def estimate_P(C, reversible = True, fixed_statdist=None):
# import emma
import pyemma.msm.estimation as msmest
# output matrix. Initially eye
n = np.shape(C)[0]
P = np.eye((n), dtype=np.float64)
# treat each connected set separately
S = msmest.connected_sets(C)
for s in S:
if len(s) > 1: # if there's only one state, there's nothing to estimate and we leave it with diagonal 1
# compute transition sub-matrix on s
Cs = C[s,:][:,s]
Ps = msmest.transition_matrix(Cs, reversible = reversible, mu=fixed_statdist)
# write back to matrix
for i,I in enumerate(s):
for j,J in enumerate(s):
P[I,J] = Ps[i,j]
P[s,:][:,s] = Ps
# done
return P
def test_transition_matrix(self):
"""Non-reversible"""
T = transition_matrix(self.C1).toarray()
assert_allclose(T, self.T1.toarray())
T = transition_matrix(self.C2).toarray()
assert_allclose(T, self.T2.toarray())
"""Reversible"""
T = transition_matrix(self.C1, rversible=True).toarray()
assert_allclose(T, self.T1.toarray())
T = transition_matrix(self.C2, reversible=True).toarray()
assert_allclose(T, self.T2.toarray())
"""Reversible with fixed pi"""
T = transition_matrix(self.C1, rversible=True, pi=self.pi1).toarray()
assert_allclose(T, self.T1.toarray())
T = transition_matrix(self.C2, rversible=True, pi=self.pi2).toarray()
assert_allclose(T, self.T2.toarray())
def test_transition_matrix(self):
"""Non-reversible"""
T = transition_matrix(self.C1).toarray()
assert_allclose(T, self.T1.toarray())
T = transition_matrix(self.C2).toarray()
assert_allclose(T, self.T2.toarray())
"""Reversible"""
T = transition_matrix(self.C1, rversible=True).toarray()
assert_allclose(T, self.T1.toarray())
T = transition_matrix(self.C2, reversible=True).toarray()
assert_allclose(T, self.T2.toarray())
"""Reversible with fixed pi"""
T = transition_matrix(self.C1, rversible=True, pi=self.pi1).toarray()
assert_allclose(T, self.T1.toarray())
T = transition_matrix(self.C2, rversible=True, pi=self.pi2).toarray()
assert_allclose(T, self.T2.toarray())
def initial_model_gaussian1d(observations, nstates, reversible=True):
"""Generate an initial model with 1D-Gaussian output densities
Parameters
----------
observations : list of ndarray((T_i), dtype=float)
list of arrays of length T_i with observation data
nstates : int
The number of states.
Examples
--------
Generate initial model for a gaussian output model.
>>> from bhmm import testsystems
>>> [model, observations, states] = testsystems.generate_synthetic_observations(output_model_type='gaussian')
>>> initial_model = initial_model_gaussian1d(observations, model.nstates)
"""
ntrajectories = len(observations)
# Concatenate all observations.
collected_observations = np.array([], dtype=config.dtype)
for o_t in observations:
collected_observations = np.append(collected_observations, o_t)
# Fit a Gaussian mixture model to obtain emission distributions and state stationary probabilities.
from sklearn import mixture
gmm = mixture.GMM(n_components=nstates)
gmm.fit(collected_observations[:,None])
from bhmm import GaussianOutputModel
output_model = GaussianOutputModel(nstates, means=gmm.means_[:,0], sigmas=np.sqrt(gmm.covars_[:,0]))
logger().info("Gaussian output model:\n"+str(output_model))
# Extract stationary distributions.
Pi = np.zeros([nstates], np.float64)
Pi[:] = gmm.weights_[:]
logger().info("GMM weights: %s" % str(gmm.weights_))
# Compute fractional state memberships.
Nij = np.zeros([nstates, nstates], np.float64)
for o_t in observations:
# length of trajectory
T = o_t.shape[0]
# output probability
pobs = output_model.p_obs(o_t)
# normalize
pobs /= pobs.sum(axis=1)[:,None]
# Accumulate fractional transition counts from this trajectory.
for t in range(T-1):
Nij[:,:] = Nij[:,:] + np.outer(pobs[t,:], pobs[t+1,:])
logger().info("Nij\n"+str(Nij))
# Compute transition matrix maximum likelihood estimate.
import pyemma.msm.estimation as msmest
Tij = msmest.transition_matrix(Nij, reversible=reversible)
# Update model.
model = HMM(Tij, output_model, reversible=reversible)
return model