def test_discrete_4_2(self):
# 4x4 transition matrix
nstates = 2
P = np.array([[0.90, 0.10, 0.00, 0.00], [0.10, 0.89, 0.01, 0.00],
[0.00, 0.01, 0.89, 0.10], [0.00, 0.00, 0.10, 0.90]])
# generate realization
import msmtools.generation as msmgen
T = 10000
dtrajs = [msmgen.generate_traj(P, T)]
# estimate initial HMM with 2 states - should be identical to P
hmm = initdisc.initial_model_discrete(dtrajs, nstates)
# Test if model fit is close to reference. Note that we do not have an exact reference, so we cannot set the
# tolerance in a rigorous way to test statistical significance. These are just sanity checks.
Tij = hmm.transition_matrix
B = hmm.output_model.output_probabilities
# Test stochasticity
import msmtools.analysis as msmana
msmana.is_transition_matrix(Tij)
np.allclose(B.sum(axis=1), np.ones(B.shape[0]))
#if (B[0,0]<B[1,0]):
# B = B[np.array([1,0]),:]
Tij_ref = np.array([[0.99, 0.01], [0.01, 0.99]])
Bref = np.array([[0.5, 0.5, 0.0, 0.0], [0.0, 0.0, 0.5, 0.5]])
assert (np.max(Tij - Tij_ref) < 0.01)
assert (np.max(B - Bref) < 0.05 or np.max(B[[1, 0]] - Bref) < 0.05)
def test_discrete_4_2(self):
# 4x4 transition matrix
nstates = 2
P = np.array([[0.90, 0.10, 0.00, 0.00],
[0.10, 0.89, 0.01, 0.00],
[0.00, 0.01, 0.89, 0.10],
[0.00, 0.00, 0.10, 0.90]])
# generate realization
import pyemma.msm.generation as msmgen
T = 10000
dtrajs = [msmgen.generate_traj(P, T)]
# estimate initial HMM with 2 states - should be identical to P
hmm = initdisc.initial_model_discrete(dtrajs, nstates)
# Test if model fit is close to reference. Note that we do not have an exact reference, so we cannot set the
# tolerance in a rigorous way to test statistical significance. These are just sanity checks.
Tij = hmm.transition_matrix
B = hmm.output_model.output_probabilities
# Test stochasticity
import pyemma.msm.analysis as msmana
msmana.is_transition_matrix(Tij)
np.allclose(B.sum(axis=1), np.ones(B.shape[0]))
#if (B[0,0]<B[1,0]):
# B = B[np.array([1,0]),:]
Tij_ref = np.array([[0.99, 0.01],
[0.01, 0.99]])
Bref = np.array([[0.5, 0.5, 0.0, 0.0],
[0.0, 0.0, 0.5, 0.5]])
assert(np.max(Tij-Tij_ref) < 0.01)
assert(np.max(B-Bref) < 0.05 or np.max(B[[1,0]]-Bref) < 0.05)
def init_hmm(observations, nstates, lag=1, type=None):
"""Use a heuristic scheme to generate an initial model.
Parameters
----------
observations : list of ndarray((T_i))
list of arrays of length T_i with observation data
nstates : int
The number of states.
type : str, optional, default=None
Output model type from [None, 'gaussian', 'discrete']. If None, will automatically select an output
model type based on the format of observations.
Examples
--------
Generate initial model for a gaussian output model.
>>> import bhmm
>>> [model, observations, states] = bhmm.testsystems.generate_synthetic_observations(output_model_type='gaussian')
>>> initial_model = init_hmm(observations, model.nstates, type='gaussian')
Generate initial model for a discrete output model.
>>> import bhmm
>>> [model, observations, states] = bhmm.testsystems.generate_synthetic_observations(output_model_type='discrete')
>>> initial_model = init_hmm(observations, model.nstates, type='discrete')
"""
# select output model type
if (type is None):
type = _guess_model_type(observations)
if type == 'discrete':
from bhmm.init import discrete
return discrete.initial_model_discrete(observations,
nstates,
lag=lag,
reversible=True)
elif type == 'gaussian':
from bhmm.init import gaussian
return gaussian.initial_model_gaussian1d(observations,
nstates,
reversible=True)
else:
raise NotImplementedError('output model type ' + str(type) +
' not yet implemented.')
def init_hmm(observations, nstates, lag=1, type=None):
"""Use a heuristic scheme to generate an initial model.
Parameters
----------
observations : list of ndarray((T_i))
list of arrays of length T_i with observation data
nstates : int
The number of states.
type : str, optional, default=None
Output model type from [None, 'gaussian', 'discrete']. If None, will automatically select an output
model type based on the format of observations.
Examples
--------
Generate initial model for a gaussian output model.
