Actual source code: baijsolvtrannat1.c

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

      3: PetscErrorCode MatSolveTranspose_SeqBAIJ_1_NaturalOrdering(Mat A, Vec bb, Vec xx)
      4: {
      5:   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
      6:   const PetscInt    *adiag = a->diag, *ai = a->i, *aj = a->j, *vi;
      7:   PetscInt           i, n = a->mbs, j;
      8:   PetscInt           nz;
      9:   PetscScalar       *x, *tmp, s1;
     10:   const MatScalar   *aa = a->a, *v;
     11:   const PetscScalar *b;

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

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

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

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

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

     44:   PetscCall(VecRestoreArrayRead(bb, &b));
     45:   PetscCall(VecRestoreArray(xx, &x));

     47:   PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n));
     48:   PetscFunctionReturn(PETSC_SUCCESS);
     49: }

     51: PetscErrorCode MatSolveTranspose_SeqBAIJ_1_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
     52: {
     53:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
     54:   PetscInt         i, nz;
     55:   const PetscInt  *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
     56:   const MatScalar *aa = a->a, *v;
     57:   PetscScalar      s1, *x;

     59:   PetscFunctionBegin;
     60:   PetscCall(VecCopy(bb, xx));
     61:   PetscCall(VecGetArray(xx, &x));

     63:   /* forward solve the U^T */
     64:   for (i = 0; i < n; i++) {
     65:     v = aa + diag[i];
     66:     /* multiply by the inverse of the block diagonal */
     67:     s1 = (*v++) * x[i];
     68:     vi = aj + diag[i] + 1;
     69:     nz = ai[i + 1] - diag[i] - 1;
     70:     while (nz--) x[*vi++] -= (*v++) * s1;
     71:     x[i] = s1;
     72:   }
     73:   /* backward solve the L^T */
     74:   for (i = n - 1; i >= 0; i--) {
     75:     v  = aa + diag[i] - 1;
     76:     vi = aj + diag[i] - 1;
     77:     nz = diag[i] - ai[i];
     78:     s1 = x[i];
     79:     while (nz--) x[*vi--] -= (*v--) * s1;
     80:   }
     81:   PetscCall(VecRestoreArray(xx, &x));
     82:   PetscCall(PetscLogFlops(2.0 * (a->nz) - A->cmap->n));
     83:   PetscFunctionReturn(PETSC_SUCCESS);
     84: }