8/code/graph2.py - master - levg/numm

8/code/graph2.py
81 строка3 KB
Лев Черняховский
29 окт 2024, 10:38
29 окт 2024, 10:38d9048cd
import numpy as np
import matplotlib.pyplot as plt
import math


def load_data(filename):
    data = np.loadtxt('C:/Users/Aser/source/repos/Chisl2sem1homework/'+filename)
    return data[:, 0], data[:, 1], data[:, 2], data[:, 3]

def compute_theoretical_error(x, nodes_x, max_derivative):
    n = len(nodes_x) - 1
    theoretical_error = np.zeros_like(x)
    
    for i in range(len(x)):
        product = 1.0
        for node in nodes_x:
            if (x[i] - node)!=0:
                product *= (x[i] - node)

        if product == 0:
            print(f"Внимание: Произведение равно 0 для x[{i}]={x[i]}")

        theoretical_error[i] = abs(product * 10**130 / np.math.factorial(n + 1))
    
    return theoretical_error

def plot_functions_and_interpolations(interp_files, labels, title):
    plt.figure(figsize=(10, 6))
    
    for i, interp_file in enumerate(interp_files):
        x, f_value, p_value, error = load_data(interp_file)
        
        if i == 0:
            plt.plot(x, f_value, label='Функция', color='black', linewidth=2)
        
        plt.plot(x, p_value, label=labels[i])

    plt.title(title)
    plt.xlabel('x')
    plt.ylabel('y')
    plt.legend()
    plt.grid(True)
    plt.show()

def plot_errors(interp_files, labels, title, max_derivative):
    plt.figure(figsize=(10, 6))
    
    for i, interp_file in enumerate(interp_files):
        x, f_value, p_value, error = load_data(interp_file)
        
        nodes_x = np.unique(x)
        
        plt.plot(x, error, label=f'Ошибка: {labels[i]}')
        
        theoretical_error = compute_theoretical_error(x, nodes_x, max_derivative)
        print(theoretical_error)
        if i==0: 
            plt.plot(x, theoretical_error, label=f'Теоретическая ошибка {labels[i]}', linestyle=':')

    plt.title(title)
    plt.xlabel('x')
    plt.ylabel('Ошибка')
    plt.legend()
    plt.grid(True)
    plt.show()

nfunc = 2
interp_files1_uniform = [f'error_uniform_func{nfunc}_5.txt', f'error_uniform_func{nfunc}_6.txt', f'error_uniform_func{nfunc}_7.txt']
interp_files1_chebyshev = [f'error_chebyshev_func{nfunc}_5.txt', f'error_chebyshev_func{nfunc}_6.txt', f'error_chebyshev_func{nfunc}_7.txt']

max_derivative_uniform = 8
max_derivative_chebyshev =8

labels_uniform = [
    'Полином 5 узлов',
    'Полином 6 узлов',
    'Полином 7 узлов'
]

plot_errors(interp_files1_uniform, labels_uniform, f"Ошибка интерполяции для функции {nfunc} (Равномерная сетка)", max_derivative_uniform)
plot_errors(interp_files1_chebyshev, labels_uniform, f"Ошибка интерполяции для функции {nfunc} (Чебышевская сетка)", max_derivative_chebyshev)