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P3: sens figure

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ntnt
2026-01-19 14:15:51 +08:00
parent d4d7f7d94b
commit 73ae99885a
3 changed files with 160 additions and 168 deletions
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task3/07_sensitivity.py
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@@ -1,24 +1,35 @@
"""
Task 3 - Step 7: 敏感性分析
============================
Task 3 - Step 7: 敏感性分析 (Refined)
=====================================
分析以下参数对模型输出的影响：
1. 合并比例 r_merge: [1/3, 1/2, 2/3]
2. 距离阈值 l_max: [30, 40, 50, 60, 70]
3. 容量上限 μ_sum_max: [400, 425, 450, 475, 500]
4. CV阈值: [0.3, 0.4, 0.5, 0.6]
分析以下参数对模型输出的影响 (高分辨率扫描):
1. 合并比例 r_merge: 0.1 ~ 0.9 (步长 0.01)
2. 距离阈值 l_max: 10 ~ 100 miles (步长 1)
3. 容量上限 μ_sum_max: 350 ~ 550 (步长 5)
4. CV阈值: 0.1 ~ 1.0 (步长 0.01)
输出: 07_sensitivity.xlsx (各参数对E1', E2', F1', R1的影响)
输出:
- 07_sensitivity.xlsx (详细数据)
- figures/fig3_sensitivity.png (敏感性曲线图)
"""
import pandas as pd
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
import warnings
import os
from pathlib import Path
warnings.filterwarnings('ignore')
# 设置绘图风格
plt.style.use('seaborn-v0_8-whitegrid')
plt.rcParams['font.sans-serif'] = ['Arial Unicode MS', 'SimHei', 'DejaVu Sans'] # 适配中文
plt.rcParams['axes.unicode_minus'] = False
# ============================================
# 基础参数和函数
# 基础参数和函数 (保持不变)
# ============================================
Q = 400
QUALITY_THRESHOLD = 250
@@ -61,10 +72,23 @@ def calc_distance(lat1, lon1, lat2, lon2):
delta_lon = lon1 - lon2
return 69.0 * np.sqrt(delta_lat**2 + (np.cos(lat_avg_rad) * delta_lon)**2)
def compute_distance_matrix(sites_df: pd.DataFrame) -> np.ndarray:
lat = sites_df['lat'].to_numpy(dtype=float)
lon = sites_df['lon'].to_numpy(dtype=float)
lat_avg = (lat[:, None] + lat[None, :]) / 2.0
lat_avg_rad = np.radians(lat_avg)
delta_lat = lat[:, None] - lat[None, :]
delta_lon = lon[:, None] - lon[None, :]
dist = 69.0 * np.sqrt(delta_lat**2 + (np.cos(lat_avg_rad) * delta_lon)**2)
np.fill_diagonal(dist, 0.0)
return dist
# ============================================
# 完整流水线函数
# ============================================
def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5):
def run_pipeline(sites_df, distance_matrix, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5):
"""
运行完整的Task 3流水线，返回评估指标
"""
@@ -72,23 +96,15 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
sites['cv'] = sites['sigma'] / sites['mu']
n = len(sites)
# Step 1: 计算距离矩阵
distance_matrix = np.zeros((n, n))
for i in range(n):
for j in range(n):
if i != j:
distance_matrix[i, j] = calc_distance(
sites.iloc[i]['lat'], sites.iloc[i]['lon'],
sites.iloc[j]['lat'], sites.iloc[j]['lon']
)
# Step 2: 配对筛选
candidates = []
for i in range(n):
for j in range(i + 1, n):
site_i = sites.iloc[i]
site_j = sites.iloc[j]
dist = distance_matrix[i, j]
dist = float(distance_matrix[i, j])
if dist > l_max:
continue
@@ -113,7 +129,6 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
})
if len(candidates) == 0:
# 无可行配对，返回Task 1的指标
E1 = (sites['k'] * sites['mu']).sum()
E2 = sum(sites['k'] * sites['mu'].apply(quality_factor) * sites['mu'])
rates = [row['k'] * row['mu'] / row['mu_tilde'] for _, row in sites.iterrows()]
@@ -145,8 +160,6 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
# Step 4: 重分配访问次数
sites['k_single'] = sites['k'].copy()
sites['k_dual'] = 0
