xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 3eee16b04de4467482e6ce56cbcc0108d577ea39)

#ifndef lint
static char vcid[] = "$Id: baijfact.c,v 1.47 1997/06/10 04:06:15 bsmith Exp bsmith $";
#endif
/*
    Factorization code for BAIJ format.
*/

#include "src/mat/impls/baij/seq/baij.h"
#include "src/vec/vecimpl.h"
#include "src/inline/ilu.h"


/*
    The symbolic factorization code is identical to that for AIJ format,
  except for very small changes since this is now a SeqBAIJ datastructure.
  NOT good code reuse.
*/
#undef __FUNC__
#define __FUNC__ "MatLUFactorSymbolic_SeqBAIJ"
int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
  IS          isicol;
  int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
  int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
  int         *idnew, idx, row,m,fm, nnz, nzi,realloc = 0,nzbd,*im;

  PetscValidHeaderSpecific(isrow,IS_COOKIE);
  PetscValidHeaderSpecific(iscol,IS_COOKIE);
  ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
  ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);

  /* get new row pointers */
  ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
  ainew[0] = 0;
  /* don't know how many column pointers are needed so estimate */
  jmax = (int) (f*ai[n] + 1);
  ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
  /* fill is a linked list of nonzeros in active row */
  fill = (int *) PetscMalloc( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
  im = fill + n + 1;
  /* idnew is location of diagonal in factor */
  idnew = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(idnew);
  idnew[0] = 0;

  for ( i=0; i<n; i++ ) {
    /* first copy previous fill into linked list */
    nnz     = nz    = ai[r[i]+1] - ai[r[i]];
    if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
    ajtmp   = aj + ai[r[i]];
    fill[n] = n;
    while (nz--) {
      fm  = n;
      idx = ic[*ajtmp++];
      do {
        m  = fm;
        fm = fill[m];
      } while (fm < idx);
      fill[m]   = idx;
      fill[idx] = fm;
    }
    row = fill[n];
    while ( row < i ) {
      ajtmp = ajnew + idnew[row] + 1;
      nzbd  = 1 + idnew[row] - ainew[row];
      nz    = im[row] - nzbd;
      fm    = row;
      while (nz-- > 0) {
        idx = *ajtmp++;
        nzbd++;
        if (idx == i) im[row] = nzbd;
        do {
          m  = fm;
          fm = fill[m];
        } while (fm < idx);
        if (fm != idx) {
          fill[m]   = idx;
          fill[idx] = fm;
          fm        = idx;
          nnz++;
        }
      }
      row = fill[row];
    }
    /* copy new filled row into permanent storage */
    ainew[i+1] = ainew[i] + nnz;
    if (ainew[i+1] > jmax) {
      /* allocate a longer ajnew */
      int maxadd;
      maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
      if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
      jmax += maxadd;
      ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
      PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
      PetscFree(ajnew);
      ajnew = ajtmp;
      realloc++; /* count how many times we realloc */
    }
    ajtmp = ajnew + ainew[i];
    fm    = fill[n];
    nzi   = 0;
    im[i] = nnz;
    while (nnz--) {
      if (fm < i) nzi++;
      *ajtmp++ = fm;
      fm       = fill[fm];
    }
    idnew[i] = ainew[i] + nzi;
  }

  if (ai[n] != 0) {
    double af = ((double)ainew[n])/((double)ai[n]);
    PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
             realloc,f,af);
    af += .01;
    PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:Run with -pc_lu_fill %g or use \n",af);
    PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:PCLUSetFill(pc,%g);\n",af);
    PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:for best performance.\n");
  } else {
     PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:Empty matrix.\n");
  }

  ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);

  PetscFree(fill);

  /* put together the new matrix */
  ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
  PLogObjectParent(*B,isicol);
  ierr = ISDestroy(isicol); CHKERRQ(ierr);
  b = (Mat_SeqBAIJ *) (*B)->data;
  PetscFree(b->imax);
  b->singlemalloc = 0;
  /* the next line frees the default space generated by the Create() */
  PetscFree(b->a); PetscFree(b->ilen);
  b->a          = (Scalar *) PetscMalloc((ainew[n]+1)*sizeof(Scalar)*bs2);CHKPTRQ(b->a);
  b->j          = ajnew;
  b->i          = ainew;
  b->diag       = idnew;
  b->ilen       = 0;
  b->imax       = 0;
  b->row        = isrow;
  b->col        = iscol;
  b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
  CHKPTRQ(b->solve_work);
  /* In b structure:  Free imax, ilen, old a, old j.
     Allocate idnew, solve_work, new a, new j */
  PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
  b->maxnz = b->nz = ainew[n];

