Q: How to subtract one dataframe from another? First, let me set the stage.
I start with a pandas dataframe klmn, that looks like this:
In [15]: klmn
Out[15]: 
    K  L         M   N
0   0  a -1.374201  35
1   0  b  1.415697  29
2   0  a  0.233841  18
3   0  b  1.550599  30
4   0  a -0.178370  63
5   0  b -1.235956  42
6   0  a  0.088046   2
7   0  b  0.074238  84
8   1  a  0.469924  44
9   1  b  1.231064  68
10  2  a -0.979462  73
11  2  b  0.322454  97

Next I split klmn into two dataframes, klmn0 and klmn1, according to the value in the 'K' column:
In [16]: k0 = klmn.groupby(klmn['K'] == 0)
In [17]: klmn0, klmn1 = [klmn.ix[k0.indices[tf]] for tf in (True, False)]
In [18]: klmn0, klmn1
Out[18]: 
(   K  L         M   N
0  0  a -1.374201  35
1  0  b  1.415697  29
2  0  a  0.233841  18
3  0  b  1.550599  30
4  0  a -0.178370  63
5  0  b -1.235956  42
6  0  a  0.088046   2
7  0  b  0.074238  84,
     K  L         M   N
8   1  a  0.469924  44
9   1  b  1.231064  68
10  2  a -0.979462  73
11  2  b  0.322454  97)

Finally, I compute the mean of the M column in klmn0, grouped by the value in the L column:
In [19]: m0 = klmn0.groupby('L')['M'].mean(); m0
Out[19]: 
L
a   -0.307671
b    0.451144
Name: M

Now, my question is, how can I subtract m0 from the M column of the klmn1 sub-dataframe, respecting the value in the L column?  (By this I mean that m0['a'] gets subtracted from the M column of each row in klmn1 that has 'a' in the L column, and likewise for m0['b'].)
One could imagine doing this in a way that replaces the the values in the M column of klmn1 with the new values (after subtracting the value from m0).  Alternatively, one could imagine doing this in a way that leaves klmn1 unchanged, and instead produces a new dataframe klmn11 with an updated M column.  I'm interested in both approaches.

A: If you reset the index of your klmn1 dataframe to be that of the column L, then your dataframe will automatically align the indices with any series you subtract from it:
In [1]: klmn1.set_index('L')['M'] - m0
Out[1]:
L
a    0.777595
a   -0.671791
b    0.779920
b   -0.128690
Name: M


A: Option #1:
df1.subtract(df2, fill_value=0) 

Option #2:
df1.subtract(df2, fill_value=None) 

