/pandas/core/groupby.py

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import types
from functools import wraps
import numpy as np
import datetime
import collections

from pandas.compat import(
    zip, builtins, range, long, lzip,
    OrderedDict, callable
)
from pandas import compat

from pandas.core.base import PandasObject
from pandas.core.categorical import Categorical
from pandas.core.frame import DataFrame
from pandas.core.generic import NDFrame
from pandas.core.index import Index, MultiIndex, _ensure_index, _union_indexes
from pandas.core.internals import BlockManager, make_block
from pandas.core.series import Series
from pandas.core.panel import Panel
from pandas.util.decorators import cache_readonly, Appender
import pandas.core.algorithms as algos
import pandas.core.common as com
from pandas.core.common import(_possibly_downcast_to_dtype, isnull,
                               notnull, _DATELIKE_DTYPES, is_numeric_dtype,
                               is_timedelta64_dtype, is_datetime64_dtype)

from pandas import _np_version_under1p7
import pandas.lib as lib
from pandas.lib import Timestamp
import pandas.tslib as tslib
import pandas.algos as _algos
import pandas.hashtable as _hash

_agg_doc = """Aggregate using input function or dict of {column -> function}

Parameters
----------
arg : function or dict
    Function to use for aggregating groups. If a function, must either
    work when passed a DataFrame or when passed to DataFrame.apply. If
    passed a dict, the keys must be DataFrame column names.

Notes
-----
Numpy functions mean/median/prod/sum/std/var are special cased so the
default behavior is applying the function along axis=0
(e.g., np.mean(arr_2d, axis=0)) as opposed to
mimicking the default Numpy behavior (e.g., np.mean(arr_2d)).

Returns
-------
aggregated : DataFrame
"""


# special case to prevent duplicate plots when catching exceptions when
# forwarding methods from NDFrames
_plotting_methods = frozenset(['plot', 'boxplot', 'hist'])

_common_apply_whitelist = frozenset([
    'last', 'first',
    'head', 'tail', 'median',
    'mean', 'sum', 'min', 'max',
    'cumsum', 'cumprod', 'cummin', 'cummax', 'cumcount',
    'resample',
    'describe',
    'rank', 'quantile', 'count',
    'fillna',
    'mad',
    'any', 'all',
    'irow', 'take',
    'idxmax', 'idxmin',
    'shift', 'tshift',
    'ffill', 'bfill',
    'pct_change', 'skew',
    'corr', 'cov', 'diff',
]) | _plotting_methods

_series_apply_whitelist = \
    (_common_apply_whitelist - set(['boxplot'])) | \
    frozenset(['dtype', 'value_counts', 'unique', 'nunique',
               'nlargest', 'nsmallest'])

_dataframe_apply_whitelist = \
    _common_apply_whitelist | frozenset(['dtypes', 'corrwith'])


class GroupByError(Exception):
    pass


class DataError(GroupByError):
    pass


class SpecificationError(GroupByError):
    pass


def _groupby_function(name, alias, npfunc, numeric_only=True,
                      _convert=False):
    def f(self):
        self._set_selection_from_grouper()
        try:
            return self._cython_agg_general(alias, numeric_only=numeric_only)
        except AssertionError as e:
            raise SpecificationError(str(e))
        except Exception:
            result = self.aggregate(lambda x: npfunc(x, axis=self.axis))
            if _convert:
                result = result.convert_objects()
            return result

    f.__doc__ = "Compute %s of group values" % name
    f.__name__ = name

    return f


def _first_compat(x, axis=0):
    def _first(x):
        x = np.asarray(x)
        x = x[notnull(x)]
        if len(x) == 0:
            return np.nan
        return x[0]

    if isinstance(x, DataFrame):
        return x.apply(_first, axis=axis)
    else:
        return _first(x)


def _last_compat(x, axis=0):
    def _last(x):
        x = np.asarray(x)
        x = x[notnull(x)]
        if len(x) == 0:
            return np.nan
        return x[-1]

    if isinstance(x, DataFrame):
        return x.apply(_last, axis=axis)
    else:
        return _last(x)


def _count_compat(x, axis=0):
    return x.size


class Grouper(object):
    """
    A Grouper allows the user to specify a groupby instruction for a target object

    This specification will select a column via the key parameter, or if the level and/or
    axis parameters are given, a level of the index of the target object.

    These are local specifications and will override 'global' settings, that is the parameters
    axis and level which are passed to the groupby itself.

    Parameters
    ----------
    key : string, defaults to None
        groupby key, which selects the grouping column of the target
    level : name/number, defaults to None
        the level for the target index
    freq : string / freqency object, defaults to None
        This will groupby the specified frequency if the target selection (via key or level) is
        a datetime-like object
    axis : number/name of the axis, defaults to None
    sort : boolean, default to False
        whether to sort the resulting labels

    additional kwargs to control time-like groupers (when freq is passed)

    closed : closed end of interval; left or right
    label : interval boundary to use for labeling; left or right
    convention : {'start', 'end', 'e', 's'}
        If grouper is PeriodIndex

    Returns
    -------
    A specification for a groupby instruction

    Examples
    --------
    >>> df.groupby(Grouper(key='A')) : syntatic sugar for df.groupby('A')
    >>> df.groupby(Grouper(key='date',freq='60s')) : specify a resample on the column 'date'
    >>> df.groupby(Grouper(level='date',freq='60s',axis=1)) :
        specify a resample on the level 'date' on the columns axis with a frequency of 60s

