human
Solve the following python programming problem given the following code:
@verbose
def _gamma_map_opt(M, G, alpha, maxit=10000, tol=1e-06, update_mode=1, group_size=1, gammas=None, verbose=None):
assistant
#Here is the Python code you requested.

    """Hierarchical Bayes (Gamma-MAP).
    Parameters
    M : array, shape=(n_sensors, n_times)
    Observation.
    G : array, shape=(n_sensors, n_sources)
    Forward operator.
    alpha : float
    Regularization parameter (noise variance).
    maxit : int
    Maximum number of iterations.
    tol : float
    Tolerance parameter for convergence.
    group_size : int
    Number of consecutive sources which use the same gamma.
    update_mode : int
    Update mode, 1: MacKay update (default), 3: Modified MacKay update.
    gammas : array, shape=(n_sources,)
    Initial values for posterior variances (gammas). If None, a
    variance of 1.0 is used.
    verbose : bool, str, int, or None
    If not None, override default verbose level (see :func:`mne.verbose`
    and :ref:`Logging documentation <tut_logging>` for more).
    Returns
    X : array, shape=(n_active, n_times)
    Estimated source time courses.
    active_set : array, shape=(n_active,)
    Indices of active sources.
    """
    G = G.copy()
    M = M.copy()
    if (gammas is None):
        gammas = np.ones(G.shape[1], dtype=np.float)
    eps = np.finfo(float).eps
    n_sources = G.shape[1]
    (n_sensors, n_times) = M.shape
    M_normalize_constant = linalg.norm(np.dot(M, M.T), ord='fro')
    M /= np.sqrt(M_normalize_constant)
    alpha /= M_normalize_constant
    G_normalize_constant = linalg.norm(G, ord=np.inf)
    G /= G_normalize_constant
    if ((n_sources % group_size) != 0):
        raise ValueError('Number    of    sources    has    to    be    evenly    dividable    by    the    group    size')
    n_active = n_sources
    active_set = np.arange(n_sources)
    gammas_full_old = gammas.copy()
    if (update_mode == 2):
        denom_fun = np.sqrt
    else:
        def denom_fun(x):
            return x
    last_size = (-1)
    for itno in range(maxit):
        gammas[np.isnan(gammas)] = 0.0
        gidx = (np.abs(gammas) > eps)
        active_set = active_set[gidx]
        gammas = gammas[gidx]
        if (n_active > len(active_set)):
            n_active = active_set.size
            G = G[:, gidx]
        CM = ((alpha * np.eye(n_sensors)) + np.dot((G * gammas[np.newaxis, :]), G.T))
        (U, S, V) = linalg.svd(CM, full_matrices=False)
        S = S[np.newaxis, :]
        CM = np.dot((U * S), U.T)
        CMinv = np.dot((U / (S + eps)), U.T)
        CMinvG = np.dot(CMinv, G)
        A = np.dot(CMinvG.T, M)
        if (update_mode == 1):
            numer = ((gammas ** 2) * np.mean((A * A.conj()).real, axis=1))
            denom = (gammas * np.sum((G * CMinvG), axis=0))
        elif (update_mode == 2):
            numer = (gammas * np.sqrt(np.mean((A * A.conj()).real, axis=1)))
            denom = np.sum((G * CMinvG), axis=0)
        else:
            raise ValueError('Invalid    value    for    update_mode')
        if (group_size == 1):
            if (denom is None):
                gammas = numer
            else:
                gammas = (numer / denom_fun(denom))
        else:
            numer_comb =...