  w    = a->sor_work;

  PetscCall(VecGetArray(xx, &x));
  PetscCall(VecGetArrayRead(bb, &b));

  if (flag & SOR_ZERO_INITIAL_GUESS) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
      switch (bs) {
      case 1:
        PetscKernel_v_gets_A_times_w_1(x, idiag, b);
        t[0] = b[0];
        i2   = 1;
        idiag += 1;
        for (i = 1; i < m; i++) {
          v    = aa + ai[i];
          vi   = aj + ai[i];
          nz   = diag[i] - ai[i];
          s[0] = b[i2];
          for (j = 0; j < nz; j++) {
            xw[0] = x[vi[j]];
            PetscKernel_v_gets_v_minus_A_times_w_1(s, (v + j), xw);
          }
          t[i2] = s[0];
          PetscKernel_v_gets_A_times_w_1(xw, idiag, s);
          x[i2] = xw[0];
          idiag += 1;
          i2 += 1;
        }
        break;
      case 2:
        PetscKernel_v_gets_A_times_w_2(x, idiag, b);
        t[0] = b[0];
        t[1] = b[1];
        i2   = 2;
        idiag += 4;
        for (i = 1; i < m; i++) {
          v    = aa + 4 * ai[i];
          vi   = aj + ai[i];
          nz   = diag[i] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          for (j = 0; j < nz; j++) {
            idx   = 2 * vi[j];
            it    = 4 * j;
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_2(s, (v + it), xw);
          }
          t[i2]     = s[0];
          t[i2 + 1] = s[1];
          PetscKernel_v_gets_A_times_w_2(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          idiag += 4;
          i2 += 2;
        }
        break;
      case 3:
        PetscKernel_v_gets_A_times_w_3(x, idiag, b);
        t[0] = b[0];
        t[1] = b[1];
        t[2] = b[2];
        i2   = 3;
        idiag += 9;
        for (i = 1; i < m; i++) {
          v    = aa + 9 * ai[i];
          vi   = aj + ai[i];
          nz   = diag[i] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          while (nz--) {
            idx   = 3 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_3(s, v, xw);
            v += 9;
          }
          t[i2]     = s[0];
          t[i2 + 1] = s[1];
          t[i2 + 2] = s[2];
          PetscKernel_v_gets_A_times_w_3(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          idiag += 9;
          i2 += 3;
        }
        break;
      case 4:
        PetscKernel_v_gets_A_times_w_4(x, idiag, b);
        t[0] = b[0];
        t[1] = b[1];
        t[2] = b[2];
        t[3] = b[3];
        i2   = 4;
        idiag += 16;
        for (i = 1; i < m; i++) {
          v    = aa + 16 * ai[i];
          vi   = aj + ai[i];
          nz   = diag[i] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          while (nz--) {
            idx   = 4 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_4(s, v, xw);
            v += 16;
          }
          t[i2]     = s[0];
          t[i2 + 1] = s[1];
          t[i2 + 2] = s[2];
          t[i2 + 3] = s[3];
          PetscKernel_v_gets_A_times_w_4(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          x[i2 + 3] = xw[3];
          idiag += 16;
          i2 += 4;
        }
        break;
      case 5:
        PetscKernel_v_gets_A_times_w_5(x, idiag, b);
        t[0] = b[0];
        t[1] = b[1];
        t[2] = b[2];
        t[3] = b[3];
        t[4] = b[4];
        i2   = 5;
        idiag += 25;
        for (i = 1; i < m; i++) {
          v    = aa + 25 * ai[i];
          vi   = aj + ai[i];
          nz   = diag[i] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          while (nz--) {
            idx   = 5 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_5(s, v, xw);
            v += 25;
          }
          t[i2]     = s[0];
          t[i2 + 1] = s[1];
          t[i2 + 2] = s[2];
          t[i2 + 3] = s[3];
          t[i2 + 4] = s[4];
          PetscKernel_v_gets_A_times_w_5(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          x[i2 + 3] = xw[3];
          x[i2 + 4] = xw[4];
          idiag += 25;
          i2 += 5;
        }
        break;
      case 6:
        PetscKernel_v_gets_A_times_w_6(x, idiag, b);
        t[0] = b[0];
        t[1] = b[1];
        t[2] = b[2];
        t[3] = b[3];
        t[4] = b[4];
        t[5] = b[5];
        i2   = 6;
        idiag += 36;
        for (i = 1; i < m; i++) {
          v    = aa + 36 * ai[i];
          vi   = aj + ai[i];
          nz   = diag[i] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          s[5] = b[i2 + 5];
          while (nz--) {
            idx   = 6 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            xw[5] = x[5 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_6(s, v, xw);
            v += 36;
          }
          t[i2]     = s[0];
          t[i2 + 1] = s[1];
          t[i2 + 2] = s[2];
          t[i2 + 3] = s[3];
          t[i2 + 4] = s[4];
          t[i2 + 5] = s[5];
          PetscKernel_v_gets_A_times_w_6(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          x[i2 + 3] = xw[3];
          x[i2 + 4] = xw[4];
          x[i2 + 5] = xw[5];
          idiag += 36;
          i2 += 6;
        }
        break;
      case 7:
        PetscKernel_v_gets_A_times_w_7(x, idiag, b);
        t[0] = b[0];
        t[1] = b[1];
        t[2] = b[2];
        t[3] = b[3];
        t[4] = b[4];
        t[5] = b[5];
        t[6] = b[6];
        i2   = 7;
        idiag += 49;
        for (i = 1; i < m; i++) {
          v    = aa + 49 * ai[i];
          vi   = aj + ai[i];
          nz   = diag[i] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          s[5] = b[i2 + 5];
          s[6] = b[i2 + 6];
          while (nz--) {
            idx   = 7 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            xw[5] = x[5 + idx];
            xw[6] = x[6 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_7(s, v, xw);
            v += 49;
          }
          t[i2]     = s[0];
          t[i2 + 1] = s[1];
          t[i2 + 2] = s[2];
          t[i2 + 3] = s[3];
          t[i2 + 4] = s[4];
          t[i2 + 5] = s[5];
          t[i2 + 6] = s[6];
          PetscKernel_v_gets_A_times_w_7(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          x[i2 + 3] = xw[3];
          x[i2 + 4] = xw[4];
          x[i2 + 5] = xw[5];
          x[i2 + 6] = xw[6];
          idiag += 49;
          i2 += 7;
        }
        break;
      default:
        PetscKernel_w_gets_Ar_times_v(bs, bs, b, idiag, x);
        PetscCall(PetscArraycpy(t, b, bs));
        i2 = bs;
        idiag += bs2;
        for (i = 1; i < m; i++) {
          v  = aa + bs2 * ai[i];
          vi = aj + ai[i];
          nz = diag[i] - ai[i];

          PetscCall(PetscArraycpy(w, b + i2, bs));
          /* copy all rows of x that are needed into contiguous space */
          workt = work;
          for (j = 0; j < nz; j++) {
            PetscCall(PetscArraycpy(workt, x + bs * (*vi++), bs));
            workt += bs;
          }
          PetscKernel_w_gets_w_minus_Ar_times_v(bs, bs * nz, w, v, work);
          PetscCall(PetscArraycpy(t + i2, w, bs));
          PetscKernel_w_gets_Ar_times_v(bs, bs, w, idiag, x + i2);

          idiag += bs2;
          i2 += bs;
        }
        break;
      }
      /* for logging purposes assume number of nonzero in lower half is 1/2 of total */
      PetscCall(PetscLogFlops(1.0 * bs2 * a->nz));
      xb = t;
    } else xb = b;
    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
      idiag = a->idiag + bs2 * (a->mbs - 1);
      i2    = bs * (m - 1);
      switch (bs) {
      case 1:
        s[0] = xb[i2];
        PetscKernel_v_gets_A_times_w_1(xw, idiag, s);
        x[i2] = xw[0];
        i2 -= 1;
        for (i = m - 2; i >= 0; i--) {
          v    = aa + (diag[i] + 1);
          vi   = aj + diag[i] + 1;
          nz   = ai[i + 1] - diag[i] - 1;
          s[0] = xb[i2];
          for (j = 0; j < nz; j++) {
            xw[0] = x[vi[j]];
            PetscKernel_v_gets_v_minus_A_times_w_1(s, (v + j), xw);
          }
          PetscKernel_v_gets_A_times_w_1(xw, idiag, s);
          x[i2] = xw[0];
          idiag -= 1;
          i2 -= 1;
        }
        break;
      case 2:
        s[0] = xb[i2];
        s[1] = xb[i2 + 1];
        PetscKernel_v_gets_A_times_w_2(xw, idiag, s);
        x[i2]     = xw[0];
        x[i2 + 1] = xw[1];
        i2 -= 2;
        idiag -= 4;
        for (i = m - 2; i >= 0; i--) {
          v    = aa + 4 * (diag[i] + 1);
          vi   = aj + diag[i] + 1;
          nz   = ai[i + 1] - diag[i] - 1;
          s[0] = xb[i2];
          s[1] = xb[i2 + 1];
          for (j = 0; j < nz; j++) {
            idx   = 2 * vi[j];
            it    = 4 * j;
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_2(s, (v + it), xw);
          }
          PetscKernel_v_gets_A_times_w_2(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          idiag -= 4;
          i2 -= 2;
        }
        break;
      case 3:
        s[0] = xb[i2];
        s[1] = xb[i2 + 1];
        s[2] = xb[i2 + 2];
        PetscKernel_v_gets_A_times_w_3(xw, idiag, s);
        x[i2]     = xw[0];
        x[i2 + 1] = xw[1];
        x[i2 + 2] = xw[2];
        i2 -= 3;
        idiag -= 9;
        for (i = m - 2; i >= 0; i--) {
          v    = aa + 9 * (diag[i] + 1);
          vi   = aj + diag[i] + 1;
          nz   = ai[i + 1] - diag[i] - 1;
          s[0] = xb[i2];
          s[1] = xb[i2 + 1];
          s[2] = xb[i2 + 2];
          while (nz--) {
            idx   = 3 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_3(s, v, xw);
            v += 9;
          }
          PetscKernel_v_gets_A_times_w_3(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          idiag -= 9;
          i2 -= 3;
        }
        break;
      case 4:
        s[0] = xb[i2];
        s[1] = xb[i2 + 1];
        s[2] = xb[i2 + 2];
        s[3] = xb[i2 + 3];
        PetscKernel_v_gets_A_times_w_4(xw, idiag, s);
        x[i2]     = xw[0];
        x[i2 + 1] = xw[1];
        x[i2 + 2] = xw[2];
        x[i2 + 3] = xw[3];
        i2 -= 4;
        idiag -= 16;
        for (i = m - 2; i >= 0; i--) {
          v    = aa + 16 * (diag[i] + 1);
          vi   = aj + diag[i] + 1;
          nz   = ai[i + 1] - diag[i] - 1;
          s[0] = xb[i2];
          s[1] = xb[i2 + 1];
          s[2] = xb[i2 + 2];
          s[3] = xb[i2 + 3];
          while (nz--) {
            idx   = 4 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_4(s, v, xw);
            v += 16;
          }
          PetscKernel_v_gets_A_times_w_4(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          x[i2 + 3] = xw[3];
          idiag -= 16;
          i2 -= 4;
        }
        break;
      case 5:
        s[0] = xb[i2];
        s[1] = xb[i2 + 1];
        s[2] = xb[i2 + 2];
        s[3] = xb[i2 + 3];
        s[4] = xb[i2 + 4];
        PetscKernel_v_gets_A_times_w_5(xw, idiag, s);
        x[i2]     = xw[0];
        x[i2 + 1] = xw[1];
        x[i2 + 2] = xw[2];
        x[i2 + 3] = xw[3];
        x[i2 + 4] = xw[4];
        i2 -= 5;
        idiag -= 25;
        for (i = m - 2; i >= 0; i--) {
          v    = aa + 25 * (diag[i] + 1);
          vi   = aj + diag[i] + 1;
          nz   = ai[i + 1] - diag[i] - 1;
          s[0] = xb[i2];
          s[1] = xb[i2 + 1];
          s[2] = xb[i2 + 2];
          s[3] = xb[i2 + 3];
          s[4] = xb[i2 + 4];
          while (nz--) {
            idx   = 5 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_5(s, v, xw);
            v += 25;
          }
          PetscKernel_v_gets_A_times_w_5(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          x[i2 + 3] = xw[3];
          x[i2 + 4] = xw[4];
          idiag -= 25;
          i2 -= 5;
        }
        break;
      case 6:
        s[0] = xb[i2];
        s[1] = xb[i2 + 1];
        s[2] = xb[i2 + 2];
        s[3] = xb[i2 + 3];
        s[4] = xb[i2 + 4];
        s[5] = xb[i2 + 5];
        PetscKernel_v_gets_A_times_w_6(xw, idiag, s);
        x[i2]     = xw[0];
        x[i2 + 1] = xw[1];
        x[i2 + 2] = xw[2];
        x[i2 + 3] = xw[3];
        x[i2 + 4] = xw[4];
        x[i2 + 5] = xw[5];
        i2 -= 6;
        idiag -= 36;
        for (i = m - 2; i >= 0; i--) {
          v    = aa + 36 * (diag[i] + 1);
          vi   = aj + diag[i] + 1;
          nz   = ai[i + 1] - diag[i] - 1;
          s[0] = xb[i2];
          s[1] = xb[i2 + 1];
          s[2] = xb[i2 + 2];
          s[3] = xb[i2 + 3];
          s[4] = xb[i2 + 4];
          s[5] = xb[i2 + 5];
          while (nz--) {
            idx   = 6 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            xw[5] = x[5 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_6(s, v, xw);
            v += 36;
          }
          PetscKernel_v_gets_A_times_w_6(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          x[i2 + 3] = xw[3];
          x[i2 + 4] = xw[4];
          x[i2 + 5] = xw[5];
          idiag -= 36;
          i2 -= 6;
        }
        break;
      case 7:
        s[0] = xb[i2];
        s[1] = xb[i2 + 1];
        s[2] = xb[i2 + 2];
        s[3] = xb[i2 + 3];
        s[4] = xb[i2 + 4];
        s[5] = xb[i2 + 5];
        s[6] = xb[i2 + 6];
        PetscKernel_v_gets_A_times_w_7(x, idiag, b);
        x[i2]     = xw[0];
        x[i2 + 1] = xw[1];
        x[i2 + 2] = xw[2];
        x[i2 + 3] = xw[3];
        x[i2 + 4] = xw[4];
        x[i2 + 5] = xw[5];
        x[i2 + 6] = xw[6];
        i2 -= 7;
        idiag -= 49;
        for (i = m - 2; i >= 0; i--) {
          v    = aa + 49 * (diag[i] + 1);
          vi   = aj + diag[i] + 1;
          nz   = ai[i + 1] - diag[i] - 1;
          s[0] = xb[i2];
          s[1] = xb[i2 + 1];
          s[2] = xb[i2 + 2];
          s[3] = xb[i2 + 3];
          s[4] = xb[i2 + 4];
          s[5] = xb[i2 + 5];
          s[6] = xb[i2 + 6];
          while (nz--) {
            idx   = 7 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            xw[5] = x[5 + idx];
            xw[6] = x[6 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_7(s, v, xw);
            v += 49;
          }
          PetscKernel_v_gets_A_times_w_7(xw, idiag, s);
          x[i2]     = xw[0];
          x[i2 + 1] = xw[1];
          x[i2 + 2] = xw[2];
          x[i2 + 3] = xw[3];
          x[i2 + 4] = xw[4];
          x[i2 + 5] = xw[5];
          x[i2 + 6] = xw[6];
          idiag -= 49;
          i2 -= 7;
        }
        break;
      default:
        PetscCall(PetscArraycpy(w, xb + i2, bs));
        PetscKernel_w_gets_Ar_times_v(bs, bs, w, idiag, x + i2);
        i2 -= bs;
        idiag -= bs2;
        for (i = m - 2; i >= 0; i--) {
          v  = aa + bs2 * (diag[i] + 1);
          vi = aj + diag[i] + 1;
          nz = ai[i + 1] - diag[i] - 1;