    """

    def __new__(cls, *args, **kwargs):
        if kwargs.get('freq') is not None:
            from pandas.tseries.resample import TimeGrouper
            cls = TimeGrouper
        return super(Grouper, cls).__new__(cls)

    def __init__(self, key=None, level=None, freq=None, axis=None, sort=False):
        self.key=key
        self.level=level
        self.freq=freq
        self.axis=axis
        self.sort=sort

        self.grouper=None
        self.obj=None
        self.indexer=None
        self.binner=None
        self.grouper=None

    @property
    def ax(self):
        return self.grouper

    def _get_grouper(self, obj):

        """
        Parameters
        ----------
        obj : the subject object

        Returns
        -------
        a tuple of binner, grouper, obj (possibly sorted)
        """

        self._set_grouper(obj)
        return self.binner, self.grouper, self.obj

    def _set_grouper(self, obj, sort=False):
        """
        given an object and the specifcations, setup the internal grouper for this particular specification

        Parameters
        ----------
        obj : the subject object

        """

        if self.key is not None and self.level is not None:
            raise ValueError("The Grouper cannot specify both a key and a level!")

        # the key must be a valid info item
        if self.key is not None:
            key = self.key
            if key not in obj._info_axis:
                raise KeyError("The grouper name {0} is not found".format(key))
            ax = Index(obj[key],name=key)

        else:
            ax = obj._get_axis(self.axis)
            if self.level is not None:
                level = self.level

                # if a level is given it must be a mi level or
                # equivalent to the axis name
                if isinstance(ax, MultiIndex):

                    if isinstance(level, compat.string_types):
                        if obj.index.name != level:
                            raise ValueError('level name %s is not the name of the '
                                             'index' % level)
                    elif level > 0:
                        raise ValueError('level > 0 only valid with MultiIndex')
                    ax = Index(ax.get_level_values(level), name=level)

                else:
                    if not (level == 0 or level == ax.name):
                        raise ValueError("The grouper level {0} is not valid".format(level))

        # possibly sort
        if (self.sort or sort) and not ax.is_monotonic:
            indexer = self.indexer = ax.argsort(kind='quicksort')
            ax = ax.take(indexer)
            obj = obj.take(indexer, axis=self.axis, convert=False, is_copy=False)

        self.obj = obj
        self.grouper = ax
        return self.grouper

    def _get_binner_for_grouping(self, obj):
        raise NotImplementedError

    @property
    def groups(self):
        return self.grouper.groups

class GroupBy(PandasObject):

    """
    Class for grouping and aggregating relational data. See aggregate,
    transform, and apply functions on this object.

    It's easiest to use obj.groupby(...) to use GroupBy, but you can also do:

    ::

        grouped = groupby(obj, ...)

    Parameters
    ----------
    obj : pandas object
    axis : int, default 0
    level : int, default None
        Level of MultiIndex
    groupings : list of Grouping objects
        Most users should ignore this
    exclusions : array-like, optional
        List of columns to exclude
    name : string
        Most users should ignore this

    Notes
    -----
    After grouping, see aggregate, apply, and transform functions. Here are
    some other brief notes about usage. When grouping by multiple groups, the
    result index will be a MultiIndex (hierarchical) by default.

    Iteration produces (key, group) tuples, i.e. chunking the data by group. So
    you can write code like:

    ::

        grouped = obj.groupby(keys, axis=axis)
        for key, group in grouped:
            # do something with the data

    Function calls on GroupBy, if not specially implemented, "dispatch" to the
    grouped data. So if you group a DataFrame and wish to invoke the std()
    method on each group, you can simply do:

    ::

        df.groupby(mapper).std()

    rather than

    ::

        df.groupby(mapper).aggregate(np.std)

    You can pass arguments to these "wrapped" functions, too.

    See the online documentation for full exposition on these topics and much
    more

    Returns
    -------
    **Attributes**
    groups : dict
        {group name -> group labels}
    len(grouped) : int
        Number of groups
    """
    _apply_whitelist = _common_apply_whitelist
    _internal_names = ['_cache']
    _internal_names_set = set(_internal_names)
    _group_selection = None

    def __init__(self, obj, keys=None, axis=0, level=None,
                 grouper=None, exclusions=None, selection=None, as_index=True,
                 sort=True, group_keys=True, squeeze=False):
        self._selection = selection

        if isinstance(obj, NDFrame):
            obj._consolidate_inplace()

        self.level = level

        if not as_index:
            if not isinstance(obj, DataFrame):
                raise TypeError('as_index=False only valid with DataFrame')
            if axis != 0:
                raise ValueError('as_index=False only valid for axis=0')

        self.as_index = as_index
        self.keys = keys
        self.sort = sort
        self.group_keys = group_keys
        self.squeeze = squeeze

        if grouper is None:
            grouper, exclusions, obj = _get_grouper(obj, keys, axis=axis,
                                                    level=level, sort=sort)

        self.obj = obj
        self.axis = obj._get_axis_number(axis)
        self.grouper = grouper
        self.exclusions = set(exclusions) if exclusions else set()

    def __len__(self):
        return len(self.indices)

    def __unicode__(self):
        # TODO: Better unicode/repr for GroupBy object
        return object.__repr__(self)

    @property
    def groups(self):
        """ dict {group name -> group labels} """
        return self.grouper.groups

