from math import *
import numpy as np


def lin_intp(x, fx, num):
    '''
    :param x: x values (np array!)
    :param fx: f(x) exact values
    :param num: num to find
    :return: [y, r] where y - f(num), r - mistake
    '''
    def find_nearest(array, value):
        idx = (np.abs(array - value)).argmin()
        return idx
    nearest = x[find_nearest(x, num)]
    q = (num - nearest) / (x[1] - x[0])
    y0 = fx[find_nearest(x, num)]
    dlty = fx[find_nearest(x, num) + 1] - fx[find_nearest(x, num)]
    y = y0 + q * dlty
    delta = [dlty, fx[find_nearest(x, num) + 2] - fx[find_nearest(x, num) + 1]]
    delta = round(round(delta[1], 4) - round(delta[0], 4), 4)
    r = abs((delta * y0) / 2 * q * (q - 1))
    return [y, r]


x = np.array([0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6])
fx = [round(exp(i), 4) for i in x]
num = 0.541
answer = lin_intp(x, fx, num)
print(f'Ответ: {answer[0]}')
print(f'Ошибка: {answer[1]}')


def sq_intp(x, fx, num):
    '''
    :param x: x values (np array!)
    :param fx: f(x) exact values
    :param num: num to find
    :return: [y, r] where y - f(num), r - mistake
    '''
    def find_nearest(array, value):
            idx = (np.abs(array - value)).argmin()
            return idx
    nearest = x[find_nearest(x, num)]
    q = (num - nearest) / (x[1] - x[0])
    y0 = fx[find_nearest(x, num)]
    dlty1 = fx[find_nearest(x, num) + 1] - fx[find_nearest(x, num)]
    dlty2 = abs(dlty1 - (fx[find_nearest(x, num)] - fx[find_nearest(x, num) - 1]))
    dlty3 = dlty2 - (abs(fx[find_nearest(x, num) + 2] - fx[find_nearest(x, num) + 1]) - dlty1)
    y = y0 + q * dlty1 + abs(q*(q-1)/2) * dlty2
    r = dlty3/6 * abs(q*(q-1)*(q-2))
    return [y, r]


x = np.array([1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5])
fx = [0.89121, 0.93204, 0.96356, 0.98545, 0.99749, 0.99957, 0.99166, 0.97385, 0.9463, 0.9093, 0.86321, 0.8085, 0.74571, 0.67546, 0.59847]
num = 1.538
answer = sq_intp(x, fx, num)
print(f'Ответ: {answer[0]}')
print(f'Ошибка: {answer[1]}')