eja: remove a completed TODO.

[sage.d.git] / mjo / cone / doubly_nonnegative.py

diff --git a/mjo/cone/doubly_nonnegative.py b/mjo/cone/doubly_nonnegative.py
index a30a827d158f3b99d7d9df5d295096e7cc349e0f..e8cacda5cd492100096eff2cf557c8992a34d9b3 100644 (file)
--- a/mjo/cone/doubly_nonnegative.py
+++ b/mjo/cone/doubly_nonnegative.py
@@ -1,4 +1,4 @@
-"""
+r"""
 The doubly-nonnegative cone in `S^{n}` is the set of all such matrices
 that both,
 
@@ -16,7 +16,7 @@ from sage.all import *
 from mjo.cone.symmetric_psd import (factor_psd,
                                     is_symmetric_psd,
                                     random_symmetric_psd)
-from mjo.matrix_vector import isomorphism
+from mjo.basis_repr import basis_repr
 
 
 def is_doubly_nonnegative(A):
@@ -68,7 +68,7 @@ def is_doubly_nonnegative(A):
 
 
 def is_admissible_extreme_rank(r, n):
-    """
+    r"""
     The extreme matrices of the doubly-nonnegative cone have some
     restrictions on their ranks. This function checks to see whether the
     rank ``r`` would be an admissible rank for an ``n``-by-``n`` matrix.
@@ -371,8 +371,8 @@ def is_extreme_doubly_nonnegative(A):
     # whenever we come across an index pair `$(i,j)$` with
     # `$A_{ij} = 0$`.
     spanning_set = []
-    for j in xrange(A.ncols()):
-        for i in xrange(j):
+    for j in range(A.ncols()):
+        for i in range(j):
             if A[i,j] == 0:
                 M = A.matrix_space()
                 S = X.transpose() * (stdE(M,i,j) + stdE(M,j,i)) * X
@@ -383,7 +383,7 @@ def is_extreme_doubly_nonnegative(A):
     # can't compute the dimension of a set of matrices anyway, so we
     # convert them all to vectors and just ask for the dimension of the
     # resulting vector space.
-    (phi, phi_inverse) = isomorphism(A.matrix_space())
+    (phi, phi_inverse) = basis_repr(A.matrix_space())
     vectors = map(phi,spanning_set)
 
     V = span(vectors, A.base_ring())
@@ -530,7 +530,7 @@ def random_extreme_doubly_nonnegative(V, accept_zero=True, rank=None):
 
     """
 
-    if not is_admissible_extreme_rank(rank, V.dimension()):
+    if rank is not None and not is_admissible_extreme_rank(rank, V.dimension()):
         msg = 'Rank %d not possible in dimension %d.'
         raise ValueError(msg % (rank, V.dimension()))