Python_Pandasベース
88845 ワード
Python_Pandasベース
By:
参考ブログ1参考ブログ_2参考ブログ_3 Pandasは、データ分析タスクを解決するために作成されたPythonのデータ分析パッケージです. Pandasは、大量のライブラリと標準データモデルを組み込み、データセットを効率的に操作するために必要なツールを提供します. Pandasは、データを迅速かつ容易に処理できる多くの関数と方法を提供しています. Pandasは辞書形式で、NumPyに基づいて作成され、NumPyを中心としたアプリケーションをより簡単にする Pandas取付
Pandas導入
データ構造 series DataFrame
Series
DataFrame
Pandas選択データ特定列のデータ を選択する.特定行のデータ を選択する.特定行and列のデータ を選択する.シーケンスiloc行番号に従って選択データ 条件判断による選別 マルチインデックス
a
b
c
d
one
73.506341
75.662735
74.675325
7.697207
two
73.055825
83.222481
4.777599
82.534340
three
89.156683
85.001712
47.443443
73.379189
four
95.648043
64.162408
26.731916
73.839172
特定の列のデータの選択
特定の行のデータの選択
特定の行and列のデータの選択
シーケンスiloc-行番号に基づいてデータを選択
条件判断による選別
マルチインデックス
Pandas設定データ
Pandasは損失データを処理する処理データ中のNaNデータ dropna()関数を使用してNaNの行または列を削除する fillna()関数を使用してNaN値 を置換 isnull()関数を用いてデータが失われたか否かを判断する .
処理データ中のNaNデータ
dropna()関数を使用してNaNの行または列を削除
Fillna()関数を使用してNaN値を置換
isnull()関数を使用して、データが失われたかどうかを判断します.
Pandasインポートエクスポート
Pandas連結データ axisマージ方向 joinマージ方式 append追加データ axisマージ方向
joinマージ方式
append追加データ
Pandasマージ一組のkeyに従って を合併するは2組のkeyに基づいて を合併する. Indicator合併 indexによる のマージ
一連のkeyに基づいてマージ
2組のkeyによるマージ
Indicatorマージ
indexによるマージ
By:
? 参考ブログ1参考ブログ_2参考ブログ_3
pip3 install pandas
Pandas導入
import pandas as pd # pandas pd
データ構造
Series
import numpy as np
import pandas as pd
s=pd.Series([1,2,3,np.nan,5,6])
print(s)#
0 1.0
1 2.0
2 3.0
3 NaN
4 5.0
5 6.0
dtype: float64
DataFrame
dates=pd.date_range('20180310',periods=6)
df = pd.DataFrame(np.random.randn(6,4), index=dates, columns=['A','B','C','D'])# 6 4
print(df)# 6 4
print(df['B'])
print("----------------
----------------")
# DataFrame
df_1=pd.DataFrame({'A' : 1.,
'B' : pd.Timestamp('20180310'),
'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'
})
print(df_1)
print(df_1.dtypes)
print(df_1.index)#
#Int64Index([0, 1, 2, 3], dtype='int64')
print(df_1.columns)#
print("----------------
----------------")
#Index(['A', 'B', 'C', 'D', 'E', 'F'], dtype='object')
print(df_1.values)#
print(df_1.describe())#
print(df_1.T)#
print("----------------
----------------")
print(df_1.sort_index(axis=1, ascending=False))#axis 1 ABCDEFG ascending
print(df_1.sort_values(by='E'))#
A B C D
2018-03-10 0.872767 2.188739 0.766781 -0.001429
2018-03-11 0.218740 -0.556263 -0.047700 0.470347
2018-03-12 -0.816785 0.479690 1.722349 1.116260
2018-03-13 0.988138 -0.025760 -0.971384 -0.558211
2018-03-14 -0.581776 1.021027 -1.280569 1.022587
2018-03-15 0.061455 -1.647589 -1.568288 -0.467407
2018-03-10 2.188739
2018-03-11 -0.556263
2018-03-12 0.479690
2018-03-13 -0.025760
2018-03-14 1.021027
2018-03-15 -1.647589
Freq: D, Name: B, dtype: float64
----------------
----------------
A B C D E F
