msmtools.analysis.expected_counts_stationary¶

msmtools.analysis.
expected_counts_stationary
(T, N, mu=None)¶ Expected transition counts for Markov chain in equilibrium.
Parameters:  T ((M, M) ndarray or sparse matrix) – Transition matrix.
 N (int) – Number of steps for chain.
 mu ((M,) ndarray (optional)) – Stationary distribution for T. If mu is not specified it will be computed from T.
Returns: EC – Expected value for transition counts after N steps.
Return type: (M, M) ndarray or sparse matrix
Notes
Since \(\mu\) is stationary for \(T\) we have
\[\mathbb{E}[C^{(N)}]=N D_{\mu}T.\]\(D_{\mu}\) is a diagonal matrix. Elements on the diagonal are given by the stationary vector \(\mu\)
Examples
>>> import numpy as np >>> from msmtools.analysis import expected_counts_stationary
>>> T = np.array([[0.9, 0.1, 0.0], [0.5, 0.0, 0.5], [0.0, 0.1, 0.9]]) >>> N = 100 >>> EC = expected_counts_stationary(T, N)
>>> EC array([[ 40.90909091, 4.54545455, 0. ], [ 4.54545455, 0. , 4.54545455], [ 0. , 4.54545455, 40.90909091]])