pandas教程:Data Transformation 数据变换、删除和替换

文章目录

  • 7.2 Data Transformation(数据变换)
  • 1 删除重复值
  • 2 Transforming Data Using a Function or Mapping(用函数和映射来转换数据)
  • 3 Replacing Values(替换值)
  • 4 Renaming Axis Indexes(重命名Axis Indexes)
  • 5 Discretization and Binning(离散化和装箱)
  • 6 Detecting and Filtering Outliers(检测和过滤异常值)
  • 7 Permutation and Random Sampling(排列和随机采样)
  • 8 Computing Indicator/Dummy Variables(计算指示器/假变量)

7.2 Data Transformation(数据变换)

1 删除重复值

import pandas as pd
import numpy as np
data = pd.DataFrame({'k1': ['one', 'two'] * 3 + ['two'],
                     'k2': [1, 1, 2, 3, 3, 4, 4]})
data
k1 k2
0 one 1
1 two 1
2 one 2
3 two 3
4 one 3
5 two 4
6 two 4

DataFrame方法duplicated返回的是一个boolean Series,表示一个row是否是重复的(根据前一行来判断):

data.duplicated()
0    False
1    False
2    False
3    False
4    False
5    False
6     True
dtype: bool

drop_duplicateds返回一个DataFrame,会删除重复的部分:

data.drop_duplicates()
k1 k2
0 one 1
1 two 1
2 one 2
3 two 3
4 one 3
5 two 4

上面两种方法都默认考虑所有列;另外,我们可以指定一部分来检测重复值。假设我们只想检测’k1’列的重复值:

data['v1'] = range(7)
data
k1 k2 v1
0 one 1 0
1 two 1 1
2 one 2 2
3 two 3 3
4 one 3 4
5 two 4 5
6 two 4 6
data.drop_duplicates(['k1'])
k1 k2 v1
0 one 1 0
1 two 1 1

duplicateddrop_duplicated默认保留第一次观测到的数值组合。设置keep='last'能返回最后一个:

data.drop_duplicates(['k1', 'k2'], keep='last')
k1 k2 v1
0 one 1 0
1 two 1 1
2 one 2 2
3 two 3 3
4 one 3 4
6 two 4 6

2 Transforming Data Using a Function or Mapping(用函数和映射来转换数据)

有时候我们可能希望做一些数据转换。比如下面一个例子,有不同种类的肉:

data = pd.DataFrame({'food': ['bacon', 'pulled pork', 'bacon',
                              'Pastrami', 'corned beef', 'Bacon',
                              'pastrami', 'honey ham', 'nova lox'],
                     'ounces': [4, 3, 12, 6, 7.5, 8, 3, 5, 6]})
data
food ounces
0 bacon 4.0
1 pulled pork 3.0
2 bacon 12.0
3 Pastrami 6.0
4 corned beef 7.5
5 Bacon 8.0
6 pastrami 3.0
7 honey ham 5.0
8 nova lox 6.0

假设你想加一列,表明每种肉来源的动物是什么。我们可以写一个映射:

meat_to_animal = {
    'bacon': 'pig',
    'pulled pork': 'pig',
    'pastrami': 'cow',
    'corned beef': 'cow',
    'honey ham': 'pig',
    'nova lox': 'salmon'
}

用于seriesmap方法接受一个函数,或是一个字典,包含着映射关系,但这里有一个小问题,有些肉是大写,有些是小写。因此,我们先用str.lower把所有的值变为小写:

lowercased = data['food'].str.lower()
lowercased
0          bacon
1    pulled pork
2          bacon
3       pastrami
4    corned beef
5          bacon
6       pastrami
7      honey ham
8       nova lox
Name: food, dtype: object
data['animal'] = lowercased.map(meat_to_animal)
data
food ounces animal
0 bacon 4.0 pig
1 pulled pork 3.0 pig
2 bacon 12.0 pig
3 Pastrami 6.0 cow
4 corned beef 7.5 cow
5 Bacon 8.0 pig
6 pastrami 3.0 cow
7 honey ham 5.0 pig
8 nova lox 6.0 salmon

