How to Efficiently Extract Subarrays with a Given Stride from a NumPy Array?

Taking Subarrays from Numpy Array with Given Stride/Stepsize Efficiently

In the world of data analysis, often we need to extract subarrays with specific strides or stepsizes from a larger array. Numpy, the popular Python library for numerical operations, offers several methods to achieve this efficiently.

Problem Statement:
Given a Numpy array, we want to extract a matrix of subarrays of a fixed length with a specific stride or stepsize. A stride is the distance between the start of consecutive subarrays.

Discussion:

One straightforward way to create subarrays is to iterate over the original array using a for-loop. While this approach works, it can be slow for large arrays.

Approach 1: Broadcasting

NumPy's broadcasting mechanism allows us to create subarrays without loops. We can use the following function that takes the array, subarray length (L), and stride (S):

def broadcasting_app(a, L, S):
    nrows = ((a.size - L) // S) + 1
    return a[S * np.arange(nrows)[:, None] + np.arange(L)]

Explanation:
np.arange(nrows) creates an array of indices with a stride of 1. By multiplying this with S, we get the starting indices of each subarray. We then broadcast these indices across the rows of a to obtain the subarrays.

Approach 2: NumPy Strides

Another efficient method uses NumPy's strides feature. Strides represent the number of bytes between consecutive elements along each axis. We can use this information to create subarrays:

def strided_app(a, L, S):
    nrows = ((a.size - L) // S) + 1
    n = a.strides[0]
    return np.lib.stride_tricks.as_strided(a, shape=(nrows, L), strides=(S * n, n))

Explanation:
We use np.lib.stride_tricks.as_strided to reshape a by taking advantage of its strides. The resulting array has the desired number of rows (nrows) and subarray length (L), while maintaining the stride of S.

Sample Code:

To illustrate the approaches:

a = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])

print(broadcasting_app(a, L=5, S=3))
print(strided_app(a, L=5, S=3))

Output:

[[ 1  2  3  4  5]
 [ 4  5  6  7  8]
 [ 7  8  9 10 11]]
[[ 1  2  3  4  5]
 [ 4  5  6  7  8]
 [ 7  8  9 10 11]]

Both approaches efficiently generate the matrix of subarrays with the desired stride.

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