main.py

# Press the green button in the gutter to run the script.
def alpha(a, b, pi, sequence):
    alpha = list()

    curr = []
    for i in range(0, len(a[0])):
        var = float(pi[i] * b[i][sequence[0] - 1])
        curr.append(var)
    alpha.append(curr)

    for x in range(1, len(sequence)):
        curr = []
        for i in range(0, len(a[0])):
            var = 0
            for j in range(0, len(a[0])):
                var += float(a[j][i] * alpha[x - 1][j])
            curr.append(var * b[i][sequence[x] - 1])
        alpha.append(curr)

    for x in range(0, len(alpha)):
        print(f" alpha_t({x + 1})  |", end="")
    print("\n", "______________ " * len(alpha[0]))
    for x in alpha:
        for y in x:
            print(str(round(y, 6)).center(13), end="|")
        print("\n", "______________ " * len(alpha[0]))
    return alpha


def delta(a, b, pi, sequence):
    delta = list()

    curr = []
    for i in range(0, len(a[0])):
        var = float(pi[i] * b[i][sequence[0] - 1])
        curr.append(var)
    delta.append(curr)

    for x in range(1, len(sequence)):
        curr = []
        for i in range(0, len(a[0])):
            var = -1.0
            for j in range(0, len(a[0])):
                var = max(var, float(a[j][i] * delta[x - 1][j]))
            curr.append(var * b[i][sequence[x] - 1])
        delta.append(curr)

    for x in range(0, len(delta[0])):
        print(f" delta_t({x + 1})  |", end="")
    print("\n", "______________ " * len(delta[0]))
    for x in delta:
        for y in x:
            print(str(round(y, 6)).center(18), end="|")
        print("\n", "______________ " * len(delta[0]))
    return delta


if __name__ == '__main__':
    # Transition properties
    # a[i][j] = probability of traveling to state j from state i
    a = [[0.3, 0.3, 0.4],
         [0.2, 0.7, 0.1],
         [0.2, 0.5, 0.3]]

    # Emission probabilities
    # b[i][x] = Probability of emitting output x at state i
    b = [[0.1, 0.0, 0.9],
         [0.3, 0.4, 0.3],
         [0.7, 0.2, 0.1]]

    # pi[i] = Probability of starting at state i
    pi = [0.2, 0.5, 0.3]

    # Observed output sequence
    sequence = [1, 2, 3, 1, 1, 4]

    #  Prints alpha table and returns matrix
    alpha_table = alpha(a, b, pi, sequence)

    # Prints delta table and returns matrix
    delta_table = delta(a, b, pi, sequence)