示例06 圆环 vs 随机点对照

"""ex06_circle_vs_random.py — 第 5 章 圆环 vs 随机点的拓扑差异

对应教程：tutorials/05-visualization.md 5.7 节。

对照实验：

• 圆环：H1 有显著高持久点
• 均匀随机：H1 大量短命点（贴近对角线）
  用瓶颈距离量化两者差异。

运行：
python ex06_circle_vs_random.py
"""

import numpy as np
from ripser import ripser
from persim import plot_diagrams, bottleneck
import matplotlib.pyplot as plt

from common import sample_circle, sample_random

def main():
circle = sample_circle(n=100, noise=0.05, seed=11)
random = sample_random(n=100, dim=2, seed=11)

dgms_c = ripser(circle, maxdim=1)['dgms']
dgms_r = ripser(random, maxdim=1)['dgms']

# ── 可视化 ──
fig, axes = plt.subplots(2, 2, figsize=(11, 8))

axes[0, 0].scatter(circle[:, 0], circle[:, 1], s=12, alpha=0.7)
axes[0, 0].set_aspect('equal'); axes[0, 0].set_title('圆环点云')
axes[0, 0].grid(alpha=0.3)

axes[0, 1].scatter(random[:, 0], random[:, 1], s=12, alpha=0.7, c='C2')
axes[0, 1].set_aspect('equal'); axes[0, 1].set_title('均匀随机点')
axes[0, 1].grid(alpha=0.3)

plot_diagrams(dgms_c, ax=axes[1, 0], labels=['H0', 'H1'], show=False)
axes[1, 0].set_title('圆环持久图')

plot_diagrams(dgms_r, ax=axes[1, 1], labels=['H0', 'H1'], show=False)
axes[1, 1].set_title('随机点持久图')

plt.tight_layout()

# ── 瓶颈距离对比 ──
print("=== H1 持久性对比 ===")
for name, dgm in [("圆环", dgms_c[1]), ("随机", dgms_r[1])]:
    pers = dgm[:, 1] - dgm[:, 0]
    pers = pers[np.isfinite(pers)]
    print(f"  {name}: {len(dgm)} 点, max persistence="
          f"{pers.max() if len(pers) else 0:.4f}")

d_cc, _ = bottleneck(dgms_c[1], dgms_r[1])
print(f"\nbottleneck(圆环 H1, 随机 H1) = {d_cc:.4f}（应较大）")

# 同类对比：两个独立圆环
circle2 = sample_circle(n=100, noise=0.05, seed=22)
dgm_c2 = ripser(circle2, maxdim=1)['dgms'][1]
d_same, _ = bottleneck(dgms_c[1], dgm_c2)
print(f"bottleneck(圆环1 H1, 圆环2 H1) = {d_same:.4f}（应较小）")

plt.show()
​

if name == "main":
main()