sem4

import numpy as np
import matplotlib.pyplot as plt

a = 1e-2
b = 5 * np.exp(1)


def f_(x):
    return np.log(x)


def g(x, a, b):
    return a0(a, b) + x * a1(a, b)


def a0_opt(x):
    n = len(x)
    return (np.sum(x ** 2) * np.sum(f_(x)) - np.sum(x) * np.sum(x * f_(x))) / ((n * np.sum(x ** 2)) - np.sum(x) ** 2)


def a1_opt(x):
    n = len(x)
    return (n * np.sum(x * f_(x)) - np.sum(x) * np.sum(f_(x))) / ((n * np.sum(x ** 2)) - np.sum(x) ** 2)


def f(x):
    return a0_opt(x) + a1_opt(x) * x


def approximation(a, b):
    f_xNodes = np.linspace(a, b, 1000)
    f_yNodes = [f_(x) for x in f_xNodes]
    plt.plot(f_xNodes, f_yNodes, color='red', label='f(x) = ln(x)')

    for n in range(3, 301):
        xNodes = np.linspace(a, b, n)
        yNodes = f(xNodes)
        plt.plot(xNodes, yNodes)

    plt.legend()
    plt.grid(True)
    plt.show()


def a0(a, b):
    return (b * (np.log(b) - 1) - a * (np.log(a) - 1)) / (b - a)


def a1(a, b):
    return ((((b ** 2) * (2 * np.log(b) - 1))/4) - ((a ** 2) * (2 * np.log(a) - 1)/4)) / (b ** 2 / 2 - a ** 2 / 2)


def app(a, b):
    g_xNodes = np.linspace(a, b, 1000)
    # ln(x)
    f_yNodes = [f_(x) for x in g_xNodes]
    # g(x)
    g_yNodes = [g(x, a, b) for x in g_xNodes]
    plt.plot(g_xNodes, f_yNodes, color='red', label='ln(x)')
    plt.plot(g_xNodes, g_yNodes, color='blue', label='g(x)')
    plt.legend()
    plt.grid(True)
    plt.show()


if __name__ == '__main__':
    # approximation(a, b)
    print(a0(a, b))
    print(a1(a, b))
    app(a, b)