示例10 工程实践五件套

"""ex10_practices.py — 第 9 章 工程实践要点

汇总工程上常踩的坑：

• 短序列、无偏 DFA 的取舍
• polOrd 选择对趋势序列的影响
• wins 上限的统计稳定性
• log-log 拟合区间的选择（避免曲尾）
• 用 surrogate / shuffle 估计置信区间

对应教程：tutorials/09-practices.md。

运行：
python ex10_practices.py
"""

import numpy as np
import fathon
from fathon import fathonUtils as fu

def estimate_H(profile, wins, **kw):
dfa = fathon.DFA(profile)
dfa.computeFlucVec(wins, **kw)
H, _ = dfa.fitFlucVec()
return H

def short_sequence_bias():
"""短序列下 unbiased 的作用。"""
print("=== 短序列 (L=500) unbiased 对比 ===")
np.random.seed(0)
profile = fu.toAggregated(np.random.randn(500))
wins = fu.linRangeByStep(10, 120)
H_biased = estimate_H(profile, wins, revSeg=False, unbiased=False)
H_unbiased = estimate_H(profile, wins, revSeg=False, unbiased=True)
print(f" biased H = {H_biased:.4f}")
print(f" unbiased H = {H_unbiased:.4f}")
print(f" 白噪声理论 H = 0.5；unbiased 通常更接近。")

def polord_on_trend():
"""对带趋势的序列，不同 polOrd 的表现。"""
print("\n=== polOrd 对带趋势序列的影响 ===")
np.random.seed(1)
L = 5000
t = np.arange(L)
trend = 0.0008 * t + 0.0000001 * t ** 2 # 线性 + 微弱二次趋势
noise = np.random.randn(L)
series = noise + trend
profile = fu.toAggregated(series)
wins = fu.linRangeByStep(10, L // 4, step=20)
for polOrd in [1, 2, 3]:
H = estimate_H(profile, wins, revSeg=True, polOrd=polOrd)
print(f" polOrd={polOrd} H={H:.4f}")
print(" 含二次趋势时，polOrd=2 通常比 polOrd=1 更稳。")

def window_upper_bound_stability():
"""窗口上限对 H 稳定性的影响。"""
print("\n=== 窗口上限对 H 的影响 ===")
np.random.seed(2)
profile = fu.toAggregated(np.random.randn(8000))
for hi_frac in [0.1, 0.25, 0.4, 0.5]:
wins = fu.linRangeByStep(10, int(8000 * hi_frac), step=20)
H = estimate_H(profile, wins, revSeg=True)
print(f" 上限 = L*{hi_frac:.2f} (={int(8000*hi_frac):4d}) H={H:.4f}")
print(" 上限超过 L/4 后，段数过少，H 估计方差变大。")

def surrogate_confidence():
"""打乱（shuffle）surrogate：估计 H 的零假设分布。"""
print("\n=== shuffle surrogate 置信区间 ===")
rng = np.random.default_rng(3)
increments = rng.standard_normal(4000)
profile = fu.toAggregated(increments)
wins = fu.linRangeByStep(10, 1000, step=20)

H_real = estimate_H(profile, wins, revSeg=True)

# 打乱增量顺序：破坏长记忆，但保留边缘分布。期望 H ≈ 0.5
H_shuffled = []
for _ in range(30):
    shuffled = rng.permutation(increments)
    H_shuffled.append(estimate_H(fu.toAggregated(shuffled), wins, revSeg=True))
H_shuffled = np.array(H_shuffled)

print(f"  原序列     H = {H_real:.4f}")
print(f"  shuffled   H 均值={H_shuffled.mean():.4f}  "
      f"95% 区间=[{np.percentile(H_shuffled, 2.5):.4f}, "
      f"{np.percentile(H_shuffled, 97.5):.4f}]")
print("  若原序列 H 显著偏离 shuffled 区间，提示存在真实长记忆。")
​

def fit_range_selection():
"""拟合区间的取舍：避免曲线两端的曲尾。"""
print("\n=== 拟合区间选择 (nStart / nEnd) ===")
np.random.seed(4)
profile = fu.toAggregated(np.random.randn(6000))
wins = fu.linRangeByStep(10, 1500)
dfa = fathon.DFA(profile)
dfa.computeFlucVec(wins, revSeg=True)

# 全区间 vs 去掉两端
H_full, _ = dfa.fitFlucVec()
H_trim, _ = dfa.fitFlucVec(nStart=20, nEnd=800)
print(f"  全区间 [10, 1500]     H = {H_full:.4f}")
print(f"  裁剪后 [20, 800]      H = {H_trim:.4f}")
print("  曲尾（极大/极小窗口）易受边界效应影响，裁剪后 H 更可信。")
​

def main():
short_sequence_bias()
polord_on_trend()
window_upper_bound_stability()
surrogate_confidence()
fit_range_selection()

if name == "main":
main()