>>> import bhmm
>>> [model, observations, states] = bhmm.testsystems.generate_synthetic_observations(output_model_type='gaussian')
>>> initial_model = init_hmm(observations, model.nstates, type='gaussian')
Generate initial model for a discrete output model.
>>> import bhmm
>>> [model, observations, states] = bhmm.testsystems.generate_synthetic_observations(output_model_type='discrete')
>>> initial_model = init_hmm(observations, model.nstates, type='discrete')
"""
# select output model type
if (type is None):
type = _guess_model_type(observations)
if type == 'discrete':
from bhmm.init import discrete
return discrete.initial_model_discrete(observations, nstates, lag=lag, reversible=True)
elif type == 'gaussian':
from bhmm.init import gaussian
return gaussian.initial_model_gaussian1d(observations, nstates, reversible=True)
else:
raise NotImplementedError('output model type '+str(type)+' not yet implemented.')
def test_discrete_2_2(self):
# 2x2 transition matrix
P = np.array([[0.99, 0.01], [0.01, 0.99]])
# generate realization
import msmtools.generation as msmgen
T = 10000
dtrajs = [msmgen.generate_traj(P, T)]
# estimate initial HMM with 2 states - should be identical to P
hmm = initdisc.initial_model_discrete(dtrajs, 2)
# test
A = hmm.transition_matrix
B = hmm.output_model.output_probabilities
# Test stochasticity
import msmtools.analysis as msmana
msmana.is_transition_matrix(A)
np.allclose(B.sum(axis=1), np.ones(B.shape[0]))
# A should be close to P
if (B[0, 0] < B[1, 0]):
B = B[np.array([1, 0]), :]
assert (np.max(A - P) < 0.01)
assert (np.max(B - np.eye(2)) < 0.01)
def test_discrete_2_2(self):
# 2x2 transition matrix
P = np.array([[0.99,0.01],[0.01,0.99]])
# generate realization
import pyemma.msm.generation as msmgen
T = 10000
dtrajs = [msmgen.generate_traj(P, T)]
# estimate initial HMM with 2 states - should be identical to P
hmm = initdisc.initial_model_discrete(dtrajs, 2)
# test
A = hmm.transition_matrix
B = hmm.output_model.output_probabilities
# Test stochasticity
import pyemma.msm.analysis as msmana
msmana.is_transition_matrix(A)
np.allclose(B.sum(axis=1), np.ones(B.shape[0]))
# A should be close to P
if (B[0,0]<B[1,0]):
B = B[np.array([1,0]),:]
assert(np.max(A-P) < 0.01)
assert(np.max(B-np.eye(2)) < 0.01)
def test_discrete_6_3(self):
# 4x4 transition matrix
nstates = 3
P = np.array([[0.90, 0.10, 0.00, 0.00, 0.00, 0.00],
[0.20, 0.79, 0.01, 0.00, 0.00, 0.00],
[0.00, 0.01, 0.84, 0.15, 0.00, 0.00],
[0.00, 0.00, 0.05, 0.94, 0.01, 0.00],
[0.00, 0.00, 0.00, 0.02, 0.78, 0.20],
[0.00, 0.00, 0.00, 0.00, 0.10, 0.90]])
# generate realization
import msmtools.generation as msmgen
T = 10000
dtrajs = [msmgen.generate_traj(P, T)]
# estimate initial HMM with 2 states - should be identical to P
hmm = initdisc.initial_model_discrete(dtrajs, nstates)
# Test stochasticity and reversibility
Tij = hmm.transition_matrix
B = hmm.output_model.output_probabilities
import msmtools.analysis as msmana
msmana.is_transition_matrix(Tij)
msmana.is_reversible(Tij)
np.allclose(B.sum(axis=1), np.ones(B.shape[0]))
def test_discrete_6_3(self):
# 4x4 transition matrix
nstates = 3
P = np.array([[0.90, 0.10, 0.00, 0.00, 0.00, 0.00],
[0.20, 0.79, 0.01, 0.00, 0.00, 0.00],
[0.00, 0.01, 0.84, 0.15, 0.00, 0.00],
[0.00, 0.00, 0.05, 0.94, 0.01, 0.00],
[0.00, 0.00, 0.00, 0.02, 0.78, 0.20],
[0.00, 0.00, 0.00, 0.00, 0.10, 0.90]])
# generate realization
import pyemma.msm.generation as msmgen
T = 10000
dtrajs = [msmgen.generate_traj(P, T)]
# estimate initial HMM with 2 states - should be identical to P
hmm = initdisc.initial_model_discrete(dtrajs, nstates)
# Test stochasticity and reversibility
Tij = hmm.transition_matrix
B = hmm.output_model.output_probabilities
import pyemma.msm.analysis as msmana
msmana.is_transition_matrix(Tij)
msmana.is_reversible(Tij)
np.allclose(B.sum(axis=1), np.ones(B.shape[0]))
