window.py

"""
Provide a generic structure to support window functions,
similar to how we have a Groupby object.
"""
from collections import defaultdict
from datetime import timedelta
from textwrap import dedent
from typing import Callable, List, Optional, Set, Union
import warnings

import numpy as np

import pandas._libs.window as libwindow
from pandas.compat._optional import import_optional_dependency
from pandas.compat.numpy import function as nv
from pandas.util._decorators import Appender, Substitution, cache_readonly

from pandas.core.dtypes.common import (
    ensure_float64,
    is_bool,
    is_float_dtype,
    is_integer,
    is_integer_dtype,
    is_list_like,
    is_scalar,
    is_timedelta64_dtype,
    needs_i8_conversion,
)
from pandas.core.dtypes.generic import (
    ABCDataFrame,
    ABCDateOffset,
    ABCDatetimeIndex,
    ABCPeriodIndex,
    ABCSeries,
    ABCTimedeltaIndex,
)

from pandas._typing import Axis, FrameOrSeries, Scalar
from pandas.core.base import DataError, PandasObject, SelectionMixin
import pandas.core.common as com
from pandas.core.generic import _shared_docs
from pandas.core.groupby.base import GroupByMixin
from pandas.core.index import Index, MultiIndex, ensure_index

_shared_docs = dict(**_shared_docs)
_doc_template = """
        Returns
        -------
        Series or DataFrame
            Return type is determined by the caller.

        See Also
        --------
        Series.%(name)s : Series %(name)s.
        DataFrame.%(name)s : DataFrame %(name)s.
"""


class _Window(PandasObject, SelectionMixin):
    _attributes = [
        "window",
        "min_periods",
        "center",
        "win_type",
        "axis",
        "on",
        "closed",
    ]  # type: List[str]
    exclusions = set()  # type: Set[str]

    def __init__(
        self,
        obj,
        window=None,
        min_periods: Optional[int] = None,
        center: Optional[bool] = False,
        win_type: Optional[str] = None,
        axis: Axis = 0,
        on: Optional[str] = None,
        closed: Optional[str] = None,
        **kwargs
    ):

        self.__dict__.update(kwargs)
        self.obj = obj
        self.on = on
        self.closed = closed
        self.window = window
        self.min_periods = min_periods
        self.center = center
        self.win_type = win_type
        self.win_freq = None
        self.axis = obj._get_axis_number(axis) if axis is not None else None
        self.validate()

    @property
    def _constructor(self):
        return Window

    @property
    def is_datetimelike(self) -> Optional[bool]:
        return None

    @property
    def _on(self):
        return None

    @property
    def is_freq_type(self) -> bool:
        return self.win_type == "freq"

    def validate(self):
        if self.center is not None and not is_bool(self.center):
            raise ValueError("center must be a boolean")
        if self.min_periods is not None and not is_integer(self.min_periods):
            raise ValueError("min_periods must be an integer")
        if self.closed is not None and self.closed not in [
            "right",
            "both",
            "left",
            "neither",
        ]:
            raise ValueError("closed must be 'right', 'left', 'both' or 'neither'")

    def _create_blocks(self):
        """
        Split data into blocks & return conformed data.
        """

        obj = self._selected_obj

        # filter out the on from the object
        if self.on is not None:
            if obj.ndim == 2:
                obj = obj.reindex(columns=obj.columns.difference([self.on]), copy=False)
        blocks = obj._to_dict_of_blocks(copy=False).values()

        return blocks, obj

    def _gotitem(self, key, ndim, subset=None):
        """
        Sub-classes to define. Return a sliced object.

        Parameters
        ----------
        key : str / list of selections
        ndim : 1,2
            requested ndim of result
        subset : object, default None
            subset to act on
        """

        # create a new object to prevent aliasing
        if subset is None:
            subset = self.obj
        self = self._shallow_copy(subset)
        self._reset_cache()
        if subset.ndim == 2:
            if is_scalar(key) and key in subset or is_list_like(key):
                self._selection = key
        return self

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

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

    def _dir_additions(self):
        return self.obj._dir_additions()

    def _get_window(self, other=None, **kwargs) -> int:
        """
        Returns window length

        Parameters
        ----------
        other:
            ignored, exists for compatibility

        Returns
        -------
        window : int
        """
        return self.window

    @property
    def _window_type(self) -> str:
        return self.__class__.__name__

    def __repr__(self) -> str:
        """
        Provide a nice str repr of our rolling object.
        """

        attrs = (
            "{k}={v}".format(k=k, v=getattr(self, k))
            for k in self._attributes
            if getattr(self, k, None) is not None
        )
        return "{klass} [{attrs}]".format(
            klass=self._window_type, attrs=",".join(attrs)
        )

    def __iter__(self):
        url = "https://github.com/pandas-dev/pandas/issues/11704"
        raise NotImplementedError("See issue #11704 {url}".format(url=url))

    def _get_index(self) -> Optional[np.ndarray]:
        """
        Return integer representations as an ndarray if index is frequency.

        Returns
        -------
        None or ndarray
        """

        if self.is_freq_type:
            return self._on.asi8
        return None

    def _prep_values(self, values: Optional[np.ndarray] = None) -> np.ndarray:
        """Convert input to numpy arrays for Cython routines"""
        if values is None:
            values = getattr(self._selected_obj, "values", self._selected_obj)

        # GH #12373 : rolling functions error on float32 data
        # make sure the data is coerced to float64
        if is_float_dtype(values.dtype):
            values = ensure_float64(values)
        elif is_integer_dtype(values.dtype):
            values = ensure_float64(values)
        elif needs_i8_conversion(values.dtype):
            raise NotImplementedError(
                "ops for {action} for this "
                "dtype {dtype} are not "
                "implemented".format(action=self._window_type, dtype=values.dtype)
            )
        else:
            try:
                values = ensure_float64(values)
            except (ValueError, TypeError):
                raise TypeError("cannot handle this type -> {0}".format(values.dtype))

        # Convert inf to nan for C funcs
        inf = np.isinf(values)
        if inf.any():
            values = np.where(inf, np.nan, values)

        return values

    def _wrap_result(self, result, block=None, obj=None):
        """
        Wrap a single result.
        """

        if obj is None:
            obj = self._selected_obj
        index = obj.index

        if isinstance(result, np.ndarray):

            # coerce if necessary
            if block is not None:
                if is_timedelta64_dtype(block.values.dtype):
                    # TODO: do we know what result.dtype is at this point?
                    #  i.e. can we just do an astype?
                    from pandas import to_timedelta

                    result = to_timedelta(result.ravel(), unit="ns").values.reshape(
                        result.shape
                    )

            if result.ndim == 1:
                from pandas import Series

                return Series(result, index, name=obj.name)

            return type(obj)(result, index=index, columns=block.columns)
        return result

    def _wrap_results(self, results, blocks, obj, exclude=None) -> FrameOrSeries:
        """
        Wrap the results.