          PetscCall(PetscArraycpy(w, xb + i2, bs));
          /* copy all rows of x that are needed into contiguous space */
          workt = work;
          for (j = 0; j < nz; j++) {
            PetscCall(PetscArraycpy(workt, x + bs * (*vi++), bs));
            workt += bs;
          }
          PetscKernel_w_gets_w_minus_Ar_times_v(bs, bs * nz, w, v, work);
          PetscKernel_w_gets_Ar_times_v(bs, bs, w, idiag, x + i2);

          idiag -= bs2;
          i2 -= bs;
        }
        break;
      }
      PetscCall(PetscLogFlops(1.0 * bs2 * (a->nz)));
    }
    its--;
  }
  while (its--) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
      idiag = a->idiag;
      i2    = 0;
      switch (bs) {
      case 1:
        for (i = 0; i < m; i++) {
          v    = aa + ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          for (j = 0; j < nz; j++) {
            xw[0] = x[vi[j]];
            PetscKernel_v_gets_v_minus_A_times_w_1(s, (v + j), xw);
          }
          PetscKernel_v_gets_A_times_w_1(xw, idiag, s);
          x[i2] += xw[0];
          idiag += 1;
          i2 += 1;
        }
        break;
      case 2:
        for (i = 0; i < m; i++) {
          v    = aa + 4 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          for (j = 0; j < nz; j++) {
            idx   = 2 * vi[j];
            it    = 4 * j;
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_2(s, (v + it), xw);
          }
          PetscKernel_v_gets_A_times_w_2(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          idiag += 4;
          i2 += 2;
        }
        break;
      case 3:
        for (i = 0; i < m; i++) {
          v    = aa + 9 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          while (nz--) {
            idx   = 3 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_3(s, v, xw);
            v += 9;
          }
          PetscKernel_v_gets_A_times_w_3(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          idiag += 9;
          i2 += 3;
        }
        break;
      case 4:
        for (i = 0; i < m; i++) {
          v    = aa + 16 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          while (nz--) {
            idx   = 4 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_4(s, v, xw);
            v += 16;
          }
          PetscKernel_v_gets_A_times_w_4(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          x[i2 + 3] += xw[3];
          idiag += 16;
          i2 += 4;
        }
        break;
      case 5:
        for (i = 0; i < m; i++) {
          v    = aa + 25 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          while (nz--) {
            idx   = 5 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_5(s, v, xw);
            v += 25;
          }
          PetscKernel_v_gets_A_times_w_5(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          x[i2 + 3] += xw[3];
          x[i2 + 4] += xw[4];
          idiag += 25;
          i2 += 5;
        }
        break;
      case 6:
        for (i = 0; i < m; i++) {
          v    = aa + 36 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          s[5] = b[i2 + 5];
          while (nz--) {
            idx   = 6 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            xw[5] = x[5 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_6(s, v, xw);
            v += 36;
          }
          PetscKernel_v_gets_A_times_w_6(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          x[i2 + 3] += xw[3];
          x[i2 + 4] += xw[4];
          x[i2 + 5] += xw[5];
          idiag += 36;
          i2 += 6;
        }
        break;
      case 7:
        for (i = 0; i < m; i++) {
          v    = aa + 49 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          s[5] = b[i2 + 5];
          s[6] = b[i2 + 6];
          while (nz--) {
            idx   = 7 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            xw[5] = x[5 + idx];
            xw[6] = x[6 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_7(s, v, xw);
            v += 49;
          }
          PetscKernel_v_gets_A_times_w_7(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          x[i2 + 3] += xw[3];
          x[i2 + 4] += xw[4];
          x[i2 + 5] += xw[5];
          x[i2 + 6] += xw[6];
          idiag += 49;
          i2 += 7;
        }
        break;
      default:
        for (i = 0; i < m; i++) {
          v  = aa + bs2 * ai[i];
          vi = aj + ai[i];
          nz = ai[i + 1] - ai[i];

          PetscCall(PetscArraycpy(w, b + i2, bs));
          /* copy all rows of x that are needed into contiguous space */
          workt = work;
          for (j = 0; j < nz; j++) {
            PetscCall(PetscArraycpy(workt, x + bs * (*vi++), bs));
            workt += bs;
          }
          PetscKernel_w_gets_w_minus_Ar_times_v(bs, bs * nz, w, v, work);
          PetscKernel_w_gets_w_plus_Ar_times_v(bs, bs, w, idiag, x + i2);

          idiag += bs2;
          i2 += bs;
        }
        break;
      }
      PetscCall(PetscLogFlops(2.0 * bs2 * a->nz));
    }
    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
      idiag = a->idiag + bs2 * (a->mbs - 1);
      i2    = bs * (m - 1);
      switch (bs) {
      case 1:
        for (i = m - 1; i >= 0; i--) {
          v    = aa + ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          for (j = 0; j < nz; j++) {
            xw[0] = x[vi[j]];
            PetscKernel_v_gets_v_minus_A_times_w_1(s, (v + j), xw);
          }
          PetscKernel_v_gets_A_times_w_1(xw, idiag, s);
          x[i2] += xw[0];
          idiag -= 1;
          i2 -= 1;
        }
        break;
      case 2:
        for (i = m - 1; i >= 0; i--) {
          v    = aa + 4 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          for (j = 0; j < nz; j++) {
            idx   = 2 * vi[j];
            it    = 4 * j;
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_2(s, (v + it), xw);
          }
          PetscKernel_v_gets_A_times_w_2(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          idiag -= 4;
          i2 -= 2;
        }
        break;
      case 3:
        for (i = m - 1; i >= 0; i--) {
          v    = aa + 9 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          while (nz--) {
            idx   = 3 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_3(s, v, xw);
            v += 9;
          }
          PetscKernel_v_gets_A_times_w_3(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          idiag -= 9;
          i2 -= 3;
        }
        break;
      case 4:
        for (i = m - 1; i >= 0; i--) {
          v    = aa + 16 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          while (nz--) {
            idx   = 4 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_4(s, v, xw);
            v += 16;
          }
          PetscKernel_v_gets_A_times_w_4(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          x[i2 + 3] += xw[3];
          idiag -= 16;
          i2 -= 4;
        }
        break;
      case 5:
        for (i = m - 1; i >= 0; i--) {
          v    = aa + 25 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          while (nz--) {
            idx   = 5 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_5(s, v, xw);
            v += 25;
          }
          PetscKernel_v_gets_A_times_w_5(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          x[i2 + 3] += xw[3];
          x[i2 + 4] += xw[4];
          idiag -= 25;
          i2 -= 5;
        }
        break;
      case 6:
        for (i = m - 1; i >= 0; i--) {
          v    = aa + 36 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          s[5] = b[i2 + 5];
          while (nz--) {
            idx   = 6 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            xw[5] = x[5 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_6(s, v, xw);
            v += 36;
          }
          PetscKernel_v_gets_A_times_w_6(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          x[i2 + 3] += xw[3];
          x[i2 + 4] += xw[4];
          x[i2 + 5] += xw[5];
          idiag -= 36;
          i2 -= 6;
        }
        break;
      case 7:
        for (i = m - 1; i >= 0; i--) {
          v    = aa + 49 * ai[i];
          vi   = aj + ai[i];
          nz   = ai[i + 1] - ai[i];
          s[0] = b[i2];
          s[1] = b[i2 + 1];
          s[2] = b[i2 + 2];
          s[3] = b[i2 + 3];
          s[4] = b[i2 + 4];
          s[5] = b[i2 + 5];
          s[6] = b[i2 + 6];
          while (nz--) {
            idx   = 7 * (*vi++);
            xw[0] = x[idx];
            xw[1] = x[1 + idx];
            xw[2] = x[2 + idx];
            xw[3] = x[3 + idx];
            xw[4] = x[4 + idx];
            xw[5] = x[5 + idx];
            xw[6] = x[6 + idx];
            PetscKernel_v_gets_v_minus_A_times_w_7(s, v, xw);
            v += 49;
          }
          PetscKernel_v_gets_A_times_w_7(xw, idiag, s);
          x[i2] += xw[0];
          x[i2 + 1] += xw[1];
          x[i2 + 2] += xw[2];
          x[i2 + 3] += xw[3];
          x[i2 + 4] += xw[4];
          x[i2 + 5] += xw[5];
          x[i2 + 6] += xw[6];
          idiag -= 49;
          i2 -= 7;
        }
        break;
      default:
        for (i = m - 1; i >= 0; i--) {
          v  = aa + bs2 * ai[i];
          vi = aj + ai[i];
          nz = ai[i + 1] - ai[i];

          PetscCall(PetscArraycpy(w, b + i2, bs));
          /* copy all rows of x that are needed into contiguous space */
          workt = work;
          for (j = 0; j < nz; j++) {
            PetscCall(PetscArraycpy(workt, x + bs * (*vi++), bs));
            workt += bs;
          }
          PetscKernel_w_gets_w_minus_Ar_times_v(bs, bs * nz, w, v, work);
          PetscKernel_w_gets_w_plus_Ar_times_v(bs, bs, w, idiag, x + i2);

          idiag -= bs2;
          i2 -= bs;
        }
        break;
      }
      PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz)));
    }
  }
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
    Special version for direct calls from Fortran (Used in PETSc-fun3d)
*/
#if defined(PETSC_HAVE_FORTRAN_CAPS)
  #define matsetvaluesblocked4_ MATSETVALUESBLOCKED4
#elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
  #define matsetvaluesblocked4_ matsetvaluesblocked4
#endif

PETSC_EXTERN void matsetvaluesblocked4_(Mat *AA, PetscInt *mm, const PetscInt im[], PetscInt *nn, const PetscInt in[], const PetscScalar v[])
{
  Mat                A = *AA;
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  PetscInt          *rp, k, low, high, t, ii, jj, row, nrow, i, col, l, N, m = *mm, n = *nn;
  PetscInt          *ai = a->i, *ailen = a->ilen;
  PetscInt          *aj = a->j, stepval, lastcol = -1;
  const PetscScalar *value = v;
  MatScalar         *ap, *aa = a->a, *bap;

  PetscFunctionBegin;
  if (A->rmap->bs != 4) SETERRABORT(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Can only be called with a block size of 4");
  stepval = (n - 1) * 4;
  for (k = 0; k < m; k++) { /* loop over added rows */
    row  = im[k];
    rp   = aj + ai[row];
    ap   = aa + 16 * ai[row];
    nrow = ailen[row];
    low  = 0;
    high = nrow;
    for (l = 0; l < n; l++) { /* loop over added columns */
      col = in[l];
      if (col <= lastcol) low = 0;
      else high = nrow;
      lastcol = col;
      value   = v + k * (stepval + 4 + l) * 4;
      while (high - low > 7) {
        t = (low + high) / 2;
        if (rp[t] > col) high = t;
        else low = t;
      }
      for (i = low; i < high; i++) {
        if (rp[i] > col) break;
        if (rp[i] == col) {
          bap = ap + 16 * i;
          for (ii = 0; ii < 4; ii++, value += stepval) {
            for (jj = ii; jj < 16; jj += 4) bap[jj] += *value++;
          }
          goto noinsert2;
        }
      }
      N = nrow++ - 1;
      high++; /* added new column index thus must search to one higher than before */
      /* shift up all the later entries in this row */
      for (ii = N; ii >= i; ii--) {
        rp[ii + 1] = rp[ii];
        PetscCallVoid(PetscArraycpy(ap + 16 * (ii + 1), ap + 16 * (ii), 16));
      }
      if (N >= i) PetscCallVoid(PetscArrayzero(ap + 16 * i, 16));
      rp[i] = col;
      bap   = ap + 16 * i;
      for (ii = 0; ii < 4; ii++, value += stepval) {
        for (jj = ii; jj < 16; jj += 4) bap[jj] = *value++;
      }
    noinsert2:;
      low = i;
    }
    ailen[row] = nrow;
  }
  PetscFunctionReturnVoid();
}

#if defined(PETSC_HAVE_FORTRAN_CAPS)
  #define matsetvalues4_ MATSETVALUES4
#elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
  #define matsetvalues4_ matsetvalues4
#endif

PETSC_EXTERN void matsetvalues4_(Mat *AA, PetscInt *mm, PetscInt *im, PetscInt *nn, PetscInt *in, PetscScalar *v)
{
  Mat          A = *AA;
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt    *rp, k, low, high, t, row, nrow, i, col, l, N, n = *nn, m = *mm;
  PetscInt    *ai = a->i, *ailen = a->ilen;
  PetscInt    *aj = a->j, brow, bcol;
  PetscInt     ridx, cidx, lastcol = -1;
  MatScalar   *ap, value, *aa      = a->a, *bap;

  PetscFunctionBegin;
  for (k = 0; k < m; k++) { /* loop over added rows */
    row  = im[k];
    brow = row / 4;
    rp   = aj + ai[brow];
    ap   = aa + 16 * ai[brow];
    nrow = ailen[brow];
    low  = 0;
    high = nrow;
    for (l = 0; l < n; l++) { /* loop over added columns */
      col   = in[l];
      bcol  = col / 4;
      ridx  = row % 4;
      cidx  = col % 4;
      value = v[l + k * n];
      if (col <= lastcol) low = 0;
      else high = nrow;
      lastcol = col;
      while (high - low > 7) {
        t = (low + high) / 2;
        if (rp[t] > bcol) high = t;
        else low = t;
      }
      for (i = low; i < high; i++) {
        if (rp[i] > bcol) break;
        if (rp[i] == bcol) {
          bap = ap + 16 * i + 4 * cidx + ridx;
          *bap += value;
          goto noinsert1;
        }
      }
      N = nrow++ - 1;
      high++; /* added new column thus must search to one higher than before */
      /* shift up all the later entries in this row */
      PetscCallVoid(PetscArraymove(rp + i + 1, rp + i, N - i + 1));
      PetscCallVoid(PetscArraymove(ap + 16 * i + 16, ap + 16 * i, 16 * (N - i + 1)));
      PetscCallVoid(PetscArrayzero(ap + 16 * i, 16));
      rp[i]                        = bcol;
      ap[16 * i + 4 * cidx + ridx] = value;
    noinsert1:;
      low = i;
    }
    ailen[brow] = nrow;
  }
  PetscFunctionReturnVoid();
}