pair_k = {}
for pair in selected:
k_i, k_j = pair['k_i'], pair['k_j']
@@ -158,9 +171,7 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
idx_i, idx_j = pair['idx_i'], pair['idx_j']
sites.loc[idx_i, 'k_single'] = k_i - k_ij
sites.loc[idx_i, 'k_dual'] = k_ij
sites.loc[idx_j, 'k_single'] = k_j - k_ij
sites.loc[idx_j, 'k_dual'] = k_ij
pair_k[(pair['site_i_id'], pair['site_j_id'])] = k_ij
# 计算释放槽位并重分配
@@ -181,13 +192,11 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
sites['k_single_final'] = sites['k_single']
# Step 5: 计算指标
# E1'
E1 = (sites['k_single_final'] * sites['mu']).sum()
for pair in selected:
k_ij = pair_k.get((pair['site_i_id'], pair['site_j_id']), 0)
E1 += k_ij * pair['E_total']
# E2'
E2 = sum(sites['k_single_final'] * sites['mu'].apply(quality_factor) * sites['mu'])
for pair in selected:
k_ij = pair_k.get((pair['site_i_id'], pair['site_j_id']), 0)
@@ -195,7 +204,6 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
q_factor = quality_factor(mu_sum)
E2 += k_ij * q_factor * pair['E_total']
# 满足率
site_satisfaction = {}
for idx, row in sites.iterrows():
r = row['k_single_final'] * row['mu'] / row['mu_tilde'] if row['mu_tilde'] > 0 else 0
@@ -212,7 +220,6 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
F1 = gini_coefficient(rates)
F2 = min(rates) if rates else 0
# R1: 缺口风险
shortfall_probs = []
for pair in selected:
q = pair['q_final']
@@ -221,7 +228,6 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
shortfall_probs.append(1 - (1 - p_i) * (1 - p_j))
R1 = np.mean(shortfall_probs) if shortfall_probs else 0
# RS: 资源节省率
RS = total_dual / 730
return {
@@ -234,12 +240,21 @@ def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5
# 主程序
# ============================================
print("=" * 60)
print("Task 3 - Step 7: 敏感性分析")
print("Task 3 - Step 7: 敏感性分析 (High Res)")
print("=" * 60)
# 读取基础数据
sites_df = pd.read_excel('../task1/03_allocate.xlsx')
print(f"\n读取站点数据: {len(sites_df)} 个站点")
BASE_DIR = Path(__file__).resolve().parent
SITES_PATH = BASE_DIR.parent / 'task1' / '03_allocate.xlsx'
OUTPUT_XLSX = BASE_DIR / '07_sensitivity.xlsx'
OUTPUT_FIG = BASE_DIR / 'figures' / 'fig3_sensitivity.png'
OUTPUT_FIG.parent.mkdir(parents=True, exist_ok=True)
sites_df = pd.read_excel(SITES_PATH)
print(f"站点数据: {len(sites_df)} 个")
# 预计算距离矩阵（高分辨率扫描时显著加速）
distance_matrix = compute_distance_matrix(sites_df)
# 基准参数
BASE_L_MAX = 50
@@ -248,153 +263,130 @@ BASE_CV_MAX = 0.5
BASE_MERGE_RATIO = 0.5
# 计算基准结果
print(f"\n计算基准结果...")
base_result = run_pipeline(sites_df, BASE_L_MAX, BASE_MU_SUM_MAX, BASE_CV_MAX, BASE_MERGE_RATIO)
print(f"基准: E1={base_result['E1']:.0f}, E2={base_result['E2']:.0f}, F1={base_result['F1']:.4f}, R1={base_result['R1']:.4f}")
base_result = run_pipeline(sites_df, distance_matrix, BASE_L_MAX, BASE_MU_SUM_MAX, BASE_CV_MAX, BASE_MERGE_RATIO)
print(f"基准结果: E1={base_result['E1']:.0f}, R1={base_result['R1']:.4f}")
# 定义扫描参数
params_config = {
'merge_ratio': np.round(np.arange(0.10, 0.90 + 1e-9, 0.01), 2),
'l_max': np.arange(10, 100 + 1e-9, 1, dtype=float),
'mu_sum_max': np.arange(350, 550 + 1e-9, 5, dtype=float),
'cv_max': np.round(np.arange(0.10, 1.00 + 1e-9, 0.01), 2),
}
# ============================================
# 敏感性分析
# ============================================
all_results = []
# 1. 合并比例敏感性
print(f"\n" + "-" * 40)
print("1. 合并比例敏感性 (merge_ratio)")
print("-" * 40)
# 执行扫描
print("\n开始参数扫描...")