        Parameters
        ----------
        results : list of ndarrays
        blocks : list of blocks
        obj : conformed data (may be resampled)
        exclude: list of columns to exclude, default to None
        """

        from pandas import Series, concat

        final = []
        for result, block in zip(results, blocks):

            result = self._wrap_result(result, block=block, obj=obj)
            if result.ndim == 1:
                return result
            final.append(result)

        # if we have an 'on' column
        # we want to put it back into the results
        # in the same location
        columns = self._selected_obj.columns
        if self.on is not None and not self._on.equals(obj.index):

            name = self._on.name
            final.append(Series(self._on, index=obj.index, name=name))

            if self._selection is not None:

                selection = ensure_index(self._selection)

                # need to reorder to include original location of
                # the on column (if its not already there)
                if name not in selection:
                    columns = self.obj.columns
                    indexer = columns.get_indexer(selection.tolist() + [name])
                    columns = columns.take(sorted(indexer))

        # exclude nuisance columns so that they are not reindexed
        if exclude is not None and exclude:
            columns = [c for c in columns if c not in exclude]

            if not columns:
                raise DataError("No numeric types to aggregate")

        if not len(final):
            return obj.astype("float64")
        return concat(final, axis=1).reindex(columns=columns, copy=False)

    def _center_window(self, result, window) -> np.ndarray:
        """
        Center the result in the window.
        """
        if self.axis > result.ndim - 1:
            raise ValueError("Requested axis is larger then no. of argument dimensions")

        offset = _offset(window, True)
        if offset > 0:
            if isinstance(result, (ABCSeries, ABCDataFrame)):
                result = result.slice_shift(-offset, axis=self.axis)
            else:
                lead_indexer = [slice(None)] * result.ndim
                lead_indexer[self.axis] = slice(offset, None)
                result = np.copy(result[tuple(lead_indexer)])
        return result

    def _get_roll_func(
        self, cfunc: Callable, check_minp: Callable, index: np.ndarray, **kwargs
    ) -> Callable:
        """
        Wrap rolling function to check values passed.

        Parameters
        ----------
        cfunc : callable
            Cython function used to calculate rolling statistics
        check_minp : callable
            function to check minimum period parameter
        index : ndarray
            used for variable window

        Returns
        -------
        func : callable
        """

        def func(arg, window, min_periods=None, closed=None):
            minp = check_minp(min_periods, window)
            return cfunc(arg, window, minp, index, closed, **kwargs)

        return func

    def _apply(
        self,
        func: Union[str, Callable],
        name: Optional[str] = None,
        window: Optional[Union[int, str]] = None,
        center: Optional[bool] = None,
        check_minp: Optional[Callable] = None,
        **kwargs
    ):
        """
        Rolling statistical measure using supplied function.

        Designed to be used with passed-in Cython array-based functions.

        Parameters
        ----------
        func : str/callable to apply
        name : str, optional
           name of this function
        window : int/str, default to _get_window()
            window length or offset
        center : bool, default to self.center
        check_minp : function, default to _use_window
        **kwargs
            additional arguments for rolling function and window function

        Returns
        -------
        y : type of input
        """
        if center is None:
            center = self.center

        if check_minp is None:
            check_minp = _use_window

        if window is None:
            window = self._get_window(**kwargs)

        blocks, obj = self._create_blocks()
        block_list = list(blocks)
        index_as_array = self._get_index()

        results = []
        exclude = []  # type: List[Scalar]
        for i, b in enumerate(blocks):
            try:
                values = self._prep_values(b.values)

            except (TypeError, NotImplementedError):
                if isinstance(obj, ABCDataFrame):
                    exclude.extend(b.columns)
                    del block_list[i]
                    continue
                else:
                    raise DataError("No numeric types to aggregate")

            if values.size == 0:
                results.append(values.copy())
                continue

            # if we have a string function name, wrap it
            if isinstance(func, str):
                cfunc = getattr(libwindow, func, None)
                if cfunc is None:
                    raise ValueError(
                        "we do not support this function "
                        "in libwindow.{func}".format(func=func)
                    )

                func = self._get_roll_func(cfunc, check_minp, index_as_array, **kwargs)

            # calculation function
            if center:
                offset = _offset(window, center)
                additional_nans = np.array([np.NaN] * offset)

                def calc(x):
                    return func(
                        np.concatenate((x, additional_nans)),
                        window,
                        min_periods=self.min_periods,
                        closed=self.closed,
                    )

            else:

                def calc(x):
                    return func(
                        x, window, min_periods=self.min_periods, closed=self.closed
                    )

            with np.errstate(all="ignore"):
                if values.ndim > 1:
                    result = np.apply_along_axis(calc, self.axis, values)
                else:
                    result = calc(values)
                    result = np.asarray(result)

            if center:
                result = self._center_window(result, window)

            results.append(result)

        return self._wrap_results(results, block_list, obj, exclude)

    def aggregate(self, func, *args, **kwargs):
        result, how = self._aggregate(func, *args, **kwargs)
        if result is None:
            return self.apply(func, raw=False, args=args, kwargs=kwargs)
        return result

    agg = aggregate

    _shared_docs["sum"] = dedent(
        """
    Calculate %(name)s sum of given DataFrame or Series.

    Parameters
    ----------
    *args, **kwargs
        For compatibility with other %(name)s methods. Has no effect
        on the computed value.

    Returns
    -------
    Series or DataFrame
        Same type as the input, with the same index, containing the
        %(name)s sum.

    See Also
    --------
    Series.sum : Reducing sum for Series.
    DataFrame.sum : Reducing sum for DataFrame.

    Examples
    --------
    >>> s = pd.Series([1, 2, 3, 4, 5])
    >>> s
    0    1
    1    2
    2    3
    3    4
    4    5
    dtype: int64

    >>> s.rolling(3).sum()
    0     NaN
    1     NaN
    2     6.0
    3     9.0
    4    12.0
    dtype: float64

    >>> s.expanding(3).sum()
    0     NaN
    1     NaN
    2     6.0
    3    10.0
    4    15.0
    dtype: float64

    >>> s.rolling(3, center=True).sum()
    0     NaN
    1     6.0
    2     9.0
    3    12.0
    4     NaN
    dtype: float64

    For DataFrame, each %(name)s sum is computed column-wise.

    >>> df = pd.DataFrame({"A": s, "B": s ** 2})
    >>> df
       A   B
    0  1   1
    1  2   4
    2  3   9
    3  4  16
    4  5  25

    >>> df.rolling(3).sum()
          A     B
    0   NaN   NaN
    1   NaN   NaN
    2   6.0  14.0
    3   9.0  29.0
    4  12.0  50.0
    """
    )

    _shared_docs["mean"] = dedent(
        """
    Calculate the %(name)s mean of the values.

    Parameters
    ----------
    *args
        Under Review.
    **kwargs
        Under Review.

    Returns
    -------
    Series or DataFrame
        Returned object type is determined by the caller of the %(name)s
        calculation.

    See Also
    --------
    Series.%(name)s : Calling object with Series data.
    DataFrame.%(name)s : Calling object with DataFrames.
    Series.mean : Equivalent method for Series.
    DataFrame.mean : Equivalent method for DataFrame.

    Examples
    --------
    The below examples will show rolling mean calculations with window sizes of
    two and three, respectively.

    >>> s = pd.Series([1, 2, 3, 4])
    >>> s.rolling(2).mean()
    0    NaN
    1    1.5
    2    2.5
    3    3.5
    dtype: float64

    >>> s.rolling(3).mean()
    0    NaN
    1    NaN
    2    2.0
    3    3.0
    dtype: float64
    """
    )


class Window(_Window):
    """
    Provide rolling window calculations.

