/*$Id: sbaijfact2.c,v 1.1 2000/06/21 15:47:02 balay Exp balay $*/
/*
    Factorization code for SBAIJ format. 
*/

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

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_1_NaturalOrdering"
int MatSolveTranspose_SeqSBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  int             ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
  int             *diag = a->diag;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,*x,*b;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);

  /* forward solve the U^T */
  for (i=0; i<n; i++) {

    v     = aa + diag[i];
    /* multiply by the inverse of the block diagonal */
    s1    = (*v++)*b[i];
    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      x[*vi++]  -= (*v++)*s1;
    }
    x[i]   = s1;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + diag[i] - 1;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    s1   = x[i];
    while (nz--) {
      x[*vi--]   -=  (*v--)*s1;
    }
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*(a->nz) - a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_2_NaturalOrdering"
int MatSolveTranspose_SeqSBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  int             ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
  int             *diag = a->diag,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,x1,x2;
  Scalar          *x,*b;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 4*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1 = b[idx];   x2 = b[1+idx];
    s1 = v[0]*x1  +  v[1]*x2;
    s2 = v[2]*x1  +  v[3]*x2;
    v += 4;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 2*(*vi++);
      x[oidx]   -= v[0]*s1  +  v[1]*s2;
      x[oidx+1] -= v[2]*s1  +  v[3]*s2;
      v  += 4;
    }
    x[idx]   = s1;x[1+idx] = s2;
    idx += 2;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 4*diag[i] - 4;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 2*i;
    s1   = x[idt];  s2 = x[1+idt];
    while (nz--) {
      idx   = 2*(*vi--);
      x[idx]   -=  v[0]*s1 +  v[1]*s2;
      x[idx+1] -=  v[2]*s1 +  v[3]*s2;
      v -= 4;
    }
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*4*(a->nz) - 2*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_3_NaturalOrdering"
int MatSolveTranspose_SeqSBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  int             ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
  int             *diag = a->diag,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,x1,x2,x3;
  Scalar          *x,*b;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 9*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1 = b[idx];   x2 = b[1+idx]; x3    = b[2+idx];
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3;
    s2 = v[3]*x1  +  v[4]*x2 +  v[5]*x3;
    s3 = v[6]*x1  +  v[7]*x2 + v[8]*x3;
    v += 9;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 3*(*vi++);
      x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3;
      x[oidx+1] -= v[3]*s1  +  v[4]*s2 +  v[5]*s3;
      x[oidx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
      v  += 9;
    }
    x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;
    idx += 3;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 9*diag[i] - 9;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 3*i;
    s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];
    while (nz--) {
      idx   = 3*(*vi--);
      x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3;
      x[idx+1] -=  v[3]*s1 +  v[4]*s2 +  v[5]*s3;
      x[idx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
      v -= 9;
    }
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*9*(a->nz) - 3*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_4_NaturalOrdering"
int MatSolveTranspose_SeqSBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  int             ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
  int             *diag = a->diag,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,x1,x2,x3,x4;
  Scalar          *x,*b;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 16*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = b[idx];   x2 = b[1+idx]; x3    = b[2+idx]; x4 = b[3+idx];
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4;
    s2 = v[4]*x1  +  v[5]*x2 +  v[6]*x3 +  v[7]*x4;
    s3 = v[8]*x1  +  v[9]*x2 + v[10]*x3 + v[11]*x4;
    s4 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
    v += 16;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 4*(*vi++);
      x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
      x[oidx+1] -= v[4]*s1  +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
      x[oidx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
      x[oidx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
      v  += 16;
    }
    x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4;
    idx += 4;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 16*diag[i] - 16;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 4*i;
    s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt];
    while (nz--) {
      idx   = 4*(*vi--);
      x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
      x[idx+1] -=  v[4]*s1 +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
      x[idx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
      x[idx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
      v -= 16;
    }
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*16*(a->nz) - 4*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_5_NaturalOrdering"
int MatSolveTranspose_SeqSBAIJ_5_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  int             ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
  int             *diag = a->diag,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
  Scalar          *x,*b;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 25*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = b[idx];   x2 = b[1+idx]; x3    = b[2+idx]; x4 = b[3+idx]; x5 = b[4+idx];
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5;
    s2 = v[5]*x1  +  v[6]*x2 +  v[7]*x3 +  v[8]*x4 +  v[9]*x5;
    s3 = v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4 + v[14]*x5;
    s4 = v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4 + v[19]*x5;
    s5 = v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4 + v[24]*x5;
    v += 25;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 5*(*vi++);
      x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5;
      x[oidx+1] -= v[5]*s1  +  v[6]*s2 +  v[7]*s3 +  v[8]*s4 +  v[9]*s5;
      x[oidx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5;
      x[oidx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5;
      x[oidx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5;
      v  += 25;
    }
    x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5;
    idx += 5;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 25*diag[i] - 25;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 5*i;
    s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
    while (nz--) {
      idx   = 5*(*vi--);
      x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5;
      x[idx+1] -=  v[5]*s1 +  v[6]*s2 +  v[7]*s3 +  v[8]*s4 +  v[9]*s5;
      x[idx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5;
      x[idx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5;
      x[idx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5;
      v -= 25;
    }
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*25*(a->nz) - 5*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_6_NaturalOrdering"
int MatSolveTranspose_SeqSBAIJ_6_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  int             ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
  int             *diag = a->diag,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
  Scalar          *x,*b;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 36*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = b[idx];   x2 = b[1+idx]; x3    = b[2+idx]; x4 = b[3+idx]; x5 = b[4+idx];
    x6    = b[5+idx]; 
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6;
    s2 = v[6]*x1  +  v[7]*x2 +  v[8]*x3 +  v[9]*x4 + v[10]*x5 + v[11]*x6;
    s3 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4 + v[16]*x5 + v[17]*x6;
    s4 = v[18]*x1 + v[19]*x2 + v[20]*x3 + v[21]*x4 + v[22]*x5 + v[23]*x6;
    s5 = v[24]*x1 + v[25]*x2 + v[26]*x3 + v[27]*x4 + v[28]*x5 + v[29]*x6;
    s6 = v[30]*x1 + v[31]*x2 + v[32]*x3 + v[33]*x4 + v[34]*x5 + v[35]*x6;
    v += 36;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 6*(*vi++);
      x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
      x[oidx+1] -= v[6]*s1  +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
      x[oidx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
      x[oidx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
      x[oidx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
      x[oidx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
      v  += 36;
    }
    x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5;
    x[5+idx] = s6;
    idx += 6;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 36*diag[i] - 36;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 6*i;
    s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
    s6 = x[5+idt];
    while (nz--) {
      idx   = 6*(*vi--);
      x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
      x[idx+1] -=  v[6]*s1 +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
      x[idx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
      x[idx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
      x[idx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
      x[idx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
      v -= 36;
    }
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*36*(a->nz) - 6*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_7_NaturalOrdering"
int MatSolveTranspose_SeqSBAIJ_7_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
  int             ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
  int             *diag = a->diag,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
  Scalar          *x,*b;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 49*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = b[idx];   x2 = b[1+idx]; x3    = b[2+idx]; x4 = b[3+idx]; x5 = b[4+idx];
    x6    = b[5+idx]; x7 = b[6+idx];
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6 +  v[6]*x7;
    s2 = v[7]*x1  +  v[8]*x2 +  v[9]*x3 + v[10]*x4 + v[11]*x5 + v[12]*x6 + v[13]*x7;
    s3 = v[14]*x1 + v[15]*x2 + v[16]*x3 + v[17]*x4 + v[18]*x5 + v[19]*x6 + v[20]*x7;
    s4 = v[21]*x1 + v[22]*x2 + v[23]*x3 + v[24]*x4 + v[25]*x5 + v[26]*x6 + v[27]*x7;
    s5 = v[28]*x1 + v[29]*x2 + v[30]*x3 + v[31]*x4 + v[32]*x5 + v[33]*x6 + v[34]*x7;
    s6 = v[35]*x1 + v[36]*x2 + v[37]*x3 + v[38]*x4 + v[39]*x5 + v[40]*x6 + v[41]*x7;
    s7 = v[42]*x1 + v[43]*x2 + v[44]*x3 + v[45]*x4 + v[46]*x5 + v[47]*x6 + v[48]*x7;
    v += 49;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 7*(*vi++);
      x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
      x[oidx+1] -= v[7]*s1  +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
      x[oidx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
      x[oidx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
      x[oidx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
      x[oidx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
      x[oidx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
      v  += 49;
    }
    x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5;
    x[5+idx] = s6;x[6+idx] = s7;
    idx += 7;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 49*diag[i] - 49;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 7*i;
    s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
    s6 = x[5+idt];s7 = x[6+idt]; 
    while (nz--) {
      idx   = 7*(*vi--);
      x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
      x[idx+1] -=  v[7]*s1 +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
      x[idx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
      x[idx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
      x[idx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
      x[idx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
      x[idx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
      v -= 49;
    }
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*49*(a->nz) - 7*a->n);
  PetscFunctionReturn(0);
}

