Mean of a correlation matrix - pandas data fram

Question

I have a large correlation matrix in a pandas python DataFrame: df (342, 342).

How do I take the mean, sd, etc. of all of the numbers in the upper triangle not including the 1's along the diagonal?

Thank you.

Answer 1

Another potential one line answer:

In [1]: corr
Out[1]:
          a         b         c         d         e
a  1.000000  0.022246  0.018614  0.022592  0.008520
b  0.022246  1.000000  0.033029  0.049714 -0.008243
c  0.018614  0.033029  1.000000 -0.016244  0.049010
d  0.022592  0.049714 -0.016244  1.000000 -0.015428
e  0.008520 -0.008243  0.049010 -0.015428  1.000000

In [2]: corr.values[np.triu_indices_from(corr.values,1)].mean()
Out[2]: 0.016381

Edit: added performance metrics

Performance of my solution:

In [3]: %timeit corr.values[np.triu_indices_from(corr.values,1)].mean()
10000 loops, best of 3: 48.1 us per loop

Performance of Theodros Zelleke's one-line solution:

In [4]: %timeit corr.unstack().ix[zip(*np.triu_indices_from(corr, 1))].mean()
1000 loops, best of 3: 823 us per loop

Performance of DSM's solution:

In [5]: def method1(df):
   ...:     df2 = df.copy()
   ...:     df2.values[np.tril_indices_from(df2)] = np.nan
   ...:     return df2.unstack().mean()
   ...:

In [5]: %timeit method1(corr)
1000 loops, best of 3: 242 us per loop

Answer 2

This is kind of fun. I make no guarantees that this is the real pandas-fu; I'm still at the "numpy + better indexing" stage of learning pandas myself. That said, something like this should get the job done.

First, we make a toy correlation matrix to play with:

>>> import pandas as pd
>>> import numpy as np
>>> frame = pd.DataFrame(np.random.randn(1000, 5), columns=['a', 'b', 'c', 'd', 'e'])
>>> corr = frame.corr()
>>> corr
          a         b         c         d         e
a  1.000000  0.022246  0.018614  0.022592  0.008520
b  0.022246  1.000000  0.033029  0.049714 -0.008243
c  0.018614  0.033029  1.000000 -0.016244  0.049010
d  0.022592  0.049714 -0.016244  1.000000 -0.015428
e  0.008520 -0.008243  0.049010 -0.015428  1.000000

Then we make a copy, and use tril_indices_from to get at the lower indices to mask them:

>>> c2 = corr.copy()
>>> c2.values[np.tril_indices_from(c2)] = np.nan
>>> c2
    a        b         c         d         e
a NaN  0.06952 -0.021632 -0.028412 -0.029729
b NaN      NaN -0.022343 -0.063658  0.055247
c NaN      NaN       NaN -0.013272  0.029102
d NaN      NaN       NaN       NaN -0.046877
e NaN      NaN       NaN       NaN       NaN

and now we can do stats on the flattened array:

>>> c2.unstack().mean()
-0.0072054178481488901
>>> c2.unstack().std()
0.043839624201635466