def test_uncertainties_backward():
n = 4
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
trajs = DoubleWell(random_state=0).get_cached().trajectories
seqs = grid.fit_transform(trajs)
model = PESContinuousTimeMSM(verbose=False).fit(seqs)
sigma_ts = model.uncertainty_timescales()
sigma_lambda = model.uncertainty_eigenvalues()
sigma_pi = model.uncertainty_pi()
sigma_K = model.uncertainty_K()
yield lambda: np.testing.assert_array_almost_equal(
sigma_ts, [9.508936, 0.124428, 0.117638])
yield lambda: np.testing.assert_array_almost_equal(
sigma_lambda,
[1.76569687e-19, 7.14216858e-05, 3.31210649e-04, 3.55556718e-04])
yield lambda: np.testing.assert_array_almost_equal(
sigma_pi, [0.007496, 0.006564, 0.006348, 0.007863])
yield lambda: np.testing.assert_array_almost_equal(
sigma_K,
[[0.000339, 0.000339, 0., 0.],
[0.000352, 0.000372, 0.000122, 0.],
[0., 0.000103, 0.000344, 0.000329],
[0., 0., 0.00029, 0.00029]])
yield lambda: np.testing.assert_array_almost_equal(
model.ratemat_,
[[-0.0254, 0.0254, 0., 0.],
[0.02636, -0.029629, 0.003269, 0.],
[0., 0.002764, -0.030085, 0.027321],
[0., 0., 0.024098, -0.024098]])
def test_hessian_2():
n = 3
seqs = [
[1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2,
2, 1, 1, 1, 1, 2, 3, 3, 3, 3]]
model = PESContinuousTimeMSM().fit(seqs)
print(model.timescales_)
print(model.uncertainty_timescales())
theta = model.theta_
C = model.countsmat_
print(C)
C_flat = (C + C.T)[np.triu_indices_from(C, k=1)]
print(C_flat)
print('theta', theta, '\n')
inds = np.where(theta != 0)[0]
hessian1 = _ratematrix_PES.hessian(theta, C, inds=inds)
hessian2 = nd.Jacobian(lambda x: _ratematrix_PES.loglikelihood(x, C)[1])(theta)
hessian3 = nd.Hessian(lambda x: _ratematrix_PES.loglikelihood(x, C)[0])(theta)
np.set_printoptions(precision=3)
# H1 = hessian1[np.ix_(active, active)]
# H2 = hessian2[np.ix_(active, active)]
# H3 = hessian2[np.ix_(active, active)]
print(hessian1, '\n')
print(hessian2, '\n')
# print(hessian3)
print('\n')
info1 = np.zeros((len(theta), len(theta)))
info2 = np.zeros((len(theta), len(theta)))
info1[np.ix_(inds, inds)] = scipy.linalg.pinv(-hessian1)
info2[np.ix_(inds, inds)] = scipy.linalg.pinv(-hessian2[np.ix_(inds, inds)])
print('Inverse Hessian')
print(info1)
print(info2)
# print(scipy.linalg.pinv(hessian2))
# print(scipy.linalg.pinv(hessian1)[np.ix_(last, last)])
# print(scipy.linalg.pinv(hessian2)[np.ix_(last, last)])
print(_ratematrix_PES.sigma_pi(info1, theta, n))
print(_ratematrix_PES.sigma_pi(info2, theta, n))