PyDTMC 4.7.0

A framework for discrete-time Markov chains analysis.

PyDTMC is a full-featured, lightweight library for discrete-time Markov chains analysis. It provides classes and functions for creating, manipulating and simulating markovian stochastic processes.

Requirements

PyDTMC supports only Python 3 and the minimum required version is 3.6. In addition, the environment must include the following libraries:

• Matplotlib
• NetworkX
• Numpy
• PyTest
• SciPy

For a better user experience, it's recommended to install Graphviz and PyDot before using the plot_graph function.

Installation & Upgrade

Via PyPI:

$ pip install PyDTMC
$ pip install --upgrade PyDTMC

Via GitHub:

$ pip install git+https://github.com/TommasoBelluzzo/PyDTMC.git@master#egg=PyDTMC
$ pip install --upgrade git+https://github.com/TommasoBelluzzo/PyDTMC.git@master#egg=PyDTMC

Usage

The core element of the library is the MarkovChain class, which can be instantiated as follows:

>>> import numpy as np
>>> p = np.array([[0.2, 0.7, 0.0, 0.1], [0.0, 0.6, 0.3, 0.1], [0.0, 0.0, 1.0, 0.0], [0.5, 0.0, 0.5, 0.0]])
>>> mc = MarkovChain(p, ['A', 'B', 'C', 'D'])
>>> print(mc)

DISCRETE-TIME MARKOV CHAIN
 SIZE:         4
 CLASSES:      2
  > RECURRENT: 1
  > TRANSIENT: 1
 ERGODIC:      NO
  > APERIODIC:    YES
  > IRREDUCIBLE:  NO
 ABSORBING:    YES
 REGULAR:      NO
 REVERSIBLE:   NO
 SYMMETRIC:    NO

Static values of MarkovChain instances can be retrieved through their properties:

>>> print(mc.recurrent_states)
['C']

>>> print(mc.transient_states)
['A', 'B', 'D']

>>> print(mc.steady_states)
[array([0., 0., 1., 0.])]

>>> print(mc.fundamental_matrix)
[[1.50943396 2.64150943 0.41509434]
 [0.18867925 2.83018868 0.30188679]
 [0.75471698 1.32075472 1.20754717]]

>>> print(mc.absorption_times)
[4.56603774 3.32075472 3.28301887]

>>> print(mc.topological_entropy)
0.6931471805599457

Dynamic computations on MarkovChain instances can be performed through their methods:

>>> print(mc.expected_rewards(10, [2, -3, 8, -7]))
[-2.76071635 -12.01665113  23.23460025  -8.45723276]

>>> print(mc.expected_transitions(2))
[[0.085  0.2975 0.     0.0425]
 [0.     0.345  0.1725 0.0575]
 [0.     0.     0.7    0.    ]
 [0.15   0.     0.15   0.    ]]
 
>>> print(mc.walk(10))
['D', 'A', 'B', 'C', 'C', 'C', 'C', 'C', 'C', 'C']

Plotting functions can provide a visual representation of a MarkovChain instance; in order to display function outputs immediately, the interactive mode of Matplotlib must be turned on:

>>> plot_eigenvalues(mc)

>>> plot_graph(mc)

>>> plot_walk(mc, 10, 'sequence')