xref: /petsc/src/mat/impls/baij/seq/baijfact2.c (revision 8661488fb92ba91cb78c9e304187e826d99e60dc)

/*$Id: baijfact2.c,v 1.57 2001/07/11 04:50:20 buschelm Exp buschelm $*/
/*
    Factorization code for BAIJ format.
*/

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

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_1_NaturalOrdering"
int MatSolveTranspose_SeqBAIJ_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);
  PetscLogFlops(2*(a->nz) - A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_2_NaturalOrdering"
int MatSolveTranspose_SeqBAIJ_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);
  PetscLogFlops(2*4*(a->nz) - 2*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_3_NaturalOrdering"
int MatSolveTranspose_SeqBAIJ_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);
  PetscLogFlops(2*9*(a->nz) - 3*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_4_NaturalOrdering"
int MatSolveTranspose_SeqBAIJ_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);
  PetscLogFlops(2*16*(a->nz) - 4*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_5_NaturalOrdering"
int MatSolveTranspose_SeqBAIJ_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);
  PetscLogFlops(2*25*(a->nz) - 5*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_6_NaturalOrdering"
int MatSolveTranspose_SeqBAIJ_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);
  PetscLogFlops(2*36*(a->nz) - 6*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_7_NaturalOrdering"
int MatSolveTranspose_SeqBAIJ_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);
  PetscLogFlops(2*49*(a->nz) - 7*A->n);
  PetscFunctionReturn(0);
}

/*---------------------------------------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_1"
int MatSolveTranspose_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;
  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);
  PetscLogFlops(2*(a->nz) - A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_2"
int MatSolveTranspose_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,*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);
  PetscLogFlops(2*4*(a->nz) - 2*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_3"
int MatSolveTranspose_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,*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);
  PetscLogFlops(2*9*(a->nz) - 3*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_4"
int MatSolveTranspose_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,*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);
  PetscLogFlops(2*16*(a->nz) - 4*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_5"
int MatSolveTranspose_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,*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);
  PetscLogFlops(2*25*(a->nz) - 5*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_6"
int MatSolveTranspose_SeqBAIJ_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);
  PetscLogFlops(2*36*(a->nz) - 6*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose_SeqBAIJ_7"
int MatSolveTranspose_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,*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);
  PetscLogFlops(2*49*(a->nz) - 7*A->n);
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------- */
#undef __FUNCT__
#define __FUNCT__ "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;
  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);
  PetscLogFlops(2*(a->bs2)*(a->nz) - a->bs*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "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;
  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);
  PetscLogFlops(2*49*(a->nz) - 7*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_7_NaturalOrdering"
int MatSolve_SeqBAIJ_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);
  PetscLogFlops(2*36*(a->nz) - 6*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_6"
int MatSolve_SeqBAIJ_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);
  PetscLogFlops(2*36*(a->nz) - 6*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_6_NaturalOrdering"
int MatSolve_SeqBAIJ_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);
  PetscLogFlops(2*36*(a->nz) - 6*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "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;
  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);
  PetscLogFlops(2*25*(a->nz) - 5*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_5_NaturalOrdering"
int MatSolve_SeqBAIJ_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);
  PetscLogFlops(2*25*(a->nz) - 5*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "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;
  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);
  PetscLogFlops(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 __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
int MatSolve_SeqBAIJ_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);
  PetscLogFlops(2*16*(a->nz) - 4*A->n);
  PetscFunctionReturn(0);
}

#if defined (PETSC_HAVE_SSE)

#include PETSC_HAVE_SSE

#undef __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion"
int MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion(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;
  SSE_SCOPE_BEGIN;
  /*
     Note: This code currently uses demotion of double
     to float when performing the mixed-mode computation.
     This may not be numerically reasonable for all applications.
  */
  PREFETCH_NTA(aa+16*ai[1]);

  ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  {
    MatScalar     *v;
    int           jdx,idt,idx,nz,*vi,i,ai16;

    /* Make space in temp stack for 16 Byte Aligned arrays */
    float         ssealignedspace[11],*tmps,*tmpx;
    unsigned long offset = (unsigned long)ssealignedspace % 16;
    if (offset) offset = (16 - offset)/4;
    tmps = &ssealignedspace[offset];
    tmpx = &ssealignedspace[offset+4];

