giddy.markov.sojourn_time¶

giddy.markov.sojourn_time(p, summary=True)[source]¶

Calculate sojourn time based on a given transition probability matrix.

Parameters:

parray

(k, k), a Markov transition probability matrix.

summarybool

If True and the Markov Chain has absorbing states whose sojourn time is infinitely large, print out the information about the absorbing states. Default is True.

Returns

——-

: array: (k, ), sojourn times. Each element is the expected time a Markov chain spends in each state before leaving that state.

Notes

Refer to [Ibe09] for more details on sojourn times for Markov chains.

Examples

>>> from giddy.markov import sojourn_time
>>> import numpy as np
>>> p = np.array([[.5, .25, .25], [.5, 0, .5], [.25, .25, .5]])
>>> sojourn_time(p)
array([2., 1., 2.])

Non-ergodic Markov Chains with rows full of 0

>>> p = np.array([[.5, .25, .25], [.5, 0, .5],[ 0, 0, 0]])
>>> sojourn_time(p)
Sojourn times are infinite for absorbing states! In this Markov Chain, states [2] are absorbing states.
array([ 2.,  1., inf])