Python Pandas库

发表于 22-07-2020 更新于 02-02-2023 分类于 Python

引子

Numpy 在向量化的数值计算中表现优异

但是在处理更灵活、复杂的数据任务：

如为数据添加标签、处理缺失值、分组和透视表等方面

Numpy显得力不从心

而基于Numpy构建的Pandas库，提供了使得数据分析变得更快更简单的高级数据结构和操作工具

12.1 对象创建

12.1.1 Pandas Series对象

Series 是带标签数据的一维数组

Series对象的创建

通用结构: pd.Series(data, index=index, dtype=dtype)

data：数据，可以是列表，字典或Numpy数组

index：索引，为可选参数

dtype: 数据类型，为可选参数

1、用列表创建

index缺省，默认为整数序列

import pandas as pd

data = pd.Series([1.5, 3, 4.5, 6])
data

0    1.5
1    3.0
2    4.5
3    6.0
dtype: float64

增加index

1 2	data = pd.Series([1.5, 3, 4.5, 6], index=["a", "b", "c", "d"]) data

a    1.5
b    3.0
c    4.5
d    6.0
dtype: float64

增加数据类型

1	缺省则从传入的数据自动判断

1 2	data = pd.Series([1, 2, 3, 4], index=["a", "b", "c", "d"]) data

a    1
b    2
c    3
d    4
dtype: int64

1 2	data = pd.Series([1, 2, 3, 4], index=["a", "b", "c", "d"], dtype="float") data

a    1.0
b    2.0
c    3.0
d    4.0
dtype: float64

注意：数据支持多种类型

1 2	data = pd.Series([1, 2, "3", 4], index=["a", "b", "c", "d"]) data

a    1
b    2
c    3
d    4
dtype: object

data["a"]

data["c"]

'3'

数据类型可被强制改变

1 2	data = pd.Series([1, 2, "3", 4], index=["a", "b", "c", "d"], dtype=float) data

a    1.0
b    2.0
c    3.0
d    4.0
dtype: float64

data["c"]

3.0

1 2	data = pd.Series([1, 2, "a", 4], index=["a", "b", "c", "d"], dtype=float) data

ValueError: could not convert string to float: 'a'

2、用一维numpy数组创建

import numpy as np

x = np.arange(5)
pd.Series(x)

0    0
1    1
2    2
3    3
4    4
dtype: int32

3、用字典创建

默认以键为index 值为data

population_dict = {"BeiJing": 2154,
                   "ShangHai": 2424,
                   "ShenZhen": 1303,
                   "HangZhou": 981 }
population = pd.Series(population_dict)    
population

BeiJing     2154
ShangHai    2424
ShenZhen    1303
HangZhou     981
dtype: int64

字典创建，如果指定index，则会到字典的键中筛选，找不到的，值设为NaN

1 2	population = pd.Series(population_dict, index=["BeiJing", "HangZhou", "c", "d"]) population

BeiJing     2154.0
HangZhou     981.0
c              NaN
d              NaN
dtype: float64

4、data为标量的情况

1	pd.Series(5, index=[100, 200, 300])

100    5
200    5
300    5
dtype: int64

12.1.2 Pandas DataFrame对象

DataFrame 是带标签数据的多维数组

DataFrame对象的创建

通用结构: pd.DataFrame(data, index=index, columns=columns)

data：数据，可以是列表，字典或Numpy数组

index：索引，为可选参数

columns: 列标签，为可选参数

1、通过Series对象创建

population_dict = {"BeiJing": 2154,
                   "ShangHai": 2424,
                   "ShenZhen": 1303,
                   "HangZhou": 981 }

population = pd.Series(population_dict)    
pd.DataFrame(population)

	0
BeiJing	2154
ShangHai	2424
ShenZhen	1303
HangZhou	981

1	pd.DataFrame(population, columns=["population"])

	population
BeiJing	2154
ShangHai	2424
ShenZhen	1303
HangZhou	981

2、通过Series对象字典创建

GDP_dict = {"BeiJing": 30320,
            "ShangHai": 32680,
            "ShenZhen": 24222,
            "HangZhou": 13468 }

GDP = pd.Series(GDP_dict)
GDP

BeiJing     30320
ShangHai    32680
ShenZhen    24222
HangZhou    13468
dtype: int64

1 2	pd.DataFrame({"population": population, "GDP": GDP})

	population	GDP
BeiJing	2154	30320
ShangHai	2424	32680
ShenZhen	1303	24222
HangZhou	981	13468

注意：数量不够的会自动补齐

1
2
3

pd.DataFrame({"population": population,
              "GDP": GDP,
              "country": "China"})

	population	GDP	country
BeiJing	2154	30320	China
ShangHai	2424	32680	China
ShenZhen	1303	24222	China
HangZhou	981	13468	China

3、通过字典列表对象创建

字典索引作为index，字典键作为columns

import numpy as np
import pandas as pd

data = [{"a": i, "b": 2*i} for i in range(3)]
data

[{'a': 0, 'b': 0}, {'a': 1, 'b': 2}, {'a': 2, 'b': 4}]

1 2	data = pd.DataFrame(data) data

	a	b
0	0	0
1	1	2
2	2	4

1 2	data1 = data["a"].copy() data1

0    0
1    1
2    2
Name: a, dtype: int64

1 2	data1[0] = 10 data1

0    10
1     1
2     2
Name: a, dtype: int64

data

	a	b
0	0	0
1	1	2
2	2	4

不存在的键，会默认值为NaN

1 2	data = [{"a": 1, "b":1},{"b": 3, "c":4}] data

[{'a': 1, 'b': 1}, {'b': 3, 'c': 4}]

1	pd.DataFrame(data)

	a	b	c
0	1.0	1	NaN
1	NaN	3	4.0

4、通过Numpy二维数组创建

1 2	data = np.random.randint(10, size=(3, 2)) data

array([[3, 0],
       [9, 6],
       [7, 7]])

1	pd.DataFrame(data, columns=["foo", "bar"], index=["a", "b", "c"])

	foo	bar
a	3	0
b	9	6
c	7	7

12.2 DataFrame性质

1、属性

1 2	data = pd.DataFrame({"pop": population, "GDP": GDP}) data

	pop	GDP
BeiJing	2154	30320
ShangHai	2424	32680
ShenZhen	1303	24222
HangZhou	981	13468

（1）df.values 返回numpy数组表示的数据

1	data.values

array([[ 2154, 30320],
       [ 2424, 32680],
       [ 1303, 24222],
       [  981, 13468]], dtype=int64)

（2）df.index 返回行索引

1	data.index

Index(['BeiJing', 'ShangHai', 'ShenZhen', 'HangZhou'], dtype='object')

（3）df.columns 返回列索引

1	data.columns

Index(['pop', 'GDP'], dtype='object')

（4）df.shape 形状

1	data.shape

(4, 2)

（5） pd.size 大小

data.size

（6）pd.dtypes 返回每列数据类型

1	data.dtypes

pop    int64
GDP    int64
dtype: object

2、索引

方法太多脑子容易懵，我总结一下loc和iloc的方法（推荐使用这两种方法来索引）：

选择行
- data.loc[‘名称’]，返回Series对象
- data.loc[[‘名称’]]，返回dataframe对象
- data.loc[[‘名称1’, ‘名称2’]]，选择多行，返回dataframe对象
- data.loc[‘名称1’ : ‘名称3’]，选择’名称1’到’名称3’多行，返回dataframe对象
- data.iloc[1]，选择行1，返回Series对象
- data.iloc[[1]]，选择行1，返回dataframe对象
- data.iloc[[1, 3]]，选择行1和行3，返回dataframe对象
- data.iloc[0:3]，选择行0到行2，返回dataframe对象
- 注：其实上面可以全部写成(i)loc[行索引信息 , : ]，不写第二个冒号也可以默认选择的是行
选择列
- data.loc[ : , ‘名称’]，返回Series对象
- data.loc[ : , [‘名称’]]，返回dataframe对象
- data.loc[ : , [‘名称1’, ‘名称2’]]，选择多列，返回dataframe对象
- data.loc[ : , ‘名称1’ : ‘名称3’]，选择’名称1’到’名称3’多列，返回dataframe对象
- data.iloc[ : , 1]，选择列1，返回Series对象
- data.iloc[ : , [1]]，选择列1，返回dataframe对象
- data.iloc[ : , [1, 3]]，选择列1和列3，返回dataframe对象
- data.iloc[ : , 0:3]，选择列0到列2，返回dataframe对象
选择元素
- data.loc[ ‘行名称’ , ‘列名称’]，返回元素
- data.loc[[‘行名称’], [‘列名称’]]，返回dataframe对象
- data.loc[[‘行名称1’ , ‘行名称2’], [‘列名称1’ , ‘列名称2’]]，返回dataframe对象
- data.loc[‘行名称1’ : ‘行名称3’, ‘列名称1’ : ‘列名称2’]]，选择’行名称1’到’行名称3’多行和’列名称1’到’列名称2’多列的相交元素，返回dataframe对象
- data.iloc[1 , 2]，选择行1列2的元素，返回元素
- data.iloc[[1] , [2]]，选择行1列2的元素，返回dataframe对象
- data.iloc[[1, 0] , [1, 3]]，选择行1行0与列1列3交叉位置的四个元素，返回dataframe对象
- data.iloc[1 : 3, 1 : 2]，选择行1到行3多行和列1到列2多列的相交元素，返回dataframe对象

data

	pop	GDP
BeiJing	2154	30320
ShangHai	2424	32680
ShenZhen	1303	24222
HangZhou	981	13468

（1）获取列

字典式

1	data["pop"]

BeiJing     2154
ShangHai    2424
ShenZhen    1303
HangZhou     981
Name: pop, dtype: int64

1	data[["pop"]]

	pop
BeiJing	2154
ShangHai	2424
ShenZhen	1303
HangZhou	981

1	data[["GDP", "pop"]]

	GDP	pop
BeiJing	30320	2154
ShangHai	32680	2424
ShenZhen	24222	1303
HangZhou	13468	981

对象属性式

data.GDP

BeiJing     30320
ShangHai    32680
ShenZhen    24222
HangZhou    13468
Name: GDP, dtype: int64

（2）获取行

绝对索引 df.loc

1	data.loc["BeiJing"]

pop     2154
GDP    30320
Name: BeiJing, dtype: int64

1	data.loc[["BeiJing"]]

	pop	GDP
BeiJing	2154	30320

1	data.loc[["BeiJing", "HangZhou"]]

	pop	GDP
BeiJing	2154	30320
HangZhou	981	13468

相对索引 df.iloc

data

	pop	GDP
BeiJing	2154	30320
ShangHai	2424	32680
ShenZhen	1303	24222
HangZhou	981	13468

1	data.iloc[0]

pop     2154
GDP    30320
Name: BeiJing, dtype: int64

1	data.iloc[[0]]

	pop	GDP
BeiJing	2154	30320

1	data.iloc[[1, 3]]

	pop	GDP
ShangHai	2424	32680
HangZhou	981	13468

（3）获取标量

data

	pop	GDP
BeiJing	2154	30320
ShangHai	2424	32680
ShenZhen	1303	24222
HangZhou	981	13468

1	data.loc["BeiJing", "GDP"]

1	data.iloc[0, 1]

1	data.values[0][1]

（4）Series对象的索引

1	type(data.GDP)

pandas.core.series.Series

GDP

BeiJing     30320
ShangHai    32680
ShenZhen    24222
HangZhou    13468
dtype: int64

1	GDP["BeiJing"]

3、切片

1 2	df = pd.DataFrame(np.random.randn(6,4), index=['2019-01-01', '2019-01-02', '2019-01-03', '2019-01-04', '2019-01-05', '2019-01-06'], columns=["A", "B", "C", "D"]) df

	A	B	C	D
2019-01-01	-0.242680	0.310893	-2.323013	0.725643
2019-01-02	-1.683455	0.442882	0.061800	0.522243
2019-01-03	0.320874	-1.309343	0.418429	0.084683
2019-01-04	-0.894394	0.698045	1.695152	-0.122940
2019-01-05	0.731645	0.663405	0.189481	-0.872651
2019-01-06	0.050233	-1.236851	-0.246509	-0.328486

（1）行切片

1	df["2019-01-01": "2019-01-03"]

	A	B	C	D
2019-01-01	-0.242680	0.310893	-2.323013	0.725643
2019-01-02	-1.683455	0.442882	0.061800	0.522243
2019-01-03	0.320874	-1.309343	0.418429	0.084683

1	df.loc["2019-01-01": "2019-01-03"]

	A	B	C	D
2019-01-01	-0.242680	0.310893	-2.323013	0.725643
2019-01-02	-1.683455	0.442882	0.061800	0.522243
2019-01-03	0.320874	-1.309343	0.418429	0.084683

1	df.iloc[0: 3]

	A	B	C	D
2019-01-01	-0.242680	0.310893	-2.323013	0.725643
2019-01-02	-1.683455	0.442882	0.061800	0.522243
2019-01-03	0.320874	-1.309343	0.418429	0.084683

（2）列切片

df

	A	B	C	D
2019-01-01	-0.242680	0.310893	-2.323013	0.725643
2019-01-02	-1.683455	0.442882	0.061800	0.522243
2019-01-03	0.320874	-1.309343	0.418429	0.084683
2019-01-04	-0.894394	0.698045	1.695152	-0.122940
2019-01-05	0.731645	0.663405	0.189481	-0.872651
2019-01-06	0.050233	-1.236851	-0.246509	-0.328486

1	df.loc[:, "A": "C"]

	A	B	C
2019-01-01	-0.242680	0.310893	-2.323013
2019-01-02	-1.683455	0.442882	0.061800
2019-01-03	0.320874	-1.309343	0.418429
2019-01-04	-0.894394	0.698045	1.695152
2019-01-05	0.731645	0.663405	0.189481
2019-01-06	0.050233	-1.236851	-0.246509

1	df.iloc[:, 0: 3]

	A	B	C
2019-01-01	-0.242680	0.310893	-2.323013
2019-01-02	-1.683455	0.442882	0.061800
2019-01-03	0.320874	-1.309343	0.418429
2019-01-04	-0.894394	0.698045	1.695152
2019-01-05	0.731645	0.663405	0.189481
2019-01-06	0.050233	-1.236851	-0.246509

（3）多种多样的取值

df

	A	B	C	D
2019-01-01	-0.242680	0.310893	-2.323013	0.725643
2019-01-02	-1.683455	0.442882	0.061800	0.522243
2019-01-03	0.320874	-1.309343	0.418429	0.084683
2019-01-04	-0.894394	0.698045	1.695152	-0.122940
2019-01-05	0.731645	0.663405	0.189481	-0.872651
2019-01-06	0.050233	-1.236851	-0.246509	-0.328486

行、列同时切片

1	df.loc["2019-01-02": "2019-01-03", "C":"D"]

	C	D
2019-01-02	0.061800	0.522243
2019-01-03	0.418429	0.084683

1	df.iloc[1: 3, 2:]

	C	D
2019-01-02	0.061800	0.522243
2019-01-03	0.418429	0.084683

行切片，列分散取值

1	df.loc["2019-01-04": "2019-01-06", ["A", "C"]]

	A	C
2019-01-04	-0.894394	1.695152
2019-01-05	0.731645	0.189481
2019-01-06	0.050233	-0.246509

1	df.iloc[3:, [0, 2]]

	A	C
2019-01-04	-0.894394	1.695152
2019-01-05	0.731645	0.189481
2019-01-06	0.050233	-0.246509

行分散取值，列切片

1	df.loc[["2019-01-02", "2019-01-06"], "C": "D"]

	C	D
2019-01-02	0.061800	0.522243
2019-01-06	-0.246509	-0.328486

1	df.iloc[[1, 5], 0: 3]

	A	B	C
2019-01-02	-1.683455	0.442882	0.061800
2019-01-06	0.050233	-1.236851	-0.246509

行、列均分散取值

1	df.loc[["2019-01-04", "2019-01-06"], ["A", "D"]]

	A	D
2019-01-04	-0.894394	-0.122940
2019-01-06	0.050233	-0.328486

1	df.iloc[[1, 5], [0, 3]]

