create and return a BaseGrouper, which is an internal
    mapping of how to create the grouper indexers.
    This may be composed of multiple Grouping objects, indicating
    multiple groupers

    Groupers are ultimately index mappings. They can originate as:
    index mappings, keys to columns, functions, or Groupers

    Groupers enable local references to axis,level,sort, while
    the passed in axis, level, and sort are 'global'.

    This routine tries to figure out what the passing in references
    are and then creates a Grouping for each one, combined into
    a BaseGrouper.

    If observed & we have a categorical grouper, only show the observed
    values

    If validate, then check for key/level overlaps

def _get_grouper(obj, key=None, axis=0, level=None, sort=True,
                 observed=False, mutated=False, validate=True):
    """
    create and return a BaseGrouper, which is an internal
    mapping of how to create the grouper indexers.
    This may be composed of multiple Grouping objects, indicating
    multiple groupers

    Groupers are ultimately index mappings. They can originate as:
    index mappings, keys to columns, functions, or Groupers

    Groupers enable local references to axis,level,sort, while
    the passed in axis, level, and sort are 'global'.

    This routine tries to figure out what the passing in references
    are and then creates a Grouping for each one, combined into
    a BaseGrouper.

    If observed & we have a categorical grouper, only show the observed
    values

    If validate, then check for key/level overlaps

    """
    group_axis = obj._get_axis(axis)

    # validate that the passed single level is compatible with the passed
    # axis of the object
    if level is not None:
        # TODO: These if-block and else-block are almost same.
        # MultiIndex instance check is removable, but it seems that there are
        # some processes only for non-MultiIndex in else-block,
        # eg. `obj.index.name != level`. We have to consider carefully whether
        # these are applicable for MultiIndex. Even if these are applicable,
        # we need to check if it makes no side effect to subsequent processes
        # on the outside of this condition.
        # (GH 17621)
        if isinstance(group_axis, MultiIndex):
            if is_list_like(level) and len(level) == 1:
                level = level[0]

            if key is None and is_scalar(level):
                # Get the level values from group_axis
                key = group_axis.get_level_values(level)
                level = None

        else:
            # allow level to be a length-one list-like object
            # (e.g., level=[0])
            # GH 13901
            if is_list_like(level):
                nlevels = len(level)
                if nlevels == 1:
                    level = level[0]
                elif nlevels == 0:
                    raise ValueError('No group keys passed!')
                else:
                    raise ValueError('multiple levels only valid with '
                                     'MultiIndex')

            if isinstance(level, str):
                if obj.index.name != level:
                    raise ValueError('level name {} is not the name of the '
                                     'index'.format(level))
            elif level > 0 or level < -1:
                raise ValueError(
                    'level > 0 or level < -1 only valid with MultiIndex')

            # NOTE: `group_axis` and `group_axis.get_level_values(level)`
            # are same in this section.
            level = None
            key = group_axis

    # a passed-in Grouper, directly convert
    if isinstance(key, Grouper):
        binner, grouper, obj = key._get_grouper(obj, validate=False)
        if key.key is None:
            return grouper, [], obj
        else:
            return grouper, {key.key}, obj

    # already have a BaseGrouper, just return it
    elif isinstance(key, BaseGrouper):
        return key, [], obj

    # In the future, a tuple key will always mean an actual key,
    # not an iterable of keys. In the meantime, we attempt to provide
    # a warning. We can assume that the user wanted a list of keys when
    # the key is not in the index. We just have to be careful with
    # unhashble elements of `key`. Any unhashable elements implies that
    # they wanted a list of keys.
    # https://github.com/pandas-dev/pandas/issues/18314
    is_tuple = isinstance(key, tuple)
    all_hashable = is_tuple and is_hashable(key)

    if is_tuple:
        if ((all_hashable and key not in obj and set(key).issubset(obj))
                or not all_hashable):
            # column names ('a', 'b') -> ['a', 'b']
            # arrays like (a, b) -> [a, b]
            msg = ("Interpreting tuple 'by' as a list of keys, rather than "
                   "a single key. Use 'by=[...]' instead of 'by=(...)'. In "
                   "the future, a tuple will always mean a single key.")
            warnings.warn(msg, FutureWarning, stacklevel=5)
            key = list(key)

    if not isinstance(key, list):
        keys = [key]
        match_axis_length = False
    else:
        keys = key
        match_axis_length = len(keys) == len(group_axis)

    # what are we after, exactly?
    any_callable = any(callable(g) or isinstance(g, dict) for g in keys)
    any_groupers = any(isinstance(g, Grouper) for g in keys)
    any_arraylike = any(isinstance(g, (list, tuple, Series, Index, np.ndarray))
                        for g in keys)

    # is this an index replacement?
    if (not any_callable and not any_arraylike and not any_groupers and
            match_axis_length and level is None):
        if isinstance(obj, DataFrame):
            all_in_columns_index = all(g in obj.columns or g in
                                       obj.index.names for g in keys)
        elif isinstance(obj, Series):
            all_in_columns_index = all(g in obj.index.names for g in keys)

        if not all_in_columns_index:
            keys = [com.asarray_tuplesafe(keys)]

    if isinstance(level, (tuple, list)):
        if key is None:
            keys = [None] * len(level)
        levels = level
    else:
        levels = [level] * len(keys)

    groupings = []
    exclusions = []

    # if the actual grouper should be obj[key]
    def is_in_axis(key):
        if not _is_label_like(key):
            try:
                obj._data.items.get_loc(key)
            except Exception:
                return False

        return True

    # if the grouper is obj[name]
    def is_in_obj(gpr):
        try:
            return id(gpr) == id(obj[gpr.name])
        except Exception:
            return False

    for i, (gpr, level) in enumerate(zip(keys, levels)):

        if is_in_obj(gpr):  # df.groupby(df['name'])
            in_axis, name = True, gpr.name
            exclusions.append(name)

        elif is_in_axis(gpr):  # df.groupby('name')
            if gpr in obj:
                if validate:
                    obj._check_label_or_level_ambiguity(gpr)
                in_axis, name, gpr = True, gpr, obj[gpr]
                exclusions.append(name)
            elif obj._is_level_reference(gpr):
                in_axis, name, level, gpr = False, None, gpr, None
            else:
                raise KeyError(gpr)
        elif isinstance(gpr, Grouper) and gpr.key is not None:
            # Add key to exclusions
            exclusions.append(gpr.key)
            in_axis, name = False, None
        else:
            in_axis, name = False, None

        if is_categorical_dtype(gpr) and len(gpr) != obj.shape[axis]:
            raise ValueError(
                ("Length of grouper ({len_gpr}) and axis ({len_axis})"
                 " must be same length"
                 .format(len_gpr=len(gpr), len_axis=obj.shape[axis])))

        # create the Grouping
        # allow us to passing the actual Grouping as the gpr
        ping = (Grouping(group_axis,
                         gpr,
                         obj=obj,
                         name=name,
                         level=level,
                         sort=sort,
                         observed=observed,
                         in_axis=in_axis)
                if not isinstance(gpr, Grouping) else gpr)

        groupings.append(ping)

    if len(groupings) == 0:
        raise ValueError('No group keys passed!')

    # create the internals grouper
    grouper = BaseGrouper(group_axis, groupings, sort=sort, mutated=mutated)
    return grouper, exclusions, obj