from math import sqrt
from cvxopt import matrix
+from cvxopt.lapack import syev
def append_col(left, right):
"""
"""
return matrix([top, bottom])
+
+def eigenvalues(real_matrix):
+ """
+ Return the eigenvalues of the given ``real_matrix``.
+
+ EXAMPLES:
+
+ >>> A = matrix([[2,1],[1,2]], tc='d')
+ >>> eigenvalues(A)
+ [1.0, 3.0]
+
+ """
+ domain_dim = real_matrix.size[0] # Assume ``real_matrix`` is square.
+ eigs = matrix(0, (domain_dim, 1), tc='d')
+ syev(real_matrix, eigs)
+ return list(eigs)
+
+
def identity(domain_dim):
"""
Return a ``domain_dim``-by-``domain_dim`` dense integer identity
"""
return sqrt(sum([x**2 for x in matrix_or_vector]))
+
+
+def vec(real_matrix):
+ """
+ Create a long vector in column-major order from ``real_matrix``.
+
+ EXAMPLES:
+
+ >>> A = matrix([[1,2],[3,4]])
+ >>> print(A)
+ [ 1 3]
+ [ 2 4]
+ <BLANKLINE>
+
+ >>> print(vec(A))
+ [ 1]
+ [ 2]
+ [ 3]
+ [ 4]
+ <BLANKLINE>
+
+ """
+ return matrix(real_matrix, (len(real_matrix), 1))