    @property
    def ngroups(self):
        return self.grouper.ngroups

    @property
    def indices(self):
        """ dict {group name -> group indices} """
        return self.grouper.indices

    def _get_index(self, name):
        """ safe get index, translate keys for datelike to underlying repr """

        def convert(key, s):
            # possibly convert to they actual key types
            # in the indices, could be a Timestamp or a np.datetime64

            if isinstance(s, (Timestamp,datetime.datetime)):
                return Timestamp(key)
            elif isinstance(s, np.datetime64):
                return Timestamp(key).asm8
            return key

        sample = next(iter(self.indices))
        if isinstance(sample, tuple):
            if not isinstance(name, tuple):
                raise ValueError("must supply a tuple to get_group with multiple grouping keys")
            if not len(name) == len(sample):
                raise ValueError("must supply a a same-length tuple to get_group with multiple grouping keys")

            name = tuple([ convert(n, k) for n, k in zip(name,sample) ])

        else:

            name = convert(name, sample)

        return self.indices[name]

    @property
    def name(self):
        if self._selection is None:
            return None  # 'result'
        else:
            return self._selection

    @property
    def _selection_list(self):
        if not isinstance(self._selection, (list, tuple, Series, np.ndarray)):
            return [self._selection]
        return self._selection

    @cache_readonly
    def _selected_obj(self):

        if self._selection is None or isinstance(self.obj, Series):
            if self._group_selection is not None:
                return self.obj[self._group_selection]
            return self.obj
        else:
            return self.obj[self._selection]

    def _set_selection_from_grouper(self):
        """ we may need create a selection if we have non-level groupers """
        grp = self.grouper
        if self.as_index and getattr(grp,'groupings',None) is not None and self.obj.ndim > 1:
            ax = self.obj._info_axis
            groupers = [ g.name for g in grp.groupings if g.level is None and g.name is not None and g.name in ax ]
            if len(groupers):
                self._group_selection = (ax-Index(groupers)).tolist()

    def _local_dir(self):
        return sorted(set(self.obj._local_dir() + list(self._apply_whitelist)))

    def __getattr__(self, attr):
        if attr in self._internal_names_set:
            return object.__getattribute__(self, attr)
        if attr in self.obj:
            return self[attr]
        if hasattr(self.obj, attr):
            return self._make_wrapper(attr)

        raise AttributeError("%r object has no attribute %r" %
                             (type(self).__name__, attr))

    def __getitem__(self, key):
        raise NotImplementedError('Not implemented: %s' % key)

    def _make_wrapper(self, name):
        if name not in self._apply_whitelist:
            is_callable = callable(getattr(self._selected_obj, name, None))
            kind = ' callable ' if is_callable else ' '
            msg = ("Cannot access{0}attribute {1!r} of {2!r} objects, try "
                   "using the 'apply' method".format(kind, name,
                                                     type(self).__name__))
            raise AttributeError(msg)

        # need to setup the selection
        # as are not passed directly but in the grouper
        self._set_selection_from_grouper()

        f = getattr(self._selected_obj, name)
        if not isinstance(f, types.MethodType):
            return self.apply(lambda self: getattr(self, name))

        f = getattr(type(self._selected_obj), name)

        def wrapper(*args, **kwargs):
            # a little trickery for aggregation functions that need an axis
            # argument
            kwargs_with_axis = kwargs.copy()
            if 'axis' not in kwargs_with_axis:
                kwargs_with_axis['axis'] = self.axis

            def curried_with_axis(x):
                return f(x, *args, **kwargs_with_axis)

            def curried(x):
                return f(x, *args, **kwargs)

            # preserve the name so we can detect it when calling plot methods,
            # to avoid duplicates
            curried.__name__ = curried_with_axis.__name__ = name

            # special case otherwise extra plots are created when catching the
            # exception below
            if name in _plotting_methods:
                return self.apply(curried)

            try:
                return self.apply(curried_with_axis)
            except Exception:
                try:
                    return self.apply(curried)
                except Exception:

                    # related to : GH3688
                    # try item-by-item
                    # this can be called recursively, so need to raise ValueError if
                    # we don't have this method to indicated to aggregate to
                    # mark this column as an error
                    try:
                        return self._aggregate_item_by_item(name, *args, **kwargs)
                    except (AttributeError):
                        raise ValueError

        return wrapper

    def get_group(self, name, obj=None):
        """
        Constructs NDFrame from group with provided name

        Parameters
        ----------
        name : object
            the name of the group to get as a DataFrame
        obj : NDFrame, default None
            the NDFrame to take the DataFrame out of.  If
            it is None, the object groupby was called on will
            be used

        Returns
        -------
        group : type of obj
        """
        if obj is None:
            obj = self._selected_obj

        inds = self._get_index(name)
        return obj.take(inds, axis=self.axis, convert=False)

    def __iter__(self):
        """
        Groupby iterator

        Returns
        -------
        Generator yielding sequence of (name, subsetted object)
        for each group
        """
        return self.grouper.get_iterator(self.obj, axis=self.axis)

    def apply(self, func, *args, **kwargs):
        """
        Apply function and combine results together in an intelligent way. The
        split-apply-combine combination rules attempt to be as common sense
        based as possible. For example:

        case 1:
        group DataFrame
        apply aggregation function (f(chunk) -> Series)
        yield DataFrame, with group axis having group labels

        case 2:
        group DataFrame
        apply transform function ((f(chunk) -> DataFrame with same indexes)
        yield DataFrame with resulting chunks glued together

        case 3:
        group Series
        apply function with f(chunk) -> DataFrame
        yield DataFrame with result of chunks glued together

        Parameters
        ----------
        func : function

        Notes
        -----
        See online documentation for full exposition on how to use apply.

