ter inf 5, 6 lab

5.1.py

import formulas as f

matrix: list = [
    [1/16, 6/16, 1/16],
    [3/16, 2/16, 3/16],
]


if __name__ == '__main__':
    h_a, h_b = f.H(matrix)
    h_b_if_a = f.H_B_if_A(matrix)
    h_ab = f.H_AB(h_a, h_b_if_a)
    
    I_B = f.I_B(h_b, h_b_if_a)
    I_A = f.I_A(h_a, h_b, h_ab)
    print(
        f'I_B = {I_B} == I_A = {I_A}'
    )

    mean_x, mean_y, mean_xy = f.mean(matrix)
    print(
        f'MX = {mean_x}  MY = {mean_y} MXY = {mean_xy}'
    )

    cov = f.covariation(mean_x, mean_y, mean_xy)
    dispersion_x, dispersion_y = f.dispersion(matrix, mean_x, mean_y)
    correlation = f.correlation(
        cov,
        f.standart_deviation(dispersion_x),
        f.standart_deviation(dispersion_y)
    )
    print(
        f'COV = {cov} DX = {dispersion_x} DY = {dispersion_y} COR = {correlation}'
    )

5.2.py

import formulas as f


matrix: list = [
    [1/36, 0, 0, 0, 0, 0],
    [0, 2/36, 0, 0, 0, 0],
    [0, 1/36, 2/36, 0, 0, 0],
    [0, 0, 2/36, 2/36, 0, 0],
    [0, 0, 1/36, 2/36, 2/36, 0],
    [0, 0, 0, 2/36, 2/36, 2/36],
    [0, 0, 0, 1/36, 2/36, 2/36],
    [0, 0, 0, 0, 2/36, 2/36],
    [0, 0, 0, 0, 1/36, 2/36],
    [0, 0, 0, 0, 0, 2/36],
    [0, 0, 0, 0, 0, 1/36],
]


if __name__ == '__main__':
    mean_x, mean_y, mean_xy = f.mean(matrix)
    print(f'MX = {mean_x}  MY = {mean_y}')

    dispersion_x, dispersion_y = f.dispersion(matrix, mean_x, mean_y)
    print(f'DX = {dispersion_x}  DY = {dispersion_y}')
    
    correlation = f.correlation(
        f.covariation(mean_x, mean_y, mean_xy),
        f.standart_deviation(dispersion_x),
        f.standart_deviation(dispersion_y)
    )
    print(f'cor = {correlation}')

    print(
        f'r(SM)(DS/DM)^1/2 = {correlation * ((dispersion_x/dispersion_y) ** 0.5)}'
    )

    h_s, h_m = f.H(matrix)
    print(f'HS = {h_s}  HM = {h_m}')


    i_m = f.I_B(h_m, f.H_B_if_A(matrix))
    print(f'IM = {i_m}')

    h_s_if_m = f.H_A_if_B(matrix, True)

6.py

import pandas as pd
from pandas.core.frame import DataFrame

import formulas as f


def init(file_name: str) -> DataFrame:
    return pd.read_csv(file_name)


def task1(data: DataFrame, n_columns: int) -> None:
    for i in range(n_columns):
        item = data.columns[i]
        unique_elems = ' '.join(data[item].unique())
        print(f'{item} : {unique_elems}')


def task2(data: DataFrame) -> None:
    for i in range(1, 4):
        column = data.columns[-i]
        data[column] = data[column].map(range_marks)
    #print(data)


def range_marks(x) -> str:
    if x < 50:
        return 'очень плохо'
    elif x < 60:
        return 'плохо'
    elif x < 66:
        return 'посредственно'
    elif x < 72:
        return 'хорошо'
    elif x < 78:
        return 'очень хорошо'
    elif x < 85:
        return 'отлично'
    elif x <= 100:
        return 'превосходно'
    else:
        return 'unexpected value'


def task3(data: DataFrame, row: str, col: str) -> DataFrame:
    unique_row = data[row].unique()
    unique_col = data[col].unique()

    res = pd.DataFrame(columns=unique_col, index=unique_row)
    for r in unique_row:
        for c in unique_col:
            res.at[r, c] = len(
                data[(data[row] == r) & (data[col] == c)]
            ) / len(data)
    #print(res)
    return res


def task4(data: DataFrame) -> float:
    h_a, h_b = f.H(data.values.tolist())
    h_b_if_a = f.H_B_if_A(data.values.tolist())
    return f.H_AB(h_a, h_b_if_a)


def task5(data: DataFrame) -> float:
    h_a, h_b = f.H(data.values.tolist())
    h_b_if_a = f.H_B_if_A(data.values.tolist())
    h_ab = f.H_AB(h_a, h_b_if_a)
    return f.I_A(h_a, h_b, h_ab)