0 1.0 2018-03-10 1.0 3 test foo
1 1.0 2018-03-10 1.0 3 train foo
2 1.0 2018-03-10 1.0 3 test foo
3 1.0 2018-03-10 1.0 3 train foo
A float64
B datetime64[ns]
C float32
D int32
E category
F object
dtype: object
Int64Index([0, 1, 2, 3], dtype='int64')
Index(['A', 'B', 'C', 'D', 'E', 'F'], dtype='object')
----------------
----------------
[[1.0 Timestamp('2018-03-10 00:00:00') 1.0 3 'test' 'foo']
[1.0 Timestamp('2018-03-10 00:00:00') 1.0 3 'train' 'foo']
[1.0 Timestamp('2018-03-10 00:00:00') 1.0 3 'test' 'foo']
[1.0 Timestamp('2018-03-10 00:00:00') 1.0 3 'train' 'foo']]
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 2018-03-10 00:00:00 2018-03-10 00:00:00 2018-03-10 00:00:00
C 1 1 1
D 3 3 3
E test train test
F foo foo foo
3
A 1
B 2018-03-10 00:00:00
C 1
D 3
E train
F foo
----------------
----------------
F E D C B A
0 foo test 3 1.0 2018-03-10 1.0
1 foo train 3 1.0 2018-03-10 1.0
2 foo test 3 1.0 2018-03-10 1.0
3 foo train 3 1.0 2018-03-10 1.0
A B C D E F
0 1.0 2018-03-10 1.0 3 test foo
2 1.0 2018-03-10 1.0 3 test foo
1 1.0 2018-03-10 1.0 3 train foo
3 1.0 2018-03-10 1.0 3 train foo
Pandas選択データ
df = pd.DataFrame(np.random.rand(16).reshape(4,4)*100,
index = ['one','two','three','four'],
columns = ['a','b','c','d'])
df
a
b
c
d
one
73.506341
75.662735
74.675325
7.697207
two
73.055825
83.222481
4.777599
82.534340
three
89.156683
85.001712
47.443443
73.379189
four
95.648043
64.162408
26.731916
73.839172
特定の列のデータの選択
#
print(df["a"])
print("----------------
----------------")
#
print(df[["a","b"]])
print("----------------
----------------")
# _
print(df.loc[:,"b":"d"])
one 73.506341
two 73.055825
three 89.156683
four 95.648043
Name: a, dtype: float64
----------------
----------------
a b
one 73.506341 75.662735
two 73.055825 83.222481
three 89.156683 85.001712
four 95.648043 64.162408
----------------
----------------
b c d
one 75.662735 74.675325 7.697207
two 83.222481 4.777599 82.534340
three 85.001712 47.443443 73.379189
four 64.162408 26.731916 73.839172
特定の行のデータの選択
#
print(df.loc["one"])
print("----------------
----------------")
#
print(df.loc[["one","two"]])
print("----------------
----------------")
# _
print(df[0:3])
print(df['one':'three'])
a 73.506341
b 75.662735
c 74.675325
d 7.697207
Name: one, dtype: float64
----------------
----------------
a b c d
one 73.506341 75.662735 74.675325 7.697207
two 73.055825 83.222481 4.777599 82.534340
----------------
----------------
a b c d
one 73.506341 75.662735 74.675325 7.697207
two 73.055825 83.222481 4.777599 82.534340
three 89.156683 85.001712 47.443443 73.379189
a b c d
one 73.506341 75.662735 74.675325 7.697207
two 73.055825 83.222481 4.777599 82.534340
three 89.156683 85.001712 47.443443 73.379189
