почему возникает ошибка "index 4 is out of bounds for axis 0 with size 4"

import numpy as np
import matplotlib.pyplot as plt


def cubic_spline(x, y, y_prime):
    n = len(x)
    h = np.diff(x)

    alpha = np.zeros(n - 1)
    beta = np.zeros(n - 1)
    for i in range(1, n - 1):
        alpha[i] = h[i - 1] / (h[i - 1] + h[i])
        beta[i] = (3 / h[i]) * (y[i + 1] - y[i]) - (3 / h[i - 1]) * (y[i] - y[i - 1])

    c = np.zeros(n)
    l = np.zeros(n)
    mu = np.zeros(n)
    z = np.zeros(n)

    l[0] = 1
    mu[0] = 0
    z[0] = 0

    for i in range(1, n - 1):
        l[i] = 2 * (x[i + 1] - x[i - 1]) - h[i - 1] * mu[i - 1]
        mu[i] = h[i] / l[i]
        z[i] = (beta[i] - h[i - 1] * z[i - 1]) / l[i]

    l[-1] = 1
    z[-1] = 0
    c[-1] = 0

    for j in range(n - 2, -1, -1):
        c[j] = z[j] - mu[j] * c[j + 1]

    b = np.zeros(n - 1)
    d = np.zeros(n - 1)
    for j in range(n - 1):
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2 * c[j]) / 3
        d[j] = (c[j + 1] - c[j]) / (3 * h[j])

    return b, c, d


def evaluate_spline(x, a, b, c, d):
    n = len(a) + 1
    y = np.zeros_like(x)
    for i in range(n - 1):
        mask = (x >= x[i]) & (x <= x[i + 1])
        y[mask] = a[i] + b[i] * (x[mask] - x[i]) + c[i] * (x[mask] - x[i]) ** 2 + d[i] * (x[mask] - x[i]) ** 3
    return y


# Пример использования
x = np.array([0, 1, 2, 3, 4])  # Узлы сплайна
y = np.array([0, 1, 4, 1, 0])  # Значения функции в узлах сплайна
y_prime = np.array([1, 2, 1, -1, -2])  # Значения производной функции в узлах сплайна

b, c, d = cubic_spline(x, y, y_prime)

x_eval = np.linspace(0, 4, 100)
y_eval = evaluate_spline(x_eval, y, b, c, d)

plt.plot(x_eval, y_eval, label='Cubic Spline')
plt.scatter(x, y, color='red', label='Data Points')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.grid(True)
plt.show()

Ошибка после запуска следующая:

Traceback (most recent call last):   
  File "D:\pythonProject2\main1.py", line 62, in <module>
    y_eval = evaluate_spline(x_eval, y, b, c, d) 
  File "D:\pythonProject2\main1.py", line 50, in evaluate_spline
    y[mask] = a[i] + b[i] * (x[mask] - x[i]) + c[i] * (x[mask] - x[i]) ** 2 + d[i] * (x[mask] - x[i]) ** 3 
IndexError: index 4 is out of bounds for axis 0 with size 4