/*---------------------------------------------------------------------------------------------*/
#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_1"
int MatSolveTranspose_SeqSBAIJ_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;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,*x,*b,*t;

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

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

  /* copy the b into temp work space according to permutation */
  for (i=0; i<n; i++) {
    t[i] = b[c[i]];
  } 

  /* forward solve the U^T */
  for (i=0; i<n; i++) {

    v     = aa + diag[i];
    /* multiply by the inverse of the block diagonal */
    s1    = (*v++)*t[i];
    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      t[*vi++]  -= (*v++)*s1;
    }
    t[i]   = s1;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + diag[i] - 1;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    s1   = t[i];
    while (nz--) {
      t[*vi--]   -=  (*v--)*s1;
    }
  }

  /* copy t into x according to permutation */
  for (i=0; i<n; i++) {
    x[r[i]]   = t[i];
  } 

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

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_2"
int MatSolveTranspose_SeqSBAIJ_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,*rout,*cout;
  int             *diag = a->diag,ii,ic,ir,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,x1,x2;
  Scalar          *x,*b,*t;

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

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

  /* copy the b into temp work space according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ic      = 2*c[i];
    t[ii]   = b[ic];
    t[ii+1] = b[ic+1];
    ii += 2;
  } 

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 4*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = t[idx];   x2 = t[1+idx];
    s1 = v[0]*x1  +  v[1]*x2;
    s2 = v[2]*x1  +  v[3]*x2;
    v += 4;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 2*(*vi++);
      t[oidx]   -= v[0]*s1  +  v[1]*s2;
      t[oidx+1] -= v[2]*s1  +  v[3]*s2;
      v  += 4;
    }
    t[idx]   = s1;t[1+idx] = s2;
    idx += 2;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 4*diag[i] - 4;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 2*i;
    s1 = t[idt];  s2 = t[1+idt];
    while (nz--) {
      idx   = 2*(*vi--);
      t[idx]   -=  v[0]*s1 +  v[1]*s2;
      t[idx+1] -=  v[2]*s1 +  v[3]*s2;
      v -= 4;
    }
  }

  /* copy t into x according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ir      = 2*r[i];
    x[ir]   = t[ii];
    x[ir+1] = t[ii+1];
    ii += 2;
  } 

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*4*(a->nz) - 2*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_3"
int MatSolveTranspose_SeqSBAIJ_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,*rout,*cout;
  int             *diag = a->diag,ii,ic,ir,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,x1,x2,x3;
  Scalar          *x,*b,*t;

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

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

  /* copy the b into temp work space according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ic      = 3*c[i];
    t[ii]   = b[ic];
    t[ii+1] = b[ic+1];
    t[ii+2] = b[ic+2];
    ii += 3;
  } 

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 9*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx];
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3;
    s2 = v[3]*x1  +  v[4]*x2 +  v[5]*x3;
    s3 = v[6]*x1  +  v[7]*x2 + v[8]*x3;
    v += 9;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 3*(*vi++);
      t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3;
      t[oidx+1] -= v[3]*s1  +  v[4]*s2 +  v[5]*s3;
      t[oidx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
      v  += 9;
    }
    t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;
    idx += 3;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 9*diag[i] - 9;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 3*i;
    s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];
    while (nz--) {
      idx   = 3*(*vi--);
      t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3;
      t[idx+1] -=  v[3]*s1 +  v[4]*s2 +  v[5]*s3;
      t[idx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
      v -= 9;
    }
  }

  /* copy t into x according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ir      = 3*r[i];
    x[ir]   = t[ii];
    x[ir+1] = t[ii+1];
    x[ir+2] = t[ii+2];
    ii += 3;
  } 

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*9*(a->nz) - 3*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_4"
int MatSolveTranspose_SeqSBAIJ_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,*rout,*cout;
  int             *diag = a->diag,ii,ic,ir,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,x1,x2,x3,x4;
  Scalar          *x,*b,*t;

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

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

  /* copy the b into temp work space according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ic      = 4*c[i];
    t[ii]   = b[ic];
    t[ii+1] = b[ic+1];
    t[ii+2] = b[ic+2];
    t[ii+3] = b[ic+3];
    ii += 4;
  } 

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 16*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx];
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4;
    s2 = v[4]*x1  +  v[5]*x2 +  v[6]*x3 +  v[7]*x4;
    s3 = v[8]*x1  +  v[9]*x2 + v[10]*x3 + v[11]*x4;
    s4 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
    v += 16;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 4*(*vi++);
      t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
      t[oidx+1] -= v[4]*s1  +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
      t[oidx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
      t[oidx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
      v  += 16;
    }
    t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4;
    idx += 4;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 16*diag[i] - 16;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 4*i;
    s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt];
    while (nz--) {
      idx   = 4*(*vi--);
      t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
      t[idx+1] -=  v[4]*s1 +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
      t[idx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
      t[idx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
      v -= 16;
    }
  }

  /* copy t into x according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ir      = 4*r[i];
    x[ir]   = t[ii];
    x[ir+1] = t[ii+1];
    x[ir+2] = t[ii+2];
    x[ir+3] = t[ii+3];
    ii += 4;
  } 

