numerical error

[hailunforthree]

if the random varible is close to zero, i.e., x->0, the result of pdf is not stable.
import numpy as np
import matplotlib.pyplot as plt

from torchquad import set_up_backend # Necessary to enable GPU support

import torch

if torch.cuda.is_available():

set_up_backend("torch", data_type="float32")

from torchlevy import stable_dist
eps=1e-6

1. 生成噪声样本

alpha = 1.5 # 稳定参数
beta = 0 # 对称
x = torch.linspace(-20,20,10000)
print(x.dtype)
f1 = stable_dist.pdf(x,alpha,beta)

3. 数值求导计算 f_v'(x)

f1_ = (stable_dist.pdf(x+eps,alpha,beta)-stable_dist.pdf(x,alpha,beta))/eps # 计算差分作为近似导数

将导数结果对齐为 bin_centers 的长度

4. 计算 g(x) = f_v'(x) / f_v(x)

threshold = 1e-3 # 避免除零的阈值
g1 = torch.where(f1 > threshold, -f1_ / f1 , 0)

5. 可视化结果

plt.figure(figsize=(20, 12))
plt.plot(x.cpu(),f1_.cpu()-f_, label="g(x) = f_v'(x) / f_v(x)")
plt.xlabel("x")
plt.ylabel("g(x)")
plt.xlim([-1, 1])
plt.legend()
plt.show()