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    "info": {
        "author": "Vladimir Ignatev",
        "author_email": "ya.na.pochte@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 3 - Alpha",
            "Intended Audience :: Developers",
            "License :: CC0 1.0 Universal (CC0 1.0) Public Domain Dedication",
            "License :: OSI Approved :: MIT License",
            "Natural Language :: English",
            "Programming Language :: Python :: 2",
            "Programming Language :: Python :: 2.6",
            "Programming Language :: Python :: 2.7",
            "Programming Language :: Python :: 3",
            "Programming Language :: Python :: 3.2",
            "Programming Language :: Python :: 3.3",
            "Programming Language :: Python :: 3.4",
            "Topic :: Scientific/Engineering :: Artificial Intelligence",
            "Topic :: Scientific/Engineering :: Information Analysis",
            "Topic :: Software Development :: Libraries"
        ],
        "description": "# Markov Chain and Finite-State Stochastic Machine\n\nThis package implements functionality for analyzing stochastic (or random)\nfinite state (Markov) processes.\n\nIt can build a Markov chain from the states of the process.\n\nAlso the package provides non-deterministic FSM (finite-state machine)\nfunctionality for evaluating of Markov chains. You can easily build \na probabilistic automaton from the Markov chain.\n\nOne more feature is an integration with amazing [Graphviz](http://www.graphviz.org/) tool.\n`markovfsm` plots a state transitions graph of Markov model for you.\n\n# Installation\nAs usual, `pip install markovfsm`\n\nNo special prerequisites required, expect the Graphviz, if you want to use plotting features.\nIn such case, you have to install Graphviz and [`graphviz` PyPI package](https://pypi.org/project/graphviz/).\n\n# Usage examples\n## Coin flipping\nLet's start with the simplest Markov process - a flipping of perfect coin.\nLet '0' state be 'tails' and '1' state correspond to 'heads'.\n\nWe define a random function (`coin()`), once being evaluated, returns the next state of the process.\n\nLet's create a `Chain` object and perform big enough count of experiments:\n```python\nfrom random import random\nfrom graphviz import Digraph\n\nfrom markovfsm import Chain\nfrom markovfsm.plot import transitions_to_graph\n\n\ndef coin():               # random process: the perfect coin flipping\n    return 1 if random() > 0.5 else 0\n\nchain = Chain(2, coin())  # create an empty Markov chain with 2 states\n\nfor i in range(1000000):  # let the Markov chain build state transition matrix\n    chain.learn(coin())   # based on 1000000 of coin flips\n```\nLet's plot a graph of state transitions.\n```python\ng = Digraph(format='svg', engine='dot',\n            graph_attr={'pad': '0.1', 'nodesep': '0.4', 'ranksep': '1.0'},\n            node_attr={'fontname': 'Helvetica'},\n            edge_attr={'fontsize': '8.0', 'fontname': 'Helvetica'})\n\ntransitions_to_graph(g, chain.transition_matrix(),\n                     lambda s: \"tails\" if s == 0 else \"heads\")\n\ng.render('./graph')       # this will output ``graph.svg`` (SVG graphics)\n                          # and ``graph`` (DOT language) files\n```\n\n## Rigged dice\nAnother illustrative example is the process of rolling a rigged dice.\nWe use beta distribution to emulate non-perfect dice.\n\nThe remaining part of the code almost the same.\n```python\n#!coding:utf-8\n\nfrom random import betavariate\nfrom graphviz import Digraph\n\nfrom markovfsm import Chain\nfrom markovfsm.plot import transitions_to_graph\n\n\ndef rigged_dice():\n    return int((betavariate(0.5, 0.7) * 6))\n\nchain = Chain(6, rigged_dice())\n\n# roll dice many times to build Markov chain for this process\nfor i in range(100000):\n    chain.learn(rigged_dice())\n```\n\nAnd then let's plot states transitions.\n```python\ndef state_mapping(state):\n    if state == 0: return u'\u2680'\n    if state == 1: return u'\u2681'\n    if state == 2: return u'\u2682'\n    if state == 3: return u'\u2683'\n    if state == 4: return u'\u2684'\n    if state == 5: return u'\u2685'\n\ng = Digraph(format='svg', engine='dot',\n            graph_attr={'pad': '0.1', 'nodesep': '0.15', 'ranksep': '0.5'},\n            edge_attr={'fontsize': '6.0', 'fontname':'Helvetica'})\n\ntransitions_to_graph(g, chain.transition_matrix(), state_mapping)\ng.render('./graph')\n```\n\n# Probabilistic finite-state machine\nFinite-state machine (FSM, or state machine) is a model of computation.\nThe machine can be in exactly one of finite number of states.\nProbabilistic automaton is a FSM where transitions between states are probabilistic.\nUnlike normal FSM, requiring only a graph of possible transitions between states,\nprobabilistic automaton adds probability of every transition.\n```python\nfrom random import random\n\n# build Markov chain with 2 states, init with random state\nchain = Chain(2, 0 if random() > 0.5 else 1)\n\n# flip coin many times and build Markov chain for this process\n# let 0 be heads and 1 tails\nfor i in range(1000000):\n    chain.learn(0 if random() > 0.5 else 1)\n\n# get transition matrix\n#   It should look like:\n#\n#    P = | 0.5 0.5 |\n#        | 0.5 0.5 |\n#\nP = chain.transition_matrix()\n\nprint \"%s %s\" % (P[0][0], P[0][1])\nprint \"%s %s\" % (P[1][0], P[1][1])\n\n# get probabilities of transition from state 0 to other states (0 and 1)\n# actually, the line in the transition matrix\nprint chain.get_transitions_probs(0)\n\n# let's make a FSM with stochastic properties equal to described by Markov chain\n# use rnd() as a random numbers generator, and 0 (heads) as initial state\nfsm = FSM(chain, 0)\n\nfsm.next()  # will change the state of automaton randomly in a such way that\n            # the statistics of such transition will be equal to Markov process\n            # statistics\n```\n\n# API\n`chain.transition_matrix()` will return transition matrix: a matrix N x N,\nwhere N is the number of states, where each i-row correspond to the state of the process\nand each j-element in the row contains the probability of transition to state ``j``\nfrom the state ``i``.\n\n`chain.learn(state)` will learn Markov chain from new `state` transition\n\n`FSM(chain, initial_state)` - object, representing probabilistic automaton,\nbuilt from `chain` in state `initial_state`\n\n\n# License\nMIT License. Creative Commons CC0.\n\n\nNews\n====\n\n0.2\n---\n\n*Release date: 25-Mar-2019*\n\n* Updated usage information and added illustrations\n* Better documentation\n\n\n0.1\n---\n\n*Release date: 20-Dec-2017*\n\n* Initial release",
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