        In the current implementation apply calls func twice on the
        first group to decide whether it can take a fast or slow code
        path. This can lead to unexpected behavior if func has
        side-effects, as they will take effect twice for the first
        group.


        See also
        --------
        aggregate, transform

        Returns
        -------
        applied : type depending on grouped object and function
        """
        func = _intercept_function(func)

        @wraps(func)
        def f(g):
            return func(g, *args, **kwargs)

        return self._python_apply_general(f)

    def _python_apply_general(self, f):
        keys, values, mutated = self.grouper.apply(f, self._selected_obj,
                                                   self.axis)

        return self._wrap_applied_output(keys, values,
                                         not_indexed_same=mutated)

    def aggregate(self, func, *args, **kwargs):
        raise NotImplementedError

    @Appender(_agg_doc)
    def agg(self, func, *args, **kwargs):
        return self.aggregate(func, *args, **kwargs)

    def _iterate_slices(self):
        yield self.name, self._selected_obj

    def transform(self, func, *args, **kwargs):
        raise NotImplementedError

    def mean(self):
        """
        Compute mean of groups, excluding missing values

        For multiple groupings, the result index will be a MultiIndex
        """
        try:
            return self._cython_agg_general('mean')
        except GroupByError:
            raise
        except Exception:  # pragma: no cover
            self._set_selection_from_grouper()
            f = lambda x: x.mean(axis=self.axis)
            return self._python_agg_general(f)

    def median(self):
        """
        Compute median of groups, excluding missing values

        For multiple groupings, the result index will be a MultiIndex
        """
        try:
            return self._cython_agg_general('median')
        except GroupByError:
            raise
        except Exception:  # pragma: no cover

            self._set_selection_from_grouper()
            def f(x):
                if isinstance(x, np.ndarray):
                    x = Series(x)
                return x.median(axis=self.axis)
            return self._python_agg_general(f)

    def std(self, ddof=1):
        """
        Compute standard deviation of groups, excluding missing values

        For multiple groupings, the result index will be a MultiIndex
        """
        # todo, implement at cython level?
        return np.sqrt(self.var(ddof=ddof))

    def var(self, ddof=1):
        """
        Compute variance of groups, excluding missing values

        For multiple groupings, the result index will be a MultiIndex
        """
        if ddof == 1:
            return self._cython_agg_general('var')
        else:
            self._set_selection_from_grouper()
            f = lambda x: x.var(ddof=ddof)
            return self._python_agg_general(f)

    def sem(self, ddof=1):
        """
        Compute standard error of the mean of groups, excluding missing values

        For multiple groupings, the result index will be a MultiIndex
        """
        return self.std(ddof=ddof)/np.sqrt(self.count())

    def size(self):
        """
        Compute group sizes

        """
        return self.grouper.size()

    sum = _groupby_function('sum', 'add', np.sum)
    prod = _groupby_function('prod', 'prod', np.prod)
    min = _groupby_function('min', 'min', np.min, numeric_only=False)
    max = _groupby_function('max', 'max', np.max, numeric_only=False)
    first = _groupby_function('first', 'first', _first_compat,
                              numeric_only=False, _convert=True)
    last = _groupby_function('last', 'last', _last_compat, numeric_only=False,
                             _convert=True)
    _count = _groupby_function('_count', 'count', _count_compat,
                               numeric_only=False)

    def count(self, axis=0):
        return self._count().astype('int64')

    def ohlc(self):
        """
        Compute sum of values, excluding missing values
        For multiple groupings, the result index will be a MultiIndex
        """
        return self._apply_to_column_groupbys(
            lambda x: x._cython_agg_general('ohlc'))

    def nth(self, n, dropna=None):
        """
        Take the nth row from each group.

        If dropna, will not show nth non-null row, dropna is either
        Truthy (if a Series) or 'all', 'any' (if a DataFrame); this is equivalent
        to calling dropna(how=dropna) before the groupby.

        Examples
        --------
        >>> df = DataFrame([[1, np.nan], [1, 4], [5, 6]], columns=['A', 'B'])
        >>> g = df.groupby('A')
        >>> g.nth(0)
           A   B
        0  1 NaN
        2  5   6
        >>> g.nth(1)
           A  B
        1  1  4
        >>> g.nth(-1)
           A  B
        1  1  4
        2  5  6
        >>> g.nth(0, dropna='any')
           B
        A
        1  4
        5  6
        >>> g.nth(1, dropna='any')  # NaNs denote group exhausted when using dropna
            B
        A
        1 NaN
        5 NaN

        """

        self._set_selection_from_grouper()
        if not dropna:  # good choice
            m = self.grouper._max_groupsize
            if n >= m or n < -m:
                return self._selected_obj.loc[[]]
            rng = np.zeros(m, dtype=bool)
            if n >= 0:
                rng[n] = True
                is_nth = self._cumcount_array(rng)
            else:
                rng[- n - 1] = True
                is_nth = self._cumcount_array(rng, ascending=False)

            result = self._selected_obj[is_nth]

