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

## Question:

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?

## Answers:

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. ])
```