def test(data: DataFrame, to_test: list) -> None:
    for testing in to_test:
        for test in data.columns:
            if testing != test:
                I = task5(task3(data, testing, test))
                alias = '-'.join([testing, test])
                print(f'{alias}: {I:.5f}')
        print()


if __name__ == '__main__':
    data = init('StudentsPerformance.csv')
    #task1(data, 5)
    task2(data)
    table = task3(data, 'gender', 'math score')
    res = task4(table)
    print(f'H(AB) = {res}')

    test(
        data,
        ['math score', 'reading score', 'writing score']
    )

formulas.py

import math


def __get_matrix(matrix: list) -> tuple:
    return len(matrix), len(matrix[0])


def mean(matrix: list) -> tuple:
    n, m = __get_matrix(matrix)
    mean_x, mean_y, mean_xy = 0, 0, 0

    for i in range(n):
        for j in range(m):
            mean_x += i * matrix[i][j]
            mean_y += j * matrix[i][j]
            mean_xy += i*j * matrix[i][j] 
    return mean_x, mean_y, mean_xy


def covariation(mean_x: float, mean_y: float, mean_xy: float) -> float:
    return mean_xy - mean_x*mean_y


def dispersion(matrix: list, mean_x: float, mean_y: float) -> tuple:
    n, m = __get_matrix(matrix)
    
    d_x, d_y = 0, 0
    for i in range(n):
        for j in range(m):
            d_x += i*i * matrix[i][j]
            d_y += j*j * matrix[i][j]
    d_x -= mean_x ** 2
    d_y -= mean_y ** 2
    return d_x, d_y


def standart_deviation(dispersion: float) -> float:
    return math.sqrt(dispersion)


def correlation(cov: float, deviation_x: float, deviation_y: float) -> float:
    return cov / (deviation_x * deviation_y)


def H(matrix: list) -> tuple:
    n, m = __get_matrix(matrix)
    
    H_A = 0
    for row in matrix:
        a_i = sum(row)
        if a_i:
            H_A += a_i * math.log2(a_i)
    
    H_B = 0
    for i in range(m):
        b_i = 0
        for j in range(n):
            b_i += matrix[j][i]
        if b_i:
            H_B += b_i * math.log2(b_i)
    
    return -H_A, -H_B


def H_B_if_A(matrix: list) -> float:
    n, m = __get_matrix(matrix)

    res = 0
    for i in range(n):
        H = 0
        for j in range(m):
            p = matrix[i][j] / sum(matrix[i])
            if p:
                H += p * math.log2(p)
        res += sum(matrix[i]) * H
    
    return -res


def H_A_if_B(matrix: list, prnt: bool=False) -> float:
    n, m = __get_matrix(matrix)

    res = 0
    for i in range(m):
        H = 0
        sum = 0
        for j in range(n):
            sum += matrix[j][i]
        for j in range(n):
            p = matrix[j][i] / sum
            if p:
                H += p * math.log2(p)
        res += H
        if prnt:
            print(f'M = {i} | {-H}')
    return -res


def H_AB(H: float, H2: float) -> float:
    """H_A + H_Bifa or HB + H_AifB"""
    return H + H2


def I_A(h_a: float, h_b: float, h_ab: float) -> float:
    return h_a + h_b - h_ab


def I_B(h_b: float, h_b_if_a: float) -> float:
    return h_b - h_b_if_a

task2.py

import formulas as f

matrix1: list = [
    
]

matrix2: list = [
    [1/36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 3/36, 0, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 3/36, 0, 0, 2/36, 0, 0, 0, 0, 0],
    [0, 0, 0, 5/36, 0, 0, 0, 2/36, 0, 0, 0],
    [0, 0, 0, 0, 3/36, 0, 2/36, 0, 2/36, 2/36, 0],
    [0, 0, 0, 0, 0, 7/36, 0, 2/36, 0, 0, 2/36],
]

matrix3: list = [
    [0, 1/32, 0, 0, 0, 0],
    [1/32, 0, 8/32, 4/32, 2/32, 1/32],
    [0, 8/32, 0, 0, 0, 0],
    [0, 4/32, 0, 0, 0, 0],
    [0, 2/32, 0, 0, 0, 0],
    [0, 1/32, 0, 0, 0, 0],
]


if __name__ == "__main__":
    matrix = matrix2
    h_a, h_b = f.H(matrix)
    print(
        f'H(A) = {h_a}  H(B) = {h_b}'
    )

    h_ab = f.H_AB(h_b, f.H_A_if_B(matrix))
    print(f'H(AB) = {h_ab}')

    i_a = f.I_A(h_a, h_b, h_ab)
    print(f'I_A(B) = {i_a}')