Python常见的pandas用法demo示例
本文实例总结了python常见的pandas用法。分享给大家供大家参考，具体如下：
import numpy as np import pandas as pd
s = pd.series([1,3,6, np.nan, 44, 1]) #定义一个序列。 序列就是一列内容，每一行有一个index值 print(s) print(s.index)
0 1.0
1 3.0
2 6.0
3 nan
4 44.0
5 1.0
dtype: float64
rangeindex(start=0, stop=6, step=1)
dates = pd.date_range('20180101', periods=6)
print(dates)
datetimeindex(['2018-01-01', '2018-01-02', '2018-01-03', '2018-01-04',
'2018-01-05', '2018-01-06'],
dtype='datetime64[ns]', freq='d')
df1 = pd.dataframe(np.arange(12).reshape(3,4)) #定义dataframe，可以看作一个有index和colunms的矩阵 print(df)
0 1 2 3
0 0 1 2 3
1 4 5 6 7
2 8 9 10 11
df2 = pd.dataframe(np.random.randn(6,4), index=dates, columns=['a', 'b', 'c', 'd']) #np.random.randn(6,4)生成6行4列矩阵 print(df)
a b c d
2018-01-01 0.300675 1.769383 1.244406 -1.058294
2018-01-02 0.832666 2.216755 0.178716 -0.156828
2018-01-03 1.314190 -0.866199 0.836150 1.001026
2018-01-04 -1.671724 1.147406 -0.148676 -0.272555
2018-01-05 1.146664 2.022861 -1.833995 -0.627568
2018-01-06 -0.192242 1.517676 0.756707 0.058869
df = pd.dataframe({'a':1.0,
'b':pd.timestamp('20180101'),
'c':pd.series(1, index=list(range(4)), dtype='float32'),
'd':np.array([3] * 4, dtype='int32'),
'e':pd.categorical(['test', 'train', 'test', 'train']),
'f':'foo'}) #按照给出的逐列定义df
print(df)
print(df.dtypes)
a b c d e f
0 1.0 2018-01-01 1.0 3 test foo
1 1.0 2018-01-01 1.0 3 train foo
2 1.0 2018-01-01 1.0 3 test foo
3 1.0 2018-01-01 1.0 3 train foo
a float64
b datetime64[ns]
c float32
d int32
e category
f object
dtype: object
#df的行、列、值 print(df.index) print(df.columns) print(df.values)
int64index([0, 1, 2, 3], dtype='int64')
index(['a', 'b', 'c', 'd', 'e', 'f'], dtype='object')
[[1.0 timestamp('2018-01-01 00:00:00') 1.0 3 'test' 'foo']
[1.0 timestamp('2018-01-01 00:00:00') 1.0 3 'train' 'foo']
[1.0 timestamp('2018-01-01 00:00:00') 1.0 3 'test' 'foo']
[1.0 timestamp('2018-01-01 00:00:00') 1.0 3 'train' 'foo']]
print(df.describe()) #统计 print(df.t) #转置
a c d
count 4.0 4.0 4.0
mean 1.0 1.0 3.0
std 0.0 0.0 0.0
min 1.0 1.0 3.0
25% 1.0 1.0 3.0
50% 1.0 1.0 3.0
75% 1.0 1.0 3.0
max 1.0 1.0 3.0
0 1 2 \
a 1 1 1
b 2018-01-01 00:00:00 2018-01-01 00:00:00 2018-01-01 00:00:00
c 1 1 1
d 3 3 3
e test train test
f foo foo foo
3
a 1
b 2018-01-01 00:00:00
c 1
d 3
e train
f foo
#df排序 print(df.sort_index(axis=1, ascending=false)) #根据索引值对各行进行排序（相当于重新排列各列的位置） print(df.sort_values(by='e')) #根据内容值对各列进行排序
f e d c b a
0 foo test 3 1.0 2018-01-01 1.0
1 foo train 3 1.0 2018-01-01 1.0
2 foo test 3 1.0 2018-01-01 1.0
3 foo train 3 1.0 2018-01-01 1.0
a b c d e f
0 1.0 2018-01-01 1.0 3 test foo
2 1.0 2018-01-01 1.0 3 test foo
1 1.0 2018-01-01 1.0 3 train foo
