xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision 421480d92be24cdb9933c60510b8e175c0a8d034)

/*
    Factorization code for BAIJ format.
*/
#include <../src/mat/impls/baij/seq/baij.h>
#include <petsc/private/kernels/blockinvert.h>

/*
      Version for when blocks are 5 by 5
*/
PetscErrorCode MatILUFactorNumeric_SeqBAIJ_5_inplace(Mat C, Mat A, const MatFactorInfo *info)
{
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
  IS               isrow = b->row, isicol = b->icol;
  const PetscInt  *r, *ic;
  PetscInt        *bi = b->i, *bj = b->j, *ajtmpold, *ajtmp;
  PetscInt         i, j, n = a->mbs, nz, row, idx, ipvt[5];
  const PetscInt  *diag_offset;
  PetscInt        *ai = a->i, *aj = a->j, *pj;
  MatScalar       *w, *pv, *rtmp, *x, *pc;
  const MatScalar *v, *aa = a->a;
  MatScalar        p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
  MatScalar        p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
  MatScalar        x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14;
  MatScalar        p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12;
  MatScalar        m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
  MatScalar       *ba    = b->a, work[25];
  PetscReal        shift = info->shiftamount;
  PetscBool        allowzeropivot, zeropivotdetected;

  PetscFunctionBegin;
  /* Since A is C and C is labeled as a factored matrix we need to lie to MatGetDiagonalMarkers_SeqBAIJ() to get it to compute the diagonals */
  A->factortype = MAT_FACTOR_NONE;
  PetscCall(MatGetDiagonalMarkers_SeqBAIJ(A, &diag_offset, NULL));
  A->factortype  = MAT_FACTOR_ILU;
  allowzeropivot = PetscNot(A->erroriffailure);
  PetscCall(ISGetIndices(isrow, &r));
  PetscCall(ISGetIndices(isicol, &ic));
  PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));

#define PETSC_USE_MEMZERO 1
#define PETSC_USE_MEMCPY  1

  for (i = 0; i < n; i++) {
    nz    = bi[i + 1] - bi[i];
    ajtmp = bj + bi[i];
    for (j = 0; j < nz; j++) {
#if defined(PETSC_USE_MEMZERO)
      PetscCall(PetscArrayzero(rtmp + 25 * ajtmp[j], 25));
#else
      x    = rtmp + 25 * ajtmp[j];
      x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
      x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
      x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
#endif
    }
    /* load in initial (unfactored row) */
    idx      = r[i];
    nz       = ai[idx + 1] - ai[idx];
    ajtmpold = aj + ai[idx];
    v        = aa + 25 * ai[idx];
    for (j = 0; j < nz; j++) {
#if defined(PETSC_USE_MEMCPY)
      PetscCall(PetscArraycpy(rtmp + 25 * ic[ajtmpold[j]], v, 25));
#else
      x     = rtmp + 25 * ic[ajtmpold[j]];
      x[0]  = v[0];
      x[1]  = v[1];
      x[2]  = v[2];
      x[3]  = v[3];
      x[4]  = v[4];
      x[5]  = v[5];
      x[6]  = v[6];
      x[7]  = v[7];
      x[8]  = v[8];
      x[9]  = v[9];
      x[10] = v[10];
      x[11] = v[11];
      x[12] = v[12];
      x[13] = v[13];
      x[14] = v[14];
      x[15] = v[15];
      x[16] = v[16];
      x[17] = v[17];
      x[18] = v[18];
      x[19] = v[19];
      x[20] = v[20];
      x[21] = v[21];
      x[22] = v[22];
      x[23] = v[23];
      x[24] = v[24];
#endif
      v += 25;
    }
    row = *ajtmp++;
    while (row < i) {
      pc  = rtmp + 25 * row;
      p1  = pc[0];
      p2  = pc[1];
      p3  = pc[2];
      p4  = pc[3];
      p5  = pc[4];
      p6  = pc[5];
      p7  = pc[6];
      p8  = pc[7];
      p9  = pc[8];
      p10 = pc[9];
      p11 = pc[10];
      p12 = pc[11];
      p13 = pc[12];
      p14 = pc[13];
      p15 = pc[14];
      p16 = pc[15];
      p17 = pc[16];
      p18 = pc[17];
      p19 = pc[18];
      p20 = pc[19];
      p21 = pc[20];
      p22 = pc[21];
      p23 = pc[22];
      p24 = pc[23];
      p25 = pc[24];
      if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
        pv    = ba + 25 * diag_offset[row];
        pj    = bj + diag_offset[row] + 1;
        x1    = pv[0];
        x2    = pv[1];
        x3    = pv[2];
        x4    = pv[3];
        x5    = pv[4];
        x6    = pv[5];
        x7    = pv[6];
        x8    = pv[7];
        x9    = pv[8];
        x10   = pv[9];
        x11   = pv[10];
        x12   = pv[11];
        x13   = pv[12];
        x14   = pv[13];
        x15   = pv[14];
        x16   = pv[15];
        x17   = pv[16];
        x18   = pv[17];
        x19   = pv[18];
        x20   = pv[19];
        x21   = pv[20];
        x22   = pv[21];
        x23   = pv[22];
        x24   = pv[23];
        x25   = pv[24];
        pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
        pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
        pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
        pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
        pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;

        pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
        pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
        pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
        pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
        pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;

        pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
        pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
        pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
        pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
        pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;

        pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
        pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
        pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
        pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
        pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;

        pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
        pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
        pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
        pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
        pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;

        nz = bi[row + 1] - diag_offset[row] - 1;
        pv += 25;
        for (j = 0; j < nz; j++) {
          x1  = pv[0];
          x2  = pv[1];
          x3  = pv[2];
          x4  = pv[3];
          x5  = pv[4];
          x6  = pv[5];
          x7  = pv[6];
          x8  = pv[7];
          x9  = pv[8];
          x10 = pv[9];
          x11 = pv[10];
          x12 = pv[11];
          x13 = pv[12];
          x14 = pv[13];
          x15 = pv[14];
          x16 = pv[15];
          x17 = pv[16];
          x18 = pv[17];
          x19 = pv[18];
          x20 = pv[19];
          x21 = pv[20];
          x22 = pv[21];
          x23 = pv[22];
          x24 = pv[23];
          x25 = pv[24];
          x   = rtmp + 25 * pj[j];
          x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
          x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
          x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
          x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
          x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;

          x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
          x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
          x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
          x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
          x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;

          x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
          x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
          x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
          x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
          x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;

          x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
          x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
          x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
          x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
          x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;

          x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
          x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
          x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
          x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
          x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;

          pv += 25;
        }
        PetscCall(PetscLogFlops(250.0 * nz + 225.0));
      }
      row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + 25 * bi[i];
    pj = bj + bi[i];
    nz = bi[i + 1] - bi[i];
    for (j = 0; j < nz; j++) {
#if defined(PETSC_USE_MEMCPY)
      PetscCall(PetscArraycpy(pv, rtmp + 25 * pj[j], 25));
#else
      x      = rtmp + 25 * pj[j];
      pv[0]  = x[0];
      pv[1]  = x[1];
      pv[2]  = x[2];
      pv[3]  = x[3];
      pv[4]  = x[4];
      pv[5]  = x[5];
      pv[6]  = x[6];
      pv[7]  = x[7];
      pv[8]  = x[8];
      pv[9]  = x[9];
      pv[10] = x[10];
      pv[11] = x[11];
      pv[12] = x[12];
      pv[13] = x[13];
      pv[14] = x[14];
      pv[15] = x[15];
      pv[16] = x[16];
      pv[17] = x[17];
      pv[18] = x[18];
      pv[19] = x[19];
      pv[20] = x[20];
      pv[21] = x[21];
      pv[22] = x[22];
      pv[23] = x[23];
      pv[24] = x[24];
#endif
      pv += 25;
    }
    /* invert diagonal block */
    w = ba + 25 * diag_offset[i];
    PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
    if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
  }

  PetscCall(PetscFree(rtmp));
  PetscCall(ISRestoreIndices(isicol, &ic));
  PetscCall(ISRestoreIndices(isrow, &r));

  C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
  C->assembled           = PETSC_TRUE;

  PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* MatLUFactorNumeric_SeqBAIJ_5 -
     copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
       PetscKernel_A_gets_A_times_B()
       PetscKernel_A_gets_A_minus_B_times_C()
       PetscKernel_A_gets_inverse_A()
*/

PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B, Mat A, const MatFactorInfo *info)
{
  Mat             C = B;
  Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
  IS              isrow = b->row, isicol = b->icol;
  const PetscInt *r, *ic;
  PetscInt        i, j, k, nz, nzL, row;
  const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
  const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
  MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a, work[25];
  PetscInt        flg, ipvt[5];
  PetscReal       shift = info->shiftamount;
  PetscBool       allowzeropivot, zeropivotdetected;

  PetscFunctionBegin;
  allowzeropivot = PetscNot(A->erroriffailure);
  PetscCall(ISGetIndices(isrow, &r));
  PetscCall(ISGetIndices(isicol, &ic));

  /* generate work space needed by the factorization */
  PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
  PetscCall(PetscArrayzero(rtmp, bs2 * n));

  for (i = 0; i < n; i++) {
    /* zero rtmp */
    /* L part */
    nz    = bi[i + 1] - bi[i];
    bjtmp = bj + bi[i];
    for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    /* U part */
    nz    = bdiag[i] - bdiag[i + 1];
    bjtmp = bj + bdiag[i + 1] + 1;
    for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    /* load in initial (unfactored row) */
    nz    = ai[r[i] + 1] - ai[r[i]];
    ajtmp = aj + ai[r[i]];
    v     = aa + bs2 * ai[r[i]];
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));