	A	D
2019-01-02	-1.683455	0.522243
2019-01-06	0.050233	-0.328486

4、布尔索引

df

	A	B	C	D
2019-01-01	-0.968004	0.024658	1.365858	-0.280383
2019-01-02	-0.409198	1.228846	0.673056	0.396339
2019-01-03	-2.356054	-0.458781	0.063541	-0.016453
2019-01-04	0.847711	-1.054088	-0.114295	0.003130
2019-01-05	1.181092	0.017556	-0.598561	-0.303268
2019-01-06	-0.084136	-0.542269	1.378498	0.919418

df > 0

	A	B	C	D
2019-01-01	False	True	True	False
2019-01-02	False	True	True	True
2019-01-03	False	False	True	False
2019-01-04	True	False	False	True
2019-01-05	True	True	False	False
2019-01-06	False	False	True	True

1	df[df > 0]

	A	B	C	D
2019-01-01	NaN	0.024658	1.365858	NaN
2019-01-02	NaN	1.228846	0.673056	0.396339
2019-01-03	NaN	NaN	0.063541	NaN
2019-01-04	0.847711	NaN	NaN	0.003130
2019-01-05	1.181092	0.017556	NaN	NaN
2019-01-06	NaN	NaN	1.378498	0.919418

df.A > 0

2019-01-01    False
2019-01-02    False
2019-01-03    False
2019-01-04     True
2019-01-05     True
2019-01-06    False
Freq: D, Name: A, dtype: bool

1	df[df.A > 0]

	A	B	C	D
2019-01-04	0.847711	-1.054088	-0.114295	0.003130
2019-01-05	1.181092	0.017556	-0.598561	-0.303268

isin（）方法

1
2
3

df2 = df.copy()
df2['E'] = ['one', 'one', 'two', 'three', 'four', 'three']
df2

	A	B	C	D	E
2019-01-01	-0.968004	0.024658	1.365858	-0.280383	one
2019-01-02	-0.409198	1.228846	0.673056	0.396339	one
2019-01-03	-2.356054	-0.458781	0.063541	-0.016453	two
2019-01-04	0.847711	-1.054088	-0.114295	0.003130	three
2019-01-05	1.181092	0.017556	-0.598561	-0.303268	four
2019-01-06	-0.084136	-0.542269	1.378498	0.919418	three

1 2	ind = df2["E"].isin(["two", "four"]) ind

2019-01-01    False
2019-01-02    False
2019-01-03     True
2019-01-04    False
2019-01-05     True
2019-01-06    False
Freq: D, Name: E, dtype: bool

df2[ind]

	A	B	C	D	E
2019-01-03	-2.356054	-0.458781	0.063541	-0.016453	two
2019-01-05	1.181092	0.017556	-0.598561	-0.303268	four

（5）赋值

df

	A	B	C	D
2019-01-01	-0.968004	0.024658	1.365858	-0.280383
2019-01-02	-0.409198	1.228846	0.673056	0.396339
2019-01-03	-2.356054	-0.458781	0.063541	-0.016453
2019-01-04	0.847711	-1.054088	-0.114295	0.003130
2019-01-05	1.181092	0.017556	-0.598561	-0.303268
2019-01-06	-0.084136	-0.542269	1.378498	0.919418

DataFrame 增加新列

1 2	s1 = pd.Series([1, 2, 3, 4, 5, 6], index=pd.date_range('20190101', periods=6)) s1

2019-01-01    1
2019-01-02    2
2019-01-03    3
2019-01-04    4
2019-01-05    5
2019-01-06    6
Freq: D, dtype: int64

1 2	df["E"] = s1 df

	A	B	C	D	E
2019-01-01	-0.968004	0.024658	1.365858	-0.280383	1
2019-01-02	-0.409198	1.228846	0.673056	0.396339	2
2019-01-03	-2.356054	-0.458781	0.063541	-0.016453	3
2019-01-04	0.847711	-1.054088	-0.114295	0.003130	4
2019-01-05	1.181092	0.017556	-0.598561	-0.303268	5
2019-01-06	-0.084136	-0.542269	1.378498	0.919418	6

修改赋值

1 2	df.loc["2019-01-01", "A"] = 0 df

	A	B	C	D	E
2019-01-01	0.000000	0.024658	1.365858	-0.280383	1
2019-01-02	-0.409198	1.228846	0.673056	0.396339	2
2019-01-03	-2.356054	-0.458781	0.063541	-0.016453	3
2019-01-04	0.847711	-1.054088	-0.114295	0.003130	4
2019-01-05	1.181092	0.017556	-0.598561	-0.303268	5
2019-01-06	-0.084136	-0.542269	1.378498	0.919418	6

1 2	df.iloc[0, 1] = 0 df

	A	B	C	D	E
2019-01-01	0.000000	0.000000	1.365858	-0.280383	1
2019-01-02	-0.409198	1.228846	0.673056	0.396339	2
2019-01-03	-2.356054	-0.458781	0.063541	-0.016453	3
2019-01-04	0.847711	-1.054088	-0.114295	0.003130	4
2019-01-05	1.181092	0.017556	-0.598561	-0.303268	5
2019-01-06	-0.084136	-0.542269	1.378498	0.919418	6

1 2	df["D"] = np.array([5]*len(df)) # 可简化成df["D"] = 5 df

	A	B	C	D	E
2019-01-01	0.000000	0.000000	1.365858	5	1
2019-01-02	-0.409198	1.228846	0.673056	5	2
2019-01-03	-2.356054	-0.458781	0.063541	5	3
2019-01-04	0.847711	-1.054088	-0.114295	5	4
2019-01-05	1.181092	0.017556	-0.598561	5	5
2019-01-06	-0.084136	-0.542269	1.378498	5	6

修改index和columns

1 2	df.index = [i for i in range(len(df))] df

	A	B	C	D	E
0	0.000000	0.000000	1.365858	5	1
1	-0.409198	1.228846	0.673056	5	2
2	-2.356054	-0.458781	0.063541	5	3
3	0.847711	-1.054088	-0.114295	5	4
4	1.181092	0.017556	-0.598561	5	5
5	-0.084136	-0.542269	1.378498	5	6

1 2	df.columns = [i for i in range(df.shape[1])] df

	0	1	2	3	4
0	0.000000	0.000000	1.365858	5	1
1	-0.409198	1.228846	0.673056	5	2
2	-2.356054	-0.458781	0.063541	5	3
3	0.847711	-1.054088	-0.114295	5	4
4	1.181092	0.017556	-0.598561	5	5
5	-0.084136	-0.542269	1.378498	5	6

12.3 数值运算及统计分析

1、数据的查看

import pandas as pd
import numpy as np

dates = pd.date_range(start='2019-01-01', periods=6)
df = pd.DataFrame(np.random.randn(6,4), index=dates, columns=["A", "B", "C", "D"])
df

	A	B	C	D
2019-01-01	1.051134	-2.357190	-0.441416	0.756528
2019-01-02	-1.779281	1.581360	2.070031	0.672192
2019-01-03	1.072005	-0.447704	0.783539	-0.962688
2019-01-04	1.306330	-1.088984	-0.122274	-0.692286
2019-01-05	-0.528289	1.637207	1.798403	0.464263
2019-01-06	1.597604	-0.099617	0.735458	1.495397

（1）查看前面的行

1	df.head() # 默认5行

	A	B	C	D
2019-01-01	1.051134	-2.357190	-0.441416	0.756528
2019-01-02	-1.779281	1.581360	2.070031	0.672192
2019-01-03	1.072005	-0.447704	0.783539	-0.962688
2019-01-04	1.306330	-1.088984	-0.122274	-0.692286
2019-01-05	-0.528289	1.637207	1.798403	0.464263

1	df.head(2)

	A	B	C	D
2019-01-01	1.051134	-2.35719	-0.441416	0.756528
2019-01-02	-1.779281	1.58136	2.070031	0.672192

（2）查看后面的行

1	df.tail() # 默认5行

	A	B	C	D
2019-01-02	-1.779281	1.581360	2.070031	0.672192
2019-01-03	1.072005	-0.447704	0.783539	-0.962688
2019-01-04	1.306330	-1.088984	-0.122274	-0.692286
2019-01-05	-0.528289	1.637207	1.798403	0.464263
2019-01-06	1.597604	-0.099617	0.735458	1.495397

1	df.tail(3)

	A	B	C	D
2019-01-04	1.306330	-1.088984	-0.122274	-0.692286
2019-01-05	-0.528289	1.637207	1.798403	0.464263
2019-01-06	1.597604	-0.099617	0.735458	1.495397

（3）查看总体信息

1 2	df.iloc[0, 3] = np.nan df

	A	B	C	D
2019-01-01	1.051134	-2.357190	-0.441416	NaN
2019-01-02	-1.779281	1.581360	2.070031	0.672192
2019-01-03	1.072005	-0.447704	0.783539	-0.962688
2019-01-04	1.306330	-1.088984	-0.122274	-0.692286
2019-01-05	-0.528289	1.637207	1.798403	0.464263
2019-01-06	1.597604	-0.099617	0.735458	1.495397

df.info()

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 6 entries, 2019-01-01 to 2019-01-06
Freq: D
Data columns (total 4 columns):
A    6 non-null float64
B    6 non-null float64
C    6 non-null float64
D    5 non-null float64
dtypes: float64(4)
memory usage: 240.0 bytes

2、Numpy通用函数同样适用于Pandas

（1）向量化运算

1 2	x = pd.DataFrame(np.arange(4).reshape(1, 4)) x

	0	1	2	3
0	0	1	2	3

x+5

	0	1	2	3
0	5	6	7	8

np.exp(x)

	0	1	2	3
0	1.0	2.718282	7.389056	20.085537

1 2	y = pd.DataFrame(np.arange(4,8).reshape(1, 4)) y

	0	1	2	3
0	4	5	6	7

x*y

	0	1	2	3
0	0	5	12	21

（2）矩阵化运算

1
2
3

np.random.seed(42)
x = pd.DataFrame(np.random.randint(10, size=(30, 30)))
x

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	6	3	7	4	6	9	2	6	7	4	...	4	0	9	5	8	0	9	2	6	3
1	8	2	4	2	6	4	8	6	1	3	...	2	0	3	1	7	3	1	5	5	9
2	3	5	1	9	1	9	3	7	6	8	...	6	8	7	0	7	7	2	0	7	2
3	2	0	4	9	6	9	8	6	8	7	...	0	2	4	2	0	4	9	6	6	8
4	9	9	2	6	0	3	3	4	6	6	...	9	6	8	6	0	0	8	8	3	8
5	2	6	5	7	8	4	0	2	9	7	...	2	0	4	0	7	0	0	1	1	5
6	6	4	0	0	2	1	4	9	5	6	...	5	0	8	5	2	3	3	2	9	2
7	2	3	6	3	8	0	7	6	1	7	...	3	0	1	0	4	4	6	8	8	2
8	2	2	3	7	5	7	0	7	3	0	...	1	1	5	2	8	3	0	3	0	4
9	3	7	7	6	2	0	0	2	5	6	...	4	2	3	2	0	0	4	5	2	8
10	4	7	0	4	2	0	3	4	6	0	...	5	6	1	9	1	9	0	7	0	8
11	5	6	9	6	9	2	1	8	7	9	...	6	5	2	8	9	5	9	9	5	0
12	3	9	5	5	4	0	7	4	4	6	...	0	7	2	9	6	9	4	9	4	6
13	8	4	0	9	9	0	1	5	8	7	...	5	8	4	0	3	4	9	9	4	6
14	3	0	4	6	9	9	5	4	3	1	...	6	1	0	3	7	1	2	0	0	2
15	4	2	0	0	7	9	1	2	1	2	...	6	3	9	4	1	7	3	8	4	8
16	3	9	4	8	7	2	0	2	3	1	...	8	0	0	3	8	5	2	0	3	8
17	2	8	6	3	2	9	4	4	2	8	...	6	9	4	2	6	1	8	9	9	0
18	5	6	7	9	8	1	9	1	4	4	...	3	5	2	5	6	9	9	2	6	2
19	1	9	3	7	8	6	0	2	8	0	...	4	3	2	2	3	8	1	8	0	0
20	4	5	5	2	6	8	9	7	5	7	...	3	5	0	8	0	4	3	2	5	1
21	2	4	8	1	9	7	1	4	6	7	...	0	1	8	2	0	4	6	5	0	4
22	4	5	2	4	6	4	4	4	9	9	...	1	7	6	9	9	1	5	5	2	1
23	0	5	4	8	0	6	4	4	1	2	...	8	5	0	7	6	9	2	0	4	3
24	9	7	0	9	0	3	7	4	1	5	...	3	7	8	2	2	1	9	2	2	4
25	4	1	9	5	4	5	0	4	8	9	...	9	3	0	7	0	2	3	7	5	9
26	6	7	1	9	7	2	6	2	6	1	...	0	6	5	9	8	0	3	8	3	9
27	2	8	1	3	5	1	7	7	0	2	...	8	0	4	5	4	5	5	6	3	7
28	6	8	6	2	2	7	4	3	7	5	...	1	7	9	2	4	5	9	5	3	2
29	3	0	3	0	0	9	5	4	3	2	...	1	3	0	4	8	0	8	7	5	6

30 rows × 30 columns

转置

1
2

z = x.T
z

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	6	8	3	2	9	2	6	2	2	3	...	4	2	4	0	9	4	6	2	6	3
1	3	2	5	0	9	6	4	3	2	7	...	5	4	5	5	7	1	7	8	8	0
2	7	4	1	4	2	5	0	6	3	7	...	5	8	2	4	0	9	1	1	6	3
3	4	2	9	9	6	7	0	3	7	6	...	2	1	4	8	9	5	9	3	2	0
4	6	6	1	6	0	8	2	8	5	2	...	6	9	6	0	0	4	7	5	2	0
5	9	4	9	9	3	4	1	0	7	0	...	8	7	4	6	3	5	2	1	7	9
6	2	8	3	8	3	0	4	7	0	0	...	9	1	4	4	7	0	6	7	4	5
7	6	6	7	6	4	2	9	6	7	2	...	7	4	4	4	4	4	2	7	3	4
8	7	1	6	8	6	9	5	1	3	5	...	5	6	9	1	1	8	6	0	7	3
9	4	3	8	7	6	7	6	7	0	6	...	7	7	9	2	5	9	1	2	5	2
10	3	8	7	1	3	5	3	0	7	5	...	4	0	2	6	4	1	9	9	1	0
11	7	1	4	0	6	7	6	8	3	5	...	7	5	0	5	1	0	5	8	3	5
12	7	9	1	6	2	8	7	8	5	5	...	9	0	4	1	2	9	2	4	3	1
13	2	8	4	6	5	3	0	1	7	2	...	3	1	8	5	8	8	2	5	5	7
14	5	9	7	7	1	0	5	6	3	5	...	9	0	0	1	6	9	8	3	5	9
15	4	4	9	4	9	0	7	9	2	7	...	7	4	2	1	6	8	6	9	0	4
16	1	1	8	2	8	9	4	2	8	1	...	9	9	3	1	5	8	4	1	7	6
17	7	3	8	7	4	3	3	6	2	4	...	1	8	0	2	7	5	9	7	5	9
18	5	6	0	5	5	6	1	9	8	0	...	4	5	0	1	3	7	6	5	2	1
19	1	7	8	2	3	1	5	8	1	0	...	8	0	7	3	7	0	8	4	8	7
20	4	2	6	0	9	2	5	3	1	4	...	3	0	1	8	3	9	0	8	1	1
21	0	0	8	2	6	0	0	0	1	2	...	5	1	7	5	7	3	6	0	7	3
22	9	3	7	4	8	4	8	1	5	3	...	0	8	6	0	8	0	5	4	9	0
23	5	1	0	2	6	0	5	0	2	2	...	8	2	9	7	2	7	9	5	2	4
24	8	7	7	0	0	7	2	4	8	0	...	0	0	9	6	2	0	8	4	4	8
25	0	3	7	4	0	0	3	4	3	0	...	4	4	1	9	1	2	0	5	5	0
26	9	1	2	9	8	0	3	6	0	4	...	3	6	5	2	9	3	3	5	9	8
27	2	5	0	6	8	1	2	8	3	5	...	2	5	5	0	2	7	8	6	5	7
28	6	5	7	6	3	1	9	8	0	2	...	5	0	2	4	2	5	3	3	3	5
29	3	9	2	8	8	5	2	2	4	8	...	1	4	1	3	4	9	9	7	2	6

