/* Given a set of equalities * * B(y) + A x = 0 (*) * * compute and return an affine transformation T, * * y = T y' * * that bijectively maps the integer vectors y' to integer * vectors y that satisfy the modulo constraints for some value of x. * * Let [H 0] be the Hermite Normal Form of A, i.e., * * A = [H 0] Q * * Then y is a solution of (*) iff * * H^-1 B(y) (= - [I 0] Q x) * * is an integer vector. Let d be the common denominator of H^-1. * We impose * * d H^-1 B(y) = 0 mod d * * and compute the solution using isl_mat_parameter_compression. */ __isl_give isl_mat *isl_mat_parameter_compression_ext(__isl_take isl_mat *B, __isl_take isl_mat *A) { isl_ctx *ctx; isl_vec *d; int n_row, n_col; if (!A) return isl_mat_free(B); ctx = isl_mat_get_ctx(A); n_row = A->n_row; n_col = A->n_col; A = isl_mat_left_hermite(A, 0, NULL, NULL); A = isl_mat_drop_cols(A, n_row, n_col - n_row); A = isl_mat_lin_to_aff(A); A = isl_mat_right_inverse(A); d = isl_vec_alloc(ctx, n_row); if (A) d = isl_vec_set(d, A->row[0][0]); A = isl_mat_drop_rows(A, 0, 1); A = isl_mat_drop_cols(A, 0, 1); B = isl_mat_product(A, B); return isl_mat_parameter_compression(B, d); }
/* Construct a parameter compression for "bset". * We basically just call isl_mat_parameter_compression with the right input * and then extend the resulting matrix to include the variables. * * Let the equalities be given as * * B(p) + A x = 0 * * and let [H 0] be the Hermite Normal Form of A, then * * H^-1 B(p) * * needs to be integer, so we impose that each row is divisible by * the denominator. */ __isl_give isl_morph *isl_basic_set_parameter_compression( __isl_keep isl_basic_set *bset) { unsigned nparam; unsigned nvar; int n_eq; isl_mat *H, *B; isl_vec *d; isl_mat *map, *inv; isl_basic_set *dom, *ran; if (!bset) return NULL; if (isl_basic_set_plain_is_empty(bset)) return isl_morph_empty(bset); if (bset->n_eq == 0) return isl_morph_identity(bset); isl_assert(bset->ctx, bset->n_div == 0, return NULL); n_eq = bset->n_eq; nparam = isl_basic_set_dim(bset, isl_dim_param); nvar = isl_basic_set_dim(bset, isl_dim_set); isl_assert(bset->ctx, n_eq <= nvar, return NULL); d = isl_vec_alloc(bset->ctx, n_eq); B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam); H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar); H = isl_mat_left_hermite(H, 0, NULL, NULL); H = isl_mat_drop_cols(H, n_eq, nvar - n_eq); H = isl_mat_lin_to_aff(H); H = isl_mat_right_inverse(H); if (!H || !d) goto error; isl_seq_set(d->el, H->row[0][0], d->size); H = isl_mat_drop_rows(H, 0, 1); H = isl_mat_drop_cols(H, 0, 1); B = isl_mat_product(H, B); inv = isl_mat_parameter_compression(B, d); inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar)); map = isl_mat_right_inverse(isl_mat_copy(inv)); dom = isl_basic_set_universe(isl_space_copy(bset->dim)); ran = isl_basic_set_universe(isl_space_copy(bset->dim)); return isl_morph_alloc(dom, ran, map, inv); error: isl_mat_free(H); isl_mat_free(B); isl_vec_free(d); return NULL; }