    /* elimination */
    bjtmp = bj + bi[i];
    nzL   = bi[i + 1] - bi[i];
    for (k = 0; k < nzL; k++) {
      row = bjtmp[k];
      pc  = rtmp + bs2 * row;
      for (flg = 0, j = 0; j < bs2; j++) {
        if (pc[j] != 0.0) {
          flg = 1;
          break;
        }
      }
      if (flg) {
        pv = b->a + bs2 * bdiag[row];
        /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
        PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));

        pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
        pv = b->a + bs2 * (bdiag[row + 1] + 1);
        nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
        for (j = 0; j < nz; j++) {
          /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
          /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
          v = rtmp + bs2 * pj[j];
          PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(v, pc, pv));
          pv += bs2;
        }
        PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
      }
    }

    /* finished row so stick it into b->a */
    /* L part */
    pv = b->a + bs2 * bi[i];
    pj = b->j + bi[i];
    nz = bi[i + 1] - bi[i];
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

    /* Mark diagonal and invert diagonal for simpler triangular solves */
    pv = b->a + bs2 * bdiag[i];
    pj = b->j + bdiag[i];
    PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
    PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
    if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    /* U part */
    pv = b->a + bs2 * (bdiag[i + 1] + 1);
    pj = b->j + bdiag[i + 1] + 1;
    nz = bdiag[i] - bdiag[i + 1] - 1;
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
  }

  PetscCall(PetscFree2(rtmp, mwork));
  PetscCall(ISRestoreIndices(isicol, &ic));
  PetscCall(ISRestoreIndices(isrow, &r));

  C->ops->solve          = MatSolve_SeqBAIJ_5;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
  C->assembled           = PETSC_TRUE;

  PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
      Version for when blocks are 5 by 5 Using natural ordering
*/
PetscErrorCode MatILUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
  PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j, ipvt[5];
  PetscInt    *ajtmpold, *ajtmp, nz, row;
  PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
  MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
  MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
  MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
  MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
  MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
  MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
  MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
  MatScalar   *ba = b->a, *aa = a->a, work[25];
  PetscReal    shift = info->shiftamount;
  PetscBool    allowzeropivot, zeropivotdetected;

  PetscFunctionBegin;
  allowzeropivot = PetscNot(A->erroriffailure);
  PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
  for (i = 0; i < n; i++) {
    nz    = bi[i + 1] - bi[i];
    ajtmp = bj + bi[i];
    for (j = 0; j < nz; j++) {
      x    = rtmp + 25 * ajtmp[j];
      x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
      x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
      x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
    }
    /* load in initial (unfactored row) */
    nz       = ai[i + 1] - ai[i];
    ajtmpold = aj + ai[i];
    v        = aa + 25 * ai[i];
    for (j = 0; j < nz; j++) {
      x     = rtmp + 25 * ajtmpold[j];
      x[0]  = v[0];
      x[1]  = v[1];
      x[2]  = v[2];
      x[3]  = v[3];
      x[4]  = v[4];
      x[5]  = v[5];
      x[6]  = v[6];
      x[7]  = v[7];
      x[8]  = v[8];
      x[9]  = v[9];
      x[10] = v[10];
      x[11] = v[11];
      x[12] = v[12];
      x[13] = v[13];
      x[14] = v[14];
      x[15] = v[15];
      x[16] = v[16];
      x[17] = v[17];
      x[18] = v[18];
      x[19] = v[19];
      x[20] = v[20];
      x[21] = v[21];
      x[22] = v[22];
      x[23] = v[23];
      x[24] = v[24];
      v += 25;
    }
    row = *ajtmp++;
    while (row < i) {
      pc  = rtmp + 25 * row;
      p1  = pc[0];
      p2  = pc[1];
      p3  = pc[2];
      p4  = pc[3];
      p5  = pc[4];
      p6  = pc[5];
      p7  = pc[6];
      p8  = pc[7];
      p9  = pc[8];
      p10 = pc[9];
      p11 = pc[10];
      p12 = pc[11];
      p13 = pc[12];
      p14 = pc[13];
      p15 = pc[14];
      p16 = pc[15];
      p17 = pc[16];
      p18 = pc[17];
      p19 = pc[18];
      p20 = pc[19];
      p21 = pc[20];
      p22 = pc[21];
      p23 = pc[22];
      p24 = pc[23];
      p25 = pc[24];
      if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
        pv    = ba + 25 * diag_offset[row];
        pj    = bj + diag_offset[row] + 1;
        x1    = pv[0];
        x2    = pv[1];
        x3    = pv[2];
        x4    = pv[3];
        x5    = pv[4];
        x6    = pv[5];
        x7    = pv[6];
        x8    = pv[7];
        x9    = pv[8];
        x10   = pv[9];
        x11   = pv[10];
        x12   = pv[11];
        x13   = pv[12];
        x14   = pv[13];
        x15   = pv[14];
        x16   = pv[15];
        x17   = pv[16];
        x18   = pv[17];
        x19   = pv[18];
        x20   = pv[19];
        x21   = pv[20];
        x22   = pv[21];
        x23   = pv[22];
        x24   = pv[23];
        x25   = pv[24];
        pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
        pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
        pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
        pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
        pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;

        pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
        pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
        pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
        pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
        pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;

        pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
        pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
        pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
        pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
        pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;

        pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
        pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
        pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
        pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
        pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;

        pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
        pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
        pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
        pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
        pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;

        nz = bi[row + 1] - diag_offset[row] - 1;
        pv += 25;
        for (j = 0; j < nz; j++) {
          x1  = pv[0];
          x2  = pv[1];
          x3  = pv[2];
          x4  = pv[3];
          x5  = pv[4];
          x6  = pv[5];
          x7  = pv[6];
          x8  = pv[7];
          x9  = pv[8];
          x10 = pv[9];
          x11 = pv[10];
          x12 = pv[11];
          x13 = pv[12];
          x14 = pv[13];
          x15 = pv[14];
          x16 = pv[15];
          x17 = pv[16];
          x18 = pv[17];
          x19 = pv[18];
          x20 = pv[19];
          x21 = pv[20];
          x22 = pv[21];
          x23 = pv[22];
          x24 = pv[23];
          x25 = pv[24];
          x   = rtmp + 25 * pj[j];
          x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
          x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
          x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
          x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
          x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;

          x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
          x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
          x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
          x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
          x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;

          x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
          x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
          x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
          x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
          x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;

          x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
          x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
          x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
          x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
          x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;

          x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
          x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
          x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
          x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
          x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
          pv += 25;
        }
        PetscCall(PetscLogFlops(250.0 * nz + 225.0));
      }
      row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + 25 * bi[i];
    pj = bj + bi[i];
    nz = bi[i + 1] - bi[i];
    for (j = 0; j < nz; j++) {
      x      = rtmp + 25 * pj[j];
      pv[0]  = x[0];
      pv[1]  = x[1];
      pv[2]  = x[2];
      pv[3]  = x[3];
      pv[4]  = x[4];
      pv[5]  = x[5];
      pv[6]  = x[6];
      pv[7]  = x[7];
      pv[8]  = x[8];
      pv[9]  = x[9];
      pv[10] = x[10];
      pv[11] = x[11];
      pv[12] = x[12];
      pv[13] = x[13];
      pv[14] = x[14];
      pv[15] = x[15];
      pv[16] = x[16];
      pv[17] = x[17];
      pv[18] = x[18];
      pv[19] = x[19];
      pv[20] = x[20];
      pv[21] = x[21];
      pv[22] = x[22];
      pv[23] = x[23];
      pv[24] = x[24];
      pv += 25;
    }
    /* invert diagonal block */
    w = ba + 25 * diag_offset[i];
    PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
    if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
  }

  PetscCall(PetscFree(rtmp));

  C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
  C->assembled           = PETSC_TRUE;

  PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
{
  Mat             C = B;
  Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
  PetscInt        i, j, k, nz, nzL, row;
  const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
  const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
  MatScalar      *rtmp, *pc, *mwork, *v, *vv, *pv, *aa = a->a, work[25];
  PetscInt        flg, ipvt[5];
  PetscReal       shift = info->shiftamount;
  PetscBool       allowzeropivot, zeropivotdetected;

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

  /* generate work space needed by the factorization */
  PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
  PetscCall(PetscArrayzero(rtmp, bs2 * n));

  for (i = 0; i < n; i++) {
    /* zero rtmp */
    /* L part */
    nz    = bi[i + 1] - bi[i];
    bjtmp = bj + bi[i];
    for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    /* U part */
    nz    = bdiag[i] - bdiag[i + 1];
    bjtmp = bj + bdiag[i + 1] + 1;
    for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    /* load in initial (unfactored row) */
    nz    = ai[i + 1] - ai[i];
    ajtmp = aj + ai[i];
    v     = aa + bs2 * ai[i];
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

    /* elimination */
    bjtmp = bj + bi[i];
    nzL   = bi[i + 1] - bi[i];
    for (k = 0; k < nzL; k++) {
      row = bjtmp[k];
      pc  = rtmp + bs2 * row;
      for (flg = 0, j = 0; j < bs2; j++) {
        if (pc[j] != 0.0) {
          flg = 1;
          break;
        }
      }
      if (flg) {
        pv = b->a + bs2 * bdiag[row];
        /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
        PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));

        pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
        pv = b->a + bs2 * (bdiag[row + 1] + 1);
        nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
        for (j = 0; j < nz; j++) {
          /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
          /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
          vv = rtmp + bs2 * pj[j];
          PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv, pc, pv));
          pv += bs2;
        }
        PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
      }
    }