merge_ratios = [1/3, 0.5, 2/3]
for mr in merge_ratios:
result = run_pipeline(sites_df, BASE_L_MAX, BASE_MU_SUM_MAX, BASE_CV_MAX, mr)
result['param'] = 'merge_ratio'
result['param_value'] = mr
all_results.append(result)
print(f" merge_ratio={mr:.3f}: pairs={result['num_pairs']}, dual={result['num_dual_visits']}, "
f"E1={result['E1']:.0f}, E2={result['E2']:.0f}, F1={result['F1']:.4f}, R1={result['R1']:.4f}")
# 1. Merge Ratio
print("Scanning Merge Ratio...")
for val in params_config['merge_ratio']:
res = run_pipeline(sites_df, distance_matrix, BASE_L_MAX, BASE_MU_SUM_MAX, BASE_CV_MAX, val)
res.update({'param': 'merge_ratio', 'value': val})
all_results.append(res)
# 2. 距离阈值敏感性
print(f"\n" + "-" * 40)
print("2. 距离阈值敏感性 (l_max)")
print("-" * 40)
# 2. Distance Threshold
print("Scanning Distance Threshold...")
for val in params_config['l_max']:
res = run_pipeline(sites_df, distance_matrix, val, BASE_MU_SUM_MAX, BASE_CV_MAX, BASE_MERGE_RATIO)
res.update({'param': 'l_max', 'value': val})
all_results.append(res)
l_max_values = [30, 40, 50, 60, 70]
for lm in l_max_values:
result = run_pipeline(sites_df, lm, BASE_MU_SUM_MAX, BASE_CV_MAX, BASE_MERGE_RATIO)
result['param'] = 'l_max'
result['param_value'] = lm
all_results.append(result)
print(f" l_max={lm}: pairs={result['num_pairs']}, dual={result['num_dual_visits']}, "
f"E1={result['E1']:.0f}, E2={result['E2']:.0f}, F1={result['F1']:.4f}, R1={result['R1']:.4f}")
# 3. Capacity Cap
print("Scanning Capacity Cap...")
for val in params_config['mu_sum_max']:
res = run_pipeline(sites_df, distance_matrix, BASE_L_MAX, val, BASE_CV_MAX, BASE_MERGE_RATIO)
res.update({'param': 'mu_sum_max', 'value': val})
all_results.append(res)
# 3. 容量上限敏感性
print(f"\n" + "-" * 40)
print("3. 容量上限敏感性 (mu_sum_max)")
print("-" * 40)
# 4. CV Threshold
print("Scanning CV Threshold...")