我们也可以用一个函数解决上面的问题:

data['food'].map(lambda x: meat_to_animal[x.lower()])
0       pig
1       pig
2       pig
3       cow
4       cow
5       pig
6       cow
7       pig
8    salmon
Name: food, dtype: object

使用map是一个很简便的方法,用于element-wise转换和其他一些数据清洗操作。

3 Replacing Values(替换值)

其实fillna是一个特殊换的替换操作。map可以用于修改一个object里的部分值,但是replace能提供一个更简单和更灵活的方法做到这点。下面是一个series

data = pd.Series([1., -999., 2., -999., -1000., 3.])
data
0       1.0
1    -999.0
2       2.0
3    -999.0
4   -1000.0
5       3.0
dtype: float64

这里-999可能是用来表示缺失值的标识符。用NA来替代的话,用replace,会产生一个新series(除非使用inplace=True):

data.replace(-999, np.nan)
0       1.0
1       NaN
2       2.0
3       NaN
4   -1000.0
5       3.0
dtype: float64

如果想要一次替换多个值,直接用一个list即可:

data.replace([-999, -1000], np.nan)
0    1.0
1    NaN
2    2.0
3    NaN
4    NaN
5    3.0
dtype: float64

对于不同的值用不同的替换值,也是导入一个list

data.replace([-999, -1000], [np.nan, 0])
0    1.0
1    NaN
2    2.0
3    NaN
4    0.0
5    3.0
dtype: float64

参数也可以是一个dict:

data.replace({-999: np.nan, -1000: 0})
0    1.0
1    NaN
2    2.0
3    NaN
4    0.0
5    3.0
dtype: float64

注意:data.replace方法和data.str.replace方法是不同的,后者会对string进行element-wise替换。

4 Renaming Axis Indexes(重命名Axis Indexes)

像是series里的value一样,axis label也能类似地是函数或映射来转换,产生一个新的object。当然也可以设置in-place不产生新的数据:

data = pd.DataFrame(np.arange(12).reshape((3, 4)),
                    index=['Ohio', 'Colorado', 'New York'],
                    columns=['one', 'two', 'three', 'four'])
data
one two three four
Ohio 0 1 2 3
Colorado 4 5 6 7
New York 8 9 10 11

series相同,axis index有一个map方法:

transform = lambda x: x[:4].upper()
transform
>
data.index
Index(['Ohio', 'Colorado', 'New York'], dtype='object')
data.index.map(transform)
array(['OHIO', 'COLO', 'NEW '], dtype=object)

可以赋值给index,以in-place的方式修改DataFrame

data.index = data.index.map(transform)
data
one two three four
OHIO 0 1 2 3
COLO 4 5 6 7
NEW 8 9 10 11

如果你想要创建一个转换后的版本,而且不用修改原始的数据,可以用rename:

data.rename(index=str.title, columns=str.upper)
ONE TWO THREE FOUR
Ohio 0 1 2 3
Colo 4 5 6 7
New 8 9 10 11

注意,rename能用于dict一样的object

data.rename(index={'OHIO': 'INDIANA'},
            columns={'three': 'pekaboo'})
one two pekaboo four
INDIANA 0 1 2 3
COLO 4 5 6 7
NEW 8 9 10 11

rename能让你避免陷入手动赋值给indexcolumns的杂务中。可以用inplace直接修改原始数据:

data.rename(index={'OHIO': 'INDIANA'}, inplace=True)
data
one two three four
INDIANA 0 1 2 3
COLO 4 5 6 7
NEW 8 9 10 11

5 Discretization and Binning(离散化和装箱)

连续型数据经常被离散化或分散成bins(分箱)来分析。假设你有一组数据,你想把人分到不同的年龄组里:

ages = [20, 22, 25, 27, 21, 23, 37, 31, 61, 45, 41, 32]