    Parameters
    ----------
    window : int, or offset
        Size of the moving window. This is the number of observations used for
        calculating the statistic. Each window will be a fixed size.

        If its an offset then this will be the time period of each window. Each
        window will be a variable sized based on the observations included in
        the time-period. This is only valid for datetimelike indexes.
    min_periods : int, default None
        Minimum number of observations in window required to have a value
        (otherwise result is NA). For a window that is specified by an offset,
        `min_periods` will default to 1. Otherwise, `min_periods` will default
        to the size of the window.
    center : bool, default False
        Set the labels at the center of the window.
    win_type : str, default None
        Provide a window type. If ``None``, all points are evenly weighted.
        See the notes below for further information.
    on : str, optional
        For a DataFrame, a datetime-like column on which to calculate the rolling
        window, rather than the DataFrame's index. Provided integer column is
        ignored and excluded from result since an integer index is not used to
        calculate the rolling window.
    axis : int or str, default 0
    closed : str, default None
        Make the interval closed on the 'right', 'left', 'both' or
        'neither' endpoints.
        For offset-based windows, it defaults to 'right'.
        For fixed windows, defaults to 'both'. Remaining cases not implemented
        for fixed windows.

        .. versionadded:: 0.20.0

    Returns
    -------
    a Window or Rolling sub-classed for the particular operation

    See Also
    --------
    expanding : Provides expanding transformations.
    ewm : Provides exponential weighted functions.

    Notes
    -----
    By default, the result is set to the right edge of the window. This can be
    changed to the center of the window by setting ``center=True``.

    To learn more about the offsets & frequency strings, please see `this link
    <http://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#offset-aliases>`__.

    The recognized win_types are:

    * ``boxcar``
    * ``triang``
    * ``blackman``
    * ``hamming``
    * ``bartlett``
    * ``parzen``
    * ``bohman``
    * ``blackmanharris``
    * ``nuttall``
    * ``barthann``
    * ``kaiser`` (needs beta)
    * ``gaussian`` (needs std)
    * ``general_gaussian`` (needs power, width)
    * ``slepian`` (needs width)
    * ``exponential`` (needs tau), center is set to None.

    If ``win_type=None`` all points are evenly weighted. To learn more about
    different window types see `scipy.signal window functions
    <https://docs.scipy.org/doc/scipy/reference/signal.html#window-functions>`__.

    Examples
    --------

    >>> df = pd.DataFrame({'B': [0, 1, 2, np.nan, 4]})
    >>> df
         B
    0  0.0
    1  1.0
    2  2.0
    3  NaN
    4  4.0

    Rolling sum with a window length of 2, using the 'triang'
    window type.

    >>> df.rolling(2, win_type='triang').sum()
         B
    0  NaN
    1  0.5
    2  1.5
    3  NaN
    4  NaN

    Rolling sum with a window length of 2, min_periods defaults
    to the window length.

    >>> df.rolling(2).sum()
         B
    0  NaN
    1  1.0
    2  3.0
    3  NaN
    4  NaN

    Same as above, but explicitly set the min_periods

    >>> df.rolling(2, min_periods=1).sum()
         B
    0  0.0
    1  1.0
    2  3.0
    3  2.0
    4  4.0

    A ragged (meaning not-a-regular frequency), time-indexed DataFrame

    >>> df = pd.DataFrame({'B': [0, 1, 2, np.nan, 4]},
    ...                   index = [pd.Timestamp('20130101 09:00:00'),
    ...                            pd.Timestamp('20130101 09:00:02'),
    ...                            pd.Timestamp('20130101 09:00:03'),
    ...                            pd.Timestamp('20130101 09:00:05'),
    ...                            pd.Timestamp('20130101 09:00:06')])

    >>> df
                           B
    2013-01-01 09:00:00  0.0
    2013-01-01 09:00:02  1.0
    2013-01-01 09:00:03  2.0
    2013-01-01 09:00:05  NaN
    2013-01-01 09:00:06  4.0

    Contrasting to an integer rolling window, this will roll a variable
    length window corresponding to the time period.
    The default for min_periods is 1.

    >>> df.rolling('2s').sum()
                           B
    2013-01-01 09:00:00  0.0
    2013-01-01 09:00:02  1.0
    2013-01-01 09:00:03  3.0
    2013-01-01 09:00:05  NaN
    2013-01-01 09:00:06  4.0
    """

    def validate(self):
        super().validate()

        window = self.window
        if isinstance(window, (list, tuple, np.ndarray)):
            pass
        elif is_integer(window):
            if window <= 0:
                raise ValueError("window must be > 0 ")
            import_optional_dependency(
                "scipy", extra="Scipy is required to generate window weight."
            )
            import scipy.signal as sig

            if not isinstance(self.win_type, str):
                raise ValueError("Invalid win_type {0}".format(self.win_type))
            if getattr(sig, self.win_type, None) is None:
                raise ValueError("Invalid win_type {0}".format(self.win_type))
        else:
            raise ValueError("Invalid window {0}".format(window))

    def _get_window(self, other=None, **kwargs) -> np.ndarray:
        """
        Provide validation for the window type, return the window
        which has already been validated.

        Parameters
        ----------
        other:
            ignored, exists for compatibility

        Returns
        -------
        window : ndarray
            the window, weights
        """

        window = self.window
        if isinstance(window, (list, tuple, np.ndarray)):
            return com.asarray_tuplesafe(window).astype(float)
        elif is_integer(window):
            import scipy.signal as sig

            # the below may pop from kwargs
            def _validate_win_type(win_type, kwargs):
                arg_map = {
                    "kaiser": ["beta"],
                    "gaussian": ["std"],
                    "general_gaussian": ["power", "width"],
                    "slepian": ["width"],
                    "exponential": ["tau"],
                }

                if win_type in arg_map:
                    win_args = _pop_args(win_type, arg_map[win_type], kwargs)
                    if win_type == "exponential":
                        # exponential window requires the first arg (center)
                        # to be set to None (necessary for symmetric window)
                        win_args.insert(0, None)

                    return tuple([win_type] + win_args)

                return win_type

            def _pop_args(win_type, arg_names, kwargs):
                msg = "%s window requires %%s" % win_type
                all_args = []
                for n in arg_names:
                    if n not in kwargs:
                        raise ValueError(msg % n)
                    all_args.append(kwargs.pop(n))
                return all_args

            win_type = _validate_win_type(self.win_type, kwargs)
            # GH #15662. `False` makes symmetric window, rather than periodic.
            return sig.get_window(win_type, window, False).astype(float)

    def _get_roll_func(
        self, cfunc: Callable, check_minp: Callable, index: np.ndarray, **kwargs
    ) -> Callable:
        def func(arg, window, min_periods=None, closed=None):
            minp = check_minp(min_periods, len(window))
            return cfunc(arg, window, minp)

        return func

    _agg_see_also_doc = dedent(
        """
    See Also
    --------
    pandas.DataFrame.rolling.aggregate
    pandas.DataFrame.aggregate
    """
    )