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*16*(a->nz) - 4*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_5"
int MatSolveTranspose_SeqSBAIJ_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,*rout,*cout;
  int             *diag = a->diag,ii,ic,ir,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
  Scalar          *x,*b,*t;

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

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

  /* copy the b into temp work space according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ic      = 5*c[i];
    t[ii]   = b[ic];
    t[ii+1] = b[ic+1];
    t[ii+2] = b[ic+2];
    t[ii+3] = b[ic+3];
    t[ii+4] = b[ic+4];
    ii += 5;
  } 

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 25*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5;
    s2 = v[5]*x1  +  v[6]*x2 +  v[7]*x3 +  v[8]*x4 +  v[9]*x5;
    s3 = v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4 + v[14]*x5;
    s4 = v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4 + v[19]*x5;
    s5 = v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4 + v[24]*x5;
    v += 25;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 5*(*vi++);
      t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5;
      t[oidx+1] -= v[5]*s1  +  v[6]*s2 +  v[7]*s3 +  v[8]*s4 +  v[9]*s5;
      t[oidx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5;
      t[oidx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5;
      t[oidx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5;
      v  += 25;
    }
    t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
    idx += 5;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 25*diag[i] - 25;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 5*i;
    s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
    while (nz--) {
      idx   = 5*(*vi--);
      t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5;
      t[idx+1] -=  v[5]*s1 +  v[6]*s2 +  v[7]*s3 +  v[8]*s4 +  v[9]*s5;
      t[idx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5;
      t[idx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5;
      t[idx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5;
      v -= 25;
    }
  }

  /* copy t into x according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ir      = 5*r[i];
    x[ir]   = t[ii];
    x[ir+1] = t[ii+1];
    x[ir+2] = t[ii+2];
    x[ir+3] = t[ii+3];
    x[ir+4] = t[ii+4];
    ii += 5;
  } 

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*25*(a->nz) - 5*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_6"
int MatSolveTranspose_SeqSBAIJ_6(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,*rout,*cout;
  int             *diag = a->diag,ii,ic,ir,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
  Scalar          *x,*b,*t;

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

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

  /* copy the b into temp work space according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ic      = 6*c[i];
    t[ii]   = b[ic];
    t[ii+1] = b[ic+1];
    t[ii+2] = b[ic+2];
    t[ii+3] = b[ic+3];
    t[ii+4] = b[ic+4];
    t[ii+5] = b[ic+5];
    ii += 6;
  } 

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 36*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
    x6    = t[5+idx]; 
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6;
    s2 = v[6]*x1  +  v[7]*x2 +  v[8]*x3 +  v[9]*x4 + v[10]*x5 + v[11]*x6;
    s3 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4 + v[16]*x5 + v[17]*x6;
    s4 = v[18]*x1 + v[19]*x2 + v[20]*x3 + v[21]*x4 + v[22]*x5 + v[23]*x6;
    s5 = v[24]*x1 + v[25]*x2 + v[26]*x3 + v[27]*x4 + v[28]*x5 + v[29]*x6;
    s6 = v[30]*x1 + v[31]*x2 + v[32]*x3 + v[33]*x4 + v[34]*x5 + v[35]*x6;
    v += 36;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 6*(*vi++);
      t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
      t[oidx+1] -= v[6]*s1  +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
      t[oidx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
      t[oidx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
      t[oidx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
      t[oidx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
      v  += 36;
    }
    t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
    t[5+idx] = s6;
    idx += 6;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 36*diag[i] - 36;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 6*i;
    s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
    s6 = t[5+idt];
    while (nz--) {
      idx   = 6*(*vi--);
      t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
      t[idx+1] -=  v[6]*s1 +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
      t[idx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
      t[idx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
      t[idx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
      t[idx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
      v -= 36;
    }
  }

  /* copy t into x according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ir      = 6*r[i];
    x[ir]   = t[ii];
    x[ir+1] = t[ii+1];
    x[ir+2] = t[ii+2];
    x[ir+3] = t[ii+3];
    x[ir+4] = t[ii+4];
    x[ir+5] = t[ii+5];
    ii += 6;
  } 

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*36*(a->nz) - 6*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolveTranspose_SeqSBAIJ_7"
int MatSolveTranspose_SeqSBAIJ_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,*rout,*cout;
  int             *diag = a->diag,ii,ic,ir,oidx;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
  Scalar          *x,*b,*t;

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

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

  /* copy the b into temp work space according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ic      = 7*c[i];
    t[ii]   = b[ic];
    t[ii+1] = b[ic+1];
    t[ii+2] = b[ic+2];
    t[ii+3] = b[ic+3];
    t[ii+4] = b[ic+4];
    t[ii+5] = b[ic+5];
    t[ii+6] = b[ic+6];
    ii += 7;
  } 

  /* forward solve the U^T */
  idx = 0;
  for (i=0; i<n; i++) {

    v     = aa + 49*diag[i];
    /* multiply by the inverse of the block diagonal */
    x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
    x6    = t[5+idx]; x7 = t[6+idx];
    s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6 +  v[6]*x7;
    s2 = v[7]*x1  +  v[8]*x2 +  v[9]*x3 + v[10]*x4 + v[11]*x5 + v[12]*x6 + v[13]*x7;
    s3 = v[14]*x1 + v[15]*x2 + v[16]*x3 + v[17]*x4 + v[18]*x5 + v[19]*x6 + v[20]*x7;
    s4 = v[21]*x1 + v[22]*x2 + v[23]*x3 + v[24]*x4 + v[25]*x5 + v[26]*x6 + v[27]*x7;
    s5 = v[28]*x1 + v[29]*x2 + v[30]*x3 + v[31]*x4 + v[32]*x5 + v[33]*x6 + v[34]*x7;
    s6 = v[35]*x1 + v[36]*x2 + v[37]*x3 + v[38]*x4 + v[39]*x5 + v[40]*x6 + v[41]*x7;
    s7 = v[42]*x1 + v[43]*x2 + v[44]*x3 + v[45]*x4 + v[46]*x5 + v[47]*x6 + v[48]*x7;
    v += 49;

    vi    = aj + diag[i] + 1;
    nz    = ai[i+1] - diag[i] - 1;
    while (nz--) {
      oidx = 7*(*vi++);
      t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
      t[oidx+1] -= v[7]*s1  +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
      t[oidx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
      t[oidx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
      t[oidx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
      t[oidx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
      t[oidx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
      v  += 49;
    }
    t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
    t[5+idx] = s6;t[6+idx] = s7;
    idx += 7;
  }
  /* backward solve the L^T */
  for (i=n-1; i>=0; i--){
    v    = aa + 49*diag[i] - 49;
    vi   = aj + diag[i] - 1;
    nz   = diag[i] - ai[i];
    idt  = 7*i;
    s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
    s6 = t[5+idt];s7 = t[6+idt]; 
    while (nz--) {
      idx   = 7*(*vi--);
      t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
      t[idx+1] -=  v[7]*s1 +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
      t[idx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
      t[idx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
      t[idx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
      t[idx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
      t[idx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
      v -= 49;
    }
  }