  /* forward solve the lower triangular */
    idx  = 0;
    x[0] = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3];
    v    =  aa + 16*ai[1];

    for (i=1; i<n;) {
      PREFETCH_NTA(&v[8]);
      vi   =  aj      + ai[i];
      nz   =  diag[i] - ai[i];
      idx +=  4;

    /* Demote sum from double to float */
      CONVERT_DOUBLE4_FLOAT4(tmps,&b[idx]);
      LOAD_PS(tmps,XMM7);

      while (nz--) {
        PREFETCH_NTA(&v[16]);
        jdx = 4*(*vi++);

        /* Demote solution (so far) from double to float */
        CONVERT_DOUBLE4_FLOAT4(tmpx,&x[jdx]);

        /* 4x4 Matrix-Vector product with negative accumulation: */
        SSE_INLINE_BEGIN_2(tmpx,v)
          SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)

          /* First Column */
          SSE_COPY_PS(XMM0,XMM6)
          SSE_SHUFFLE(XMM0,XMM0,0x00)
          SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
          SSE_SUB_PS(XMM7,XMM0)

          /* Second Column */
          SSE_COPY_PS(XMM1,XMM6)
          SSE_SHUFFLE(XMM1,XMM1,0x55)
          SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
          SSE_SUB_PS(XMM7,XMM1)

          SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)

          /* Third Column */
          SSE_COPY_PS(XMM2,XMM6)
          SSE_SHUFFLE(XMM2,XMM2,0xAA)
          SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
          SSE_SUB_PS(XMM7,XMM2)

          /* Fourth Column */
          SSE_COPY_PS(XMM3,XMM6)
          SSE_SHUFFLE(XMM3,XMM3,0xFF)
          SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
          SSE_SUB_PS(XMM7,XMM3)
        SSE_INLINE_END_2

        v  += 16;
      }
      v    =  aa + 16*ai[++i];
      PREFETCH_NTA(v);
      STORE_PS(tmps,XMM7);

      /* Promote result from float to double */
      CONVERT_FLOAT4_DOUBLE4(&x[idx],tmps);
    }
    /* backward solve the upper triangular */
    idt  = 4*(n-1);
    ai16 = 16*diag[n-1];
    v    = aa + ai16 + 16;
    for (i=n-1; i>=0;){
      PREFETCH_NTA(&v[8]);
      vi = aj + diag[i] + 1;
      nz = ai[i+1] - diag[i] - 1;

      /* Demote accumulator from double to float */
      CONVERT_DOUBLE4_FLOAT4(tmps,&x[idt]);
      LOAD_PS(tmps,XMM7);

      while (nz--) {
        PREFETCH_NTA(&v[16]);
        idx = 4*(*vi++);

        /* Demote solution (so far) from double to float */
        CONVERT_DOUBLE4_FLOAT4(tmpx,&x[idx]);

        /* 4x4 Matrix-Vector Product with negative accumulation: */
        SSE_INLINE_BEGIN_2(tmpx,v)
          SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)

          /* First Column */
          SSE_COPY_PS(XMM0,XMM6)
          SSE_SHUFFLE(XMM0,XMM0,0x00)
          SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
          SSE_SUB_PS(XMM7,XMM0)

          /* Second Column */
          SSE_COPY_PS(XMM1,XMM6)
          SSE_SHUFFLE(XMM1,XMM1,0x55)
          SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
          SSE_SUB_PS(XMM7,XMM1)

          SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)

          /* Third Column */
          SSE_COPY_PS(XMM2,XMM6)
          SSE_SHUFFLE(XMM2,XMM2,0xAA)
          SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
          SSE_SUB_PS(XMM7,XMM2)

          /* Fourth Column */
          SSE_COPY_PS(XMM3,XMM6)
          SSE_SHUFFLE(XMM3,XMM3,0xFF)
          SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
          SSE_SUB_PS(XMM7,XMM3)
        SSE_INLINE_END_2
        v  += 16;
      }
      v    = aa + ai16;
      ai16 = 16*diag[--i];
      PREFETCH_NTA(aa+ai16+16);
      /*
         Scale the result by the diagonal 4x4 block,
         which was inverted as part of the factorization
      */
      SSE_INLINE_BEGIN_3(v,tmps,aa+ai16)
        /* First Column */
        SSE_COPY_PS(XMM0,XMM7)
        SSE_SHUFFLE(XMM0,XMM0,0x00)
        SSE_MULT_PS_M(XMM0,SSE_ARG_1,FLOAT_0)