特定の行and列のデータの選択
# and
print(df.loc["one","a"])
print("----------------
----------------")
# and
print(df.loc['one', ['a','c']])
print(df.loc[['one','three'],["a","b","c"]])
print("----------------
----------------")
# and _
print(df.loc["one":"three","b":"c"])
73.50634055308014
----------------
----------------
a 73.506341
c 74.675325
Name: one, dtype: float64
a b c
one 73.506341 75.662735 74.675325
three 89.156683 85.001712 47.443443
----------------
----------------
b c
one 75.662735 74.675325
two 83.222481 4.777599
three 85.001712 47.443443
シーケンスiloc-行番号に基づいてデータを選択
#
print(df.iloc[0])
print("----------------
----------------")
#
print(df.iloc[[0,3]])
print("----------------
----------------")
# _
print(df.iloc[1:3])
print("----------------
----------------")
# and
print(df.iloc[3,1])#
print("----------------
----------------")
# and
print(df.iloc[[1,2,3],[0,2]])# ，
print("----------------
----------------")
#
print(df.iloc[2:4,0:2]) #
a 73.506341
b 75.662735
c 74.675325
d 7.697207
Name: one, dtype: float64
----------------
----------------
a b c d
one 73.506341 75.662735 74.675325 7.697207
four 95.648043 64.162408 26.731916 73.839172
----------------
----------------
a b c d
two 73.055825 83.222481 4.777599 82.534340
three 89.156683 85.001712 47.443443 73.379189
----------------
----------------
64.1624082303679
----------------
----------------
a c
two 73.055825 4.777599
three 89.156683 47.443443
four 95.648043 26.731916
----------------
----------------
a b
three 89.156683 85.001712
four 95.648043 64.162408
条件判断による選別
#
print(df[df["a"] > 0])# df.A 0
print("----------------
----------------")
#
print(df[df[["a","b"]]>0])
a b c d
one 73.506341 75.662735 74.675325 7.697207
two 73.055825 83.222481 4.777599 82.534340
three 89.156683 85.001712 47.443443 73.379189
four 95.648043 64.162408 26.731916 73.839172
a b c d
one 73.506341 75.662735 NaN NaN
two 73.055825 83.222481 NaN NaN
three 89.156683 85.001712 NaN NaN
four 95.648043 64.162408 NaN NaN
マルチインデックス
print(df['a'].loc[['one','three']]) # a one，three
print("----------------
----------------")
print(df[['b','c','d']].iloc[::2]) # b，c，d one，three
print("----------------
----------------")
print(df[df['a'] < 50].iloc[:2]) #
print("----------------
----------------")
print(df[df < 50][['a','b']])
one 73.506341
three 89.156683
Name: a, dtype: float64
----------------
----------------
b c d
one 75.662735 74.675325 7.697207
three 85.001712 47.443443 73.379189
----------------
----------------
Empty DataFrame
Columns: [a, b, c, d]
Index: []
----------------
----------------
a b
one NaN NaN
two NaN NaN
three NaN NaN
four NaN NaN
Pandas設定データ
