Numpy array filled in diamond shape

Question

I'm looking for a way to fill a numpy matrix in a diamond shape.

I know you can fill one in a circle shape like this:

radius = 1
y,x = np.ogrid[-radius: radius + 1, -radius: radius + 1]
matrix = x**2 + y**2 <= radius**2

Which give me this correct output:

[[False  True False]
 [ True  True  True]
 [False  True False]]

But obviously a circle is not a diamond and as the radius increases, the shape stops looking like a diamond.

Answer 1

Diamond mask with given matrix-length

Here's one leveraging broadcasting -

def diamond(n):
    a = np.arange(n)
    b = np.minimum(a,a[::-1])
    return (b[:,None]+b)>=(n-1)//2

Sample runs -

In [73]: diamond(3)
Out[73]: 
array([[False,  True, False],
       [ True,  True,  True],
       [False,  True, False]])

In [74]: diamond(4)
Out[74]: 
array([[False,  True,  True, False],
       [ True,  True,  True,  True],
       [ True,  True,  True,  True],
       [False,  True,  True, False]])

In [75]: diamond(5)
Out[75]: 
array([[False, False,  True, False, False],
       [False,  True,  True,  True, False],
       [ True,  True,  True,  True,  True],
       [False,  True,  True,  True, False],
       [False, False,  True, False, False]])

Diamond mask with given radius

For given radius, simplifies further -

def diamond2(r):
    b = np.r_[:r,r:-1:-1]
    return (b[:,None]+b)>=r

And that could be further simplified to a one-liner -

def diamond2(r):
    return np.add.outer(*[np.r_[:r,r:-1:-1]]*2)>=r

Sample runs -

In [19]: diamond2(1)
Out[19]: 
array([[False,  True, False],
       [ True,  True,  True],
       [False,  True, False]])

In [20]: diamond2(2)
Out[20]: 
array([[False, False,  True, False, False],
       [False,  True,  True,  True, False],
       [ True,  True,  True,  True,  True],
       [False,  True,  True,  True, False],
       [False, False,  True, False, False]])

In [21]: diamond2(3)
Out[21]: 
array([[False, False, False,  True, False, False, False],
       [False, False,  True,  True,  True, False, False],
       [False,  True,  True,  True,  True,  True, False],
       [ True,  True,  True,  True,  True,  True,  True],
       [False,  True,  True,  True,  True,  True, False],
       [False, False,  True,  True,  True, False, False],
       [False, False, False,  True, False, False, False]])