        /* Second Column */
        SSE_COPY_PS(XMM1,XMM7)
        SSE_SHUFFLE(XMM1,XMM1,0x55)
        SSE_MULT_PS_M(XMM1,SSE_ARG_1,FLOAT_4)
        SSE_ADD_PS(XMM0,XMM1)

        SSE_PREFETCH_NTA(SSE_ARG_3,FLOAT_24)

        /* Third Column */
        SSE_COPY_PS(XMM2,XMM7)
        SSE_SHUFFLE(XMM2,XMM2,0xAA)
        SSE_MULT_PS_M(XMM2,SSE_ARG_1,FLOAT_8)
        SSE_ADD_PS(XMM0,XMM2)

        /* Fourth Column */
        SSE_COPY_PS(XMM3,XMM7)
        SSE_SHUFFLE(XMM3,XMM3,0xFF)
        SSE_MULT_PS_M(XMM3,SSE_ARG_1,FLOAT_12)
        SSE_ADD_PS(XMM0,XMM3)

        SSE_STORE_PS(SSE_ARG_2,FLOAT_0,XMM0)
      SSE_INLINE_END_3

      /* Promote solution from float to double */
      CONVERT_FLOAT4_DOUBLE4(&x[idt],tmps);

      v    = aa + ai16 + 16;
      idt -= 4;
    }
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PetscLogFlops(2*16*(a->nz) - 4*A->n);
  SSE_SCOPE_END;
  PetscFunctionReturn(0);
}

#endif
#undef __FUNCT__
#define __FUNCT__ "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;
  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);
  PetscLogFlops(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 __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_3_NaturalOrdering"
int MatSolve_SeqBAIJ_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);
  PetscLogFlops(2*9*(a->nz) - 3*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "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;
  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);
  PetscLogFlops(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 __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_2_NaturalOrdering"
int MatSolve_SeqBAIJ_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);
  PetscLogFlops(2*4*(a->nz) - 2*A->n);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "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;
  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);
  PetscLogFlops(2*1*(a->nz) - 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 __FUNCT__
#define __FUNCT__ "MatSolve_SeqBAIJ_1_NaturalOrdering"
int MatSolve_SeqBAIJ_1_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;
  Scalar          s1,x1;
  MatScalar       *v;
  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];
  for (i=1; i<n; i++) {
    v     =  aa      + ai[i];
    vi    =  aj      + ai[i];
    nz    =  diag[i] - ai[i];
    idx   +=  1;
    s1  =  b[idx];
    while (nz--) {
      jdx   = *vi++;
      x1    = x[jdx];
      s1 -= v[0]*x1;
      v    += 1;
    }
    x[idx]   = 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;
    idt  = i;
    s1 = x[idt];
    while (nz--) {
      idx   = *vi++;
      x1    = x[idx];
      s1 -= v[0]*x1;
      v    += 1;
    }
    v        = aa +  diag[i];
    x[idt]   = v[0]*s1;
  }
  ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  PetscLogFlops(2*(a->nz) - A->n);
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------*/
/*
     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.
*/
EXTERN int MatMissingDiagonal_SeqBAIJ(Mat);

#undef __FUNCT__
#define __FUNCT__ "MatILUFactorSymbolic_SeqBAIJ"
int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,MatILUInfo *info,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,dcount = 0;
  int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2,levels,diagonal_fill;
  PetscTruth  col_identity,row_identity;
  PetscReal   f;

  PetscFunctionBegin;
  if (info) {
    f             = info->fill;
    levels        = (int)info->levels;
    diagonal_fill = (int)info->diagonal_fill;
  } else {
    f             = 1.0;
    levels        = 0;
    diagonal_fill = 0;
  }
  ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
  ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
  ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);

  if (!levels && row_identity && col_identity) {  /* special case copy the nonzero structure */
    ierr = MatDuplicate_SeqBAIJ(A,MAT_DO_NOT_COPY_VALUES,fact);CHKERRQ(ierr);
    (*fact)->factor = FACTOR_LU;
    b               = (Mat_SeqBAIJ*)(*fact)->data;
    if (!b->diag) {
      ierr = MatMarkDiagonal_SeqBAIJ(*fact);CHKERRQ(ierr);
    }
    ierr = MatMissingDiagonal_SeqBAIJ(*fact);CHKERRQ(ierr);
    b->row        = isrow;
    b->col        = iscol;
    ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
    ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
    b->icol       = isicol;
    ierr          = PetscMalloc(((*fact)->m+1+b->bs)*sizeof(Scalar),&b->solve_work);CHKERRQ(ierr);
  } else { /* general case perform the symbolic factorization */
    ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
    ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);