  /* copy t into x according to permutation */
  ii = 0;
  for (i=0; i<n; i++) {
    ir      = 7*r[i];
    x[ir]   = t[ii];
    x[ir+1] = t[ii+1];
    x[ir+2] = t[ii+2];
    x[ir+3] = t[ii+3];
    x[ir+4] = t[ii+4];
    x[ir+5] = t[ii+5];
    x[ir+6] = t[ii+6];
    ii += 7;
  } 

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*49*(a->nz) - 7*a->n);
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------- */
#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_N"
int MatSolve_SeqSBAIJ_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;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,*s,*t,*ls;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  t  = 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 */
  ierr = PetscMemcpy(t,b+bs*(*r++),bs*sizeof(Scalar));CHKERRQ(ierr);
  for (i=1; i<n; i++) {
    v   = aa + bs2*ai[i];
    vi  = aj + ai[i];
    nz  = a->diag[i] - ai[i];
    s = t + bs*i;
    ierr = PetscMemcpy(s,b+bs*(*r++),bs*sizeof(Scalar));CHKERRQ(ierr);
    while (nz--) {
      Kernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*(*vi++));
      v += bs2;
    }
  }
  /* backward solve the upper triangular */
  ls = 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;
    ierr = PetscMemcpy(ls,t+i*bs,bs*sizeof(Scalar));CHKERRQ(ierr);
    while (nz--) {
      Kernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*(*vi++));
      v += bs2;
    }
    Kernel_w_gets_A_times_v(bs,ls,aa+bs2*a->diag[i],t+i*bs);
    ierr = PetscMemcpy(x + bs*(*c--),t+i*bs,bs*sizeof(Scalar));CHKERRQ(ierr);
  }

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

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_7"
int MatSolve_SeqSBAIJ_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;
  MatScalar       *aa=a->a,*v;
  Scalar          s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
  Scalar          *x,*b,*t;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  t  = 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++); 
  t[0] = b[idx];   t[1] = b[1+idx]; 
  t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
  t[5] = b[5+idx]; t[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++); 
    s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
    s5  = b[4+idx];s6 = b[5+idx];s7 = b[6+idx];
    while (nz--) {
      idx   = 7*(*vi++);
      x1    = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
      x4    = t[3+idx];x5 = t[4+idx];
      x6    = t[5+idx];x7 = t[6+idx];
      s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
      s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
      s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
      s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
      s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
      s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
      s7 -= 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;
    t[idx]   = s1;t[1+idx] = s2;
    t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
    t[5+idx] = s6;t[6+idx] = s7;
  }
  /* 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;
    s1 = t[idt];  s2 = t[1+idt]; 
    s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
    s6 = t[5+idt];s7 = t[6+idt]; 
    while (nz--) {
      idx   = 7*(*vi++);
      x1    = t[idx];   x2 = t[1+idx];
      x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
      x6    = t[5+idx]; x7 = t[6+idx];
      s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
      s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
      s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
      s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
      s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
      s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
      s7 -= 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]   = t[idt]   = v[0]*s1+v[7]*s2+v[14]*s3+
                                 v[21]*s4+v[28]*s5+v[35]*s6+v[42]*s7;
    x[1+idc] = t[1+idt] = v[1]*s1+v[8]*s2+v[15]*s3+
                                 v[22]*s4+v[29]*s5+v[36]*s6+v[43]*s7;
    x[2+idc] = t[2+idt] = v[2]*s1+v[9]*s2+v[16]*s3+
                                 v[23]*s4+v[30]*s5+v[37]*s6+v[44]*s7;
    x[3+idc] = t[3+idt] = v[3]*s1+v[10]*s2+v[17]*s3+
                                 v[24]*s4+v[31]*s5+v[38]*s6+v[45]*s7;
    x[4+idc] = t[4+idt] = v[4]*s1+v[11]*s2+v[18]*s3+
                                 v[25]*s4+v[32]*s5+v[39]*s6+v[46]*s7;
    x[5+idc] = t[5+idt] = v[5]*s1+v[12]*s2+v[19]*s3+
                                 v[26]*s4+v[33]*s5+v[40]*s6+v[47]*s7;
    x[6+idc] = t[6+idt] = v[6]*s1+v[13]*s2+v[20]*s3+
                                 v[27]*s4+v[34]*s5+v[41]*s6+v[48]*s7;
  }

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*49*(a->nz) - 7*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_7_NaturalOrdering"
int MatSolve_SeqSBAIJ_7_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             ierr,*diag = a->diag,jdx;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 
  /* 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]; x[4] = b[4+idx]; x[5] = b[5+idx];
  x[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*i;
    s1  =  b[idx];   s2 = b[1+idx]; s3 = b[2+idx];
    s4  =  b[3+idx]; s5 = b[4+idx]; s6 = b[5+idx];
    s7  =  b[6+idx];
    while (nz--) {
      jdx   = 7*(*vi++);
      x1    = x[jdx];   x2 = x[1+jdx]; x3 = x[2+jdx];
      x4    = x[3+jdx]; x5 = x[4+jdx]; x6 = x[5+jdx];
      x7    = x[6+jdx];
      s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
      s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
      s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
      s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
      s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
      s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
      s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
      v += 49;
     }
    x[idx]   = s1;
    x[1+idx] = s2;
    x[2+idx] = s3;
    x[3+idx] = s4;
    x[4+idx] = s5;
    x[5+idx] = s6;
    x[6+idx] = s7;
  }
  /* 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;
    s1 = x[idt];   s2 = x[1+idt]; 
    s3 = x[2+idt]; s4 = x[3+idt]; 
    s5 = x[4+idt]; s6 = x[5+idt];
    s7 = x[6+idt];
    while (nz--) {
      idx   = 7*(*vi++);
      x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx]; 
      x4    = x[3+idx]; x5 = x[4+idx]; x6 = x[5+idx]; 
      x7    = x[6+idx];  
      s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
      s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
      s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
      s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
      s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
      s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
      s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
      v += 49;
    }
    v        = aa + 49*diag[i];
    x[idt]   = v[0]*s1 + v[7]*s2  + v[14]*s3 + v[21]*s4 
                         + v[28]*s5 + v[35]*s6 + v[42]*s7;
    x[1+idt] = v[1]*s1 + v[8]*s2  + v[15]*s3 + v[22]*s4 
                         + v[29]*s5 + v[36]*s6 + v[43]*s7;
    x[2+idt] = v[2]*s1 + v[9]*s2  + v[16]*s3 + v[23]*s4 
                         + v[30]*s5 + v[37]*s6 + v[44]*s7;
    x[3+idt] = v[3]*s1 + v[10]*s2  + v[17]*s3 + v[24]*s4 
                         + v[31]*s5 + v[38]*s6 + v[45]*s7;
    x[4+idt] = v[4]*s1 + v[11]*s2  + v[18]*s3 + v[25]*s4 
                         + v[32]*s5 + v[39]*s6 + v[46]*s7;
    x[5+idt] = v[5]*s1 + v[12]*s2  + v[19]*s3 + v[26]*s4 
                         + v[33]*s5 + v[40]*s6 + v[47]*s7;
    x[6+idt] = v[6]*s1 + v[13]*s2  + v[20]*s3 + v[27]*s4 
                         + v[34]*s5 + v[41]*s6 + v[48]*s7;
  }

