From cd27379ca353c51621a61af17411585d2542f6e5 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Wed, 19 Dec 2018 21:58:19 -0500 Subject: [PATCH] Revert "... add completely_positive_operators_gens()." This reverts commit 3d6ec3f4f138a6278be4f393b491aa1ac2bbffa8. The new function was mathematically wrong, and can't be fixed. Oops. --- mjo/cone/completely_positive.py | 54 --------------------------------- 1 file changed, 54 deletions(-) diff --git a/mjo/cone/completely_positive.py b/mjo/cone/completely_positive.py index 15be558..8638a63 100644 --- a/mjo/cone/completely_positive.py +++ b/mjo/cone/completely_positive.py @@ -195,57 +195,3 @@ def is_extreme_completely_positive(A): # factorization into `$XX^{T}$` may not be unique! raise ValueError('Unable to determine extremity of ``A``.') - - -def completely_positive_operators_gens(K): - r""" - Return a list of generators (matrices) for the completely-positive - cone of ``K``. - - INPUT: - - - ``K`` -- a closed convex rational polyhedral cone. - - OUTPUT: - - A list of matrices, the conic hull of which is the - completely-positive cone of ``K``. - - SETUP:: - - sage: from mjo.cone.completely_positive import ( - ....: completely_positive_operators_gens, - ....: is_completely_positive ) - sage: from mjo.cone.nonnegative_orthant import nonnegative_orthant - sage: from mjo.matrix_vector import isomorphism - - EXAMPLES:: - - sage: K = nonnegative_orthant(2) - sage: completely_positive_operators_gens(K) - [ - [1 0] [0 0] - [0 0], [0 1] - ] - sage: all( is_completely_positive(M) - ....: for M in completely_positive_operators_gens(K) ) - True - - TESTS: - - The completely-positive cone of ``K`` is subdual:: - - sage: K = random_cone(max_ambient_dim=8, max_rays=10) - sage: cp_gens = completely_positive_operators_gens(K) - sage: n = K.lattice_dim() - sage: M = MatrixSpace(QQ, n, n) - sage: (p, p_inv) = isomorphism(M) - sage: L = ToricLattice(n**2) - sage: cp_cone = Cone( (p(m) for m in cp_gens), lattice=L ) - sage: copos_cone = Cone(cp_cone.dual().rays(), lattice=L ) - sage: all( x in copos_cone for x in cp_cone ) - True - - """ - return [ x.tensor_product(x) for x in K ] - -- 2.43.2