Find number of non-zero elements adjacent to zeros in numpy 2D array

Question

Given a matrix, I want to count number of filled elements (non-zero cells) adjacent to empty (zero) cells, where adjacency is along rows (left/right).

I have tried playing around with np.roll and subtracting matrices, but I'm not sure how to code this without loops.

For example, given the matrix:

arr = 
[[1 1 0 0 0 0 0 0 1 0]
 [1 1 0 0 0 0 0 1 1 1]
 [0 1 1 0 0 0 0 0 0 0]
 [0 1 1 0 0 0 0 0 0 0]
 [0 1 1 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0]]

We have 12 non-zero elements adjacent to zeros.

Answer 1

Approach #1

We can use 2D convolution to solve it with an appropriate kernel ([1,1,1]) or ([1,0,1]) on the zeros mask and look for the convolution summations to be >=1, which signals at least one zero in each sliding window of three elements and with an additional check of the current element being non-zero confirms that there's at least one neighboring 0.

The implementation would look something like this -

In [245]: a  # input array
Out[245]: 
array([[1, 1, 0, 0, 0, 0, 0, 0, 1, 0],
       [1, 1, 0, 0, 0, 0, 0, 1, 1, 1],
       [0, 1, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 1, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 1, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

In [246]: from scipy.signal import convolve2d

In [248]: k = [[1,1,1]] # kernel for convolution

In [249]: ((convolve2d(a==0,k,'same')>=1) & (a!=0)).sum()
Out[249]: 12

Approach #2

Another approach would be making use of slicing as we would look for one-off offsetted elements along each row for the zeros and non-zeros matches for the left and right hand sides LHS and RHS and finally sum those -

maskRHS = (a[:,1:]==0) & (a[:,:-1]!=0)
maskLHS = (a[:,1:]!=0) & (a[:,:-1]==0)
maskRHS[:,1:] |= maskLHS[:,:-1]
out = maskRHS.sum() + maskLHS[:,-1].sum()