    /* get new row pointers */
    ierr = PetscMalloc((n+1)*sizeof(int),&ainew);CHKERRQ(ierr);
    ainew[0] = 0;
    /* don't know how many column pointers are needed so estimate */
    jmax = (int)(f*ai[n] + 1);
    ierr = PetscMalloc((jmax)*sizeof(int),&ajnew);CHKERRQ(ierr);
    /* ajfill is level of fill for each fill entry */
    ierr = PetscMalloc((jmax)*sizeof(int),&ajfill);CHKERRQ(ierr);
    /* fill is a linked list of nonzeros in active row */
    ierr = PetscMalloc((n+1)*sizeof(int),&fill);CHKERRQ(ierr);
    /* im is level for each filled value */
    ierr = PetscMalloc((n+1)*sizeof(int),&im);CHKERRQ(ierr);
    /* dloc is location of diagonal in factor */
    ierr = PetscMalloc((n+1)*sizeof(int),&dloc);CHKERRQ(ierr);
    dloc[0]  = 0;
    for (prow=0; prow<n; prow++) {

      /* copy prow into linked list */
      nzf        = nz  = ai[r[prow]+1] - ai[r[prow]];
      if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix");
      xi         = aj + ai[r[prow]];
      fill[n]    = n;
      fill[prow] = -1; /* marker for diagonal entry */
      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;
      }

      /* make sure diagonal entry is included */
      if (diagonal_fill && fill[prow] == -1) {
	fm = n;
	while (fill[fm] < prow) fm = fill[fm];
	fill[prow] = fill[fm];  /* insert diagonal into linked list */
	fill[fm]   = prow;
	im[prow]   = 0;
	nzf++;
	dcount++;
      }

      nzi = 0;
      row = fill[n];
      while (row < prow) {
	incrlev = im[row] + 1;
	nz      = dloc[row];
	xi      = ajnew  + ainew[row] + nz + 1;
	flev    = ajfill + ainew[row] + nz + 1;
	nnz     = ainew[row+1] - ainew[row] - nz - 1;
	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) {

	/* 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 */
	int maxadd = jmax;
	/* maxadd = (int)(((f*ai[n]+1)*(n-prow+5))/n); */
	if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
	jmax += maxadd;

	/* allocate a longer ajnew and ajfill */
	ierr = PetscMalloc(jmax*sizeof(int),&xi);CHKERRQ(ierr);
	ierr = PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));CHKERRQ(ierr);
	ierr = PetscFree(ajnew);CHKERRQ(ierr);
	ajnew = xi;
	ierr = PetscMalloc(jmax*sizeof(int),&xi);CHKERRQ(ierr);
	ierr = PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));CHKERRQ(ierr);
	ierr = PetscFree(ajfill);CHKERRQ(ierr);
	ajfill = xi;
	realloc++; /* count how many reallocations are needed */
      }
      xi          = ajnew + ainew[prow];
      flev        = ajfill + ainew[prow];
      dloc[prow]  = nzi;
      fm          = fill[n];
      while (nzf--) {
	*xi++   = fm;
	*flev++ = im[fm];
	fm      = fill[fm];
      }
      /* make sure row has diagonal entry */
      if (ajnew[ainew[prow]+dloc[prow]] != prow) {
	SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %d has missing diagonal in factored matrix\n\
    try running with -pc_ilu_nonzeros_along_diagonal or -pc_ilu_diagonal_fill",prow);
      }
    }
    ierr = PetscFree(ajfill);CHKERRQ(ierr);
    ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
    ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
    ierr = PetscFree(fill);CHKERRQ(ierr);
    ierr = PetscFree(im);CHKERRQ(ierr);

    {
      PetscReal af = ((PetscReal)ainew[n])/((PetscReal)ai[n]);
      PetscLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
      PetscLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af);
      PetscLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af);
      PetscLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:for best performance.\n");
      if (diagonal_fill) {
	PetscLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Detected and replace %d missing diagonals",dcount);
      }
    }

