如何用Pandas实现三维数组的宽表转长表（类似stack）

架构老林

2026-8-11

二维数组转长表示例

首先创建测试数据集：

import numpy as np
from scipy.stats import norm
import pandas as pd

np.random.seed(10)

n=3

space= norm(20, 5).rvs(n)
time= norm(10,2).rvs(n)

values = np.kron(space, time).reshape(n,n) + norm(1,1).rvs([n,n])

输出：

array([[267.39784458, 300.81493866, 229.19163206],
       [236.1940266 , 266.49469945, 204.01294305],
       [122.55912977, 140.00957047, 106.28339745]])

将其转换为Pandas宽表：

space_names = ['A','B','C']
time_names = [2000,2001,2002]

df = pd.DataFrame(values, index=space_names, columns=time_names)
df

输出：

2000        2001        2002
A   267.397845  300.814939  229.191632
B   236.194027  266.494699  204.012943
C   122.559130  140.009570  106.283397

这是典型的宽表结构，每个观测值由两个变量作为坐标标识。我们可通过Pandas的.stack()方法将其转换为整洁的长表：

df.columns.name = 'time'
df.index.name = 'space'

df.stack().rename('value').reset_index()

输出：

space   time    value
0   A      2000    267.397845
1   A      2001    300.814939
2   A      2002    229.191632
3   B      2000    236.194027
4   B      2001    266.494699
5   B      2002    204.012943
6   C      2000    122.559130
7   C      2001    140.009570
8   C      2002    106.283397

三维数组转长表需求

现在需要对三维数组执行类似操作：每个时空组合对应2个观测值，测试数据如下：

s = 3
t = 4
r = 2

space_mus = norm(20, 5).rvs(s)
time_mus = norm(10,2).rvs(t)

values = np.kron(space_mus, time_mus)
values = values.repeat(r).reshape(s,t,r) + norm(0,1).rvs([s,t,r])
values

输出：

array([[[286.50322099, 288.51266345],
        [176.64303485, 175.38175877],
        [136.01675917, 134.44328617]],

       [[187.07608546, 185.4068411 ],
        [112.86398438, 111.983463  ],
        [ 85.99035255,  86.67236986]],

       [[267.66833894, 269.45295404],
        [162.30044715, 162.50564386],
        [124.6374401 , 126.2315447 ]]])

如何将该三维数组转换为类似上述的整洁长表结构？

现有不够优雅的实现

本人实现了一种可用但不够Pythonic的方法，现寻求更简洁优雅的解决方案：

labels = ['{}{}{}'.format(i,j,k) for i in range(s) for j in range(t) for k in range(r)] #space, time, repetition

def flatten3d(k):
    return [i for l in k for s in l for i in s]

value_series = pd.Series(flatten3d(values)).rename('y')

split_labels= [[i for i in l] for l in labels]
df = pd.DataFrame(split_labels, columns=['s','t','r'])

pd.concat([df, value_series], axis=1)

输出：

s   t   r   y
0   0   0   0   266.2408815208753
1   0   0   1   266.13662442609433
2   0   1   0   299.53178992512954
3   0   1   1   300.13941632567605
4   0   2   0   229.39037800681405
5   0   2   1   227.22227496248507
6   0   3   0   281.76357915411995
7   0   3   1   280.9639352062619
8   1   0   0   235.8137644198259
9   1   0   1   234.23202459516452
10  1   1   0   265.19681013560034
11  1   1   1   266.5462102589883
12  1   2   0   200.730100791878
13  1   2   1   199.83217739700535
14  1   3   0   246.54018839875374
15  1   3   1   248.5496308586532
16  2   0   0   124.90916276929234
17  2   0   1   123.64788669199066
18  2   1   0   139.65391860786775
19  2   1   1   138.08044561039517
20  2   2   0   106.45276370157518
21  2   2   1   104.78351933651582
22  2   3   0   129.86043618610572
23  2   3   1   128.97991481257253

内容的提问来源于stack exchange，提问作者StackyGuy