    _agg_examples_doc = dedent(
        """
    Examples
    --------

    >>> df = pd.DataFrame(np.random.randn(10, 3), columns=['A', 'B', 'C'])
    >>> df
              A         B         C
    0 -2.385977 -0.102758  0.438822
    1 -1.004295  0.905829 -0.954544
    2  0.735167 -0.165272 -1.619346
    3 -0.702657 -1.340923 -0.706334
    4 -0.246845  0.211596 -0.901819
    5  2.463718  3.157577 -1.380906
    6 -1.142255  2.340594 -0.039875
    7  1.396598 -1.647453  1.677227
    8 -0.543425  1.761277 -0.220481
    9 -0.640505  0.289374 -1.550670

    >>> df.rolling(3, win_type='boxcar').agg('mean')
              A         B         C
    0       NaN       NaN       NaN
    1       NaN       NaN       NaN
    2 -0.885035  0.212600 -0.711689
    3 -0.323928 -0.200122 -1.093408
    4 -0.071445 -0.431533 -1.075833
    5  0.504739  0.676083 -0.996353
    6  0.358206  1.903256 -0.774200
    7  0.906020  1.283573  0.085482
    8 -0.096361  0.818139  0.472290
    9  0.070889  0.134399 -0.031308
    """
    )

    @Substitution(
        see_also=_agg_see_also_doc,
        examples=_agg_examples_doc,
        versionadded="",
        klass="Series/DataFrame",
        axis="",
    )
    @Appender(_shared_docs["aggregate"])
    def aggregate(self, arg, *args, **kwargs):
        result, how = self._aggregate(arg, *args, **kwargs)
        if result is None:

            # these must apply directly
            result = arg(self)

        return result

    agg = aggregate

    @Substitution(name="window")
    @Appender(_shared_docs["sum"])
    def sum(self, *args, **kwargs):
        nv.validate_window_func("sum", args, kwargs)
        return self._apply("roll_weighted_sum", **kwargs)

    @Substitution(name="window")
    @Appender(_shared_docs["mean"])
    def mean(self, *args, **kwargs):
        nv.validate_window_func("mean", args, kwargs)
        return self._apply("roll_weighted_mean", **kwargs)


class _GroupByMixin(GroupByMixin):
    """
    Provide the groupby facilities.
    """

    def __init__(self, obj, *args, **kwargs):
        parent = kwargs.pop("parent", None)  # noqa
        groupby = kwargs.pop("groupby", None)
        if groupby is None:
            groupby, obj = obj, obj.obj
        self._groupby = groupby
        self._groupby.mutated = True
        self._groupby.grouper.mutated = True
        super().__init__(obj, *args, **kwargs)

    count = GroupByMixin._dispatch("count")
    corr = GroupByMixin._dispatch("corr", other=None, pairwise=None)
    cov = GroupByMixin._dispatch("cov", other=None, pairwise=None)

    def _apply(
        self, func, name=None, window=None, center=None, check_minp=None, **kwargs
    ):
        """
        Dispatch to apply; we are stripping all of the _apply kwargs and
        performing the original function call on the grouped object.
        """

        def f(x, name=name, *args):
            x = self._shallow_copy(x)

            if isinstance(name, str):
                return getattr(x, name)(*args, **kwargs)

            return x.apply(name, *args, **kwargs)

        return self._groupby.apply(f)


class _Rolling(_Window):
    @property
    def _constructor(self):
        return Rolling


class _Rolling_and_Expanding(_Rolling):

    _shared_docs["count"] = dedent(
        r"""
    The %(name)s count of any non-NaN observations inside the window.

    Returns
    -------
    Series or DataFrame
        Returned object type is determined by the caller of the %(name)s
        calculation.

    See Also
    --------
    Series.%(name)s : Calling object with Series data.
    DataFrame.%(name)s : Calling object with DataFrames.
    DataFrame.count : Count of the full DataFrame.

    Examples
    --------
    >>> s = pd.Series([2, 3, np.nan, 10])
    >>> s.rolling(2).count()
    0    1.0
    1    2.0
    2    1.0
    3    1.0
    dtype: float64
    >>> s.rolling(3).count()
    0    1.0
    1    2.0
    2    2.0
    3    2.0
    dtype: float64
    >>> s.rolling(4).count()
    0    1.0
    1    2.0
    2    2.0
    3    3.0
    dtype: float64
    """
    )

    def count(self):

        blocks, obj = self._create_blocks()
        # Validate the index
        self._get_index()

        window = self._get_window()
        window = min(window, len(obj)) if not self.center else window

        results = []
        for b in blocks:
            result = b.notna().astype(int)
            result = self._constructor(
                result,
                window=window,
                min_periods=0,
                center=self.center,
                axis=self.axis,
                closed=self.closed,
            ).sum()
            results.append(result)

        return self._wrap_results(results, blocks, obj)

    _shared_docs["apply"] = dedent(
        r"""
    The %(name)s function's apply function.

    Parameters
    ----------
    func : function
        Must produce a single value from an ndarray input if ``raw=True``
        or a single value from a Series if ``raw=False``.
    raw : bool, default None
        * ``False`` : passes each row or column as a Series to the
          function.
        * ``True`` or ``None`` : the passed function will receive ndarray
          objects instead.
          If you are just applying a NumPy reduction function this will
          achieve much better performance.

        The `raw` parameter is required and will show a FutureWarning if
        not passed. In the future `raw` will default to False.

        .. versionadded:: 0.23.0
    *args, **kwargs
        Arguments and keyword arguments to be passed into func.

    Returns
    -------
    Series or DataFrame
        Return type is determined by the caller.

    See Also
    --------
    Series.%(name)s : Series %(name)s.
    DataFrame.%(name)s : DataFrame %(name)s.
    """
    )

    def apply(self, func, raw=None, args=(), kwargs={}):
        from pandas import Series

        kwargs.pop("_level", None)
        window = self._get_window()
        offset = _offset(window, self.center)
        index_as_array = self._get_index()

        # TODO: default is for backward compat
        # change to False in the future
        if raw is None:
            warnings.warn(
                "Currently, 'apply' passes the values as ndarrays to the "
                "applied function. In the future, this will change to passing "
                "it as Series objects. You need to specify 'raw=True' to keep "
                "the current behaviour, and you can pass 'raw=False' to "
                "silence this warning",
                FutureWarning,
                stacklevel=3,
            )
            raw = True

        def f(arg, window, min_periods, closed):
            minp = _use_window(min_periods, window)
            if not raw:
                arg = Series(arg, index=self.obj.index)
            return libwindow.roll_generic(
                arg,
                window,
                minp,
                index_as_array,
                closed,
                offset,
                func,
                raw,
                args,
                kwargs,
            )

        return self._apply(f, func, args=args, kwargs=kwargs, center=False, raw=raw)

    def sum(self, *args, **kwargs):
        nv.validate_window_func("sum", args, kwargs)
        return self._apply("roll_sum", "sum", **kwargs)

    _shared_docs["max"] = dedent(
        """
    Calculate the %(name)s maximum.

    Parameters
    ----------
    *args, **kwargs
        Arguments and keyword arguments to be passed into func.
    """
    )

    def max(self, *args, **kwargs):
        nv.validate_window_func("max", args, kwargs)
        return self._apply("roll_max", "max", **kwargs)

    _shared_docs["min"] = dedent(
        """
    Calculate the %(name)s minimum.

    Parameters
    ----------
    **kwargs
        Under Review.

    Returns
    -------
    Series or DataFrame
        Returned object type is determined by the caller of the %(name)s
        calculation.

