# -*- coding: utf-8 -*-
"""
Интерполяционный многочлен Лагранжа
"""

import numpy as np
import matplotlib.pyplot as plt

class Interpolation:

    def __init__(self, x_points, y_points, x_Lagrange, y_Lagrange):
        self.x_points = x_points
        self.y_points = y_points
        self.x_Lagrange = x_Lagrange
        self.y_Lagrange = y_Lagrange

    def Lagrange_Interpolating_Polynomial(self, x_array, y_array, x_argument):
        y_argument = 0
        for i in range(len(y_array)):
            p1 = 1; p2 = 1
            for j in range(len(x_array)):
                if i == j:
                    p1 = p1; p2 = p2
                else:
                    p1 *= (x_argument - x_array[j])
                    p2 *= (x_array[i] - x_array[j])
            y_argument += y_array[i] * p1 / p2
        return y_argument

    def Plot(self):
        x_interpolation = np.linspace(np.min(self.x_points), np.max(self.x_points), 100)
        y_interpolation = [self.Lagrange_Interpolating_Polynomial(self.x_Lagrange, self.y_Lagrange, i) for i in x_interpolation]
        plt.plot(self.x_points, self.y_points, 'o--', x_interpolation, y_interpolation, '-.')
        plt.legend(['Точки', 'Многочлен Лагранжа'])
        plt.grid(True)
        plt.show()

if __name__ == '__main__':

    x_points = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
    y_points = np.array([88, 136, 188, 244, 304, 368, 436, 508, 584, 664, 748])
    x_Lagrange = np.array([0, 1, 2])
    y_Lagrange = np.array([88, 136, 188])
    interpolation = Interpolation(x_points, y_points, x_Lagrange, y_Lagrange)
    interpolation.Plot()
    #Проверка
    for i in x_points:
        print(i*0.5, interpolation.Lagrange_Interpolating_Polynomial(x_Lagrange, y_Lagrange, i*0.5))