How to divide a 2D matrix into patches and multiply each patch by its center element?

Question

I need to divide a 2D matrix into a set of 2D patches with a certain stride, then multiply every patch by its center element and sum the elements of each patch.

It feels not unlike a convolution where a separate kernel is used for every element of the matrix.

Below is a visual illustration. The elements of the result matrix are calculated like this:

The result should look like this:

Here's a solution I came up with:

window_shape = (2, 2)
stride = 1

# Matrix
m = np.arange(1, 17).reshape((4, 4))

# Pad it once per axis to make sure the number of views
# equals the number of elements
m_padded = np.pad(m, (0, 1))

# This function divides the array into `windows`, from:
# https://stackoverflow.com/questions/45960192/using-numpy-as-strided-function-to-create-patches-tiles-rolling-or-sliding-w#45960193
w = window_nd(m_padded, window_shape, stride)
ww, wh, *_ = w.shape
w = w.reshape((ww * wh, 4))  # Two first dimensions multiplied is the number of rows

# Tile each center element for element-wise multiplication
m_tiled = np.tile(m.ravel(), (4, 1)).transpose()

result = (w * m_tiled).sum(axis = 1).reshape(m.shape)

In my view it's not very efficient as a few arrays are allocated in the intermediary steps.

What is a better or more efficient way to accomplish this?

Answer 1

Try scipy.signal.convolve

from scipy.signal import convolve

window_shape = (2, 2)
stride = 1

# Matrix
m = np.arange(1, 17).reshape((4, 4))

# Pad it once per axis to make sure the number of views
# equals the number of elements
m_padded = np.pad(m, (0, 1))

output = convolve(m_padded, np.ones(window_shape), 'valid') * m
print(output)

Output:

array([[ 14.,  36.,  66.,  48.],
       [150., 204., 266., 160.],
       [414., 500., 594., 336.],
       [351., 406., 465., 256.]])