    See Also
    --------
    Series.%(name)s : Calling object with a Series.
    DataFrame.%(name)s : Calling object with a DataFrame.
    Series.min : Similar method for Series.
    DataFrame.min : Similar method for DataFrame.

    Examples
    --------
    Performing a rolling minimum with a window size of 3.

    >>> s = pd.Series([4, 3, 5, 2, 6])
    >>> s.rolling(3).min()
    0    NaN
    1    NaN
    2    3.0
    3    2.0
    4    2.0
    dtype: float64
    """
    )

    def min(self, *args, **kwargs):
        nv.validate_window_func("min", args, kwargs)
        return self._apply("roll_min", "min", **kwargs)

    def mean(self, *args, **kwargs):
        nv.validate_window_func("mean", args, kwargs)
        return self._apply("roll_mean", "mean", **kwargs)

    _shared_docs["median"] = dedent(
        """
    Calculate the %(name)s median.

    Parameters
    ----------
    **kwargs
        For compatibility with other %(name)s methods. Has no effect
        on the computed median.

    Returns
    -------
    Series or DataFrame
        Returned type is the same as the original object.

    See Also
    --------
    Series.%(name)s : Calling object with Series data.
    DataFrame.%(name)s : Calling object with DataFrames.
    Series.median : Equivalent method for Series.
    DataFrame.median : Equivalent method for DataFrame.

    Examples
    --------
    Compute the rolling median of a series with a window size of 3.

    >>> s = pd.Series([0, 1, 2, 3, 4])
    >>> s.rolling(3).median()
    0    NaN
    1    NaN
    2    1.0
    3    2.0
    4    3.0
    dtype: float64
    """
    )

    def median(self, **kwargs):
        return self._apply("roll_median_c", "median", **kwargs)

    _shared_docs["std"] = dedent(
        """
    Calculate %(name)s standard deviation.

    Normalized by N-1 by default. This can be changed using the `ddof`
    argument.

    Parameters
    ----------
    ddof : int, default 1
        Delta Degrees of Freedom.  The divisor used in calculations
        is ``N - ddof``, where ``N`` represents the number of elements.
    *args, **kwargs
        For NumPy compatibility. No additional arguments are used.

    Returns
    -------
    Series or DataFrame
        Returns the same object type as the caller of the %(name)s calculation.

    See Also
    --------
    Series.%(name)s : Calling object with Series data.
    DataFrame.%(name)s : Calling object with DataFrames.
    Series.std : Equivalent method for Series.
    DataFrame.std : Equivalent method for DataFrame.
    numpy.std : Equivalent method for Numpy array.

    Notes
    -----
    The default `ddof` of 1 used in Series.std is different than the default
    `ddof` of 0 in numpy.std.

    A minimum of one period is required for the rolling calculation.

    Examples
    --------
    >>> s = pd.Series([5, 5, 6, 7, 5, 5, 5])
    >>> s.rolling(3).std()
    0         NaN
    1         NaN
    2    0.577350
    3    1.000000
    4    1.000000
    5    1.154701
    6    0.000000
    dtype: float64

    >>> s.expanding(3).std()
    0         NaN
    1         NaN
    2    0.577350
    3    0.957427
    4    0.894427
    5    0.836660
    6    0.786796
    dtype: float64
    """
    )

    def std(self, ddof=1, *args, **kwargs):
        nv.validate_window_func("std", args, kwargs)
        window = self._get_window()
        index_as_array = self._get_index()

        def f(arg, *args, **kwargs):
            minp = _require_min_periods(1)(self.min_periods, window)
            return _zsqrt(
                libwindow.roll_var(arg, window, minp, index_as_array, self.closed, ddof)
            )

        return self._apply(
            f, "std", check_minp=_require_min_periods(1), ddof=ddof, **kwargs
        )

    _shared_docs["var"] = dedent(
        """
    Calculate unbiased %(name)s variance.

    Normalized by N-1 by default. This can be changed using the `ddof`
    argument.

    Parameters
    ----------
    ddof : int, default 1
        Delta Degrees of Freedom.  The divisor used in calculations
        is ``N - ddof``, where ``N`` represents the number of elements.
    *args, **kwargs
        For NumPy compatibility. No additional arguments are used.

    Returns
    -------
    Series or DataFrame
        Returns the same object type as the caller of the %(name)s calculation.

    See Also
    --------
    Series.%(name)s : Calling object with Series data.
    DataFrame.%(name)s : Calling object with DataFrames.
    Series.var : Equivalent method for Series.
    DataFrame.var : Equivalent method for DataFrame.
    numpy.var : Equivalent method for Numpy array.

    Notes
    -----
    The default `ddof` of 1 used in :meth:`Series.var` is different than the
    default `ddof` of 0 in :func:`numpy.var`.

    A minimum of 1 period is required for the rolling calculation.

    Examples
    --------
    >>> s = pd.Series([5, 5, 6, 7, 5, 5, 5])
    >>> s.rolling(3).var()
    0         NaN
    1         NaN
    2    0.333333
    3    1.000000
    4    1.000000
    5    1.333333
    6    0.000000
    dtype: float64

    >>> s.expanding(3).var()
    0         NaN
    1         NaN
    2    0.333333
    3    0.916667
    4    0.800000
    5    0.700000
    6    0.619048
    dtype: float64
    """
    )

    def var(self, ddof=1, *args, **kwargs):
        nv.validate_window_func("var", args, kwargs)
        return self._apply(
            "roll_var", "var", check_minp=_require_min_periods(1), ddof=ddof, **kwargs
        )

    _shared_docs[
        "skew"
    ] = """
    Unbiased %(name)s skewness.

    Parameters
    ----------
    **kwargs
        Keyword arguments to be passed into func.
    """

    def skew(self, **kwargs):
        return self._apply(
            "roll_skew", "skew", check_minp=_require_min_periods(3), **kwargs
        )

    _shared_docs["kurt"] = dedent(
        """
    Calculate unbiased %(name)s kurtosis.

    This function uses Fisher's definition of kurtosis without bias.

    Parameters
    ----------
    **kwargs
        Under Review.

    Returns
    -------
    Series or DataFrame
        Returned object type is determined by the caller of the %(name)s
        calculation.

    See Also
    --------
    Series.%(name)s : Calling object with Series data.
    DataFrame.%(name)s : Calling object with DataFrames.
    Series.kurt : Equivalent method for Series.
    DataFrame.kurt : Equivalent method for DataFrame.
    scipy.stats.skew : Third moment of a probability density.
    scipy.stats.kurtosis : Reference SciPy method.

    Notes
    -----
    A minimum of 4 periods is required for the %(name)s calculation.
    """
    )

    def kurt(self, **kwargs):
        return self._apply(
            "roll_kurt", "kurt", check_minp=_require_min_periods(4), **kwargs
        )

    _shared_docs["quantile"] = dedent(
        """
    Calculate the %(name)s quantile.

    Parameters
    ----------
    quantile : float
        Quantile to compute. 0 <= quantile <= 1.
    interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
        .. versionadded:: 0.23.0

        This optional parameter specifies the interpolation method to use,
        when the desired quantile lies between two data points `i` and `j`:

            * linear: `i + (j - i) * fraction`, where `fraction` is the
              fractional part of the index surrounded by `i` and `j`.
            * lower: `i`.
            * higher: `j`.
            * nearest: `i` or `j` whichever is nearest.
            * midpoint: (`i` + `j`) / 2.
    **kwargs:
        For compatibility with other %(name)s methods. Has no effect on
        the result.