    /* put together the new matrix */
    ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
    PetscLogObjectParent(*fact,isicol);
    b = (Mat_SeqBAIJ*)(*fact)->data;
    ierr = PetscFree(b->imax);CHKERRQ(ierr);
    b->singlemalloc = PETSC_FALSE;
    len = bs2*ainew[n]*sizeof(MatScalar);
    /* the next line frees the default space generated by the Create() */
    ierr = PetscFree(b->a);CHKERRQ(ierr);
    ierr = PetscFree(b->ilen);CHKERRQ(ierr);
    ierr = PetscMalloc(len,&b->a);CHKERRQ(ierr);
    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;
    ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
    ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
    b->icol       = isicol;
    ierr = PetscMalloc((bs*n+bs)*sizeof(Scalar),&b->solve_work);CHKERRQ(ierr);
    /* In b structure:  Free imax, ilen, old a, old j.
       Allocate dloc, solve_work, new a, new j */
    PetscLogObjectMemory(*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 = ((PetscReal)ainew[n])/((PetscReal)ai[prow]);
  }

  if (row_identity && col_identity) {
    ierr = MatSeqBAIJ_UpdateFactorizerSolver_NaturalOrdering(*fact);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

int MatSeqBAIJ_UpdateFactorizerSolver_NaturalOrdering(Mat inA)
{
  /*
      Blocksize 2, 3, 4, 5, 6 and 7 have a special faster factorization/solver
      with natural ordering
  */
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)inA->data;

  PetscFunctionBegin;
  switch (a->bs) {
  case 1:
    inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_1;
    inA->ops->solve           = MatSolve_SeqBAIJ_1_NaturalOrdering;
    inA->ops->solvetranspose  = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering;
    PetscLogInfo(inA,"MatILUFactor_SeqBAIJ:Using special in-place natural ordering factor and solve BS=1\n");
  case 2:
    inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering;
    inA->ops->solve           = MatSolve_SeqBAIJ_2_NaturalOrdering;
    inA->ops->solvetranspose  = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering;
    PetscLogInfo(inA,"MatILUFactor_SeqBAIJ:Using special in-place natural ordering factor and solve BS=2\n");
    break;
  case 3:
    inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering;
    inA->ops->solve           = MatSolve_SeqBAIJ_3_NaturalOrdering;
    inA->ops->solvetranspose  = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
    PetscLogInfo(inA,"MatILUFactor_SeqBAIJ:Using special in-place natural ordering factor and solve BS=3\n");
    break;
  case 4:
#if defined(PETSC_HAVE_SSE)
    {
      PetscTruth sse_enabled;
      int        ierr;

      ierr = PetscSSEIsEnabled(&sse_enabled);CHKERRQ(ierr);
      if (sse_enabled) {
        inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE;
      } else {
        inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering;
      }
    }
#else
    inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering;
#endif
    if (!a->single_precision_solves) { /* If this option was set, don't clobber this pointer */
      inA->ops->solve           = MatSolve_SeqBAIJ_4_NaturalOrdering;
    }
    inA->ops->solvetranspose  = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering;
    PetscLogInfo(inA,"MatILUFactor_SeqBAIJ:Using special in-place natural ordering factor and solve BS=4\n");
    break;
  case 5:
    inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering;
    inA->ops->solve           = MatSolve_SeqBAIJ_5_NaturalOrdering;
    inA->ops->solvetranspose  = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
    PetscLogInfo(inA,"MatILUFactor_SeqBAIJ:Using special in-place natural ordering factor and solve BS=5\n");
    break;
  case 6:
    inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering;
    inA->ops->solve           = MatSolve_SeqBAIJ_6_NaturalOrdering;
    inA->ops->solvetranspose  = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering;
    PetscLogInfo(inA,"MatILUFactor_SeqBAIJ:Using special in-place natural ordering factor and solve BS=6\n");
    break;
  case 7:
    inA->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_7_NaturalOrdering;
    inA->ops->solvetranspose  = MatSolveTranspose_SeqBAIJ_7_NaturalOrdering;
    inA->ops->solve           = MatSolve_SeqBAIJ_7_NaturalOrdering;
    PetscLogInfo(inA,"MatILUFactor_SeqBAIJ:Using special in-place natural ordering factor and solve BS=7\n");
    break;
  }
  PetscFunctionReturn(0);
}