Date: 2022-03-31T04:46:52+00:00

Actual source code: baijsolvtran1.c

      1: #include <../src/mat/impls/baij/seq/baij.h>
      2: #include <petsc/private/kernels/blockinvert.h>

      4: PetscErrorCode MatSolveTranspose_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
      5: {
      6:   Mat_SeqBAIJ       *a    = (Mat_SeqBAIJ*)A->data;
      7:   IS                iscol = a->col,isrow = a->row;
      8:   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
      9:   PetscInt          i,n = a->mbs,j;
     10:   PetscInt          nz;
     11:   PetscScalar       *x,*tmp,s1;
     12:   const MatScalar   *aa = a->a,*v;
     13:   const PetscScalar *b;

     15:   VecGetArrayRead(bb,&b);
     16:   VecGetArray(xx,&x);
     17:   tmp  = a->solve_work;

     19:   ISGetIndices(isrow,&rout); r = rout;
     20:   ISGetIndices(iscol,&cout); c = cout;

     22:   /* copy the b into temp work space according to permutation */
     23:   for (i=0; i<n; i++) tmp[i] = b[c[i]];

     25:   /* forward solve the U^T */
     26:   for (i=0; i<n; i++) {
     27:     v   = aa + adiag[i+1] + 1;
     28:     vi  = aj + adiag[i+1] + 1;
     29:     nz  = adiag[i] - adiag[i+1] - 1;
     30:     s1  = tmp[i];
     31:     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
     32:     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
     33:     tmp[i] = s1;
     34:   }

     36:   /* backward solve the L^T */
     37:   for (i=n-1; i>=0; i--) {
     38:     v  = aa + ai[i];
     39:     vi = aj + ai[i];
     40:     nz = ai[i+1] - ai[i];
     41:     s1 = tmp[i];
     42:     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
     43:   }

     45:   /* copy tmp into x according to permutation */
     46:   for (i=0; i<n; i++) x[r[i]] = tmp[i];

     48:   ISRestoreIndices(isrow,&rout);
     49:   ISRestoreIndices(iscol,&cout);
     50:   VecRestoreArrayRead(bb,&b);
     51:   VecRestoreArray(xx,&x);

     53:   PetscLogFlops(2.0*a->nz-A->cmap->n);
     54:   return 0;
     55: }

     57: PetscErrorCode MatSolveTranspose_SeqBAIJ_1_inplace(Mat A,Vec bb,Vec xx)
     58: {
     59:   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
     60:   IS                iscol=a->col,isrow=a->row;
     61:   const PetscInt    *r,*c,*rout,*cout;
     62:   const PetscInt    *diag=a->diag,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
     63:   PetscInt          i,nz;
     64:   const MatScalar   *aa=a->a,*v;
     65:   PetscScalar       s1,*x,*t;
     66:   const PetscScalar *b;

     68:   VecGetArrayRead(bb,&b);
     69:   VecGetArray(xx,&x);
     70:   t    = a->solve_work;

     72:   ISGetIndices(isrow,&rout); r = rout;
     73:   ISGetIndices(iscol,&cout); c = cout;

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

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

     81:     v = aa + diag[i];
     82:     /* multiply by the inverse of the block diagonal */
     83:     s1 = (*v++)*t[i];
     84:     vi = aj + diag[i] + 1;
     85:     nz = ai[i+1] - diag[i] - 1;
     86:     while (nz--) {
     87:       t[*vi++] -= (*v++)*s1;
     88:     }
     89:     t[i] = s1;
     90:   }
     91:   /* backward solve the L^T */
     92:   for (i=n-1; i>=0; i--) {
     93:     v  = aa + diag[i] - 1;
     94:     vi = aj + diag[i] - 1;
     95:     nz = diag[i] - ai[i];
     96:     s1 = t[i];
     97:     while (nz--) {
     98:       t[*vi--] -=  (*v--)*s1;
     99:     }
    100:   }

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

    105:   ISRestoreIndices(isrow,&rout);
    106:   ISRestoreIndices(iscol,&cout);
    107:   VecRestoreArrayRead(bb,&b);
    108:   VecRestoreArray(xx,&x);
    109:   PetscLogFlops(2.0*(a->nz) - A->cmap->n);
    110:   return 0;
    111: }