[python] Why does corrcoef return a matrix?

It seems strange to me that np.corrcoef returns a matrix.

 correlation1 = corrcoef(Strategy1Returns,Strategy2Returns)

[[ 1.         -0.99598935]
 [-0.99598935  1.        ]]

Does anyone know why this is the case and whether it is possible to return just one value in the classical sense?

Consider using matplotlib.cbook pieces

for example:

import matplotlib.cbook as cbook
segments = cbook.pieces(np.arange(20), 3)
for s in segments:
     print s

It allows you to compute correlation coefficients of >2 data sets, e.g.

>>> from numpy import *
>>> a = array([1,2,3,4,6,7,8,9])
>>> b = array([2,4,6,8,10,12,13,15])
>>> c = array([-1,-2,-2,-3,-4,-6,-7,-8])
>>> corrcoef([a,b,c])
array([[ 1.        ,  0.99535001, -0.9805214 ],
       [ 0.99535001,  1.        , -0.97172394],
       [-0.9805214 , -0.97172394,  1.        ]])

Here we can get the correlation coefficient of a,b (0.995), a,c (-0.981) and b,c (-0.972) at once. The two-data-set case is just a special case of N-data-set class. And probably it's better to keep the same return type. Since the "one value" can be obtained simply with

>>> corrcoef(a,b)[1,0]
0.99535001355530017

there's no big reason to create the special case.

The correlation matrix is the standard way to express correlations between an arbitrary finite number of variables. The correlation matrix of N data vectors is a symmetric N × N matrix with unity diagonal. Only in the case N = 2 does this matrix have one free parameter.

The function Correlate of numpy works with 2 1D arrays that you want to correlate and returns one correlation value.

corrcoef returns the normalised covariance matrix.

The covariance matrix is the matrix

Cov( X, X )    Cov( X, Y )

Cov( Y, X )    Cov( Y, Y )

Normalised, this will yield the matrix:

Corr( X, X )    Corr( X, Y )

Corr( Y, X )    Corr( Y, Y )

correlation1[0, 0 ] is the correlation between Strategy1Returns and itself, which must be 1. You just want correlation1[ 0, 1 ].

You can use the following function to return only the correlation coefficient:

def pearson_r(x, y):
"""Compute Pearson correlation coefficient between two arrays."""

   # Compute correlation matrix
   corr_mat = np.corrcoef(x, y)

   # Return entry [0,1]
   return corr_mat[0,1]