How to create a 2D array of weighted+shifted unit impulses?

January 20, 2023

I’m looking for an efficient way to get a 2D array like this:

array([[ 2., -0., -0.,  0., -0., -0.,  0.,  0., -0.,  0.],
       [ 0., -1., -0.,  0., -0., -0.,  0.,  0., -0.,  0.],
       [ 0., -0., -5.,  0., -0., -0.,  0.,  0., -0.,  0.],
       [ 0., -0., -0.,  2., -0., -0.,  0.,  0., -0.,  0.],
       [ 0., -0., -0.,  0., -5., -0.,  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.,  2., -0.,  0.],
       [ 0., -0., -0.,  0., -0., -0.,  0.,  0., -5.,  0.],
       [ 0., -0., -0.,  0., -0., -0.,  0.,  0., -0.,  4.]])

Diagonal elements contains values.
My current attempt:

import numpy as np
N = 10
k = np.random.randint(-5, 5, size=N) # weights
xk = k * np.identity(N) # shifted+weighted unit impulses

Is there a way to get directly k*np.identity()? perhaps in scipy as this type of array is common in DSP.

>Solution :

np.diag([1,2,3]

gives

[[1 0 0]
 [0 2 0]
 [0 0 3]]

Creates a diagonal matrix for you. In this case you just need to create the diagonal elements accordingly.

So as per your case:

import numpy as np
N = 10
k = np.random.randint(-5, 5, size=N) # weights
xk = np.diag(k)
print(xk)

gives

[[-4  0  0  0  0  0  0  0  0  0]
 [ 0  1  0  0  0  0  0  0  0  0]
 [ 0  0  1  0  0  0  0  0  0  0]
 [ 0  0  0  4  0  0  0  0  0  0]
 [ 0  0  0  0  3  0  0  0  0  0]
 [ 0  0  0  0  0 -3  0  0  0  0]
 [ 0  0  0  0  0  0  4  0  0  0]
 [ 0  0  0  0  0  0  0  1  0  0]
 [ 0  0  0  0  0  0  0  0  4  0]
 [ 0  0  0  0  0  0  0  0  0 -1]]