447 lines
9.6 KiB
Python
447 lines
9.6 KiB
Python
#!/usr/bin/env python3
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"""拟合版新增注册用户数：LOESS + 星期因子修正"""
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import numpy as np
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from datetime import date, timedelta
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from collections import defaultdict
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# ---- 原始每日新增数据 ----
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raw_data = """2025-09-01,3
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2025-09-02,10
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2025-09-03,4
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2025-09-04,5
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2025-09-05,11
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2025-09-06,8
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2025-09-07,16
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2025-09-08,11
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2025-09-09,137
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2025-09-10,63
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2025-09-11,26
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2025-09-12,27
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2025-09-13,41
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2025-09-14,39
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2025-09-15,27
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2025-09-16,57
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2025-09-17,58
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2025-09-18,55
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2025-09-19,133
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2025-09-20,104
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2025-09-21,101
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2025-09-22,132
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2025-09-23,126
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2025-09-24,71
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2025-09-25,37
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2025-09-26,34
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2025-09-27,81
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2025-09-28,35
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2025-09-29,47
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2025-09-30,30
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2025-10-01,48
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2025-10-02,62
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2025-10-03,45
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2025-10-04,42
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2025-10-05,45
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2025-10-06,62
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2025-10-07,42
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2025-10-08,45
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2025-10-09,36
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2025-10-10,62
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2025-10-11,90
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2025-10-12,93
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2025-10-13,162
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2025-10-14,131
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2025-10-15,112
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2025-10-16,131
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2025-10-17,215
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2025-10-18,129
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2025-10-19,81
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2025-10-20,44
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2025-10-21,41
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2025-10-22,45
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2025-10-23,37
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2025-10-24,56
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2025-10-25,79
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2025-10-26,50
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2025-10-27,89
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2025-10-28,86
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2025-10-29,82
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2025-10-30,92
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2025-10-31,78
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2025-11-01,129
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2025-11-02,168
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2025-11-03,77
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2025-11-04,68
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2025-11-05,48
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2025-11-06,67
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2025-11-07,177
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2025-11-08,160
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2025-11-09,105
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2025-11-10,78
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2025-11-11,72
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2025-11-12,234
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2025-11-13,104
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2025-11-14,69
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2025-11-15,89
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2025-11-16,63
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2025-11-17,70
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2025-11-18,82
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2025-11-19,155
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2025-11-20,71
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2025-11-21,90
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2025-11-22,71
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2025-11-23,91
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2025-11-24,47
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2025-11-25,77
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2025-11-26,93
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2025-11-27,92
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2025-11-28,77
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2025-11-29,122
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2025-11-30,125
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2025-12-01,91
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2025-12-02,94
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2025-12-03,188
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2025-12-04,131
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2025-12-05,125
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2025-12-06,190
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2025-12-07,194
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2025-12-08,108
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2025-12-09,116
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2025-12-10,110
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2025-12-11,104
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2025-12-12,120
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2025-12-13,190
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2025-12-14,172
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2025-12-15,98
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2025-12-16,100
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2025-12-17,97
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2025-12-18,85
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2025-12-19,142
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2025-12-20,127
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2025-12-21,131
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2025-12-22,69
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2025-12-23,77
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2025-12-24,108
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2025-12-25,84
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2025-12-26,89
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2025-12-27,107
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2025-12-28,95
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2025-12-29,50
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2025-12-30,67
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2025-12-31,64
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2026-01-01,77
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2026-01-02,74
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2026-01-03,69
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2026-01-04,42
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2026-01-05,56
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2026-01-06,33
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2026-01-07,52
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2026-01-08,59
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2026-01-09,58
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2026-01-10,83
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2026-01-11,75
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2026-01-12,34
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2026-01-13,46
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2026-01-14,59
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2026-01-15,31
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2026-01-16,31
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2026-01-17,66
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2026-01-18,71
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2026-01-19,53
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2026-01-20,48
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2026-01-21,40
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2026-01-22,62
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2026-01-23,46
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2026-01-24,72
