"""

Show mutual information decay for a reversible continuous time Markov process.

When a reversible finite-state continuous-time

Markov process is at equilibrium,

two observations separated by time t

will be non-independent

in a way that can be quantified by their mutual information.

This mutual information is also mathematically equivalent

to the expected log-likelihood ratio

of T=t vs. T=infinity given that the true time is T=t.

In this script we empirically investigate the asymptotic

properties of the decay of the mutual information.

The hypothesis is that the decay is

bounded above and below by an exponentially decreasing function

whose decay rate depends only on the smallest magnitude nonzero

eigenvalue of the rate matrix that defines the Markov process.

"""

from StringIO import StringIO

import math

import numpy as np

import scipy

from scipy import linalg

import Form

import FormOut

from MatrixUtil import ndot

import mrate

import divtime

import ctmcmi

def get_form():

return form_objects

def get_form_out():

return FormOut.Report()

def get_response_content(fs):

return out.getvalue()