我们把这些分到四个bin里,18~25, 26~35, 36~60, >60。可以用pandas里的cut

bins = [18, 25, 35, 60, 100]

cats = pd.cut(ages, bins)

cats
[(18, 25], (18, 25], (18, 25], (25, 35], (18, 25], ..., (25, 35], (60, 100], (35, 60], (35, 60], (25, 35]]
Length: 12
Categories (4, object): [(18, 25] < (25, 35] < (35, 60] < (60, 100]]

返回的是一个特殊的Categorical object。我们看到的结果描述了pandas.cut如何得到bins。可以看作是一个string数组用来表示bin的名字,它内部包含了一个categories数组,用来记录不同类别的名字,并伴有表示ageslabel(可以通过codes属性查看):

cats.codes
array([0, 0, 0, 1, 0, 0, 2, 1, 3, 2, 2, 1], dtype=int8)
cats.categories
Index(['(18, 25]', '(25, 35]', '(35, 60]', '(60, 100]'], dtype='object')
pd.value_counts(cats)
(18, 25]     5
(35, 60]     3
(25, 35]     3
(60, 100]    1
dtype: int64

这里pd.value_counts(cats)pandas.cutbin的数量。

这里我们注意一下区间。括号表示不包含,方括号表示包含。你可以自己设定哪一边关闭(right=False):

pd.cut(ages, [18, 26, 36, 61, 100], right=False)
[[18, 26), [18, 26), [18, 26), [26, 36), [18, 26), ..., [26, 36), [61, 100), [36, 61), [36, 61), [26, 36)]
Length: 12
Categories (4, object): [[18, 26) < [26, 36) < [36, 61) < [61, 100)]

你也可以用一个list或数组给labels选项来设定bin的名字:

group_names = ['Youth', 'YoungAdult', 'MiddleAged', 'Senior']
pd.cut(ages, bins, labels=group_names)
[Youth, Youth, Youth, YoungAdult, Youth, ..., YoungAdult, Senior, MiddleAged, MiddleAged, YoungAdult]
Length: 12
Categories (4, object): [Youth < YoungAdult < MiddleAged < Senior]

如果你只是给一个bins的数量来cut,而不是自己设定每个bind的范围,cut会根据最大值和最小值来计算等长的bins。比如下面我们想要做一个均匀分布的四个bins

data = np.random.rand(20)
pd.cut(data, 4, precision=2)
[(0.77, 0.98], (0.33, 0.55], (0.77, 0.98], (0.55, 0.77], (0.55, 0.77], ..., (0.77, 0.98], (0.11, 0.33], (0.11, 0.33], (0.33, 0.55], (0.11, 0.33]]
Length: 20
Categories (4, object): [(0.11, 0.33] < (0.33, 0.55] < (0.55, 0.77] < (0.77, 0.98]]

precision=2选项表示精确到小数点后两位。

一个近似的函数,qcut,会按照数据的分位数来分箱。取决于数据的分布,用cut通常不能保证每一个bin有一个相同数量的数据点。而qcut是按百分比来切的,所以可以得到等数量的bins

data = np.random.randn(1000) # Normally distributed
cats = pd.qcut(data, 4) # Cut into quartiles
cats
[(-0.717, -0.0981], (-0.717, -0.0981], (-0.0981, 0.639], (0.639, 3.434], [-2.86, -0.717], ..., (-0.0981, 0.639], (-0.717, -0.0981], (-0.0981, 0.639], (0.639, 3.434], (-0.0981, 0.639]]
Length: 1000
Categories (4, object): [[-2.86, -0.717] < (-0.717, -0.0981] < (-0.0981, 0.639] < (0.639, 3.434]]
pd.value_counts(cats)
(0.639, 3.434]       250
(-0.0981, 0.639]     250
(-0.717, -0.0981]    250
[-2.86, -0.717]      250
dtype: int64

类似的,在cut中我们可以自己指定百分比:

cats2 = pd.cut(data, [0, 0.1, 0.5, 0.9, 1.]) # 累进的百分比
cats2
[NaN, NaN, (0.1, 0.5], NaN, NaN, ..., (0.1, 0.5], NaN, (0.5, 0.9], NaN, (0.5, 0.9]]
Length: 1000
Categories (4, object): [(0, 0.1] < (0.1, 0.5] < (0.5, 0.9] < (0.9, 1]]
pd.value_counts(cats2)
(0.1, 0.5]    135
(0.5, 0.9]    124
(0, 0.1]       40
(0.9, 1]       21
dtype: int64