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2026-01-25,86
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2026-01-26,61
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2026-01-27,57
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2026-01-28,146
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2026-01-29,102
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2026-01-30,87
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2026-01-31,61
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2026-02-01,54
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2026-02-02,53
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2026-02-03,42
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2026-02-04,39
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2026-02-05,42
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2026-02-06,55
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2026-02-07,36
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2026-02-08,47
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2026-02-09,40
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2026-02-10,60
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2026-02-11,265
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2026-02-12,59
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2026-02-13,42
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2026-02-14,31
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2026-02-15,41
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2026-02-16,28
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2026-02-17,52
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2026-02-18,23
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2026-02-19,34
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2026-02-20,26
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2026-02-21,36
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2026-02-22,35
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2026-02-23,46
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2026-02-24,45
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2026-02-25,64
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2026-02-26,180
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2026-02-27,101
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2026-02-28,167
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2026-03-01,124
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2026-03-02,106
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2026-03-03,76
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2026-03-04,105
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2026-03-05,447
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2026-03-06,216
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2026-03-07,239
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2026-03-08,206
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2026-03-09,167
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2026-03-10,108
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2026-03-11,131
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2026-03-12,177
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2026-03-13,243
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2026-03-14,131
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2026-03-15,131
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2026-03-16,108
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2026-03-17,94
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2026-03-18,95
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2026-03-19,77
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2026-03-20,103
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2026-03-21,133
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2026-03-22,126
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2026-03-23,84
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2026-03-24,80
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2026-03-25,94
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2026-03-26,85
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2026-03-27,95
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2026-03-28,104
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2026-03-29,101
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2026-03-30,81
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2026-03-31,99
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2026-04-01,138
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2026-04-02,162
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2026-04-03,771
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2026-04-04,340
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2026-04-05,185
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2026-04-06,206
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2026-04-07,212
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2026-04-08,749
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2026-04-09,336
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2026-04-10,128
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2026-04-11,174
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2026-04-12,150
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2026-04-13,116
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2026-04-14,132
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2026-04-15,126
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2026-04-16,115
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2026-04-17,84
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2026-04-18,117
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2026-04-19,119
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2026-04-20,88
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2026-04-21,97
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2026-04-22,179
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2026-04-23,139
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2026-04-24,121
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2026-04-25,140
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2026-04-26,137
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2026-04-27,120
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2026-04-28,163
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2026-04-29,65
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2026-04-30,58
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2026-05-01,63
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2026-05-02,60
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2026-05-03,60
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2026-05-04,52
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2026-05-05,70
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2026-05-06,98
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2026-05-07,133
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2026-05-08,86
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2026-05-09,89
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2026-05-10,106
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2026-05-11,98
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2026-05-12,82
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2026-05-13,99
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2026-05-14,98
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2026-05-15,166
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2026-05-16,116
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2026-05-17,123
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2026-05-18,88
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2026-05-19,115
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2026-05-20,132
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2026-05-21,130
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2026-05-22,127
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2026-05-23,200
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2026-05-24,121
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2026-05-25,67
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2026-05-26,104
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2026-05-27,99
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2026-05-28,112
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2026-05-29,107
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2026-05-30,121
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2026-05-31,178"""
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# 解析数据
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data = {}
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for line in raw_data.strip().split('\n'):
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dt, nu = line.split(',')
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data[dt] = int(nu)
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dates = sorted(data.keys())
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start_date = date.fromisoformat(dates[0])
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end_date = date.fromisoformat(dates[-1])
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# ---- 活动日历（活动日+余波日） ----
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activity_dates = set()
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# 2025: 9/9-10, 9/19-23, 10/13-14, 10/16-17, 11/2, 11/7, 11/10, 11/12, 11/19, 12/3
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for d in ['2025-09-09','2025-09-10','2025-09-19','2025-09-20','2025-09-21','2025-09-22','2025-09-23',
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'2025-10-13','2025-10-14','2025-10-16','2025-10-17',
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'2025-11-02','2025-11-07','2025-11-10','2025-11-12','2025-11-19',
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'2025-12-03']:
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activity_dates.add(d)
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# 2026: 1/28-29(余波1天), 2/11, 2/26-3/2(余波4天), 3/5-8(余波3天), 3/9, 3/12-13, 4/3-7(余波4天), 4/8-10(余波2天), 4/22-23(余波1天), 4/28, 5/6-7
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for d in ['2026-01-28','2026-01-29',
