def test_pcca_5(self):
P = np.array([[0.9, 0.1, 0.0, 0.0, 0.0], [0.1, 0.9, 0.0, 0.0, 0.0],
[0.0, 0.1, 0.8, 0.1, 0.0], [0.0, 0.0, 0.0, 0.8, 0.2],
[0.0, 0.0, 0.0, 0.2, 0.8]])
# n=2
chi = pcca(P, 2)
sol = np.array([[1., 0.], [1., 0.], [0.5, 0.5], [0., 1.], [0., 1.]])
assert_allclose(chi, sol)
# n=4
chi = pcca(P, 4)
sol = np.array([[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0.5, 0.5, 0.],
[0., 0., 1., 0.], [0., 0., 0., 1.]])
assert_allclose(chi, sol)
def test_pcca_large(self):
import os
P = np.loadtxt(os.path.split(__file__)[0] + '/../../P_rev_251x251.dat')
# n=2
chi = pcca(P, 2)
assert (np.alltrue(chi >= 0))
assert (np.alltrue(chi <= 1))
# n=3
chi = pcca(P, 3)
assert (np.alltrue(chi >= 0))
assert (np.alltrue(chi <= 1))
# n=4
chi = pcca(P, 4)
assert (np.alltrue(chi >= 0))
assert (np.alltrue(chi <= 1))
def test_multiple_components(self):
L = np.array([[0, 1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0],
[1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1],
[0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0, 1],
[0, 0, 0, 1, 0, 1, 0]])
transition_matrix = L / np.sum(L, 1).reshape(-1, 1)
pi = np.zeros((transition_matrix.shape[0], ))
for cs in connected_sets(transition_matrix):
P_sub = transition_matrix[cs, :][:, cs]
pi[cs] = stationary_distribution(P_sub)
chi = pcca(transition_matrix, 2, pi=pi)
expected = np.array([[0., 1.], [0., 1.], [0., 1.], [1., 0.], [1., 0.],
[1., 0.], [1., 0.]])
np.testing.assert_equal(chi, expected)
def test_pcca_coarsegrain(self):
# fine-grained transition matrix
P = np.array([[0.9, 0.1, 0.0, 0.0, 0.0], [0.1, 0.89, 0.01, 0.0, 0.0],
[0.0, 0.1, 0.8, 0.1, 0.0], [0.0, 0.0, 0.01, 0.79, 0.2],
[0.0, 0.0, 0.0, 0.2, 0.8]])
from deeptime.markov.tools.analysis import stationary_distribution
pi = stationary_distribution(P)
Pi = np.diag(pi)
m = 3
# Susanna+Marcus' expression ------------
M = pcca(P, m)
pi_c = np.dot(M.T, pi)
Pi_c_inv = np.diag(1.0 / pi_c)
# restriction and interpolation operators
R = M.T
I = np.dot(np.dot(Pi, M), Pi_c_inv)
# result
ms1 = np.linalg.inv(np.dot(R, I)).T
ms2 = np.dot(np.dot(I.T, P), R.T)
Pc_ref = np.dot(ms1, ms2)
# ---------------------------------------
Pc = coarsegrain(P, 3)
# test against Marcus+Susanna's expression
assert np.max(np.abs(Pc - Pc_ref)) < 1e-10
# test mass conservation
assert np.allclose(Pc.sum(axis=1), np.ones(m))
p = PCCA(P, m)
# test against Marcus+Susanna's expression
assert np.max(
np.abs(p.coarse_grained_transition_matrix - Pc_ref)) < 1e-10
# test against the present coarse-grained stationary dist
assert np.max(
np.abs(p.coarse_grained_stationary_probability - pi_c)) < 1e-10
# test mass conservation
assert np.allclose(p.coarse_grained_transition_matrix.sum(axis=1),
np.ones(m))
def test_pcca_2(self):
P = np.array([[0.0, 1.0, 0.0], [0.0, 0.999, 0.001],
[0.0, 0.001, 0.999]])
chi = pcca(P, 2)
sol = np.array([[1., 0.], [1., 0.], [0., 1.]])
assert_allclose(chi, sol)
def test_pcca_1(self):
P = np.array([[1, 0], [0, 1]])
chi = pcca(P, 2)
sol = np.array([[1., 0.], [0., 1.]])
assert_allclose(chi, sol)
def test_pcca_no_detailed_balance(self):
P = np.array([[0.8, 0.1, 0.1], [0.3, 0.2, 0.5], [0.6, 0.3, 0.1]])
with self.assertRaises(ValueError):
pcca(P, 2)
def test_pcca_no_transition_matrix(self):
P = np.array([[1.0, 1.0], [0.1, 0.9]])
with self.assertRaises(ValueError):
pcca(P, 2)