-"""
+r"""
The doubly-nonnegative cone in `S^{n}` is the set of all such matrices
that both,
from sage.all import *
-from mjo.cone.symmetric_psd import factor_psd, is_symmetric_psd, random_psd
+from mjo.cone.symmetric_psd import (factor_psd,
+ is_symmetric_psd,
+ random_symmetric_psd)
from mjo.matrix_vector import isomorphism
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
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.
# 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
# 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
"""
- 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()))