def test_is_transition_matrix(self):
self.assertTrue(is_transition_matrix(self.T))
"""Larger test-case to prevent too restrictive tolerance settings"""
X = np.random.random((2000, 2000))
Tlarge = X / X.sum(axis=1)[:, np.newaxis]
self.assertTrue(is_transition_matrix(Tlarge))
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)]
C = msmest.count_matrix(dtrajs, 1).toarray()
# estimate initial HMM with 2 states - should be identical to P
hmm = init_discrete_hmm(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_sample_nonrev_1(self):
P = sample_tmatrix(self.C, reversible=False)
assert np.all(P.shape == self.C.shape)
assert is_transition_matrix(P)
# same with boject
sampler = tmatrix_sampler(self.C, reversible=False)
P = sampler.sample()
assert np.all(P.shape == self.C.shape)
assert is_transition_matrix(P)
def test_sample_nonrev_10(self):
sampler = tmatrix_sampler(self.C, reversible=False)
Ps = sampler.sample(nsamples=10)
assert len(Ps) == 10
for i in range(10):
assert np.all(Ps[i].shape == self.C.shape)
assert is_transition_matrix(Ps[i])
def update(self, Tij, Pi=None):
r""" Updates the transition matrix and recomputes all derived quantities """
# EMMA imports
from msmtools import analysis as msmana
# save a copy of the transition matrix
self._Tij = np.array(Tij)
assert msmana.is_transition_matrix(
self._Tij), 'Given transition matrix is not a stochastic matrix'
assert self._Tij.shape[
0] == self._nstates, 'Given transition matrix has unexpected number of states '
# initial / stationary distribution
if (Pi is not None):
assert np.all(
Pi >= 0
), 'Given initial distribution contains negative elements.'
Pi = np.array(Pi) / np.sum(
Pi) # ensure normalization and make a copy
if (self._stationary):
pT = msmana.stationary_distribution(self._Tij)
if Pi is None: # stationary and no stationary distribution fixed, so computing it from trans. mat.
self._Pi = pT
else: # stationary but stationary distribution is fixed, so the transition matrix must be consistent
assert np.allclose(Pi, pT), 'Stationary HMM requested, but given distribution is not the ' \
'stationary distribution of the given transition matrix.'
self._Pi = Pi
else:
if Pi is None: # no initial distribution given, so use stationary distribution anyway
self._Pi = msmana.stationary_distribution(self._Tij)
else:
self._Pi = Pi
# reversible
if self._reversible:
assert msmana.is_reversible(
Tij
), 'Reversible HMM requested, but given transition matrix is not reversible.'
# try to do eigendecomposition by default, because it's very cheap for hidden transition matrices
from scipy.linalg import LinAlgError
try:
if self._reversible:
self._R, self._D, self._L = msmana.rdl_decomposition(
self._Tij, norm='reversible')
# everything must be real-valued
self._R = self._R.real
self._D = self._D.real
self._L = self._L.real
else:
self._R, self._D, self._L = msmana.rdl_decomposition(
self._Tij, norm='standard')
self._eigenvalues = np.diag(self._D)
self._spectral_decomp_available = True
except LinAlgError:
logger().warn('Eigendecomposition failed for transition matrix\n' +
str(self._Tij) +
'\nspectral properties will not be available')
self._spectral_decomp_available = False
def test_discrete_4_2(self):
# 4x4 transition matrix
n_states = 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
T = 50000
dtrajs = [MarkovStateModel(P).simulate(T)]
# estimate initial HMM with 2 states - should be identical to P
hmm = initial_guess_discrete_from_data(dtrajs, n_states, lagtime=1, regularize=False)
# 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_model.transition_matrix
B = hmm.output_model.output_probabilities
# Test stochasticity
np.testing.assert_(msmana.is_transition_matrix(Tij))
np.testing.assert_allclose(B.sum(axis=1), np.ones(B.shape[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]])
np.testing.assert_array_almost_equal(Tij, Tij_ref, decimal=2)
if np.max(B - Bref) < .05:
np.testing.assert_allclose(B, Bref, atol=0.06)
else:
np.testing.assert_allclose(B[[1, 0]], Bref, atol=0.06)
def test_transition_matrix(self):
import msmtools.analysis as msmana
for P in [
self.hmm_lag1.transition_model.transition_matrix,
self.hmm_lag10.transition_model.transition_matrix
]:
np.testing.assert_(msmana.is_transition_matrix(P))
np.testing.assert_(msmana.is_reversible(P))
def test_transition_matrix(self):
import msmtools.analysis as msmana
for P in [
self.hmsm_lag1.transition_matrix,
self.hmsm_lag1.transition_matrix
]:
assert msmana.is_transition_matrix(P)
assert msmana.is_reversible(P)
def test_transition_matrix(self):
"""Test example transition matrices.
