1:  #include <../src/mat/impls/baij/seq/baij.h>

  3: PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
  4: {
  5:   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ*)A->data;
  6:   PetscErrorCode  ierr;
  7:   const PetscInt  *diag=a->diag,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
  8:   PetscInt        i,nz,idx,idt,oidx;
  9:   const MatScalar *aa=a->a,*v;
 10:   PetscScalar     s1,s2,s3,s4,x1,x2,x3,x4,*x;

 13:   VecCopy(bb,xx);
 14:   VecGetArray(xx,&x);

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

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

 29:     vi = aj + diag[i] + 1;
 30:     nz = ai[i+1] - diag[i] - 1;
 31:     while (nz--) {
 32:       oidx       = 4*(*vi++);
 33:       x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
 34:       x[oidx+1] -= v[4]*s1  +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
 35:       x[oidx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
 36:       x[oidx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
 37:       v         += 16;
 38:     }
 39:     x[idx] = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4;
 40:     idx   += 4;
 41:   }
 42:   /* backward solve the L^T */
 43:   for (i=n-1; i>=0; i--) {
 44:     v   = aa + 16*diag[i] - 16;
 45:     vi  = aj + diag[i] - 1;
 46:     nz  = diag[i] - ai[i];
 47:     idt = 4*i;
 48:     s1  = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt];
 49:     while (nz--) {
 50:       idx       = 4*(*vi--);
 51:       x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
 52:       x[idx+1] -=  v[4]*s1 +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
 53:       x[idx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
 54:       x[idx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
 55:       v        -= 16;
 56:     }
 57:   }
 58:   VecRestoreArray(xx,&x);
 59:   PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);
 60:   return(0);
 61: }

 63: PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
 64: {
 65:   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ*)A->data;
 66:   PetscErrorCode  ierr;
 67:   const PetscInt  n=a->mbs,*vi,*ai=a->i,*aj=a->j,*diag=a->diag;
 68:   PetscInt        nz,idx,idt,j,i,oidx;
 69:   const PetscInt  bs =A->rmap->bs,bs2=a->bs2;
 70:   const MatScalar *aa=a->a,*v;
 71:   PetscScalar     s1,s2,s3,s4,x1,x2,x3,x4,*x;

 74:   VecCopy(bb,xx);
 75:   VecGetArray(xx,&x);

 77:   /* forward solve the U^T */
 78:   idx = 0;
 79:   for (i=0; i<n; i++) {
 80:     v = aa + bs2*diag[i];
 81:     /* multiply by the inverse of the block diagonal */
 82:     x1 = x[idx];   x2 = x[1+idx];  x3 = x[2+idx];  x4 = x[3+idx];
 83:     s1 =  v[0]*x1  +  v[1]*x2  + v[2]*x3  + v[3]*x4;
 84:     s2 =  v[4]*x1  +  v[5]*x2  + v[6]*x3  + v[7]*x4;
 85:     s3 =  v[8]*x1  +  v[9]*x2  + v[10]*x3 + v[11]*x4;
 86:     s4 =  v[12]*x1 +  v[13]*x2 + v[14]*x3 + v[15]*x4;
 87:     v -= bs2;

 89:     vi = aj + diag[i] - 1;
 90:     nz = diag[i] - diag[i+1] - 1;
 91:     for (j=0; j>-nz; j--) {
 92:       oidx       = bs*vi[j];
 93:       x[oidx]   -=  v[0]*s1  +  v[1]*s2  + v[2]*s3  + v[3]*s4;
 94:       x[oidx+1] -=  v[4]*s1  +  v[5]*s2  + v[6]*s3  + v[7]*s4;
 95:       x[oidx+2] -=  v[8]*s1  +  v[9]*s2  + v[10]*s3 + v[11]*s4;
 96:       x[oidx+3] -=  v[12]*s1 +  v[13]*s2 + v[14]*s3 + v[15]*s4;
 97:       v         -= bs2;
 98:     }
 99:     x[idx] = s1;x[1+idx] = s2;  x[2+idx] = s3;  x[3+idx] = s4;
100:     idx   += bs;
101:   }
102:   /* backward solve the L^T */
103:   for (i=n-1; i>=0; i--) {
104:     v   = aa + bs2*ai[i];
105:     vi  = aj + ai[i];
106:     nz  = ai[i+1] - ai[i];
107:     idt = bs*i;
108:     s1  = x[idt];  s2 = x[1+idt];  s3 = x[2+idt];  s4 = x[3+idt];
109:     for (j=0; j<nz; j++) {
110:       idx       = bs*vi[j];
111:       x[idx]   -=  v[0]*s1  +  v[1]*s2  + v[2]*s3  + v[3]*s4;
112:       x[idx+1] -=  v[4]*s1  +  v[5]*s2  + v[6]*s3  + v[7]*s4;
113:       x[idx+2] -=  v[8]*s1  +  v[9]*s2  + v[10]*s3 + v[11]*s4;
114:       x[idx+3] -=  v[12]*s1 +  v[13]*s2 + v[14]*s3 + v[15]*s4;
115:       v        += bs2;
116:     }
117:   }
118:   VecRestoreArray(xx,&x);
119:   PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);
120:   return(0);
121: }