Check if all True elements in sliding windows through a 2D array - Python

Question

I have a numpy multidimensional array in which elements are True or False:

import numpy as np 
#just making a toy array grid to show what I want to do 
grid = np.ones((4,4),dtype = 'bool')
grid[0,0]=False 
grid[-1,-1]=False 
#now grid has a few false values but is a 4x4 filled with mostly true values

Now I need to generate another array M, where the value on each site M [i, j] depends on the grid [i: i + 2, j: j + 2], as in

M = np.empty((4x4)) #elements to be filled

#here is the part I want to clean up 
for ii in range(4): 
    for jj in range(4): 

        #details here are unimportant. It just that M[ii,jj] depends on 
        #multiple elements of grid in some way
        if ii+2<=4 and jj+2<=4:     
            M[ii,jj] = np.all(grid[ii:ii+2,jj:jj+2]==True)
        else: 
            M[ii,jj] = False 

Is there a way to populate an array M using elements from a grid without double loops?

Answer 1

Approach No. 1

Here's one approach with 2Dconvolution -

from scipy.signal import convolve2d as conv2

out = (conv2(grid,np.ones((2,2),dtype=int),'valid')==4).astype(int)

Run Example -

In [118]: grid
Out[118]: 
array([[False,  True,  True,  True],
       [ True,  True,  True,  True],
       [ True,  True,  True,  True],
       [ True,  True,  True, False]], dtype=bool)

In [119]: (conv2(grid,np.ones((2,2),dtype=int),'valid')==4).astype(int)
Out[119]: 
array([[0, 1, 1],
       [1, 1, 1],
       [1, 1, 0]])

, . - , .

# 2

2D -

from scipy.ndimage.filters import uniform_filter as unif2d

out = unif2d(grid,size=2).astype(int)[1:,1:]

№ 3

4D -

from skimage.util import view_as_windows as viewW

out = viewW(grid,(2,2)).all(axis=(2,3)).astype(int)

all(axis=(2,3)) True .

---

In [122]: grid = np.random.rand(5000,5000)>0.1

In [123]: %timeit (conv2(grid,np.ones((2,2),dtype=int),'valid')==4).astype(int)
1 loops, best of 3: 520 ms per loop

In [124]: %timeit unif2d(grid,size=2).astype(int)[1:,1:]
1 loops, best of 3: 210 ms per loop

In [125]: %timeit viewW(grid,(2,2)).all(axis=(2,3)).astype(int)
1 loops, best of 3: 614 ms per loop