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

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

PetscErrorCode MatMarkDiagonal_SeqBAIJ(Mat A)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, j, m = a->mbs;

  PetscFunctionBegin;
  if (!a->diag) {
    PetscCall(PetscMalloc1(m, &a->diag));
    a->free_diag = PETSC_TRUE;
  }
  for (i = 0; i < m; i++) {
    a->diag[i] = a->i[i + 1];
    for (j = a->i[i]; j < a->i[i + 1]; j++) {
      if (a->j[j] == i) {
        a->diag[i] = j;
        break;
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetRowIJ_SeqBAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *nn, const PetscInt *inia[], const PetscInt *inja[], PetscBool *done)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, j, n = a->mbs, nz = a->i[n], *tia, *tja, bs = A->rmap->bs, k, l, cnt;
  PetscInt   **ia = (PetscInt **)inia, **ja = (PetscInt **)inja;

  PetscFunctionBegin;
  *nn = n;
  if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
  if (symmetric) {
    PetscCall(MatToSymmetricIJ_SeqAIJ(n, a->i, a->j, PETSC_TRUE, 0, 0, &tia, &tja));
    nz = tia[n];
  } else {
    tia = a->i;
    tja = a->j;
  }

  if (!blockcompressed && bs > 1) {
    (*nn) *= bs;
    /* malloc & create the natural set of indices */
    PetscCall(PetscMalloc1((n + 1) * bs, ia));
    if (n) {
      (*ia)[0] = oshift;
      for (j = 1; j < bs; j++) (*ia)[j] = (tia[1] - tia[0]) * bs + (*ia)[j - 1];
    }

    for (i = 1; i < n; i++) {
      (*ia)[i * bs] = (tia[i] - tia[i - 1]) * bs + (*ia)[i * bs - 1];
      for (j = 1; j < bs; j++) (*ia)[i * bs + j] = (tia[i + 1] - tia[i]) * bs + (*ia)[i * bs + j - 1];
    }
    if (n) (*ia)[n * bs] = (tia[n] - tia[n - 1]) * bs + (*ia)[n * bs - 1];

    if (inja) {
      PetscCall(PetscMalloc1(nz * bs * bs, ja));
      cnt = 0;
      for (i = 0; i < n; i++) {
        for (j = 0; j < bs; j++) {
          for (k = tia[i]; k < tia[i + 1]; k++) {
            for (l = 0; l < bs; l++) (*ja)[cnt++] = bs * tja[k] + l;
          }
        }
      }
    }

    if (symmetric) { /* deallocate memory allocated in MatToSymmetricIJ_SeqAIJ() */
      PetscCall(PetscFree(tia));
      PetscCall(PetscFree(tja));
    }
  } else if (oshift == 1) {
    if (symmetric) {
      nz = tia[A->rmap->n / bs];
      /*  add 1 to i and j indices */
      for (i = 0; i < A->rmap->n / bs + 1; i++) tia[i] = tia[i] + 1;
      *ia = tia;
      if (ja) {
        for (i = 0; i < nz; i++) tja[i] = tja[i] + 1;
        *ja = tja;
      }
    } else {
      nz = a->i[A->rmap->n / bs];
      /* malloc space and  add 1 to i and j indices */
      PetscCall(PetscMalloc1(A->rmap->n / bs + 1, ia));
      for (i = 0; i < A->rmap->n / bs + 1; i++) (*ia)[i] = a->i[i] + 1;
      if (ja) {
        PetscCall(PetscMalloc1(nz, ja));
        for (i = 0; i < nz; i++) (*ja)[i] = a->j[i] + 1;
      }
    }
  } else {
    *ia = tia;
    if (ja) *ja = tja;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatRestoreRowIJ_SeqBAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *nn, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
{
  PetscFunctionBegin;
  if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
  if ((!blockcompressed && A->rmap->bs > 1) || (symmetric || oshift == 1)) {
    PetscCall(PetscFree(*ia));
    if (ja) PetscCall(PetscFree(*ja));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatDestroy_SeqBAIJ(Mat A)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;

  PetscFunctionBegin;
  if (A->hash_active) {
    PetscInt bs;
    A->ops[0] = a->cops;
    PetscCall(PetscHMapIJVDestroy(&a->ht));
    PetscCall(MatGetBlockSize(A, &bs));
    if (bs > 1) PetscCall(PetscHSetIJDestroy(&a->bht));
    PetscCall(PetscFree(a->dnz));
    PetscCall(PetscFree(a->bdnz));
    A->hash_active = PETSC_FALSE;
  }
  PetscCall(PetscLogObjectState((PetscObject)A, "Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT ", NZ=%" PetscInt_FMT, A->rmap->N, A->cmap->n, a->nz));
  PetscCall(MatSeqXAIJFreeAIJ(A, &a->a, &a->j, &a->i));
  PetscCall(ISDestroy(&a->row));
  PetscCall(ISDestroy(&a->col));
  if (a->free_diag) PetscCall(PetscFree(a->diag));
  PetscCall(PetscFree(a->idiag));
  if (a->free_imax_ilen) PetscCall(PetscFree2(a->imax, a->ilen));
  PetscCall(PetscFree(a->solve_work));
  PetscCall(PetscFree(a->mult_work));
  PetscCall(PetscFree(a->sor_workt));
  PetscCall(PetscFree(a->sor_work));
  PetscCall(ISDestroy(&a->icol));
  PetscCall(PetscFree(a->saved_values));
  PetscCall(PetscFree2(a->compressedrow.i, a->compressedrow.rindex));

  PetscCall(MatDestroy(&a->sbaijMat));
  PetscCall(MatDestroy(&a->parent));
  PetscCall(PetscFree(A->data));

  PetscCall(PetscObjectChangeTypeName((PetscObject)A, NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqBAIJGetArray_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqBAIJRestoreArray_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatStoreValues_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatRetrieveValues_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqBAIJSetColumnIndices_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqbaij_seqaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqbaij_seqsbaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqBAIJSetPreallocation_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqBAIJSetPreallocationCSR_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqbaij_seqbstrm_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatIsTranspose_C", NULL));
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqbaij_hypre_C", NULL));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqbaij_is_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  switch (op) {
  case MAT_ROW_ORIENTED:
    a->roworiented = flg;
    break;
  case MAT_KEEP_NONZERO_PATTERN:
    a->keepnonzeropattern = flg;
    break;
  case MAT_NEW_NONZERO_LOCATIONS:
    a->nonew = (flg ? 0 : 1);
    break;
  case MAT_NEW_NONZERO_LOCATION_ERR:
    a->nonew = (flg ? -1 : 0);
    break;
  case MAT_NEW_NONZERO_ALLOCATION_ERR:
    a->nonew = (flg ? -2 : 0);
    break;
  case MAT_UNUSED_NONZERO_LOCATION_ERR:
    a->nounused = (flg ? -1 : 0);
    break;
  case MAT_FORCE_DIAGONAL_ENTRIES:
  case MAT_IGNORE_OFF_PROC_ENTRIES:
  case MAT_USE_HASH_TABLE:
  case MAT_SORTED_FULL:
    PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
    break;
  case MAT_SPD:
  case MAT_SYMMETRIC:
  case MAT_STRUCTURALLY_SYMMETRIC:
  case MAT_HERMITIAN:
  case MAT_SYMMETRY_ETERNAL:
  case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
  case MAT_SUBMAT_SINGLEIS:
  case MAT_STRUCTURE_ONLY:
  case MAT_SPD_ETERNAL:
    /* if the diagonal matrix is square it inherits some of the properties above */
    break;
  default:
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unknown option %d", op);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* used for both SeqBAIJ and SeqSBAIJ matrices */
PetscErrorCode MatGetRow_SeqBAIJ_private(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v, PetscInt *ai, PetscInt *aj, PetscScalar *aa)
{
  PetscInt     itmp, i, j, k, M, bn, bp, *idx_i, bs, bs2;
  MatScalar   *aa_i;
  PetscScalar *v_i;

  PetscFunctionBegin;
  bs  = A->rmap->bs;
  bs2 = bs * bs;
  PetscCheck(row >= 0 && row < A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row %" PetscInt_FMT " out of range", row);

  bn  = row / bs; /* Block number */
  bp  = row % bs; /* Block Position */
  M   = ai[bn + 1] - ai[bn];
  *nz = bs * M;

  if (v) {
    *v = NULL;
    if (*nz) {
      PetscCall(PetscMalloc1(*nz, v));
      for (i = 0; i < M; i++) { /* for each block in the block row */
        v_i  = *v + i * bs;
        aa_i = aa + bs2 * (ai[bn] + i);
        for (j = bp, k = 0; j < bs2; j += bs, k++) v_i[k] = aa_i[j];
      }
    }
  }

  if (idx) {
    *idx = NULL;
    if (*nz) {
      PetscCall(PetscMalloc1(*nz, idx));
      for (i = 0; i < M; i++) { /* for each block in the block row */
        idx_i = *idx + i * bs;
        itmp  = bs * aj[ai[bn] + i];
        for (j = 0; j < bs; j++) idx_i[j] = itmp++;
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatGetRow_SeqBAIJ(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;

  PetscFunctionBegin;
  PetscCall(MatGetRow_SeqBAIJ_private(A, row, nz, idx, v, a->i, a->j, a->a));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatRestoreRow_SeqBAIJ(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
{
  PetscFunctionBegin;
  if (idx) PetscCall(PetscFree(*idx));
  if (v) PetscCall(PetscFree(*v));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatTranspose_SeqBAIJ(Mat A, MatReuse reuse, Mat *B)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *at;
  Mat          C;
  PetscInt     i, j, k, *aj = a->j, *ai = a->i, bs = A->rmap->bs, mbs = a->mbs, nbs = a->nbs, *atfill;
  PetscInt     bs2 = a->bs2, *ati, *atj, anzj, kr;
  MatScalar   *ata, *aa = a->a;

  PetscFunctionBegin;
  if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *B));
  PetscCall(PetscCalloc1(1 + nbs, &atfill));
  if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_INPLACE_MATRIX) {
    for (i = 0; i < ai[mbs]; i++) atfill[aj[i]] += 1; /* count num of non-zeros in row aj[i] */

    PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
    PetscCall(MatSetSizes(C, A->cmap->n, A->rmap->N, A->cmap->n, A->rmap->N));
    PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    PetscCall(MatSeqBAIJSetPreallocation(C, bs, 0, atfill));

    at  = (Mat_SeqBAIJ *)C->data;
    ati = at->i;
    for (i = 0; i < nbs; i++) at->ilen[i] = at->imax[i] = ati[i + 1] - ati[i];
  } else {
    C   = *B;
    at  = (Mat_SeqBAIJ *)C->data;
    ati = at->i;
  }

  atj = at->j;
  ata = at->a;

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

  /* Walk through A row-wise and mark nonzero entries of A^T. */
  for (i = 0; i < mbs; i++) {
    anzj = ai[i + 1] - ai[i];
    for (j = 0; j < anzj; j++) {
      atj[atfill[*aj]] = i;
      for (kr = 0; kr < bs; kr++) {
        for (k = 0; k < bs; k++) ata[bs2 * atfill[*aj] + k * bs + kr] = *aa++;
      }
      atfill[*aj++] += 1;
    }
  }
  PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

  /* Clean up temporary space and complete requests. */
  PetscCall(PetscFree(atfill));

  if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
    PetscCall(MatSetBlockSizes(C, PetscAbs(A->cmap->bs), PetscAbs(A->rmap->bs)));
    *B = C;
  } else {
    PetscCall(MatHeaderMerge(A, &C));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatIsTranspose_SeqBAIJ(Mat A, Mat B, PetscReal tol, PetscBool *f)
{
  Mat Btrans;

  PetscFunctionBegin;
  *f = PETSC_FALSE;
  PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &Btrans));
  PetscCall(MatEqual_SeqBAIJ(B, Btrans, f));
  PetscCall(MatDestroy(&Btrans));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Used for both SeqBAIJ and SeqSBAIJ matrices */
PetscErrorCode MatView_SeqBAIJ_Binary(Mat mat, PetscViewer viewer)
{
  Mat_SeqBAIJ *A = (Mat_SeqBAIJ *)mat->data;
  PetscInt     header[4], M, N, m, bs, nz, cnt, i, j, k, l;
  PetscInt    *rowlens, *colidxs;
  PetscScalar *matvals;

  PetscFunctionBegin;
  PetscCall(PetscViewerSetUp(viewer));

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

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

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

  /* store column indices  */
  PetscCall(PetscMalloc1(nz, &colidxs));
  for (cnt = 0, i = 0; i < A->mbs; i++)
    for (k = 0; k < bs; k++)
      for (j = A->i[i]; j < A->i[i + 1]; j++)
        for (l = 0; l < bs; l++) colidxs[cnt++] = bs * A->j[j] + l;
  PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_LIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt_FMT, cnt, nz);
  PetscCall(PetscViewerBinaryWrite(viewer, colidxs, nz, PETSC_INT));
  PetscCall(PetscFree(colidxs));

  /* store nonzero values */
  PetscCall(PetscMalloc1(nz, &matvals));
  for (cnt = 0, i = 0; i < A->mbs; i++)
    for (k = 0; k < bs; k++)
      for (j = A->i[i]; j < A->i[i + 1]; j++)
        for (l = 0; l < bs; l++) matvals[cnt++] = A->a[bs * (bs * j + l) + k];
  PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_LIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt_FMT, cnt, nz);
  PetscCall(PetscViewerBinaryWrite(viewer, matvals, nz, PETSC_SCALAR));
  PetscCall(PetscFree(matvals));

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

static PetscErrorCode MatView_SeqBAIJ_ASCII_structonly(Mat A, PetscViewer viewer)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, bs = A->rmap->bs, k;

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

static PetscErrorCode MatView_SeqBAIJ_ASCII(Mat A, PetscViewer viewer)
{
  Mat_SeqBAIJ      *a = (Mat_SeqBAIJ *)A->data;
  PetscInt          i, j, bs = A->rmap->bs, k, l, bs2 = a->bs2;
  PetscViewerFormat format;

