Date: 2022-03-04T17:37:49+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:   PetscErrorCode  ierr;
      7:   PetscInt        i,nz,idx,idt,oidx;
      8:   const PetscInt  *diag = a->diag,*vi,n=a->mbs,*ai=a->i,*aj=a->j;
      9:   const MatScalar *aa   =a->a,*v;
     10:   PetscScalar     s1,s2,x1,x2,*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 + 4*diag[i];
     21:     /* multiply by the inverse of the block diagonal */
     22:     x1 = x[idx];   x2 = x[1+idx];
     23:     s1 = v[0]*x1  +  v[1]*x2;
     24:     s2 = v[2]*x1  +  v[3]*x2;
     25:     v += 4;

     27:     vi = aj + diag[i] + 1;
     28:     nz = ai[i+1] - diag[i] - 1;
     29:     while (nz--) {
     30:       oidx       = 2*(*vi++);
     31:       x[oidx]   -= v[0]*s1  +  v[1]*s2;
     32:       x[oidx+1] -= v[2]*s1  +  v[3]*s2;
     33:       v         += 4;
     34:     }
     35:     x[idx] = s1;x[1+idx] = s2;
     36:     idx   += 2;
     37:   }
     38:   /* backward solve the L^T */
     39:   for (i=n-1; i>=0; i--) {
     40:     v   = aa + 4*diag[i] - 4;
     41:     vi  = aj + diag[i] - 1;
     42:     nz  = diag[i] - ai[i];
     43:     idt = 2*i;
     44:     s1  = x[idt];  s2 = x[1+idt];
     45:     while (nz--) {
     46:       idx       = 2*(*vi--);
     47:       x[idx]   -=  v[0]*s1 +  v[1]*s2;
     48:       x[idx+1] -=  v[2]*s1 +  v[3]*s2;
     49:       v        -= 4;
     50:     }
     51:   }
     52:   VecRestoreArray(xx,&x);
     53:   PetscLogFlops(2.0*4.0*(a->nz) - 2.0*A->cmap->n);
     54:   return(0);
     55: }

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

     68:   VecCopy(bb,xx);
     69:   VecGetArray(xx,&x);

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

     81:     vi = aj + diag[i] - 1;
     82:     nz = diag[i] - diag[i+1] - 1;
     83:     for (j=0; j>-nz; j--) {
     84:       oidx       = bs*vi[j];
     85:       x[oidx]   -= v[0]*s1  +  v[1]*s2;
     86:       x[oidx+1] -= v[2]*s1  +  v[3]*s2;
     87:       v         -= bs2;
     88:     }
     89:     x[idx] = s1;x[1+idx] = s2;
     90:     idx   += bs;
     91:   }
     92:   /* backward solve the L^T */
     93:   for (i=n-1; i>=0; i--) {
     94:     v   = aa + bs2*ai[i];
     95:     vi  = aj + ai[i];
     96:     nz  = ai[i+1] - ai[i];
     97:     idt = bs*i;
     98:     s1  = x[idt];  s2 = x[1+idt];
     99:     for (j=0; j<nz; j++) {
    100:       idx       = bs*vi[j];
    101:       x[idx]   -=  v[0]*s1 +  v[1]*s2;
    102:       x[idx+1] -=  v[2]*s1 +  v[3]*s2;
    103:       v        += bs2;
    104:     }
    105:   }
    106:   VecRestoreArray(xx,&x);
    107:   PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);
    108:   return(0);
    109: }