示例04 DFA 全 API 演练

"""ex04_dfa_api_full.py — 第 4 章 DFA 核心 API 全家桶

演示：

• computeFlucVec 的关键参数（polOrd / revSeg / unbiased）
• fitFlucVec 的多区间拟合 multiFitFlucVec
• saveObject 序列化、还原后直接 fitFlucVec 跳过重算

对应教程：tutorials/04-dfa-api.md、tutorials/03-dfa-principles.md 3.7 节。

运行：
python ex04_dfa_api_full.py
"""

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

def demo_polord_revesg():
"""polOrd 与 revSeg 对 H 的影响。"""
np.random.seed(1)
profile = fu.toAggregated(np.random.randn(8000))
wins = fu.linRangeByStep(10, 2000)

print("=== polOrd / revSeg 对比 ===")
for polOrd in [1, 2, 3]:
    for revSeg in [False, True]:
        dfa = fathon.DFA(profile)
        dfa.computeFlucVec(wins, revSeg=revSeg, polOrd=polOrd)
        H, _ = dfa.fitFlucVec()
        print(f"  polOrd={polOrd} revSeg={revSeg!s:5s}  H={H:.4f}")
​

def demo_multi_fit():
"""multiFitFlucVec：对多个尺度区间分别拟合，揭示多重标度。"""
np.random.seed(2)
profile = fu.toAggregated(np.cumsum(np.random.randn(8000)))
wins = fu.linRangeByStep(10, 2000)

dfa = fathon.DFA(profile)
dfa.computeFlucVec(wins, revSeg=True)

# 两个拟合区间：短尺度 vs 长尺度
limits = np.array([[15, 200], [200, 1800]], dtype=int)
H_list, _ = dfa.multiFitFlucVec(limits)

print("\n=== multiFitFlucVec 多区间拟合 ===")
for (lo, hi), H in zip(limits, H_list):
    print(f"  区间 [{lo:4d}, {hi:4d}]  H={H:.4f}")
print("若两区间 H 差异显著，提示多重标度 → 考虑 MFDFA（ex05）。")
​

def demo_save_object():
"""saveObject / 还原：把计算结果存盘，下次跳过 computeFlucVec。"""
import os
np.random.seed(3)
profile = fu.toAggregated(np.random.randn(5000))

dfa = fathon.DFA(profile)
dfa.computeFlucVec(fu.linRangeByStep(10, 1000))
H_save, _ = dfa.fitFlucVec()
dfa.saveObject("ex04_analysis")     # 写入 ex04_analysis.fathon

# 下次直接还原并 fit，不必重算波动
dfa2 = fathon.DFA()
dfa2.loadObject("ex04_analysis")
H_load, _ = dfa2.fitFlucVec()

print("\n=== saveObject / loadObject ===")
print(f"  保存时 H = {H_save:.4f}")
print(f"  还原后 H = {H_load:.4f}")
print(f"  差异     = {abs(H_save - H_load):.2e}")

# 清理演示文件
try:
    os.remove("ex04_analysis.fathon")
except OSError:
    pass
​

def demo_unbiased_short():
"""短序列下 unbiased=True vs False 的 H 差异。"""
np.random.seed(4)
# 故意用短序列（L=500）放大有限样本偏差
profile = fu.toAggregated(np.random.randn(500))
wins = fu.linRangeByStep(10, 120)

print("\n=== unbiased (短序列 L=500) ===")
for unbiased in [False, True]:
    dfa = fathon.DFA(profile)
    # 注意：unbiased=True 时 revSeg 被忽略（教程 3.7）
    dfa.computeFlucVec(wins, revSeg=False, unbiased=unbiased)
    H, _ = dfa.fitFlucVec()
    print(f"  unbiased={unbiased!s:5s}  H={H:.4f}")
print("短序列 unbiased 通常更接近渐近 0.5。")
​

def main():
demo_polord_revesg()
demo_multi_fit()
demo_save_object()
demo_unbiased_short()

if name == "main":
main()