mjo/cone: drop is_symmetric_p{s,}d() methods.

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

diff --git a/mjo/cone/doubly_nonnegative.py b/mjo/cone/doubly_nonnegative.py
index 583c3c60e8b46d43f9226e413eea70e83000d969..5e10e1aebaad4c17de9e129681a57bb736e72886 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,
 
@@ -13,8 +13,9 @@ It is represented typically by either `\mathcal{D}^{n}` or
 
 from sage.all import *
 
-from mjo.cone.symmetric_psd import factor_psd, is_symmetric_psd, random_psd
-from mjo.matrix_vector import isomorphism
+from mjo.cone.symmetric_psd import (factor_psd,
+                                    random_symmetric_psd)
+from mjo.basis_repr import basis_repr
 
 
 def is_doubly_nonnegative(A):
@@ -56,17 +57,17 @@ def is_doubly_nonnegative(A):
         raise ValueError.new(msg)
 
     # Check that all of the entries of ``A`` are nonnegative.
-    if not all([ a >= 0 for a in A.list() ]):
+    if not all( a >= 0 for a in A.list() ):
         return False
 
     # It's nonnegative, so all we need to do is check that it's
     # symmetric positive-semidefinite.
-    return is_symmetric_psd(A)
+    return A.is_positive_semidefinite()
 
 
 
 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.
@@ -352,7 +353,7 @@ def is_extreme_doubly_nonnegative(A):
         # Short circuit, we know the zero matrix is extreme.
         return True
 
-    if not is_symmetric_psd(A):
+    if not A.is_positive_semidefinite():
         return False
 
     # Step 1.5, appeal to Theorem 3.1 in reference #1 to short
@@ -369,8 +370,8 @@ def is_extreme_doubly_nonnegative(A):
     # whenever we come across an index pair `$(i,j)$` with
     # `$A_{ij} = 0$`.
     spanning_set = []
-    for j in range(0, A.ncols()):
-        for i in range(0,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
@@ -381,7 +382,7 @@ 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())
@@ -458,10 +459,10 @@ def random_doubly_nonnegative(V, accept_zero=True, rank=None):
 
     # Generate random symmetric positive-semidefinite matrices until
     # one of them is nonnegative, then return that.
-    A = random_psd(V, accept_zero, rank)
+    A = random_symmetric_psd(V, accept_zero, rank)
 
-    while not all([ x >= 0 for x in A.list() ]):
-        A = random_psd(V, accept_zero, rank)
+    while not all( x >= 0 for x in A.list() ):
+        A = random_symmetric_psd(V, accept_zero, rank)
 
     return A
 
@@ -528,7 +529,7 @@ 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()))