-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
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.
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.
if A[i,j] == 0:
M = A.matrix_space()
S = X.transpose() * (stdE(M,i,j) + stdE(M,j,i)) * X
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.
# 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.
vectors = map(phi,spanning_set)
V = span(vectors, A.base_ring())
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.
# Generate random symmetric positive-semidefinite matrices until
# one of them is nonnegative, then return that.
msg = 'Rank %d not possible in dimension %d.'
raise ValueError(msg % (rank, V.dimension()))
msg = 'Rank %d not possible in dimension %d.'
raise ValueError(msg % (rank, V.dimension()))