docs: def mtakfac(m):
    """Modified Takagi factorization of a (complex) symmetric matrix.
  
    Returns U, S where U^T M U = diag(S) and the singular values
    are sorted in ascending order (small to large).
    """
    u, s, v = msvd(np.asarray(m, dtype=complex))
    f = np.sqrt(u.conj().T @ v.conj())
    w = v @ f
    return w, s