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算术和广播

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当对两个Series或者DataFrame对象进行算术运算的时候,返回的结果是两个对象的并集。如果存在某个索引不匹配时,将以缺失值NaN的方式体现,并对以后的操作产生影响。这类似数据库的外连接操作。

In [58]: s1 = pd.Series([4.2,2.6, 5.4, -1.9], index=list('acde'))

In [60]: s2 = pd.Series([-2.3, 1.2, 5.6, 7.2, 3.4], index= list('acefg'))

In [61]: s1
Out[61]:
a    4.2
c    2.6
d    5.4
e   -1.9
dtype: float64

In [62]: s2
Out[62]:
a   -2.3
c    1.2
e    5.6
f    7.2
g    3.4
dtype: float64

In [63]: s1+s2
Out[63]:
a    1.9
c    3.8
d    NaN
e    3.7
f    NaN
g    NaN
dtype: float64

In [64]: s1-s2
Out[64]:
a    6.5
c    1.4
d    NaN
e   -7.5
f    NaN
g    NaN
dtype: float64

In [65]: s1* s2
Out[65]:
a    -9.66
c     3.12
d      NaN
e   -10.64
f      NaN
g      NaN
dtype: float64

In [66]: df1 = pd.DataFrame(np.arange(9).reshape(3,3),columns=list('bcd'),index=['one','two','three'])

In [67]: df2 = pd.DataFrame(np.arange(12).reshape(4,3),columns=list('bde'),index=['two','three','five','six'])

In [68]: df1
Out[68]:
       b  c  d
one    0  1  2
two    3  4  5
three  6  7  8

In [69]: df2
Out[69]:
       b   d   e
two    0   1   2
three  3   4   5
five   6   7   8
six    9  10  11

In [70]: df1 + df2
Out[70]:
         b   c     d   e
five   NaN NaN   NaN NaN
one    NaN NaN   NaN NaN
six    NaN NaN   NaN NaN
three  9.0 NaN  12.0 NaN
two    3.0 NaN   6.0 NaN

其实,在上述过程中,为了防止NaN对后续的影响,很多时候我们要使用一些填充值:

In [71]: df1.add(df2, fill_value=0)
Out[71]:
         b    c     d     e
five   6.0  NaN   7.0   8.0
one    0.0  1.0   2.0   NaN
six    9.0  NaN  10.0  11.0
three  9.0  7.0  12.0   5.0
two    3.0  4.0   6.0   2.0

In [74]: df1.reindex(columns=df2.columns, fill_value=0) # 也可以这么干
Out[74]:
       b  d  e
one    0  2  0
two    3  5  0
three  6  8  0

注意,这里填充的意思是,如果某一方有值,另一方没有的话,将没有的那方的值填充为指定的参数值。而不是在最终结果中,将所有的NaN替换为填充值。

类似add的方法还有:

  • add:加法
  • sub:减法
  • div:除法
  • floordiv:整除
  • mul:乘法
  • pow:幂次方

DataFrame也可以和Series进行操作,这类似于numpy中不同维度数组间的操作,其中将使用广播机制。我们先看看numpy中的机制:

In [75]: a = np.arange(12).reshape(3,4)

In [76]: a
Out[76]:
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

In [78]: a[0]   # 取a的第一行,这是一个一维数组
Out[78]: array([0, 1, 2, 3])

In [79]: a - a[0] # 二维数组减一维数组,在行方向上进行了广播
Out[79]:
array([[0, 0, 0, 0],
       [4, 4, 4, 4],
       [8, 8, 8, 8]])

DataFrame和Series之间的操作是类似的:

In [80]: df = pd.DataFrame(np.arange(12).reshape(4,3),columns=list('bde'),index=['one','two','three','four'])

In [81]: s = df.iloc[0]  # 取df的第一行生成一个Series

In [82]: df
Out[82]:
       b   d   e
one    0   1   2
two    3   4   5
three  6   7   8
four   9  10  11

In [83]: s
Out[83]:
b    0
d    1
e    2
Name: one, dtype: int32

In [84]: df - s # 减法会广播
Out[84]:
       b  d  e
one    0  0  0
two    3  3  3
three  6  6  6
four   9  9  9

In [85]: s2 = pd.Series(range(3), index=list('bef')) 

In [86]: df + s2  # 如果存在不匹配的列索引,则引入缺失值
Out[86]:
         b   d     e   f
one    0.0 NaN   3.0 NaN
two    3.0 NaN   6.0 NaN
three  6.0 NaN   9.0 NaN
four   9.0 NaN  12.0 NaN

In [87]: s3 = df['d'] # 取df的一列

In [88]: s3
Out[88]:
one       1
two       4
three     7
four     10
Name: d, dtype: int32

In [89]: df.sub(s3, axis='index')  # 指定按列进行广播
Out[89]:
       b  d  e
one   -1  0  1
two   -1  0  1
three -1  0  1
four  -1  0  1

在上面最后的例子中,我们通过axis='index'或者axis=0,在另外一个方向广播。


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