Matrices for image blurring

In [1]: 
import numpy as np
import matplotlib.pyplot as pt
In [30]: 
from PIL import Image

with Image.open("cat.jpeg").resize((500,500)) as img:
    img = np.array(img).sum(axis=-1)
    
h, w = img.shape
In [31]: 
pt.figure(figsize=(8,8))
pt.imshow(img, cmap="gray")
Out[31]:
<matplotlib.image.AxesImage at 0x7f118ce0ed68>

Now make a Gaussian with as many pixels as the image is wide.

In [38]: 
x = np.linspace(-1, 1, w)
gaussian = np.exp(-500*x**2)
gaussian = np.roll(gaussian, -w//2)
pt.plot(x, gaussian)
Out[38]:
[<matplotlib.lines.Line2D at 0x7f118cc6e9e8>]

Now, fill a $w\times w$ matrix with shifted versions of this:

In [39]: 
A = np.zeros((w,w))
for i in range(w):
    A[:, i] = np.roll(gaussian, i)

Multiply the cat by this.

In [40]: 
blurrycat = np.einsum("nx,yx->yn", A, img)
In [43]: 
pt.figure(figsize=(8,8))
pt.imshow(blurrycat, cmap="gray")
Out[43]:
<matplotlib.image.AxesImage at 0x7f118cb744e0>
In []: