def find_omega_min(omega_levelu, Neu, Nl, xiu):
    r"""Find the smallest transition frequency for each field.

    >>> Ne = 6
    >>> Nl = 2
    >>> omega_level = [0.0, 100.0, 100.0, 200.0, 200.0, 300.0]
    >>> xi = np.zeros((Nl, Ne, Ne))
    >>> coup = [[(1, 0), (2, 0)], [(3, 0), (4, 0), (5, 0)]]
    >>> for l in range(Nl):
    ...     for pair in coup[l]:
    ...         xi[l, pair[0], pair[1]] = 1.0
    ...         xi[l, pair[1], pair[0]] = 1.0

    >>> aux = define_simplification(omega_level, xi, Nl)
    >>> u, invu, omega_levelu, Neu, xiu = aux
    >>> find_omega_min(omega_levelu, Neu, Nl, xiu)
    ([100.0, 200.0], [1, 2], [0, 0])

    """
    omega_min = []; iu0 = []; ju0 = []
    for l in range(Nl):
        omegasl = []
        for iu in range(Neu):
            for ju in range(iu):
                if xiu[l, iu, ju] == 1:
                    omegasl += [(omega_levelu[iu]-omega_levelu[ju], iu, ju)]
        omegasl = list(sorted(omegasl))
        omega_min += [omegasl[0][0]]
        iu0 += [omegasl[0][1]]
        ju0 += [omegasl[0][2]]

    return omega_min, iu0, ju0
def find_omega_min ( omega_levelu , Neu , Nl , xiu ) : omega_min = [ ] ; iu0 = [ ] ; ju0 = [ ] for l in range ( Nl ) : omegasl = [ ] for iu in range ( Neu ) : for ju in range ( iu ) : if xiu [ l , iu , ju ] == 1 : omegasl += [ ( omega_levelu [ iu ] - omega_levelu [ ju ] , iu , ju ) ] omegasl = list ( sorted ( omegasl ) ) omega_min += [ omegasl [ 0 ] [ 0 ] ] iu0 += [ omegasl [ 0 ] [ 1 ] ] ju0 += [ omegasl [ 0 ] [ 2 ] ] return omega_min , iu0 , ju0
r"""Find the smallest transition frequency for each field.

    >>> Ne = 6
    >>> Nl = 2
    >>> omega_level = [0.0, 100.0, 100.0, 200.0, 200.0, 300.0]
    >>> xi = np.zeros((Nl, Ne, Ne))
    >>> coup = [[(1, 0), (2, 0)], [(3, 0), (4, 0), (5, 0)]]
    >>> for l in range(Nl):
    ...     for pair in coup[l]:
    ...         xi[l, pair[0], pair[1]] = 1.0
    ...         xi[l, pair[1], pair[0]] = 1.0

    >>> aux = define_simplification(omega_level, xi, Nl)
    >>> u, invu, omega_levelu, Neu, xiu = aux
    >>> find_omega_min(omega_levelu, Neu, Nl, xiu)
    ([100.0, 200.0], [1, 2], [0, 0])