    Returns
    -------
    Series or DataFrame
        Returned object type is determined by the caller of the %(name)s
        calculation.

    See Also
    --------
    Series.quantile : Computes value at the given quantile over all data
        in Series.
    DataFrame.quantile : Computes values at the given quantile over
        requested axis in DataFrame.

    Examples
    --------
    >>> s = pd.Series([1, 2, 3, 4])
    >>> s.rolling(2).quantile(.4, interpolation='lower')
    0    NaN
    1    1.0
    2    2.0
    3    3.0
    dtype: float64

    >>> s.rolling(2).quantile(.4, interpolation='midpoint')
    0    NaN
    1    1.5
    2    2.5
    3    3.5
    dtype: float64
    """
    )

    def quantile(self, quantile, interpolation="linear", **kwargs):
        window = self._get_window()
        index_as_array = self._get_index()

        def f(arg, *args, **kwargs):
            minp = _use_window(self.min_periods, window)
            if quantile == 1.0:
                return libwindow.roll_max(
                    arg, window, minp, index_as_array, self.closed
                )
            elif quantile == 0.0:
                return libwindow.roll_min(
                    arg, window, minp, index_as_array, self.closed
                )
            else:
                return libwindow.roll_quantile(
                    arg,
                    window,
                    minp,
                    index_as_array,
                    self.closed,
                    quantile,
                    interpolation,
                )

        return self._apply(f, "quantile", quantile=quantile, **kwargs)

    _shared_docs[
        "cov"
    ] = """
        Calculate the %(name)s sample covariance.

        Parameters
        ----------
        other : Series, DataFrame, or ndarray, optional
            If not supplied then will default to self and produce pairwise
            output.
        pairwise : bool, default None
            If False then only matching columns between self and other will be
            used and the output will be a DataFrame.
            If True then all pairwise combinations will be calculated and the
            output will be a MultiIndexed DataFrame in the case of DataFrame
            inputs. In the case of missing elements, only complete pairwise
            observations will be used.
        ddof : int, default 1
            Delta Degrees of Freedom.  The divisor used in calculations
            is ``N - ddof``, where ``N`` represents the number of elements.
        **kwargs
            Keyword arguments to be passed into func.
    """

    def cov(self, other=None, pairwise=None, ddof=1, **kwargs):
        if other is None:
            other = self._selected_obj
            # only default unset
            pairwise = True if pairwise is None else pairwise
        other = self._shallow_copy(other)

        # GH 16058: offset window
        if self.is_freq_type:
            window = self.win_freq
        else:
            window = self._get_window(other)

        def _get_cov(X, Y):
            # GH #12373 : rolling functions error on float32 data
            # to avoid potential overflow, cast the data to float64
            X = X.astype("float64")
            Y = Y.astype("float64")
            mean = lambda x: x.rolling(
                window, self.min_periods, center=self.center
            ).mean(**kwargs)
            count = (X + Y).rolling(window=window, center=self.center).count(**kwargs)
            bias_adj = count / (count - ddof)
            return (mean(X * Y) - mean(X) * mean(Y)) * bias_adj

        return _flex_binary_moment(
            self._selected_obj, other._selected_obj, _get_cov, pairwise=bool(pairwise)
        )

    _shared_docs["corr"] = dedent(
        """
    Calculate %(name)s correlation.

    Parameters
    ----------
    other : Series, DataFrame, or ndarray, optional
        If not supplied then will default to self.
    pairwise : bool, default None
        Calculate pairwise combinations of columns within a
        DataFrame. If `other` is not specified, defaults to `True`,
        otherwise defaults to `False`.
        Not relevant for :class:`~pandas.Series`.
    **kwargs
        Unused.

    Returns
    -------
    Series or DataFrame
        Returned object type is determined by the caller of the
        %(name)s calculation.

    See Also
    --------
    Series.%(name)s : Calling object with Series data.
    DataFrame.%(name)s : Calling object with DataFrames.
    Series.corr : Equivalent method for Series.
    DataFrame.corr : Equivalent method for DataFrame.
    %(name)s.cov : Similar method to calculate covariance.
    numpy.corrcoef : NumPy Pearson's correlation calculation.

    Notes
    -----
    This function uses Pearson's definition of correlation
    (https://en.wikipedia.org/wiki/Pearson_correlation_coefficient).

    When `other` is not specified, the output will be self correlation (e.g.
    all 1's), except for :class:`~pandas.DataFrame` inputs with `pairwise`
    set to `True`.

    Function will return ``NaN`` for correlations of equal valued sequences;
    this is the result of a 0/0 division error.

    When `pairwise` is set to `False`, only matching columns between `self` and
    `other` will be used.

    When `pairwise` is set to `True`, the output will be a MultiIndex DataFrame
    with the original index on the first level, and the `other` DataFrame
    columns on the second level.

    In the case of missing elements, only complete pairwise observations
    will be used.

    Examples
    --------
    The below example shows a rolling calculation with a window size of
    four matching the equivalent function call using :meth:`numpy.corrcoef`.

    >>> v1 = [3, 3, 3, 5, 8]
    >>> v2 = [3, 4, 4, 4, 8]
    >>> fmt = "{0:.6f}"  # limit the printed precision to 6 digits
    >>> # numpy returns a 2X2 array, the correlation coefficient
    >>> # is the number at entry [0][1]
    >>> print(fmt.format(np.corrcoef(v1[:-1], v2[:-1])[0][1]))
    0.333333
    >>> print(fmt.format(np.corrcoef(v1[1:], v2[1:])[0][1]))
    0.916949
    >>> s1 = pd.Series(v1)
    >>> s2 = pd.Series(v2)
    >>> s1.rolling(4).corr(s2)
    0         NaN
    1         NaN
    2         NaN
    3    0.333333
    4    0.916949
    dtype: float64

    The below example shows a similar rolling calculation on a
    DataFrame using the pairwise option.

    >>> matrix = np.array([[51., 35.], [49., 30.], [47., 32.],\
    [46., 31.], [50., 36.]])
    >>> print(np.corrcoef(matrix[:-1,0], matrix[:-1,1]).round(7))
    [[1.         0.6263001]
     [0.6263001  1.       ]]
    >>> print(np.corrcoef(matrix[1:,0], matrix[1:,1]).round(7))
    [[1.         0.5553681]
     [0.5553681  1.        ]]
    >>> df = pd.DataFrame(matrix, columns=['X','Y'])
    >>> df
          X     Y
    0  51.0  35.0
    1  49.0  30.0
    2  47.0  32.0
    3  46.0  31.0
    4  50.0  36.0
    >>> df.rolling(4).corr(pairwise=True)
                X         Y
    0 X       NaN       NaN
      Y       NaN       NaN
    1 X       NaN       NaN
      Y       NaN       NaN
    2 X       NaN       NaN
      Y       NaN       NaN
    3 X  1.000000  0.626300
      Y  0.626300  1.000000
    4 X  1.000000  0.555368
      Y  0.555368  1.000000
    """
    )

    def corr(self, other=None, pairwise=None, **kwargs):
        if other is None:
            other = self._selected_obj
            # only default unset
            pairwise = True if pairwise is None else pairwise
        other = self._shallow_copy(other)
        window = self._get_window(other)

        def _get_corr(a, b):
            a = a.rolling(
                window=window, min_periods=self.min_periods, center=self.center
            )
            b = b.rolling(
                window=window, min_periods=self.min_periods, center=self.center
            )

            return a.cov(b, **kwargs) / (a.std(**kwargs) * b.std(**kwargs))

        return _flex_binary_moment(
            self._selected_obj, other._selected_obj, _get_corr, pairwise=bool(pairwise)
        )


class Rolling(_Rolling_and_Expanding):
    @cache_readonly
    def is_datetimelike(self):
        return isinstance(
            self._on, (ABCDatetimeIndex, ABCTimedeltaIndex, ABCPeriodIndex)
        )

