=head3 Lexicographic Optimization
-Given a basic set C<bset> and a zero-dimensional domain C<dom>,
+Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
the following functions
compute a set that contains the lexicographic minimum or maximum
-of the elements in C<bset> for those values of the parameters
+of the elements in C<set> (or C<bset>) for those values of the parameters
that satisfy C<dom>.
If C<empty> is not C<NULL>, then C<*empty> is assigned a set
-that contains the parameter values in C<dom> for which C<bset>
+that contains the parameter values in C<dom> for which C<set> (or C<bset>)
has no elements.
In other words, the union of the parameter values
for which the result is non-empty and of C<*empty>
__isl_take isl_basic_set *bset,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
+ __isl_give isl_set *isl_set_partial_lexmin(
+ __isl_take isl_set *set, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
+ __isl_give isl_set *isl_set_partial_lexmax(
+ __isl_take isl_set *set, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
-Given a basic set C<bset>, the following functions simply
+Given a (basic) set C<set> (or C<bset>), the following functions simply
return a set containing the lexicographic minimum or maximum
-of the elements in C<bset>.
+of the elements in C<set> (or C<bset>).
__isl_give isl_set *isl_basic_set_lexmin(
__isl_take isl_basic_set *bset);
__isl_give isl_set *isl_basic_set_lexmax(
__isl_take isl_basic_set *bset);
+ __isl_give isl_set *isl_set_lexmin(
+ __isl_take isl_set *set);
+ __isl_give isl_set *isl_set_lexmax(
+ __isl_take isl_set *set);
-Given a basic relation C<bmap> and a domain C<dom>,
+Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
the following functions
compute a relation that maps each element of C<dom>
to the single lexicographic minimum or maximum
of the elements that are associated to that same
-element in C<bmap>.
+element in C<map> (or C<bmap>).
If C<empty> is not C<NULL>, then C<*empty> is assigned a set
that contains the elements in C<dom> that do not map
-to any elements in C<bmap>.
+to any elements in C<map> (or C<bmap>).
In other words, the union of the domain of the result and of C<*empty>
is equal to C<dom>.
__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
+ __isl_give isl_map *isl_map_partial_lexmax(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
+ __isl_give isl_map *isl_map_partial_lexmin(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
-Given a basic map C<bmap>, the following functions simply
+Given a (basic) map C<map> (or C<bmap>), the following functions simply
return a map mapping each element in the domain of
-C<bmap> to the lexicographic minimum or maximum
+C<map> (or C<bmap>) to the lexicographic minimum or maximum
of all elements associated to that element.
__isl_give isl_map *isl_basic_map_lexmin(
__isl_take isl_basic_map *bmap);
__isl_give isl_map *isl_basic_map_lexmax(
__isl_take isl_basic_map *bmap);
+ __isl_give isl_map *isl_map_lexmin(
+ __isl_take isl_map *map);
+ __isl_give isl_map *isl_map_lexmax(
+ __isl_take isl_map *map);
=head1 Applications
dom, empty);
}
+/* Given a basic map "bmap", compute the lexicograhically minimal
+ * (or maximal) image element for each domain element in dom.
+ * Set *empty to those elements in dom that do not have an image element.
+ *
+ * We first make sure the basic sets in dom are disjoint and then
+ * simply collect the results over each of the basic sets separately.
+ * We could probably improve the efficiency a bit by moving the union
+ * domain down into the parametric integer programming.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt(
+ __isl_take isl_basic_map *bmap, __isl_take isl_set *dom,
+ __isl_give isl_set **empty, int max)
+{
+ int i;
+ struct isl_map *res;
+
+ dom = isl_set_make_disjoint(dom);
+ if (!dom)
+ goto error;
+
+ if (isl_set_fast_is_empty(dom)) {
+ res = isl_map_empty_like_basic_map(bmap);
+ *empty = isl_set_empty_like(dom);
+ isl_set_free(dom);
+ isl_basic_map_free(bmap);
+ return res;
+ }
+
+ res = isl_basic_map_partial_lexopt(isl_basic_map_copy(bmap),
+ isl_basic_set_copy(dom->p[0]), empty, max);
+
+ for (i = 1; i < dom->n; ++i) {
+ struct isl_map *res_i;
+ struct isl_set *empty_i;
+
+ res_i = isl_basic_map_partial_lexopt(isl_basic_map_copy(bmap),
+ isl_basic_set_copy(dom->p[i]), &empty_i, max);
+
+ res = isl_map_union_disjoint(res, res_i);
+ *empty = isl_set_union_disjoint(*empty, empty_i);
+ }
+
+ isl_set_free(dom);
+ isl_basic_map_free(bmap);
+ return res;
+error:
+ *empty = NULL;
+ isl_set_free(dom);
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+/* Given a map "map", compute the lexicograhically minimal
+ * (or maximal) image element for each domain element in dom.
+ * Set *empty to those elements in dom that do not have an image element.
+ *
+ * We first compute the lexicographically minimal or maximal element
+ * in the first basic map. This results in a partial solution "res"
+ * and a subset "todo" of dom that still need to be handled.