            # the result index
            if self.as_index:
                ax = self.obj._info_axis
                names = self.grouper.names
                if self.obj.ndim == 1:
                    # this is a pass-thru
                    pass
                elif all([ n in ax for n in names ]):
                    result.index = Index(self.obj[names][is_nth].values.ravel()).set_names(names)
                elif self._group_selection is not None:
                    result.index = self.obj._get_axis(self.axis)[is_nth]

                result = result.sort_index()

            return result

        if (isinstance(self._selected_obj, DataFrame)
           and dropna not in ['any', 'all']):
            # Note: when agg-ing picker doesn't raise this, just returns NaN
            raise ValueError("For a DataFrame groupby, dropna must be "
                             "either None, 'any' or 'all', "
                             "(was passed %s)." % (dropna),)

        # old behaviour, but with all and any support for DataFrames.
        # modified in GH 7559 to have better perf
        max_len = n if n >= 0 else - 1 - n
        dropped = self.obj.dropna(how=dropna, axis=self.axis)

        # get a new grouper for our dropped obj
        if self.keys is None and self.level is None:

            # we don't have the grouper info available (e.g. we have selected out
            # a column that is not in the current object)
            axis = self.grouper.axis
            grouper = axis[axis.isin(dropped.index)]
            keys = self.grouper.names
        else:

            # create a grouper with the original parameters, but on the dropped object
            grouper, _, _ = _get_grouper(dropped, key=self.keys, axis=self.axis,
                                         level=self.level, sort=self.sort)

        sizes = dropped.groupby(grouper).size()
        result = dropped.groupby(grouper).nth(n)
        mask = (sizes<max_len).values

        # set the results which don't meet the criteria
        if len(result) and mask.any():
            result.loc[mask] = np.nan

        # reset/reindex to the original groups
        if len(self.obj) == len(dropped) or len(result) == len(self.grouper.result_index):
            result.index = self.grouper.result_index
        else:
            result = result.reindex(self.grouper.result_index)

        return result

    def cumcount(self, **kwargs):
        """
        Number each item in each group from 0 to the length of that group - 1.

        Essentially this is equivalent to

        >>> self.apply(lambda x: Series(np.arange(len(x)), x.index))

        Parameters
        ----------
        ascending : bool, default True
            If False, number in reverse, from length of group - 1 to 0.

        Example
        -------

        >>> df = pd.DataFrame([['a'], ['a'], ['a'], ['b'], ['b'], ['a']],
        ...                   columns=['A'])
        >>> df
           A
        0  a
        1  a
        2  a
        3  b
        4  b
        5  a
        >>> df.groupby('A').cumcount()
        0    0
        1    1
        2    2
        3    0
        4    1
        5    3
        dtype: int64
        >>> df.groupby('A').cumcount(ascending=False)
        0    3
        1    2
        2    1
        3    1
        4    0
        5    0
        dtype: int64

        """
        self._set_selection_from_grouper()
        ascending = kwargs.pop('ascending', True)

        index = self._selected_obj.index
        cumcounts = self._cumcount_array(ascending=ascending)
        return Series(cumcounts, index)

    def head(self, n=5):
        """
        Returns first n rows of each group.

        Essentially equivalent to ``.apply(lambda x: x.head(n))``,
        except ignores as_index flag.

        Example
        -------

        >>> df = DataFrame([[1, 2], [1, 4], [5, 6]],
                            columns=['A', 'B'])
        >>> df.groupby('A', as_index=False).head(1)
           A  B
        0  1  2
        2  5  6
        >>> df.groupby('A').head(1)
           A  B
        0  1  2
        2  5  6

        """
        obj = self._selected_obj
        in_head = self._cumcount_array() < n
        head = obj[in_head]
        return head

    def tail(self, n=5):
        """
        Returns last n rows of each group

        Essentially equivalent to ``.apply(lambda x: x.tail(n))``,
        except ignores as_index flag.

        Example
        -------

        >>> df = DataFrame([[1, 2], [1, 4], [5, 6]],
                            columns=['A', 'B'])
        >>> df.groupby('A', as_index=False).tail(1)
           A  B
        0  1  2
        2  5  6
        >>> df.groupby('A').head(1)
           A  B
        0  1  2
        2  5  6

        """
        obj = self._selected_obj
        rng = np.arange(0, -self.grouper._max_groupsize, -1, dtype='int64')
        in_tail = self._cumcount_array(rng, ascending=False) > -n
        tail = obj[in_tail]
        return tail

    def _cumcount_array(self, arr=None, **kwargs):
        """
        arr is where cumcount gets it's values from

        note: this is currently implementing sort=False (though the default is sort=True)
              for groupby in general
        """
        ascending = kwargs.pop('ascending', True)

        if arr is None:
            arr = np.arange(self.grouper._max_groupsize, dtype='int64')

        len_index = len(self._selected_obj.index)
        cumcounts = np.zeros(len_index, dtype=arr.dtype)
        if not len_index:
            return cumcounts

        indices, values = [], []
        for v in self.indices.values():
            indices.append(v)

            if ascending:
                values.append(arr[:len(v)])
            else:
                values.append(arr[len(v)-1::-1])

        indices = np.concatenate(indices)
        values = np.concatenate(values)
        cumcounts[indices] = values

        return cumcounts

    def _index_with_as_index(self, b):
        """
        Take boolean mask of index to be returned from apply, if as_index=True