3 1.0 2018-01-01 1.0 3 train foo
indexes = pd.date_range('20180101', periods=6)
df3 = pd.dataframe(np.arange(24).reshape(6, 4), index=indexes, columns=['a', 'b', 'c', 'd'])
print(df3)
print()
#选择column
print(df3['a'])
print()
print(df3.a)
a b c d
2018-01-01 0 1 2 3
2018-01-02 4 5 6 7
2018-01-03 8 9 10 11
2018-01-04 12 13 14 15
2018-01-05 16 17 18 19
2018-01-06 20 21 22 23
2018-01-01 0
2018-01-02 4
2018-01-03 8
2018-01-04 12
2018-01-05 16
2018-01-06 20
freq: d, name: a, dtype: int32
2018-01-01 0
2018-01-02 4
2018-01-03 8
2018-01-04 12
2018-01-05 16
2018-01-06 20
freq: d, name: a, dtype: int32
a b c d
2018-01-01 0 1 2 3
2018-01-02 4 5 6 7
2018-01-03 8 9 10 11
#选择行， 类似limit语句 print(df3[0:0]) print() print(df3[0:3]) print() print(df3['20180103':'20180105'])
empty dataframe
columns: [a, b, c, d]
index: []
a b c d
2018-01-01 0 1 2 3
2018-01-02 4 5 6 7
2018-01-03 8 9 10 11
a b c d
2018-01-03 8 9 10 11
2018-01-04 12 13 14 15
2018-01-05 16 17 18 19
print(df3.loc['20180102']) #返回指定行构成的序列
a 4
b 5
c 6
d 7
name: 2018-01-02 00:00:00, dtype: int32
print(df3.loc['20180103', ['a','c']]) #列筛选 print() print(df3.loc['20180103':'20180105', ['a','c']]) #子df，类似select a, c from df limit ... print() print(df3.loc[:, ['a', 'b']])
a 8
c 10
name: 2018-01-03 00:00:00, dtype: int32
a c
2018-01-03 8 10
2018-01-04 12 14
2018-01-05 16 18
a b
2018-01-01 0 1
2018-01-02 4 5
2018-01-03 8 9
2018-01-04 12 13
2018-01-05 16 17
2018-01-06 20 21
print(df3);print() print(df3.iloc[1]);print() print(df3.iloc[1,1]);print() print(df3.iloc[:,1]);print() print(df3.iloc[0:3,1:3]);print() print(df3.iloc[[1,3,5],[0,2]]) #行可以不连续，limit做不到
a b c d
2018-01-01 0 1 2 3
2018-01-02 4 5 6 7
2018-01-03 8 9 10 11
2018-01-04 12 13 14 15
2018-01-05 16 17 18 19
2018-01-06 20 21 22 23
a 4
b 5
c 6
d 7
name: 2018-01-02 00:00:00, dtype: int32
5
2018-01-01 1
2018-01-02 5
2018-01-03 9
2018-01-04 13
2018-01-05 17
2018-01-06 21
freq: d, name: b, dtype: int32
b c
2018-01-01 1 2
2018-01-02 5 6
2018-01-03 9 10
a c
2018-01-02 4 6
2018-01-04 12 14
2018-01-06 20 22
# print(df3.ix[:3, ['a', 'c']])\ print(df3);print() print(df3[df3.a >= 8]) #根据值进行条件过滤，类似where a >= 8条件语句
a b c d
2018-01-01 0 1 2 3
2018-01-02 4 5 6 7
2018-01-03 8 9 10 11
2018-01-04 12 13 14 15
2018-01-05 16 17 18 19
2018-01-06 20 21 22 23
a b c d
2018-01-03 8 9 10 11
2018-01-04 12 13 14 15
2018-01-05 16 17 18 19
2018-01-06 20 21 22 23
indexes1 = pd.date_range('20180101', periods=6)
df4 = pd.dataframe(np.arange(24).reshape(6, 4), index=indexes1, columns=['a', 'b', 'c', 'd'])
print(df4);print()
#给某个元素赋值
df4.a[1] = 1111
df4.b['20180103'] = 2222
df4.iloc[3, 2] = 3333
df4.loc['20180105', 'd'] = 4444
print(df4);print()
