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: }