dates = pd.date_range('20180310', periods=6)
df = pd.DataFrame(np.arange(24).reshape((6,4)), index=dates, columns=['A', 'B', 'C', 'D'])
print(df)
'''
A B C D
2018-03-10 0 1 2 3
2018-03-11 4 5 6 7
2018-03-12 8 9 1111 11
2018-03-13 12 13 14 15
2018-03-14 16 17 18 19
2018-03-15 20 21 22 23
'''
df.iloc[2,2] = 999#
df.loc['2018-03-13', 'D'] = 999
print(df)
A B C D
2018-03-10 0 1 2 3
2018-03-11 4 5 6 7
2018-03-12 8 9 10 11
2018-03-13 12 13 14 15
2018-03-14 16 17 18 19
2018-03-15 20 21 22 23
A B C D
2018-03-10 0 1 2 3
2018-03-11 4 5 6 7
2018-03-12 8 9 999 11
2018-03-13 12 13 14 999
2018-03-14 16 17 18 19
2018-03-15 20 21 22 23
df[df.A>10]=999# df.A 10
print(df)
A B C D
2018-03-10 0 1 2 3
2018-03-11 4 5 6 7
2018-03-12 8 9 999 11
2018-03-13 999 999 999 999
2018-03-14 999 999 999 999
2018-03-15 999 999 999 999
df['F']=np.nan
print(df)
A B C D F
2018-03-10 0 1 2 3 NaN
2018-03-11 4 5 6 7 NaN
2018-03-12 8 9 999 11 NaN
2018-03-13 999 999 999 999 NaN
2018-03-14 999 999 999 999 NaN
2018-03-15 999 999 999 999 NaN
df['E'] = pd.Series([1,2,3,4,5,6], index=pd.date_range('20180310', periods=6))#
print(df)
A B C D E
2018-03-10 0 1 2 3 1
2018-03-11 4 5 6 7 2
2018-03-12 8 9 999 11 3
2018-03-13 12 13 14 999 4
2018-03-14 16 17 18 19 5
2018-03-15 20 21 22 23 6
Pandasは損失データを処理する
処理データ中のNaNデータ
dates = pd.date_range('20180310', periods=6)
df = pd.DataFrame(np.arange(24).reshape((6,4)), index=dates, columns=['A', 'B', 'C', 'D'])
df.iloc[0,1]=np.nan
df.iloc[1]=np.nan
print(df)
A B C D
2018-03-10 0.0 NaN 2.0 3.0
2018-03-11 NaN NaN NaN NaN
2018-03-12 8.0 9.0 10.0 11.0
2018-03-13 12.0 13.0 14.0 15.0
2018-03-14 16.0 17.0 18.0 19.0
2018-03-15 20.0 21.0 22.0 23.0
dropna()関数を使用してNaNの行または列を削除
#0 1
#any: NaN drop
#all: NaN drop
print(df.dropna(axis=0,how='any'))
print(df.dropna(axis=0,how='all'))
A B C D
2018-03-10 0.872767 2.188739 0.766781 -0.001429
2018-03-11 0.218740 -0.556263 -0.047700 0.470347
2018-03-12 -0.816785 0.479690 1.722349 1.116260
2018-03-13 0.988138 -0.025760 -0.971384 -0.558211
2018-03-14 -0.581776 1.021027 -1.280569 1.022587
2018-03-15 0.061455 -1.647589 -1.568288 -0.467407
A B C D
2018-03-10 0.872767 2.188739 0.766781 -0.001429
2018-03-11 0.218740 -0.556263 -0.047700 0.470347
2018-03-12 -0.816785 0.479690 1.722349 1.116260
2018-03-13 0.988138 -0.025760 -0.971384 -0.558211
2018-03-14 -0.581776 1.021027 -1.280569 1.022587
2018-03-15 0.061455 -1.647589 -1.568288 -0.467407
Fillna()関数を使用してNaN値を置換
print(df.fillna(value=233))# NaN 0
A B C D
2018-03-10 0.0 233.0 2.0 3.0
2018-03-11 233.0 233.0 233.0 233.0
2018-03-12 8.0 9.0 10.0 11.0
2018-03-13 12.0 13.0 14.0 15.0
2018-03-14 16.0 17.0 18.0 19.0
2018-03-15 20.0 21.0 22.0 23.0
isnull()関数を使用して、データが失われたかどうかを判断します.
