Reconstruct the actual Cholesky factor of a covariance matrix parameterized using the LKJ "onion method"

reconstruct_lkj_cholesky.py

def reconstruct_lkj_cholesky(ell, R2):
    num_items = len(R2) + 1
    L = np.zeros((num_items, num_items))
    L[0, 0] = 1.
    L[1, 0] = 2. * R2[0] - 1.0
    L[1, 1] = np.sqrt(1.0 - L[1, 0])

    start = 0
    for i in range(2, num_items):
        ell_row = ell[start:start+i]
        assert len(ell_row) == i
        scale = np.sqrt(R2[i-1] / np.dot(ell_row, ell_row))
        L[i, :i] = scale * ell_row
        L[i, i] = np.sqrt(1.0 - R2[i-1])
        start += i
    return L