Create a matrix from a vector where each row is a shifted version of the vector

Question

I have a numpy array like this

import numpy as np

ar = np.array([1, 2, 3, 4])

and I want to create an array that looks like this:

Answer 1

Both of the existing answers are fine; this answer is probably only of interest if you are already using scipy.

The matrix that you describe is known as a circulant matrix. If you don't mind the dependency on scipy, you can use scipy.linalg.circulant to create one:

In [136]: from scipy.linalg import circulant

In [137]: ar = np.array([1, 2, 3, 4])

In [138]: circulant(ar[::-1])
Out[138]: 
array([[4, 1, 2, 3],
       [3, 4, 1, 2],
       [2, 3, 4, 1],
       [1, 2, 3, 4]])