Date: 2022-08-02T03:13:51+00:00

Actual source code: baijsolvtrannat2.c

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

      3: PetscErrorCode MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
      4: {
      5:   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ*)A->data;
      6:   PetscInt        i,nz,idx,idt,oidx;
      7:   const PetscInt  *diag = a->diag,*vi,n=a->mbs,*ai=a->i,*aj=a->j;
      8:   const MatScalar *aa   =a->a,*v;
      9:   PetscScalar     s1,s2,x1,x2,*x;

     11:   VecCopy(bb,xx);
     12:   VecGetArray(xx,&x);

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

     18:     v = aa + 4*diag[i];
     19:     /* multiply by the inverse of the block diagonal */
     20:     x1 = x[idx];   x2 = x[1+idx];
     21:     s1 = v[0]*x1  +  v[1]*x2;
     22:     s2 = v[2]*x1  +  v[3]*x2;
     23:     v += 4;

     25:     vi = aj + diag[i] + 1;
     26:     nz = ai[i+1] - diag[i] - 1;
     27:     while (nz--) {
     28:       oidx       = 2*(*vi++);
     29:       x[oidx]   -= v[0]*s1  +  v[1]*s2;
     30:       x[oidx+1] -= v[2]*s1  +  v[3]*s2;
     31:       v         += 4;
     32:     }
     33:     x[idx] = s1;x[1+idx] = s2;
     34:     idx   += 2;
     35:   }
     36:   /* backward solve the L^T */
     37:   for (i=n-1; i>=0; i--) {
     38:     v   = aa + 4*diag[i] - 4;
     39:     vi  = aj + diag[i] - 1;
     40:     nz  = diag[i] - ai[i];
     41:     idt = 2*i;
     42:     s1  = x[idt];  s2 = x[1+idt];
     43:     while (nz--) {
     44:       idx       = 2*(*vi--);
     45:       x[idx]   -=  v[0]*s1 +  v[1]*s2;
     46:       x[idx+1] -=  v[2]*s1 +  v[3]*s2;
     47:       v        -= 4;
     48:     }
     49:   }
     50:   VecRestoreArray(xx,&x);
     51:   PetscLogFlops(2.0*4.0*(a->nz) - 2.0*A->cmap->n);
     52:   return 0;
     53: }

     55: PetscErrorCode MatSolveTranspose_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
     56: {
     57:   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ*)A->data;
     58:   const PetscInt  n=a->mbs,*vi,*ai=a->i,*aj=a->j,*diag=a->diag;
     59:   PetscInt        nz,idx,idt,j,i,oidx;
     60:   const PetscInt  bs =A->rmap->bs,bs2=a->bs2;
     61:   const MatScalar *aa=a->a,*v;
     62:   PetscScalar     s1,s2,x1,x2,*x;

     64:   VecCopy(bb,xx);
     65:   VecGetArray(xx,&x);

     67:   /* forward solve the U^T */
     68:   idx = 0;
     69:   for (i=0; i<n; i++) {
     70:     v = aa + bs2*diag[i];
     71:     /* multiply by the inverse of the block diagonal */
     72:     x1 = x[idx];   x2 = x[1+idx];
     73:     s1 = v[0]*x1  +  v[1]*x2;
     74:     s2 = v[2]*x1  +  v[3]*x2;
     75:     v -= bs2;

     77:     vi = aj + diag[i] - 1;
     78:     nz = diag[i] - diag[i+1] - 1;
     79:     for (j=0; j>-nz; j--) {
     80:       oidx       = bs*vi[j];
     81:       x[oidx]   -= v[0]*s1  +  v[1]*s2;
     82:       x[oidx+1] -= v[2]*s1  +  v[3]*s2;
     83:       v         -= bs2;
     84:     }
     85:     x[idx] = s1;x[1+idx] = s2;
     86:     idx   += bs;
     87:   }
     88:   /* backward solve the L^T */
     89:   for (i=n-1; i>=0; i--) {
     90:     v   = aa + bs2*ai[i];
     91:     vi  = aj + ai[i];
     92:     nz  = ai[i+1] - ai[i];
     93:     idt = bs*i;
     94:     s1  = x[idt];  s2 = x[1+idt];
     95:     for (j=0; j<nz; j++) {
     96:       idx       = bs*vi[j];
     97:       x[idx]   -=  v[0]*s1 +  v[1]*s2;
     98:       x[idx+1] -=  v[2]*s1 +  v[3]*s2;
     99:       v        += bs2;
    100:     }
    101:   }
    102:   VecRestoreArray(xx,&x);
    103:   PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);
    104:   return 0;
    105: }