markov_chains/examples.py at main · enlacroix/markov_chains · GitHub

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import numpy as np

MATRICES = {
    '1': np.array([
        [0.5, 0.1, 0.4, 0, 0],
        [0.8, 0.2, 0, 0, 0],
        [0, 1, 0, 0, 0],
        [0, 0, 0, 0.9, 0.1],
        [0, 0, 0, 1, 0]]),

    '2': np.array([
        [0, 0.2, 0.8, 0, 0],
        [0, 0, 0, 0.9, 0.1],
        [0, 0, 0, 0.1, 0.9],
        [1, 0, 0, 0, 0],
        [1, 0, 0, 0, 0]]),

    '3': np.array([
        [0, 1, 0, 0, 0],
        [1, 0, 0, 0, 0],
        [0.2, 0.2, 0.2, 0.4, 0],
        [0.2, 0.8, 0, 0, 0],
        [0.4, 0.1, 0.1, 0, 0.4]]),

    '4': np.array([
        [0, 0, 1, 0],
        [1, 0, 0, 0],
        [0.4, 0.6, 0, 0],
        [0.1, 0.4, 0.2, 0.3]]),

    '5': np.array([
        [0.5, 0.5, 0, 0, 0, 0],
        [0, 0, 1, 0, 0, 0],
        [1 / 3, 0, 0, 1 / 3, 1 / 3, 0],
        [0, 0, 0, 1 / 2, 1 / 2, 0],
        [0, 0, 0, 0, 0, 1],
        [0, 0, 0, 0, 1, 0]]),

    '6': np.array([
        [1 / 2, 0, 0, 0, 1 / 2],
        [0, 1 / 2, 0, 1 / 2, 0],
        [0, 0, 1, 0, 0],
        [0, 1 / 4, 1 / 4, 1 / 4, 1 / 4],
        [1 / 2, 0, 0, 0, 1 / 2]]),

    '7': np.array([
        [0, 0, 1 / 3, 1 / 3, 1 / 3, 0, 0, 0],
        [0, 0, 1 / 4, 3 / 4, 0, 0, 0, 0],
        [1 / 6, 5 / 6, 0, 0, 0, 0, 0, 0],
        [1 / 2, 1 / 2, 0, 0, 0, 0, 0, 0],
        [1 / 5, 4 / 5, 0, 0, 0, 0, 0, 0],
        [0, 0, 0, 0, 1 / 3, 2 / 3, 0, 0],
        [0, 0, 0, 0, 0, 1 / 2, 0, 1 / 2],
        [0, 0, 0, 0, 0, 0, 1, 0]]),

    '8': np.array([
        [0, 0, 0, 2 / 3, 0, 0, 1 / 3, 0],
        [0, 0, 0, 0, 1, 0, 0, 0],
        [5 / 6, 0, 0, 0, 0, 1 / 6, 0, 0],
        [1 / 4, 0, 0, 0, 0, 3 / 4, 0, 0],
        [0, 2 / 3, 0, 0, 0, 0, 1 / 3, 0],
        [0, 0, 3 / 4, 1 / 8, 0, 0, 1 / 8, 0],
        [1 / 2, 0, 0, 0, 0, 1 / 2, 0, 0],
        [0, 2 / 5, 0, 0, 0, 0, 0, 3 / 5]]),

    '9': np.array([
        [0, 1, 0, 0, 0, 0, 0],
        [1 / 3, 0, 1 / 3, 0, 1 / 3, 0, 0],
        [0, 0, 0, 1, 0, 0, 0],
        [1 / 2, 0, 1 / 4, 0, 1 / 4, 0, 0],
        [0, 1, 0, 0, 0, 0, 0],
        [1 / 4, 1 / 4, 0, 0, 1 / 4, 1 / 4, 0],
        [0, 0, 0, 1 / 3, 1 / 3, 1 / 3, 0]]),

    '10': np.array([
        [0, 0.5, 0.25, 0, 0.25],
        [0.167, 0, 0, 0.833, 0],
        [0.333, 0, 0, 0.667, 0],
        [0, 0.25, 0, 0, 0.75],
        [0.125, 0, 0, 0.875, 0]]),
}