30 rows × 30 columns

1
2
3

np.random.seed(1)
y = pd.DataFrame(np.random.randint(10, size=(30, 30)))
y

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	5	8	9	5	0	0	1	7	6	9	...	1	7	0	6	9	9	7	6	9	1
1	0	1	8	8	3	9	8	7	3	6	...	9	2	0	4	9	2	7	7	9	8
2	6	9	3	7	7	4	5	9	3	6	...	7	7	1	1	3	0	8	6	4	5
3	6	2	5	7	8	4	4	7	7	4	...	0	1	9	8	2	3	1	2	7	2
4	6	0	9	2	6	6	2	7	7	0	...	1	5	4	0	7	8	9	5	7	0
5	9	3	9	1	4	4	6	8	8	9	...	1	8	7	0	3	4	2	0	3	5
6	1	2	4	3	0	6	0	7	2	8	...	4	3	3	6	7	3	5	3	2	4
7	4	0	3	3	8	3	5	6	7	5	...	1	7	3	1	6	6	9	6	9	6
8	0	0	2	9	6	0	6	7	0	3	...	6	7	9	5	4	9	5	2	5	6
9	6	8	7	7	7	2	6	0	5	2	...	7	0	6	2	4	3	6	7	6	3
10	0	6	4	7	6	2	9	5	9	9	...	4	9	3	9	1	2	5	4	0	8
11	2	3	9	9	4	4	8	2	1	6	...	0	5	9	8	6	6	0	4	7	3
12	0	1	6	0	6	1	6	4	2	5	...	8	8	0	7	2	0	7	1	1	9
13	5	1	5	9	6	4	9	8	7	5	...	2	4	3	2	0	0	4	2	5	0
14	0	3	8	5	3	1	4	7	3	2	...	8	5	5	7	5	9	1	3	9	3
15	3	3	6	1	3	0	5	0	5	2	...	7	1	7	7	3	8	3	0	6	3
16	0	6	5	9	6	4	6	6	2	2	...	3	6	8	6	5	1	3	2	6	3
17	6	7	2	8	0	1	8	6	0	0	...	5	6	2	5	4	3	0	6	2	1
18	9	4	4	0	9	8	7	7	6	1	...	7	9	9	7	1	1	4	6	5	6
19	4	1	1	5	1	2	6	2	3	3	...	0	0	0	9	8	5	9	3	4	0
20	9	8	6	3	9	9	0	8	1	6	...	2	9	0	1	3	9	4	8	8	8
21	2	8	6	4	9	0	5	5	6	1	...	6	7	5	6	8	7	4	2	4	0
22	0	3	5	9	0	3	6	5	1	1	...	6	2	5	3	9	3	9	5	1	9
23	7	7	0	8	6	1	2	0	4	4	...	1	9	6	0	2	8	3	7	2	5
24	6	0	4	2	3	1	0	5	7	0	...	1	1	2	7	5	2	9	4	7	3
25	5	0	2	1	4	9	4	6	9	3	...	5	5	3	5	9	2	7	4	1	6
26	9	8	1	8	1	6	2	6	1	8	...	2	5	1	2	5	3	3	6	1	8
27	1	8	6	4	6	9	5	4	7	2	...	9	3	1	5	1	1	7	1	2	6
28	0	7	7	4	3	2	7	8	5	2	...	0	2	8	3	7	3	9	2	3	8
29	8	0	2	6	8	3	6	4	9	7	...	6	7	8	5	7	2	5	3	4	5

30 rows × 30 columns

x.dot(y)

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	616	560	723	739	612	457	681	799	575	590	...	523	739	613	580	668	602	733	585	657	700
1	520	438	691	600	612	455	666	764	707	592	...	555	681	503	679	641	506	779	494	633	590
2	557	570	786	807	690	469	804	828	704	573	...	563	675	712	758	793	672	754	550	756	638
3	605	507	664	701	660	496	698	806	651	575	...	582	685	668	586	629	534	678	484	591	626
4	599	681	753	873	721	563	754	770	620	654	...	633	747	661	677	726	649	716	610	735	706
5	422	354	602	627	613	396	617	627	489	423	...	456	572	559	537	499	384	589	436	574	507
6	359	446	599	599	481	357	577	572	451	464	...	449	550	495	532	633	554	663	476	565	602
7	531	520	698	590	607	537	665	696	571	472	...	576	588	551	665	652	527	742	528	650	599
8	449	322	547	533	593	399	584	638	587	424	...	402	596	523	523	447	362	561	386	529	484
9	373	433	525	601	522	345	551	521	434	447	...	508	498	438	478	459	418	488	407	503	496
10	500	427	574	607	667	477	652	656	615	477	...	622	702	531	610	558	532	598	471	582	561
11	664	694	772	841	779	574	730	810	711	608	...	591	760	616	638	721	676	846	678	754	708
12	545	547	687	701	721	576	689	724	710	532	...	674	684	648	694	710	564	757	571	671	656
13	574	586	723	750	691	494	696	787	667	523	...	618	681	568	682	715	644	756	557	690	604
14	502	382	645	557	570	403	538	677	500	501	...	369	650	507	576	546	531	554	437	616	463
15	510	505	736	651	649	510	719	733	694	557	...	605	717	574	642	678	576	755	455	598	654
16	567	376	614	612	643	514	598	724	547	464	...	456	639	520	560	569	442	596	517	659	532
17	626	716	828	765	740	603	809	852	692	591	...	664	716	655	721	742	612	819	593	744	712
18	600	559	667	664	641	556	624	815	638	564	...	581	701	559	677	710	554	748	597	614	657
19	445	431	661	681	641	552	690	719	602	474	...	515	637	576	620	572	512	599	455	622	538
20	523	569	784	725	713	501	740	772	638	640	...	589	775	664	686	726	672	747	548	723	645
21	487	465	553	639	517	449	592	609	454	398	...	492	567	534	404	554	417	561	466	498	492
22	479	449	574	686	583	377	566	614	563	455	...	453	539	491	501	596	520	722	478	565	501
23	483	386	476	526	550	426	492	585	536	482	...	322	541	438	456	487	408	502	426	474	481
24	523	551	658	767	537	444	663	731	576	577	...	522	590	525	664	691	548	635	526	641	538
25	652	656	738	753	853	508	752	815	669	576	...	694	833	693	606	575	616	704	559	728	672
26	578	577	744	856	699	497	779	800	733	587	...	630	754	704	834	760	680	765	592	731	629
27	554	494	665	689	630	574	695	703	636	599	...	554	685	532	658	649	554	693	577	634	668
28	498	552	659	784	552	492	690	775	544	551	...	567	636	518	599	742	521	733	533	605	604
29	513	491	563	642	477	367	589	647	516	484	...	428	574	504	548	553	483	540	407	547	455

30 rows × 30 columns

1	%timeit x.dot(y)

264 µs ± 12.3 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

1	%timeit np.dot(x, y)

103 µs ± 8.07 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

执行相同运算，Numpy与Pandas的对比

1 2	x1 = np.array(x) x1

array([[6, 3, 7, 4, 6, 9, 2, 6, 7, 4, 3, 7, 7, 2, 5, 4, 1, 7, 5, 1, 4, 0,
        9, 5, 8, 0, 9, 2, 6, 3],
       [8, 2, 4, 2, 6, 4, 8, 6, 1, 3, 8, 1, 9, 8, 9, 4, 1, 3, 6, 7, 2, 0,
        3, 1, 7, 3, 1, 5, 5, 9],
       [3, 5, 1, 9, 1, 9, 3, 7, 6, 8, 7, 4, 1, 4, 7, 9, 8, 8, 0, 8, 6, 8,
        7, 0, 7, 7, 2, 0, 7, 2],
       [2, 0, 4, 9, 6, 9, 8, 6, 8, 7, 1, 0, 6, 6, 7, 4, 2, 7, 5, 2, 0, 2,
        4, 2, 0, 4, 9, 6, 6, 8],
       [9, 9, 2, 6, 0, 3, 3, 4, 6, 6, 3, 6, 2, 5, 1, 9, 8, 4, 5, 3, 9, 6,
        8, 6, 0, 0, 8, 8, 3, 8],
       [2, 6, 5, 7, 8, 4, 0, 2, 9, 7, 5, 7, 8, 3, 0, 0, 9, 3, 6, 1, 2, 0,
        4, 0, 7, 0, 0, 1, 1, 5],
       [6, 4, 0, 0, 2, 1, 4, 9, 5, 6, 3, 6, 7, 0, 5, 7, 4, 3, 1, 5, 5, 0,
        8, 5, 2, 3, 3, 2, 9, 2],
       [2, 3, 6, 3, 8, 0, 7, 6, 1, 7, 0, 8, 8, 1, 6, 9, 2, 6, 9, 8, 3, 0,
        1, 0, 4, 4, 6, 8, 8, 2],
       [2, 2, 3, 7, 5, 7, 0, 7, 3, 0, 7, 3, 5, 7, 3, 2, 8, 2, 8, 1, 1, 1,
        5, 2, 8, 3, 0, 3, 0, 4],
       [3, 7, 7, 6, 2, 0, 0, 2, 5, 6, 5, 5, 5, 2, 5, 7, 1, 4, 0, 0, 4, 2,
        3, 2, 0, 0, 4, 5, 2, 8],
       [4, 7, 0, 4, 2, 0, 3, 4, 6, 0, 2, 1, 8, 9, 5, 9, 2, 7, 7, 1, 5, 6,
        1, 9, 1, 9, 0, 7, 0, 8],
       [5, 6, 9, 6, 9, 2, 1, 8, 7, 9, 6, 8, 3, 3, 0, 7, 2, 6, 1, 1, 6, 5,
        2, 8, 9, 5, 9, 9, 5, 0],
       [3, 9, 5, 5, 4, 0, 7, 4, 4, 6, 3, 5, 3, 2, 6, 7, 3, 1, 9, 2, 0, 7,
        2, 9, 6, 9, 4, 9, 4, 6],
       [8, 4, 0, 9, 9, 0, 1, 5, 8, 7, 4, 0, 6, 4, 5, 6, 2, 9, 2, 4, 5, 8,
        4, 0, 3, 4, 9, 9, 4, 6],
       [3, 0, 4, 6, 9, 9, 5, 4, 3, 1, 3, 9, 9, 2, 9, 0, 7, 4, 3, 7, 6, 1,
        0, 3, 7, 1, 2, 0, 0, 2],
       [4, 2, 0, 0, 7, 9, 1, 2, 1, 2, 6, 0, 9, 7, 9, 9, 9, 1, 2, 8, 6, 3,
        9, 4, 1, 7, 3, 8, 4, 8],
       [3, 9, 4, 8, 7, 2, 0, 2, 3, 1, 0, 6, 7, 6, 4, 0, 6, 6, 8, 2, 8, 0,
        0, 3, 8, 5, 2, 0, 3, 8],
       [2, 8, 6, 3, 2, 9, 4, 4, 2, 8, 3, 4, 3, 4, 6, 8, 6, 4, 9, 9, 6, 9,
        4, 2, 6, 1, 8, 9, 9, 0],
       [5, 6, 7, 9, 8, 1, 9, 1, 4, 4, 5, 2, 7, 0, 5, 3, 0, 6, 8, 3, 3, 5,
        2, 5, 6, 9, 9, 2, 6, 2],
       [1, 9, 3, 7, 8, 6, 0, 2, 8, 0, 8, 7, 0, 5, 4, 5, 9, 4, 5, 4, 4, 3,
        2, 2, 3, 8, 1, 8, 0, 0],
       [4, 5, 5, 2, 6, 8, 9, 7, 5, 7, 4, 7, 9, 3, 9, 7, 9, 1, 4, 8, 3, 5,
        0, 8, 0, 4, 3, 2, 5, 1],
       [2, 4, 8, 1, 9, 7, 1, 4, 6, 7, 0, 5, 0, 1, 0, 4, 9, 8, 5, 0, 0, 1,
        8, 2, 0, 4, 6, 5, 0, 4],
       [4, 5, 2, 4, 6, 4, 4, 4, 9, 9, 2, 0, 4, 8, 0, 2, 3, 0, 0, 7, 1, 7,
        6, 9, 9, 1, 5, 5, 2, 1],
       [0, 5, 4, 8, 0, 6, 4, 4, 1, 2, 6, 5, 1, 5, 1, 1, 1, 2, 1, 3, 8, 5,
        0, 7, 6, 9, 2, 0, 4, 3],
       [9, 7, 0, 9, 0, 3, 7, 4, 1, 5, 4, 1, 2, 8, 6, 6, 5, 7, 3, 7, 3, 7,
        8, 2, 2, 1, 9, 2, 2, 4],
       [4, 1, 9, 5, 4, 5, 0, 4, 8, 9, 1, 0, 9, 8, 9, 8, 8, 5, 7, 0, 9, 3,
        0, 7, 0, 2, 3, 7, 5, 9],
       [6, 7, 1, 9, 7, 2, 6, 2, 6, 1, 9, 5, 2, 2, 8, 6, 4, 9, 6, 8, 0, 6,
        5, 9, 8, 0, 3, 8, 3, 9],
       [2, 8, 1, 3, 5, 1, 7, 7, 0, 2, 9, 8, 4, 5, 3, 9, 1, 7, 5, 4, 8, 0,
        4, 5, 4, 5, 5, 6, 3, 7],
       [6, 8, 6, 2, 2, 7, 4, 3, 7, 5, 1, 3, 3, 5, 5, 0, 7, 5, 2, 8, 1, 7,
        9, 2, 4, 5, 9, 5, 3, 2],
       [3, 0, 3, 0, 0, 9, 5, 4, 3, 2, 0, 5, 1, 7, 9, 4, 6, 9, 1, 7, 1, 3,
        0, 4, 8, 0, 8, 7, 5, 6]])

