From cd746d047748a9aa56c51bb78c3db9882ea16a16 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Wed, 30 Dec 2015 23:22:41 -0500 Subject: [PATCH] More examples and a better implementation for random_element(). --- mjo/cone/cone.py | 37 ++++++++++++++++++++++++++++--------- 1 file changed, 28 insertions(+), 9 deletions(-) diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 0209433..a5f5f2f 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -99,27 +99,46 @@ def random_element(K): sage: random_element(K) (0, 0, 0) + A random element of the nonnegative orthant should have all + components nonnegative:: + + sage: set_random_seed() + sage: K = Cone([(1,0,0),(0,1,0),(0,0,1)]) + sage: all([ x >= 0 for x in random_element(K) ]) + True + TESTS: - Any cone should contain an element of itself:: + Any cone should contain a random element of itself:: sage: set_random_seed() - sage: K = random_cone(max_rays = 8) + sage: K = random_cone(max_ambient_dim=8) sage: K.contains(random_element(K)) True + A strictly convex cone contains no lines, and thus no negative + multiples of any of its elements besides zero:: + + sage: set_random_seed() + sage: K = random_cone(max_ambient_dim=8, strictly_convex=True) + sage: x = random_element(K) + sage: x.is_zero() or not K.contains(-x) + True + + The sum of random elements of a cone lies in the cone:: + + sage: set_random_seed() + sage: K = random_cone(max_ambient_dim=8) + sage: K.contains(sum([random_element(K) for i in range(10)])) + True + """ V = K.lattice().vector_space() - F = V.base_ring() - coefficients = [ F.random_element().abs() for i in range(K.nrays()) ] - vector_gens = map(V, K.rays()) - scaled_gens = [ coefficients[i]*vector_gens[i] - for i in range(len(vector_gens)) ] + scaled_gens = [ V.base_field().random_element().abs()*V(r) for r in K ] # Make sure we return a vector. Without the coercion, we might # return ``0`` when ``K`` has no rays. - v = V(sum(scaled_gens)) - return v + return V(sum(scaled_gens)) def positive_operator_gens(K): -- 2.44.2