    /* finished row so stick it into b->a */
    /* L part */
    pv = b->a + bs2 * bi[i];
    pj = b->j + bi[i];
    nz = bi[i + 1] - bi[i];
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

    /* Mark diagonal and invert diagonal for simpler triangular solves */
    pv = b->a + bs2 * bdiag[i];
    pj = b->j + bdiag[i];
    PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
    PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
    if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    /* U part */
    pv = b->a + bs2 * (bdiag[i + 1] + 1);
    pj = b->j + bdiag[i + 1] + 1;
    nz = bdiag[i] - bdiag[i + 1] - 1;
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
  }
  PetscCall(PetscFree2(rtmp, mwork));

  C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
  C->assembled           = PETSC_TRUE;

  PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   Version for when blocks are 9 by 9
 */
#if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  #include <immintrin.h>
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_9_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
{
  Mat             C = B;
  Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
  PetscInt        i, j, k, nz, nzL, row;
  const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
  const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
  MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
  PetscInt        flg;
  PetscReal       shift = info->shiftamount;
  PetscBool       allowzeropivot, zeropivotdetected;

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

  /* generate work space needed by the factorization */
  PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
  PetscCall(PetscArrayzero(rtmp, bs2 * n));

  for (i = 0; i < n; i++) {
    /* zero rtmp */
    /* L part */
    nz    = bi[i + 1] - bi[i];
    bjtmp = bj + bi[i];
    for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    /* U part */
    nz    = bdiag[i] - bdiag[i + 1];
    bjtmp = bj + bdiag[i + 1] + 1;
    for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    /* load in initial (unfactored row) */
    nz    = ai[i + 1] - ai[i];
    ajtmp = aj + ai[i];
    v     = aa + bs2 * ai[i];
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

    /* elimination */
    bjtmp = bj + bi[i];
    nzL   = bi[i + 1] - bi[i];
    for (k = 0; k < nzL; k++) {
      row = bjtmp[k];
      pc  = rtmp + bs2 * row;
      for (flg = 0, j = 0; j < bs2; j++) {
        if (pc[j] != 0.0) {
          flg = 1;
          break;
        }
      }
      if (flg) {
        pv = b->a + bs2 * bdiag[row];
        /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
        PetscCall(PetscKernel_A_gets_A_times_B_9(pc, pv, mwork));

        pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
        pv = b->a + bs2 * (bdiag[row + 1] + 1);
        nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
        for (j = 0; j < nz; j++) {
          /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
          /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
          v = rtmp + bs2 * pj[j];
          PetscCall(PetscKernel_A_gets_A_minus_B_times_C_9(v, pc, pv + 81 * j));
          /* pv incremented in PetscKernel_A_gets_A_minus_B_times_C_9 */
        }
        PetscCall(PetscLogFlops(1458 * nz + 1377)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
      }
    }

    /* finished row so stick it into b->a */
    /* L part */
    pv = b->a + bs2 * bi[i];
    pj = b->j + bi[i];
    nz = bi[i + 1] - bi[i];
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

    /* Mark diagonal and invert diagonal for simpler triangular solves */
    pv = b->a + bs2 * bdiag[i];
    pj = b->j + bdiag[i];
    PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
    PetscCall(PetscKernel_A_gets_inverse_A_9(pv, shift, allowzeropivot, &zeropivotdetected));
    if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    /* U part */
    pv = b->a + bs2 * (bdiag[i + 1] + 1);
    pj = b->j + bdiag[i + 1] + 1;
    nz = bdiag[i] - bdiag[i + 1] - 1;
    for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
  }
  PetscCall(PetscFree2(rtmp, mwork));

  C->ops->solve          = MatSolve_SeqBAIJ_9_NaturalOrdering;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_N;
  C->assembled           = PETSC_TRUE;

  PetscCall(PetscLogFlops(1.333333333333 * 9 * 9 * 9 * n)); /* from inverting diagonal blocks */
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSolve_SeqBAIJ_9_NaturalOrdering(Mat A, Vec bb, Vec xx)
{
  Mat_SeqBAIJ       *a  = (Mat_SeqBAIJ *)A->data;
  const PetscInt    *ai = a->i, *aj = a->j, *adiag = a->diag, *vi;
  PetscInt           i, k, n                       = a->mbs;
  PetscInt           nz, bs = A->rmap->bs, bs2 = a->bs2;
  const MatScalar   *aa = a->a, *v;
  PetscScalar       *x, *s, *t, *ls;
  const PetscScalar *b;
  __m256d            a0, a1, a2, a3, a4, a5, w0, w1, w2, w3, s0, s1, s2, v0, v1, v2, v3;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(bb, &b));
  PetscCall(VecGetArray(xx, &x));
  t = a->solve_work;

