def local_log_scale(start_dec, end_dec, N_per_dec, dtype='int64'):
    """returns a vector of integers on logarithmic scale starting from decade start, ending decade end with M per decade
    Parameters
    ----------
    start_dec (integer)
    end_dec (integer)
    N_per_dec (integer)
    dtype (string)

    Returns
    -------
    array (numpy array)

    Examples
    --------
    >>> arr = local_log_scale(start_dec = -9, end_dec = 1, N_per_dec = 4, dtype = 'int64')
    """
    from numpy import logspace, around
    arr = logspace(start_dec, end_dec, (end_dec - start_dec) * N_per_dec,
        endpoint=False, dtype=dtype)
    return arr