  (*B)->info.factor_mallocs    = realloc;
  (*B)->info.fill_ratio_given  = f;
  if (ai[i] != 0) {
    (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[i]);
  } else {
    (*B)->info.fill_ratio_needed = 0.0;
  }


  return 0;
}

/* ----------------------------------------------------------- */
#undef __FUNC__
#define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_N"
int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
{
  Mat             C = *B;
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
  IS              iscol = b->col, isrow = b->row, isicol;
  int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
  int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j,k,flg;
  int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots;
  Scalar          *ba = b->a,*aa = a->a;
  register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
  register int    *pj;

  ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
  PLogObjectParent(*B,isicol);
  ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
  ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
  rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
  PetscMemzero(rtmp,bs2*(n+1)*sizeof(Scalar));
  /* generate work space needed by dense LU factorization */
  v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
               CHKPTRQ(v_work);
  multiplier = v_work + bs;
  v_pivots   = (int *) (multiplier + bs2);

  /* flops in while loop */
  bslog = 2*bs*bs2;

  for ( i=0; i<n; i++ ) {
    nz    = bi[i+1] - bi[i];
    ajtmp = bj + bi[i];
    for  ( j=0; j<nz; j++ ) {
      PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
    }
    /* load in initial (unfactored row) */
    nz       = ai[r[i]+1] - ai[r[i]];
    ajtmpold = aj + ai[r[i]];
    v        = aa + bs2*ai[r[i]];
    for ( j=0; j<nz; j++ ) {
      PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
    }
    row = *ajtmp++;
    while (row < i) {
      pc = rtmp + bs2*row;
/*      if (*pc) { */
      for ( flg=0,k=0; k<bs2; k++ ) { if (pc[k]!=0.0) { flg =1; break; }}
      if (flg) {
        pv = ba + bs2*diag_offset[row];
        pj = bj + diag_offset[row] + 1;
        Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
        nz = bi[row+1] - diag_offset[row] - 1;
        pv += bs2;
        for (j=0; j<nz; j++) {
          Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
        }
        PLogFlops(bslog*(nz+1)-bs);
      }
        row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + bs2*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];
    for ( j=0; j<nz; j++ ) {
      PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
    }
    diag = diag_offset[i] - bi[i];
    /* invert diagonal block */
    w = pv + bs2*diag;
    Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
  }

  PetscFree(rtmp); PetscFree(v_work);
  ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISDestroy(isicol); CHKERRQ(ierr);
  C->factor = FACTOR_LU;
  C->assembled = PETSC_TRUE;
  PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
  return 0;
}
/* ------------------------------------------------------------*/
/*
      Version for when blocks are 5 by 5
*/
#undef __FUNC__
#define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_5"
int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
{
  Mat             C = *B;
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
  IS              iscol = b->col, isrow = b->row, isicol;
  int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
  int             *ajtmpold, *ajtmp, nz, row;
  int             *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j;
  register Scalar *pv,*v,*rtmp,*pc,*w,*x;
  Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
  Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
  Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
  Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
  Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
  Scalar          *ba = b->a,*aa = a->a;
  register int    *pj;

  ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
  PLogObjectParent(*B,isicol);
  ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
  ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
  rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(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] = x[16] = x[17] = 0.0;
      x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
    }
    /* 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++ ) {
      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];
      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;
        }
        PLogFlops(250*nz+225);
      }
      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];
    ierr = Kernel_A_gets_inverse_A_5(w); CHKERRQ(ierr);
  }

  PetscFree(rtmp);
  ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISDestroy(isicol); CHKERRQ(ierr);
  C->factor = FACTOR_LU;
  C->assembled = PETSC_TRUE;
  PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
  return 0;
}

/* ------------------------------------------------------------*/
/*
      Version for when blocks are 4 by 4
*/
#undef __FUNC__
#define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_4"
int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
{
  Mat             C = *B;
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
  IS              iscol = b->col, isrow = b->row, isicol;
  int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
  int             *ajtmpold, *ajtmp, nz, row;
  int             *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j;
  register Scalar *pv,*v,*rtmp,*pc,*w,*x;
  Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
  Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
  Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
  Scalar          m13,m14,m15,m16;
  Scalar          *ba = b->a,*aa = a->a;
  register int    *pj;

  ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
  PLogObjectParent(*B,isicol);
  ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
  ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
  rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(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+16*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;
    }
    /* load in initial (unfactored row) */
    idx      = r[i];
    nz       = ai[idx+1] - ai[idx];
    ajtmpold = aj + ai[idx];
    v        = aa + 16*ai[idx];
    for ( j=0; j<nz; j++ ) {
      x    = rtmp+16*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];
      v    += 16;
    }
    row = *ajtmp++;
    while (row < i) {
      pc = rtmp + 16*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];
      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) {
        pv = ba + 16*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];
        pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
        pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
        pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
        pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;

        pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
        pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
        pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
        pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;

        pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
        pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
        pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
        pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;

        pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
        pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
        pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
        pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;

        nz = bi[row+1] - diag_offset[row] - 1;
        pv += 16;
        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];
          x    = rtmp + 16*pj[j];
          x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
          x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
          x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
          x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;

          x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
          x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
          x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
          x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;

          x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
          x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
          x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
          x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;

          x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
          x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
          x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
          x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;

          pv   += 16;
        }
        PLogFlops(128*nz+112);
      }
      row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + 16*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];
    for ( j=0; j<nz; j++ ) {
      x     = rtmp+16*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;
    }
    /* invert diagonal block */
    w = ba + 16*diag_offset[i];
    ierr = Kernel_A_gets_inverse_A_4(w); CHKERRQ(ierr);
  }

  PetscFree(rtmp);
  ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISDestroy(isicol); CHKERRQ(ierr);
  C->factor = FACTOR_LU;
  C->assembled = PETSC_TRUE;
  PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
  return 0;
}
/* ------------------------------------------------------------*/
/*
      Version for when blocks are 3 by 3
*/
#undef __FUNC__
#define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_3"
int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
{
  Mat             C = *B;
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
  IS              iscol = b->col, isrow = b->row, isicol;
  int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
  int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
  int             *diag_offset = b->diag,idx;
  register Scalar *pv,*v,*rtmp,*pc,*w,*x;
  Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
  Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
  Scalar          *ba = b->a,*aa = a->a;
  register int    *pj;

  ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
  PLogObjectParent(*B,isicol);
  ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
  ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
  rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(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 + 9*ajtmp[j];
      x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
    }
    /* load in initial (unfactored row) */
    idx      = r[i];
    nz       = ai[idx+1] - ai[idx];
    ajtmpold = aj + ai[idx];
    v        = aa + 9*ai[idx];
    for ( j=0; j<nz; j++ ) {
      x    = rtmp + 9*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];
      v    += 9;
    }
    row = *ajtmp++;
    while (row < i) {
      pc = rtmp + 9*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];
      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) {
        pv = ba + 9*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];
        pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
        pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
        pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;

        pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
        pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
        pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;

        pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
        pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
        pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
        nz = bi[row+1] - diag_offset[row] - 1;
        pv += 9;
        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];
          x    = rtmp + 9*pj[j];
          x[0] -= m1*x1 + m4*x2 + m7*x3;
          x[1] -= m2*x1 + m5*x2 + m8*x3;
          x[2] -= m3*x1 + m6*x2 + m9*x3;

          x[3] -= m1*x4 + m4*x5 + m7*x6;
          x[4] -= m2*x4 + m5*x5 + m8*x6;
          x[5] -= m3*x4 + m6*x5 + m9*x6;

          x[6] -= m1*x7 + m4*x8 + m7*x9;
          x[7] -= m2*x7 + m5*x8 + m8*x9;
          x[8] -= m3*x7 + m6*x8 + m9*x9;
          pv   += 9;
        }
        PLogFlops(54*nz+36);
      }
      row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + 9*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];
    for ( j=0; j<nz; j++ ) {
      x     = rtmp + 9*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;
    }
    /* invert diagonal block */
    w = ba + 9*diag_offset[i];
    ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
  }

  PetscFree(rtmp);
  ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISDestroy(isicol); CHKERRQ(ierr);
  C->factor = FACTOR_LU;
  C->assembled = PETSC_TRUE;
  PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
  return 0;
}

/* ------------------------------------------------------------*/
/*
      Version for when blocks are 2 by 2
*/
#undef __FUNC__
#define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_2"
int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
{
  Mat             C = *B;
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
  IS              iscol = b->col, isrow = b->row, isicol;
  int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
  int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
  int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
  register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
  Scalar          p1,p2,p3,p4,v_work[2];
  Scalar          *ba = b->a,*aa = a->a;
  register int    *pj;

  ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
  PLogObjectParent(*B,isicol);
  ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
  ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
  rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(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+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
    }
    /* load in initial (unfactored row) */
    idx      = r[i];
    nz       = ai[idx+1] - ai[idx];
    ajtmpold = aj + ai[idx];
    v        = aa + 4*ai[idx];
    for ( j=0; j<nz; j++ ) {
      x    = rtmp+4*ic[ajtmpold[j]];
      x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
      v    += 4;
    }
    row = *ajtmp++;
    while (row < i) {
      pc = rtmp + 4*row;
      p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
      if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
        pv = ba + 4*diag_offset[row];
        pj = bj + diag_offset[row] + 1;
        x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
        pc[0] = m1 = p1*x1 + p3*x2;
        pc[1] = m2 = p2*x1 + p4*x2;
        pc[2] = m3 = p1*x3 + p3*x4;
        pc[3] = m4 = p2*x3 + p4*x4;
        nz = bi[row+1] - diag_offset[row] - 1;
        pv += 4;
        for (j=0; j<nz; j++) {
          x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
          x    = rtmp + 4*pj[j];
          x[0] -= m1*x1 + m3*x2;
          x[1] -= m2*x1 + m4*x2;
          x[2] -= m1*x3 + m3*x4;
          x[3] -= m2*x3 + m4*x4;
          pv   += 4;
        }
        PLogFlops(16*nz+12);
      }
      row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + 4*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];
    for ( j=0; j<nz; j++ ) {
      x     = rtmp+4*pj[j];
      pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
      pv   += 4;
    }
    /* invert diagonal block */
    w = ba + 4*diag_offset[i];
    Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
  }

  PetscFree(rtmp);
  ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISDestroy(isicol); CHKERRQ(ierr);
  C->factor = FACTOR_LU;
  C->assembled = PETSC_TRUE;
  PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
  return 0;
}

/* ----------------------------------------------------------- */
/*
     Version for when blocks are 1 by 1.
*/
#undef __FUNC__
#define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_1"
int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
{
  Mat             C = *B;
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
  IS              iscol = b->col, isrow = b->row, isicol;
  int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
  int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
  int             *diag_offset = b->diag,diag;
  register Scalar *pv,*v,*rtmp,multiplier,*pc;
  Scalar          *ba = b->a,*aa = a->a;
  register int    *pj;

  ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
  PLogObjectParent(*B,isicol);
  ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
  ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
  rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);

  for ( i=0; i<n; i++ ) {
    nz    = bi[i+1] - bi[i];
    ajtmp = bj + bi[i];
    for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;

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

    row = *ajtmp++;
    while (row < i) {
      pc = rtmp + row;
      if (*pc != 0.0) {
        pv         = ba + diag_offset[row];
        pj         = bj + diag_offset[row] + 1;
        multiplier = *pc * *pv++;
        *pc        = multiplier;
        nz         = bi[row+1] - diag_offset[row] - 1;
        for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
        PLogFlops(1+2*nz);
      }
      row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];
    for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
    diag = diag_offset[i] - bi[i];
    /* check pivot entry for current row */
    if (pv[diag] == 0.0) {
      SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
    }
    pv[diag] = 1.0/pv[diag];
  }

  PetscFree(rtmp);
  ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISDestroy(isicol); CHKERRQ(ierr);
  C->factor    = FACTOR_LU;
  C->assembled = PETSC_TRUE;
  PLogFlops(b->n);
  return 0;
}

/* ----------------------------------------------------------- */
#undef __FUNC__
#define __FUNC__ "MatLUFactor_SeqBAIJ"
int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
{
  Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
  int         ierr;
  Mat         C;

  ierr = MatLUFactorSymbolic(A,row,col,f,&C); CHKERRQ(ierr);
  ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);

  /* free all the data structures from mat */
  PetscFree(mat->a);
  if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
  if (mat->diag) PetscFree(mat->diag);
  if (mat->ilen) PetscFree(mat->ilen);
  if (mat->imax) PetscFree(mat->imax);
  if (mat->solve_work) PetscFree(mat->solve_work);
  if (mat->mult_work) PetscFree(mat->mult_work);
  PetscFree(mat);

  PetscMemcpy(A,C,sizeof(struct _p_Mat));
  PetscHeaderDestroy(C);
  return 0;
}
/* ----------------------------------------------------------- */
#undef __FUNC__
#define __FUNC__ "MatSolve_SeqBAIJ_N"
int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  IS              iscol=a->col,isrow=a->row;
  int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
  int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
  Scalar          *aa=a->a,*sum;
  register Scalar *x,*b,*lsum,*tmp,*v;

  VecGetArray_Fast(bb,b);
  VecGetArray_Fast(xx,x);
  tmp  = a->solve_work;

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

  /* forward solve the lower triangular */
  PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
  for ( i=1; i<n; i++ ) {
    v   = aa + bs2*ai[i];
    vi  = aj + ai[i];
    nz  = a->diag[i] - ai[i];
    sum = tmp + bs*i;
    PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
    while (nz--) {
      Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
      v += bs2;
    }
  }
  /* backward solve the upper triangular */
  lsum = a->solve_work + a->n;
  for ( i=n-1; i>=0; i-- ){
    v   = aa + bs2*(a->diag[i] + 1);
    vi  = aj + a->diag[i] + 1;
    nz  = ai[i+1] - a->diag[i] - 1;
    PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
    while (nz--) {
      Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
      v += bs2;
    }
    Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
    PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
  }

  ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
  VecRestoreArray_Fast(bb,b);
  VecRestoreArray_Fast(xx,x);
  PLogFlops(2*(a->bs2)*(a->nz) - a->n);
  return 0;
}

#undef __FUNC__
#define __FUNC__ "MatSolve_SeqBAIJ_7"
int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  IS              iscol=a->col,isrow=a->row;
  int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
  int             *diag = a->diag;
  Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
  register Scalar *x,*b,*tmp,*v;

  VecGetArray_Fast(bb,b);
  VecGetArray_Fast(xx,x);
  tmp  = a->solve_work;

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

  /* forward solve the lower triangular */
  idx    = 7*(*r++);
  tmp[0] = b[idx];   tmp[1] = b[1+idx];
  tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
  tmp[5] = b[5+idx]; tmp[6] = b[6+idx];

  for ( i=1; i<n; i++ ) {
    v     = aa + 49*ai[i];
    vi    = aj + ai[i];
    nz    = diag[i] - ai[i];
    idx   = 7*(*r++);
    sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
    sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
    while (nz--) {
      idx   = 7*(*vi++);
      x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
      x4    = tmp[3+idx];x5 = tmp[4+idx];
      x6    = tmp[5+idx];x7 = tmp[6+idx];
      sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
      sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
      sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
      sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
      sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
      sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
      sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
      v += 49;
    }
    idx = 7*i;
    tmp[idx]   = sum1;tmp[1+idx] = sum2;
    tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
    tmp[5+idx] = sum6;tmp[6+idx] = sum7;
  }
  /* backward solve the upper triangular */
  for ( i=n-1; i>=0; i-- ){
    v    = aa + 49*diag[i] + 49;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    idt  = 7*i;
    sum1 = tmp[idt];  sum2 = tmp[1+idt];
    sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
    sum6 = tmp[5+idt];sum7 = tmp[6+idt];
    while (nz--) {
      idx   = 7*(*vi++);
      x1    = tmp[idx];   x2 = tmp[1+idx];
      x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
      x6    = tmp[5+idx]; x7 = tmp[6+idx];
      sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
      sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
      sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
      sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
      sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
      sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
      sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
      v += 49;
    }
    idc = 7*(*c--);
    v   = aa + 49*diag[i];
    x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
                                 v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
    x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
                                 v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
    x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
                                 v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
    x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
                                 v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
    x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
                                 v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
    x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
                                 v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
    x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
                                 v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
  }

  ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
  VecRestoreArray_Fast(bb,b);
  VecRestoreArray_Fast(xx,x);
  PLogFlops(2*49*(a->nz) - a->n);
  return 0;
}

#undef __FUNC__
#define __FUNC__ "MatSolve_SeqBAIJ_5"
int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  IS              iscol=a->col,isrow=a->row;
  int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
  int             *diag = a->diag;
  Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
  register Scalar *x,*b,*tmp,*v;

  VecGetArray_Fast(bb,b);
  VecGetArray_Fast(xx,x);
  tmp  = a->solve_work;

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

  /* forward solve the lower triangular */
  idx    = 5*(*r++);
  tmp[0] = b[idx];   tmp[1] = b[1+idx];
  tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
  for ( i=1; i<n; i++ ) {
    v     = aa + 25*ai[i];
    vi    = aj + ai[i];
    nz    = diag[i] - ai[i];
    idx   = 5*(*r++);
    sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
    sum5  = b[4+idx];
    while (nz--) {
      idx   = 5*(*vi++);
      x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
      x4    = tmp[3+idx];x5 = tmp[4+idx];
      sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
      sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
      sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
      sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
      sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
      v += 25;
    }
    idx = 5*i;
    tmp[idx]   = sum1;tmp[1+idx] = sum2;
    tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
  }
  /* backward solve the upper triangular */
  for ( i=n-1; i>=0; i-- ){
    v    = aa + 25*diag[i] + 25;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    idt  = 5*i;
    sum1 = tmp[idt];  sum2 = tmp[1+idt];
    sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
    while (nz--) {
      idx   = 5*(*vi++);
      x1    = tmp[idx];   x2 = tmp[1+idx];
      x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
      sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
      sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
      sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
      sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
      sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
      v += 25;
    }
    idc = 5*(*c--);
    v   = aa + 25*diag[i];
    x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
                                 v[15]*sum4+v[20]*sum5;
    x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
                                 v[16]*sum4+v[21]*sum5;
    x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
                                 v[17]*sum4+v[22]*sum5;
    x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
                                 v[18]*sum4+v[23]*sum5;
    x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
                                 v[19]*sum4+v[24]*sum5;
  }

  ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
  VecRestoreArray_Fast(bb,b);
  VecRestoreArray_Fast(xx,x);
  PLogFlops(2*25*(a->nz) - a->n);
  return 0;
}

#undef __FUNC__
#define __FUNC__ "MatSolve_SeqBAIJ_4"
int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
  IS              iscol=a->col,isrow=a->row;
  int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
  int             *diag = a->diag;
  Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
  register Scalar *x,*b,*tmp,*v;

  VecGetArray_Fast(bb,b);
  VecGetArray_Fast(xx,x);
  tmp  = a->solve_work;

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

  /* forward solve the lower triangular */
  idx    = 4*(*r++);
  tmp[0] = b[idx];   tmp[1] = b[1+idx];
  tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
  for ( i=1; i<n; i++ ) {
    v     = aa + 16*ai[i];
    vi    = aj + ai[i];
    nz    = diag[i] - ai[i];
    idx   = 4*(*r++);
    sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
    while (nz--) {
      idx   = 4*(*vi++);
      x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
      sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
      sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
      sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
      sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
      v    += 16;
    }
    idx        = 4*i;
    tmp[idx]   = sum1;tmp[1+idx] = sum2;
    tmp[2+idx] = sum3;tmp[3+idx] = sum4;
  }
  /* backward solve the upper triangular */
  for ( i=n-1; i>=0; i-- ){
    v    = aa + 16*diag[i] + 16;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    idt  = 4*i;
    sum1 = tmp[idt];  sum2 = tmp[1+idt];
    sum3 = tmp[2+idt];sum4 = tmp[3+idt];
    while (nz--) {
      idx   = 4*(*vi++);
      x1    = tmp[idx];   x2 = tmp[1+idx];
      x3    = tmp[2+idx]; x4 = tmp[3+idx];
      sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
      sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
      sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
      sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
      v += 16;
    }
    idc      = 4*(*c--);
    v        = aa + 16*diag[i];
    x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
    x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
    x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
    x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
  }

  ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
  VecRestoreArray_Fast(bb,b);
  VecRestoreArray_Fast(xx,x);
  PLogFlops(2*16*(a->nz) - a->n);
  return 0;
}

/*
      Special case where the matrix was ILU(0) factored in the natural
   ordering. This eliminates the need for the column and row permutation.
*/
#undef __FUNC__
#define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
  int             i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
  int             *diag = a->diag,jdx;
  Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
  register Scalar *x,*b,*v;

  VecGetArray_Fast(bb,b);
  VecGetArray_Fast(xx,x);

  /* forward solve the lower triangular */
  idx    = 0;
  x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];
  for ( i=1; i<n; i++ ) {
    v     =  aa + 16*ai[i];
    vi    =  aj + ai[i];
    nz    =  diag[i] - ai[i];
    idx   =  4*i;
    sum1  =  b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
    while (nz--) {
      jdx   = 4*(*vi++);
      x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
      sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
      sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
      sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
      sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
      v    += 16;
    }
    x[idx]   = sum1;
    x[1+idx] = sum2;
    x[2+idx] = sum3;
    x[3+idx] = sum4;
  }
  /* backward solve the upper triangular */
  for ( i=n-1; i>=0; i-- ){
    v    = aa + 16*diag[i] + 16;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    idt  = 4*i;
    sum1 = x[idt];  sum2 = x[1+idt];
    sum3 = x[2+idt];sum4 = x[3+idt];
    while (nz--) {
      idx   = 4*(*vi++);
      x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
      sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
      sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
      sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
      sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
      v += 16;
    }
    v        = aa + 16*diag[i];
    x[idt]   = v[0]*sum1 + v[4]*sum2 + v[8]*sum3  + v[12]*sum4;
    x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3  + v[13]*sum4;
    x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4;
    x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4;
  }

  VecRestoreArray_Fast(bb,b);
  VecRestoreArray_Fast(xx,x);
  PLogFlops(2*16*(a->nz) - a->n);
  return 0;
}


#undef __FUNC__
#define __FUNC__ "MatSolve_SeqBAIJ_3"
int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  IS              iscol=a->col,isrow=a->row;
  int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
  int             *diag = a->diag;
  Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
  register Scalar *x,*b,*tmp,*v;

  VecGetArray_Fast(bb,b);
  VecGetArray_Fast(xx,x);
  tmp  = a->solve_work;