1 2	y1 = np.array(y) y1

array([[5, 8, 9, 5, 0, 0, 1, 7, 6, 9, 2, 4, 5, 2, 4, 2, 4, 7, 7, 9, 1, 7,
        0, 6, 9, 9, 7, 6, 9, 1],
       [0, 1, 8, 8, 3, 9, 8, 7, 3, 6, 5, 1, 9, 3, 4, 8, 1, 4, 0, 3, 9, 2,
        0, 4, 9, 2, 7, 7, 9, 8],
       [6, 9, 3, 7, 7, 4, 5, 9, 3, 6, 8, 0, 2, 7, 7, 9, 7, 3, 0, 8, 7, 7,
        1, 1, 3, 0, 8, 6, 4, 5],
       [6, 2, 5, 7, 8, 4, 4, 7, 7, 4, 9, 0, 2, 0, 7, 1, 7, 9, 8, 4, 0, 1,
        9, 8, 2, 3, 1, 2, 7, 2],
       [6, 0, 9, 2, 6, 6, 2, 7, 7, 0, 6, 5, 1, 4, 6, 0, 6, 5, 1, 2, 1, 5,
        4, 0, 7, 8, 9, 5, 7, 0],
       [9, 3, 9, 1, 4, 4, 6, 8, 8, 9, 2, 7, 5, 5, 4, 5, 8, 5, 8, 1, 1, 8,
        7, 0, 3, 4, 2, 0, 3, 5],
       [1, 2, 4, 3, 0, 6, 0, 7, 2, 8, 3, 0, 8, 4, 2, 9, 0, 3, 8, 1, 4, 3,
        3, 6, 7, 3, 5, 3, 2, 4],
       [4, 0, 3, 3, 8, 3, 5, 6, 7, 5, 1, 7, 0, 2, 8, 2, 1, 4, 0, 4, 1, 7,
        3, 1, 6, 6, 9, 6, 9, 6],
       [0, 0, 2, 9, 6, 0, 6, 7, 0, 3, 9, 0, 3, 4, 7, 5, 3, 8, 8, 0, 6, 7,
        9, 5, 4, 9, 5, 2, 5, 6],
       [6, 8, 7, 7, 7, 2, 6, 0, 5, 2, 1, 8, 5, 9, 4, 9, 1, 2, 0, 4, 7, 0,
        6, 2, 4, 3, 6, 7, 6, 3],
       [0, 6, 4, 7, 6, 2, 9, 5, 9, 9, 9, 8, 6, 4, 2, 9, 4, 0, 0, 3, 4, 9,
        3, 9, 1, 2, 5, 4, 0, 8],
       [2, 3, 9, 9, 4, 4, 8, 2, 1, 6, 3, 8, 9, 7, 0, 5, 2, 2, 8, 5, 0, 5,
        9, 8, 6, 6, 0, 4, 7, 3],
       [0, 1, 6, 0, 6, 1, 6, 4, 2, 5, 4, 6, 2, 9, 2, 7, 5, 0, 7, 8, 8, 8,
        0, 7, 2, 0, 7, 1, 1, 9],
       [5, 1, 5, 9, 6, 4, 9, 8, 7, 5, 1, 8, 0, 5, 3, 9, 0, 4, 8, 6, 2, 4,
        3, 2, 0, 0, 4, 2, 5, 0],
       [0, 3, 8, 5, 3, 1, 4, 7, 3, 2, 2, 2, 6, 6, 0, 1, 5, 6, 5, 8, 8, 5,
        5, 7, 5, 9, 1, 3, 9, 3],
       [3, 3, 6, 1, 3, 0, 5, 0, 5, 2, 7, 6, 4, 0, 2, 4, 8, 7, 6, 7, 7, 1,
        7, 7, 3, 8, 3, 0, 6, 3],
       [0, 6, 5, 9, 6, 4, 6, 6, 2, 2, 4, 1, 2, 3, 9, 3, 6, 7, 0, 3, 3, 6,
        8, 6, 5, 1, 3, 2, 6, 3],
       [6, 7, 2, 8, 0, 1, 8, 6, 0, 0, 1, 2, 7, 7, 4, 4, 0, 1, 0, 8, 5, 6,
        2, 5, 4, 3, 0, 6, 2, 1],
       [9, 4, 4, 0, 9, 8, 7, 7, 6, 1, 7, 2, 4, 5, 6, 7, 2, 0, 5, 2, 7, 9,
        9, 7, 1, 1, 4, 6, 5, 6],
       [4, 1, 1, 5, 1, 2, 6, 2, 3, 3, 2, 3, 0, 0, 1, 5, 0, 5, 8, 8, 0, 0,
        0, 9, 8, 5, 9, 3, 4, 0],
       [9, 8, 6, 3, 9, 9, 0, 8, 1, 6, 6, 1, 3, 7, 3, 2, 3, 0, 2, 8, 2, 9,
        0, 1, 3, 9, 4, 8, 8, 8],
       [2, 8, 6, 4, 9, 0, 5, 5, 6, 1, 7, 6, 5, 7, 1, 9, 7, 5, 6, 7, 6, 7,
        5, 6, 8, 7, 4, 2, 4, 0],
       [0, 3, 5, 9, 0, 3, 6, 5, 1, 1, 8, 4, 7, 0, 1, 7, 1, 5, 4, 5, 6, 2,
        5, 3, 9, 3, 9, 5, 1, 9],
       [7, 7, 0, 8, 6, 1, 2, 0, 4, 4, 6, 1, 0, 9, 4, 9, 3, 0, 5, 1, 1, 9,
        6, 0, 2, 8, 3, 7, 2, 5],
       [6, 0, 4, 2, 3, 1, 0, 5, 7, 0, 2, 2, 0, 9, 5, 1, 1, 6, 3, 2, 1, 1,
        2, 7, 5, 2, 9, 4, 7, 3],
       [5, 0, 2, 1, 4, 9, 4, 6, 9, 3, 8, 8, 7, 1, 8, 7, 8, 9, 2, 2, 5, 5,
        3, 5, 9, 2, 7, 4, 1, 6],
       [9, 8, 1, 8, 1, 6, 2, 6, 1, 8, 3, 7, 0, 7, 0, 0, 7, 3, 9, 5, 2, 5,
        1, 2, 5, 3, 3, 6, 1, 8],
       [1, 8, 6, 4, 6, 9, 5, 4, 7, 2, 0, 2, 0, 5, 9, 4, 1, 4, 5, 2, 9, 3,
        1, 5, 1, 1, 7, 1, 2, 6],
       [0, 7, 7, 4, 3, 2, 7, 8, 5, 2, 4, 9, 2, 2, 3, 5, 9, 6, 4, 9, 0, 2,
        8, 3, 7, 3, 9, 2, 3, 8],
       [8, 0, 2, 6, 8, 3, 6, 4, 9, 7, 6, 3, 2, 9, 1, 5, 5, 6, 9, 4, 6, 7,
        8, 5, 7, 2, 5, 3, 4, 5]])

1	%timeit x1.dot(y1)

24.7 µs ± 3.2 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

1	%timeit np.dot(x1, y1)

22 µs ± 344 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

1	%timeit np.dot(x.values, y.values)

43.4 µs ± 2.55 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

x2 = list(x1)
y2 = list(y1)
x3 = []
y3 = []
for i in x2:
    res = []
    for j in i:
        res.append(int(j))
    x3.append(res)
for i in y2:
    res = []
    for j in i:
        res.append(int(j))
    y3.append(res)

def f(x, y):
    res = []
    for i in range(len(x)):
        row = []
        for j in range(len(y[0])):
            sum_row = 0
            for k in range(len(x[0])):
                sum_row += x[i][k]*y[k][j]
            row.append(sum_row)
        res.append(row)
    return res

1	%timeit f(x3, y3)

5.86 ms ± 599 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

一般来说，纯粹的计算在Numpy里执行的更快

Numpy更侧重于计算，Pandas更侧重于数据处理

（3）广播运算

1
2
3

np.random.seed(42)
x = pd.DataFrame(np.random.randint(10, size=(3, 3)), columns=list("ABC"))
x

	A	B	C
0	6	3	7
1	4	6	9
2	2	6	7

按行广播

x.iloc[0]

A    6
B    3
C    7
Name: 0, dtype: int32

1	x/x.iloc[0]

	A	B	C
0	1.000000	1.0	1.000000
1	0.666667	2.0	1.285714
2	0.333333	2.0	1.000000

按列广播

x.A

0    6
1    4
2    2
Name: A, dtype: int32

1	x.div(x.A, axis=0) # add sub div mul

	A	B	C
0	1.0	0.5	1.166667
1	1.0	1.5	2.250000
2	1.0	3.0	3.500000

1	x.div(x.iloc[0], axis=1)

	A	B	C
0	1.000000	1.0	1.000000
1	0.666667	2.0	1.285714
2	0.333333	2.0	1.000000

3、新的用法

（1）索引对齐

1 2	A = pd.DataFrame(np.random.randint(0, 20, size=(2, 2)), columns=list("AB")) A

	A	B
0	3	7
1	2	1

1 2	B = pd.DataFrame(np.random.randint(0, 10, size=(3, 3)), columns=list("ABC")) B

	A	B	C
0	7	5	1
1	4	0	9
2	5	8	0

pandas会自动对齐两个对象的索引，没有的值用np.nan表示

A+B

	A	B	C
0	10.0	12.0	NaN
1	6.0	1.0	NaN
2	NaN	NaN	NaN

缺省值也可用fill_value来填充

1	A.add(B, fill_value=0)

	A	B	C
0	10.0	12.0	1.0
1	6.0	1.0	9.0
2	5.0	8.0	0.0

A*B

	A	B	C
0	21.0	35.0	NaN
1	8.0	0.0	NaN
2	NaN	NaN	NaN

（2）统计相关

数据种类统计

1 2	y = np.random.randint(3, size=20) y

array([2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 1])

1	np.unique(y)

array([0, 1, 2])

1 2	from collections import Counter Counter(y)

Counter({2: 11, 1: 5, 0: 4})

1 2	y1 = pd.DataFrame(y, columns=["A"]) y1

	A
0	2
1	2
2	2
3	1
4	2
5	1
6	1
7	2
8	1
9	2
10	2
11	0
12	2
13	0
14	2
15	2
16	0
17	0
18	2
19	1

1	np.unique(y1)

array([0, 1, 2])

1	y1["A"].value_counts()

2    11
1     5
0     4
Name: A, dtype: int64

产生新的结果，并进行排序

population_dict = {"BeiJing": 2154,
                   "ShangHai": 2424,
                   "ShenZhen": 1303,
                   "HangZhou": 981 }
population = pd.Series(population_dict) 

GDP_dict = {"BeiJing": 30320,
            "ShangHai": 32680,
            "ShenZhen": 24222,
            "HangZhou": 13468 }
GDP = pd.Series(GDP_dict)

city_info = pd.DataFrame({"population": population,"GDP": GDP})
city_info

	population	GDP
BeiJing	2154	30320
ShangHai	2424	32680
ShenZhen	1303	24222
HangZhou	981	13468

1 2	city_info["per_GDP"] = city_info["GDP"]/city_info["population"] city_info

	population	GDP	per_GDP
BeiJing	2154	30320	14.076137
ShangHai	2424	32680	13.481848
ShenZhen	1303	24222	18.589409
HangZhou	981	13468	13.728848

递增排序

1	city_info.sort_values(by="per_GDP")

	population	GDP	per_GDP
ShangHai	2424	32680	13.481848
HangZhou	981	13468	13.728848
BeiJing	2154	30320	14.076137
ShenZhen	1303	24222	18.589409

递减排序

1	city_info.sort_values(by="per_GDP", ascending=False)

	population	GDP	per_GDP
ShenZhen	1303	24222	18.589409
BeiJing	2154	30320	14.076137
HangZhou	981	13468	13.728848
ShangHai	2424	32680	13.481848

按轴进行排序

1 2	data = pd.DataFrame(np.random.randint(20, size=(3, 4)), index=[2, 1, 0], columns=list("CBAD")) data

	C	B	A	D
2	3	13	17	8
1	1	19	14	6
0	11	7	14	2

行排序

1	data.sort_index()

	C	B	A	D
0	11	7	14	2
1	1	19	14	6
2	3	13	17	8

列排序

1	data.sort_index(axis=1)

	A	B	C	D
2	17	13	3	8
1	14	19	1	6
0	14	7	11	2

1	data.sort_index(axis=1, ascending=False)

	D	C	B	A
2	8	3	13	17
1	6	1	19	14
0	2	11	7	14

统计方法

1 2	df = pd.DataFrame(np.random.normal(2, 4, size=(6, 4)),columns=list("ABCD")) df

	A	B	C	D
0	1.082198	3.557396	-3.060476	6.367969
1	13.113252	6.774559	2.874553	5.527044
2	-2.036341	-4.333177	5.094802	-0.152567
3	-3.386712	-1.522365	-2.522209	2.537716
4	4.328491	5.550994	5.577329	5.019991
5	1.171336	-0.493910	-4.032613	6.398588

非空个数

1	df.count()

A    6
B    6
C    6
D    6
dtype: int64

求和

df.sum()

A    14.272224
B     9.533497
C     3.931385
D    25.698741
dtype: float64

1	df.sum(axis=1)

0     7.947086
1    28.289408
2    -1.427283
3    -4.893571
4    20.476806
5     3.043402
dtype: float64

最大值最小值

df.min()

A   -3.386712
B   -4.333177
C   -4.032613
D   -0.152567
dtype: float64

1	df.max(axis=1)

0     6.367969
1    13.113252
2     5.094802
3     2.537716
4     5.577329
5     6.398588
dtype: float64

df

	A	B	C	D
0	1.082198	3.557396	-3.060476	6.367969
1	13.113252	6.774559	2.874553	5.527044
2	-2.036341	-4.333177	5.094802	-0.152567
3	-3.386712	-1.522365	-2.522209	2.537716
4	4.328491	5.550994	5.577329	5.019991
5	1.171336	-0.493910	-4.032613	6.398588

1	df.idxmax()

A    1
B    1
C    4
D    5
dtype: int64

均值

df.mean()

A    2.378704
B    1.588916
C    0.655231
D    4.283124
dtype: float64

方差

df.var()

A    34.980702
B    19.110656
C    18.948144
D     6.726776
dtype: float64

标准差

df.std()

A    5.914449
B    4.371574
C    4.352947
D    2.593603
dtype: float64

中位数

1	df.median()

A    1.126767
B    1.531743
C    0.176172
D    5.273518
dtype: float64

众数

1 2	data = pd.DataFrame(np.random.randint(5, size=(10, 2)), columns=list("AB")) data

	A	B
0	4	2
1	3	2
2	2	0
3	2	4
4	2	0
5	4	1
6	2	0
7	1	1
8	3	4
9	2	0

1	data.mode()

	A	B
0	2	0

75%分位数

1	df.quantile(0.75)

A    3.539202
B    5.052594
C    4.539740
D    6.157738
Name: 0.75, dtype: float64

一网打尽

1	df.describe()

	A	B	C	D
count	6.000000	6.000000	6.000000	6.000000
mean	2.378704	1.588916	0.655231	4.283124
std	5.914449	4.371574	4.352947	2.593603
min	-3.386712	-4.333177	-4.032613	-0.152567
25%	-1.256706	-1.265251	-2.925910	3.158284
50%	1.126767	1.531743	0.176172	5.273518
75%	3.539202	5.052594	4.539740	6.157738
max	13.113252	6.774559	5.577329	6.398588

data_2 = pd.DataFrame([["a", "a", "c", "d"],
                       ["c", "a", "c", "b"],
                       ["a", "a", "d", "c"]], columns=list("ABCD"))
data_2

	A	B	C	D
0	a	a	c	d
1	c	a	c	b
2	a	a	d	c

1	data_2.describe()

	A	B	C	D
count	3	3	3	3
unique	2	1	2	3
top	a	a	c	c
freq	2	3	2	1

12.4 缺失值处理

1、发现缺失值

import pandas as pd
import numpy as np

data = pd.DataFrame(np.array([[1, np.nan, 2],
                              [np.nan, 3, 4],
                              [5, 6, None]]), columns=["A", "B", "C"])
data

	A	B	C
0	1	NaN	2
1	NaN	3	4
2	5	6	None

注意：有None、字符串等，数据类型全部变为object，它比int和float更消耗资源

1	data.dtypes

A    object
B    object
C    object
dtype: object

1	data.isnull()

	A	B	C
0	False	True	False
1	True	False	False
2	False	False	True

1	data.notnull()

	A	B	C
0	True	False	True
1	False	True	True
2	True	True	False

2、删除缺失值

data = pd.DataFrame(np.array([[1, np.nan, 2, 3],
                              [np.nan, 4, 5, 6],
                              [7, 8, np.nan, 9],
                              [10, 11 , 12, 13]]), columns=["A", "B", "C", "D"])
data

	A	B	C	D
0	1.0	NaN	2.0	3.0
1	NaN	4.0	5.0	6.0
2	7.0	8.0	NaN	9.0
3	10.0	11.0	12.0	13.0

注意：np.nan是一种特殊的浮点数

1	data.dtypes

A    float64
B    float64
C    float64
D    float64
dtype: object

（1）删除整行

1	data.dropna()

	A	B	C	D
3	10.0	11.0	12.0	13.0

（2）删除整列

1	data.dropna(axis="columns")

	D
0	3.0
1	6.0
2	9.0
3	13.0

1 2	data["D"] = np.nan data

	A	B	C	D
0	1.0	NaN	2.0	NaN
1	NaN	4.0	5.0	NaN
2	7.0	8.0	NaN	NaN
3	10.0	11.0	12.0	NaN

1	data.dropna(axis="columns", how="all")

	A	B	C
0	1.0	NaN	2.0
1	NaN	4.0	5.0
2	7.0	8.0	NaN
3	10.0	11.0	12.0

1	data.dropna(axis="columns", how="any")