"""
Tij = testsystems.generate_transition_matrix(n_states=3, reversible=False)
assert not is_reversible(Tij)
Tij = testsystems.generate_transition_matrix(n_states=3, reversible=True)
assert Tij.shape == (3, 3)
assert is_transition_matrix(Tij)
def test_3state_prev(self):
dtraj = np.array([0, 1, 2, 0, 3, 4])
import msmtools.estimation as msmest
for rev in [True, False]:
hmm = initial_guess_discrete_from_data(dtraj, n_hidden_states=3, lagtime=1, reversible=rev)
assert msmana.is_transition_matrix(hmm.transition_model.transition_matrix)
if rev:
assert msmana.is_reversible(hmm.transition_model.transition_matrix)
assert np.allclose(hmm.output_probabilities.sum(axis=1), 1)
for rev in [True, False]:
C = TransitionCountEstimator(lagtime=1, count_mode="sliding").fit(dtraj).fetch_model().count_matrix
C += msmest.prior_neighbor(C, 0.001)
hmm = initial_guess_discrete_from_data(dtraj, n_hidden_states=3, lagtime=1, reversible=rev)
np.testing.assert_(msmana.is_transition_matrix(hmm.transition_model.transition_matrix))
if rev:
np.testing.assert_(msmana.is_reversible(hmm.transition_model.transition_matrix))
np.testing.assert_allclose(hmm.output_model.output_probabilities.sum(axis=1), 1.)
def test_transition_matrix_obs(self):
assert np.array_equal(self.hmsm_lag1.transition_matrix_obs().shape, (self.hmsm_lag1.nstates_obs,self.hmsm_lag1.nstates_obs))
assert np.array_equal(self.hmsm_lag10.transition_matrix_obs().shape, (self.hmsm_lag10.nstates_obs,self.hmsm_lag10.nstates_obs))
for T in [self.hmsm_lag1.transition_matrix_obs(),
self.hmsm_lag1.transition_matrix_obs(k=2),
self.hmsm_lag10.transition_matrix_obs(),
self.hmsm_lag10.transition_matrix_obs(k=4)]:
assert msmana.is_transition_matrix(T)
assert msmana.is_reversible(T)
def test_transition_matrix_samples(self):
Psamples = self.sampled_hmm_lag10.transition_matrix_samples
# shape
assert np.array_equal(Psamples.shape, (self.nsamples, self.nstates, self.nstates))
# consistency
import msmtools.analysis as msmana
for P in Psamples:
assert msmana.is_transition_matrix(P)
assert msmana.is_reversible(P)
def test_transition_matrix_samples(self):
Psamples = np.array([m.transition_matrix for m in self.bhmm])
# shape
assert np.array_equal(np.shape(Psamples), (self.n_samples, self.n_states, self.n_states))
# consistency
import msmtools.analysis as msmana
for P in Psamples:
assert msmana.is_transition_matrix(P)
assert msmana.is_reversible(P)
def _transition_matrix_samples(self, msm):
Psamples = msm.sample_f('transition_matrix')
# shape
assert np.array_equal(np.shape(Psamples), (self.nsamples, self.nstates, self.nstates))
# consistency
import msmtools.analysis as msmana
for P in Psamples:
assert msmana.is_transition_matrix(P)
assert msmana.is_reversible(P)
def test_2state_2obs_Pgiven(self):
obs = np.array([0, 0, 1, 1, 0])
Aref = np.array([[1.0]])
for rev in [True, False]: # reversibiliy doesn't matter in this example
hmm = initial_guess_discrete_from_data(obs, n_hidden_states=1, lagtime=1, reversible=rev)
np.testing.assert_(msmana.is_transition_matrix(hmm.transition_model.transition_matrix))
np.testing.assert_allclose(hmm.transition_model.transition_matrix, Aref)
# output must be 1 x 2, and no zeros
np.testing.assert_equal(hmm.output_model.output_probabilities.shape, (1, 2))
np.testing.assert_(np.all(hmm.output_model.output_probabilities > 0))
def test_3state_prev(self):
import msmtools.analysis as msmana
dtraj = np.array([0, 1, 2, 0, 3, 4])
C = msmest.count_matrix(dtraj, 1).toarray()
for rev in [True, False]:
hmm = init_discrete_hmm(dtraj, 3, reversible=rev)
assert msmana.is_transition_matrix(hmm.transition_matrix)
if rev:
assert msmana.is_reversible(hmm.transition_matrix)
assert np.allclose(hmm.output_model.output_probabilities.sum(axis=1), 1)
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_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_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)]
C = msmest.count_matrix(dtrajs, 1).toarray()
# estimate initial HMM with 2 states - should be identical to P
hmm = init_discrete_hmm(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_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)]
C = msmest.count_matrix(dtrajs, 1).toarray()
# estimate initial HMM with 2 states - should be identical to P
hmm = init_discrete_hmm(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 P(self, value):
self._P = value
import msmtools.analysis as msmana
# check input
if self._P is not None:
if not msmana.is_transition_matrix(self._P, tol=1e-8):
raise ValueError('T is not a transition matrix.')