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

  /* forward solve the lower triangular */
  idx    = 3*(*r++);
  tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
  for ( i=1; i<n; i++ ) {
    v     = aa + 9*ai[i];
    vi    = aj + ai[i];
    nz    = diag[i] - ai[i];
    idx   = 3*(*r++);
    sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
    while (nz--) {
      idx   = 3*(*vi++);
      x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
      sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
      sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
      sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
      v += 9;
    }
    idx = 3*i;
    tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
  }
  /* backward solve the upper triangular */
  for ( i=n-1; i>=0; i-- ){
    v    = aa + 9*diag[i] + 9;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    idt  = 3*i;
    sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
    while (nz--) {
      idx   = 3*(*vi++);
      x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
      sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
      sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
      sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
      v += 9;
    }
    idc = 3*(*c--);
    v   = aa + 9*diag[i];
    x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
    x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
    x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
  }
  ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
  VecRestoreArray_Fast(bb,b);
  VecRestoreArray_Fast(xx,x);
  PLogFlops(2*9*(a->nz) - a->n);
  return 0;
}

#undef __FUNC__
#define __FUNC__ "MatSolve_SeqBAIJ_2"
int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  IS              iscol=a->col,isrow=a->row;
  int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
  int             *diag = a->diag;
  Scalar          *aa=a->a,sum1,sum2,x1,x2;
  register Scalar *x,*b,*tmp,*v;

  VecGetArray_Fast(bb,b);
  VecGetArray_Fast(xx,x);
  tmp  = a->solve_work;

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

  /* forward solve the lower triangular */
  idx    = 2*(*r++);
  tmp[0] = b[idx]; tmp[1] = b[1+idx];
  for ( i=1; i<n; i++ ) {
    v     = aa + 4*ai[i];
    vi    = aj + ai[i];
    nz    = diag[i] - ai[i];
    idx   = 2*(*r++);
    sum1  = b[idx]; sum2 = b[1+idx];
    while (nz--) {
      idx   = 2*(*vi++);
      x1    = tmp[idx]; x2 = tmp[1+idx];
      sum1 -= v[0]*x1 + v[2]*x2;
      sum2 -= v[1]*x1 + v[3]*x2;
      v += 4;
    }
    idx = 2*i;
    tmp[idx] = sum1; tmp[1+idx] = sum2;
  }
  /* backward solve the upper triangular */
  for ( i=n-1; i>=0; i-- ){
    v    = aa + 4*diag[i] + 4;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    idt  = 2*i;
    sum1 = tmp[idt]; sum2 = tmp[1+idt];
    while (nz--) {
      idx   = 2*(*vi++);
      x1    = tmp[idx]; x2 = tmp[1+idx];
      sum1 -= v[0]*x1 + v[2]*x2;
      sum2 -= v[1]*x1 + v[3]*x2;
      v += 4;
    }
    idc = 2*(*c--);
    v   = aa + 4*diag[i];
    x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
    x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
  }
  ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
  VecRestoreArray_Fast(bb,b);
  VecRestoreArray_Fast(xx,x);
  PLogFlops(2*4*(a->nz) - a->n);
  return 0;
}


#undef __FUNC__
#define __FUNC__ "MatSolve_SeqBAIJ_1"
int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  IS              iscol=a->col,isrow=a->row;
  int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
  int             *diag = a->diag;
  Scalar          *aa=a->a,sum1;
  register Scalar *x,*b,*tmp,*v;

  if (!n) return 0;

  VecGetArray_Fast(bb,b);
  VecGetArray_Fast(xx,x);
  tmp  = a->solve_work;

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

  /* forward solve the lower triangular */
  tmp[0] = b[*r++];
  for ( i=1; i<n; i++ ) {
    v     = aa + ai[i];
    vi    = aj + ai[i];
    nz    = diag[i] - ai[i];
    sum1  = b[*r++];
    while (nz--) {
      sum1 -= (*v++)*tmp[*vi++];
    }
    tmp[i] = sum1;
  }
  /* backward solve the upper triangular */
  for ( i=n-1; i>=0; i-- ){
    v    = aa + diag[i] + 1;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    sum1 = tmp[i];
    while (nz--) {
      sum1 -= (*v++)*tmp[*vi++];
    }
    x[*c--] = tmp[i] = aa[diag[i]]*sum1;
  }

  ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
  VecRestoreArray_Fast(bb,b);
  VecRestoreArray_Fast(xx,x);
  PLogFlops(2*1*(a->nz) - a->n);
  return 0;
}

extern int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat,Vec,Vec);
/* ----------------------------------------------------------------*/
/*
     This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
   except that the data structure of Mat_SeqAIJ is slightly different.
   Not a good example of code reuse.
*/
#undef __FUNC__
#define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
                                 Mat *fact)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
  IS          isicol;
  int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
  int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
  int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
  int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
  PetscTruth  col_identity, row_identity;

