在python中应用具有周期性边界条件的圆形掩模

Question

This question is related to: How to apply a disc shaped mask to a numpy array?

From the solution: https://stackoverflow.com/a/8650741/4484153 , is it possible to obtain circular mask in the following manner:

>>> new_arr
array([[ True,  True,  True,  True,    1.,  1.,  1.,  True],
       [ True,  True,  True,  True,  True,  1., True, True],
       [ True,  True,  True,  True,    1.,  1.,  1.,  True],
       [ True,  True,  True,  True,    1.,  1.,  1.,  True],
       [ 1.,    True,    1.,    1.,    1.,  1.,  1.,  1.  ],
       [ 1.,      1.,    1.,    1.,    1.,  1.,  1.,  1.  ],
       [ 1.,    True,    1.,    1.,    1.,  1.,  1.,  1.  ],
       [ True,  True,  True,  True,    1.,  1.,  1.,  True]])

in such a way that the array wraps around its columns and rows?

Answer 1

One way could just be to create the mask of required size in the center of the array and then use np.roll to shift the mask along an axis (this causes the mask to wrap around the edges of the array).

Following the method in the linked question and answer:

ones = np.ones((8, 8))

a, b = 3, 3
n = 8
r = 3
mask = x**2 + y**2 <= r**2

constructs mask like this:

array([[False, False, False,  True, False, False, False, False],
       [False,  True,  True,  True,  True,  True, False, False],
       [False,  True,  True,  True,  True,  True, False, False],
       [ True,  True,  True,  True,  True,  True,  True, False],
       [False,  True,  True,  True,  True,  True, False, False],
       [False,  True,  True,  True,  True,  True, False, False],
       [False, False, False,  True, False, False, False, False],
       [False, False, False, False, False, False, False, False]], dtype=bool)

Then rolling mask two places up and two places left and using it on ones ...

>>> rolled_mask = np.roll(np.roll(mask, -2, axis=0), -2, axis=1)
>>> ones[rolled_mask] = 255
>>> ones
array([[ 255.,  255.,  255.,  255.,    1.,    1.,    1.,  255.],
       [ 255.,  255.,  255.,  255.,  255.,    1.,  255.,  255.],
       [ 255.,  255.,  255.,  255.,    1.,    1.,    1.,  255.],
       [ 255.,  255.,  255.,  255.,    1.,    1.,    1.,  255.],
       [   1.,  255.,    1.,    1.,    1.,    1.,    1.,    1.],
       [   1.,    1.,    1.,    1.,    1.,    1.,    1.,    1.],
       [   1.,  255.,    1.,    1.,    1.,    1.,    1.,    1.],
       [ 255.,  255.,  255.,  255.,    1.,    1.,    1.,  255.]])

Answer 2

If you want to create the mask directly, the following works:

>>> N = 10
>>> row, col = 8, 7
>>> radius = 4
>>> rows = np.arange(N) - row
>>> rows = np.minimum(np.abs(rows), rows % N)
>>> cols = np.arange(N) - col
>>> cols = np.minimum(np.abs(cols), cols % N)
>>> (rows[:, None]**2 + cols**2 <= radius**2).astype(int)
array([[1, 0, 0, 0, 1, 1, 1, 1, 1, 1],
       [0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
       [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, 1, 0, 0],
       [0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
       [1, 0, 0, 0, 1, 1, 1, 1, 1, 1],
       [1, 0, 0, 0, 1, 1, 1, 1, 1, 1],
       [1, 1, 0, 1, 1, 1, 1, 1, 1, 1],
       [1, 0, 0, 0, 1, 1, 1, 1, 1, 1]])