-"""
+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.matrix_vector import isomorphism
+from mjo.cone.symmetric_psd import (factor_psd,
+ is_symmetric_psd,
+ random_symmetric_psd)
+from mjo.basis_repr import basis_repr
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.
# 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
# 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())
# 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)
+ 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()))