# set states
self.nstates = _np.shape(self._P)[0]
if self.reversible is None:
self.reversible = msmana.is_reversible(self._P)
from scipy.sparse import issparse
self.sparse = issparse(self._P)
def transition_matrix(self, T):
# Check transition matrix.
if mana.is_transition_matrix(T):
if not mana.is_reversible(T):
warnings.warn("The transition matrix is not reversible.")
if not mana.is_connected(T):
warnings.warn("The transition matrix is not connected.")
self._transition_matrix = T
else:
warnings.warn(
"Not a transition matrix. Has to be square and rows must sum to one."
)
def update(self, Tij, Pi=None):
r""" Updates the transition matrix and recomputes all derived quantities """
# EMMA imports
from msmtools import analysis as msmana
# save a copy of the transition matrix
self._Tij = np.array(Tij)
assert msmana.is_transition_matrix(self._Tij), 'Given transition matrix is not a stochastic matrix'
assert self._Tij.shape[0] == self._nstates, 'Given transition matrix has unexpected number of states '
# initial / stationary distribution
if (Pi is not None):
assert np.all(Pi >= 0), 'Given initial distribution contains negative elements.'
Pi = np.array(Pi) / np.sum(Pi) # ensure normalization and make a copy
if (self._stationary):
pT = msmana.stationary_distribution(self._Tij)
if Pi is None: # stationary and no stationary distribution fixed, so computing it from trans. mat.
self._Pi = pT
else: # stationary but stationary distribution is fixed, so the transition matrix must be consistent
assert np.allclose(Pi, pT), 'Stationary HMM requested, but given distribution is not the ' \
'stationary distribution of the given transition matrix.'
self._Pi = Pi
else:
if Pi is None: # no initial distribution given, so use stationary distribution anyway
self._Pi = msmana.stationary_distribution(self._Tij)
else:
self._Pi = Pi
# reversible
if self._reversible:
assert msmana.is_reversible(Tij), 'Reversible HMM requested, but given transition matrix is not reversible.'
# try to do eigendecomposition by default, because it's very cheap for hidden transition matrices
from scipy.linalg import LinAlgError
try:
if self._reversible:
self._R, self._D, self._L = msmana.rdl_decomposition(self._Tij, norm='reversible')
# everything must be real-valued
self._R = self._R.real
self._D = self._D.real
self._L = self._L.real
else:
self._R, self._D, self._L = msmana.rdl_decomposition(self._Tij, norm='standard')
self._eigenvalues = np.diag(self._D)
self._spectral_decomp_available = True
except LinAlgError:
logger().warn('Eigendecomposition failed for transition matrix\n'+str(self._Tij)+
'\nspectral properties will not be available')
self._spectral_decomp_available = False
def is_reversible(P):
""" Returns if P is reversible on its weakly connected sets """
import msmtools.analysis as msmana
# treat each weakly connected set separately
sets = connected_sets(P, strong=False)
for s in sets:
Ps = P[s, :][:, s]
if not msmana.is_transition_matrix(Ps):
return False # isn't even a transition matrix!