        """
        # TODO perf, it feels like this should already be somewhere...
        from itertools import chain
        original = self._selected_obj.index
        gp = self.grouper
        levels = chain((gp.levels[i][gp.labels[i][b]]
                        for i in range(len(gp.groupings))),
                       (original.get_level_values(i)[b]
                        for i in range(original.nlevels)))
        new = MultiIndex.from_arrays(list(levels))
        new.names = gp.names + original.names
        return new

    def _try_cast(self, result, obj):
        """
        try to cast the result to our obj original type,
        we may have roundtripped thru object in the mean-time

        """
        if obj.ndim > 1:
            dtype = obj.values.dtype
        else:
            dtype = obj.dtype

        if not np.isscalar(result):
            result = _possibly_downcast_to_dtype(result, dtype)

        return result

    def _cython_agg_general(self, how, numeric_only=True):
        output = {}
        for name, obj in self._iterate_slices():
            is_numeric = is_numeric_dtype(obj.dtype)
            if numeric_only and not is_numeric:
                continue

            try:
                result, names = self.grouper.aggregate(obj.values, how)
            except AssertionError as e:
                raise GroupByError(str(e))
            output[name] = self._try_cast(result, obj)

        if len(output) == 0:
            raise DataError('No numeric types to aggregate')

        return self._wrap_aggregated_output(output, names)

    def _python_agg_general(self, func, *args, **kwargs):
        func = _intercept_function(func)
        f = lambda x: func(x, *args, **kwargs)

        # iterate through "columns" ex exclusions to populate output dict
        output = {}
        for name, obj in self._iterate_slices():
            try:
                result, counts = self.grouper.agg_series(obj, f)
                output[name] = self._try_cast(result, obj)
            except TypeError:
                continue

        if len(output) == 0:
            return self._python_apply_general(f)

        if self.grouper._filter_empty_groups:

            mask = counts.ravel() > 0
            for name, result in compat.iteritems(output):

                # since we are masking, make sure that we have a float object
                values = result
                if is_numeric_dtype(values.dtype):
                    values = com.ensure_float(values)

                output[name] = self._try_cast(values[mask], result)

        return self._wrap_aggregated_output(output)

    def _wrap_applied_output(self, *args, **kwargs):
        raise NotImplementedError

    def _concat_objects(self, keys, values, not_indexed_same=False):
        from pandas.tools.merge import concat

        if not not_indexed_same:
            result = concat(values, axis=self.axis)
            ax = self._selected_obj._get_axis(self.axis)

            if isinstance(result, Series):
                result = result.reindex(ax)
            else:
                result = result.reindex_axis(ax, axis=self.axis)

        elif self.group_keys:

            if self.as_index:

                # possible MI return case
                group_keys = keys
                group_levels = self.grouper.levels
                group_names = self.grouper.names
                result = concat(values, axis=self.axis, keys=group_keys,
                                levels=group_levels, names=group_names)
            else:

                # GH5610, returns a MI, with the first level being a
                # range index
                keys = list(range(len(values)))
                result = concat(values, axis=self.axis, keys=keys)
        else:
            result = concat(values, axis=self.axis)

        return result

    def _apply_filter(self, indices, dropna):
        if len(indices) == 0:
            indices = []
        else:
            indices = np.sort(np.concatenate(indices))
        if dropna:
            filtered = self._selected_obj.take(indices)
        else:
            mask = np.empty(len(self._selected_obj.index), dtype=bool)
            mask.fill(False)
            mask[indices.astype(int)] = True
            # mask fails to broadcast when passed to where; broadcast manually.
            mask = np.tile(mask, list(self._selected_obj.shape[1:]) + [1]).T
            filtered = self._selected_obj.where(mask)  # Fill with NaNs.
        return filtered


@Appender(GroupBy.__doc__)
def groupby(obj, by, **kwds):
    if isinstance(obj, Series):
        klass = SeriesGroupBy
    elif isinstance(obj, DataFrame):
        klass = DataFrameGroupBy
    else:  # pragma: no cover
        raise TypeError('invalid type: %s' % type(obj))

    return klass(obj, by, **kwds)


def _get_axes(group):
    if isinstance(group, Series):
        return [group.index]
    else:
        return group.axes


def _is_indexed_like(obj, axes):
    if isinstance(obj, Series):
        if len(axes) > 1:
            return False
        return obj.index.equals(axes[0])
    elif isinstance(obj, DataFrame):
        return obj.index.equals(axes[0])

    return False


class BaseGrouper(object):
    """
    This is an internal Grouper class, which actually holds the generated groups
    """

    def __init__(self, axis, groupings, sort=True, group_keys=True):
        self.axis = axis
        self.groupings = groupings
        self.sort = sort
        self.group_keys = group_keys
        self.compressed = True

    @property
    def shape(self):
        return tuple(ping.ngroups for ping in self.groupings)

    def __iter__(self):
        return iter(self.indices)

    @property
    def nkeys(self):
        return len(self.groupings)

    def get_iterator(self, data, axis=0):
        """
        Groupby iterator

        Returns
        -------
        Generator yielding sequence of (name, subsetted object)
        for each group
        """
        splitter = self._get_splitter(data, axis=axis)
        keys = self._get_group_keys()
        for key, (i, group) in zip(keys, splitter):
            yield key, group

    def _get_splitter(self, data, axis=0):
        comp_ids, _, ngroups = self.group_info
        return get_splitter(data, comp_ids, ngroups, axis=axis)

    def _get_group_keys(self):
        if len(self.groupings) == 1:
            return self.levels[0]
        else:
            comp_ids, _, ngroups = self.group_info
            # provide "flattened" iterator for multi-group setting
            mapper = _KeyMapper(comp_ids, ngroups, self.labels, self.levels)
            return [mapper.get_key(i) for i in range(ngroups)]

    def apply(self, f, data, axis=0):
        mutated = False
        splitter = self._get_splitter(data, axis=axis)
        group_keys = self._get_group_keys()

