def test_pcca_3(self):
P = np.array([[0.9, 0.1, 0.0, 0.0],
[0.1, 0.9, 0.0, 0.0],
[0.0, 0.0, 0.8, 0.2],
[0.0, 0.0, 0.2, 0.8]])
# n=2
chi = pcca(P, 2)
sol = np.array([[1., 0.],
[1., 0.],
[0., 1.],
[0., 1.]])
assert_allclose(chi, sol)
# n=3
chi = pcca(P, 3)
sol = np.array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.],
[0., 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., 1., 0.],
[0., 0., 0., 1.]])
assert_allclose(chi, sol)
def ALA4_msstates( T_AA ):
# Define the metastable states from analysis of T_AA_mle
membership=pcca(T_AA, 4)
# the precise definitions were fine-tuned by hand, I should plot the PCCA states to double check!
E1 = np.where(membership[:,0]>0.4)[0]
E2 = np.where(membership[:,1]>0.5)[0]
H = np.where(membership[:,2]>0.5)[0]
I = np.where(membership[:,3]>0.5)[0]
# make sure there is no overlap
#print "checking the overlap of metastable states:"
check = [val for val in H if val in I]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in H if val in E1]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in H if val in E2]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in I if val in E1]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in I if val in E2]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in E1 if val in E2]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
return H, I, E2, E1
def ALA4_msstates( T_AA ):
# Define the metastable states from analysis of T_AA_mle
membership=pcca(T_AA, 4)
# the precise definitions were fine-tuned by hand, I should plot the PCCA states to double check!
E1 = np.where(membership[:,0]>0.4)[0]
E2 = np.where(membership[:,1]>0.75)[0]
H = np.where(membership[:,2]>0.6)[0]
I = np.where(membership[:,3]>0.75)[0]
# make sure there is no overlap
#print "checking the overlap of metastable states:"
check = [val for val in H if val in I]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in H if val in E1]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in H if val in E2]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in I if val in E1]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in I if val in E2]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in E1 if val in E2]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
return H, I, E2, E1
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_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_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_4(self):
P = np.array([[0.9, 0.1, 0.0, 0.0],
[0.1, 0.8, 0.1, 0.0],
[0.0, 0.0, 0.8, 0.2],
[0.0, 0.0, 0.2, 0.8]])
chi = pcca(P, 2)
sol = np.array([[1., 0.],
[1., 0.],
[1., 0.],
[0., 1.]])
assert_allclose(chi, sol)
def set_model_params(self, P, m):
"""
Parameters
----------
P : ndarray (n,n)
Transition matrix.
m : int
Number of clusters to group to.
"""
# remember input
from scipy.sparse import issparse
if issparse(P):
warnings.warn(
'PCCA is only implemented for dense matrices, '
'converting sparse transition matrix to dense ndarray.')
P = P.toarray()
self.P = P
self.m = m
# pcca coarse-graining
# --------------------
# PCCA memberships
# TODO: can be improved. pcca computes stationary distribution internally, we don't need to compute it twice.
from msmtools.analysis.dense.pcca import pcca
self._M = pcca(P, m)
# stationary distribution
# TODO: in msmtools we recomputed this from P, we actually want to use pi from the msm obj, but this caused #1208
from msmtools.analysis import stationary_distribution
self._pi = stationary_distribution(P)
# coarse-grained stationary distribution
self._pi_coarse = np.dot(self._M.T, self._pi)
# HMM output matrix
self._B = np.dot(np.dot(np.diag(1.0 / self._pi_coarse), self._M.T),
np.diag(self._pi))
# renormalize B to make it row-stochastic
self._B /= self._B.sum(axis=1)[:, None]
self._B /= self._B.sum(axis=1)[:, None]
# coarse-grained transition matrix
W = np.linalg.inv(np.dot(self._M.T, self._M))
A = np.dot(np.dot(self._M.T, P), self._M)
self._P_coarse = np.dot(W, A)
# symmetrize and renormalize to eliminate numerical errors
X = np.dot(np.diag(self._pi_coarse), self._P_coarse)
self._P_coarse = X / X.sum(axis=1)[:, None]
def ALA3_msstates( T_AA ):
# Define the metastable states from analysis of T_AA_mle
membership=pcca(T_AA, 3)
# the precise definitions were fine-tuned by hand, I should plot the PCCA states to double check!
lH = np.where(membership[:,0]>0.60)[0]
aH = np.where(membership[:,1]>0.60)[0]
B = np.where(membership[:,2]>0.60)[0]
# make sure there is no overlap
#print "checking the overlap of metastable states:"
check = [val for val in lH if val in aH]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in lH if val in B]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
check = [val for val in aH if val in B]
if (len(check) != 0 ): raise ValueError('Some metastable states are overlapping!')
return B, aH, lH
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)
chi = pcca(transition_matrix, 2)
expected = np.array([[0., 1.],
[0., 1.],
[0., 1.],
[1., 0.],
[1., 0.],
[1., 0.],
[1., 0.]])
np.testing.assert_equal(chi, expected)
def ALA3_msstates(T_AA):
# Define the metastable states from analysis of T_AA_mle
membership = pcca(T_AA, 3)
# the precise definitions were fine-tuned by hand, I should plot the PCCA states to double check!
lH = np.where(membership[:, 0] > 0.60)[0]
aH = np.where(membership[:, 1] > 0.60)[0]
B = np.where(membership[:, 2] > 0.60)[0]
# make sure there is no overlap
#print "checking the overlap of metastable states:"
check = [val for val in lH if val in aH]
if (len(check) != 0):
raise ValueError('Some metastable states are overlapping!')
check = [val for val in lH if val in B]
if (len(check) != 0):
raise ValueError('Some metastable states are overlapping!')
check = [val for val in aH if val in B]
if (len(check) != 0):
raise ValueError('Some metastable states are overlapping!')
return B, aH, lH
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 msmtools.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_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)