  PetscFunctionBegin;
  if (A->structure_only) {
    PetscCall(MatView_SeqBAIJ_ASCII_structonly(A, viewer));
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  PetscCall(PetscViewerGetFormat(viewer, &format));
  if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    PetscCall(PetscViewerASCIIPrintf(viewer, "  block size is %" PetscInt_FMT "\n", bs));
  } else if (format == PETSC_VIEWER_ASCII_MATLAB) {
    const char *matname;
    Mat         aij;
    PetscCall(MatConvert(A, MATSEQAIJ, MAT_INITIAL_MATRIX, &aij));
    PetscCall(PetscObjectGetName((PetscObject)A, &matname));
    PetscCall(PetscObjectSetName((PetscObject)aij, matname));
    PetscCall(MatView(aij, viewer));
    PetscCall(MatDestroy(&aij));
  } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
    PetscFunctionReturn(PETSC_SUCCESS);
  } else if (format == PETSC_VIEWER_ASCII_COMMON) {
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
    for (i = 0; i < a->mbs; i++) {
      for (j = 0; j < bs; j++) {
        PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i * bs + j));
        for (k = a->i[i]; k < a->i[i + 1]; k++) {
          for (l = 0; l < bs; l++) {
#if defined(PETSC_USE_COMPLEX)
            if (PetscImaginaryPart(a->a[bs2 * k + l * bs + j]) > 0.0 && PetscRealPart(a->a[bs2 * k + l * bs + j]) != 0.0) {
              PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %gi) ", bs * a->j[k] + l, (double)PetscRealPart(a->a[bs2 * k + l * bs + j]), (double)PetscImaginaryPart(a->a[bs2 * k + l * bs + j])));
            } else if (PetscImaginaryPart(a->a[bs2 * k + l * bs + j]) < 0.0 && PetscRealPart(a->a[bs2 * k + l * bs + j]) != 0.0) {
              PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %gi) ", bs * a->j[k] + l, (double)PetscRealPart(a->a[bs2 * k + l * bs + j]), -(double)PetscImaginaryPart(a->a[bs2 * k + l * bs + j])));
            } else if (PetscRealPart(a->a[bs2 * k + l * bs + j]) != 0.0) {
              PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", bs * a->j[k] + l, (double)PetscRealPart(a->a[bs2 * k + l * bs + j])));
            }
#else
            if (a->a[bs2 * k + l * bs + j] != 0.0) PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", bs * a->j[k] + l, (double)a->a[bs2 * k + l * bs + j]));
#endif
          }
        }
        PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
      }
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
  } else {
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
    for (i = 0; i < a->mbs; i++) {
      for (j = 0; j < bs; j++) {
        PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i * bs + j));
        for (k = a->i[i]; k < a->i[i + 1]; k++) {
          for (l = 0; l < bs; l++) {
#if defined(PETSC_USE_COMPLEX)
            if (PetscImaginaryPart(a->a[bs2 * k + l * bs + j]) > 0.0) {
              PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i) ", bs * a->j[k] + l, (double)PetscRealPart(a->a[bs2 * k + l * bs + j]), (double)PetscImaginaryPart(a->a[bs2 * k + l * bs + j])));
            } else if (PetscImaginaryPart(a->a[bs2 * k + l * bs + j]) < 0.0) {
              PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i) ", bs * a->j[k] + l, (double)PetscRealPart(a->a[bs2 * k + l * bs + j]), -(double)PetscImaginaryPart(a->a[bs2 * k + l * bs + j])));
            } else {
              PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", bs * a->j[k] + l, (double)PetscRealPart(a->a[bs2 * k + l * bs + j])));
            }
#else
            PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", bs * a->j[k] + l, (double)a->a[bs2 * k + l * bs + j]));
#endif
          }
        }
        PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
      }
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
  }
  PetscCall(PetscViewerFlush(viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

#include <petscdraw.h>
static PetscErrorCode MatView_SeqBAIJ_Draw_Zoom(PetscDraw draw, void *Aa)
{
  Mat               A = (Mat)Aa;
  Mat_SeqBAIJ      *a = (Mat_SeqBAIJ *)A->data;
  PetscInt          row, i, j, k, l, mbs = a->mbs, color, bs = A->rmap->bs, bs2 = a->bs2;
  PetscReal         xl, yl, xr, yr, x_l, x_r, y_l, y_r;
  MatScalar        *aa;
  PetscViewer       viewer;
  PetscViewerFormat format;

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

  /* loop over matrix elements drawing boxes */

  if (format != PETSC_VIEWER_DRAW_CONTOUR) {
    PetscDrawCollectiveBegin(draw);
    /* Blue for negative, Cyan for zero and  Red for positive */
    color = PETSC_DRAW_BLUE;
    for (i = 0, row = 0; i < mbs; i++, row += bs) {
      for (j = a->i[i]; j < a->i[i + 1]; j++) {
        y_l = A->rmap->N - row - 1.0;
        y_r = y_l + 1.0;
        x_l = a->j[j] * bs;
        x_r = x_l + 1.0;
        aa  = a->a + j * bs2;
        for (k = 0; k < bs; k++) {
          for (l = 0; l < bs; l++) {
            if (PetscRealPart(*aa++) >= 0.) continue;
            PetscCall(PetscDrawRectangle(draw, x_l + k, y_l - l, x_r + k, y_r - l, color, color, color, color));
          }
        }
      }
    }
    color = PETSC_DRAW_CYAN;
    for (i = 0, row = 0; i < mbs; i++, row += bs) {
      for (j = a->i[i]; j < a->i[i + 1]; j++) {
        y_l = A->rmap->N - row - 1.0;
        y_r = y_l + 1.0;
        x_l = a->j[j] * bs;
        x_r = x_l + 1.0;
        aa  = a->a + j * bs2;
        for (k = 0; k < bs; k++) {
          for (l = 0; l < bs; l++) {
            if (PetscRealPart(*aa++) != 0.) continue;
            PetscCall(PetscDrawRectangle(draw, x_l + k, y_l - l, x_r + k, y_r - l, color, color, color, color));
          }
        }
      }
    }
    color = PETSC_DRAW_RED;
    for (i = 0, row = 0; i < mbs; i++, row += bs) {
      for (j = a->i[i]; j < a->i[i + 1]; j++) {
        y_l = A->rmap->N - row - 1.0;
        y_r = y_l + 1.0;
        x_l = a->j[j] * bs;
        x_r = x_l + 1.0;
        aa  = a->a + j * bs2;
        for (k = 0; k < bs; k++) {
          for (l = 0; l < bs; l++) {
            if (PetscRealPart(*aa++) <= 0.) continue;
            PetscCall(PetscDrawRectangle(draw, x_l + k, y_l - l, x_r + k, y_r - l, color, color, color, color));
          }
        }
      }
    }
    PetscDrawCollectiveEnd(draw);
  } else {
    /* use contour shading to indicate magnitude of values */
    /* first determine max of all nonzero values */
    PetscReal minv = 0.0, maxv = 0.0;
    PetscDraw popup;

    for (i = 0; i < a->nz * a->bs2; i++) {
      if (PetscAbsScalar(a->a[i]) > maxv) maxv = PetscAbsScalar(a->a[i]);
    }
    if (minv >= maxv) maxv = minv + PETSC_SMALL;
    PetscCall(PetscDrawGetPopup(draw, &popup));
    PetscCall(PetscDrawScalePopup(popup, 0.0, maxv));

    PetscDrawCollectiveBegin(draw);
    for (i = 0, row = 0; i < mbs; i++, row += bs) {
      for (j = a->i[i]; j < a->i[i + 1]; j++) {
        y_l = A->rmap->N - row - 1.0;
        y_r = y_l + 1.0;
        x_l = a->j[j] * bs;
        x_r = x_l + 1.0;
        aa  = a->a + j * bs2;
        for (k = 0; k < bs; k++) {
          for (l = 0; l < bs; l++) {
            MatScalar v = *aa++;
            color       = PetscDrawRealToColor(PetscAbsScalar(v), minv, maxv);
            PetscCall(PetscDrawRectangle(draw, x_l + k, y_l - l, x_r + k, y_r - l, color, color, color, color));
          }
        }
      }
    }
    PetscDrawCollectiveEnd(draw);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatView_SeqBAIJ_Draw(Mat A, PetscViewer viewer)
{
  PetscReal xl, yl, xr, yr, w, h;
  PetscDraw draw;
  PetscBool isnull;

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

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

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

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
  if (iascii) {
    PetscCall(MatView_SeqBAIJ_ASCII(A, viewer));
  } else if (isbinary) {
    PetscCall(MatView_SeqBAIJ_Binary(A, viewer));
  } else if (isdraw) {
    PetscCall(MatView_SeqBAIJ_Draw(A, viewer));
  } else {
    Mat B;
    PetscCall(MatConvert(A, MATSEQAIJ, MAT_INITIAL_MATRIX, &B));
    PetscCall(MatView(B, viewer));
    PetscCall(MatDestroy(&B));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatGetValues_SeqBAIJ(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], PetscScalar v[])
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt    *rp, k, low, high, t, row, nrow, i, col, l, *aj = a->j;
  PetscInt    *ai = a->i, *ailen = a->ilen;
  PetscInt     brow, bcol, ridx, cidx, bs = A->rmap->bs, bs2 = a->bs2;
  MatScalar   *ap, *aa = a->a;

  PetscFunctionBegin;
  for (k = 0; k < m; k++) { /* loop over rows */
    row  = im[k];
    brow = row / bs;
    if (row < 0) {
      v += n;
      continue;
    } /* negative row */
    PetscCheck(row < A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row %" PetscInt_FMT " too large", row);
    rp   = PetscSafePointerPlusOffset(aj, ai[brow]);
    ap   = PetscSafePointerPlusOffset(aa, bs2 * ai[brow]);
    nrow = ailen[brow];
    for (l = 0; l < n; l++) { /* loop over columns */
      if (in[l] < 0) {
        v++;
        continue;
      } /* negative column */
      PetscCheck(in[l] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column %" PetscInt_FMT " too large", in[l]);
      col  = in[l];
      bcol = col / bs;
      cidx = col % bs;
      ridx = row % bs;
      high = nrow;
      low  = 0; /* assume unsorted */
      while (high - low > 5) {
        t = (low + high) / 2;
        if (rp[t] > bcol) high = t;
        else low = t;
      }
      for (i = low; i < high; i++) {
        if (rp[i] > bcol) break;
        if (rp[i] == bcol) {
          *v++ = ap[bs2 * i + bs * cidx + ridx];
          goto finished;
        }
      }
      *v++ = 0.0;
    finished:;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSetValuesBlocked_SeqBAIJ(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
{
  Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
  PetscInt          *rp, k, low, high, t, ii, jj, row, nrow, i, col, l, rmax, N, lastcol = -1;
  PetscInt          *imax = a->imax, *ai = a->i, *ailen = a->ilen;
  PetscInt          *aj = a->j, nonew = a->nonew, bs2 = a->bs2, bs = A->rmap->bs, stepval;
  PetscBool          roworiented = a->roworiented;
  const PetscScalar *value       = v;
  MatScalar         *ap = NULL, *aa = a->a, *bap;

  PetscFunctionBegin;
  if (roworiented) {
    stepval = (n - 1) * bs;
  } else {
    stepval = (m - 1) * bs;
  }
  for (k = 0; k < m; k++) { /* loop over added rows */
    row = im[k];
    if (row < 0) continue;
    PetscCheck(row < a->mbs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Block row index too large %" PetscInt_FMT " max %" PetscInt_FMT, row, a->mbs - 1);
    rp = aj + ai[row];
    if (!A->structure_only) ap = aa + bs2 * ai[row];
    rmax = imax[row];
    nrow = ailen[row];
    low  = 0;
    high = nrow;
    for (l = 0; l < n; l++) { /* loop over added columns */
      if (in[l] < 0) continue;
      PetscCheck(in[l] < a->nbs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Block column index too large %" PetscInt_FMT " max %" PetscInt_FMT, in[l], a->nbs - 1);
      col = in[l];
      if (!A->structure_only) {
        if (roworiented) {
          value = v + (k * (stepval + bs) + l) * bs;
        } else {
          value = v + (l * (stepval + bs) + k) * bs;
        }
      }
      if (col <= lastcol) low = 0;
      else high = nrow;
      lastcol = col;
      while (high - low > 7) {
        t = (low + high) / 2;
        if (rp[t] > col) high = t;
        else low = t;
      }
      for (i = low; i < high; i++) {
        if (rp[i] > col) break;
        if (rp[i] == col) {
          if (A->structure_only) goto noinsert2;
          bap = ap + bs2 * i;
          if (roworiented) {
            if (is == ADD_VALUES) {
              for (ii = 0; ii < bs; ii++, value += stepval) {
                for (jj = ii; jj < bs2; jj += bs) bap[jj] += *value++;
              }
            } else {
              for (ii = 0; ii < bs; ii++, value += stepval) {
                for (jj = ii; jj < bs2; jj += bs) bap[jj] = *value++;
              }
            }
          } else {
            if (is == ADD_VALUES) {
              for (ii = 0; ii < bs; ii++, value += bs + stepval) {
                for (jj = 0; jj < bs; jj++) bap[jj] += value[jj];
                bap += bs;
              }
            } else {
              for (ii = 0; ii < bs; ii++, value += bs + stepval) {
                for (jj = 0; jj < bs; jj++) bap[jj] = value[jj];
                bap += bs;
              }
            }
          }
          goto noinsert2;
        }
      }
      if (nonew == 1) goto noinsert2;
      PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new blocked index new nonzero block (%" PetscInt_FMT ", %" PetscInt_FMT ") in the matrix", row, col);
      if (A->structure_only) {
        MatSeqXAIJReallocateAIJ_structure_only(A, a->mbs, bs2, nrow, row, col, rmax, ai, aj, rp, imax, nonew, MatScalar);
      } else {
        MatSeqXAIJReallocateAIJ(A, a->mbs, bs2, nrow, row, col, rmax, aa, ai, aj, rp, ap, imax, nonew, MatScalar);
      }
      N = nrow++ - 1;
      high++;
      /* shift up all the later entries in this row */
      PetscCall(PetscArraymove(rp + i + 1, rp + i, N - i + 1));
      rp[i] = col;
      if (!A->structure_only) {
        PetscCall(PetscArraymove(ap + bs2 * (i + 1), ap + bs2 * i, bs2 * (N - i + 1)));
        bap = ap + bs2 * i;
        if (roworiented) {
          for (ii = 0; ii < bs; ii++, value += stepval) {
            for (jj = ii; jj < bs2; jj += bs) bap[jj] = *value++;
          }
        } else {
          for (ii = 0; ii < bs; ii++, value += stepval) {
            for (jj = 0; jj < bs; jj++) *bap++ = *value++;
          }
        }
      }
    noinsert2:;
      low = i;
    }
    ailen[row] = nrow;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatAssemblyEnd_SeqBAIJ(Mat A, MatAssemblyType mode)
{
  Mat_SeqBAIJ *a      = (Mat_SeqBAIJ *)A->data;
  PetscInt     fshift = 0, i, *ai = a->i, *aj = a->j, *imax = a->imax;
  PetscInt     m = A->rmap->N, *ip, N, *ailen = a->ilen;
  PetscInt     mbs = a->mbs, bs2 = a->bs2, rmax = 0;
  MatScalar   *aa    = a->a, *ap;
  PetscReal    ratio = 0.6;

  PetscFunctionBegin;
  if (mode == MAT_FLUSH_ASSEMBLY || (A->was_assembled && A->ass_nonzerostate == A->nonzerostate)) PetscFunctionReturn(PETSC_SUCCESS);

  if (m) rmax = ailen[0];
  for (i = 1; i < mbs; i++) {
    /* move each row back by the amount of empty slots (fshift) before it*/
    fshift += imax[i - 1] - ailen[i - 1];
    rmax = PetscMax(rmax, ailen[i]);
    if (fshift) {
      ip = aj + ai[i];
      ap = aa + bs2 * ai[i];
      N  = ailen[i];
      PetscCall(PetscArraymove(ip - fshift, ip, N));
      if (!A->structure_only) PetscCall(PetscArraymove(ap - bs2 * fshift, ap, bs2 * N));
    }
    ai[i] = ai[i - 1] + ailen[i - 1];
  }
  if (mbs) {
    fshift += imax[mbs - 1] - ailen[mbs - 1];
    ai[mbs] = ai[mbs - 1] + ailen[mbs - 1];
  }

