Arithmetic and aligning DataFrames with same columns, different index levels

Question

I have two pandas DataFrames - weight has a simple Index on a Land Use columns. concentration has a MultiIndex on Land Use and Parameter.

import pandas
from io import StringIO

conc_string = StringIO("""\
Land Use,Parameter,1E,1N,1S,2
Airfield,BOD5 (mg/l),0.418,0.118,0.226,1.063
Airfield,Ortho P (mg/l),0.002,0.001,0.001,0.002
Airfield,TSS (mg/l),1.773,11.47,0.862,0.183
Airfield,Zn (mg/l),0.001,0.001,4.95E-05,0.001
"Commercial",BOD5 (mg/l),0.036,0.0419,,0.315
"Commercial",Cu (mg/l),4.37E-05,7.34E-05,,0.00039
"Commercial",O&G (mg/l),0.0385,0.127,,0.263
Open Space,TSS (mg/l),0.371,3.01,1.209,0.147
Open Space,Zn (mg/l),0.0127,0.0069,0.0132,0.007
"Parking Lot",BOD5 (mg/l),0.924,0.0668,2.603,3.19
"Parking Lot",O&G (mg/l),1.02,0.149,1.347,1.88
"Rooftops",BOD5 (mg/l),0.135,1.00,0.0562,0.310""")

weight_string = StringIO("""\
Land Use,1E,1N,1S,2
Airfield,0.511,0.0227,0.0616,0.394
Commercial,0.0005,0.1704,0,0.1065
Open Space,0.0008,0.005,0.0002,0.0004
"Parking Lot",0.33,0.514,0.252,0.171
Rooftops,0.081,0.028,8.50E-05,0.003""")

concentration = pandas.read_csv(conc_string, index_col=[0,1])
weight = pandas.read_csv(weight_string, index_col=0)

In this case, the columns (1E, 1N, 1S, and 2) are drainage basins.

What I would like to do is divide all of the concentrations independent of Parameter by the weights where the basin (column names) and Land Use.

I'm not having much luck here. concentration / weight certainly does't work. I'm not having much luck stacking the dataframes and joining either

wstk = pandas.DataFrame(weight.stack())
wstk.index.names = ['Land Use', 'Basin']
wstk.rename(columns={0:'weight'}, inplace=True)

cstk = pandas.DataFrame(concentration.stack())
cstk.index.names = ['Land Use', 'Parameter', 'Basin']
cstk.rename(columns={0:'concentration'}, inplace=True)

wstk.join(cstk, on=['Land Use', 'Basin']) # fails 
cstk.join(wstk, on=['Land Use', 'Basin']) # fails 

The last two lines don't raise an error when I leave off the on kwarg, but return NaN results for the joined column. They also fail if I drop the index on both stacked DataFrames (e.g., do wstk.reset_index(inplace=True) before the join).

Any suggestions?

Answer 1

Use the DataFrame div method and pass matchkey for the multi-index you want to broadcast across:

From the documentation for div:

level : int or name
    Broadcast across a level, matching Index values on the
    passed MultiIndex level

In [39]: concentration.div(weight, level='Land Use')
Out[39]:
                                    1E          1N           1S           2
Land Use    Parameter
Airfield    BOD5 (mg/l)       0.818004    5.198238     3.668831    2.697970
            Ortho P (mg/l)    0.003914    0.044053     0.016234    0.005076
            TSS (mg/l)        3.469667  505.286344    13.993506    0.464467
            Zn (mg/l)         0.001957    0.044053     0.000804    0.002538
Commercial  BOD5 (mg/l)      72.000000    0.245892          NaN    2.957746
            Cu (mg/l)         0.087400    0.000431          NaN    0.003662
            O&G (mg/l)       77.000000    0.745305          NaN    2.469484
Open Space  TSS (mg/l)      463.750000  602.000000  6045.000000  367.500000
            Zn (mg/l)        15.875000    1.380000    66.000000   17.500000
Parking Lot BOD5 (mg/l)       2.800000    0.129961    10.329365   18.654971
            O&G (mg/l)        3.090909    0.289883     5.345238   10.994152
Rooftops    BOD5 (mg/l)       1.666667   35.714286   661.176471  103.333333