0
1
2
3

1 2	data.loc[3] = np.nan data

	A	B	C	D
0	1.0	NaN	2.0	NaN
1	NaN	4.0	5.0	NaN
2	7.0	8.0	NaN	NaN
3	NaN	NaN	NaN	NaN

1	data.dropna(how="all")

	A	B	C	D
0	1.0	NaN	2.0	NaN
1	NaN	4.0	5.0	NaN
2	7.0	8.0	NaN	NaN

3、填充缺失值

data = pd.DataFrame(np.array([[1, np.nan, 2, 3],
                              [np.nan, 4, 5, 6],
                              [7, 8, np.nan, 9],
                              [10, 11 , 12, 13]]), columns=["A", "B", "C", "D"])
data

	A	B	C	D
0	1.0	NaN	2.0	3.0
1	NaN	4.0	5.0	6.0
2	7.0	8.0	NaN	9.0
3	10.0	11.0	12.0	13.0

1	data.fillna(value=5)

	A	B	C	D
0	1.0	5.0	2.0	3.0
1	5.0	4.0	5.0	6.0
2	7.0	8.0	5.0	9.0
3	10.0	11.0	12.0	13.0

用均值进行替换

1 2	fill = data.mean() fill

A    6.000000
B    7.666667
C    6.333333
D    7.750000
dtype: float64

1	data.fillna(value=fill)

	A	B	C	D
0	1.0	7.666667	2.000000	3.0
1	6.0	4.000000	5.000000	6.0
2	7.0	8.000000	6.333333	9.0
3	10.0	11.000000	12.000000	13.0

1 2	fill = data.stack().mean() fill

7.0

1	data.fillna(value=fill)

	A	B	C	D
0	1.0	7.0	2.0	3.0
1	7.0	4.0	5.0	6.0
2	7.0	8.0	7.0	9.0
3	10.0	11.0	12.0	13.0

12.5 合并数据

构造一个生产DataFrame的函数

import pandas as pd
import numpy as np

def make_df(cols, ind):
    "一个简单的DataFrame"
    data = {c: [str(c)+str(i) for i in ind]  for c in cols}
    return pd.DataFrame(data, ind)

make_df("ABC", range(3))

	A	B	C
0	A0	B0	C0
1	A1	B1	C1
2	A2	B2	C2

垂直合并

df_1 = make_df("AB", [1, 2])
df_2 = make_df("AB", [3, 4])
print(df_1)
print(df_2)

    A   B
1  A1  B1
2  A2  B2
    A   B
3  A3  B3
4  A4  B4

1	pd.concat([df_1, df_2])

	A	B
1	A1	B1
2	A2	B2
3	A3	B3
4	A4	B4

水平合并

df_3 = make_df("AB", [0, 1])
df_4 = make_df("CD", [0, 1])
print(df_3)
print(df_4)

    A   B
0  A0  B0
1  A1  B1
    C   D
0  C0  D0
1  C1  D1

1	pd.concat([df_3, df_4], axis=1)

	A	B	C	D
0	A0	B0	C0	D0
1	A1	B1	C1	D1

索引重叠

行重叠

df_5 = make_df("AB", [1, 2])
df_6 = make_df("AB", [1, 2])
print(df_5)
print(df_6)

    A   B
1  A1  B1
2  A2  B2
    A   B
1  A1  B1
2  A2  B2

1	pd.concat([df_5, df_6])

	A	B
1	A1	B1
2	A2	B2
1	A1	B1
2	A2	B2

1	pd.concat([df_5, df_6],ignore_index=True)

	A	B
0	A1	B1
1	A2	B2
2	A1	B1
3	A2	B2

列重叠

df_7 = make_df("ABC", [1, 2])
df_8 = make_df("BCD", [1, 2])
print(df_7)
print(df_8)

    A   B   C
1  A1  B1  C1
2  A2  B2  C2
    B   C   D
1  B1  C1  D1
2  B2  C2  D2

1	pd.concat([df_7, df_8], axis=1)

	A	B	C	B	C	D
1	A1	B1	C1	B1	C1	D1
2	A2	B2	C2	B2	C2	D2

1	pd.concat([df_7, df_8],axis=1, ignore_index=True)

	0	1	2	3	4	5
1	A1	B1	C1	B1	C1	D1
2	A2	B2	C2	B2	C2	D2

对齐合并merge()

df_9 = make_df("AB", [1, 2])
df_10 = make_df("BC", [1, 2])
print(df_9)
print(df_10)

    A   B
1  A1  B1
2  A2  B2
    B   C
1  B1  C1
2  B2  C2

1	pd.merge(df_9, df_10)

	A	B	C
0	A1	B1	C1
1	A2	B2	C2

df_9 = make_df("AB", [1, 2])
df_10 = make_df("CB", [2, 1])
print(df_9)
print(df_10)

    A   B
1  A1  B1
2  A2  B2
    C   B
2  C2  B2
1  C1  B1

1	pd.merge(df_9, df_10)

	A	B	C
0	A1	B1	C1
1	A2	B2	C2

【例】合并城市信息

population_dict = {"city": ("BeiJing", "HangZhou", "ShenZhen"),
                   "pop": (2154, 981, 1303)}
population = pd.DataFrame(population_dict)
population

	city	pop
0	BeiJing	2154
1	HangZhou	981
2	ShenZhen	1303

GDP_dict = {"city": ("BeiJing", "ShangHai", "HangZhou"),
            "GDP": (30320, 32680, 13468)}
GDP = pd.DataFrame(GDP_dict)
GDP

	city	GDP
0	BeiJing	30320
1	ShangHai	32680
2	HangZhou	13468

1 2	city_info = pd.merge(population, GDP) city_info

	city	pop	GDP
0	BeiJing	2154	30320
1	HangZhou	981	13468

1 2	city_info = pd.merge(population, GDP, how="outer") city_info

	city	pop	GDP
0	BeiJing	2154.0	30320.0
1	HangZhou	981.0	13468.0
2	ShenZhen	1303.0	NaN
3	ShangHai	NaN	32680.0

12.6 分组和数据透视表

df = pd.DataFrame({"key":["A", "B", "C", "C", "B", "A"],
                  "data1": range(6),
                  "data2": np.random.randint(0, 10, size=6)})
df

	key	data1	data2
0	A	0	3
1	B	1	3
2	C	2	4
3	C	3	6
4	B	4	6
5	A	5	3

（1）分组

延迟计算

1	df.groupby("key")

<pandas.core.groupby.generic.DataFrameGroupBy object at 0x0000018DD1697308>

1	df.groupby("key").sum()

	data1	data2
key
A	5	6
B	5	9
C	5	10

1	df.groupby("key").mean()

	data1	data2
key
A	2.5	3.0
B	2.5	4.5
C	2.5	5.0

1 2	for i in df.groupby("key"): print(str(i))

('A',   key  data1  data2
0   A      0      3
5   A      5      3)
('B',   key  data1  data2
1   B      1      3
4   B      4      6)
('C',   key  data1  data2
2   C      2      4
3   C      3      6)

按列取值

1	df.groupby("key")["data2"].sum()

key
A     6
B     9
C    10
Name: data2, dtype: int32

按组迭代

1 2	for data, group in df.groupby("key"): print("{0:5} shape={1}".format(data, group.shape))

A     shape=(2, 3)
B     shape=(2, 3)
C     shape=(2, 3)

调用方法

1	df.groupby("key")["data1"].describe()

	count	mean	std	min	25%	50%	75%	max
key
A	2.0	2.5	3.535534	0.0	1.25	2.5	3.75	5.0
B	2.0	2.5	2.121320	1.0	1.75	2.5	3.25	4.0
C	2.0	2.5	0.707107	2.0	2.25	2.5	2.75	3.0

支持更复杂的操作

1	df.groupby("key").aggregate(["min", "median", "max"])

	data1			data2
	min	median	max	min	median	max
key
A	0	2.5	5	3	3.0	3
B	1	2.5	4	3	4.5	6
C	2	2.5	3	4	5.0	6

过滤

1
2
3

def filter_func(x):
    return x["data2"].std() > 3
df.groupby("key")["data2"].std()

key
A    0.000000
B    2.121320
C    1.414214
Name: data2, dtype: float64

1	df.groupby("key").filter(filter_func)

	key	data1	data2

转换

df

	key	data1	data2
0	A	0	3
1	B	1	3
2	C	2	4
3	C	3	6
4	B	4	6
5	A	5	3

1	df.groupby("key").transform(lambda x: x-x.mean())

	data1	data2
0	-2.5	0.0
1	-1.5	-1.5
2	-0.5	-1.0
3	0.5	1.0
4	1.5	1.5
5	2.5	0.0

df

	key	data1	data2
0	A	0	3
1	B	1	3
2	C	2	4
3	C	3	6
4	B	4	6
5	A	5	3

1	df.groupby("key").apply(lambda x: x-x.mean())

	data1	data2
0	-2.5	0.0
1	-1.5	-1.5
2	-0.5	-1.0
3	0.5	1.0
4	1.5	1.5
5	2.5	0.0

apply（）方法

df

	key	data1	data2
0	A	0	3
1	B	1	3
2	C	2	4
3	C	3	6
4	B	4	6
5	A	5	3

1
2
3

def norm_by_data2(x):
    x["data1"] /= x["data2"].sum()
    return x

1	df.groupby("key").apply(norm_by_data2)

	key	data1	data2
0	A	0.000000	3
1	B	0.111111	3
2	C	0.200000	4
3	C	0.300000	6
4	B	0.444444	6
5	A	0.833333	3

将列表、数组设为分组键

1 2	L = [0, 1, 0, 1, 2, 0] df

	key	data1	data2
0	A	0	3
1	B	1	3
2	C	2	4
3	C	3	6
4	B	4	6
5	A	5	3

1	df.groupby(L).sum()

	data1	data2
0	7	10
1	4	9
2	4	6

用字典将索引映射到分组

1 2	df2 = df.set_index("key") df2

	data1	data2
key
A	0	3
B	1	3
C	2	4
C	3	6
B	4	6
A	5	3

1 2	mapping = {"A": "first", "B": "constant", "C": "constant"} df2.groupby(mapping).sum()

	data1	data2
constant	10	19
first	5	6

任意Python函数

1	df2.groupby(str.lower).mean()

	data1	data2
a	2.5	3.0
b	2.5	4.5
c	2.5	5.0

多个有效值组成的列表

1	df2.groupby([str.lower, mapping]).mean()

		data1	data2
a	first	2.5	3.0
b	constant	2.5	4.5
c	constant	2.5	5.0

【例1】行星观测数据处理

1
2
3

import seaborn as sns

planets = sns.load_dataset("planets")

1	planets.shape

(1035, 6)

1	planets.head()

	method	number	orbital_period	mass	distance	year
0	Radial Velocity	1	269.300	7.10	77.40	2006
1	Radial Velocity	1	874.774	2.21	56.95	2008
2	Radial Velocity	1	763.000	2.60	19.84	2011
3	Radial Velocity	1	326.030	19.40	110.62	2007
4	Radial Velocity	1	516.220	10.50	119.47	2009

1	planets.describe()

	number	orbital_period	mass	distance	year
count	1035.000000	992.000000	513.000000	808.000000	1035.000000
mean	1.785507	2002.917596	2.638161	264.069282	2009.070531
std	1.240976	26014.728304	3.818617	733.116493	3.972567
min	1.000000	0.090706	0.003600	1.350000	1989.000000
25%	1.000000	5.442540	0.229000	32.560000	2007.000000
50%	1.000000	39.979500	1.260000	55.250000	2010.000000
75%	2.000000	526.005000	3.040000	178.500000	2012.000000
max	7.000000	730000.000000	25.000000	8500.000000	2014.000000

1	planets.head()

	method	number	orbital_period	mass	distance	year
0	Radial Velocity	1	269.300	7.10	77.40	2006
1	Radial Velocity	1	874.774	2.21	56.95	2008
2	Radial Velocity	1	763.000	2.60	19.84	2011
3	Radial Velocity	1	326.030	19.40	110.62	2007
4	Radial Velocity	1	516.220	10.50	119.47	2009

1 2	decade = 10 * (planets["year"] // 10) decade.head()

0    2000
1    2000
2    2010
3    2000
4    2000
Name: year, dtype: int64

1
2
3

decade = decade.astype(str) + "s"
decade.name = "decade"
decade.head()

0    2000s
1    2000s
2    2010s
3    2000s
4    2000s
Name: decade, dtype: object

1	planets.head()

	method	number	orbital_period	mass	distance	year
0	Radial Velocity	1	269.300	7.10	77.40	2006
1	Radial Velocity	1	874.774	2.21	56.95	2008
2	Radial Velocity	1	763.000	2.60	19.84	2011
3	Radial Velocity	1	326.030	19.40	110.62	2007
4	Radial Velocity	1	516.220	10.50	119.47	2009

1	planets.groupby(["method", decade]).sum()

		number	orbital_period	mass	distance	year
method	decade
Astrometry	2010s	2	1.262360e+03	0.00000	35.75	4023
Eclipse Timing Variations	2000s	5	1.930800e+04	6.05000	261.44	6025
Eclipse Timing Variations	2010s	10	2.345680e+04	4.20000	1000.00	12065
Imaging	2000s	29	1.350935e+06	0.00000	956.83	40139
Imaging	2010s	21	6.803750e+04	0.00000	1210.08	36208
Microlensing	2000s	12	1.732500e+04	0.00000	0.00	20070
Microlensing	2010s	15	4.750000e+03	0.00000	41440.00	26155
Orbital Brightness Modulation	2010s	5	2.127920e+00	0.00000	2360.00	6035
Pulsar Timing	1990s	9	1.900153e+02	0.00000	0.00	5978
	2000s	1	3.652500e+04	0.00000	0.00	2003
	2010s	1	9.070629e-02	0.00000	1200.00	2011
Pulsation Timing Variations	2000s	1	1.170000e+03	0.00000	0.00	2007
Radial Velocity	1980s	1	8.388800e+01	11.68000	40.57	1989
	1990s	52	1.091561e+04	68.17820	723.71	55943
	2000s	475	2.633526e+05	945.31928	15201.16	619775
	2010s	424	1.809630e+05	316.47890	11382.67	432451
Transit	2000s	64	2.897102e+02	0.00000	31823.31	124462
Transit	2010s	712	8.087813e+03	1.47000	102419.46	673999
Transit Timing Variations	2010s	9	2.393505e+02	0.00000	3313.00	8050

1	planets.groupby(["method", decade])[["number"]].sum().unstack().fillna(0)

	number
decade	1980s	1990s	2000s	2010s
method
Astrometry	0.0	0.0	0.0	2.0
Eclipse Timing Variations	0.0	0.0	5.0	10.0
Imaging	0.0	0.0	29.0	21.0
Microlensing	0.0	0.0	12.0	15.0
Orbital Brightness Modulation	0.0	0.0	0.0	5.0
Pulsar Timing	0.0	9.0	1.0	1.0
Pulsation Timing Variations	0.0	0.0	1.0	0.0
Radial Velocity	1.0	52.0	475.0	424.0
Transit	0.0	0.0	64.0	712.0
Transit Timing Variations	0.0	0.0	0.0	9.0

（2）数据透视表

【例2】泰坦尼克号乘客数据分析

1
2
3

import seaborn as sns

titanic = sns.load_dataset("titanic")

1	titanic.head()

	survived	pclass	sex	age	sibsp	fare	embarked	class	who	adult_male	deck	embark_town	alive	alone
0	0	3	male	22.0	1	7.2500	S	Third	man	True	NaN	Southampton	no	False
1	1	1	female	38.0	1	71.2833	C	First	woman	False	C	Cherbourg	yes	False
2	1	3	female	26.0	0	7.9250	S	Third	woman	False	NaN	Southampton	yes	True
3	1	1	female	35.0	1	53.1000	S	First	woman	False	C	Southampton	yes	False
4	0	3	male	35.0	0	8.0500	S	Third	man	True	NaN	Southampton	no	True