#范围赋值
df4.b[df4.a < 10] = -1
print(df4);print()
df4[df4.a < 10] = 0
print(df4);print()
a b c d
2018-01-01 0 1 2 3
2018-01-02 4 5 6 7
2018-01-03 8 9 10 11
2018-01-04 12 13 14 15
2018-01-05 16 17 18 19
2018-01-06 20 21 22 23
a b c d
2018-01-01 0 1 2 3
2018-01-02 1111 5 6 7
2018-01-03 8 2222 10 11
2018-01-04 12 13 3333 15
2018-01-05 16 17 18 4444
2018-01-06 20 21 22 23
a b c d
2018-01-01 0 -1 2 3
2018-01-02 1111 5 6 7
2018-01-03 8 -1 10 11
2018-01-04 12 13 3333 15
2018-01-05 16 17 18 4444
2018-01-06 20 21 22 23
a b c d
2018-01-01 0 0 0 0
2018-01-02 1111 5 6 7
2018-01-03 0 0 0 0
2018-01-04 12 13 3333 15
2018-01-05 16 17 18 4444
2018-01-06 20 21 22 23
indexes1 = pd.date_range('20180101', periods=6)
df4 = pd.dataframe(np.arange(24).reshape(6, 4), index=indexes1, columns=['a', 'b', 'c', 'd'])
print(df4);print()
#添加一列
df4['e'] = np.nan
print(df4);print()
#由于index没对齐，原df没有的行默认为nan，类型为float64,多出的行丢弃
df4['f'] = pd.series([1,2,3,4,5,6], index=pd.date_range('20180102', periods=6))
print(df4);print()
print(df4.dtypes)
a b c d
2018-01-01 0 1 2 3
2018-01-02 4 5 6 7
2018-01-03 8 9 10 11
2018-01-04 12 13 14 15
2018-01-05 16 17 18 19
2018-01-06 20 21 22 23
a b c d e
2018-01-01 0 1 2 3 nan
2018-01-02 4 5 6 7 nan
2018-01-03 8 9 10 11 nan
2018-01-04 12 13 14 15 nan
2018-01-05 16 17 18 19 nan
2018-01-06 20 21 22 23 nan
a b c d e f
2018-01-01 0 1 2 3 nan nan
2018-01-02 4 5 6 7 nan 1.0
2018-01-03 8 9 10 11 nan 2.0
2018-01-04 12 13 14 15 nan 3.0
2018-01-05 16 17 18 19 nan 4.0
2018-01-06 20 21 22 23 nan 5.0
a int32
b int32
c int32
d int32
e float64
f float64
dtype: object
df_t = pd.dataframe(np.arange(24).reshape(6, 4), index=[1,2,3,4,5,6], columns=['a', 'b', 'c', 'd']) df_t.iloc[0, 1] = np.nan df_t.iloc[1, 2] = np.nan df = df_t.copy() print(df);print() print(df.dropna(axis=0, how='any'));print() df = df_t.copy() print(df.dropna(axis=1, how='any'));print() df = df_t.copy() df.c = np.nan print(df);print() print(df.dropna(axis=1, how='all'));print()
a b c d
1 0 nan 2.0 3
2 4 5.0 nan 7
3 8 9.0 10.0 11
4 12 13.0 14.0 15
5 16 17.0 18.0 19
6 20 21.0 22.0 23
a b c d
3 8 9.0 10.0 11
4 12 13.0 14.0 15
5 16 17.0 18.0 19
6 20 21.0 22.0 23
a d
1 0 3
2 4 7
3 8 11
4 12 15
5 16 19
6 20 23
a b c d
1 0 nan nan 3
2 4 5.0 nan 7
3 8 9.0 nan 11
4 12 13.0 nan 15
5 16 17.0 nan 19
6 20 21.0 nan 23
a b d
1 0 nan 3
2 4 5.0 7
3 8 9.0 11
4 12 13.0 15
5 16 17.0 19
6 20 21.0 23
df = df_t.copy() print(df);print() print(df.isna());print() print(df.isnull().any());print() #isnull是isna别名，功能一样 print(df.isnull().any(axis=1));print() print(np.any(df.isna() == true));print() print(df.fillna(value=0)) #将nan赋值
a b c d
1 0 nan 2.0 3
2 4 5.0 nan 7
3 8 9.0 10.0 11
