def test_grad_f_graphlasso():
Theta_inv = Theta_[1].dot(np.diag(1. / Theta_[0]).dot(Theta_[1].T))
# the optimal should be when S = inv(Theta), hence zero gradient
assert_almost_equal(fista_gl.grad_f_graphlasso(Theta, Theta_inv),
np.zeros((p, p)))
assert_almost_equal(fista_gl.grad_f_graphlasso(Theta, Theta_inv),
np.zeros((p, p)), Hessian=True)
# test whether this works for the eigen decomposition
assert_almost_equal(fista_gl.grad_f_graphlasso(Theta_, Theta_inv),
np.zeros((p, p)))
assert_almost_equal(fista_gl.grad_f_graphlasso(Theta_, Theta_inv),
np.zeros((p, p)), Hessian=True)
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))
def test_pL_graphlasso():
grad = fista_gl.grad_f_graphlasso(Theta, S)
pL_Theta = fista_gl.pL_graphlasso(Theta, .5, grad, 1.)
# in absolute value the soft thresholding should have lower values
assert_array_less(np.abs(pL_Theta), np.abs(Theta - grad))
pL_sign = np.sign(pL_Theta)
T_sign0 = np.abs(np.sign(Theta - grad)) < 1. / 2
# if not put to zero, sign should not change
assert_equal(np.sign(pL_Theta) * pL_sign,
np.sign(Theta - grad) * pL_sign)
# zeros in original Theta must remain zero
assert_equal(np.sign(pL_Theta) * T_sign0,
np.sign(Theta - grad) * T_sign0)