+ * We then consider each of the remaining maps in "map" and successively
+ * improve both "res" and "todo".
+ *
+ * Let res^k and todo^k be the results after k steps and let i = k + 1.
+ * Assume we are computing the lexicographical maximum.
+ * We first intersect basic map i with a relation that maps elements
+ * to elements that are lexicographically larger than the image elements
+ * in res^k and the compute the maximum image element of this intersection.
+ * The result ("better") corresponds to those image elements in basic map i
+ * that are better than what we had before. The remainder ("keep") are the
+ * domain elements for which the image element in res_k was better.
+ * We also compute the lexicographical maximum of basic map i in todo^k.
+ * res^i is the result of the operation + better + those elements in
+ * res^k that we should keep
+ * todo^i is the remainder of the maximum operation on todo^k.
+ */
+static __isl_give isl_map *isl_map_partial_lexopt(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty, int max)
+{
+ int i;
+ struct isl_map *res;
+ struct isl_set *todo;
+
+ if (!map || !dom)
+ goto error;
+
+ if (isl_map_fast_is_empty(map)) {
+ if (empty)
+ *empty = dom;
+ else
+ isl_set_free(dom);
+ return map;
+ }
+
+ res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
+ isl_set_copy(dom), &todo, max);
+
+ for (i = 1; i < map->n; ++i) {
+ struct isl_map *lt;
+ struct isl_map *better;
+ struct isl_set *keep;
+ struct isl_map *res_i;
+ struct isl_set *todo_i;
+ struct isl_dim *dim = isl_map_get_dim(res);
+
+ dim = isl_dim_range(dim);
+ if (max)
+ lt = isl_map_lex_lt(dim);
+ else
+ lt = isl_map_lex_gt(dim);
+ lt = isl_map_apply_range(isl_map_copy(res), lt);
+ lt = isl_map_intersect(lt,
+ isl_map_from_basic_map(isl_basic_map_copy(map->p[i])));
+ better = isl_map_partial_lexopt(lt,
+ isl_map_domain(isl_map_copy(res)),
+ &keep, max);
+
+ res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
+ todo, &todo_i, max);
+
+ res = isl_map_intersect_domain(res, keep);
+ res = isl_map_union_disjoint(res, res_i);
+ res = isl_map_union_disjoint(res, better);
+ todo = todo_i;
+ }
+
+ isl_set_free(dom);
+ isl_map_free(map);
+
+ if (empty)
+ *empty = todo;
+ else
+ isl_set_free(todo);
+
+ return res;
+error:
+ if (empty)
+ *empty = NULL;
+ isl_set_free(dom);
+ isl_map_free(map);
+ return NULL;
+}
+
+__isl_give isl_map *isl_map_partial_lexmax(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty)
+{
+ return isl_map_partial_lexopt(map, dom, empty, 1);
+}
+
+__isl_give isl_map *isl_map_partial_lexmin(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty)
+{
+ return isl_map_partial_lexopt(map, dom, empty, 0);
+}
+
+__isl_give isl_set *isl_set_partial_lexmin(
+ __isl_take isl_set *set, __isl_take isl_set *dom,
+ __isl_give isl_set **empty)
+{
+ return (struct isl_set *)
+ isl_map_partial_lexmin((struct isl_map *)set,
+ dom, empty);
+}
+
+__isl_give isl_set *isl_set_partial_lexmax(
+ __isl_take isl_set *set, __isl_take isl_set *dom,
+ __isl_give isl_set **empty)
+{
+ return (struct isl_set *)
+ isl_map_partial_lexmax((struct isl_map *)set,
+ dom, empty);
+}
+
__isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
{
struct isl_basic_set *dom = NULL;
return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
}
+__isl_give isl_map *isl_map_lexopt(__isl_take isl_map *map, int max)
+{
+ struct isl_set *dom = NULL;
+ struct isl_dim *dom_dim;
+
+ if (!map)
+ goto error;
+ dom_dim = isl_dim_domain(isl_dim_copy(map->dim));
+ dom = isl_set_universe(dom_dim);
+ return isl_map_partial_lexopt(map, dom, NULL, max);
+error:
+ isl_map_free(map);
+ return NULL;
+}
+
+__isl_give isl_map *isl_map_lexmin(__isl_take isl_map *map)
+{
+ return isl_map_lexopt(map, 0);
+}
+
+__isl_give isl_map *isl_map_lexmax(__isl_take isl_map *map)
+{
+ return isl_map_lexopt(map, 1);
+}
+
+__isl_give isl_set *isl_set_lexmin(__isl_take isl_set *set)
+{
+ return (isl_set *)isl_map_lexmin((isl_map *)set);
+}
+
+__isl_give isl_set *isl_set_lexmax(__isl_take isl_set *set)
+{
+ return (isl_set *)isl_map_lexmax((isl_map *)set);
+}
+
static struct isl_map *isl_map_reset_dim(struct isl_map *map,
struct isl_dim *dim)
{
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