/* 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;
}
__isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
enum isl_dim_type type, unsigned first, unsigned n)
{
unsigned ran_offset;
if (n == 0)
return morph;
morph = isl_morph_cow(morph);
if (!morph)
return NULL;
ran_offset = 1 + isl_space_offset(morph->ran->dim, type);
morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);
morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
if (morph->dom && morph->ran && morph->map && morph->inv)
return morph;
isl_morph_free(morph);
return NULL;
}
/* Compute the affine hull of "bset", where "cone" is the recession cone
* of "bset".
*
* We first compute a unimodular transformation that puts the unbounded
* directions in the last dimensions. In particular, we take a transformation
* that maps all equalities to equalities (in HNF) on the first dimensions.
* Let x be the original dimensions and y the transformed, with y_1 bounded
* and y_2 unbounded.
*
* [ y_1 ] [ y_1 ] [ Q_1 ]
* x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x
*
* Let's call the input basic set S. We compute S' = preimage(S, U)
* and drop the final dimensions including any constraints involving them.
* This results in set S''.
* Then we compute the affine hull A'' of S''.
* Let F y_1 >= g be the constraint system of A''. In the transformed
* space the y_2 are unbounded, so we can add them back without any constraints,
* resulting in
*
* [ y_1 ]
* [ F 0 ] [ y_2 ] >= g
* or
* [ Q_1 ]
* [ F 0 ] [ Q_2 ] x >= g
* or
* F Q_1 x >= g
*
* The affine hull in the original space is then obtained as
* A = preimage(A'', Q_1).
*/
static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
struct isl_basic_set *cone)
{
unsigned total;
unsigned cone_dim;
struct isl_basic_set *hull;
struct isl_mat *M, *U, *Q;
if (!bset || !cone)
goto error;
total = isl_basic_set_total_dim(cone);
cone_dim = total - cone->n_eq;
M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
M = isl_mat_left_hermite(M, 0, &U, &Q);
if (!M)
goto error;
isl_mat_free(M);
U = isl_mat_lin_to_aff(U);
bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim,
cone_dim);
bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
Q = isl_mat_lin_to_aff(Q);
Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
if (bset && bset->sample && bset->sample->size == 1 + total)
bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
hull = uset_affine_hull_bounded(bset);
if (!hull)
isl_mat_free(U);
else {
struct isl_vec *sample = isl_vec_copy(hull->sample);
U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim);
if (sample && sample->size > 0)
sample = isl_mat_vec_product(U, sample);
else
isl_mat_free(U);
hull = isl_basic_set_preimage(hull, Q);
if (hull) {
isl_vec_free(hull->sample);
hull->sample = sample;
} else
isl_vec_free(sample);
}
isl_basic_set_free(cone);
return hull;
error:
isl_basic_set_free(bset);
isl_basic_set_free(cone);
return NULL;
}