  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(2*36*(a->nz) - 6*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_6"
int MatSolve_SeqSBAIJ_6(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;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*t;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  t  = 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    = 6*(*r++); 
  t[0] = b[idx];   t[1] = b[1+idx]; 
  t[2] = b[2+idx]; t[3] = b[3+idx]; 
  t[4] = b[4+idx]; t[5] = b[5+idx];
  for (i=1; i<n; i++) {
    v     = aa + 36*ai[i];
    vi    = aj + ai[i];
    nz    = diag[i] - ai[i];
    idx   = 6*(*r++); 
    s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
    s5  = b[4+idx]; s6 = b[5+idx];
    while (nz--) {
      idx   = 6*(*vi++);
      x1    = t[idx];   x2 = t[1+idx]; x3 = t[2+idx];
      x4    = t[3+idx]; x5 = t[4+idx]; x6 = t[5+idx];
      s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
      s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
      s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
      s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
      s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
      s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
      v += 36;
    }
    idx = 6*i;
    t[idx]   = s1;t[1+idx] = s2;
    t[2+idx] = s3;t[3+idx] = s4; 
    t[4+idx] = s5;t[5+idx] = s6;
  }
  /* backward solve the upper triangular */
  for (i=n-1; i>=0; i--){
    v    = aa + 36*diag[i] + 36;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    idt  = 6*i;
    s1 = t[idt];  s2 = t[1+idt]; 
    s3 = t[2+idt];s4 = t[3+idt]; 
    s5 = t[4+idt];s6 = t[5+idt];
    while (nz--) {
      idx   = 6*(*vi++);
      x1    = t[idx];   x2 = t[1+idx];
      x3    = t[2+idx]; x4 = t[3+idx]; 
      x5    = t[4+idx]; x6 = t[5+idx];
      s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
      s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
      s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
      s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
      s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
      s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
      v += 36;
    }
    idc = 6*(*c--);
    v   = aa + 36*diag[i];
    x[idc]   = t[idt]   = v[0]*s1+v[6]*s2+v[12]*s3+
                                 v[18]*s4+v[24]*s5+v[30]*s6;
    x[1+idc] = t[1+idt] = v[1]*s1+v[7]*s2+v[13]*s3+
                                 v[19]*s4+v[25]*s5+v[31]*s6;
    x[2+idc] = t[2+idt] = v[2]*s1+v[8]*s2+v[14]*s3+
                                 v[20]*s4+v[26]*s5+v[32]*s6;
    x[3+idc] = t[3+idt] = v[3]*s1+v[9]*s2+v[15]*s3+
                                 v[21]*s4+v[27]*s5+v[33]*s6;
    x[4+idc] = t[4+idt] = v[4]*s1+v[10]*s2+v[16]*s3+
                                 v[22]*s4+v[28]*s5+v[34]*s6;
    x[5+idc] = t[5+idt] = v[5]*s1+v[11]*s2+v[17]*s3+
                                 v[23]*s4+v[29]*s5+v[35]*s6;
  }

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*36*(a->nz) - 6*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_6_NaturalOrdering"
int MatSolve_SeqSBAIJ_6_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             ierr,*diag = a->diag,jdx;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 
  /* 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]; x[4] = b[4+idx]; x[5] = b[5+idx];
  for (i=1; i<n; i++) {
    v     =  aa + 36*ai[i];
    vi    =  aj + ai[i];
    nz    =  diag[i] - ai[i];
    idx   =  6*i;
    s1  =  b[idx];   s2 = b[1+idx]; s3 = b[2+idx];
    s4  =  b[3+idx]; s5 = b[4+idx]; s6 = b[5+idx];
    while (nz--) {
      jdx   = 6*(*vi++);
      x1    = x[jdx];   x2 = x[1+jdx]; x3 = x[2+jdx];
      x4    = x[3+jdx]; x5 = x[4+jdx]; x6 = x[5+jdx];
      s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
      s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
      s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
      s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
      s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
      s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
      v += 36;
     }
    x[idx]   = s1;
    x[1+idx] = s2;
    x[2+idx] = s3;
    x[3+idx] = s4;
    x[4+idx] = s5;
    x[5+idx] = s6;
  }
  /* backward solve the upper triangular */
  for (i=n-1; i>=0; i--){
    v    = aa + 36*diag[i] + 36;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    idt  = 6*i;
    s1 = x[idt];   s2 = x[1+idt]; 
    s3 = x[2+idt]; s4 = x[3+idt]; 
    s5 = x[4+idt]; s6 = x[5+idt];
    while (nz--) {
      idx   = 6*(*vi++);
      x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx]; 
      x4    = x[3+idx]; x5 = x[4+idx]; x6 = x[5+idx];   
      s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
      s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
      s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
      s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
      s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
      s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
      v += 36;
    }
    v        = aa + 36*diag[i];
    x[idt]   = v[0]*s1 + v[6]*s2  + v[12]*s3 + v[18]*s4 + v[24]*s5 + v[30]*s6;
    x[1+idt] = v[1]*s1 + v[7]*s2  + v[13]*s3 + v[19]*s4 + v[25]*s5 + v[31]*s6;
    x[2+idt] = v[2]*s1 + v[8]*s2  + v[14]*s3 + v[20]*s4 + v[26]*s5 + v[32]*s6;
    x[3+idt] = v[3]*s1 + v[9]*s2  + v[15]*s3 + v[21]*s4 + v[27]*s5 + v[33]*s6;
    x[4+idt] = v[4]*s1 + v[10]*s2 + v[16]*s3 + v[22]*s4 + v[28]*s5 + v[34]*s6;
    x[5+idt] = v[5]*s1 + v[11]*s2 + v[17]*s3 + v[23]*s4 + v[29]*s5 + v[35]*s6;
  }

  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(2*36*(a->nz) - 6*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_5"
int MatSolve_SeqSBAIJ_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;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5,*t;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  t  = 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++); 
  t[0] = b[idx];   t[1] = b[1+idx]; 
  t[2] = b[2+idx]; t[3] = b[3+idx]; t[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++); 
    s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
    s5  = b[4+idx];
    while (nz--) {
      idx   = 5*(*vi++);
      x1    = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
      x4    = t[3+idx];x5 = t[4+idx];
      s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
      s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
      s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
      s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
      s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
      v += 25;
    }
    idx = 5*i;
    t[idx]   = s1;t[1+idx] = s2;
    t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
  }
  /* 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;
    s1 = t[idt];  s2 = t[1+idt]; 
    s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
    while (nz--) {
      idx   = 5*(*vi++);
      x1    = t[idx];   x2 = t[1+idx];
      x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
      s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
      s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5; 
      s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
      s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
      s5 -= 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]   = t[idt]   = v[0]*s1+v[5]*s2+v[10]*s3+
                                 v[15]*s4+v[20]*s5;
    x[1+idc] = t[1+idt] = v[1]*s1+v[6]*s2+v[11]*s3+
                                 v[16]*s4+v[21]*s5;
    x[2+idc] = t[2+idt] = v[2]*s1+v[7]*s2+v[12]*s3+
                                 v[17]*s4+v[22]*s5;
    x[3+idc] = t[3+idt] = v[3]*s1+v[8]*s2+v[13]*s3+
                                 v[18]*s4+v[23]*s5;
    x[4+idc] = t[4+idt] = v[4]*s1+v[9]*s2+v[14]*s3+
                                 v[19]*s4+v[24]*s5;
  }