        # oh boy
        if (f.__name__ not in _plotting_methods and
                hasattr(splitter, 'fast_apply') and axis == 0):
            try:
                values, mutated = splitter.fast_apply(f, group_keys)
                return group_keys, values, mutated
            except (lib.InvalidApply):
                # we detect a mutation of some kind
                # so take slow path
                pass
            except (Exception) as e:
                # raise this error to the caller
                pass

        result_values = []
        for key, (i, group) in zip(group_keys, splitter):
            object.__setattr__(group, 'name', key)

            # group might be modified
            group_axes = _get_axes(group)
            res = f(group)
            if not _is_indexed_like(res, group_axes):
                mutated = True
            result_values.append(res)

        return group_keys, result_values, mutated

    @cache_readonly
    def indices(self):
        """ dict {group name -> group indices} """
        if len(self.groupings) == 1:
            return self.groupings[0].indices
        else:
            label_list = [ping.labels for ping in self.groupings]
            keys = [ping.group_index for ping in self.groupings]
            return _get_indices_dict(label_list, keys)

    @property
    def labels(self):
        return [ping.labels for ping in self.groupings]

    @property
    def levels(self):
        return [ping.group_index for ping in self.groupings]

    @property
    def names(self):
        return [ping.name for ping in self.groupings]

    def size(self):
        """
        Compute group sizes

        """
        # TODO: better impl
        labels, _, ngroups = self.group_info
        bin_counts = algos.value_counts(labels, sort=False)
        bin_counts = bin_counts.reindex(np.arange(ngroups))
        bin_counts.index = self.result_index
        return bin_counts

    @cache_readonly
    def _max_groupsize(self):
        '''
        Compute size of largest group

        '''
        # For many items in each group this is much faster than
        # self.size().max(), in worst case marginally slower
        if self.indices:
            return max(len(v) for v in self.indices.values())
        else:
            return 0

    @cache_readonly
    def groups(self):
        """ dict {group name -> group labels} """
        if len(self.groupings) == 1:
            return self.groupings[0].groups
        else:
            to_groupby = lzip(*(ping.grouper for ping in self.groupings))
            to_groupby = Index(to_groupby)
            return self.axis.groupby(to_groupby.values)

    @cache_readonly
    def group_info(self):
        comp_ids, obs_group_ids = self._get_compressed_labels()

        ngroups = len(obs_group_ids)
        comp_ids = com._ensure_int64(comp_ids)
        return comp_ids, obs_group_ids, ngroups


    def _get_compressed_labels(self):
        all_labels = [ping.labels for ping in self.groupings]
        if self._overflow_possible:
            tups = lib.fast_zip(all_labels)
            labs, uniques = algos.factorize(tups)

            if self.sort:
                uniques, labs = _reorder_by_uniques(uniques, labs)

            return labs, uniques
        else:
            if len(all_labels) > 1:
                group_index = get_group_index(all_labels, self.shape)
                comp_ids, obs_group_ids = _compress_group_index(group_index)
            else:
                ping = self.groupings[0]
                comp_ids = ping.labels
                obs_group_ids = np.arange(len(ping.group_index))
                self.compressed = False
                self._filter_empty_groups = False

            return comp_ids, obs_group_ids

    @cache_readonly
    def _overflow_possible(self):
        return _int64_overflow_possible(self.shape)

    @cache_readonly
    def ngroups(self):
        return len(self.result_index)

    @cache_readonly
    def result_index(self):
        recons = self.get_group_levels()
        return MultiIndex.from_arrays(recons, names=self.names)

    def get_group_levels(self):
        obs_ids = self.group_info[1]

        if not self.compressed and len(self.groupings) == 1:
            return [self.groupings[0].group_index]

        if self._overflow_possible:
            recons_labels = [np.array(x) for x in zip(*obs_ids)]
        else:
            recons_labels = decons_group_index(obs_ids, self.shape)

        name_list = []
        for ping, labels in zip(self.groupings, recons_labels):
            labels = com._ensure_platform_int(labels)
            name_list.append(ping.group_index.take(labels))

        return name_list

    #------------------------------------------------------------
    # Aggregation functions

    _cython_functions = {
        'add': 'group_add',
        'prod': 'group_prod',
        'min': 'group_min',
        'max': 'group_max',
        'mean': 'group_mean',
        'median': {
            'name': 'group_median'
        },
        'var': 'group_var',
        'first': {
            'name': 'group_nth',
            'f': lambda func, a, b, c, d: func(a, b, c, d, 1)
        },
        'last': 'group_last',
        'count': 'group_count',
    }

    _cython_arity = {
        'ohlc': 4,  # OHLC
    }

    _name_functions = {}

    _filter_empty_groups = True

    def _get_aggregate_function(self, how, values):

        dtype_str = values.dtype.name

        def get_func(fname):
            # find the function, or use the object function, or return a
            # generic
            for dt in [dtype_str, 'object']:
                f = getattr(_algos, "%s_%s" % (fname, dtype_str), None)
                if f is not None:
                    return f
            return getattr(_algos, fname, None)

        ftype = self._cython_functions[how]

        if isinstance(ftype, dict):
            func = afunc = get_func(ftype['name'])

            # a sub-function
            f = ftype.get('f')
            if f is not None:

                def wrapper(*args, **kwargs):
                    return f(afunc, *args, **kwargs)

                # need to curry our sub-function
                func = wrapper

        else:
            func = get_func(ftype)

        if func is None:
            raise NotImplementedError("function is not implemented for this"
                                      "dtype: [how->%s,dtype->%s]" %
                                      (how, dtype_str))
        return func, dtype_str

    def aggregate(self, values, how, axis=0):

        arity = self._cython_arity.get(how, 1)

        vdim = values.ndim
        swapped = False
        if vdim == 1:
            values = values[:, None]
            out_shape = (self.ngroups, arity)
        else:
            if axis > 0:
                swapped = True
                values = values.swapaxes(0, axis)
            if arity > 1:
                raise NotImplementedError
            out_shape = (self.ngroups,) + values.shape[1:]

        if is_numeric_dtype(values.dtype):
            values = com.ensure_float(values)
            is_numeric = True
            out_dtype = 'f%d' % values.dtype.itemsize
        else:
            is_numeric = issubclass(values.dtype.type, (np.datetime64,
                                                        np.timedelta64))
            if is_numeric:
                out_dtype = 'float64'
                values = values.view('int64')
            else:
                out_dtype = 'object'
                values = values.astype(object)

        # will be filled in Cython function
        result = np.empty(out_shape, dtype=out_dtype)

        result.fill(np.nan)
        counts = np.zeros(self.ngroups, dtype=np.int64)

        result = self._aggregate(result, counts, values, how, is_numeric)

        if self._filter_empty_groups:
            if result.ndim == 2:
                try:
                    result = lib.row_bool_subset(
                        result, (counts > 0).view(np.uint8))
                except ValueError:
                    result = lib.row_bool_subset_object(
                        result, (counts > 0).view(np.uint8))
            else:
                result = result[counts > 0]

        if vdim == 1 and arity == 1:
            result = result[:, 0]

        if how in self._name_functions:
            # TODO
            names = self._name_functions[how]()
        else:
            names = None

        if swapped:
            result = result.swapaxes(0, axis)

        return result, names

    def _aggregate(self, result, counts, values, how, is_numeric):
        agg_func, dtype = self._get_aggregate_function(how, values)

        comp_ids, _, ngroups = self.group_info
        if values.ndim > 3:
            # punting for now
            raise NotImplementedError
        elif values.ndim > 2:
            for i, chunk in enumerate(values.transpose(2, 0, 1)):

                chunk = chunk.squeeze()
                agg_func(result[:, :, i], counts, chunk, comp_ids)
        else:
            agg_func(result, counts, values, comp_ids)

        return result

    def agg_series(self, obj, func):
        try:
            return self._aggregate_series_fast(obj, func)
        except Exception:
            return self._aggregate_series_pure_python(obj, func)

    def _aggregate_series_fast(self, obj, func):
        func = _intercept_function(func)

        if obj.index._has_complex_internals:
            raise TypeError('Incompatible index for Cython grouper')

        group_index, _, ngroups = self.group_info

        # avoids object / Series creation overhead
        dummy = obj._get_values(slice(None, 0)).to_dense()
        indexer = _algos.groupsort_indexer(group_index, ngroups)[0]
        obj = obj.take(indexer, convert=False)
        group_index = com.take_nd(group_index, indexer, allow_fill=False)
        grouper = lib.SeriesGrouper(obj, func, group_index, ngroups,
                                    dummy)
        result, counts = grouper.get_result()
        return result, counts

    def _aggregate_series_pure_python(self, obj, func):

        group_index, _, ngroups = self.group_info

        counts = np.zeros(ngroups, dtype=int)
        result = None

        splitter = get_splitter(obj, group_index, ngroups, axis=self.axis)

        for label, group in splitter:
            res = func(group)
            if result is None:
                if (isinstance(res, (Series, np.ndarray)) or
                        isinstance(res, list)):
                    raise ValueError('Function does not reduce')
                result = np.empty(ngroups, dtype='O')

            counts[label] = group.shape[0]
            result[label] = res

        result = lib.maybe_convert_objects(result, try_float=0)
        return result, counts


def generate_bins_generic(values, binner, closed):
    """
    Generate bin edge offsets and bin labels for one array using another array
    which has bin edge values. Both arrays must be sorted.

    Parameters
    ----------
    values : array of values
    binner : a comparable array of values representing bins into which to bin
        the first array. Note, 'values' end-points must fall within 'binner'
        end-points.
    closed : which end of bin is closed; left (default), right

    Returns
    -------
    bins : array of offsets (into 'values' argument) of bins.
        Zero and last edge are excluded in result, so for instance the first
        bin is values[0:bin[0]] and the last is values[bin[-1]:]
    """
    lenidx = len(values)
    lenbin = len(binner)

    if lenidx <= 0 or lenbin <= 0:
        raise ValueError("Invalid length for values or for binner")

    # check binner fits data
    if values[0] < binner[0]:
        raise ValueError("Values falls before first bin")

    if values[lenidx - 1] > binner[lenbin - 1]:
        raise ValueError("Values falls after last bin")

    bins = np.empty(lenbin - 1, dtype=np.int64)

    j = 0  # index into values
    bc = 0  # bin count

    # linear scan, presume nothing about values/binner except that it fits ok
    for i in range(0, lenbin - 1):
        r_bin = binner[i + 1]

        # count …