  /* reset ilen and imax for each row */
  a->nonzerorowcnt = 0;
  if (A->structure_only) {
    PetscCall(PetscFree2(a->imax, a->ilen));
  } else { /* !A->structure_only */
    for (i = 0; i < mbs; i++) {
      ailen[i] = imax[i] = ai[i + 1] - ai[i];
      a->nonzerorowcnt += ((ai[i + 1] - ai[i]) > 0);
    }
  }
  a->nz = ai[mbs];

  /* diagonals may have moved, so kill the diagonal pointers */
  a->idiagvalid = PETSC_FALSE;
  if (fshift && a->diag) PetscCall(PetscFree(a->diag));
  if (fshift) PetscCheck(a->nounused != -1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unused space detected in matrix: %" PetscInt_FMT " X %" PetscInt_FMT " block size %" PetscInt_FMT ", %" PetscInt_FMT " unneeded", m, A->cmap->n, A->rmap->bs, fshift * bs2);
  PetscCall(PetscInfo(A, "Matrix size: %" PetscInt_FMT " X %" PetscInt_FMT ", block size %" PetscInt_FMT "; storage space: %" PetscInt_FMT " unneeded, %" PetscInt_FMT " used\n", m, A->cmap->n, A->rmap->bs, fshift * bs2, a->nz * bs2));
  PetscCall(PetscInfo(A, "Number of mallocs during MatSetValues is %" PetscInt_FMT "\n", a->reallocs));
  PetscCall(PetscInfo(A, "Most nonzeros blocks in any row is %" PetscInt_FMT "\n", rmax));

  A->info.mallocs += a->reallocs;
  a->reallocs         = 0;
  A->info.nz_unneeded = (PetscReal)fshift * bs2;
  a->rmax             = rmax;

  if (!A->structure_only) PetscCall(MatCheckCompressedRow(A, a->nonzerorowcnt, &a->compressedrow, a->i, mbs, ratio));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   This function returns an array of flags which indicate the locations of contiguous
   blocks that should be zeroed. for eg: if bs = 3  and is = [0,1,2,3,5,6,7,8,9]
   then the resulting sizes = [3,1,1,3,1] corresponding to sets [(0,1,2),(3),(5),(6,7,8),(9)]
   Assume: sizes should be long enough to hold all the values.
*/
static PetscErrorCode MatZeroRows_SeqBAIJ_Check_Blocks(PetscInt idx[], PetscInt n, PetscInt bs, PetscInt sizes[], PetscInt *bs_max)
{
  PetscInt j = 0;

  PetscFunctionBegin;
  for (PetscInt i = 0; i < n; j++) {
    PetscInt row = idx[i];
    if (row % bs != 0) { /* Not the beginning of a block */
      sizes[j] = 1;
      i++;
    } else if (i + bs > n) { /* complete block doesn't exist (at idx end) */
      sizes[j] = 1;          /* Also makes sure at least 'bs' values exist for next else */
      i++;
    } else { /* Beginning of the block, so check if the complete block exists */
      PetscBool flg = PETSC_TRUE;
      for (PetscInt k = 1; k < bs; k++) {
        if (row + k != idx[i + k]) { /* break in the block */
          flg = PETSC_FALSE;
          break;
        }
      }
      if (flg) { /* No break in the bs */
        sizes[j] = bs;
        i += bs;
      } else {
        sizes[j] = 1;
        i++;
      }
    }
  }
  *bs_max = j;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatZeroRows_SeqBAIJ(Mat A, PetscInt is_n, const PetscInt is_idx[], PetscScalar diag, Vec x, Vec b)
{
  Mat_SeqBAIJ       *baij = (Mat_SeqBAIJ *)A->data;
  PetscInt           i, j, k, count, *rows;
  PetscInt           bs = A->rmap->bs, bs2 = baij->bs2, *sizes, row, bs_max;
  PetscScalar        zero = 0.0;
  MatScalar         *aa;
  const PetscScalar *xx;
  PetscScalar       *bb;

  PetscFunctionBegin;
  /* fix right hand side if needed */
  if (x && b) {
    PetscCall(VecGetArrayRead(x, &xx));
    PetscCall(VecGetArray(b, &bb));
    for (i = 0; i < is_n; i++) bb[is_idx[i]] = diag * xx[is_idx[i]];
    PetscCall(VecRestoreArrayRead(x, &xx));
    PetscCall(VecRestoreArray(b, &bb));
  }

  /* Make a copy of the IS and  sort it */
  /* allocate memory for rows,sizes */
  PetscCall(PetscMalloc2(is_n, &rows, 2 * is_n, &sizes));

  /* copy IS values to rows, and sort them */
  for (i = 0; i < is_n; i++) rows[i] = is_idx[i];
  PetscCall(PetscSortInt(is_n, rows));

  if (baij->keepnonzeropattern) {
    for (i = 0; i < is_n; i++) sizes[i] = 1;
    bs_max = is_n;
  } else {
    PetscCall(MatZeroRows_SeqBAIJ_Check_Blocks(rows, is_n, bs, sizes, &bs_max));
    A->nonzerostate++;
  }

  for (i = 0, j = 0; i < bs_max; j += sizes[i], i++) {
    row = rows[j];
    PetscCheck(row >= 0 && row <= A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", row);
    count = (baij->i[row / bs + 1] - baij->i[row / bs]) * bs;
    aa    = ((MatScalar *)(baij->a)) + baij->i[row / bs] * bs2 + (row % bs);
    if (sizes[i] == bs && !baij->keepnonzeropattern) {
      if (diag != (PetscScalar)0.0) {
        if (baij->ilen[row / bs] > 0) {
          baij->ilen[row / bs]       = 1;
          baij->j[baij->i[row / bs]] = row / bs;

          PetscCall(PetscArrayzero(aa, count * bs));
        }
        /* Now insert all the diagonal values for this bs */
        for (k = 0; k < bs; k++) PetscUseTypeMethod(A, setvalues, 1, rows + j + k, 1, rows + j + k, &diag, INSERT_VALUES);
      } else { /* (diag == 0.0) */
        baij->ilen[row / bs] = 0;
      }      /* end (diag == 0.0) */
    } else { /* (sizes[i] != bs) */
      PetscAssert(sizes[i] == 1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Internal Error. Value should be 1");
      for (k = 0; k < count; k++) {
        aa[0] = zero;
        aa += bs;
      }
      if (diag != (PetscScalar)0.0) PetscUseTypeMethod(A, setvalues, 1, rows + j, 1, rows + j, &diag, INSERT_VALUES);
    }
  }

  PetscCall(PetscFree2(rows, sizes));
  PetscCall(MatAssemblyEnd_SeqBAIJ(A, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroRowsColumns_SeqBAIJ(Mat A, PetscInt is_n, const PetscInt is_idx[], PetscScalar diag, Vec x, Vec b)
{
  Mat_SeqBAIJ       *baij = (Mat_SeqBAIJ *)A->data;
  PetscInt           i, j, k, count;
  PetscInt           bs = A->rmap->bs, bs2 = baij->bs2, row, col;
  PetscScalar        zero = 0.0;
  MatScalar         *aa;
  const PetscScalar *xx;
  PetscScalar       *bb;
  PetscBool         *zeroed, vecs = PETSC_FALSE;

  PetscFunctionBegin;
  /* fix right hand side if needed */
  if (x && b) {
    PetscCall(VecGetArrayRead(x, &xx));
    PetscCall(VecGetArray(b, &bb));
    vecs = PETSC_TRUE;
  }

  /* zero the columns */
  PetscCall(PetscCalloc1(A->rmap->n, &zeroed));
  for (i = 0; i < is_n; i++) {
    PetscCheck(is_idx[i] >= 0 && is_idx[i] < A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", is_idx[i]);
    zeroed[is_idx[i]] = PETSC_TRUE;
  }
  for (i = 0; i < A->rmap->N; i++) {
    if (!zeroed[i]) {
      row = i / bs;
      for (j = baij->i[row]; j < baij->i[row + 1]; j++) {
        for (k = 0; k < bs; k++) {
          col = bs * baij->j[j] + k;
          if (zeroed[col]) {
            aa = ((MatScalar *)(baij->a)) + j * bs2 + (i % bs) + bs * k;
            if (vecs) bb[i] -= aa[0] * xx[col];
            aa[0] = 0.0;
          }
        }
      }
    } else if (vecs) bb[i] = diag * xx[i];
  }
  PetscCall(PetscFree(zeroed));
  if (vecs) {
    PetscCall(VecRestoreArrayRead(x, &xx));
    PetscCall(VecRestoreArray(b, &bb));
  }

  /* zero the rows */
  for (i = 0; i < is_n; i++) {
    row   = is_idx[i];
    count = (baij->i[row / bs + 1] - baij->i[row / bs]) * bs;
    aa    = ((MatScalar *)(baij->a)) + baij->i[row / bs] * bs2 + (row % bs);
    for (k = 0; k < count; k++) {
      aa[0] = zero;
      aa += bs;
    }
    if (diag != (PetscScalar)0.0) PetscUseTypeMethod(A, setvalues, 1, &row, 1, &row, &diag, INSERT_VALUES);
  }
  PetscCall(MatAssemblyEnd_SeqBAIJ(A, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSetValues_SeqBAIJ(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt    *rp, k, low, high, t, ii, row, nrow, i, col, l, rmax, N, lastcol = -1;
  PetscInt    *imax = a->imax, *ai = a->i, *ailen = a->ilen;
  PetscInt    *aj = a->j, nonew = a->nonew, bs = A->rmap->bs, brow, bcol;
  PetscInt     ridx, cidx, bs2                 = a->bs2;
  PetscBool    roworiented = a->roworiented;
  MatScalar   *ap = NULL, value = 0.0, *aa = a->a, *bap;

  PetscFunctionBegin;
  for (k = 0; k < m; k++) { /* loop over added rows */
    row  = im[k];
    brow = row / bs;
    if (row < 0) continue;
    PetscCheck(row < A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, row, A->rmap->N - 1);
    rp = PetscSafePointerPlusOffset(aj, ai[brow]);
    if (!A->structure_only) ap = PetscSafePointerPlusOffset(aa, bs2 * ai[brow]);
    rmax = imax[brow];
    nrow = ailen[brow];
    low  = 0;
    high = nrow;
    for (l = 0; l < n; l++) { /* loop over added columns */
      if (in[l] < 0) continue;
      PetscCheck(in[l] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[l], A->cmap->n - 1);
      col  = in[l];
      bcol = col / bs;
      ridx = row % bs;
      cidx = col % bs;
      if (!A->structure_only) {
        if (roworiented) {
          value = v[l + k * n];
        } else {
          value = v[k + l * m];
        }
      }
      if (col <= lastcol) low = 0;
      else high = nrow;
      lastcol = col;
      while (high - low > 7) {
        t = (low + high) / 2;
        if (rp[t] > bcol) high = t;
        else low = t;
      }
      for (i = low; i < high; i++) {
        if (rp[i] > bcol) break;
        if (rp[i] == bcol) {
          bap = PetscSafePointerPlusOffset(ap, bs2 * i + bs * cidx + ridx);
          if (!A->structure_only) {
            if (is == ADD_VALUES) *bap += value;
            else *bap = value;
          }
          goto noinsert1;
        }
      }
      if (nonew == 1) goto noinsert1;
      PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero (%" PetscInt_FMT ", %" PetscInt_FMT ") in the matrix", row, col);
      if (A->structure_only) {
        MatSeqXAIJReallocateAIJ_structure_only(A, a->mbs, bs2, nrow, brow, bcol, rmax, ai, aj, rp, imax, nonew, MatScalar);
      } else {
        MatSeqXAIJReallocateAIJ(A, a->mbs, bs2, nrow, brow, bcol, rmax, aa, ai, aj, rp, ap, imax, nonew, MatScalar);
      }
      N = nrow++ - 1;
      high++;
      /* shift up all the later entries in this row */
      PetscCall(PetscArraymove(rp + i + 1, rp + i, N - i + 1));
      rp[i] = bcol;
      if (!A->structure_only) {
        PetscCall(PetscArraymove(ap + bs2 * (i + 1), ap + bs2 * i, bs2 * (N - i + 1)));
        PetscCall(PetscArrayzero(ap + bs2 * i, bs2));
        ap[bs2 * i + bs * cidx + ridx] = value;
      }
      a->nz++;
      A->nonzerostate++;
    noinsert1:;
      low = i;
    }
    ailen[brow] = nrow;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  PetscCheck(info->levels == 0, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only levels = 0 supported for in-place ILU");
  PetscCall(ISIdentity(row, &row_identity));
  PetscCall(ISIdentity(col, &col_identity));
  PetscCheck(row_identity && col_identity, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Row and column permutations must be identity for in-place ILU");

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

  PetscCall(MatMarkDiagonal_SeqBAIJ(inA));

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

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

  PetscCall(MatSeqBAIJSetNumericFactorization_inplace(inA, (PetscBool)(row_identity && col_identity)));
  if (!a->solve_work) PetscCall(PetscMalloc1(inA->rmap->N + inA->rmap->bs, &a->solve_work));
  PetscCall(MatLUFactorNumeric(outA, inA, info));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqBAIJSetColumnIndices_SeqBAIJ(Mat mat, const PetscInt *indices)
{
  Mat_SeqBAIJ *baij = (Mat_SeqBAIJ *)mat->data;

  PetscFunctionBegin;
  baij->nz = baij->maxnz;
  PetscCall(PetscArraycpy(baij->j, indices, baij->nz));
  PetscCall(PetscArraycpy(baij->ilen, baij->imax, baij->mbs));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  Input Parameters:
+ mat     - the `MATSEQBAIJ` matrix
- indices - the block column indices

  Level: advanced

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

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

  MUST be called before any calls to `MatSetValues()`

.seealso: [](ch_matrices), `Mat`, `MATSEQBAIJ`, `MatSetValues()`
@*/
PetscErrorCode MatSeqBAIJSetColumnIndices(Mat mat, PetscInt *indices)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
  PetscAssertPointer(indices, 2);
  PetscUseMethod(mat, "MatSeqBAIJSetColumnIndices_C", (Mat, const PetscInt *), (mat, (const PetscInt *)indices));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetRowMaxAbs_SeqBAIJ(Mat A, Vec v, PetscInt idx[])
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, j, n, row, bs, *ai, *aj, mbs;
  PetscReal    atmp;
  PetscScalar *x, zero = 0.0;
  MatScalar   *aa;
  PetscInt     ncols, brow, krow, kcol;

  PetscFunctionBegin;
  /* why is this not a macro???????????????????????????????????????????????????????????????? */
  PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
  bs  = A->rmap->bs;
  aa  = a->a;
  ai  = a->i;
  aj  = a->j;
  mbs = a->mbs;

