task_2.py

import numpy as np


def check_convergence(A):
    for row in range(len(A)):
        if  (A[row][row] + A[row][row]) <= sum(A[row]):
            return False

    return True

def is_converged(diff, A_norm, eps):
    return np.linalg.norm(diff) <= eps \
                or A_norm > 1 / 2 and np.linalg.norm(diff) <= ((1 - A_norm) / A_norm) * eps

def solve_system(alpha, beta, eps):
    """
    Решает систему уравнений с помощью простого итерационного метода.

    Parameters:
        alpha (numpy.ndarray): Двумерный массив коэффициентов при неизвестных.
        beta (numpy.ndarray): Правая часть СЛАУ.
        eps (float): Критерий остановки.

    Returns:
        x (numpy.ndarray): Вектор решения системы уравнений.
    """
    size = len(alpha)
    solution = [0] * size

    for column in range(size):
        max_value = alpha[column][column]
        index = column
        for row in range(size):
            if max_value < alpha[row][column]:
                max_value = alpha[row][column]
                index = row        

        for el in range(size):
            alpha[column][el], alpha[index][el] = alpha[index][el], alpha[column][el]
  
    A_norm = np.linalg.norm(alpha)

    if not check_convergence(alpha):
        return None 
    
    while True:

        next_step = [0] * size

        for row in range(size):
            sum = beta[row]

            for column in range(size):
                if column != row:
                    sum -= float(alpha[row][column]) * float(solution[column])

            next_step[row] = sum / float(alpha[row][row])

        diff = [0] * size
        for i in range(size):
            diff[i] = solution[i] - next_step[i]

        
        solution = next_step

        if is_converged(diff, A_norm, eps):
            return solution


alpha = np.array([
    [1, 12, -2, -5],
    [5, -3, 13, 0],
    [20, 2, 3, 7], 
    [0, 0, -1, 15]
    ])
beta = np.array([5, 4, -3, 7])
x = solve_system(alpha, beta, 1e-3)
print(x)