4 12 13.0 14.0 15
5 16 17.0 18.0 19
6 20 21.0 22.0 23
a b c d
1 false true false false
2 false false true false
3 false false false false
4 false false false false
5 false false false false
6 false false false false
a false
b true
c true
d false
dtype: bool
1 true
2 true
3 false
4 false
5 false
6 false
dtype: bool
true
a b c d
1 0 0.0 2.0 3
2 4 5.0 0.0 7
3 8 9.0 10.0 11
4 12 13.0 14.0 15
5 16 17.0 18.0 19
6 20 21.0 22.0 23
data = pd.read_csv('d:/pythonwp/test/student.csv')
print(data)
data.to_pickle('d:/pythonwp/test/student.pickle')
id name age gender
0 1 牛帅 23 male
1 2 gyb 89 male
2 3 xxs 27 male
3 4 hey 24 female
4 5 奥莱利赫本 66 female
5 6 jackson 61 male
6 7 牛帅 23 male
df0 = pd.dataframe(np.ones((3, 4)) * 0, columns=['a', 'b', 'c', 'd']) df1 = pd.dataframe(np.ones((3, 4)) * 1, columns=['a', 'b', 'c', 'd']) df2 = pd.dataframe(np.ones((3, 4)) * 2, columns=['a', 'b', 'c', 'd']) print(df0); print() print(df1); print() print(df2); print() res = pd.concat([df0, df1, df2], axis = 0) print(res); print() res = pd.concat([df0, df1, df2], axis = 0, ignore_index=true) print(res)
a b c d
0 0.0 0.0 0.0 0.0
1 0.0 0.0 0.0 0.0
2 0.0 0.0 0.0 0.0
a b c d
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
a b c d
0 2.0 2.0 2.0 2.0
1 2.0 2.0 2.0 2.0
2 2.0 2.0 2.0 2.0
a b c d
0 0.0 0.0 0.0 0.0
1 0.0 0.0 0.0 0.0
2 0.0 0.0 0.0 0.0
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
0 2.0 2.0 2.0 2.0
1 2.0 2.0 2.0 2.0
2 2.0 2.0 2.0 2.0
a b c d
0 0.0 0.0 0.0 0.0
1 0.0 0.0 0.0 0.0
2 0.0 0.0 0.0 0.0
3 1.0 1.0 1.0 1.0
4 1.0 1.0 1.0 1.0
5 1.0 1.0 1.0 1.0
6 2.0 2.0 2.0 2.0
7 2.0 2.0 2.0 2.0
8 2.0 2.0 2.0 2.0
df0 = pd.dataframe(np.ones((3, 4)) * 0, columns=['a', 'b', 'c', 'd']) df1 = pd.dataframe(np.ones((3, 4)) * 1, columns=['e', 'f', 'c', 'd']) res = pd.concat([df0, df1], ignore_index=true) print(res);print() res = pd.concat([df0, df1], join='outer', ignore_index=true) print(res);print() res = pd.concat([df0, df1], join='inner',ignore_index=true) print(res);print()
a b c d e f
0 0.0 0.0 0.0 0.0 nan nan
1 0.0 0.0 0.0 0.0 nan nan
2 0.0 0.0 0.0 0.0 nan nan
3 nan nan 1.0 1.0 1.0 1.0
4 nan nan 1.0 1.0 1.0 1.0
5 nan nan 1.0 1.0 1.0 1.0
a b c d e f
0 0.0 0.0 0.0 0.0 nan nan
1 0.0 0.0 0.0 0.0 nan nan
2 0.0 0.0 0.0 0.0 nan nan
3 nan nan 1.0 1.0 1.0 1.0
4 nan nan 1.0 1.0 1.0 1.0
5 nan nan 1.0 1.0 1.0 1.0
c d
0 0.0 0.0
1 0.0 0.0
2 0.0 0.0
3 1.0 1.0
4 1.0 1.0
5 1.0 1.0
#横向合并 df0 = pd.dataframe(np.ones((3, 4)) * 0, index=['1', '2', '3'], columns=['a', 'b', 'c', 'd']) df1 = pd.dataframe(np.ones((3, 4)) * 1, index=['2', '3', '4'], columns=['a', 'b', 'c', 'd']) print(df0);print() print(df1);print() res = pd.concat([df0, df1], axis=1) print(res);print() res = pd.concat([df0, df1], axis=1, join='inner', ignore_index=true) print(res);print() res = pd.concat([df0, df1], axis=1, join_axes=[df0.index]) print(res);print()