  /* special case that simply copies fill pattern */
  PetscValidHeaderSpecific(isrow,IS_COOKIE);
  PetscValidHeaderSpecific(iscol,IS_COOKIE);
  ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
  if (levels == 0 && row_identity && col_identity) {
    ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
    (*fact)->factor = FACTOR_LU;
    b               = (Mat_SeqBAIJ *) (*fact)->data;
    if (!b->diag) {
      ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
    }
    b->row        = isrow;
    b->col        = iscol;
    b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
    /*
        Blocksize 4 has a special faster solver for ILU(0) factorization
        with natural ordering
    */
    if (b->bs == 4) {
      (*fact)->ops.solve = MatSolve_SeqBAIJ_4_NaturalOrdering;
    }
    return 0;
  }

  ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
  ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);

  /* get new row pointers */
  ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
  ainew[0] = 0;
  /* don't know how many column pointers are needed so estimate */
  jmax = (int) (f*ai[n] + 1);
  ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
  /* ajfill is level of fill for each fill entry */
  ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
  /* fill is a linked list of nonzeros in active row */
  fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
  /* im is level for each filled value */
  im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
  /* dloc is location of diagonal in factor */
  dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
  dloc[0]  = 0;
  for ( prow=0; prow<n; prow++ ) {
    /* first copy previous fill into linked list */
    nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
    if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
    xi      = aj + ai[r[prow]];
    fill[n] = n;
    while (nz--) {
      fm  = n;
      idx = ic[*xi++];
      do {
        m  = fm;
        fm = fill[m];
      } while (fm < idx);
      fill[m]   = idx;
      fill[idx] = fm;
      im[idx]   = 0;
    }
    nzi = 0;
    row = fill[n];
    while ( row < prow ) {
      incrlev = im[row] + 1;
      nz      = dloc[row];
      xi      = ajnew  + ainew[row] + nz;
      flev    = ajfill + ainew[row] + nz + 1;
      nnz     = ainew[row+1] - ainew[row] - nz - 1;
      if (*xi++ != row) {
        SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"zero pivot");
      }
      fm      = row;
      while (nnz-- > 0) {
        idx = *xi++;
        if (*flev + incrlev > levels) {
          flev++;
          continue;
        }
        do {
          m  = fm;
          fm = fill[m];
        } while (fm < idx);
        if (fm != idx) {
          im[idx]   = *flev + incrlev;
          fill[m]   = idx;
          fill[idx] = fm;
          fm        = idx;
          nzf++;
        }
        else {
          if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
        }
        flev++;
      }
      row = fill[row];
      nzi++;
    }
    /* copy new filled row into permanent storage */
    ainew[prow+1] = ainew[prow] + nzf;
    if (ainew[prow+1] > jmax) {
      /* allocate a longer ajnew */
      int maxadd;
      maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
      if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
      jmax += maxadd;
      xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
      PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
      PetscFree(ajnew);
      ajnew = xi;
      /* allocate a longer ajfill */
      xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
      PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
      PetscFree(ajfill);
      ajfill = xi;
      realloc++;
    }
    xi          = ajnew + ainew[prow];
    flev        = ajfill + ainew[prow];
    dloc[prow]  = nzi;
    fm          = fill[n];
    while (nzf--) {
      *xi++   = fm;
      *flev++ = im[fm];
      fm      = fill[fm];
    }
  }
  PetscFree(ajfill);
  ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
  ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
  ierr = ISDestroy(isicol); CHKERRQ(ierr);
  PetscFree(fill); PetscFree(im);

  {
    double af = ((double)ainew[n])/((double)ai[n]);
    PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
             realloc,f,af);
    af += .01;
    PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af);
    PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af);
    PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:for best performance.\n");
  }

  /* put together the new matrix */
  ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
  b = (Mat_SeqBAIJ *) (*fact)->data;
  PetscFree(b->imax);
  b->singlemalloc = 0;
  len = bs2*ainew[n]*sizeof(Scalar);
  /* the next line frees the default space generated by the Create() */
  PetscFree(b->a); PetscFree(b->ilen);
  b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
  b->j          = ajnew;
  b->i          = ainew;
  for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
  b->diag       = dloc;
  b->ilen       = 0;
  b->imax       = 0;
  b->row        = isrow;
  b->col        = iscol;
  b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
  CHKPTRQ(b->solve_work);
  /* In b structure:  Free imax, ilen, old a, old j.
     Allocate dloc, solve_work, new a, new j */
  PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
  b->maxnz          = b->nz = ainew[n];
  (*fact)->factor   = FACTOR_LU;

  (*fact)->info.factor_mallocs    = realloc;
  (*fact)->info.fill_ratio_given  = f;
  (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);

  return 0;
}