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 decomposition import stationary_distribution_from_backward_iteration as statdist
mu = statdist(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.")
T = T.tocsr()
if mu is None:
from decomposition import stationary_distribution_from_backward_iteration as statdist
mu = statdist(T)
Mu = diags(mu, 0)
prod = Mu * T
return allclose_sparse(prod, prod.transpose(), rtol=tol)
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))
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))