在之后的章节我们还会用到cutqcut,这些离散函数对于量化和群聚分析很有用。

6 Detecting and Filtering Outliers(检测和过滤异常值)

过滤或转换异常值是数组操作的一个重头戏。下面的DataFrame有正态分布的数据:

data = pd.DataFrame(np.random.randn(1000, 4))
data.describe()
0 1 2 3
count 1000.000000 1000.000000 1000.000000 1000.000000
mean 0.010953 0.012928 0.033165 -0.031257
std 1.011621 1.013341 1.004356 0.996333
min -2.994342 -4.328036 -3.303616 -3.133495
25% -0.654483 -0.662177 -0.644982 -0.670813
50% -0.000637 -0.033241 0.050481 -0.074641
75% 0.723100 0.725839 0.708452 0.643418
max 3.318499 3.353001 3.002853 3.002868

假设我们想要找一个列中,绝对值大于3的数字:

data.head()
0 1 2 3
0 1.123766 0.933920 0.494755 0.690507
1 2.513636 0.575393 -0.323590 0.586833
2 -0.335958 -0.843735 0.302201 -0.490675
3 -1.307658 -0.485670 1.612787 0.210169
4 -0.793757 -0.693757 -1.718367 0.515088
col = data[2]
col.head()
0    0.494755
1   -0.323590
2    0.302201
3    1.612787
4   -1.718367
Name: 2, dtype: float64
col[np.abs(col) > 3]
339   -3.303616
932    3.002853
Name: 2, dtype: float64

选中所有绝对值大于3的行,可以用any方法在一个boolean DataFrame上:

data[(np.abs(data) > 3)].head()
0 1 2 3
0 NaN NaN NaN NaN
1 NaN NaN NaN NaN
2 NaN NaN NaN NaN
3 NaN NaN NaN NaN
4 NaN NaN NaN NaN
data[(np.abs(data) > 3).any(1)] # any中axis=1表示column
0 1 2 3
22 1.075728 0.250000 0.951303 -3.133495
155 0.064837 -4.328036 1.121061 -0.574203
224 -0.289148 -2.912116 0.332218 -3.129604
339 -0.098352 -0.610929 -3.303616 -2.072304
609 0.983240 1.372633 0.018172 3.002868
735 3.318499 -2.573122 -1.515901 -1.204596
822 1.810396 3.353001 -1.283856 -1.166749
856 -0.795070 3.204789 -0.211642 1.278828
932 0.898147 -0.961850 3.002853 -0.128494

下面是把绝对值大于3的数字直接变成-3或3:

data[np.abs(data) > 3] = np.sign(data) * 3
data[21:23]
0 1 2 3
21 -0.066111 -1.159064 0.518720 -0.284596
22 1.075728 0.250000 0.951303 -3.000000
data.describe()
0 1 2 3
count 1000.000000 1000.000000 1000.000000 1000.000000
mean 0.010634 0.013698 0.033466 -0.030997
std 1.010629 1.006768 1.003383 0.995521
min -2.994342 -3.000000 -3.000000 -3.000000
25% -0.654483 -0.662177 -0.644982 -0.670813
50% -0.000637 -0.033241 0.050481 -0.074641
75% 0.723100 0.725839 0.708452 0.643418
max 3.000000 3.000000 3.000000 3.000000

np.sign(data)会根据值的正负号来得到1或-1:

np.sign(data).head()
0 1 2 3
0 1.0 1.0 1.0 1.0
1 1.0 1.0 -1.0 1.0
2 -1.0 -1.0 1.0 -1.0
3 -1.0 -1.0 1.0 1.0
4 -1.0 -1.0 -1.0 1.0