  /* forward solve the lower triangular */
  PetscCall(PetscArraycpy(t, b, bs)); /* copy 1st block of b to t */

  for (i = 1; i < n; i++) {
    v  = aa + bs2 * ai[i];
    vi = aj + ai[i];
    nz = ai[i + 1] - ai[i];
    s  = t + bs * i;
    PetscCall(PetscArraycpy(s, b + bs * i, bs)); /* copy i_th block of b to t */

    __m256d s0, s1, s2;
    s0 = _mm256_loadu_pd(s + 0);
    s1 = _mm256_loadu_pd(s + 4);
    s2 = _mm256_maskload_pd(s + 8, _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));

    for (k = 0; k < nz; k++) {
      w0 = _mm256_set1_pd((t + bs * vi[k])[0]);
      a0 = _mm256_loadu_pd(&v[0]);
      s0 = _mm256_fnmadd_pd(a0, w0, s0);
      a1 = _mm256_loadu_pd(&v[4]);
      s1 = _mm256_fnmadd_pd(a1, w0, s1);
      a2 = _mm256_loadu_pd(&v[8]);
      s2 = _mm256_fnmadd_pd(a2, w0, s2);

      w1 = _mm256_set1_pd((t + bs * vi[k])[1]);
      a3 = _mm256_loadu_pd(&v[9]);
      s0 = _mm256_fnmadd_pd(a3, w1, s0);
      a4 = _mm256_loadu_pd(&v[13]);
      s1 = _mm256_fnmadd_pd(a4, w1, s1);
      a5 = _mm256_loadu_pd(&v[17]);
      s2 = _mm256_fnmadd_pd(a5, w1, s2);

      w2 = _mm256_set1_pd((t + bs * vi[k])[2]);
      a0 = _mm256_loadu_pd(&v[18]);
      s0 = _mm256_fnmadd_pd(a0, w2, s0);
      a1 = _mm256_loadu_pd(&v[22]);
      s1 = _mm256_fnmadd_pd(a1, w2, s1);
      a2 = _mm256_loadu_pd(&v[26]);
      s2 = _mm256_fnmadd_pd(a2, w2, s2);

      w3 = _mm256_set1_pd((t + bs * vi[k])[3]);
      a3 = _mm256_loadu_pd(&v[27]);
      s0 = _mm256_fnmadd_pd(a3, w3, s0);
      a4 = _mm256_loadu_pd(&v[31]);
      s1 = _mm256_fnmadd_pd(a4, w3, s1);
      a5 = _mm256_loadu_pd(&v[35]);
      s2 = _mm256_fnmadd_pd(a5, w3, s2);

      w0 = _mm256_set1_pd((t + bs * vi[k])[4]);
      a0 = _mm256_loadu_pd(&v[36]);
      s0 = _mm256_fnmadd_pd(a0, w0, s0);
      a1 = _mm256_loadu_pd(&v[40]);
      s1 = _mm256_fnmadd_pd(a1, w0, s1);
      a2 = _mm256_loadu_pd(&v[44]);
      s2 = _mm256_fnmadd_pd(a2, w0, s2);

      w1 = _mm256_set1_pd((t + bs * vi[k])[5]);
      a3 = _mm256_loadu_pd(&v[45]);
      s0 = _mm256_fnmadd_pd(a3, w1, s0);
      a4 = _mm256_loadu_pd(&v[49]);
      s1 = _mm256_fnmadd_pd(a4, w1, s1);
      a5 = _mm256_loadu_pd(&v[53]);
      s2 = _mm256_fnmadd_pd(a5, w1, s2);

      w2 = _mm256_set1_pd((t + bs * vi[k])[6]);
      a0 = _mm256_loadu_pd(&v[54]);
      s0 = _mm256_fnmadd_pd(a0, w2, s0);
      a1 = _mm256_loadu_pd(&v[58]);
      s1 = _mm256_fnmadd_pd(a1, w2, s1);
      a2 = _mm256_loadu_pd(&v[62]);
      s2 = _mm256_fnmadd_pd(a2, w2, s2);

      w3 = _mm256_set1_pd((t + bs * vi[k])[7]);
      a3 = _mm256_loadu_pd(&v[63]);
      s0 = _mm256_fnmadd_pd(a3, w3, s0);
      a4 = _mm256_loadu_pd(&v[67]);
      s1 = _mm256_fnmadd_pd(a4, w3, s1);
      a5 = _mm256_loadu_pd(&v[71]);
      s2 = _mm256_fnmadd_pd(a5, w3, s2);

      w0 = _mm256_set1_pd((t + bs * vi[k])[8]);
      a0 = _mm256_loadu_pd(&v[72]);
      s0 = _mm256_fnmadd_pd(a0, w0, s0);
      a1 = _mm256_loadu_pd(&v[76]);
      s1 = _mm256_fnmadd_pd(a1, w0, s1);
      a2 = _mm256_maskload_pd(v + 80, _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));
      s2 = _mm256_fnmadd_pd(a2, w0, s2);
      v += bs2;
    }
    _mm256_storeu_pd(&s[0], s0);
    _mm256_storeu_pd(&s[4], s1);
    _mm256_maskstore_pd(&s[8], _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63), s2);
  }

