X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fcompletely_positive.py;h=3dc66b454dfb8a85a4aa2ba4a4be03978a5b3690;hb=7af2b9d146a6bf2fb8acc3c342983de577b417ce;hp=15be5587cca1e85f50121fd020eb727fda568c36;hpb=3d6ec3f4f138a6278be4f393b491aa1ac2bbffa8;p=sage.d.git

diff --git a/mjo/cone/completely_positive.py b/mjo/cone/completely_positive.py
index 15be558..3dc66b4 100644
--- a/mjo/cone/completely_positive.py
+++ b/mjo/cone/completely_positive.py
@@ -1,4 +1,4 @@
-"""
+r"""
 The completely positive cone `$\mathcal{K}$` over `\mathbb{R}^{n}$` is
 the set of all matrices `$A$`of the form `$\sum uu^{T}$` for `$u \in
 \mathbb{R}^{n}_{+}$`. Equivalently, `$A = XX{T}$` where all entries of
@@ -6,7 +6,7 @@ the set of all matrices `$A$`of the form `$\sum uu^{T}$` for `$u \in
 """
 
 from sage.all import *
-from mjo.cone.symmetric_psd import factor_psd, is_symmetric_psd
+from mjo.cone.symmetric_psd import factor_psd
 from mjo.cone.doubly_nonnegative import (is_doubly_nonnegative,
                                          is_extreme_doubly_nonnegative)
 
@@ -89,7 +89,7 @@ def is_completely_positive(A):
         msg = 'The matrix ``A`` cannot be symbolic.'
         raise ValueError.new(msg)
 
-    if not is_symmetric_psd(A):
+    if not A.is_positive_semidefinite():
         return False
 
     n = A.nrows() # Makes sense since ``A`` is symmetric.
@@ -176,7 +176,7 @@ def is_extreme_completely_positive(A):
         msg = 'The matrix ``A`` cannot be symbolic.'
         raise ValueError(msg)
 
-    if not is_symmetric_psd(A):
+    if not A.is_positive_semidefinite():
         return False
 
     n = A.nrows() # Makes sense since ``A`` is symmetric.
@@ -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 ]
-