7 Permutation and Random Sampling(排列和随机采样)

排列(随机排序)一个seriesDataFrame中的row,用numpy.random.permutation函数很容易就能做到。调用permutation的时候设定好你想要进行排列的axis,会产生一个整数数组表示新的顺序:

df = pd.DataFrame(np.arange(5 * 4).reshape((5, 4)))
df
0 1 2 3
0 0 1 2 3
1 4 5 6 7
2 8 9 10 11
3 12 13 14 15
4 16 17 18 19
sampler = np.random.permutation(5)
sampler
array([4, 3, 2, 1, 0])

这个数组能被用在基于iloc上的indexingtake函数:

df.take(sampler)
0 1 2 3
4 16 17 18 19
3 12 13 14 15
2 8 9 10 11
1 4 5 6 7
0 0 1 2 3

为了选中一个随机的子集,而且没有代替功能(既不影响原来的值,返回一个新的seriesDataFrame),可以用sample方法:

df.sample(n=3)
0 1 2 3
0 0 1 2 3
3 12 13 14 15
4 16 17 18 19

如果想要生成的样本带有替代功能(即允许重复),给sample中设定replace=True:

choices = pd.Series([5, 7, -1, 6, 4])

draws = choices.sample(n=10, replace=True)

draws
4    4
4    4
1    7
1    7
1    7
1    7
4    4
3    6
1    7
1    7
dtype: int64

8 Computing Indicator/Dummy Variables(计算指示器/假变量)

另一种在统计模型上的转换或机器学习应用是把一个categorical variable(类别变量)变为一个dummy or indicator matrix(假或指示器矩阵)。如果DataFrame中的一列有k个不同的值,我们可以用一个矩阵或DataFrame用k列来表示,1或0。pandas有一个get_dummies函数实现这个工作,当然,你自己设计一个其实也不难。这里举个例子:

df = pd.DataFrame({'key': ['b', 'b', 'a', 'c', 'a', 'b'],
                   'data1': range(6)})
df
data1 key
0 0 b
1 1 b
2 2 a
3 3 c
4 4 a
5 5 b
pd.get_dummies(df['key'])
a b c
0 0.0 1.0 0.0
1 0.0 1.0 0.0
2 1.0 0.0 0.0
3 0.0 0.0 1.0
4 1.0 0.0 0.0
5 0.0 1.0 0.0

在一些情况里,如果我们想要给column加一个prefix, 可以用data.get_dummies里的prefix参数来实现:

dummies = pd.get_dummies(df['key'], prefix='key')
df_with_dummy = df[['data1']].join(dummies)
df_with_dummy
data1 key_a key_b key_c
0 0 0.0 1.0 0.0
1 1 0.0 1.0 0.0
2 2 1.0 0.0 0.0
3 3 0.0 0.0 1.0
4 4 1.0 0.0 0.0
5 5 0.0 1.0 0.0

如果DataFrame中的a row属于多个类别,事情会变得复杂一些。我们来看一下MoviesLens 1M 数据集:

mnames = ['movie_id', 'title', 'genres']
movies = pd.read_table('../datasets/movielens/movies.dat', sep='::',
                       header=None, names=mnames, engine='python')
movies[:10]
movie_id title genres
0 1 Toy Story (1995) Animation|Children's|Comedy
1 2 Jumanji (1995) Adventure|Children's|Fantasy
2 3 Grumpier Old Men (1995) Comedy|Romance
3 4 Waiting to Exhale (1995) Comedy|Drama
4 5 Father of the Bride Part II (1995) Comedy
5 6 Heat (1995) Action|Crime|Thriller
6 7 Sabrina (1995) Comedy|Romance
7 8 Tom and Huck (1995) Adventure|Children's
8 9 Sudden Death (1995) Action
9 10 GoldenEye (1995) Action|Adventure|Thriller

给每个genre添加一个指示变量比较麻烦。首先我们先取出所有不同的类别:

all_genres = []

for x in movies.genres:
    all_genres.extend(x.split('|'))
    
genres = pd.unique(all_genres)
genres
array(['Animation', "Children's", 'Comedy', 'Adventure', 'Fantasy',
       'Romance', 'Drama', 'Action', 'Crime', 'Thriller', 'Horror',
       'Sci-Fi', 'Documentary', 'War', 'Musical', 'Mystery', 'Film-Noir',
       'Western'], dtype=object)

