Generate random circulant Gram matrix of specified dimension.

[vprusso]

Task: Function that allows one to generate a random circulant Gram matrix of a requested dimension.

In toqito/rand, adding the following function:

import numpy as np

def random_circulant_gram(dim: int) -> np.ndarray:
    # Step 1: Generate a random diagonal matrix with non-negative entries
    diag_mat = np.diag(np.random.rand(dim))
    
    # Step 2: Construct the normalized DFT matrix
    dft_mat = np.fft.fft(np.eye(dim)) / np.sqrt(dim)
    
    # Step 3: Compute the circulant matrix. Since circ_mat is formed from the DFT of a real 
    # diagonal matrix, it should be real
    return np.real(np.conj(dft_mat.T) @ diag_mat @ dft_mat)

Would also need to add appropriate tests in rand/tests as well adding a link in the .rst docs.

[ankit-pn]

I would like to work on this, if no one is working on this then pls it to me!
Thanks

[vprusso]

Thanks for the interest, @ankit-pn. Assigned!