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*25*(a->nz) - 5*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_5_NaturalOrdering"
int MatSolve_SeqSBAIJ_5_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             ierr,*diag = a->diag,jdx;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 
  /* 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];x[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*i;
    s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];s5 = b[4+idx];
    while (nz--) {
      jdx   = 5*(*vi++);
      x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];x5 = x[4+jdx];
      s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
      s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
      s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
      s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
      s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
      v    += 25;
    }
    x[idx]   = s1;
    x[1+idx] = s2;
    x[2+idx] = s3;
    x[3+idx] = s4;
    x[4+idx] = s5;
  }
  /* 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;
    s1 = x[idt];  s2 = x[1+idt]; 
    s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
    while (nz--) {
      idx   = 5*(*vi++);
      x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
      s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
      s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
      s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
      s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
      s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
      v    += 25;
    }
    v        = aa + 25*diag[i];
    x[idt]   = v[0]*s1 + v[5]*s2 + v[10]*s3  + v[15]*s4 + v[20]*s5;
    x[1+idt] = v[1]*s1 + v[6]*s2 + v[11]*s3  + v[16]*s4 + v[21]*s5;
    x[2+idt] = v[2]*s1 + v[7]*s2 + v[12]*s3  + v[17]*s4 + v[22]*s5;
    x[3+idt] = v[3]*s1 + v[8]*s2 + v[13]*s3  + v[18]*s4 + v[23]*s5;
    x[4+idt] = v[4]*s1 + v[9]*s2 + v[14]*s3  + v[19]*s4 + v[24]*s5;
  }

  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(2*25*(a->nz) - 5*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_4"
int MatSolve_SeqSBAIJ_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;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,s3,s4,x1,x2,x3,x4,*t;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  t  = 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++); 
  t[0] = b[idx];   t[1] = b[1+idx]; 
  t[2] = b[2+idx]; t[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++); 
    s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
    while (nz--) {
      idx   = 4*(*vi++);
      x1    = t[idx];x2 = t[1+idx];x3 = t[2+idx];x4 = t[3+idx];
      s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
      s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
      s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
      s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
      v    += 16;
    }
    idx        = 4*i;
    t[idx]   = s1;t[1+idx] = s2;
    t[2+idx] = s3;t[3+idx] = s4;
  }
  /* 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;
    s1 = t[idt];  s2 = t[1+idt]; 
    s3 = t[2+idt];s4 = t[3+idt];
    while (nz--) {
      idx   = 4*(*vi++);
      x1    = t[idx];   x2 = t[1+idx];
      x3    = t[2+idx]; x4 = t[3+idx];
      s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
      s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4; 
      s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
      s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
      v += 16;
    }
    idc      = 4*(*c--);
    v        = aa + 16*diag[i];
    x[idc]   = t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
    x[1+idc] = t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
    x[2+idc] = t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
    x[3+idc] = t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
  }

  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PLogFlops(2*16*(a->nz) - 4*a->n);
  PetscFunctionReturn(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_SeqSBAIJ_4_NaturalOrdering"
int MatSolve_SeqSBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
  int             n=a->mbs,*ai=a->i,*aj=a->j;
  int             ierr,*diag = a->diag;
  MatScalar       *aa=a->a;
  Scalar          *x,*b;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 

#if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJBLAS)
  {
    static Scalar w[2000]; /* very BAD need to fix */
    fortransolvebaij4blas_(&n,x,ai,aj,diag,aa,b,w);
  }
#elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJ)
  {
    static Scalar w[2000]; /* very BAD need to fix */
    fortransolvebaij4_(&n,x,ai,aj,diag,aa,b,w);
  }
#elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL)
  fortransolvebaij4unroll_(&n,x,ai,aj,diag,aa,b);
#else
  {
    Scalar    s1,s2,s3,s4,x1,x2,x3,x4;
    MatScalar *v;
    int       jdx,idt,idx,nz,*vi,i,ai16;

  /* forward solve the lower triangular */
  idx    = 0;
  x[0]   = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3];
  for (i=1; i<n; i++) {
    v     =  aa      + 16*ai[i];
    vi    =  aj      + ai[i];
    nz    =  diag[i] - ai[i];
    idx   +=  4;
    s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
    while (nz--) {
      jdx   = 4*(*vi++);
      x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
      s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
      s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
      s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
      s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
      v    += 16;
    }
    x[idx]   = s1;
    x[1+idx] = s2;
    x[2+idx] = s3;
    x[3+idx] = s4;
  }
  /* backward solve the upper triangular */
  idt = 4*(n-1);
  for (i=n-1; i>=0; i--){
    ai16 = 16*diag[i];
    v    = aa + ai16 + 16;
    vi   = aj + diag[i] + 1;
    nz   = ai[i+1] - diag[i] - 1;
    s1 = x[idt];  s2 = x[1+idt]; 
    s3 = x[2+idt];s4 = x[3+idt];
    while (nz--) {
      idx   = 4*(*vi++);
      x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
      s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
      s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4; 
      s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
      s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
      v    += 16;
    }
    v        = aa + ai16;
    x[idt]   = v[0]*s1 + v[4]*s2 + v[8]*s3  + v[12]*s4;
    x[1+idt] = v[1]*s1 + v[5]*s2 + v[9]*s3  + v[13]*s4;
    x[2+idt] = v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4;
    x[3+idt] = v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4;
    idt -= 4;
  }
  }
#endif

  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(2*16*(a->nz) - 4*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_3"
int MatSolve_SeqSBAIJ_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;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,s3,x1,x2,x3,*t;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  t  = 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++); 
  t[0] = b[idx]; t[1] = b[1+idx]; t[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++); 
    s1  = b[idx]; s2 = b[1+idx]; s3 = b[2+idx];
    while (nz--) {
      idx   = 3*(*vi++);
      x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
      s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
      s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
      s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
      v += 9;
    }
    idx = 3*i;
    t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3;
  }
  /* 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;
    s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];
    while (nz--) {
      idx   = 3*(*vi++);
      x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
      s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
      s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
      s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
      v += 9;
    }
    idc = 3*(*c--);
    v   = aa + 9*diag[i];
    x[idc]   = t[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
    x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
    x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
  }
  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(2*9*(a->nz) - 3*a->n);
  PetscFunctionReturn(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_SeqSBAIJ_3_NaturalOrdering"
int MatSolve_SeqSBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
  int             n=a->mbs,*ai=a->i,*aj=a->j;
  int             ierr,*diag = a->diag;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,s3,x1,x2,x3;
  int             jdx,idt,idx,nz,*vi,i;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 