一种构建indicator dataframe的方法是先构建一个全是0的DataFrame

zero_matrix = np.zeros((len(movies), len(genres)))

zero_matrix.shape
(3883, 18)
dummies = pd.DataFrame(zero_matrix, columns=genres)
dummies.head()
Animation Children's Comedy Adventure Fantasy Romance Drama Action Crime Thriller Horror Sci-Fi Documentary War Musical Mystery Film-Noir Western
0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

然后迭代每一部movie,并设置每一行中的dummies为1。使用dummies.columns来计算每一列的genre的指示器:

gen = movies.genres[0]
gen.split('|')
['Animation', "Children's", 'Comedy']
dummies.columns.get_indexer(gen.split('|'))
array([0, 1, 2])

然后,使用.iloc,根据索引来设定值:

for i, gen in enumerate(movies.genres):
    indices = dummies.columns.get_indexer(gen.split('|'))
    dummies.iloc[i, indices] = 1
dummies.head()
Animation Children's Comedy Adventure Fantasy Romance Drama Action Crime Thriller Horror Sci-Fi Documentary War Musical Mystery Film-Noir Western
0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1 0.0 1.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2 0.0 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
4 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

然后,我们可以结合这个和movies:

movies_windic = movies.join(dummies.add_prefix('Genre_'))
movies_windic.iloc[0]
movie_id                                       1
title                           Toy Story (1995)
genres               Animation|Children's|Comedy
Genre_Animation                                1
Genre_Children's                               1
Genre_Comedy                                   1
Genre_Adventure                                0
Genre_Fantasy                                  0
Genre_Romance                                  0
Genre_Drama                                    0
Genre_Action                                   0
Genre_Crime                                    0
Genre_Thriller                                 0
Genre_Horror                                   0
Genre_Sci-Fi                                   0
Genre_Documentary                              0
Genre_War                                      0
Genre_Musical                                  0
Genre_Mystery                                  0
Genre_Film-Noir                                0
Genre_Western                                  0
Name: 0, dtype: object

对于一个很大的数据集,这种构建多个成员指示变量的方法并不会加快速度。写一个低层级的函数来直接写一个numpy array,并把写过整合到DataFrame会更快一些。

一个有用的recipe诀窍是把get_dummies和离散函数(比如cut)结合起来:

np.random.seed(12345)
values = np.random.rand(10)
values
array([ 0.92961609,  0.31637555,  0.18391881,  0.20456028,  0.56772503,
        0.5955447 ,  0.96451452,  0.6531771 ,  0.74890664,  0.65356987])
bins = [0, 0.2, 0.4, 0.6, 0.8, 1.]
pd.cut(values, bins)
[(0.8, 1], (0.2, 0.4], (0, 0.2], (0.2, 0.4], (0.4, 0.6], (0.4, 0.6], (0.8, 1], (0.6, 0.8], (0.6, 0.8], (0.6, 0.8]]
Categories (5, object): [(0, 0.2] < (0.2, 0.4] < (0.4, 0.6] < (0.6, 0.8] < (0.8, 1]]
pd.get_dummies(pd.cut(values, bins))
(0, 0.2] (0.2, 0.4] (0.4, 0.6] (0.6, 0.8] (0.8, 1]
0 0.0 0.0 0.0 0.0 1.0
1 0.0 1.0 0.0 0.0 0.0
2 1.0 0.0 0.0 0.0 0.0
3 0.0 1.0 0.0 0.0 0.0
4 0.0 0.0 1.0 0.0 0.0
5 0.0 0.0 1.0 0.0 0.0
6 0.0 0.0 0.0 0.0 1.0
7 0.0 0.0 0.0 1.0 0.0
8 0.0 0.0 0.0 1.0 0.0
9 0.0 0.0 0.0 1.0 0.0

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