  /* backward solve the upper triangular */
  ls = a->solve_work + A->cmap->n;
  for (i = n - 1; i >= 0; i--) {
    v  = aa + bs2 * (adiag[i + 1] + 1);
    vi = aj + adiag[i + 1] + 1;
    nz = adiag[i] - adiag[i + 1] - 1;
    PetscCall(PetscArraycpy(ls, t + i * bs, bs));

    s0 = _mm256_loadu_pd(ls + 0);
    s1 = _mm256_loadu_pd(ls + 4);
    s2 = _mm256_maskload_pd(ls + 8, _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));

    for (k = 0; k < nz; k++) {
      w0 = _mm256_set1_pd((t + bs * vi[k])[0]);
      a0 = _mm256_loadu_pd(&v[0]);
      s0 = _mm256_fnmadd_pd(a0, w0, s0);
      a1 = _mm256_loadu_pd(&v[4]);
      s1 = _mm256_fnmadd_pd(a1, w0, s1);
      a2 = _mm256_loadu_pd(&v[8]);
      s2 = _mm256_fnmadd_pd(a2, w0, s2);

      /* v += 9; */
      w1 = _mm256_set1_pd((t + bs * vi[k])[1]);
      a3 = _mm256_loadu_pd(&v[9]);
      s0 = _mm256_fnmadd_pd(a3, w1, s0);
      a4 = _mm256_loadu_pd(&v[13]);
      s1 = _mm256_fnmadd_pd(a4, w1, s1);
      a5 = _mm256_loadu_pd(&v[17]);
      s2 = _mm256_fnmadd_pd(a5, w1, s2);

      /* v += 9; */
      w2 = _mm256_set1_pd((t + bs * vi[k])[2]);
      a0 = _mm256_loadu_pd(&v[18]);
      s0 = _mm256_fnmadd_pd(a0, w2, s0);
      a1 = _mm256_loadu_pd(&v[22]);
      s1 = _mm256_fnmadd_pd(a1, w2, s1);
      a2 = _mm256_loadu_pd(&v[26]);
      s2 = _mm256_fnmadd_pd(a2, w2, s2);

      /* v += 9; */
      w3 = _mm256_set1_pd((t + bs * vi[k])[3]);
      a3 = _mm256_loadu_pd(&v[27]);
      s0 = _mm256_fnmadd_pd(a3, w3, s0);
      a4 = _mm256_loadu_pd(&v[31]);
      s1 = _mm256_fnmadd_pd(a4, w3, s1);
      a5 = _mm256_loadu_pd(&v[35]);
      s2 = _mm256_fnmadd_pd(a5, w3, s2);

      /* v += 9; */
      w0 = _mm256_set1_pd((t + bs * vi[k])[4]);
      a0 = _mm256_loadu_pd(&v[36]);
      s0 = _mm256_fnmadd_pd(a0, w0, s0);
      a1 = _mm256_loadu_pd(&v[40]);
      s1 = _mm256_fnmadd_pd(a1, w0, s1);
      a2 = _mm256_loadu_pd(&v[44]);
      s2 = _mm256_fnmadd_pd(a2, w0, s2);

      /* v += 9; */
      w1 = _mm256_set1_pd((t + bs * vi[k])[5]);
      a3 = _mm256_loadu_pd(&v[45]);
      s0 = _mm256_fnmadd_pd(a3, w1, s0);
      a4 = _mm256_loadu_pd(&v[49]);
      s1 = _mm256_fnmadd_pd(a4, w1, s1);
      a5 = _mm256_loadu_pd(&v[53]);
      s2 = _mm256_fnmadd_pd(a5, w1, s2);

      /* v += 9; */
      w2 = _mm256_set1_pd((t + bs * vi[k])[6]);
      a0 = _mm256_loadu_pd(&v[54]);
      s0 = _mm256_fnmadd_pd(a0, w2, s0);
      a1 = _mm256_loadu_pd(&v[58]);
      s1 = _mm256_fnmadd_pd(a1, w2, s1);
      a2 = _mm256_loadu_pd(&v[62]);
      s2 = _mm256_fnmadd_pd(a2, w2, s2);

      /* v += 9; */
      w3 = _mm256_set1_pd((t + bs * vi[k])[7]);
      a3 = _mm256_loadu_pd(&v[63]);
      s0 = _mm256_fnmadd_pd(a3, w3, s0);
      a4 = _mm256_loadu_pd(&v[67]);
      s1 = _mm256_fnmadd_pd(a4, w3, s1);
      a5 = _mm256_loadu_pd(&v[71]);
      s2 = _mm256_fnmadd_pd(a5, w3, s2);

