№6 Приложения метода Гаусса

import numpy as np


def print_matrix(matrix):
    print(np.array_str(matrix, precision=5, suppress_small=True))

def gauss(A):
    A = np.array(A, dtype=float)
    n, m = A.shape

    # Прямой ход
    for i in range(n):
        max_row = i + np.argmax(np.abs(A[i:, i]))
        A[[i, max_row]] = A[[max_row, i]]

        div = A[i, i]
        A[i] /= div

        for j in range(i + 1, n):
            factor = A[j, i]
            A[j] -= factor * A[i]

    print(f"\nМатрица после прямого хода:")
    print_matrix(A)

    # Обратный ход
    for j in range(n - 1, -1, -1):
        for i in range(j - 1, -1, -1):
            d = A[i, j] / A[j, j]
            A[i, j:] -= A[j, j:] * d

    print("Обратный ход метода Гаусса:")
    print_matrix(A)
    print()

    s = [round(A[i, -1] / A[i, i], 4) for i in range(n)]
    print("Решение СЛАУ:")
    print(*s)

    return A


def determinant(A):
    A = np.array(A, dtype=float)
    n = A.shape[0]
    det = 1
    for j in range(n):
        if A[j, j] == 0:
            return 0  # Если на диагонали 0, то матрица вырождена
        det *= A[j, j]
        for i in range(j + 1, n):
            if A[i, j] != 0:
                d = A[i, j] / A[j, j]
                A[i, j:] -= A[j, j:] * d
    return det


def inverse_matrix(A):
    n = len(A)
    A = np.array(A, dtype=float)
    inv_A = np.hstack([A, np.eye(n)])
    res_A = gauss(inv_A)
    return res_A[:, n:]


A = np.array([
    [7, 0, 1, 2],
    [5, 4, 3, 8],
    [1, 2, 3, 4],
    [5, 2, 2, 5]])

det = determinant(A)
print(f"\nОпределитель: {det:0.4f}")

inv_A = inverse_matrix(A)
print("\nОбратная матрица:")
for row in inv_A:
    print(" ".join([f"{x:0.4f}" for x in row]))