from dataclasses import dataclass
import matplotlib.pyplot as plt
import numpy as np


@dataclass
class Point:
    x: float
    y: float


def interpolation_lagrange(points: list[Point], x: float, show_polynome: bool=False) -> float:
    """

    :param points: Les points de la courbe représentant une fonction
    :param x: le x en entrée de la fonction où on veut interpoler
    :return: L'interpolation
    """

    interpolation: float = 0.
    n = len(points) # nombre de points
    for i in range(n):
        term: float = 1. # 0.0 will always give 0, it's a product ! So lets put 1
        # Lagrange L(x)
        for k in range(n):
            if k != i:
                term *= ((x - points[k].x) / (points[i].x - points[k].x))

            # erreur ici, voir le chat
            if show_polynome:
                print(f'P(x) = (({x} - {points[k].x}) / ({points[i].x} - {points[k].x}))')

        # interpolation with a piece of Lagrange (y_i)
        interpolation += term * points[i].y

    return interpolation


def interpolation_newton(points: list[Point], x: float) -> float:
    interpolation = 0. # alpha sum
    n = len(points)
    for i in range(n):
        a_i = 1.
        for k in range(n-1):
            a_i *= (points[k+1].y - points[k].y) / (points[k+1].x - points[k].x)

    return interpolation


def interpolation_moindre_carree(points: list[Point], x: float) -> float:
    interpolation = 0.

    pass


def test() -> None:
    points = [Point(0, 1), Point(1, 3), Point(2, 2)]
    x = 1.5
    result = interpolation_lagrange(points, x)
    print(f"P({x}) = {result}")  # Doit afficher 2.875


def exercice1() -> None:
    points = [Point(-1,0), Point(0,-1), Point(1,0), Point(3,70)]

    inter_x2 = interpolation_lagrange(points, 2, True)
    inter_x3 = interpolation_lagrange(points, 3, True)
    print(f"X2={inter_x2}, X3={inter_x3}")

    x = np.linspace(0, 4, 300)
    y = [interpolation_lagrange(points, x[i]) for i in range(len(x))]

    # extrapolation
    plt.plot(x, y)
    plt.title('fonction f(x) ex 1')
    plt.show()


def exercice2() -> None:
    pass

if __name__ == '__main__':
    exercice1()