1	T = titanic[titanic.age.notnull()].copy()

1 2	T.age.apply(lambda x: 60 if x>=60 else x) T.age.value_counts()

0      22.0
1      38.0
2      26.0
3      35.0
4      35.0
       ... 
885    39.0
886    27.0
887    19.0
889    26.0
890    32.0
Name: age, Length: 714, dtype: float64






24.00    30
22.00    27
18.00    26
19.00    25
30.00    25
         ..
55.50     1
70.50     1
66.00     1
23.50     1
0.42      1
Name: age, Length: 88, dtype: int64

Age = 10*(T["age"]//10)
Age = Age.astype(int)
Age.head()
Age.value_counts()

0    20
1    30
2    20
3    30
4    30
Name: age, dtype: int32






20    220
30    167
10    102
40     89
0      62
50     48
60     19
70      6
80      1
Name: age, dtype: int64

1	Age.astype(str)+"s"

0      20s
1      30s
2      20s
3      30s
4      30s
      ... 
885    30s
886    20s
887    10s
889    20s
890    30s
Name: age, Length: 714, dtype: object

1	T.groupby(["sex", Age])["survived"].mean().unstack()

age	0	10	20	30	40	50	60	70	80
sex
female	0.633333	0.755556	0.722222	0.833333	0.687500	0.888889	1.000000	NaN	NaN
male	0.593750	0.122807	0.168919	0.214953	0.210526	0.133333	0.133333	0.0	1.0

1 2	T.age = Age T.pivot_table("survived", index="sex", columns="age")

age	0	10	20	30	40	50	60	70	80
sex
female	0.633333	0.755556	0.722222	0.833333	0.687500	0.888889	1.000000	NaN	NaN
male	0.593750	0.122807	0.168919	0.214953	0.210526	0.133333	0.133333	0.0	1.0

1	titanic.describe()

	survived	pclass	age	sibsp	parch	fare
count	891.000000	891.000000	714.000000	891.000000	891.000000	891.000000
mean	0.383838	2.308642	29.699118	0.523008	0.381594	32.204208
std	0.486592	0.836071	14.526497	1.102743	0.806057	49.693429
min	0.000000	1.000000	0.420000	0.000000	0.000000	0.000000
25%	0.000000	2.000000	20.125000	0.000000	0.000000	7.910400
50%	0.000000	3.000000	28.000000	0.000000	0.000000	14.454200
75%	1.000000	3.000000	38.000000	1.000000	0.000000	31.000000
max	1.000000	3.000000	80.000000	8.000000	6.000000	512.329200

1	titanic.groupby("sex")[["survived"]].mean()

	survived
sex
female	0.742038
male	0.188908

1	titanic.groupby("sex")["survived"].mean()

sex
female    0.742038
male      0.188908
Name: survived, dtype: float64

1	titanic.groupby(["sex", "class"])["survived"].aggregate("mean").unstack()

class	First	Second	Third
sex
female	0.968085	0.921053	0.500000
male	0.368852	0.157407	0.135447

数据透视表

1	titanic.pivot_table("survived", index="sex", columns="class")

class	First	Second	Third
sex
female	0.968085	0.921053	0.500000
male	0.368852	0.157407	0.135447

1	titanic.pivot_table("survived", index="sex", columns="class", aggfunc="mean", margins=True)

class	First	Second	Third	All
sex
female	0.968085	0.921053	0.500000	0.742038
male	0.368852	0.157407	0.135447	0.188908
All	0.629630	0.472826	0.242363	0.383838

1	titanic.pivot_table(index="sex", columns="class", aggfunc={"survived": "sum", "fare": "mean"})

	fare			survived
class	First	Second	Third	First	Second	Third
sex
female	106.125798	21.970121	16.118810	91	70	72
male	67.226127	19.741782	12.661633	45	17	47

12.7 其他

（1）向量化字符串操作

（2）处理时间序列

（3）多级索引：用于多维数据

base_data = np.array([[1771, 11115 ],
                      [2154, 30320],
                      [2141, 14070],
                      [2424, 32680],
                      [1077, 7806],
                      [1303, 24222],
                      [798, 4789],
                      [981, 13468]]) 
data = pd.DataFrame(base_data, index=[["BeiJing","BeiJing","ShangHai","ShangHai","ShenZhen","ShenZhen","HangZhou","HangZhou"]\
                                     , [2008, 2018]*4], columns=["population", "GDP"])
data

		population	GDP
BeiJing	2008	1771	11115
BeiJing	2018	2154	30320
ShangHai	2008	2141	14070
ShangHai	2018	2424	32680
ShenZhen	2008	1077	7806
ShenZhen	2018	1303	24222
HangZhou	2008	798	4789
HangZhou	2018	981	13468

1 2	data.index.names = ["city", "year"] data

		population	GDP
city	year
BeiJing	2008	1771	11115
BeiJing	2018	2154	30320
ShangHai	2008	2141	14070
ShangHai	2018	2424	32680
ShenZhen	2008	1077	7806
ShenZhen	2018	1303	24222
HangZhou	2008	798	4789
HangZhou	2018	981	13468

1	data["GDP"]

city      year
BeiJing   2008    11115
          2018    30320
ShangHai  2008    14070
          2018    32680
ShenZhen  2008     7806
          2018    24222
HangZhou  2008     4789
          2018    13468
Name: GDP, dtype: int32

1	data.loc["ShangHai", "GDP"]

year
2008    14070
2018    32680
Name: GDP, dtype: int32

1	data.loc["ShangHai", 2018]["GDP"]

（4）高性能的Pandas：eval（）

1	df1, df2, df3, df4 = (pd.DataFrame(np.random.random((10000,100))) for i in range(4))

1	%timeit (df1+df2)/(df3+df4)

19.1 ms ± 784 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

减少了复合代数式计算中间过程的内存分配

1	%timeit pd.eval("(df1+df2)/(df3+df4)")

14 ms ± 1.05 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)

1	np.allclose((df1+df2)/(df3+df4), pd.eval("(df1+df2)/(df3+df4)"))

True

实现列间运算

1 2	df = pd.DataFrame(np.random.random((1000, 3)), columns=list("ABC")) df.head()

	A	B	C
0	0.444109	0.403663	0.865813
1	0.294881	0.458937	0.235739
2	0.312199	0.256650	0.393556
3	0.080160	0.176736	0.385579
4	0.830258	0.352358	0.186917

1	res_1 = pd.eval("(df.A+df.B)/(df.C-1)")

1	res_2 = df.eval("(A+B)/(C-1)")

1	np.allclose(res_1, res_2)

True

1 2	df["D"] = pd.eval("(df.A+df.B)/(df.C-1)") df.head()

	A	B	C	D
0	0.444109	0.403663	0.865813	-6.317854
1	0.294881	0.458937	0.235739	-0.986336
2	0.312199	0.256650	0.393556	-0.938006
3	0.080160	0.176736	0.385579	-0.418112
4	0.830258	0.352358	0.186917	-1.454484

1 2	df.eval("D=(A+B)/(C-1)", inplace=True) df.head()

	A	B	C	D
0	0.444109	0.403663	0.865813	-6.317854
1	0.294881	0.458937	0.235739	-0.986336
2	0.312199	0.256650	0.393556	-0.938006
3	0.080160	0.176736	0.385579	-0.418112
4	0.830258	0.352358	0.186917	-1.454484

使用局部变量

1
2
3

column_mean = df.mean(axis=1)
res = df.eval("A+@column_mean")
res.head()

0   -0.706958
1    0.295687
2    0.318299
3    0.136251
4    0.809020
dtype: float64

（4）高性能的Pandas：query（）

df.head()

	A	B	C	D
0	0.444109	0.403663	0.865813	-6.317854
1	0.294881	0.458937	0.235739	-0.986336
2	0.312199	0.256650	0.393556	-0.938006
3	0.080160	0.176736	0.385579	-0.418112
4	0.830258	0.352358	0.186917	-1.454484

1	%timeit df[(df.A < 0.5) & (df.B > 0.5)]

1.97 ms ± 307 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

1	%timeit df.query("(A < 0.5)&(B > 0.5)")

3.35 ms ± 440 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

1	df.query("(A < 0.5)&(B > 0.5)").head()

	A	B	C	D
5	0.125739	0.557392	0.556752	-1.541193
6	0.264407	0.738427	0.669857	-3.037572
11	0.427045	0.719621	0.732786	-4.291193
12	0.050538	0.864942	0.883998	-7.891950
19	0.310231	0.558427	0.627987	-2.335022

1	np.allclose(df[(df.A < 0.5) & (df.B > 0.5)], df.query("(A < 0.5)&(B > 0.5)"))

True

（5）eval（）和query（）的使用时机

小数组时，普通方法反而更快

1	df.values.nbytes

1	df1.values.nbytes

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	6	3	7	4	6	9	2	6	7	4	...	4	0	9	5	8	0	9	2	6	3
1	8	2	4	2	6	4	8	6	1	3	...	2	0	3	1	7	3	1	5	5	9
2	3	5	1	9	1	9	3	7	6	8	...	6	8	7	0	7	7	2	0	7	2
3	2	0	4	9	6	9	8	6	8	7	...	0	2	4	2	0	4	9	6	6	8
4	9	9	2	6	0	3	3	4	6	6	...	9	6	8	6	0	0	8	8	3	8
5	2	6	5	7	8	4	0	2	9	7	...	2	0	4	0	7	0	0	1	1	5
6	6	4	0	0	2	1	4	9	5	6	...	5	0	8	5	2	3	3	2	9	2
7	2	3	6	3	8	0	7	6	1	7	...	3	0	1	0	4	4	6	8	8	2
8	2	2	3	7	5	7	0	7	3	0	...	1	1	5	2	8	3	0	3	0	4
9	3	7	7	6	2	0	0	2	5	6	...	4	2	3	2	0	0	4	5	2	8
10	4	7	0	4	2	0	3	4	6	0	...	5	6	1	9	1	9	0	7	0	8
11	5	6	9	6	9	2	1	8	7	9	...	6	5	2	8	9	5	9	9	5	0
12	3	9	5	5	4	0	7	4	4	6	...	0	7	2	9	6	9	4	9	4	6
13	8	4	0	9	9	0	1	5	8	7	...	5	8	4	0	3	4	9	9	4	6
14	3	0	4	6	9	9	5	4	3	1	...	6	1	0	3	7	1	2	0	0	2
15	4	2	0	0	7	9	1	2	1	2	...	6	3	9	4	1	7	3	8	4	8
16	3	9	4	8	7	2	0	2	3	1	...	8	0	0	3	8	5	2	0	3	8
17	2	8	6	3	2	9	4	4	2	8	...	6	9	4	2	6	1	8	9	9	0
18	5	6	7	9	8	1	9	1	4	4	...	3	5	2	5	6	9	9	2	6	2
19	1	9	3	7	8	6	0	2	8	0	...	4	3	2	2	3	8	1	8	0	0
20	4	5	5	2	6	8	9	7	5	7	...	3	5	0	8	0	4	3	2	5	1
21	2	4	8	1	9	7	1	4	6	7	...	0	1	8	2	0	4	6	5	0	4
22	4	5	2	4	6	4	4	4	9	9	...	1	7	6	9	9	1	5	5	2	1
23	0	5	4	8	0	6	4	4	1	2	...	8	5	0	7	6	9	2	0	4	3
24	9	7	0	9	0	3	7	4	1	5	...	3	7	8	2	2	1	9	2	2	4
25	4	1	9	5	4	5	0	4	8	9	...	9	3	0	7	0	2	3	7	5	9
26	6	7	1	9	7	2	6	2	6	1	...	0	6	5	9	8	0	3	8	3	9
27	2	8	1	3	5	1	7	7	0	2	...	8	0	4	5	4	5	5	6	3	7
28	6	8	6	2	2	7	4	3	7	5	...	1	7	9	2	4	5	9	5	3	2
29	3	0	3	0	0	9	5	4	3	2	...	1	3	0	4	8	0	8	7	5	6

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	6	8	3	2	9	2	6	2	2	3	...	4	2	4	0	9	4	6	2	6	3
1	3	2	5	0	9	6	4	3	2	7	...	5	4	5	5	7	1	7	8	8	0
2	7	4	1	4	2	5	0	6	3	7	...	5	8	2	4	0	9	1	1	6	3
3	4	2	9	9	6	7	0	3	7	6	...	2	1	4	8	9	5	9	3	2	0
4	6	6	1	6	0	8	2	8	5	2	...	6	9	6	0	0	4	7	5	2	0
5	9	4	9	9	3	4	1	0	7	0	...	8	7	4	6	3	5	2	1	7	9
6	2	8	3	8	3	0	4	7	0	0	...	9	1	4	4	7	0	6	7	4	5
7	6	6	7	6	4	2	9	6	7	2	...	7	4	4	4	4	4	2	7	3	4
8	7	1	6	8	6	9	5	1	3	5	...	5	6	9	1	1	8	6	0	7	3
9	4	3	8	7	6	7	6	7	0	6	...	7	7	9	2	5	9	1	2	5	2
10	3	8	7	1	3	5	3	0	7	5	...	4	0	2	6	4	1	9	9	1	0
11	7	1	4	0	6	7	6	8	3	5	...	7	5	0	5	1	0	5	8	3	5
12	7	9	1	6	2	8	7	8	5	5	...	9	0	4	1	2	9	2	4	3	1
13	2	8	4	6	5	3	0	1	7	2	...	3	1	8	5	8	8	2	5	5	7
14	5	9	7	7	1	0	5	6	3	5	...	9	0	0	1	6	9	8	3	5	9
15	4	4	9	4	9	0	7	9	2	7	...	7	4	2	1	6	8	6	9	0	4
16	1	1	8	2	8	9	4	2	8	1	...	9	9	3	1	5	8	4	1	7	6
17	7	3	8	7	4	3	3	6	2	4	...	1	8	0	2	7	5	9	7	5	9
18	5	6	0	5	5	6	1	9	8	0	...	4	5	0	1	3	7	6	5	2	1
19	1	7	8	2	3	1	5	8	1	0	...	8	0	7	3	7	0	8	4	8	7
20	4	2	6	0	9	2	5	3	1	4	...	3	0	1	8	3	9	0	8	1	1
21	0	0	8	2	6	0	0	0	1	2	...	5	1	7	5	7	3	6	0	7	3
22	9	3	7	4	8	4	8	1	5	3	...	0	8	6	0	8	0	5	4	9	0
23	5	1	0	2	6	0	5	0	2	2	...	8	2	9	7	2	7	9	5	2	4
24	8	7	7	0	0	7	2	4	8	0	...	0	0	9	6	2	0	8	4	4	8
25	0	3	7	4	0	0	3	4	3	0	...	4	4	1	9	1	2	0	5	5	0
26	9	1	2	9	8	0	3	6	0	4	...	3	6	5	2	9	3	3	5	9	8
27	2	5	0	6	8	1	2	8	3	5	...	2	5	5	0	2	7	8	6	5	7
28	6	5	7	6	3	1	9	8	0	2	...	5	0	2	4	2	5	3	3	3	5
29	3	9	2	8	8	5	2	2	4	8	...	1	4	1	3	4	9	9	7	2	6