  PetscCall(VecSet(v, zero));
  PetscCall(VecGetArray(v, &x));
  PetscCall(VecGetLocalSize(v, &n));
  PetscCheck(n == A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
  for (i = 0; i < mbs; i++) {
    ncols = ai[1] - ai[0];
    ai++;
    brow = bs * i;
    for (j = 0; j < ncols; j++) {
      for (kcol = 0; kcol < bs; kcol++) {
        for (krow = 0; krow < bs; krow++) {
          atmp = PetscAbsScalar(*aa);
          aa++;
          row = brow + krow; /* row index */
          if (PetscAbsScalar(x[row]) < atmp) {
            x[row] = atmp;
            if (idx) idx[row] = bs * (*aj) + kcol;
          }
        }
      }
      aj++;
    }
  }
  PetscCall(VecRestoreArray(v, &x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetRowSumAbs_SeqBAIJ(Mat A, Vec v)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, j, n, row, bs, *ai, mbs;
  PetscReal    atmp;
  PetscScalar *x, zero = 0.0;
  MatScalar   *aa;
  PetscInt     ncols, brow, krow, kcol;

  PetscFunctionBegin;
  PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
  bs  = A->rmap->bs;
  aa  = a->a;
  ai  = a->i;
  mbs = a->mbs;

  PetscCall(VecSet(v, zero));
  PetscCall(VecGetArrayWrite(v, &x));
  PetscCall(VecGetLocalSize(v, &n));
  PetscCheck(n == A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
  for (i = 0; i < mbs; i++) {
    ncols = ai[1] - ai[0];
    ai++;
    brow = bs * i;
    for (j = 0; j < ncols; j++) {
      for (kcol = 0; kcol < bs; kcol++) {
        for (krow = 0; krow < bs; krow++) {
          atmp = PetscAbsScalar(*aa);
          aa++;
          row = brow + krow; /* row index */
          x[row] += atmp;
        }
      }
    }
  }
  PetscCall(VecRestoreArrayWrite(v, &x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCopy_SeqBAIJ(Mat A, Mat B, MatStructure str)
{
  PetscFunctionBegin;
  /* If the two matrices have the same copy implementation, use fast copy. */
  if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
    Mat_SeqBAIJ *a    = (Mat_SeqBAIJ *)A->data;
    Mat_SeqBAIJ *b    = (Mat_SeqBAIJ *)B->data;
    PetscInt     ambs = a->mbs, bmbs = b->mbs, abs = A->rmap->bs, bbs = B->rmap->bs, bs2 = abs * abs;

    PetscCheck(a->i[ambs] == b->i[bmbs], PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Number of nonzero blocks in matrices A %" PetscInt_FMT " and B %" PetscInt_FMT " are different", a->i[ambs], b->i[bmbs]);
    PetscCheck(abs == bbs, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Block size A %" PetscInt_FMT " and B %" PetscInt_FMT " are different", abs, bbs);
    PetscCall(PetscArraycpy(b->a, a->a, bs2 * a->i[ambs]));
    PetscCall(PetscObjectStateIncrease((PetscObject)B));
  } else {
    PetscCall(MatCopy_Basic(A, B, str));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqBAIJGetArray_SeqBAIJ(Mat A, PetscScalar *array[])
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;

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

static PetscErrorCode MatSeqBAIJRestoreArray_SeqBAIJ(Mat A, PetscScalar *array[])
{
  PetscFunctionBegin;
  *array = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatAXPYGetPreallocation_SeqBAIJ(Mat Y, Mat X, PetscInt *nnz)
{
  PetscInt     bs = Y->rmap->bs, mbs = Y->rmap->N / bs;
  Mat_SeqBAIJ *x = (Mat_SeqBAIJ *)X->data;
  Mat_SeqBAIJ *y = (Mat_SeqBAIJ *)Y->data;

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

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

  PetscFunctionBegin;
  if (str == UNKNOWN_NONZERO_PATTERN || (PetscDefined(USE_DEBUG) && str == SAME_NONZERO_PATTERN)) {
    PetscBool e = x->nz == y->nz && x->mbs == y->mbs && bs == X->rmap->bs ? PETSC_TRUE : PETSC_FALSE;
    if (e) {
      PetscCall(PetscArraycmp(x->i, y->i, x->mbs + 1, &e));
      if (e) {
        PetscCall(PetscArraycmp(x->j, y->j, x->i[x->mbs], &e));
        if (e) str = SAME_NONZERO_PATTERN;
      }
    }
    if (!e) PetscCheck(str != SAME_NONZERO_PATTERN, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatStructure is not SAME_NONZERO_PATTERN");
  }
  if (str == SAME_NONZERO_PATTERN) {
    PetscScalar  alpha = a;
    PetscBLASInt bnz;
    PetscCall(PetscBLASIntCast(x->nz * bs2, &bnz));
    PetscCallBLAS("BLASaxpy", BLASaxpy_(&bnz, &alpha, x->a, &one, y->a, &one));
    PetscCall(PetscObjectStateIncrease((PetscObject)Y));
  } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
    PetscCall(MatAXPY_Basic(Y, a, X, str));
  } else {
    Mat       B;
    PetscInt *nnz;
    PetscCheck(bs == X->rmap->bs, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrices must have same block size");
    PetscCall(PetscMalloc1(Y->rmap->N, &nnz));
    PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
    PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
    PetscCall(MatSetSizes(B, Y->rmap->n, Y->cmap->n, Y->rmap->N, Y->cmap->N));
    PetscCall(MatSetBlockSizesFromMats(B, Y, Y));
    PetscCall(MatSetType(B, (MatType)((PetscObject)Y)->type_name));
    PetscCall(MatAXPYGetPreallocation_SeqBAIJ(Y, X, nnz));
    PetscCall(MatSeqBAIJSetPreallocation(B, bs, 0, nnz));
    PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
    PetscCall(MatHeaderMerge(Y, &B));
    PetscCall(PetscFree(nnz));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatConjugate_SeqBAIJ(Mat A)
{
#if PetscDefined(USE_COMPLEX)
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, nz = a->bs2 * a->i[a->mbs];
  MatScalar   *aa = a->a;

  PetscFunctionBegin;
  for (i = 0; i < nz; i++) aa[i] = PetscConj(aa[i]);
  PetscFunctionReturn(PETSC_SUCCESS);
#else
  (void)A;
  return PETSC_SUCCESS;
#endif
}

static PetscErrorCode MatRealPart_SeqBAIJ(Mat A)
{
#if PetscDefined(USE_COMPLEX)
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, nz = a->bs2 * a->i[a->mbs];
  MatScalar   *aa = a->a;

  PetscFunctionBegin;
  for (i = 0; i < nz; i++) aa[i] = PetscRealPart(aa[i]);
  PetscFunctionReturn(PETSC_SUCCESS);
#else
  (void)A;
  return PETSC_SUCCESS;
#endif
}

static PetscErrorCode MatImaginaryPart_SeqBAIJ(Mat A)
{
#if PetscDefined(USE_COMPLEX)
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, nz = a->bs2 * a->i[a->mbs];
  MatScalar   *aa = a->a;

  PetscFunctionBegin;
  for (i = 0; i < nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
  PetscFunctionReturn(PETSC_SUCCESS);
#else
  (void)A;
  return PETSC_SUCCESS;
#endif
}

/*
    Code almost identical to MatGetColumnIJ_SeqAIJ() should share common code
*/
static PetscErrorCode MatGetColumnIJ_SeqBAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *nn, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
{
  Mat_SeqBAIJ *a  = (Mat_SeqBAIJ *)A->data;
  PetscInt     bs = A->rmap->bs, i, *collengths, *cia, *cja, n = A->cmap->n / bs, m = A->rmap->n / bs;
  PetscInt     nz = a->i[m], row, *jj, mr, col;

  PetscFunctionBegin;
  *nn = n;
  if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCheck(!symmetric, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not for BAIJ matrices");
  PetscCall(PetscCalloc1(n, &collengths));
  PetscCall(PetscMalloc1(n + 1, &cia));
  PetscCall(PetscMalloc1(nz, &cja));
  jj = a->j;
  for (i = 0; i < nz; i++) collengths[jj[i]]++;
  cia[0] = oshift;
  for (i = 0; i < n; i++) cia[i + 1] = cia[i] + collengths[i];
  PetscCall(PetscArrayzero(collengths, n));
  jj = a->j;
  for (row = 0; row < m; row++) {
    mr = a->i[row + 1] - a->i[row];
    for (i = 0; i < mr; i++) {
      col = *jj++;

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

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

/*
 MatGetColumnIJ_SeqBAIJ_Color() and MatRestoreColumnIJ_SeqBAIJ_Color() are customized from
 MatGetColumnIJ_SeqBAIJ() and MatRestoreColumnIJ_SeqBAIJ() by adding an output
 spidx[], index of a->a, to be used in MatTransposeColoringCreate() and MatFDColoringCreate()
 */
PetscErrorCode MatGetColumnIJ_SeqBAIJ_Color(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *nn, const PetscInt *ia[], const PetscInt *ja[], PetscInt *spidx[], PetscBool *done)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, *collengths, *cia, *cja, n = a->nbs, m = a->mbs;
  PetscInt     nz = a->i[m], row, *jj, mr, col;
  PetscInt    *cspidx;

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

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

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

static PetscErrorCode MatShift_SeqBAIJ(Mat Y, PetscScalar a)
{
  Mat_SeqBAIJ *aij = (Mat_SeqBAIJ *)Y->data;

  PetscFunctionBegin;
  if (!Y->preallocated || !aij->nz) PetscCall(MatSeqBAIJSetPreallocation(Y, Y->rmap->bs, 1, NULL));
  PetscCall(MatShift_Basic(Y, a));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatEliminateZeros_SeqBAIJ(Mat A, PetscBool keep)
{
  Mat_SeqBAIJ *a      = (Mat_SeqBAIJ *)A->data;
  PetscInt     fshift = 0, fshift_prev = 0, i, *ai = a->i, *aj = a->j, *imax = a->imax, j, k;
  PetscInt     m = A->rmap->N, *ailen = a->ilen;
  PetscInt     mbs = a->mbs, bs2 = a->bs2, rmax = 0;
  MatScalar   *aa = a->a, *ap;
  PetscBool    zero;

  PetscFunctionBegin;
  PetscCheck(A->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot eliminate zeros for unassembled matrix");
  if (m) rmax = ailen[0];
  for (i = 1; i <= mbs; i++) {
    for (k = ai[i - 1]; k < ai[i]; k++) {
      zero = PETSC_TRUE;
      ap   = aa + bs2 * k;
      for (j = 0; j < bs2 && zero; j++) {
        if (ap[j] != 0.0) zero = PETSC_FALSE;
      }
      if (zero && (aj[k] != i - 1 || !keep)) fshift++;
      else {
        if (zero && aj[k] == i - 1) PetscCall(PetscInfo(A, "Keep the diagonal block at row %" PetscInt_FMT "\n", i - 1));
        aj[k - fshift] = aj[k];
        PetscCall(PetscArraymove(ap - bs2 * fshift, ap, bs2));
      }
    }
    ai[i - 1] -= fshift_prev;
    fshift_prev  = fshift;
    ailen[i - 1] = imax[i - 1] = ai[i] - fshift - ai[i - 1];
    a->nonzerorowcnt += ((ai[i] - fshift - ai[i - 1]) > 0);
    rmax = PetscMax(rmax, ailen[i - 1]);
  }
  if (fshift) {
    if (mbs) {
      ai[mbs] -= fshift;
      a->nz = ai[mbs];
    }
    PetscCall(PetscInfo(A, "Matrix size: %" PetscInt_FMT " X %" PetscInt_FMT "; zeros eliminated: %" PetscInt_FMT "; nonzeros left: %" PetscInt_FMT "\n", m, A->cmap->n, fshift, a->nz));
    A->nonzerostate++;
    A->info.nz_unneeded += (PetscReal)fshift;
    a->rmax = rmax;
    PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static struct _MatOps MatOps_Values = {MatSetValues_SeqBAIJ,
                                       MatGetRow_SeqBAIJ,
                                       MatRestoreRow_SeqBAIJ,
                                       MatMult_SeqBAIJ_N,
                                       /* 4*/ MatMultAdd_SeqBAIJ_N,
                                       MatMultTranspose_SeqBAIJ,
                                       MatMultTransposeAdd_SeqBAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /* 10*/ NULL,
                                       MatLUFactor_SeqBAIJ,
                                       NULL,
                                       NULL,
                                       MatTranspose_SeqBAIJ,
                                       /* 15*/ MatGetInfo_SeqBAIJ,
                                       MatEqual_SeqBAIJ,
                                       MatGetDiagonal_SeqBAIJ,
                                       MatDiagonalScale_SeqBAIJ,
                                       MatNorm_SeqBAIJ,
                                       /* 20*/ NULL,
                                       MatAssemblyEnd_SeqBAIJ,
                                       MatSetOption_SeqBAIJ,
                                       MatZeroEntries_SeqBAIJ,
                                       /* 24*/ MatZeroRows_SeqBAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /* 29*/ MatSetUp_Seq_Hash,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /* 34*/ MatDuplicate_SeqBAIJ,
                                       NULL,
                                       NULL,
                                       MatILUFactor_SeqBAIJ,
                                       NULL,
                                       /* 39*/ MatAXPY_SeqBAIJ,
                                       MatCreateSubMatrices_SeqBAIJ,
                                       MatIncreaseOverlap_SeqBAIJ,
                                       MatGetValues_SeqBAIJ,
                                       MatCopy_SeqBAIJ,
                                       /* 44*/ NULL,
                                       MatScale_SeqBAIJ,
                                       MatShift_SeqBAIJ,
                                       NULL,
                                       MatZeroRowsColumns_SeqBAIJ,
                                       /* 49*/ NULL,
                                       MatGetRowIJ_SeqBAIJ,
                                       MatRestoreRowIJ_SeqBAIJ,
                                       MatGetColumnIJ_SeqBAIJ,
                                       MatRestoreColumnIJ_SeqBAIJ,
                                       /* 54*/ MatFDColoringCreate_SeqXAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       MatSetValuesBlocked_SeqBAIJ,
                                       /* 59*/ MatCreateSubMatrix_SeqBAIJ,
                                       MatDestroy_SeqBAIJ,
                                       MatView_SeqBAIJ,
                                       NULL,
                                       NULL,
                                       /* 64*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /* 69*/ MatGetRowMaxAbs_SeqBAIJ,
                                       NULL,
                                       MatConvert_Basic,
                                       NULL,
                                       NULL,
                                       /* 74*/ NULL,
                                       MatFDColoringApply_BAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /* 79*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       MatLoad_SeqBAIJ,
                                       /* 84*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /* 89*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /* 94*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /* 99*/ NULL,
                                       NULL,
                                       NULL,
                                       MatConjugate_SeqBAIJ,
                                       NULL,
                                       /*104*/ NULL,
                                       MatRealPart_SeqBAIJ,
                                       MatImaginaryPart_SeqBAIJ,
                                       NULL,
                                       NULL,
                                       /*109*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       MatMissingDiagonal_SeqBAIJ,
                                       /*114*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*119*/ NULL,
                                       NULL,
                                       MatMultHermitianTranspose_SeqBAIJ,
                                       MatMultHermitianTransposeAdd_SeqBAIJ,
                                       NULL,
                                       /*124*/ NULL,
                                       MatGetColumnReductions_SeqBAIJ,
                                       MatInvertBlockDiagonal_SeqBAIJ,
                                       NULL,
                                       NULL,
                                       /*129*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*134*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*139*/ MatSetBlockSizes_Default,
                                       NULL,
                                       NULL,
                                       MatFDColoringSetUp_SeqXAIJ,
                                       NULL,
                                       /*144*/ MatCreateMPIMatConcatenateSeqMat_SeqBAIJ,
                                       MatDestroySubMatrices_SeqBAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*150*/ NULL,
                                       MatEliminateZeros_SeqBAIJ,
                                       MatGetRowSumAbs_SeqBAIJ};

static PetscErrorCode MatStoreValues_SeqBAIJ(Mat mat)
{
  Mat_SeqBAIJ *aij = (Mat_SeqBAIJ *)mat->data;
  PetscInt     nz  = aij->i[aij->mbs] * aij->bs2;

