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

Here's one approach

def roll_matrix(vec):
    N = len(vec)
    buffer = np.empty((N, N*2 - 1))

    # generate a wider array that we want a slice into
    buffer[:,:N] = vec
    buffer[:,N:] = vec[:-1]

    rolled = buffer.reshape(-1)[N-1:-1].reshape(N, -1)
    return rolled[:,:N]

In your case, we build buffer to be

array([[ 1.,  2.,  3.,  4.,  1.,  2.,  3.],
       [ 1.,  2.,  3.,  4.,  1.,  2.,  3.],
       [ 1.,  2.,  3.,  4.,  1.,  2.,  3.],
       [ 1.,  2.,  3.,  4.,  1.,  2.,  3.]])

Then flatten it, trim it, reshape it to get rolled:

array([[ 4.,  1.,  2.,  3.,  1.,  2.],
       [ 3.,  4.,  1.,  2.,  3.,  1.],
       [ 2.,  3.,  4.,  1.,  2.,  3.],
       [ 1.,  2.,  3.,  4.,  1.,  2.]])

And finally, slice off the garbage last columns