a b c d
1 0.0 0.0 0.0 0.0
2 0.0 0.0 0.0 0.0
3 0.0 0.0 0.0 0.0
a b c d
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
a b c d a b c d
1 0.0 0.0 0.0 0.0 nan nan nan nan
2 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0
3 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0
4 nan nan nan nan 1.0 1.0 1.0 1.0
0 1 2 3 4 5 6 7
2 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0
3 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0
a b c d a b c d
1 0.0 0.0 0.0 0.0 nan nan nan nan
2 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0
3 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0
df0 = pd.dataframe(np.ones((3, 4)) * 0, index=['1', '2', '3'], columns=['a', 'b', 'c', 'd']) df1 = pd.dataframe(np.ones((3, 4)) * 1, index=['2', '3', '4'], columns=['a', 'b', 'c', 'd']) print(df0);print() print(df1);print() res = df0.append([df1, df1], ignore_index=false) print(res);print() s = pd.series([1,2,3,4], index=['a','b','c','e']) print(df0.append(s, ignore_index=true))
a b c d
1 0.0 0.0 0.0 0.0
2 0.0 0.0 0.0 0.0
3 0.0 0.0 0.0 0.0
a b c d
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
a b c d
1 0.0 0.0 0.0 0.0
2 0.0 0.0 0.0 0.0
3 0.0 0.0 0.0 0.0
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
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
a b c d e
0 0.0 0.0 0.0 0.0 nan
1 0.0 0.0 0.0 0.0 nan
2 0.0 0.0 0.0 0.0 nan
3 1.0 2.0 3.0 nan 4.0
df1 = pd.dataframe({'key':['k0', 'k1', 'k2'],
'a':['a0', 'a1', 'a2'],
'b':['b0', 'b1', 'b2']})
df2 = pd.dataframe({'key':['k3', 'k1', 'k2'],
'c':['c3', 'c1', 'c2'],
'd':['d3', 'd1', 'd2']})
print(df1); print()
print(df2); print()
res = pd.merge(df1, df2, on='key')
print(res); print()
res = pd.merge(df1, df2, on='key', how='outer')
print(res); print()
res = pd.merge(df1, df2, on='key', how='left')
print(res); print()
res = pd.merge(df1, df2, on='key', how='right')
print(res); print()
a b key
0 a0 b0 k0
1 a1 b1 k1
2 a2 b2 k2
c d key
0 c3 d3 k3
1 c1 d1 k1
2 c2 d2 k2
a b key c d
0 a1 b1 k1 c1 d1
1 a2 b2 k2 c2 d2
a b key c d
0 a0 b0 k0 nan nan
1 a1 b1 k1 c1 d1
2 a2 b2 k2 c2 d2
3 nan nan k3 c3 d3
a b key c d
0 a0 b0 k0 nan nan
1 a1 b1 k1 c1 d1
2 a2 b2 k2 c2 d2
a b key c d
0 a1 b1 k1 c1 d1
1 a2 b2 k2 c2 d2
2 nan nan k3 c3 d3
df1 = pd.dataframe({'key1':['k0', 'k0', 'k1'],
'key2':['k0', 'k1', 'k1'],
'a':['a0', 'a1', 'a2'],
'b':['b0', 'b1', 'b2']})
df2 = pd.dataframe({'key1':['k0', 'k0', 'k1', 'k2'],
'key2':['k0', 'k0', 'k1', 'k2'],
'c':['c3', 'c1', 'c2', 'c4'],
