def is_reversible(T, mu=None, tol=1e-15):
r"""
checks whether T is reversible in terms of given stationary distribution.
If no distribution is given, it will be calculated out of T.
performs follwing check:
:math:`\pi_i P_{ij} = \pi_j P_{ji}
Parameters
----------
T : scipy.sparse matrix
Transition matrix
mu : numpy.ndarray vector
stationary distribution
tol : float
tolerance to check with
Returns
-------
Truth value : bool
True, if T is a stochastic matrix
False, otherwise
"""
if not is_transition_matrix(T, tol):
raise ValueError("given matrix is not a valid transition matrix.")
T = T.tocsr()
if mu is None:
from deeptime.markov.tools.analysis import stationary_distribution
mu = stationary_distribution(T)
Mu = diags(mu, 0)
prod = Mu * T
return allclose_sparse(prod, prod.transpose(), rtol=tol)
def is_reversible(T, mu=None, tol=1e-15):
r"""
checks whether T is reversible in terms of given stationary distribution.
If no distribution is given, it will be calculated out of T.
performs follwing check:
:math:`\pi_i P_{ij} = \pi_j P_{ji}
Parameters
----------
T : scipy.sparse matrix
Transition matrix
mu : numpy.ndarray vector
stationary distribution
tol : float
tolerance to check with
Returns
-------
Truth value : bool
True, if T is a stochastic matrix
False, otherwise
"""
if not is_transition_matrix(T, tol):
raise ValueError("given matrix is not a valid transition matrix.")
if sparse.issparse(T):
T = T.tocsr()
if mu is None:
mu = stationary_distribution(T)
if sparse.issparse(T):
prod = sparse.construct.diags(mu) * T
else:
prod = mu[:, None] * T
if sparse.issparse(T):
return allclose_sparse(prod, prod.transpose(), rtol=tol)
else:
return np.allclose(prod, prod.transpose(), rtol=tol)
def test_allclose_sparse():
A = sp.random(50, 50)
B = sp.random(50, 51)
assert allclose_sparse(A, A)
assert not allclose_sparse(A, B)
def test_prior_neighbor(self):
Bn = prior_neighbor(self.C)
self.assertTrue(allclose_sparse(Bn, self.alpha_def * self.B_neighbor))
Bn = prior_neighbor(self.C, alpha=self.alpha)
self.assertTrue(allclose_sparse(Bn, self.alpha * self.B_neighbor))