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

     20:   PetscCall(ISGetIndices(isrow, &rout));
     21:   r = rout;
     22:   PetscCall(ISGetIndices(iscol, &cout));
     23:   c = cout;

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

     28:   /* forward solve the U^T */
     29:   for (i = 0; i < n; i++) {
     30:     v  = aa + adiag[i + 1] + 1;
     31:     vi = aj + adiag[i + 1] + 1;
     32:     nz = adiag[i] - adiag[i + 1] - 1;
     33:     s1 = tmp[i];
     34:     s1 *= v[nz]; /* multiply by inverse of diagonal entry */
     35:     for (j = 0; j < nz; j++) tmp[vi[j]] -= s1 * v[j];
     36:     tmp[i] = s1;
     37:   }

     39:   /* backward solve the L^T */
     40:   for (i = n - 1; i >= 0; i--) {
     41:     v  = aa + ai[i];
     42:     vi = aj + ai[i];
     43:     nz = ai[i + 1] - ai[i];
     44:     s1 = tmp[i];
     45:     for (j = 0; j < nz; j++) tmp[vi[j]] -= s1 * v[j];
     46:   }

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

     51:   PetscCall(ISRestoreIndices(isrow, &rout));
     52:   PetscCall(ISRestoreIndices(iscol, &cout));
     53:   PetscCall(VecRestoreArrayRead(bb, &b));
     54:   PetscCall(VecRestoreArray(xx, &x));

     56:   PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n));
     57:   PetscFunctionReturn(PETSC_SUCCESS);
     58: }

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

     71:   PetscFunctionBegin;
     72:   PetscCall(VecGetArrayRead(bb, &b));
     73:   PetscCall(VecGetArray(xx, &x));
     74:   t = a->solve_work;

     76:   PetscCall(ISGetIndices(isrow, &rout));
     77:   r = rout;
     78:   PetscCall(ISGetIndices(iscol, &cout));
     79:   c = cout;

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

     84:   /* forward solve the U^T */
     85:   for (i = 0; i < n; i++) {
     86:     v = aa + diag[i];
     87:     /* multiply by the inverse of the block diagonal */
     88:     s1 = (*v++) * t[i];
     89:     vi = aj + diag[i] + 1;
     90:     nz = ai[i + 1] - diag[i] - 1;
     91:     while (nz--) t[*vi++] -= (*v++) * s1;
     92:     t[i] = s1;
     93:   }
     94:   /* backward solve the L^T */
     95:   for (i = n - 1; i >= 0; i--) {
     96:     v  = aa + diag[i] - 1;
     97:     vi = aj + diag[i] - 1;
     98:     nz = diag[i] - ai[i];
     99:     s1 = t[i];
    100:     while (nz--) t[*vi--] -= (*v--) * s1;
    101:   }

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

    106:   PetscCall(ISRestoreIndices(isrow, &rout));
    107:   PetscCall(ISRestoreIndices(iscol, &cout));
    108:   PetscCall(VecRestoreArrayRead(bb, &b));
    109:   PetscCall(VecRestoreArray(xx, &x));
    110:   PetscCall(PetscLogFlops(2.0 * (a->nz) - A->cmap->n));
    111:   PetscFunctionReturn(PETSC_SUCCESS);
    112: }