giddy.markov.sojourn_time

giddy.markov.sojourn_time(p)

Calculate sojourn time based on a given transition probability matrix.

Parameters

parray

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

Returns

: array

(k, ), sojourn times. Each element is the expected time a Markov chain spends in each states 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.])