pi = msmana.stationary_distribution(Ps)
X = pi[:, None] * Ps
if not np.allclose(X, X.T):
return False
# survived.
return True
def is_reversible(P):
""" Returns if P is reversible on its weakly connected sets """
import msmtools.analysis as msmana
# treat each weakly connected set separately
sets = connected_sets(P, strong=False)
for s in sets:
Ps = P[s, :][:, s]
if not msmana.is_transition_matrix(Ps):
return False # isn't even a transition matrix!
pi = msmana.stationary_distribution(Ps)
X = pi[:, None] * Ps
if not np.allclose(X, X.T):
return False
# survived.
return True
def update(self, Pi, Tij):
r""" Updates the transition matrix and recomputes all derived quantities """
from msmtools import analysis as msmana
# update transition matrix by copy
self._Tij = np.array(Tij)
assert msmana.is_transition_matrix(self._Tij), 'Given transition matrix is not a stochastic matrix'
assert self._Tij.shape[0] == self._nstates, 'Given transition matrix has unexpected number of states '
# reset spectral decomposition
self._spectral_decomp_available = False
# check initial distribution
assert np.all(Pi >= 0), 'Given initial distribution contains negative elements.'
assert np.any(Pi > 0), 'Given initial distribution is zero'
self._Pi = np.array(Pi) / np.sum(Pi) # ensure normalization and make a copy
def _transition_matrix(self, msm):
P = msm.transition_matrix
# should be ndarray by default
# assert (isinstance(P, np.ndarray))
assert (isinstance(P, np.ndarray) or isinstance(P, scipy.sparse.csr_matrix))
# shape
assert (np.all(P.shape == (msm.n_states, msm.n_states)))
# test transition matrix properties
import msmtools.analysis as msmana
assert (msmana.is_transition_matrix(P))
assert (msmana.is_connected(P))
# REVERSIBLE
if msm.reversible:
assert (msmana.is_reversible(P))
def update(self, Pi, Tij):
r""" Updates the transition matrix and recomputes all derived quantities """
from msmtools import analysis as msmana
# update transition matrix by copy
self._Tij = np.array(Tij)
assert msmana.is_transition_matrix(self._Tij), 'Given transition matrix is not a stochastic matrix'
assert self._Tij.shape[0] == self._nstates, 'Given transition matrix has unexpected number of states '
# reset spectral decomposition
self._spectral_decomp_available = False
# check initial distribution
assert np.all(Pi >= 0), 'Given initial distribution contains negative elements.'
assert np.any(Pi > 0), 'Given initial distribution is zero'
self._Pi = np.array(Pi) / np.sum(Pi) # ensure normalization and make a copy
def _transition_matrix_samples(self, msm, given_pi):
Psamples = [s.transition_matrix for s in msm.samples]
# shape
assert np.array_equal(np.shape(Psamples), (self.nsamples, self.n_states, self.n_states))
# consistency
import msmtools.analysis as msmana
for P in Psamples:
assert msmana.is_transition_matrix(P)
try:
assert msmana.is_reversible(P)
except AssertionError:
# re-do calculation msmtools just performed to get details
from msmtools.analysis import stationary_distribution
mu = stationary_distribution(P)
X = mu[:, np.newaxis] * P
np.testing.assert_allclose(X, np.transpose(X), atol=1e-12,
err_msg="P not reversible, given_pi={}".format(given_pi))
def __init__(self,
T,
K0,
pi,
dt=1.0,
sparsity=None,
t_agg=None,
tol=1.0E7,
maxiter=100000,
on_error='raise'):
from msmtools.analysis import is_transition_matrix
super(CrommelinVandenEijndenEstimator,
self).__init__(T,
pi,
dt=dt,
sparsity=sparsity,
t_agg=t_agg,
tol=tol,
maxiter=maxiter,
on_error=on_error)
if not K0.shape[0] == K0.shape[1] == self.N:
raise ValueError(
'Shapes of K0 matrix (initial guess) and count matrix do not match.'
)
if not is_transition_matrix(T):
raise_or_warn('T is not a valid transition matrix.', self.on_error)
evals, self.U, self.Uinv = eigen_decomposition(T, self.pi)
if not np.all(
np.abs(evals) > 0.0): # don't allow eigenvalue==exactly zero
raise ValueError(
'T has eigenvalues that are exactly zero, can\'t proceed with rate matrix estimation. '
'If the CVE method is only used to intitialize the KL method, you might try to call the KL '
'method with an initial guess of the rate matrix (K0) instead of intializing with CVE.'