  /* forward solve the lower triangular */
  idx    = 0;
  x[0]   = b[0]; x[1] = b[1]; x[2] = b[2];
  for (i=1; i<n; i++) {
    v     =  aa      + 9*ai[i];
    vi    =  aj      + ai[i];
    nz    =  diag[i] - ai[i];
    idx   +=  3;
    s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];
    while (nz--) {
      jdx   = 3*(*vi++);
      x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];
      s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
      s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
      s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
      v    += 9;
    }
    x[idx]   = s1;
    x[1+idx] = s2;
    x[2+idx] = s3;
  }
  /* 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;
    s1 = x[idt];  s2 = x[1+idt]; 
    s3 = x[2+idt];
    while (nz--) {
      idx   = 3*(*vi++);
      x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx];
      s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
      s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
      s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
      v    += 9;
    }
    v        = aa +  9*diag[i];
    x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
    x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
    x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
  }

  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(2*9*(a->nz) - 3*a->n);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_2"
int MatSolve_SeqSBAIJ_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;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,x1,x2,*t;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  t  = 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++); 
  t[0] = b[idx]; t[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++); 
    s1  = b[idx]; s2 = b[1+idx];
    while (nz--) {
      idx   = 2*(*vi++);
      x1    = t[idx]; x2 = t[1+idx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v += 4;
    }
    idx = 2*i;
    t[idx] = s1; t[1+idx] = s2;
  }
  /* 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;
    s1 = t[idt]; s2 = t[1+idt];
    while (nz--) {
      idx   = 2*(*vi++);
      x1    = t[idx]; x2 = t[1+idx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v += 4;
    }
    idc = 2*(*c--);
    v   = aa + 4*diag[i];
    x[idc]   = t[idt]   = v[0]*s1 + v[2]*s2;
    x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2;
  }
  ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
  ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(2*4*(a->nz) - 2*a->n);
  PetscFunctionReturn(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_SeqSBAIJ_2_NaturalOrdering"
int MatSolve_SeqSBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
  int             n=a->mbs,*ai=a->i,*aj=a->j;
  int             ierr,*diag = a->diag;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,s2,x1,x2;
  int             jdx,idt,idx,nz,*vi,i;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 

  /* forward solve the lower triangular */
  idx    = 0;
  x[0]   = b[0]; x[1] = b[1];
  for (i=1; i<n; i++) {
    v     =  aa      + 4*ai[i];
    vi    =  aj      + ai[i];
    nz    =  diag[i] - ai[i];
    idx   +=  2;
    s1  =  b[idx];s2 = b[1+idx];
    while (nz--) {
      jdx   = 2*(*vi++);
      x1    = x[jdx];x2 = x[1+jdx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v    += 4;
    }
    x[idx]   = s1;
    x[1+idx] = s2;
  }
  /* 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;
    s1 = x[idt];  s2 = x[1+idt]; 
    while (nz--) {
      idx   = 2*(*vi++);
      x1    = x[idx];   x2 = x[1+idx];
      s1 -= v[0]*x1 + v[2]*x2;
      s2 -= v[1]*x1 + v[3]*x2;
      v    += 4;
    }
    v        = aa +  4*diag[i];
    x[idt]   = v[0]*s1 + v[2]*s2;
    x[1+idt] = v[1]*s1 + v[3]*s2;
  }

  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(2*4*(a->nz) - 2*a->n);
  PetscFunctionReturn(0);
}

/*----------- New 1 --------------*/
#undef __FUNC__  
#define __FUNC__ "MatSolve_SeqSBAIJ_1"
int MatSolve_SeqSBAIJ_1(Mat A,Vec bb,Vec xx)
{
  Mat_SeqSBAIJ     *a = (Mat_SeqSBAIJ *)A->data;
  IS              isrow=a->row;
  int             mbs=a->mbs,*ai=a->i,*aj=a->j,ierr,*rip;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,xk,*xtmp;
  int             nz,*vj,k;

  PetscFunctionBegin;
  if (!mbs) PetscFunctionReturn(0);

  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 
  xtmp = a->solve_work;

  ierr = ISGetIndices(isrow,&rip);CHKERRQ(ierr); 
  
  /* solve U'*D*y = b by forward substitution */
  for (k=0; k<mbs; k++) xtmp[k] = b[rip[k]];   
  for (k=0; k<mbs; k++){
    v  = aa + ai[k]; 
    vj = aj + ai[k];    
    xk = xtmp[k];
    nz = ai[k+1] - ai[k];     
    while (nz--) xtmp[*vj++] += (*v++) * xk;
    xtmp[k] = xk*aa[k];  /* note: aa[k] = 1/D(k) */
  }

  /* solve U*x = y by back substitution */ 
  
  for (k=mbs-1; k>=0; k--){ 
    v  = aa + ai[k]; 
    vj = aj + ai[k]; 
    xk = xtmp[k];   
    nz = ai[k+1] - ai[k];    
    while (nz--) xk += (*v++) * xtmp[*vj++]; 
    xtmp[k] = xk;
    x[rip[k]] = xk; 
  }

  ierr = ISRestoreIndices(isrow,&rip);CHKERRQ(ierr);
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(4*a->s_nz + a->m);
  PetscFunctionReturn(0);
}


#ifdef CONT
  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;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,s1,*t;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(0);

  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  t  = 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 */
  t[0] = b[*r++];
  for (i=1; i<n; i++) {
    v     = aa + ai[i];
    vi    = aj + ai[i];
    nz    = diag[i] - ai[i];
    s1  = b[*r++];
    while (nz--) {
      s1 -= (*v++)*t[*vi++];
    }
    t[i] = s1;
  }
  /* 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;
    s1 = t[i];
    while (nz--) {
      s1 -= (*v++)*t[*vi++];
    }
    x[*c--] = t[i] = aa[diag[i]]*s1;
  }

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

#endif
/*----------- New 1 --------------*/
/*
      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_SeqSBAIJ_1_NaturalOrdering"
int MatSolve_SeqSBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  Mat_SeqSBAIJ     *a = (Mat_SeqSBAIJ *)A->data;
  int             mbs=a->mbs,*ai=a->i,*aj=a->j,ierr;
  MatScalar       *aa=a->a,*v;
  Scalar          *x,*b,xk;
  int             nz,*vj,k;

  PetscFunctionBegin;
  ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 
  
  /* solve U'*D*y = b by forward substitution */
  for (k=0; k<mbs; k++) x[k] = b[k];   
  for (k=0; k<mbs; k++){
    v  = aa + ai[k]; 
    vj = aj + ai[k];    
    xk = x[k];
    nz = ai[k+1] - ai[k];     
    while (nz--) x[*vj++] += (*v++) * xk;
    x[k] = xk*aa[k];  /* note: aa[k] = 1/D(k) */
  }

