How to evaluate the sum of values within array blocks

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Simply reshape splitting each of those two axes into two each with shape (5,20) to form a 4D array and then sum reduce along the axes having the lengths 20, like so –

Z_new = Z.reshape(5,20,5,20).sum(axis=(1,3))

Functionally the same, but potentially faster option with np.einsum –

Z_new = np.einsum('ijkl->ik',Z.reshape(5,20,5,20))

Generic block size

Extending to a generic case –

H,W = 5,5 # block-size
m,n = Z.shape
Z_new = Z.reshape(H,m//H,W,n//W).sum(axis=(1,3))

With einsum that becomes –

Z_new = np.einsum('ijkl->ik',Z.reshape(H,m//H,W,n//W))

To compute average/mean across blocks, use mean instead of sum method.

Generic block size and reduction operation

Extending to use reduction operations that have ufuncs supporting multiple axes parameter with axis for reductions, it would be –

def blockwise_reduction(a, height, width, reduction_func=np.sum):
    m,n = a.shape
    a4D = a.reshape(height,m//height,width,n//width)
    return reduction_func(a4D,axis=(1,3))

Thus, to solve our specific case, it would be :

blockwise_reduction(Z, height=5, width=5)

and for a block-wise average computation, it would be –

blockwise_reduction(Z, height=5, width=5, reduction_func=np.mean)

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