)
assert np.allclose(self.Uinv.dot(T).dot(self.U),
np.diag(evals)) # self-consistency test
self.c = np.abs(evals)
self.L = np.diag(np.log(np.abs(evals)) / self.dt)
theta = self.pi[self.I] * K0[self.I, self.J]
self.initial = np.maximum(theta, self.lower_bounds)
def _transition_matrix_stats(self, msm):
import msmtools.analysis as msmana
# mean
Pmean = msm.sample_mean('transition_matrix')
# test shape and consistency
assert np.array_equal(Pmean.shape, (self.nstates, self.nstates))
assert msmana.is_transition_matrix(Pmean)
# std
Pstd = msm.sample_std('transition_matrix')
# test shape
assert np.array_equal(Pstd.shape, (self.nstates, self.nstates))
# conf
L, R = msm.sample_conf('transition_matrix')
# test shape
assert np.array_equal(L.shape, (self.nstates, self.nstates))
assert np.array_equal(R.shape, (self.nstates, self.nstates))
# test consistency
assert np.all(L <= Pmean)
assert np.all(R >= Pmean)
def test_transition_matrix_stats(self):
import msmtools.analysis as msmana
# mean
Pmean = self.sampled_hmm_lag10.transition_matrix_mean
# test shape and consistency
assert np.array_equal(Pmean.shape, (self.nstates, self.nstates))
assert msmana.is_transition_matrix(Pmean)
# std
Pstd = self.sampled_hmm_lag10.transition_matrix_std
# test shape
assert np.array_equal(Pstd.shape, (self.nstates, self.nstates))
# conf
L, R = self.sampled_hmm_lag10.transition_matrix_conf
# test shape
assert np.array_equal(L.shape, (self.nstates, self.nstates))
assert np.array_equal(R.shape, (self.nstates, self.nstates))
# test consistency
assert np.all(L <= Pmean)
assert np.all(R >= Pmean)
def test_discrete_2_2(self):
# 2x2 transition matrix
P = np.array([[0.99, 0.01], [0.01, 0.99]])
# generate realization
T = 10000
dtrajs = [MarkovStateModel(P).simulate(T)]
# estimate initial HMM with 2 states - should be identical to P
init_hmm = initial_guess_discrete_from_data(dtrajs, n_hidden_states=2, lagtime=1)
# test
A = init_hmm.transition_model.transition_matrix
B = init_hmm.output_model.output_probabilities
# Test stochasticity
np.testing.assert_(msmana.is_transition_matrix(A))
np.testing.assert_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]), :]
np.testing.assert_array_almost_equal(A, P, decimal=2)
np.testing.assert_array_almost_equal(B, np.eye(2), decimal=2)
def transition_matrix(self, T):
"""Set transition matrix
Parameters
----------
T : 2D numpy.ndarray.
Transition matrix. Should be row stochastic and ergodic.
"""
# Check transition matrix.
if mana.is_transition_matrix(T):
if not mana.is_reversible(T):
warnings.warn("The transition matrix is not reversible.")
if not mana.is_connected(T):
warnings.warn("The transition matrix is not connected.")
else:
warnings.warn(
"Not a transition matrix. Has to be square and rows must sum to one."
)
self._transition_matrix = T
def _transition_matrix_stats(self, msm):
import msmtools.analysis as msmana
# mean
Ps = np.array([s.transition_matrix for s in msm.samples])
Pmean = Ps.mean(axis=0)
# test shape and consistency
assert np.array_equal(Pmean.shape, (self.n_states, self.n_states))
assert msmana.is_transition_matrix(Pmean)
# std
Pstd = Ps.std(axis=0)
# test shape
assert np.array_equal(Pstd.shape, (self.n_states, self.n_states))
# conf
L, R = confidence_interval(Ps)
# test shape
assert np.array_equal(L.shape, (self.n_states, self.n_states))
assert np.array_equal(R.shape, (self.n_states, self.n_states))
# test consistency
assert np.all(L <= Pmean)
assert np.all(R >= Pmean)
def test_init(self):
initial_model = init_model_gaussian1d(self._observations, self._nstates)
assert initial_model.nstates == self._nstates
assert msmana.is_transition_matrix(initial_model.transition_matrix)
def test_transition_matrix(self):
import msmtools.analysis as msmana
for P in [self.hmm_lag1.transition_matrix, self.hmm_lag1.transition_matrix]:
assert msmana.is_transition_matrix(P)
assert msmana.is_reversible(P)
