-"""
+r"""
The doubly-nonnegative cone in `S^{n}` is the set of all such matrices
that both,
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):
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.
# 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())
"""
- 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()))