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	5	8	9	5	0	0	1	7	6	9	...	1	7	0	6	9	9	7	6	9	1
1	0	1	8	8	3	9	8	7	3	6	...	9	2	0	4	9	2	7	7	9	8
2	6	9	3	7	7	4	5	9	3	6	...	7	7	1	1	3	0	8	6	4	5
3	6	2	5	7	8	4	4	7	7	4	...	0	1	9	8	2	3	1	2	7	2
4	6	0	9	2	6	6	2	7	7	0	...	1	5	4	0	7	8	9	5	7	0
5	9	3	9	1	4	4	6	8	8	9	...	1	8	7	0	3	4	2	0	3	5
6	1	2	4	3	0	6	0	7	2	8	...	4	3	3	6	7	3	5	3	2	4
7	4	0	3	3	8	3	5	6	7	5	...	1	7	3	1	6	6	9	6	9	6
8	0	0	2	9	6	0	6	7	0	3	...	6	7	9	5	4	9	5	2	5	6
9	6	8	7	7	7	2	6	0	5	2	...	7	0	6	2	4	3	6	7	6	3
10	0	6	4	7	6	2	9	5	9	9	...	4	9	3	9	1	2	5	4	0	8
11	2	3	9	9	4	4	8	2	1	6	...	0	5	9	8	6	6	0	4	7	3
12	0	1	6	0	6	1	6	4	2	5	...	8	8	0	7	2	0	7	1	1	9
13	5	1	5	9	6	4	9	8	7	5	...	2	4	3	2	0	0	4	2	5	0
14	0	3	8	5	3	1	4	7	3	2	...	8	5	5	7	5	9	1	3	9	3
15	3	3	6	1	3	0	5	0	5	2	...	7	1	7	7	3	8	3	0	6	3
16	0	6	5	9	6	4	6	6	2	2	...	3	6	8	6	5	1	3	2	6	3
17	6	7	2	8	0	1	8	6	0	0	...	5	6	2	5	4	3	0	6	2	1
18	9	4	4	0	9	8	7	7	6	1	...	7	9	9	7	1	1	4	6	5	6
19	4	1	1	5	1	2	6	2	3	3	...	0	0	0	9	8	5	9	3	4	0
20	9	8	6	3	9	9	0	8	1	6	...	2	9	0	1	3	9	4	8	8	8
21	2	8	6	4	9	0	5	5	6	1	...	6	7	5	6	8	7	4	2	4	0
22	0	3	5	9	0	3	6	5	1	1	...	6	2	5	3	9	3	9	5	1	9
23	7	7	0	8	6	1	2	0	4	4	...	1	9	6	0	2	8	3	7	2	5
24	6	0	4	2	3	1	0	5	7	0	...	1	1	2	7	5	2	9	4	7	3
25	5	0	2	1	4	9	4	6	9	3	...	5	5	3	5	9	2	7	4	1	6
26	9	8	1	8	1	6	2	6	1	8	...	2	5	1	2	5	3	3	6	1	8
27	1	8	6	4	6	9	5	4	7	2	...	9	3	1	5	1	1	7	1	2	6
28	0	7	7	4	3	2	7	8	5	2	...	0	2	8	3	7	3	9	2	3	8
29	8	0	2	6	8	3	6	4	9	7	...	6	7	8	5	7	2	5	3	4	5

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	616	560	723	739	612	457	681	799	575	590	...	523	739	613	580	668	602	733	585	657	700
1	520	438	691	600	612	455	666	764	707	592	...	555	681	503	679	641	506	779	494	633	590
2	557	570	786	807	690	469	804	828	704	573	...	563	675	712	758	793	672	754	550	756	638
3	605	507	664	701	660	496	698	806	651	575	...	582	685	668	586	629	534	678	484	591	626
4	599	681	753	873	721	563	754	770	620	654	...	633	747	661	677	726	649	716	610	735	706
5	422	354	602	627	613	396	617	627	489	423	...	456	572	559	537	499	384	589	436	574	507
6	359	446	599	599	481	357	577	572	451	464	...	449	550	495	532	633	554	663	476	565	602
7	531	520	698	590	607	537	665	696	571	472	...	576	588	551	665	652	527	742	528	650	599
8	449	322	547	533	593	399	584	638	587	424	...	402	596	523	523	447	362	561	386	529	484
9	373	433	525	601	522	345	551	521	434	447	...	508	498	438	478	459	418	488	407	503	496
10	500	427	574	607	667	477	652	656	615	477	...	622	702	531	610	558	532	598	471	582	561
11	664	694	772	841	779	574	730	810	711	608	...	591	760	616	638	721	676	846	678	754	708
12	545	547	687	701	721	576	689	724	710	532	...	674	684	648	694	710	564	757	571	671	656
13	574	586	723	750	691	494	696	787	667	523	...	618	681	568	682	715	644	756	557	690	604
14	502	382	645	557	570	403	538	677	500	501	...	369	650	507	576	546	531	554	437	616	463
15	510	505	736	651	649	510	719	733	694	557	...	605	717	574	642	678	576	755	455	598	654
16	567	376	614	612	643	514	598	724	547	464	...	456	639	520	560	569	442	596	517	659	532
17	626	716	828	765	740	603	809	852	692	591	...	664	716	655	721	742	612	819	593	744	712
18	600	559	667	664	641	556	624	815	638	564	...	581	701	559	677	710	554	748	597	614	657
19	445	431	661	681	641	552	690	719	602	474	...	515	637	576	620	572	512	599	455	622	538
20	523	569	784	725	713	501	740	772	638	640	...	589	775	664	686	726	672	747	548	723	645
21	487	465	553	639	517	449	592	609	454	398	...	492	567	534	404	554	417	561	466	498	492
22	479	449	574	686	583	377	566	614	563	455	...	453	539	491	501	596	520	722	478	565	501
23	483	386	476	526	550	426	492	585	536	482	...	322	541	438	456	487	408	502	426	474	481
24	523	551	658	767	537	444	663	731	576	577	...	522	590	525	664	691	548	635	526	641	538
25	652	656	738	753	853	508	752	815	669	576	...	694	833	693	606	575	616	704	559	728	672
26	578	577	744	856	699	497	779	800	733	587	...	630	754	704	834	760	680	765	592	731	629
27	554	494	665	689	630	574	695	703	636	599	...	554	685	532	658	649	554	693	577	634	668
28	498	552	659	784	552	492	690	775	544	551	...	567	636	518	599	742	521	733	533	605	604
29	513	491	563	642	477	367	589	647	516	484	...	428	574	504	548	553	483	540	407	547	455

	A	B	C	D
A	1.000000	0.831063	0.331060	0.510821
B	0.831063	1.000000	0.179244	0.719112
C	0.331060	0.179244	1.000000	-0.450365
D	0.510821	0.719112	-0.450365	1.000000

	A	B	C	D
0	1.082198	4.639594	1.579117	7.947086
1	13.113252	19.887811	22.762364	28.289408
2	-2.036341	-6.369518	-1.274717	-1.427283
3	-3.386712	-4.909077	-7.431287	-4.893571
4	4.328491	9.879485	15.456814	20.476806
5	1.171336	0.677427	-3.355186	3.043402

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	6	3	7	4	6	9	2	6	7	4	...	4	0	9	5	8	0	9	2	6	3
1	8	2	4	2	6	4	8	6	1	3	...	2	0	3	1	7	3	1	5	5	9
2	3	5	1	9	1	9	3	7	6	8	...	6	8	7	0	7	7	2	0	7	2
3	2	0	4	9	6	9	8	6	8	7	...	0	2	4	2	0	4	9	6	6	8
4	9	9	2	6	0	3	3	4	6	6	...	9	6	8	6	0	0	8	8	3	8
5	2	6	5	7	8	4	0	2	9	7	...	2	0	4	0	7	0	0	1	1	5
6	6	4	0	0	2	1	4	9	5	6	...	5	0	8	5	2	3	3	2	9	2
7	2	3	6	3	8	0	7	6	1	7	...	3	0	1	0	4	4	6	8	8	2
8	2	2	3	7	5	7	0	7	3	0	...	1	1	5	2	8	3	0	3	0	4
9	3	7	7	6	2	0	0	2	5	6	...	4	2	3	2	0	0	4	5	2	8
10	4	7	0	4	2	0	3	4	6	0	...	5	6	1	9	1	9	0	7	0	8
11	5	6	9	6	9	2	1	8	7	9	...	6	5	2	8	9	5	9	9	5	0
12	3	9	5	5	4	0	7	4	4	6	...	0	7	2	9	6	9	4	9	4	6
13	8	4	0	9	9	0	1	5	8	7	...	5	8	4	0	3	4	9	9	4	6
14	3	0	4	6	9	9	5	4	3	1	...	6	1	0	3	7	1	2	0	0	2
15	4	2	0	0	7	9	1	2	1	2	...	6	3	9	4	1	7	3	8	4	8
16	3	9	4	8	7	2	0	2	3	1	...	8	0	0	3	8	5	2	0	3	8
17	2	8	6	3	2	9	4	4	2	8	...	6	9	4	2	6	1	8	9	9	0
18	5	6	7	9	8	1	9	1	4	4	...	3	5	2	5	6	9	9	2	6	2
19	1	9	3	7	8	6	0	2	8	0	...	4	3	2	2	3	8	1	8	0	0
20	4	5	5	2	6	8	9	7	5	7	...	3	5	0	8	0	4	3	2	5	1
21	2	4	8	1	9	7	1	4	6	7	...	0	1	8	2	0	4	6	5	0	4
22	4	5	2	4	6	4	4	4	9	9	...	1	7	6	9	9	1	5	5	2	1
23	0	5	4	8	0	6	4	4	1	2	...	8	5	0	7	6	9	2	0	4	3
24	9	7	0	9	0	3	7	4	1	5	...	3	7	8	2	2	1	9	2	2	4
25	4	1	9	5	4	5	0	4	8	9	...	9	3	0	7	0	2	3	7	5	9
26	6	7	1	9	7	2	6	2	6	1	...	0	6	5	9	8	0	3	8	3	9
27	2	8	1	3	5	1	7	7	0	2	...	8	0	4	5	4	5	5	6	3	7
28	6	8	6	2	2	7	4	3	7	5	...	1	7	9	2	4	5	9	5	3	2
29	3	0	3	0	0	9	5	4	3	2	...	1	3	0	4	8	0	8	7	5	6

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	6	8	3	2	9	2	6	2	2	3	...	4	2	4	0	9	4	6	2	6	3
1	3	2	5	0	9	6	4	3	2	7	...	5	4	5	5	7	1	7	8	8	0
2	7	4	1	4	2	5	0	6	3	7	...	5	8	2	4	0	9	1	1	6	3
3	4	2	9	9	6	7	0	3	7	6	...	2	1	4	8	9	5	9	3	2	0
4	6	6	1	6	0	8	2	8	5	2	...	6	9	6	0	0	4	7	5	2	0
5	9	4	9	9	3	4	1	0	7	0	...	8	7	4	6	3	5	2	1	7	9
6	2	8	3	8	3	0	4	7	0	0	...	9	1	4	4	7	0	6	7	4	5
7	6	6	7	6	4	2	9	6	7	2	...	7	4	4	4	4	4	2	7	3	4
8	7	1	6	8	6	9	5	1	3	5	...	5	6	9	1	1	8	6	0	7	3
9	4	3	8	7	6	7	6	7	0	6	...	7	7	9	2	5	9	1	2	5	2
10	3	8	7	1	3	5	3	0	7	5	...	4	0	2	6	4	1	9	9	1	0
11	7	1	4	0	6	7	6	8	3	5	...	7	5	0	5	1	0	5	8	3	5
12	7	9	1	6	2	8	7	8	5	5	...	9	0	4	1	2	9	2	4	3	1
13	2	8	4	6	5	3	0	1	7	2	...	3	1	8	5	8	8	2	5	5	7
14	5	9	7	7	1	0	5	6	3	5	...	9	0	0	1	6	9	8	3	5	9
15	4	4	9	4	9	0	7	9	2	7	...	7	4	2	1	6	8	6	9	0	4
16	1	1	8	2	8	9	4	2	8	1	...	9	9	3	1	5	8	4	1	7	6
17	7	3	8	7	4	3	3	6	2	4	...	1	8	0	2	7	5	9	7	5	9
18	5	6	0	5	5	6	1	9	8	0	...	4	5	0	1	3	7	6	5	2	1
19	1	7	8	2	3	1	5	8	1	0	...	8	0	7	3	7	0	8	4	8	7
20	4	2	6	0	9	2	5	3	1	4	...	3	0	1	8	3	9	0	8	1	1
21	0	0	8	2	6	0	0	0	1	2	...	5	1	7	5	7	3	6	0	7	3
22	9	3	7	4	8	4	8	1	5	3	...	0	8	6	0	8	0	5	4	9	0
23	5	1	0	2	6	0	5	0	2	2	...	8	2	9	7	2	7	9	5	2	4
24	8	7	7	0	0	7	2	4	8	0	...	0	0	9	6	2	0	8	4	4	8
25	0	3	7	4	0	0	3	4	3	0	...	4	4	1	9	1	2	0	5	5	0
26	9	1	2	9	8	0	3	6	0	4	...	3	6	5	2	9	3	3	5	9	8
27	2	5	0	6	8	1	2	8	3	5	...	2	5	5	0	2	7	8	6	5	7
28	6	5	7	6	3	1	9	8	0	2	...	5	0	2	4	2	5	3	3	3	5
29	3	9	2	8	8	5	2	2	4	8	...	1	4	1	3	4	9	9	7	2	6

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	5	8	9	5	0	0	1	7	6	9	...	1	7	0	6	9	9	7	6	9	1
1	0	1	8	8	3	9	8	7	3	6	...	9	2	0	4	9	2	7	7	9	8
2	6	9	3	7	7	4	5	9	3	6	...	7	7	1	1	3	0	8	6	4	5
3	6	2	5	7	8	4	4	7	7	4	...	0	1	9	8	2	3	1	2	7	2
4	6	0	9	2	6	6	2	7	7	0	...	1	5	4	0	7	8	9	5	7	0
5	9	3	9	1	4	4	6	8	8	9	...	1	8	7	0	3	4	2	0	3	5
6	1	2	4	3	0	6	0	7	2	8	...	4	3	3	6	7	3	5	3	2	4
7	4	0	3	3	8	3	5	6	7	5	...	1	7	3	1	6	6	9	6	9	6
8	0	0	2	9	6	0	6	7	0	3	...	6	7	9	5	4	9	5	2	5	6
9	6	8	7	7	7	2	6	0	5	2	...	7	0	6	2	4	3	6	7	6	3
10	0	6	4	7	6	2	9	5	9	9	...	4	9	3	9	1	2	5	4	0	8
11	2	3	9	9	4	4	8	2	1	6	...	0	5	9	8	6	6	0	4	7	3
12	0	1	6	0	6	1	6	4	2	5	...	8	8	0	7	2	0	7	1	1	9
13	5	1	5	9	6	4	9	8	7	5	...	2	4	3	2	0	0	4	2	5	0
14	0	3	8	5	3	1	4	7	3	2	...	8	5	5	7	5	9	1	3	9	3
15	3	3	6	1	3	0	5	0	5	2	...	7	1	7	7	3	8	3	0	6	3
16	0	6	5	9	6	4	6	6	2	2	...	3	6	8	6	5	1	3	2	6	3
17	6	7	2	8	0	1	8	6	0	0	...	5	6	2	5	4	3	0	6	2	1
18	9	4	4	0	9	8	7	7	6	1	...	7	9	9	7	1	1	4	6	5	6
19	4	1	1	5	1	2	6	2	3	3	...	0	0	0	9	8	5	9	3	4	0
20	9	8	6	3	9	9	0	8	1	6	...	2	9	0	1	3	9	4	8	8	8
21	2	8	6	4	9	0	5	5	6	1	...	6	7	5	6	8	7	4	2	4	0
22	0	3	5	9	0	3	6	5	1	1	...	6	2	5	3	9	3	9	5	1	9
23	7	7	0	8	6	1	2	0	4	4	...	1	9	6	0	2	8	3	7	2	5
24	6	0	4	2	3	1	0	5	7	0	...	1	1	2	7	5	2	9	4	7	3
25	5	0	2	1	4	9	4	6	9	3	...	5	5	3	5	9	2	7	4	1	6
26	9	8	1	8	1	6	2	6	1	8	...	2	5	1	2	5	3	3	6	1	8
27	1	8	6	4	6	9	5	4	7	2	...	9	3	1	5	1	1	7	1	2	6
28	0	7	7	4	3	2	7	8	5	2	...	0	2	8	3	7	3	9	2	3	8
29	8	0	2	6	8	3	6	4	9	7	...	6	7	8	5	7	2	5	3	4	5

