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：
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。