  PetscFunctionBegin;
  PetscCheck(aij->nonew == 1, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");

  /* allocate space for values if not already there */
  if (!aij->saved_values) PetscCall(PetscMalloc1(nz + 1, &aij->saved_values));

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

static PetscErrorCode MatRetrieveValues_SeqBAIJ(Mat mat)
{
  Mat_SeqBAIJ *aij = (Mat_SeqBAIJ *)mat->data;
  PetscInt     nz  = aij->i[aij->mbs] * aij->bs2;

  PetscFunctionBegin;
  PetscCheck(aij->nonew == 1, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
  PetscCheck(aij->saved_values, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatStoreValues(A);first");

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

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

PetscErrorCode MatSeqBAIJSetPreallocation_SeqBAIJ(Mat B, PetscInt bs, PetscInt nz, const PetscInt nnz[])
{
  Mat_SeqBAIJ *b = (Mat_SeqBAIJ *)B->data;
  PetscInt     i, mbs, nbs, bs2;
  PetscBool    flg = PETSC_FALSE, skipallocation = PETSC_FALSE, realalloc = PETSC_FALSE;

  PetscFunctionBegin;
  if (B->hash_active) {
    PetscInt bs;
    B->ops[0] = b->cops;
    PetscCall(PetscHMapIJVDestroy(&b->ht));
    PetscCall(MatGetBlockSize(B, &bs));
    if (bs > 1) PetscCall(PetscHSetIJDestroy(&b->bht));
    PetscCall(PetscFree(b->dnz));
    PetscCall(PetscFree(b->bdnz));
    B->hash_active = PETSC_FALSE;
  }
  if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
  if (nz == MAT_SKIP_ALLOCATION) {
    skipallocation = PETSC_TRUE;
    nz             = 0;
  }

  PetscCall(MatSetBlockSize(B, PetscAbs(bs)));
  PetscCall(PetscLayoutSetUp(B->rmap));
  PetscCall(PetscLayoutSetUp(B->cmap));
  PetscCall(PetscLayoutGetBlockSize(B->rmap, &bs));

  B->preallocated = PETSC_TRUE;

  mbs = B->rmap->n / bs;
  nbs = B->cmap->n / bs;
  bs2 = bs * bs;

  PetscCheck(mbs * bs == B->rmap->n && nbs * bs == B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number rows %" PetscInt_FMT ", cols %" PetscInt_FMT " must be divisible by blocksize %" PetscInt_FMT, B->rmap->N, B->cmap->n, bs);

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

  PetscOptionsBegin(PetscObjectComm((PetscObject)B), NULL, "Optimize options for SEQBAIJ matrix 2 ", "Mat");
  PetscCall(PetscOptionsBool("-mat_no_unroll", "Do not optimize for block size (slow)", NULL, flg, &flg, NULL));
  PetscOptionsEnd();

  if (!flg) {
    switch (bs) {
    case 1:
      B->ops->mult    = MatMult_SeqBAIJ_1;
      B->ops->multadd = MatMultAdd_SeqBAIJ_1;
      break;
    case 2:
      B->ops->mult    = MatMult_SeqBAIJ_2;
      B->ops->multadd = MatMultAdd_SeqBAIJ_2;
      break;
    case 3:
      B->ops->mult    = MatMult_SeqBAIJ_3;
      B->ops->multadd = MatMultAdd_SeqBAIJ_3;
      break;
    case 4:
      B->ops->mult    = MatMult_SeqBAIJ_4;
      B->ops->multadd = MatMultAdd_SeqBAIJ_4;
      break;
    case 5:
      B->ops->mult    = MatMult_SeqBAIJ_5;
      B->ops->multadd = MatMultAdd_SeqBAIJ_5;
      break;
    case 6:
      B->ops->mult    = MatMult_SeqBAIJ_6;
      B->ops->multadd = MatMultAdd_SeqBAIJ_6;
      break;
    case 7:
      B->ops->mult    = MatMult_SeqBAIJ_7;
      B->ops->multadd = MatMultAdd_SeqBAIJ_7;
      break;
    case 9: {
      PetscInt version = 1;
      PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)B)->prefix, "-mat_baij_mult_version", &version, NULL));
      switch (version) {
#if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
      case 1:
        B->ops->mult    = MatMult_SeqBAIJ_9_AVX2;
        B->ops->multadd = MatMultAdd_SeqBAIJ_9_AVX2;
        PetscCall(PetscInfo((PetscObject)B, "Using AVX2 for MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", bs));
        break;
#endif
      default:
        B->ops->mult    = MatMult_SeqBAIJ_N;
        B->ops->multadd = MatMultAdd_SeqBAIJ_N;
        PetscCall(PetscInfo((PetscObject)B, "Using BLAS for MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", bs));
        break;
      }
      break;
    }
    case 11:
      B->ops->mult    = MatMult_SeqBAIJ_11;
      B->ops->multadd = MatMultAdd_SeqBAIJ_11;
      break;
    case 12: {
      PetscInt version = 1;
      PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)B)->prefix, "-mat_baij_mult_version", &version, NULL));
      switch (version) {
      case 1:
        B->ops->mult    = MatMult_SeqBAIJ_12_ver1;
        B->ops->multadd = MatMultAdd_SeqBAIJ_12_ver1;
        PetscCall(PetscInfo((PetscObject)B, "Using version %" PetscInt_FMT " of MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", version, bs));
        break;
      case 2:
        B->ops->mult    = MatMult_SeqBAIJ_12_ver2;
        B->ops->multadd = MatMultAdd_SeqBAIJ_12_ver2;
        PetscCall(PetscInfo((PetscObject)B, "Using version %" PetscInt_FMT " of MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", version, bs));
        break;
#if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
      case 3:
        B->ops->mult    = MatMult_SeqBAIJ_12_AVX2;
        B->ops->multadd = MatMultAdd_SeqBAIJ_12_ver1;
        PetscCall(PetscInfo((PetscObject)B, "Using AVX2 for MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", bs));
        break;
#endif
      default:
        B->ops->mult    = MatMult_SeqBAIJ_N;
        B->ops->multadd = MatMultAdd_SeqBAIJ_N;
        PetscCall(PetscInfo((PetscObject)B, "Using BLAS for MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", bs));
        break;
      }
      break;
    }
    case 15: {
      PetscInt version = 1;
      PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)B)->prefix, "-mat_baij_mult_version", &version, NULL));
      switch (version) {
      case 1:
        B->ops->mult = MatMult_SeqBAIJ_15_ver1;
        PetscCall(PetscInfo((PetscObject)B, "Using version %" PetscInt_FMT " of MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", version, bs));
        break;
      case 2:
        B->ops->mult = MatMult_SeqBAIJ_15_ver2;
        PetscCall(PetscInfo((PetscObject)B, "Using version %" PetscInt_FMT " of MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", version, bs));
        break;
      case 3:
        B->ops->mult = MatMult_SeqBAIJ_15_ver3;
        PetscCall(PetscInfo((PetscObject)B, "Using version %" PetscInt_FMT " of MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", version, bs));
        break;
      case 4:
        B->ops->mult = MatMult_SeqBAIJ_15_ver4;
        PetscCall(PetscInfo((PetscObject)B, "Using version %" PetscInt_FMT " of MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", version, bs));
        break;
      default:
        B->ops->mult = MatMult_SeqBAIJ_N;
        PetscCall(PetscInfo((PetscObject)B, "Using BLAS for MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", bs));
        break;
      }
      B->ops->multadd = MatMultAdd_SeqBAIJ_N;
      break;
    }
    default:
      B->ops->mult    = MatMult_SeqBAIJ_N;
      B->ops->multadd = MatMultAdd_SeqBAIJ_N;
      PetscCall(PetscInfo((PetscObject)B, "Using BLAS for MatMult for BAIJ for blocksize %" PetscInt_FMT "\n", bs));
      break;
    }
  }
  B->ops->sor = MatSOR_SeqBAIJ;
  b->mbs      = mbs;
  b->nbs      = nbs;
  if (!skipallocation) {
    if (!b->imax) {
      PetscCall(PetscMalloc2(mbs, &b->imax, mbs, &b->ilen));

      b->free_imax_ilen = PETSC_TRUE;
    }
    /* b->ilen will count nonzeros in each block row so far. */
    for (i = 0; i < mbs; i++) b->ilen[i] = 0;
    if (!nnz) {
      if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
      else if (nz < 0) nz = 1;
      nz = PetscMin(nz, nbs);
      for (i = 0; i < mbs; i++) b->imax[i] = nz;
      PetscCall(PetscIntMultError(nz, mbs, &nz));
    } else {
      PetscInt64 nz64 = 0;
      for (i = 0; i < mbs; i++) {
        b->imax[i] = nnz[i];
        nz64 += nnz[i];
      }
      PetscCall(PetscIntCast(nz64, &nz));
    }

    /* allocate the matrix space */
    PetscCall(MatSeqXAIJFreeAIJ(B, &b->a, &b->j, &b->i));
    if (B->structure_only) {
      PetscCall(PetscMalloc1(nz, &b->j));
      PetscCall(PetscMalloc1(B->rmap->N + 1, &b->i));
    } else {
      PetscInt nzbs2 = 0;
      PetscCall(PetscIntMultError(nz, bs2, &nzbs2));
      PetscCall(PetscMalloc3(nzbs2, &b->a, nz, &b->j, B->rmap->N + 1, &b->i));
      PetscCall(PetscArrayzero(b->a, nz * bs2));
    }
    PetscCall(PetscArrayzero(b->j, nz));

    if (B->structure_only) {
      b->singlemalloc = PETSC_FALSE;
      b->free_a       = PETSC_FALSE;
    } else {
      b->singlemalloc = PETSC_TRUE;
      b->free_a       = PETSC_TRUE;
    }
    b->free_ij = PETSC_TRUE;

    b->i[0] = 0;
    for (i = 1; i < mbs + 1; i++) b->i[i] = b->i[i - 1] + b->imax[i - 1];

  } else {
    b->free_a  = PETSC_FALSE;
    b->free_ij = PETSC_FALSE;
  }

  b->bs2              = bs2;
  b->mbs              = mbs;
  b->nz               = 0;
  b->maxnz            = nz;
  B->info.nz_unneeded = (PetscReal)b->maxnz * bs2;
  B->was_assembled    = PETSC_FALSE;
  B->assembled        = PETSC_FALSE;
  if (realalloc) PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqBAIJSetPreallocationCSR_SeqBAIJ(Mat B, PetscInt bs, const PetscInt ii[], const PetscInt jj[], const PetscScalar V[])
{
  PetscInt     i, m, nz, nz_max = 0, *nnz;
  PetscScalar *values      = NULL;
  PetscBool    roworiented = ((Mat_SeqBAIJ *)B->data)->roworiented;

  PetscFunctionBegin;
  PetscCheck(bs >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid block size specified, must be positive but it is %" PetscInt_FMT, bs);
  PetscCall(PetscLayoutSetBlockSize(B->rmap, bs));
  PetscCall(PetscLayoutSetBlockSize(B->cmap, bs));
  PetscCall(PetscLayoutSetUp(B->rmap));
  PetscCall(PetscLayoutSetUp(B->cmap));
  PetscCall(PetscLayoutGetBlockSize(B->rmap, &bs));
  m = B->rmap->n / bs;

  PetscCheck(ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "ii[0] must be 0 but it is %" PetscInt_FMT, ii[0]);
  PetscCall(PetscMalloc1(m + 1, &nnz));
  for (i = 0; i < m; i++) {
    nz = ii[i + 1] - ii[i];
    PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative number of columns %" PetscInt_FMT, i, nz);
    nz_max = PetscMax(nz_max, nz);
    nnz[i] = nz;
  }
  PetscCall(MatSeqBAIJSetPreallocation(B, bs, 0, nnz));
  PetscCall(PetscFree(nnz));

  values = (PetscScalar *)V;
  if (!values) PetscCall(PetscCalloc1(bs * bs * (nz_max + 1), &values));
  for (i = 0; i < m; i++) {
    PetscInt        ncols = ii[i + 1] - ii[i];
    const PetscInt *icols = jj + ii[i];
    if (bs == 1 || !roworiented) {
      const PetscScalar *svals = values + (V ? (bs * bs * ii[i]) : 0);
      PetscCall(MatSetValuesBlocked_SeqBAIJ(B, 1, &i, ncols, icols, svals, INSERT_VALUES));
    } else {
      PetscInt j;
      for (j = 0; j < ncols; j++) {
        const PetscScalar *svals = values + (V ? (bs * bs * (ii[i] + j)) : 0);
        PetscCall(MatSetValuesBlocked_SeqBAIJ(B, 1, &i, 1, &icols[j], svals, INSERT_VALUES));
      }
    }
  }
  if (!V) PetscCall(PetscFree(values));
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqBAIJGetArray - gives read/write access to the array where the data for a `MATSEQBAIJ` matrix is stored

  Not Collective

  Input Parameter:
. A - a `MATSEQBAIJ` matrix

  Output Parameter:
. array - pointer to the data

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MATSEQBAIJ`, `MatSeqBAIJRestoreArray()`, `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArray()`
@*/
PetscErrorCode MatSeqBAIJGetArray(Mat A, PetscScalar **array)
{
  PetscFunctionBegin;
  PetscUseMethod(A, "MatSeqBAIJGetArray_C", (Mat, PetscScalar **), (A, array));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqBAIJRestoreArray - returns access to the array where the data for a `MATSEQBAIJ` matrix is stored obtained by `MatSeqBAIJGetArray()`

  Not Collective

  Input Parameters:
+ A     - a `MATSEQBAIJ` matrix
- array - pointer to the data

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatSeqBAIJGetArray()`, `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArray()`
@*/
PetscErrorCode MatSeqBAIJRestoreArray(Mat A, PetscScalar **array)
{
  PetscFunctionBegin;
  PetscUseMethod(A, "MatSeqBAIJRestoreArray_C", (Mat, PetscScalar **), (A, array));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