    @cache_readonly
    def _on(self):

        if self.on is None:
            return self.obj.index
        elif isinstance(self.obj, ABCDataFrame) and self.on in self.obj.columns:
            return Index(self.obj[self.on])
        else:
            raise ValueError(
                "invalid on specified as {0}, "
                "must be a column (if DataFrame) "
                "or None".format(self.on)
            )

    def validate(self):
        super().validate()

        # we allow rolling on a datetimelike index
        if (self.obj.empty or self.is_datetimelike) and isinstance(
            self.window, (str, ABCDateOffset, timedelta)
        ):

            self._validate_monotonic()
            freq = self._validate_freq()

            # we don't allow center
            if self.center:
                raise NotImplementedError(
                    "center is not implemented "
                    "for datetimelike and offset "
                    "based windows"
                )

            # this will raise ValueError on non-fixed freqs
            self.win_freq = self.window
            self.window = freq.nanos
            self.win_type = "freq"

            # min_periods must be an integer
            if self.min_periods is None:
                self.min_periods = 1

        elif not is_integer(self.window):
            raise ValueError("window must be an integer")
        elif self.window < 0:
            raise ValueError("window must be non-negative")

        if not self.is_datetimelike and self.closed is not None:
            raise ValueError(
                "closed only implemented for datetimelike and offset based windows"
            )

    def _validate_monotonic(self):
        """
        Validate on is_monotonic.
        """
        if not self._on.is_monotonic:
            formatted = self.on or "index"
            raise ValueError("{0} must be monotonic".format(formatted))

    def _validate_freq(self):
        """
        Validate & return window frequency.
        """
        from pandas.tseries.frequencies import to_offset

        try:
            return to_offset(self.window)
        except (TypeError, ValueError):
            raise ValueError(
                "passed window {0} is not "
                "compatible with a datetimelike "
                "index".format(self.window)
            )

    _agg_see_also_doc = dedent(
        """
    See Also
    --------
    Series.rolling
    DataFrame.rolling
    """
    )

    _agg_examples_doc = dedent(
        """
    Examples
    --------

    >>> df = pd.DataFrame(np.random.randn(10, 3), columns=['A', 'B', 'C'])
    >>> df
              A         B         C
    0 -2.385977 -0.102758  0.438822
    1 -1.004295  0.905829 -0.954544
    2  0.735167 -0.165272 -1.619346
    3 -0.702657 -1.340923 -0.706334
    4 -0.246845  0.211596 -0.901819
    5  2.463718  3.157577 -1.380906
    6 -1.142255  2.340594 -0.039875
    7  1.396598 -1.647453  1.677227
    8 -0.543425  1.761277 -0.220481
    9 -0.640505  0.289374 -1.550670

    >>> df.rolling(3).sum()
              A         B         C
    0       NaN       NaN       NaN
    1       NaN       NaN       NaN
    2 -2.655105  0.637799 -2.135068
    3 -0.971785 -0.600366 -3.280224
    4 -0.214334 -1.294599 -3.227500
    5  1.514216  2.028250 -2.989060
    6  1.074618  5.709767 -2.322600
    7  2.718061  3.850718  0.256446
    8 -0.289082  2.454418  1.416871
    9  0.212668  0.403198 -0.093924

    >>> df.rolling(3).agg({'A':'sum', 'B':'min'})
              A         B
    0       NaN       NaN
    1       NaN       NaN
    2 -2.655105 -0.165272
    3 -0.971785 -1.340923
    4 -0.214334 -1.340923
    5  1.514216 -1.340923
    6  1.074618  0.211596
    7  2.718061 -1.647453
    8 -0.289082 -1.647453
    9  0.212668 -1.647453
    """
    )

    @Substitution(
        see_also=_agg_see_also_doc,
        examples=_agg_examples_doc,
        versionadded="",
        klass="Series/Dataframe",
        axis="",
    )
    @Appender(_shared_docs["aggregate"])
    def aggregate(self, arg, *args, **kwargs):
        return super().aggregate(arg, *args, **kwargs)

    agg = aggregate

    @Substitution(name="rolling")
    @Appender(_shared_docs["count"])
    def count(self):

        # different impl for freq counting
        if self.is_freq_type:
            return self._apply("roll_count", "count")

        return super().count()

    @Substitution(name="rolling")
    @Appender(_shared_docs["apply"])
    def apply(self, func, raw=None, args=(), kwargs={}):
        return super().apply(func, raw=raw, args=args, kwargs=kwargs)

    @Substitution(name="rolling")
    @Appender(_shared_docs["sum"])
    def sum(self, *args, **kwargs):
        nv.validate_rolling_func("sum", args, kwargs)
        return super().sum(*args, **kwargs)

    @Substitution(name="rolling")
    @Appender(_doc_template)
    @Appender(_shared_docs["max"])
    def max(self, *args, **kwargs):
        nv.validate_rolling_func("max", args, kwargs)
        return super().max(*args, **kwargs)

    @Substitution(name="rolling")
    @Appender(_shared_docs["min"])
    def min(self, *args, **kwargs):
        nv.validate_rolling_func("min", args, kwargs)
        return super().min(*args, **kwargs)

    @Substitution(name="rolling")
    @Appender(_shared_docs["mean"])
    def mean(self, *args, **kwargs):
        nv.validate_rolling_func("mean", args, kwargs)
        return super().mean(*args, **kwargs)

    @Substitution(name="rolling")
    @Appender(_shared_docs["median"])
    def median(self, **kwargs):
        return super().median(**kwargs)

    @Substitution(name="rolling")
    @Appender(_shared_docs["std"])
    def std(self, ddof=1, *args, **kwargs):
        nv.validate_rolling_func("std", args, kwargs)
        return super().std(ddof=ddof, **kwargs)

    @Substitution(name="rolling")
    @Appender(_shared_docs["var"])
    def var(self, ddof=1, *args, **kwargs):
        nv.validate_rolling_func("var", args, kwargs)
        return super().var(ddof=ddof, **kwargs)

    @Substitution(name="rolling")
    @Appender(_doc_template)
    @Appender(_shared_docs["skew"])
    def skew(self, **kwargs):
        return super().skew(**kwargs)

    _agg_doc = dedent(
        """
    Examples
    --------

    The example below will show a rolling calculation with a window size of
    four matching the equivalent function call using `scipy.stats`.