  /* solve U*x = y by back substitution */ 
  for (k=mbs-2; k>=0; k--){ 
    v  = aa + ai[k]; 
    vj = aj + ai[k]; 
    xk = x[k];   
    nz = ai[k+1] - ai[k];    
    while (nz--) xk += (*v++) * x[*vj++];    
    x[k] = xk;      
  }

  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 
  PLogFlops(4*a->s_nz + a->m);
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------*/
#undef __FUNC__  
#define __FUNC__ "MatILUFactorSymbolic_SeqSBAIJ"
int MatILUFactorSymbolic_SeqSBAIJ(Mat A,IS isrow,IS iscol,MatILUInfo *info,Mat *B)
{
  Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b;
  IS          isicol;
  int         *rip,*riip,ierr,i,mbs = a->mbs,*ai = a->i,*aj = a->j;
  int         *jutmp,bs = a->bs,bs2=a->bs2;
  int         m,nzi,realloc = 0,*levtmp;
  int         *jl,*q,jumin,jmin,jmax,juptr,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
  int         levels,incrlev,*lev,lev_ik,shift;
  PetscReal  f;

  PetscFunctionBegin;
  if (info) {
    f             = info->fill;
    levels        = (int)info->levels;
  } else {
    f             = 1.0;
    levels        = 0;
  }
  PetscValidHeaderSpecific(isrow,IS_COOKIE);
  PetscValidHeaderSpecific(iscol,IS_COOKIE);
  /* if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,0,"matrix must be square");*/
  ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
  ierr = ISGetIndices(isrow,&rip);CHKERRQ(ierr);
  ierr = ISGetIndices(isicol,&riip);CHKERRQ(ierr);
  for (k=0; k<mbs; k++) {
    if ( rip[k] - riip[k] != 0 ) {
      printf("Non-symm. permutation, use symm. permutation or general matrix format\n");
      break;
    }
  }

  /* initialization */  
  /* Don't know how many column pointers are needed so estimate. 
     Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
  
  umax = (int)(f*ai[mbs] + 1); 
  lev = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(lev);
  umax += mbs + 1; 
  shift = mbs + 1;
  ju = iu = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
  iu[0] = mbs+1; 
  juptr = mbs;
  jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
  q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
  levtmp =  (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(levtmp);
  for (i=0; i<mbs; i++){
    jl[i] = mbs; q[i] = 0;
  }

  /* for each row k */
  for (k=0; k<mbs; k++){   
    nzk = 0; 
    q[k] = mbs;
    /* initialize nonzero structure of k-th row to row rip[k] of A */
    jmin = ai[rip[k]];
    jmax = ai[rip[k]+1];
    for (j=jmin; j<jmax; j++){
      vj = riip[aj[j]]; 
      if(vj > k){
        qm = k; 
        do {
          m  = qm; qm = q[m];
        } while(qm < vj);
        if (qm == vj) {
          printf(" error: duplicate entry in A\n"); break;
        }     
        nzk++;
        q[m]   = vj;
        q[vj]  = qm;  
        levtmp[vj] = 0;   /* initialize lev for nonzero element */ 
      } /* if(vj > k) */
    } /* for (j=jmin; j<jmax; j++) */

    /* modify nonzero structure of k-th row by computing fill-in
       for each row i to be merged in */
    i = k; 
    i = jl[i]; /* next pivot row (== 0 for symbolic factorization) */
    /* printf(" next pivot row i=%d\n",i); */
    while (i < mbs){
      /* merge row i into k-th row */
      j=iu[i];
      vj = ju[j]; 
      lev_ik = lev[j-shift];  
      nzi = iu[i+1] - (iu[i]+1);
      jmin = iu[i] + 1; jmax = iu[i] + nzi;
      qm = k;
      for (j=jmin; j<jmax+1; j++){
        vj = ju[j];
        incrlev = lev[j-shift]+lev_ik+1; 

        if (incrlev > levels) continue;
        do {
          m = qm; qm = q[m];
        } while (qm < vj);
        if (qm != vj){      /* a fill */
          nzk++; q[m] = vj; q[vj] = qm; qm = vj; 
          levtmp[vj] = incrlev;
        } 
        else {              /* already a nonzero element */
          if (levtmp[vj]>incrlev) levtmp[vj] = incrlev;           
        }
      } 
      i = jl[i]; /* next pivot row */     
    }  
   
    /* add k to row list for first nonzero element in k-th row */
    if (nzk > 1){
      i = q[k]; /* col value of first nonzero element in k_th row of U */    
      jl[k] = jl[i]; jl[i] = k;
    } 
    iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/

    /* allocate more space to ju and lev if needed */
    if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
      /* estimate how much additional space we will need */
      /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
      /* just double the memory each time */
      maxadd = umax;      
      if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
      umax += maxadd;

      /* allocate a longer ju (NOTE: iu poits to the beginning of ju) */
      jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
      ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
      ierr = PetscFree(ju);CHKERRQ(ierr);       
      ju = iu = jutmp;

      jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
      ierr  = PetscMemcpy(jutmp,lev,(iu[k]-shift)*sizeof(int));CHKERRQ(ierr);
      ierr = PetscFree(lev);CHKERRQ(ierr);       
      lev = jutmp;

      realloc += 2; /* count how many times we realloc */
    }

    /* save nonzero structure of k-th row in ju */
    i=k;
    jumin = juptr + 1; juptr += nzk; 
    for (j=jumin; j<juptr+1; j++){
      i      = q[i];
      ju[j]  = i;
      lev[j-shift] = levtmp[i];
      /* printf(" k=%d, ju[%d]=%d\n",k,j,ju[j]);*/
    } 
    /* printf("\n");  */     
  } /* for (k=0; k<mbs; k++) */

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

  ierr = ISRestoreIndices(isrow,&rip);CHKERRQ(ierr);
  ierr = ISRestoreIndices(isicol,&riip);CHKERRQ(ierr);

  ierr = PetscFree(q);CHKERRQ(ierr);
  ierr = PetscFree(jl);CHKERRQ(ierr);

  /* put together the new matrix */
  ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
  PLogObjectParent(*B,isicol); 
  b = (Mat_SeqSBAIJ*)(*B)->data;
  ierr = PetscFree(b->imax);CHKERRQ(ierr);
  b->singlemalloc = PETSC_FALSE;
  /* the next line frees the default space generated by the Create() */
  ierr = PetscFree(b->a);CHKERRQ(ierr);
  ierr = PetscFree(b->ilen);CHKERRQ(ierr);
  b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
  b->j          = ju;
  b->i          = iu;
  b->diag       = 0;
  b->ilen       = 0;
  b->imax       = 0;
  b->row        = isrow;
  b->col        = iscol;
  ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
  ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
  b->icol       = isicol;
  b->solve_work = (Scalar*)PetscMalloc((bs*mbs+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,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
  b->s_maxnz = b->s_nz = iu[mbs];
  
  (*B)->factor                 = FACTOR_LU;
  (*B)->info.factor_mallocs    = realloc;
  (*B)->info.fill_ratio_given  = f;
  if (ai[mbs] != 0) {
    (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
  } else {
    (*B)->info.fill_ratio_needed = 0.0;
  }
  
  PetscFunctionReturn(0); 
}