for val in params_config['cv_max']:
res = run_pipeline(sites_df, distance_matrix, BASE_L_MAX, BASE_MU_SUM_MAX, val, BASE_MERGE_RATIO)
res.update({'param': 'cv_max', 'value': val})
all_results.append(res)
mu_sum_values = [400, 425, 450, 475, 500]
for ms in mu_sum_values:
result = run_pipeline(sites_df, BASE_L_MAX, ms, BASE_CV_MAX, BASE_MERGE_RATIO)
result['param'] = 'mu_sum_max'
result['param_value'] = ms
all_results.append(result)
print(f" mu_sum_max={ms}: pairs={result['num_pairs']}, dual={result['num_dual_visits']}, "
f"E1={result['E1']:.0f}, E2={result['E2']:.0f}, F1={result['F1']:.4f}, R1={result['R1']:.4f}")
# 4. CV阈值敏感性
print(f"\n" + "-" * 40)
print("4. CV阈值敏感性 (cv_max)")
print("-" * 40)
cv_max_values = [0.3, 0.4, 0.5, 0.6]
for cv in cv_max_values:
result = run_pipeline(sites_df, BASE_L_MAX, BASE_MU_SUM_MAX, cv, BASE_MERGE_RATIO)
result['param'] = 'cv_max'
result['param_value'] = cv
all_results.append(result)
print(f" cv_max={cv}: pairs={result['num_pairs']}, dual={result['num_dual_visits']}, "
f"E1={result['E1']:.0f}, E2={result['E2']:.0f}, F1={result['F1']:.4f}, R1={result['R1']:.4f}")
# ============================================
# 汇总分析
# ============================================
# 转换为DataFrame
df_results = pd.DataFrame(all_results)
print(f"\n" + "=" * 60)
print("敏感性分析汇总")
print("=" * 60)
# ============================================
# 绘图
# ============================================
print("\n绘制敏感性曲线...")
# 计算各参数的影响范围
for param in ['merge_ratio', 'l_max', 'mu_sum_max', 'cv_max']:
subset = df_results[df_results['param'] == param]
print(f"\n{param}:")
print(f" E1 变化范围: [{subset['E1'].min():.0f}, {subset['E1'].max():.0f}], "
f"变化幅度: {(subset['E1'].max() - subset['E1'].min()) / base_result['E1'] * 100:.2f}%")
print(f" E2 变化范围: [{subset['E2'].min():.0f}, {subset['E2'].max():.0f}], "
f"变化幅度: {(subset['E2'].max() - subset['E2'].min()) / base_result['E2'] * 100:.2f}%")
print(f" F1 变化范围: [{subset['F1'].min():.4f}, {subset['F1'].max():.4f}]")
print(f" R1 变化范围: [{subset['R1'].min():.4f}, {subset['R1'].max():.4f}]")
fig, axes = plt.subplots(2, 2, figsize=(15, 12))
fig.suptitle('Task 3 Sensitivity Analysis', fontsize=16, fontweight='bold')
# 参数对应的中文标签和单位
param_labels = {
'merge_ratio': ('Merge Ratio', 'Ratio'),
'l_max': ('Distance Threshold (l_max)', 'Miles'),
'mu_sum_max': ('Capacity Cap (μ_sum)', 'lbs (proxy)'),
'cv_max': ('CV Threshold', 'CV')
}
# 绘图循环
params_list = ['merge_ratio', 'l_max', 'mu_sum_max', 'cv_max']
for i, param in enumerate(params_list):
ax = axes[i // 2, i % 2]
data = df_results[df_results['param'] == param].sort_values('value')
# 绘制 E1/E2 - 左轴
line1, = ax.plot(data['value'], data['E1'], 'b-', linewidth=1.6, label='Expected Service (E1)')
line2, = ax.plot(data['value'], data['E2'], 'g-', linewidth=1.6, alpha=0.9, label='Quality-weighted (E2)')
ax.set_xlabel(param_labels[param][0])
ax.set_ylabel('Service (E1/E2)')
# 绘制 R1 (风险) - 右轴
ax2 = ax.twinx()
line3, = ax2.plot(data['value'], data['R1'], 'r--', linewidth=1.6, label='Shortfall Risk (R1)')
ax2.set_ylabel('Risk Probability (R1)', color='r')
ax2.tick_params(axis='y', labelcolor='r')
# 添加基准线
if param == 'merge_ratio':
base_val = BASE_MERGE_RATIO
elif param == 'l_max':
base_val = BASE_L_MAX
elif param == 'mu_sum_max':
base_val = BASE_MU_SUM_MAX
elif param == 'cv_max':