print(pd.isnull(df))# nan ture nan false
print("----------------
----------------")
print(np.any(df.isnull()))# NaN
#True
A B C D
2018-03-10 False True False False
2018-03-11 True True True True
2018-03-12 False False False False
2018-03-13 False False False False
2018-03-14 False False False False
2018-03-15 False False False False
----------------
----------------
True
Pandasインポートエクスポート
data=pd.read_csv('test1.csv')# csv
data.to_pickle('test2.pickle')# pickle
#
Pandas連結データ
df1 = pd.DataFrame(np.ones((3,4))*0, columns=['a','b','c','d'])
df2 = pd.DataFrame(np.ones((3,4))*1, columns=['a','b','c','d'])
df3 = pd.DataFrame(np.ones((3,4))*2, columns=['a','b','c','d'])
res = pd.concat([df1, df2, df3], axis=0, ignore_index=True)
#0 1 ingnore_index index index 0 1 2 3 4 5 6 7 8
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
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
joinマージ方式
df1 = pd.DataFrame(np.ones((3,4))*0, columns=['a','b','c','d'], index=[1,2,3])
df2 = pd.DataFrame(np.ones((3,4))*1, columns=['b','c','d', 'e'], index=[2,3,4])
print(df1)
print(df2)
print("----------------
----------------")
# ,join='outer'
res=pd.concat([df1,df2],axis=1,join='outer')
print(res)
print("----------------
----------------")
# ,join='inner'
res=pd.concat([df1,df2],axis=1,join='inner')
print(res)
print("----------------
----------------")
# df1 df2 NaN
res=pd.concat([df1,df2],axis=1,join_axes=[df1.index])
print(res)
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
b c d e
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 b c d e
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
----------------
----------------
a b c d b c d e
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 b c d e
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
append追加データ
df1 = pd.DataFrame(np.ones((3,4))*0, columns=['a','b','c','d'])
df2 = pd.DataFrame(np.ones((3,4))*1, columns=['a','b','c','d'])
s1 = pd.Series([1,2,3,4], index=['a','b','c','d'])
print(s1)
print("----------------
----------------")
# df2 df1 index
res=df1.append(df2,ignore_index=True)
print(res)
print("----------------
----------------")
# s1 df1 index
res=df1.append(s1,ignore_index=True)
print(res)
a 1
b 2
c 3
d 4
dtype: int64
----------------
----------------
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
----------------
----------------
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 2.0 3.0 4.0
Pandasマージ
一連のkeyに基づいてマージ
left = pd.DataFrame({'key': ['K0', 'K1', 'K2', 'K3'],
'A': ['A0', 'A1', 'A2', 'A3'],
'B': ['B0', 'B1', 'B2', 'B3']})
print(left)
print("----------------
----------------")
right = pd.DataFrame({'key': ['K0', 'K1', 'K2', 'K3'],
'C': ['C0', 'C1', 'C2', 'C3'],
'D': ['D0', 'D1', 'D2', 'D3']})
print(right)
print("----------------
----------------")
res=pd.merge(left,right,on='key')
print(res)
key A B
0 K0 A0 B0
1 K1 A1 B1
2 K2 A2 B2
3 K3 A3 B3
----------------
----------------
key C D
0 K0 C0 D0
1 K1 C1 D1
2 K2 C2 D2
3 K3 C3 D3
----------------
----------------
key A B C D
0 K0 A0 B0 C0 D0
1 K1 A1 B1 C1 D1
2 K2 A2 B2 C2 D2
3 K3 A3 B3 C3 D3
2組のkeyによるマージ
