计算数列的微分（整数阶微分）

import numpy as np
from scipy.special import gamma
from scipy.linalg import toeplitz
import matplotlib.pyplot as plt
 
# 第一种实现方式
def fgl_deriv(a, y, h=0.01):
    """
    Args:
        a: 微分阶数，整数
        y: 求微分的数列
        h: 步伐
    Returns:
    """
    n = len(y)
    J = np.arange(n)
    G1 = gamma(J + 1)
    G2 = gamma(a + 1 - J)
    s = (-1) ** J
 
    M = np.tril(np.ones((n, n)))
    R = np.array([y[i-j] for i in range(n) for j in range(n)]).reshape((n, n))
    T = (gamma(a + 1) / (h ** a)) * s / (G1 * G2)
    Y = np.sum(R * (M * T[:, None].T), axis=1)
 
    return Y
 
# # 第二种实现方式
# def fgl_deriv(a, y, h):
#     n = len(y)
#     J = np.arange(n)
#     G1 = gamma(J + 1)
#     G2 = gamma(a + 1 - J)
#     s = (-1) ** J
#
#     M = np.tril(np.ones((n, n)))
#     R = toeplitz(y)
#     T = np.meshgrid((gamma(a + 1) / (h ** a)) * s / (G1 * G2))[0]
#     Y = np.reshape(np.sum(R * M * T, axis=1), y.shape)
#
#     return Y
 
 
 
data = np.random.random((100))
data = np.sin(data)
 
dataa = fgl_deriv(1, data)
print(dataa)
# plt.plot(range(len(data)),data, label="001",linewidth=1.5)
plt.plot(range(len(data)),dataa, label="001",linewidth=1.5)
plt.show()