为何to_datetime()会扭曲（压缩）原始密度函数形态？

需求与实现思路 #

• 目标：生成一年中符合特定密度分布的时间戳
• 实现思路：先定义期望的密度函数，将其拆分为差分步骤，再通过累加得到从年初开始的实际时间点
• 使用环境：当前为Anaconda Navigator + Jupyter Notebook，未来可能切换至VSCode

遇到的问题 #

• 原代码经pd.to_datetime()处理后，得到的密度函数与原始形态差异明显，出现扭曲（压缩）情况
• 修改代码第23行diff = 1 - act中的1为2后，曲线形态有所改善，但基线会从0跃升至最大值的一半，不符合需求

现有代码 #

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# number of data points
event_num = 50000

# desired density functions
lin_up = np.linspace(0, 365, event_num)
lin_down = lin_up[::-1]
exp_up = np.exp(-lin_up / 100)[::-1]
exp_down = np.exp(-lin_up / 100)
harm_peak = 0.5 * (np.sin((lin_up / 58)-(np.pi/2)) + 1)
harm_valley = 0.5 * (np.sin((lin_up / 58)+(np.pi/2)) + 1)
ps_sigm_up = 0.5 * (np.sin((lin_up / 116)-(np.pi/2)) + 1)
ps_sigm_down = 0.5 * (np.sin((lin_up / 116)+(np.pi/2)) + 1)

act = harm_peak # so I don't have to manually update the actual function everywhere
a_magsimum = np.max(act) # normalization 1
act = act/a_magsimum # normalization 2

# difference gives the steps (the smaller the difference, the larger the density)
diff = 1 - act # here changeing the number changes the shape but the baseline too
diff_magsimum = np.max(diff)

# cumulative sum gives the actual days
cum = np.cumsum(diff)
cum_magsimum = np.max(cum)
cum = 365 * cum/cum_magsimum

plt.plot(act)
plt.title("Desired density function")
plt.show()

plt.plot(diff)
plt.title("Difference")
plt.show()

plt.plot(cum)
plt.title("Cumulative sum")
plt.show()

# saving into CSV
#df = pd.DataFrame({"Date": pd.to_datetime(cum, unit="D", origin="2024-01-01")})
#df.to_csv("events_new.csv", index=False)

# dates daily (chatGPT)
dates = pd.to_datetime(cum, unit="D", origin="2024-01-01").date
density_per_day = pd.Series(dates).value_counts().sort_index()

# dates weekly (chatGPT)
#dates = pd.to_datetime(cum, unit="D", origin="2024-01-01")
#density_per_week = dates.to_series().dt.to_period("W").value_counts().sort_index()

# plotting graph - daily breakdown
plt.plot(density_per_day.index, density_per_day.values, marker='o', linestyle='-')
plt.xlabel("Date")
plt.ylabel("Number of events / day")
plt.title("Eventdensity by time")
plt.xticks(rotation=45)
plt.grid(True)
plt.show()

# plotting graph - weekly breakdown
#plt.plot(density_per_week.index.astype(str), density_per_week.values, marker='o', linestyle='-')
#plt.xlabel("Week")
#plt.ylabel("Number of events / week")
#plt.title("Weekly event density")
#plt.xticks(rotation=45)
#plt.grid(True)
#plt.show()

内容的提问来源于stack exchange，提问作者PavelKorcsagin