'd':['d3', 'd1', 'd2', 'd4']})
print(df1); print()
print(df2); print()
res = pd.merge(df1, df2, on=['key1','key2'])
print(res); print()
res = pd.merge(df1, df2, on=['key1','key2'], how='outer', indicator='indi')
print(res); print()
a b key1 key2
0 a0 b0 k0 k0
1 a1 b1 k0 k1
2 a2 b2 k1 k1
c d key1 key2
0 c3 d3 k0 k0
1 c1 d1 k0 k0
2 c2 d2 k1 k1
3 c4 d4 k2 k2
a b key1 key2 c d
0 a0 b0 k0 k0 c3 d3
1 a0 b0 k0 k0 c1 d1
2 a2 b2 k1 k1 c2 d2
a b key1 key2 c d indi
0 a0 b0 k0 k0 c3 d3 both
1 a0 b0 k0 k0 c1 d1 both
2 a1 b1 k0 k1 nan nan left_only
3 a2 b2 k1 k1 c2 d2 both
4 nan nan k2 k2 c4 d4 right_only
#以上是根据值合并。下面根据index合并
df1 = pd.dataframe({'a':['a0', 'a1', 'a2'],
'b':['b0', 'b1', 'b2']},
index=['index0', 'index1', 'index2'])
df2 = pd.dataframe({'a':['c3', 'c1', 'c2'],
'd':['d3', 'd1', 'd2']},
index=['index3', 'index1', 'index2'])
print(df1); print()
print(df2); print()
res = pd.merge(df1, df2, left_index=true, right_index=true)
print(res); print()
res = pd.merge(df1, df2, left_index=true, right_index=true, how='outer', suffixes=['_b', '_g'])
print(res); print()
a b
index0 a0 b0
index1 a1 b1
index2 a2 b2
a d
index3 c3 d3
index1 c1 d1
index2 c2 d2
a_x b a_y d
index1 a1 b1 c1 d1
index2 a2 b2 c2 d2
a_b b a_g d
index0 a0 b0 nan nan
index1 a1 b1 c1 d1
index2 a2 b2 c2 d2
index3 nan nan c3 d3
res = df1.join(df2, how='outer', lsuffix='_left', rsuffix='_right') #不用on默认用索引合并 print(res);print() res = df1.join(df2, on='b', how='outer', lsuffix='_left', rsuffix='_right') #用on指定df1的某列和df2的索引合并 print(res);print()
a_left b a_right d
index0 a0 b0 nan nan
index1 a1 b1 c1 d1
index2 a2 b2 c2 d2
index3 nan nan c3 d3
a_left b a_right d
index0 a0 b0 nan nan
index1 a1 b1 nan nan
index2 a2 b2 nan nan
index2 nan index3 c3 d3
index2 nan index1 c1 d1
index2 nan index2 c2 d2
import numpy as np import pandas as pd import matplotlib.pyplot as plt #画图模块 s = pd.series(np.random.randn(1000), index=np.arange(1000)) s = s.cumsum() #须在命令行执行， jupyter会报错 #s.plot() #plt.show() df = pd.dataframe(np.random.randn(1000, 3), columns=['a', 'b', 'c']) df = df.cumsum() print(df.head()); print() #head默认显示前5行 #须在命令行执行， jupyter会报错 #s.plot() #plt.show() #须在命令行执行， jupyter会报错 #'bar', 'hist', 'box', 'kde', 'area', 'scatter', 'hexbin', 'pie'... #class_b = df.plot.scatter(x='a', y='b', color='darkblue', label='class b') #画图，scatter<散点图> #df.plot.scatter(x='a', y='c', color='darkred', label='class c', class_b=class_b) #plt.show()
a b c
0 -0.399363 -1.004210 0.641141
1 -1.970009 -0.608482 -0.758504
2 -3.081640 -0.617352 -1.143872
3 -2.174627 -1.383785 -1.011411
4 -1.415515 -1.892226 -2.511739
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