import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

def rolling_polyfit_curves(series, degree=3, window=50, step=10):
    curves = []  # Liste des courbes
    positions = []  # Index de départ pour chaque courbe

    for i in range(window, len(series), step):
        y = series[i - window:i].values
        x = np.arange(window)
        coeffs = np.polyfit(x, y, degree)
        poly = np.poly1d(coeffs)
        curve = poly(x)
        curves.append(curve)
        positions.append(i)

    return curves, positions

# Exemple d'utilisation

# Exemple avec une série synthétique
np.random.seed(0)
x = np.linspace(0, 20, 250)
y = 0.05 * x**3 - x**2 + 2 * x + 5 + np.random.normal(0, 15, size=len(x))
series = pd.Series(y)

# series = pd.Series(np.sin(np.linspace(0, 10*np.pi, 300)) + np.random.normal(0, 0.2, 300))
curves, positions = rolling_polyfit_curves(series, degree=3, window=50, step=10)

# Visualisation
plt.figure(figsize=(12, 6))
plt.plot(series.values, label="Original")

for curve, pos in zip(curves, positions):
    x_global = np.arange(pos - 50, pos)
    plt.plot(x_global, curve, alpha=0.6)

plt.title("Régressions polynomiales glissantes (chaque 10 bougies sur 50 précédentes)")
plt.legend()
plt.grid(True)
plt.show()