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

import numpy as np
import matplotlib.pyplot as plt

class Interpolation:
    def __init__(self):
        self.x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
        self.y = np.array([88, 136, 188, 244, 304, 368, 436, 508, 584, 664, 748])
        self.x_test = np.array([0, 1, 2])
        self.y_test = np.array([88, 136, 188])

    def Lagrange_Interpolating_Polynomial(self, x, y, t):
        z = 0
        for i in range(len(y)):
            p1 = 1; p2 = 1
            for j in range(len(x)):
                if i == j:
                    p1 = p1; p2 = p2
                else:
                    p1 *= (t-x[j])
                    p2 *= (x[i]-x[j])
            z += y[i] * p1/p2
        return z

    def Graphics(self):
        x_interpolation = np.linspace(np.min(self.x), np.max(self.x), 100)
        y_interpolation = [self.Lagrange_Interpolating_Polynomial(self.x_test, self.y_test, i) for i in x_interpolation]
        plt.plot(self.x, self.y, 'o', x_interpolation, y_interpolation)
        plt.legend(['Точки', 'Многочлен Лагранжа'])
        plt.grid(True)
        plt.show()


if __name__ == '__main__':
    i = Interpolation()
    i.Graphics()