Arithmetic operations using scalar values will be applied to every element of a DataFrame. To demonstrate, we will use a DataFrame object initialized with random values:
In [94]: # set the seed to allow replicatable results np.random.seed(123456) # create the DataFrame df = pd.DataFrame(np.random.randn(5, 4), columns=['A', 'B', 'C', 'D']) df Out[94]: A B C D 0 0.469112 -0.282863 -1.509059 -1.135632 1 1.212112 -0.173215 0.119209 -1.044236 2 -0.861849 -2.104569 -0.494929 1.071804 3 0.721555 -0.706771 -1.039575 0.271860 4 -0.424972 0.567020 0.276232 -1.087401
By default, any arithmetic operation will be applied across all rows and columns of a DataFrame and will return a new DataFrame with the results (leaving the original unchanged):
In [95]: # multiply everything by 2 df * 2 Out[95]: A B C D 0 0.938225 -0.565727 -3.018117 -2.271265 1 2.424224 -0.346429 0.238417 -2.088472 2 -1.723698 -4.209138 -0.989859 2.143608 3 1.443110 -1.413542 -2.079150 0.543720 4 -0.849945 1.134041 0.552464 -2.174801
When performing an operation between a DataFrame and a Series, pandas will align the Series index along the DataFrame columns, performing what is referred to as a row-wise broadcast.
The following example retrieves the first row of the DataFrame, and then subtracts this from each row of the DataFrame. pandas is broadcasting the Series to each row of the DataFrame, which aligns each series item with the DataFrame item of the same index label and then applies the minus operator on the matched values:
In [96]: # get first row s = df.iloc[0] # subtract first row from every row of the DataFrame diff = df - s diff Out[96]: A B C D 0 0.000000 0.000000 0.000000 0.000000 1 0.743000 0.109649 1.628267 0.091396 2 -1.330961 -1.821706 1.014129 2.207436 3 0.252443 -0.423908 0.469484 1.407492 4 -0.894085 0.849884 1.785291 0.048232
This also works when reversing the order by subtracting the DataFrame to the Series object:
In [97]: # subtract DataFrame from Series diff2 = s - df diff2 Out[97]: A B C D 0 0.000000 0.000000 0.000000 0.000000 1 -0.743000 -0.109649 -1.628267 -0.091396 2 1.330961 1.821706 -1.014129 -2.207436 3 -0.252443 0.423908 -0.469484 -1.407492 4 0.894085 -0.849884 -1.785291 -0.048232
The set of columns returned will be the union of the labels in the index of both the series and the columns index of the DataFrame object. If a label representing the result column is not found in either the Series of the DataFrame object, then the values will be NaN filled. The following code demonstrates, by creating a Series with an index representing a subset of the column in the DataFrame, but also with an additional label:
In [98]: # B, C s2 = s[1:3] # add E s2['E'] = 0 # see how alignment is applied in math df + s2 Out[98]: A B C D E 0 NaN -0.565727 -3.018117 NaN NaN 1 NaN -0.456078 -1.389850 NaN NaN 2 NaN -2.387433 -2.003988 NaN NaN 3 NaN -0.989634 -2.548633 NaN NaN 4 NaN 0.284157 -1.232826 NaN NaN
pandas aligns the index labels of df with those of s2. Since s2 does not have an A or D label, the result contains NaN in those columns. Since df has no E label, it is also NaN.
An arithmetic operation between two DataFrame objects will align by both the column and index labels. The following extracts a small portion of df and subtracts it from df. The result demonstrates that the aligned values subtract to 0, while the others are set to NaN:
In [99]: # get rows 1 through three, and only B, C columns subframe = df[1:4][['B', 'C']] # we have extracted a little square in the middle of the df subframe Out[99]: B C 1 -0.173215 0.119209 2 -2.104569 -0.494929 1 -0.706771 -1.039575 In [100]: # demonstrate the alignment of the subtraction df - subframe Out[100]: A B C D 0 NaN NaN NaN NaN 1 NaN 0 0 NaN 2 NaN 0 0 NaN 3 NaN 0 0 NaN 2 NaN NaN NaN NaN
Additional control of an arithmetic operation can be gained using the arithmetic methods provided by the DataFrame object. These methods provide the specification of a specific axis. The following demonstrates performing subtraction along a column axis by using the DataFrame objects .sub() method, subtracting the A column from every column:
In [101]: # get the A column a_col = df['A'] df.sub(a_col, axis=0) Out[101]: A B C D 0 0 -0.751976 -1.978171 -1.604745 1 0 -1.385327 -1.092903 -2.256348 2 0 -1.242720 0.366920 1.933653 3 0 -1.428326 -1.761130 -0.449695 4 0 0.991993 0.701204 -0.662428