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	616	560	723	739	612	457	681	799	575	590	...	523	739	613	580	668	602	733	585	657	700
1	520	438	691	600	612	455	666	764	707	592	...	555	681	503	679	641	506	779	494	633	590
2	557	570	786	807	690	469	804	828	704	573	...	563	675	712	758	793	672	754	550	756	638
3	605	507	664	701	660	496	698	806	651	575	...	582	685	668	586	629	534	678	484	591	626
4	599	681	753	873	721	563	754	770	620	654	...	633	747	661	677	726	649	716	610	735	706
5	422	354	602	627	613	396	617	627	489	423	...	456	572	559	537	499	384	589	436	574	507
6	359	446	599	599	481	357	577	572	451	464	...	449	550	495	532	633	554	663	476	565	602
7	531	520	698	590	607	537	665	696	571	472	...	576	588	551	665	652	527	742	528	650	599
8	449	322	547	533	593	399	584	638	587	424	...	402	596	523	523	447	362	561	386	529	484
9	373	433	525	601	522	345	551	521	434	447	...	508	498	438	478	459	418	488	407	503	496
10	500	427	574	607	667	477	652	656	615	477	...	622	702	531	610	558	532	598	471	582	561
11	664	694	772	841	779	574	730	810	711	608	...	591	760	616	638	721	676	846	678	754	708
12	545	547	687	701	721	576	689	724	710	532	...	674	684	648	694	710	564	757	571	671	656
13	574	586	723	750	691	494	696	787	667	523	...	618	681	568	682	715	644	756	557	690	604
14	502	382	645	557	570	403	538	677	500	501	...	369	650	507	576	546	531	554	437	616	463
15	510	505	736	651	649	510	719	733	694	557	...	605	717	574	642	678	576	755	455	598	654
16	567	376	614	612	643	514	598	724	547	464	...	456	639	520	560	569	442	596	517	659	532
17	626	716	828	765	740	603	809	852	692	591	...	664	716	655	721	742	612	819	593	744	712
18	600	559	667	664	641	556	624	815	638	564	...	581	701	559	677	710	554	748	597	614	657
19	445	431	661	681	641	552	690	719	602	474	...	515	637	576	620	572	512	599	455	622	538
20	523	569	784	725	713	501	740	772	638	640	...	589	775	664	686	726	672	747	548	723	645
21	487	465	553	639	517	449	592	609	454	398	...	492	567	534	404	554	417	561	466	498	492
22	479	449	574	686	583	377	566	614	563	455	...	453	539	491	501	596	520	722	478	565	501
23	483	386	476	526	550	426	492	585	536	482	...	322	541	438	456	487	408	502	426	474	481
24	523	551	658	767	537	444	663	731	576	577	...	522	590	525	664	691	548	635	526	641	538
25	652	656	738	753	853	508	752	815	669	576	...	694	833	693	606	575	616	704	559	728	672
26	578	577	744	856	699	497	779	800	733	587	...	630	754	704	834	760	680	765	592	731	629
27	554	494	665	689	630	574	695	703	636	599	...	554	685	532	658	649	554	693	577	634	668
28	498	552	659	784	552	492	690	775	544	551	...	567	636	518	599	742	521	733	533	605	604
29	513	491	563	642	477	367	589	647	516	484	...	428	574	504	548	553	483	540	407	547	455

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	6	3	7	4	6	9	2	6	7	4	...	4	0	9	5	8	0	9	2	6	3
1	8	2	4	2	6	4	8	6	1	3	...	2	0	3	1	7	3	1	5	5	9
2	3	5	1	9	1	9	3	7	6	8	...	6	8	7	0	7	7	2	0	7	2
3	2	0	4	9	6	9	8	6	8	7	...	0	2	4	2	0	4	9	6	6	8
4	9	9	2	6	0	3	3	4	6	6	...	9	6	8	6	0	0	8	8	3	8
5	2	6	5	7	8	4	0	2	9	7	...	2	0	4	0	7	0	0	1	1	5
6	6	4	0	0	2	1	4	9	5	6	...	5	0	8	5	2	3	3	2	9	2
7	2	3	6	3	8	0	7	6	1	7	...	3	0	1	0	4	4	6	8	8	2
8	2	2	3	7	5	7	0	7	3	0	...	1	1	5	2	8	3	0	3	0	4
9	3	7	7	6	2	0	0	2	5	6	...	4	2	3	2	0	0	4	5	2	8
10	4	7	0	4	2	0	3	4	6	0	...	5	6	1	9	1	9	0	7	0	8
11	5	6	9	6	9	2	1	8	7	9	...	6	5	2	8	9	5	9	9	5	0
12	3	9	5	5	4	0	7	4	4	6	...	0	7	2	9	6	9	4	9	4	6
13	8	4	0	9	9	0	1	5	8	7	...	5	8	4	0	3	4	9	9	4	6
14	3	0	4	6	9	9	5	4	3	1	...	6	1	0	3	7	1	2	0	0	2
15	4	2	0	0	7	9	1	2	1	2	...	6	3	9	4	1	7	3	8	4	8
16	3	9	4	8	7	2	0	2	3	1	...	8	0	0	3	8	5	2	0	3	8
17	2	8	6	3	2	9	4	4	2	8	...	6	9	4	2	6	1	8	9	9	0
18	5	6	7	9	8	1	9	1	4	4	...	3	5	2	5	6	9	9	2	6	2
19	1	9	3	7	8	6	0	2	8	0	...	4	3	2	2	3	8	1	8	0	0
20	4	5	5	2	6	8	9	7	5	7	...	3	5	0	8	0	4	3	2	5	1
21	2	4	8	1	9	7	1	4	6	7	...	0	1	8	2	0	4	6	5	0	4
22	4	5	2	4	6	4	4	4	9	9	...	1	7	6	9	9	1	5	5	2	1
23	0	5	4	8	0	6	4	4	1	2	...	8	5	0	7	6	9	2	0	4	3
24	9	7	0	9	0	3	7	4	1	5	...	3	7	8	2	2	1	9	2	2	4
25	4	1	9	5	4	5	0	4	8	9	...	9	3	0	7	0	2	3	7	5	9
26	6	7	1	9	7	2	6	2	6	1	...	0	6	5	9	8	0	3	8	3	9
27	2	8	1	3	5	1	7	7	0	2	...	8	0	4	5	4	5	5	6	3	7
28	6	8	6	2	2	7	4	3	7	5	...	1	7	9	2	4	5	9	5	3	2
29	3	0	3	0	0	9	5	4	3	2	...	1	3	0	4	8	0	8	7	5	6

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	6	8	3	2	9	2	6	2	2	3	...	4	2	4	0	9	4	6	2	6	3
1	3	2	5	0	9	6	4	3	2	7	...	5	4	5	5	7	1	7	8	8	0
2	7	4	1	4	2	5	0	6	3	7	...	5	8	2	4	0	9	1	1	6	3
3	4	2	9	9	6	7	0	3	7	6	...	2	1	4	8	9	5	9	3	2	0
4	6	6	1	6	0	8	2	8	5	2	...	6	9	6	0	0	4	7	5	2	0
5	9	4	9	9	3	4	1	0	7	0	...	8	7	4	6	3	5	2	1	7	9
6	2	8	3	8	3	0	4	7	0	0	...	9	1	4	4	7	0	6	7	4	5
7	6	6	7	6	4	2	9	6	7	2	...	7	4	4	4	4	4	2	7	3	4
8	7	1	6	8	6	9	5	1	3	5	...	5	6	9	1	1	8	6	0	7	3
9	4	3	8	7	6	7	6	7	0	6	...	7	7	9	2	5	9	1	2	5	2
10	3	8	7	1	3	5	3	0	7	5	...	4	0	2	6	4	1	9	9	1	0
11	7	1	4	0	6	7	6	8	3	5	...	7	5	0	5	1	0	5	8	3	5
12	7	9	1	6	2	8	7	8	5	5	...	9	0	4	1	2	9	2	4	3	1
13	2	8	4	6	5	3	0	1	7	2	...	3	1	8	5	8	8	2	5	5	7
14	5	9	7	7	1	0	5	6	3	5	...	9	0	0	1	6	9	8	3	5	9
15	4	4	9	4	9	0	7	9	2	7	...	7	4	2	1	6	8	6	9	0	4
16	1	1	8	2	8	9	4	2	8	1	...	9	9	3	1	5	8	4	1	7	6
17	7	3	8	7	4	3	3	6	2	4	...	1	8	0	2	7	5	9	7	5	9
18	5	6	0	5	5	6	1	9	8	0	...	4	5	0	1	3	7	6	5	2	1
19	1	7	8	2	3	1	5	8	1	0	...	8	0	7	3	7	0	8	4	8	7
20	4	2	6	0	9	2	5	3	1	4	...	3	0	1	8	3	9	0	8	1	1
21	0	0	8	2	6	0	0	0	1	2	...	5	1	7	5	7	3	6	0	7	3
22	9	3	7	4	8	4	8	1	5	3	...	0	8	6	0	8	0	5	4	9	0
23	5	1	0	2	6	0	5	0	2	2	...	8	2	9	7	2	7	9	5	2	4
24	8	7	7	0	0	7	2	4	8	0	...	0	0	9	6	2	0	8	4	4	8
25	0	3	7	4	0	0	3	4	3	0	...	4	4	1	9	1	2	0	5	5	0
26	9	1	2	9	8	0	3	6	0	4	...	3	6	5	2	9	3	3	5	9	8
27	2	5	0	6	8	1	2	8	3	5	...	2	5	5	0	2	7	8	6	5	7
28	6	5	7	6	3	1	9	8	0	2	...	5	0	2	4	2	5	3	3	3	5
29	3	9	2	8	8	5	2	2	4	8	...	1	4	1	3	4	9	9	7	2	6

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	5	8	9	5	0	0	1	7	6	9	...	1	7	0	6	9	9	7	6	9	1
1	0	1	8	8	3	9	8	7	3	6	...	9	2	0	4	9	2	7	7	9	8
2	6	9	3	7	7	4	5	9	3	6	...	7	7	1	1	3	0	8	6	4	5
3	6	2	5	7	8	4	4	7	7	4	...	0	1	9	8	2	3	1	2	7	2
4	6	0	9	2	6	6	2	7	7	0	...	1	5	4	0	7	8	9	5	7	0
5	9	3	9	1	4	4	6	8	8	9	...	1	8	7	0	3	4	2	0	3	5
6	1	2	4	3	0	6	0	7	2	8	...	4	3	3	6	7	3	5	3	2	4
7	4	0	3	3	8	3	5	6	7	5	...	1	7	3	1	6	6	9	6	9	6
8	0	0	2	9	6	0	6	7	0	3	...	6	7	9	5	4	9	5	2	5	6
9	6	8	7	7	7	2	6	0	5	2	...	7	0	6	2	4	3	6	7	6	3
10	0	6	4	7	6	2	9	5	9	9	...	4	9	3	9	1	2	5	4	0	8
11	2	3	9	9	4	4	8	2	1	6	...	0	5	9	8	6	6	0	4	7	3
12	0	1	6	0	6	1	6	4	2	5	...	8	8	0	7	2	0	7	1	1	9
13	5	1	5	9	6	4	9	8	7	5	...	2	4	3	2	0	0	4	2	5	0
14	0	3	8	5	3	1	4	7	3	2	...	8	5	5	7	5	9	1	3	9	3
15	3	3	6	1	3	0	5	0	5	2	...	7	1	7	7	3	8	3	0	6	3
16	0	6	5	9	6	4	6	6	2	2	...	3	6	8	6	5	1	3	2	6	3
17	6	7	2	8	0	1	8	6	0	0	...	5	6	2	5	4	3	0	6	2	1
18	9	4	4	0	9	8	7	7	6	1	...	7	9	9	7	1	1	4	6	5	6
19	4	1	1	5	1	2	6	2	3	3	...	0	0	0	9	8	5	9	3	4	0
20	9	8	6	3	9	9	0	8	1	6	...	2	9	0	1	3	9	4	8	8	8
21	2	8	6	4	9	0	5	5	6	1	...	6	7	5	6	8	7	4	2	4	0
22	0	3	5	9	0	3	6	5	1	1	...	6	2	5	3	9	3	9	5	1	9
23	7	7	0	8	6	1	2	0	4	4	...	1	9	6	0	2	8	3	7	2	5
24	6	0	4	2	3	1	0	5	7	0	...	1	1	2	7	5	2	9	4	7	3
25	5	0	2	1	4	9	4	6	9	3	...	5	5	3	5	9	2	7	4	1	6
26	9	8	1	8	1	6	2	6	1	8	...	2	5	1	2	5	3	3	6	1	8
27	1	8	6	4	6	9	5	4	7	2	...	9	3	1	5	1	1	7	1	2	6
28	0	7	7	4	3	2	7	8	5	2	...	0	2	8	3	7	3	9	2	3	8
29	8	0	2	6	8	3	6	4	9	7	...	6	7	8	5	7	2	5	3	4	5

	0	1	2	3	4	5	6	7	8	9	...	20	21	22	23	24	25	26	27	28	29
0	616	560	723	739	612	457	681	799	575	590	...	523	739	613	580	668	602	733	585	657	700
1	520	438	691	600	612	455	666	764	707	592	...	555	681	503	679	641	506	779	494	633	590
2	557	570	786	807	690	469	804	828	704	573	...	563	675	712	758	793	672	754	550	756	638
3	605	507	664	701	660	496	698	806	651	575	...	582	685	668	586	629	534	678	484	591	626
4	599	681	753	873	721	563	754	770	620	654	...	633	747	661	677	726	649	716	610	735	706
5	422	354	602	627	613	396	617	627	489	423	...	456	572	559	537	499	384	589	436	574	507
6	359	446	599	599	481	357	577	572	451	464	...	449	550	495	532	633	554	663	476	565	602
7	531	520	698	590	607	537	665	696	571	472	...	576	588	551	665	652	527	742	528	650	599
8	449	322	547	533	593	399	584	638	587	424	...	402	596	523	523	447	362	561	386	529	484
9	373	433	525	601	522	345	551	521	434	447	...	508	498	438	478	459	418	488	407	503	496
10	500	427	574	607	667	477	652	656	615	477	...	622	702	531	610	558	532	598	471	582	561
11	664	694	772	841	779	574	730	810	711	608	...	591	760	616	638	721	676	846	678	754	708
12	545	547	687	701	721	576	689	724	710	532	...	674	684	648	694	710	564	757	571	671	656
13	574	586	723	750	691	494	696	787	667	523	...	618	681	568	682	715	644	756	557	690	604
14	502	382	645	557	570	403	538	677	500	501	...	369	650	507	576	546	531	554	437	616	463
15	510	505	736	651	649	510	719	733	694	557	...	605	717	574	642	678	576	755	455	598	654
16	567	376	614	612	643	514	598	724	547	464	...	456	639	520	560	569	442	596	517	659	532
17	626	716	828	765	740	603	809	852	692	591	...	664	716	655	721	742	612	819	593	744	712
18	600	559	667	664	641	556	624	815	638	564	...	581	701	559	677	710	554	748	597	614	657
19	445	431	661	681	641	552	690	719	602	474	...	515	637	576	620	572	512	599	455	622	538
20	523	569	784	725	713	501	740	772	638	640	...	589	775	664	686	726	672	747	548	723	645
21	487	465	553	639	517	449	592	609	454	398	...	492	567	534	404	554	417	561	466	498	492
22	479	449	574	686	583	377	566	614	563	455	...	453	539	491	501	596	520	722	478	565	501
23	483	386	476	526	550	426	492	585	536	482	...	322	541	438	456	487	408	502	426	474	481
24	523	551	658	767	537	444	663	731	576	577	...	522	590	525	664	691	548	635	526	641	538
25	652	656	738	753	853	508	752	815	669	576	...	694	833	693	606	575	616	704	559	728	672
26	578	577	744	856	699	497	779	800	733	587	...	630	754	704	834	760	680	765	592	731	629
27	554	494	665	689	630	574	695	703	636	599	...	554	685	532	658	649	554	693	577	634	668
28	498	552	659	784	552	492	690	775	544	551	...	567	636	518	599	742	521	733	533	605	604
29	513	491	563	642	477	367	589	647	516	484	...	428	574	504	548	553	483	540	407	547	455