left = pd.DataFrame({'key1': ['K0', 'K0', 'K1', 'K2'],
'key2': ['K0', 'K1', 'K0', 'K1'],
'A': ['A0', 'A1', 'A2', 'A3'],
'B': ['B0', 'B1', 'B2', 'B3']})
print(left)
print("----------------
----------------")
right = pd.DataFrame({'key1': ['K0', 'K1', 'K1', 'K2'],
'key2': ['K0', 'K0', 'K0', 'K0'],
'C': ['C0', 'C1', 'C2', 'C3'],
'D': ['D0', 'D1', 'D2', 'D3']})
print(right)
print("----------------
----------------")
#
res=pd.merge(left,right,on=['key1','key2'],how='inner')
print(res)
print("----------------
----------------")
#
res=pd.merge(left,right,on=['key1','key2'],how='outer')
print(res)
print("----------------
----------------")
#
res=pd.merge(left,right,on=['key1','key2'],how='left')
print(res)
print("----------------
----------------")
#
res=pd.merge(left,right,on=['key1','key2'],how='right')
print(res)
key1 key2 A B
0 K0 K0 A0 B0
1 K0 K1 A1 B1
2 K1 K0 A2 B2
3 K2 K1 A3 B3
----------------
----------------
key1 key2 C D
0 K0 K0 C0 D0
1 K1 K0 C1 D1
2 K1 K0 C2 D2
3 K2 K0 C3 D3
----------------
----------------
key1 key2 A B C D
0 K0 K0 A0 B0 C0 D0
1 K1 K0 A2 B2 C1 D1
2 K1 K0 A2 B2 C2 D2
----------------
----------------
key1 key2 A B C D
0 K0 K0 A0 B0 C0 D0
1 K0 K1 A1 B1 NaN NaN
2 K1 K0 A2 B2 C1 D1
3 K1 K0 A2 B2 C2 D2
4 K2 K1 A3 B3 NaN NaN
5 K2 K0 NaN NaN C3 D3
----------------
----------------
key1 key2 A B C D
0 K0 K0 A0 B0 C0 D0
1 K0 K1 A1 B1 NaN NaN
2 K1 K0 A2 B2 C1 D1
3 K1 K0 A2 B2 C2 D2
4 K2 K1 A3 B3 NaN NaN
----------------
----------------
key1 key2 A B C D
0 K0 K0 A0 B0 C0 D0
1 K1 K0 A2 B2 C1 D1
2 K1 K0 A2 B2 C2 D2
3 K2 K0 NaN NaN C3 D3
Indicatorマージ
df1 = pd.DataFrame({'col1':[0,1], 'col_left':['a','b']})
print(df1)
df2 = pd.DataFrame({'col1':[1,2,2],'col_right':[2,2,2]})
print(df2)
print("----------------
----------------")
# col1 indicator=True
res=pd.merge(df1,df2,on='col1',how='outer',indicator=True)
print(res)
print("----------------
----------------")
# indicator column
res = pd.merge(df1, df2, on='col1', how='outer', indicator='indicator_column')
print(res)
col1 col_left
0 0 a
1 1 b
col1 col_right
0 1 2
1 2 2
2 2 2
----------------
----------------
col1 col_left col_right _merge
0 0 a NaN left_only
1 1 b 2.0 both
2 2 NaN 2.0 right_only
3 2 NaN 2.0 right_only
----------------
----------------
col1 col_left col_right indicator_column
0 0 a NaN left_only
1 1 b 2.0 both
2 2 NaN 2.0 right_only
3 2 NaN 2.0 right_only
indexによるマージ
left = pd.DataFrame({'A': ['A0', 'A1', 'A2'],
'B': ['B0', 'B1', 'B2']},
index=['K0', 'K1', 'K2'])
print(left)
right = pd.DataFrame({'C': ['C0', 'C2', 'C3'],
'D': ['D0', 'D2', 'D3']},
index=['K0', 'K2', 'K3'])
print(right)
print("----------------
----------------")
# index
res=pd.merge(left,right,left_index=True,right_index=True,how='outer')
print(res)
print("----------------
----------------")
res=pd.merge(left,right,left_index=True,right_index=True,how='inner')
print(res)
A B
K0 A0 B0
K1 A1 B1
K2 A2 B2
C D
K0 C0 D0
K2 C2 D2
K3 C3 D3
----------------
----------------
A B C D
K0 A0 B0 C0 D0
K1 A1 B1 NaN NaN
K2 A2 B2 C2 D2
K3 NaN NaN C3 D3
----------------
----------------
A B C D
K0 A0 B0 C0 D0
K2 A2 B2 C2 D2