base_val = BASE_CV_MAX
ax.axvline(x=base_val, color='gray', linestyle=':', alpha=0.5)
# 图例
lines = [line1, line2, line3]
labels = [l.get_label() for l in lines]
ax.legend(lines, labels, loc='best', frameon=True)
ax.set_title(f'Effect of {param_labels[param][0]}')
ax.grid(True, alpha=0.3)
plt.tight_layout(rect=[0, 0.03, 1, 0.95])
plt.savefig(OUTPUT_FIG, dpi=300)
print(f"图表已保存至: {OUTPUT_FIG}")
# ============================================
# 保存结果
# 保存详细数据
# ============================================
OUTPUT_FILE = '07_sensitivity.xlsx'
with pd.ExcelWriter(OUTPUT_XLSX, engine='openpyxl') as writer:
df_results.to_excel(writer, sheet_name='detailed_data', index=False)
with pd.ExcelWriter(OUTPUT_FILE, engine='openpyxl') as writer:
# Sheet 1: 所有结果
df_results.to_excel(writer, sheet_name='all_results', index=False)
# Sheet 2: 合并比例敏感性
df_merge = df_results[df_results['param'] == 'merge_ratio'].copy()
df_merge.to_excel(writer, sheet_name='merge_ratio', index=False)
# Sheet 3: 距离阈值敏感性
df_lmax = df_results[df_results['param'] == 'l_max'].copy()
df_lmax.to_excel(writer, sheet_name='l_max', index=False)
# Sheet 4: 容量上限敏感性
df_musum = df_results[df_results['param'] == 'mu_sum_max'].copy()
df_musum.to_excel(writer, sheet_name='mu_sum_max', index=False)
# Sheet 5: CV阈值敏感性
df_cv = df_results[df_results['param'] == 'cv_max'].copy()
df_cv.to_excel(writer, sheet_name='cv_max', index=False)
# Sheet 6: 基准结果
base_df = pd.DataFrame([{
'param': 'baseline',
'l_max': BASE_L_MAX,
'mu_sum_max': BASE_MU_SUM_MAX,
'cv_max': BASE_CV_MAX,
'merge_ratio': BASE_MERGE_RATIO,
**base_result
}])
base_df.to_excel(writer, sheet_name='baseline', index=False)
# Sheet 7: 汇总统计
summary_rows = []
for param in ['merge_ratio', 'l_max', 'mu_sum_max', 'cv_max']:
subset = df_results[df_results['param'] == param]
summary_rows.append({
'param': param,
'E1_min': subset['E1'].min(),
'E1_max': subset['E1'].max(),
'E1_range_pct': (subset['E1'].max() - subset['E1'].min()) / base_result['E1'] * 100,
'E2_min': subset['E2'].min(),
'E2_max': subset['E2'].max(),
'E2_range_pct': (subset['E2'].max() - subset['E2'].min()) / base_result['E2'] * 100,
'F1_min': subset['F1'].min(),
'F1_max': subset['F1'].max(),
'R1_min': subset['R1'].min(),
'R1_max': subset['R1'].max()
# 摘要统计
summary = []
for param in params_list:
sub = df_results[df_results['param'] == param]
summary.append({
'Parameter': param,
'E1_Range': f"{sub['E1'].min():.0f} - {sub['E1'].max():.0f}",
'E1_Var%': (sub['E1'].max() - sub['E1'].min()) / base_result['E1'] * 100,
'E2_Range': f"{sub['E2'].min():.0f} - {sub['E2'].max():.0f}",
'E2_Var%': (sub['E2'].max() - sub['E2'].min()) / base_result['E2'] * 100,
'R1_Range': f"{sub['R1'].min():.4f} - {sub['R1'].max():.4f}"
})
df_summary = pd.DataFrame(summary_rows)
df_summary.to_excel(writer, sheet_name='summary', index=False)
pd.DataFrame(summary).to_excel(writer, sheet_name='summary', index=False)
print(f"\n结果已保存至: {OUTPUT_FILE}")
print(" - Sheet 'all_results': 所有结果")
print(" - Sheet 'merge_ratio': 合并比例敏感性")
print(" - Sheet 'l_max': 距离阈值敏感性")
print(" - Sheet 'mu_sum_max': 容量上限敏感性")
print(" - Sheet 'cv_max': CV阈值敏感性")
print(" - Sheet 'baseline': 基准结果")
print(" - Sheet 'summary': 汇总统计")
print("\n" + "=" * 60)
print(f"数据已保存至: {OUTPUT_XLSX}")
print("完成!")

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