From fdc03da648dd989527ff4c12ccce04c990869e3b Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Wed, 6 Jan 2016 08:44:50 -0500 Subject: [PATCH] Add some Proposition 3 tests for positive operators. --- mjo/cone/cone.py | 38 ++++++++++++++++++++++++++++++++++++-- 1 file changed, 36 insertions(+), 2 deletions(-) diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 28a8423..d33a1c5 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -217,12 +217,46 @@ def positive_operator_gens(K): TESTS: - A positive operator on a cone should send its generators into the cone:: + Each positive operator generator should send the generators of the + cone into the cone:: sage: set_random_seed() sage: K = random_cone(max_ambient_dim=5) sage: pi_of_K = positive_operator_gens(K) - sage: all([K.contains(p*x) for p in pi_of_K for x in K.rays()]) + sage: all([ K.contains(P*x) for P in pi_of_K for x in K ]) + True + + Each positive operator generator should send a random element of the + cone into the cone:: + + sage: set_random_seed() + sage: K = random_cone(max_ambient_dim=5) + sage: pi_of_K = positive_operator_gens(K) + sage: all([ K.contains(P*K.random_element()) for P in pi_of_K ]) + True + + A random element of the positive operator cone should send the + generators of the cone into the cone:: + + sage: set_random_seed() + sage: K = random_cone(max_ambient_dim=5) + sage: pi_of_K = positive_operator_gens(K) + sage: L = ToricLattice(K.lattice_dim()**2) + sage: pi_cone = Cone([ g.list() for g in pi_of_K ], lattice=L) + sage: P = matrix(K.lattice_dim(), pi_cone.random_element().list()) + sage: all([ K.contains(P*x) for x in K ]) + True + + A random element of the positive operator cone should send a random + element of the cone into the cone:: + + sage: set_random_seed() + sage: K = random_cone(max_ambient_dim=5) + sage: pi_of_K = positive_operator_gens(K) + sage: L = ToricLattice(K.lattice_dim()**2) + sage: pi_cone = Cone([ g.list() for g in pi_of_K ], lattice=L) + sage: P = matrix(K.lattice_dim(), pi_cone.random_element().list()) + sage: K.contains(P*K.random_element()) True The dimension of the cone of positive operators is given by the -- 2.43.2