      /* v += 9; */
      w0 = _mm256_set1_pd((t + bs * vi[k])[8]);
      a0 = _mm256_loadu_pd(&v[72]);
      s0 = _mm256_fnmadd_pd(a0, w0, s0);
      a1 = _mm256_loadu_pd(&v[76]);
      s1 = _mm256_fnmadd_pd(a1, w0, s1);
      a2 = _mm256_maskload_pd(v + 80, _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));
      s2 = _mm256_fnmadd_pd(a2, w0, s2);
      v += bs2;
    }

    _mm256_storeu_pd(&ls[0], s0);
    _mm256_storeu_pd(&ls[4], s1);
    _mm256_maskstore_pd(&ls[8], _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63), s2);

    w0 = _mm256_setzero_pd();
    w1 = _mm256_setzero_pd();
    w2 = _mm256_setzero_pd();

    /* first row */
    v0 = _mm256_set1_pd(ls[0]);
    a0 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[0]);
    w0 = _mm256_fmadd_pd(a0, v0, w0);
    a1 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[4]);
    w1 = _mm256_fmadd_pd(a1, v0, w1);
    a2 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[8]);
    w2 = _mm256_fmadd_pd(a2, v0, w2);

    /* second row */
    v1 = _mm256_set1_pd(ls[1]);
    a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[9]);
    w0 = _mm256_fmadd_pd(a3, v1, w0);
    a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[13]);
    w1 = _mm256_fmadd_pd(a4, v1, w1);
    a5 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[17]);
    w2 = _mm256_fmadd_pd(a5, v1, w2);

    /* third row */
    v2 = _mm256_set1_pd(ls[2]);
    a0 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[18]);
    w0 = _mm256_fmadd_pd(a0, v2, w0);
    a1 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[22]);
    w1 = _mm256_fmadd_pd(a1, v2, w1);
    a2 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[26]);
    w2 = _mm256_fmadd_pd(a2, v2, w2);

    /* fourth row */
    v3 = _mm256_set1_pd(ls[3]);
    a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[27]);
    w0 = _mm256_fmadd_pd(a3, v3, w0);
    a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[31]);
    w1 = _mm256_fmadd_pd(a4, v3, w1);
    a5 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[35]);
    w2 = _mm256_fmadd_pd(a5, v3, w2);

    /* fifth row */
    v0 = _mm256_set1_pd(ls[4]);
    a0 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[36]);
    w0 = _mm256_fmadd_pd(a0, v0, w0);
    a1 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[40]);
    w1 = _mm256_fmadd_pd(a1, v0, w1);
    a2 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[44]);
    w2 = _mm256_fmadd_pd(a2, v0, w2);

    /* sixth row */
    v1 = _mm256_set1_pd(ls[5]);
    a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[45]);
    w0 = _mm256_fmadd_pd(a3, v1, w0);
    a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[49]);
    w1 = _mm256_fmadd_pd(a4, v1, w1);
    a5 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[53]);
    w2 = _mm256_fmadd_pd(a5, v1, w2);

    /* seventh row */
    v2 = _mm256_set1_pd(ls[6]);
    a0 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[54]);
    w0 = _mm256_fmadd_pd(a0, v2, w0);
    a1 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[58]);
    w1 = _mm256_fmadd_pd(a1, v2, w1);
    a2 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[62]);
    w2 = _mm256_fmadd_pd(a2, v2, w2);

    /* eighth row */
    v3 = _mm256_set1_pd(ls[7]);
    a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[63]);
    w0 = _mm256_fmadd_pd(a3, v3, w0);
    a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[67]);
    w1 = _mm256_fmadd_pd(a4, v3, w1);
    a5 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[71]);
    w2 = _mm256_fmadd_pd(a5, v3, w2);

    /* ninth row */
    v0 = _mm256_set1_pd(ls[8]);
    a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[72]);
    w0 = _mm256_fmadd_pd(a3, v0, w0);
    a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[76]);
    w1 = _mm256_fmadd_pd(a4, v0, w1);
    a2 = _mm256_maskload_pd(&(aa + bs2 * adiag[i])[80], _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));
    w2 = _mm256_fmadd_pd(a2, v0, w2);

    _mm256_storeu_pd(&(t + i * bs)[0], w0);
    _mm256_storeu_pd(&(t + i * bs)[4], w1);
    _mm256_maskstore_pd(&(t + i * bs)[8], _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63), w2);

    PetscCall(PetscArraycpy(x + i * bs, t + i * bs, bs));
  }

  PetscCall(VecRestoreArrayRead(bb, &b));
  PetscCall(VecRestoreArray(xx, &x));
  PetscCall(PetscLogFlops(2.0 * (a->bs2) * (a->nz) - A->rmap->bs * A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif