How to slice and calculate the pearson correlation coefficient between one big and small array with “overlapping” windows arrays

Suppose I have two very simple arrays with numpy:

import numpy as np
reference=np.array([0,1,2,3,0,0,0,7,8,9,10])
probe=np.zeros(3)

I would like to find which slice of array reference has the highest pearson’s correlation coefficient with array probe. To do that, I would like to slice the array reference using some sort of sub-arrays that are overlapped in a for loop, which means I shift one element at a time of reference, and compare it against array probe. I did the slicing using the non elegant code below:

from statistics import correlation
for i in range(0,len(reference)):
  #get the slice of the data 
  sliced_data=reference[i:i+len(probe)]
  #only calculate the correlation when probe and reference have the same number of elements 
  if len(sliced_data)==len(probe):
      my_rho = correlation(sliced_data, probe)
      

I have one issues and one question about such a code:

1-once I run the code, I have the error below:

my_rho = correlation(sliced_data, probe)
  File "/usr/lib/python3.10/statistics.py", line 919, in correlation
    raise StatisticsError('at least one of the inputs is constant')
statistics.StatisticsError: at least one of the inputs is constant

2- is there a more elegant way of doing such slicing with python?

Answer

You can use sliding_window_view to get the successive values, for a vectorized computation of the correlation, use a custom function:

from numpy.lib.stride_tricks import sliding_window_view as swv

def np_corr(X, y):
    # adapted from https://stackoverflow.com/a/71253141
    denom = (np.sqrt((len(y) * np.sum(X**2, axis=-1) - np.sum(X, axis=-1) ** 2)
                       * (len(y) * np.sum(y**2) - np.sum(y)**2)))
    return np.divide((len(y) * np.sum(X * y[None, :], axis=-1) - (np.sum(X, axis=-1) * np.sum(y))),
                     denom, where=denom!=0
                    )

corr = np_corr(swv(reference, len(probe)), probe)

Output:

array([ 1.        ,  1.        , -0.65465367, -0.8660254 ,  0.        ,
        0.8660254 ,  0.91766294,  1.        ,  1.        ])