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'2026-02-11',
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'2026-02-26','2026-02-27','2026-02-28','2026-03-01','2026-03-02',
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'2026-03-05','2026-03-06','2026-03-07','2026-03-08',
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'2026-03-09',
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'2026-03-12','2026-03-13',
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'2026-04-03','2026-04-04','2026-04-05','2026-04-06','2026-04-07',
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'2026-04-08','2026-04-09','2026-04-10',
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'2026-04-22','2026-04-23',
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'2026-04-28',
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'2026-05-06','2026-05-07']:
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activity_dates.add(d)
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print(f"活动日+余波日总数: {len(activity_dates)}")
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# ---- LOESS 实现 ----
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def loess(x, y, x_eval, frac=0.236):
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"""简单 LOESS 平滑"""
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n = len(x)
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k = max(int(n * frac), 3)
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y_smooth = np.zeros(len(x_eval))
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for i, xi in enumerate(x_eval):
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# 计算距离
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dists = np.abs(x - xi)
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idx = np.argsort(dists)[:k]
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max_dist = dists[idx[-1]]
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# tricube 权重
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weights = np.zeros(n)
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for j in idx:
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u = dists[j] / max_dist if max_dist > 0 else 0
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weights[j] = (1 - u**3)**3 if u < 1 else 0
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# 加权线性回归
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w_sum = weights.sum()
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if w_sum > 0:
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x_w = (x * weights).sum() / w_sum
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y_w = (y * weights).sum() / w_sum
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xy_w = (x * y * weights).sum() / w_sum
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x2_w = (x * x * weights).sum() / w_sum
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denom = x2_w - x_w**2
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if abs(denom) > 1e-10:
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b = (xy_w - x_w * y_w) / denom
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a = y_w - b * x_w
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y_smooth[i] = a + b * xi
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else:
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y_smooth[i] = y_w
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else:
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y_smooth[i] = y.mean()
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return y_smooth
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# 准备数据
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x_all = np.arange(len(dates))
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y_all = np.array([data[d] for d in dates])
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# 清洁日（非活动日）的索引
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clean_idx = [i for i, d in enumerate(dates) if d not in activity_dates]
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x_clean = x_all[clean_idx]
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y_clean = y_all[clean_idx]
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print(f"清洁日数量: {len(clean_idx)} / {len(dates)} ({len(clean_idx)/len(dates)*100:.1f}%)")
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# LOESS 拟合（基于清洁日）
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y_loess_clean = loess(x_clean, y_clean, x_clean, frac=0.236)
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# 在全量日期上做 LOESS（用清洁日拟合参数插值到所有日期）
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y_loess_all = loess(x_clean, y_clean, x_all, frac=0.236)
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# ---- 星期因子修正 ----
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# 基于清洁日计算每周每日的平均注册量与全局均值的比值
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weekday_sums = defaultdict(list)
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for i in clean_idx:
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d = date.fromisoformat(dates[i])
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wd = d.weekday() # 0=Mon, 6=Sun
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weekday_sums[wd].append(y_all[i])
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global_mean_clean = y_clean.mean()
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weekday_factors = {}
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for wd in range(7):
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if weekday_sums[wd]:
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wd_mean = np.mean(weekday_sums[wd])
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weekday_factors[wd] = wd_mean / global_mean_clean
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else:
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weekday_factors[wd] = 1.0
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day_names = ['周一','周二','周三','周四','周五','周六','周日']
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print("\n星期因子（基于清洁日）:")
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for wd in range(7):
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print(f" {day_names[wd]}: {weekday_factors[wd]:.4f}")
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# ---- 拟合版每日注册 ----
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fitted_daily = {}
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for i, d in enumerate(dates):
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wd = date.fromisoformat(d).weekday()
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if d in activity_dates:
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# 活动日/余波日：用星期修正后的 LOESS 拟合值
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fitted_daily[d] = y_loess_all[i] * weekday_factors[wd]
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else:
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# 非活动日：保留实际值
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fitted_daily[d] = y_all[i]
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# ---- 月度汇总 ----
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print("\n" + "=" * 70)
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print("拟合版 vs 原始版 月度新增注册用户数")
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print("=" * 70)
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print(f"{'月份':<10} {'原始新增':>8} {'拟合新增':>8} {'差值':>8} {'压降比例':>8}")
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print("-" * 50)
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monthly_original = defaultdict(int)
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monthly_fitted = defaultdict(float)
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for d in dates:
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mon = d[:7]
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monthly_original[mon] += data[d]
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monthly_fitted[mon] += fitted_daily[d]
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for mon in sorted(monthly_original.keys()):
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orig = monthly_original[mon]
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fit = monthly_fitted[mon]
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diff = orig - fit
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pct = diff / orig * 100 if orig > 0 else 0
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print(f"{mon:<10} {orig:>8,} {fit:>8,.0f} {diff:>8,.0f} {pct:>7.1f}%")
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# ---- 3/4/5月详细 ----
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print("\n" + "=" * 70)
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print("3/4/5月 拟合版详细")
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print("=" * 70)
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for mon in ['2026-03', '2026-04', '2026-05']:
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orig = monthly_original[mon]
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fit = monthly_fitted[mon]
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diff = orig - fit
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pct = diff / orig * 100
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print(f" {mon}: 原始 {orig:,} → 拟合 {fit:,.0f}（压降 {pct:.1f}%）")
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# ---- 3/4/5月每日拟合 vs 原始 ----
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print("\n" + "=" * 70)
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print("3/4/5月每日对比（活动日标记 *）")
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print("=" * 70)
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print(f"{'日期':<12} {'原始':>6} {'拟合':>8} {'是否活动':>6}")
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print("-" * 40)
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for d in dates:
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if '2026-03' <= d <= '2026-05-31':
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is_act = '*' if d in activity_dates else ''
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print(f"{d:<12} {data[d]:>6} {fitted_daily[d]:>8.0f} {is_act:>6}")
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