   Options Database Keys:
+ -mat_type seqbaij - sets the matrix type to `MATSEQBAIJ` during a call to `MatSetFromOptions()`
- -mat_baij_mult_version version - indicate the version of the matrix-vector product to use (0 often indicates using BLAS)

   Level: beginner

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

   Run with `-info` to see what version of the matrix-vector product is being used

.seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`
M*/

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

PETSC_EXTERN PetscErrorCode MatCreate_SeqBAIJ(Mat B)
{
  PetscMPIInt  size;
  Mat_SeqBAIJ *b;

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

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

  b->row          = NULL;
  b->col          = NULL;
  b->icol         = NULL;
  b->reallocs     = 0;
  b->saved_values = NULL;

  b->roworiented        = PETSC_TRUE;
  b->nonew              = 0;
  b->diag               = NULL;
  B->spptr              = NULL;
  B->info.nz_unneeded   = (PetscReal)b->maxnz * b->bs2;
  b->keepnonzeropattern = PETSC_FALSE;

  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqBAIJGetArray_C", MatSeqBAIJGetArray_SeqBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqBAIJRestoreArray_C", MatSeqBAIJRestoreArray_SeqBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_SeqBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_SeqBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqBAIJSetColumnIndices_C", MatSeqBAIJSetColumnIndices_SeqBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqbaij_seqaij_C", MatConvert_SeqBAIJ_SeqAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqbaij_seqsbaij_C", MatConvert_SeqBAIJ_SeqSBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqBAIJSetPreallocation_C", MatSeqBAIJSetPreallocation_SeqBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqBAIJSetPreallocationCSR_C", MatSeqBAIJSetPreallocationCSR_SeqBAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsTranspose_C", MatIsTranspose_SeqBAIJ));
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqbaij_hypre_C", MatConvert_AIJ_HYPRE));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqbaij_is_C", MatConvert_XAIJ_IS));
  PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQBAIJ));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatDuplicateNoCreate_SeqBAIJ(Mat C, Mat A, MatDuplicateOption cpvalues, PetscBool mallocmatspace)
{
  Mat_SeqBAIJ *c = (Mat_SeqBAIJ *)C->data, *a = (Mat_SeqBAIJ *)A->data;
  PetscInt     i, mbs = a->mbs, nz = a->nz, bs2 = a->bs2;

  PetscFunctionBegin;
  PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Cannot duplicate unassembled matrix");
  PetscCheck(a->i[mbs] == nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Corrupt matrix");

  if (cpvalues == MAT_SHARE_NONZERO_PATTERN) {
    c->imax           = a->imax;
    c->ilen           = a->ilen;
    c->free_imax_ilen = PETSC_FALSE;
  } else {
    PetscCall(PetscMalloc2(mbs, &c->imax, mbs, &c->ilen));
    for (i = 0; i < mbs; i++) {
      c->imax[i] = a->imax[i];
      c->ilen[i] = a->ilen[i];
    }
    c->free_imax_ilen = PETSC_TRUE;
  }

  /* allocate the matrix space */
  if (mallocmatspace) {
    if (cpvalues == MAT_SHARE_NONZERO_PATTERN) {
      PetscCall(PetscCalloc1(bs2 * nz, &c->a));

      c->i            = a->i;
      c->j            = a->j;
      c->singlemalloc = PETSC_FALSE;
      c->free_a       = PETSC_TRUE;
      c->free_ij      = PETSC_FALSE;
      c->parent       = A;
      C->preallocated = PETSC_TRUE;
      C->assembled    = PETSC_TRUE;

      PetscCall(PetscObjectReference((PetscObject)A));
      PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
      PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    } else {
      PetscCall(PetscMalloc3(bs2 * nz, &c->a, nz, &c->j, mbs + 1, &c->i));

      c->singlemalloc = PETSC_TRUE;
      c->free_a       = PETSC_TRUE;
      c->free_ij      = PETSC_TRUE;

      PetscCall(PetscArraycpy(c->i, a->i, mbs + 1));
      if (mbs > 0) {
        PetscCall(PetscArraycpy(c->j, a->j, nz));
        if (cpvalues == MAT_COPY_VALUES) {
          PetscCall(PetscArraycpy(c->a, a->a, bs2 * nz));
        } else {
          PetscCall(PetscArrayzero(c->a, bs2 * nz));
        }
      }
      C->preallocated = PETSC_TRUE;
      C->assembled    = PETSC_TRUE;
    }
  }

  c->roworiented = a->roworiented;
  c->nonew       = a->nonew;

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

  c->bs2 = a->bs2;
  c->mbs = a->mbs;
  c->nbs = a->nbs;

  if (a->diag) {
    if (cpvalues == MAT_SHARE_NONZERO_PATTERN) {
      c->diag      = a->diag;
      c->free_diag = PETSC_FALSE;
    } else {
      PetscCall(PetscMalloc1(mbs + 1, &c->diag));
      for (i = 0; i < mbs; i++) c->diag[i] = a->diag[i];
      c->free_diag = PETSC_TRUE;
    }
  } else c->diag = NULL;

  c->nz         = a->nz;
  c->maxnz      = a->nz; /* Since we allocate exactly the right amount */
  c->solve_work = NULL;
  c->mult_work  = NULL;
  c->sor_workt  = NULL;
  c->sor_work   = NULL;

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

  PetscCall(PetscFunctionListDuplicate(((PetscObject)A)->qlist, &((PetscObject)C)->qlist));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatDuplicate_SeqBAIJ(Mat A, MatDuplicateOption cpvalues, Mat *B)
{
  PetscFunctionBegin;
  PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
  PetscCall(MatSetSizes(*B, A->rmap->N, A->cmap->n, A->rmap->N, A->cmap->n));
  PetscCall(MatSetType(*B, MATSEQBAIJ));
  PetscCall(MatDuplicateNoCreate_SeqBAIJ(*B, A, cpvalues, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  PetscCall(PetscViewerSetUp(viewer));

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

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

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

  /* read in row lengths, column indices and nonzero values */
  PetscCall(PetscMalloc1(m + 1, &rowidxs));
  PetscCall(PetscViewerBinaryRead(viewer, rowidxs + 1, m, NULL, PETSC_INT));
  rowidxs[0] = 0;
  for (i = 0; i < m; i++) rowidxs[i + 1] += rowidxs[i];
  sum = rowidxs[m];
  PetscCheck(sum == nz, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Inconsistent matrix data in file: nonzeros = %" PetscInt_FMT ", sum-row-lengths = %" PetscInt_FMT, nz, sum);

  /* read in column indices and nonzero values */
  PetscCall(PetscMalloc2(rowidxs[m], &colidxs, nz, &matvals));
  PetscCall(PetscViewerBinaryRead(viewer, colidxs, rowidxs[m], NULL, PETSC_INT));
  PetscCall(PetscViewerBinaryRead(viewer, matvals, rowidxs[m], NULL, PETSC_SCALAR));

  {               /* preallocate matrix storage */
    PetscBT   bt; /* helper bit set to count nonzeros */
    PetscInt *nnz;
    PetscBool sbaij;

    PetscCall(PetscBTCreate(nbs, &bt));
    PetscCall(PetscCalloc1(mbs, &nnz));
    PetscCall(PetscObjectTypeCompare((PetscObject)mat, MATSEQSBAIJ, &sbaij));
    for (i = 0; i < mbs; i++) {
      PetscCall(PetscBTMemzero(nbs, bt));
      for (k = 0; k < bs; k++) {
        PetscInt row = bs * i + k;
        for (j = rowidxs[row]; j < rowidxs[row + 1]; j++) {
          PetscInt col = colidxs[j];
          if (!sbaij || col >= row)
            if (!PetscBTLookupSet(bt, col / bs)) nnz[i]++;
        }
      }
    }
    PetscCall(PetscBTDestroy(&bt));
    PetscCall(MatSeqBAIJSetPreallocation(mat, bs, 0, nnz));
    PetscCall(MatSeqSBAIJSetPreallocation(mat, bs, 0, nnz));
    PetscCall(PetscFree(nnz));
  }

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

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

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

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

/*@C
  MatCreateSeqBAIJ - Creates a sparse matrix in `MATSEQAIJ` (block
  compressed row) format.  For good matrix assembly performance the
  user should preallocate the matrix storage by setting the parameter `nz`
  (or the array `nnz`).

  Collective

  Input Parameters:
+ comm - MPI communicator, set to `PETSC_COMM_SELF`
. bs   - size of block, the blocks are ALWAYS square. One can use `MatSetBlockSizes()` to set a different row and column blocksize but the row
         blocksize always defines the size of the blocks. The column blocksize sets the blocksize of the vectors obtained with `MatCreateVecs()`
. m    - number of rows
. n    - number of columns
. nz   - number of nonzero blocks  per block row (same for all rows)
- nnz  - array containing the number of nonzero blocks in the various block rows
         (possibly different for each block row) or `NULL`

  Output Parameter:
. A - the matrix

  Options Database Keys:
+ -mat_no_unroll  - uses code that does not unroll the loops in the block calculations (much slower)
- -mat_block_size - size of the blocks to use

  Level: intermediate

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

  The number of rows and columns must be divisible by blocksize.

  If the `nnz` parameter is given then the `nz` parameter is ignored

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

  The `MATSEQBAIJ` format is fully compatible with standard Fortran
  storage.  That is, the stored row and column indices can begin at
  either one (as in Fortran) or zero.

  Specify the preallocated storage with either `nz` or `nnz` (not both).
  Set `nz` = `PETSC_DEFAULT` and `nnz` = `NULL` for PETSc to control dynamic memory
  allocation.  See [Sparse Matrices](sec_matsparse) for details.
  matrices.

.seealso: [](ch_matrices), `Mat`, [Sparse Matrices](sec_matsparse), `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatCreateBAIJ()`
@*/
PetscErrorCode MatCreateSeqBAIJ(MPI_Comm comm, PetscInt bs, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
{
  PetscFunctionBegin;
  PetscCall(MatCreate(comm, A));
  PetscCall(MatSetSizes(*A, m, n, m, n));
  PetscCall(MatSetType(*A, MATSEQBAIJ));
  PetscCall(MatSeqBAIJSetPreallocation(*A, bs, nz, (PetscInt *)nnz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqBAIJSetPreallocation - Sets the block size and expected nonzeros
  per row in the matrix. For good matrix assembly performance the
  user should preallocate the matrix storage by setting the parameter `nz`
  (or the array `nnz`).

  Collective

  Input Parameters:
+ B   - the matrix
. bs  - size of block, the blocks are ALWAYS square. One can use `MatSetBlockSizes()` to set a different row and column blocksize but the row
        blocksize always defines the size of the blocks. The column blocksize sets the blocksize of the vectors obtained with `MatCreateVecs()`
. nz  - number of block nonzeros per block row (same for all rows)
- nnz - array containing the number of block nonzeros in the various block rows
        (possibly different for each block row) or `NULL`

  Options Database Keys:
+ -mat_no_unroll  - uses code that does not unroll the loops in the block calculations (much slower)
- -mat_block_size - size of the blocks to use

  Level: intermediate

  Notes:
  If the `nnz` parameter is given then the `nz` parameter is ignored

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

  The `MATSEQBAIJ` format is fully compatible with standard Fortran
  storage.  That is, the stored row and column indices can begin at
  either one (as in Fortran) or zero.

  Specify the preallocated storage with either `nz` or `nnz` (not both).
  Set `nz` = `PETSC_DEFAULT` and `nnz` = `NULL` for PETSc to control dynamic memory
  allocation.  See [Sparse Matrices](sec_matsparse) for details.

.seealso: [](ch_matrices), `Mat`, [Sparse Matrices](sec_matsparse), `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatCreateBAIJ()`, `MatGetInfo()`
@*/
PetscErrorCode MatSeqBAIJSetPreallocation(Mat B, PetscInt bs, PetscInt nz, const PetscInt nnz[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
  PetscValidType(B, 1);
  PetscValidLogicalCollectiveInt(B, bs, 2);
  PetscTryMethod(B, "MatSeqBAIJSetPreallocation_C", (Mat, PetscInt, PetscInt, const PetscInt[]), (B, bs, nz, nnz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqBAIJSetPreallocationCSR - Creates a sparse sequential matrix in `MATSEQBAIJ` format using the given nonzero structure and (optional) numerical values

  Collective

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

  Level: advanced

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

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

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

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqBAIJ()`, `MatSetValues()`, `MatSeqBAIJSetPreallocation()`, `MATSEQBAIJ`
@*/
PetscErrorCode MatSeqBAIJSetPreallocationCSR(Mat B, PetscInt bs, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
  PetscValidType(B, 1);
  PetscValidLogicalCollectiveInt(B, bs, 2);
  PetscTryMethod(B, "MatSeqBAIJSetPreallocationCSR_C", (Mat, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, bs, i, j, v));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatCreateSeqBAIJWithArrays - Creates a `MATSEQBAIJ` matrix using matrix elements provided by the user.

  Collective

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

  Output Parameter:
. mat - the matrix

  Level: advanced

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

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

  The `i` and `j` indices are 0 based

  When block size is greater than 1 the matrix values must be stored using the `MATSEQBAIJ` storage format

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

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateBAIJ()`, `MatCreateSeqBAIJ()`
@*/
PetscErrorCode MatCreateSeqBAIJWithArrays(MPI_Comm comm, PetscInt bs, PetscInt m, PetscInt n, PetscInt i[], PetscInt j[], PetscScalar a[], Mat *mat)
{
  Mat_SeqBAIJ *baij;

  PetscFunctionBegin;
  PetscCheck(bs == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "block size %" PetscInt_FMT " > 1 is not supported yet", bs);
  if (m > 0) PetscCheck(i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");

  PetscCall(MatCreate(comm, mat));
  PetscCall(MatSetSizes(*mat, m, n, m, n));
  PetscCall(MatSetType(*mat, MATSEQBAIJ));
  PetscCall(MatSeqBAIJSetPreallocation(*mat, bs, MAT_SKIP_ALLOCATION, NULL));
  baij = (Mat_SeqBAIJ *)(*mat)->data;
  PetscCall(PetscMalloc2(m, &baij->imax, m, &baij->ilen));

  baij->i = i;
  baij->j = j;
  baij->a = a;

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

  for (PetscInt ii = 0; ii < m; ii++) {
    const PetscInt row_len = i[ii + 1] - i[ii];

    baij->ilen[ii] = baij->imax[ii] = row_len;
    PetscCheck(row_len >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative row length in i (row indices) row = %" PetscInt_FMT " length = %" PetscInt_FMT, ii, row_len);
  }
  if (PetscDefined(USE_DEBUG)) {
    for (PetscInt ii = 0; ii < baij->i[m]; ii++) {
      PetscCheck(j[ii] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative column index at location = %" PetscInt_FMT " index = %" PetscInt_FMT, ii, j[ii]);
      PetscCheck(j[ii] <= n - 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column index to large at location = %" PetscInt_FMT " index = %" PetscInt_FMT, ii, j[ii]);
    }
  }

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

PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqBAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
{
  PetscFunctionBegin;
  PetscCall(MatCreateMPIMatConcatenateSeqMat_MPIBAIJ(comm, inmat, n, scall, outmat));
  PetscFunctionReturn(PETSC_SUCCESS);
}