def test_f_graphlasso():
# whether or not eigendecomposition is used, result should be the same
assert_almost_equal(fista_gl.f_graphlasso(Theta, S),
fista_gl.f_graphlasso(Theta_, S))
# minimum at max likelihood solution inv(S)
assert_array_less(fista_gl.f_graphlasso(scipy.linalg.inv(S), S),
fista_gl.f_graphlasso(Theta, S))
def test_Q_graphlasso():
grad = fista_gl.grad_f_graphlasso(Theta, S)
Z = np.random.normal(size=(p, 2 * p))
Z = Z.dot(Z.T) / p
f_Theta = fista_gl.f_graphlasso(Theta_, S)
f_Z = fista_gl.f_graphlasso(Z, S)
g_Z = fista_gl.g_graphlasso(Z, .5)
L = np.sqrt(np.sum(1. / scipy.linalg.eigvalsh(Z) ** 2))
L *= np.sqrt(np.sum(1. / Theta_[0] ** 2))
assert_array_less(f_Z + g_Z,
fista_gl.Q_graphlasso(Z, Theta, grad, L, .5, f_Theta))
# Does this hold for the Hessian update ?
gradH = fista_gl.grad_f_graphlasso(Theta, S, Hessian=True)
assert_array_less(f_Z + g_Z,
fista_gl.Q_graphlasso(Z, Theta, gradH, L, .5, f_Theta))