    >>> arr = [1, 2, 3, 4, 999]
    >>> fmt = "{0:.6f}"  # limit the printed precision to 6 digits
    >>> import scipy.stats
    >>> print(fmt.format(scipy.stats.kurtosis(arr[:-1], bias=False)))
    -1.200000
    >>> print(fmt.format(scipy.stats.kurtosis(arr[1:], bias=False)))
    3.999946
    >>> s = pd.Series(arr)
    >>> s.rolling(4).kurt()
    0         NaN
    1         NaN
    2         NaN
    3   -1.200000
    4    3.999946
    dtype: float64
    """
    )

    @Appender(_agg_doc)
    @Substitution(name="rolling")
    @Appender(_shared_docs["kurt"])
    def kurt(self, **kwargs):
        return super().kurt(**kwargs)

    @Substitution(name="rolling")
    @Appender(_shared_docs["quantile"])
    def quantile(self, quantile, interpolation="linear", **kwargs):
        return super().quantile(
            quantile=quantile, interpolation=interpolation, **kwargs
        )

    @Substitution(name="rolling")
    @Appender(_doc_template)
    @Appender(_shared_docs["cov"])
    def cov(self, other=None, pairwise=None, ddof=1, **kwargs):
        return super().cov(other=other, pairwise=pairwise, ddof=ddof, **kwargs)

    @Substitution(name="rolling")
    @Appender(_shared_docs["corr"])
    def corr(self, other=None, pairwise=None, **kwargs):
        return super().corr(other=other, pairwise=pairwise, **kwargs)


class RollingGroupby(_GroupByMixin, Rolling):
    """
    Provide a rolling groupby implementation.
    """

    @property
    def _constructor(self):
        return Rolling

    def _gotitem(self, key, ndim, subset=None):

        # we are setting the index on the actual object
        # here so our index is carried thru to the selected obj
        # when we do the splitting for the groupby
        if self.on is not None:
            self._groupby.obj = self._groupby.obj.set_index(self._on)
            self.on = None
        return super()._gotitem(key, ndim, subset=subset)

    def _validate_monotonic(self):
        """
        Validate that on is monotonic;
        we don't care for groupby.rolling
        because we have already validated at a higher
        level.
        """
        pass


class Expanding(_Rolling_and_Expanding):
    """
    Provide expanding transformations.

    Parameters
    ----------
    min_periods : int, default 1
        Minimum number of observations in window required to have a value
        (otherwise result is NA).
    center : bool, default False
        Set the labels at the center of the window.
    axis : int or str, default 0

    Returns
    -------
    a Window sub-classed for the particular operation

    See Also
    --------
    rolling : Provides rolling window calculations.
    ewm : Provides exponential weighted functions.

    Notes
    -----
    By default, the result is set to the right edge of the window. This can be
    changed to the center of the window by setting ``center=True``.

    Examples
    --------

    >>> df = pd.DataFrame({'B': [0, 1, 2, np.nan, 4]})
         B
    0  0.0
    1  1.0
    2  2.0
    3  NaN
    4  4.0

    >>> df.expanding(2).sum()
         B
    0  NaN
    1  1.0
    2  3.0
    3  3.0
    4  7.0
    """

    _attributes = ["min_periods", "center", "axis"]

    def __init__(self, obj, min_periods=1, center=False, axis=0, **kwargs):
        super().__init__(obj=obj, min_periods=min_periods, center=center, axis=axis)

    @property
    def _constructor(self):
        return Expanding

    def _get_window(self, other=None, **kwargs):
        """
        Get the window length over which to perform some operation.

        Parameters
        ----------
        other : object, default None
            The other object that is involved in the operation.
            Such an object is involved for operations like covariance.

        Returns
        -------
        window : int
            The window length.
        """
        axis = self.obj._get_axis(self.axis)
        length = len(axis) + (other is not None) * len(axis)

        other = self.min_periods or -1
        return max(length, other)

    _agg_see_also_doc = dedent(
        """
    See Also
    --------
    DataFrame.expanding.aggregate
    DataFrame.rolling.aggregate
    DataFrame.aggregate
    """
    )

    _agg_examples_doc = dedent(
        """
    Examples
    --------

    >>> df = pd.DataFrame(np.random.randn(10, 3), columns=['A', 'B', 'C'])
    >>> df
              A         B         C
    0 -2.385977 -0.102758  0.438822
    1 -1.004295  0.905829 -0.954544
    2  0.735167 -0.165272 -1.619346
    3 -0.702657 -1.340923 -0.706334
    4 -0.246845  0.211596 -0.901819
    5  2.463718  3.157577 -1.380906
    6 -1.142255  2.340594 -0.039875
    7  1.396598 -1.647453  1.677227
    8 -0.543425  1.761277 -0.220481
    9 -0.640505  0.289374 -1.550670

    >>> df.ewm(alpha=0.5).mean()
              A         B         C
    0 -2.385977 -0.102758  0.438822
    1 -1.464856  0.569633 -0.490089
    2 -0.207700  0.149687 -1.135379
    3 -0.471677 -0.645305 -0.906555
    4 -0.355635 -0.203033 -0.904111
    5  1.076417  1.503943 -1.146293
    6 -0.041654  1.925562 -0.588728
    7  0.680292  0.132049  0.548693
    8  0.067236  0.948257  0.163353
    9 -0.286980  0.618493 -0.694496
    """
    )

    @Substitution(
        see_also=_agg_see_also_doc,
        examples=_agg_examples_doc,
        versionadded="",
        klass="Series/Dataframe",
        axis="",
    )
    @Appender(_shared_docs["aggregate"])
    def aggregate(self, arg, *args, **kwargs):
        return super().aggregate(arg, *args, **kwargs)

    agg = aggregate

    @Substitution(name="expanding")
    @Appender(_shared_docs["count"])
    def count(self, **kwargs):
        return super().count(**kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["apply"])
    def apply(self, func, raw=None, args=(), kwargs={}):
        return super().apply(func, raw=raw, args=args, kwargs=kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["sum"])
    def sum(self, *args, **kwargs):
        nv.validate_expanding_func("sum", args, kwargs)
        return super().sum(*args, **kwargs)

    @Substitution(name="expanding")
    @Appender(_doc_template)
    @Appender(_shared_docs["max"])
    def max(self, *args, **kwargs):
        nv.validate_expanding_func("max", args, kwargs)
        return super().max(*args, **kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["min"])
    def min(self, *args, **kwargs):
        nv.validate_expanding_func("min", args, kwargs)
        return super().min(*args, **kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["mean"])
    def mean(self, *args, **kwargs):
        nv.validate_expanding_func("mean", args, kwargs)
        return super().mean(*args, **kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["median"])
    def median(self, **kwargs):
        return super().median(**kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["std"])
    def std(self, ddof=1, *args, **kwargs):
        nv.validate_expanding_func("std", args, kwargs)
        return super().std(ddof=ddof, **kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["var"])
    def var(self, ddof=1, *args, **kwargs):
        nv.validate_expanding_func("var", args, kwargs)
        return super().var(ddof=ddof, **kwargs)

    @Substitution(name="expanding")
    @Appender(_doc_template)
    @Appender(_shared_docs["skew"])
    def skew(self, **kwargs):
        return super().skew(**kwargs)

    _agg_doc = dedent(
        """
    Examples
    --------

    The example below will show an expanding calculation with a window size of
    four matching the equivalent function call using `scipy.stats`.

    >>> arr = [1, 2, 3, 4, 999]
    >>> import scipy.stats
    >>> fmt = "{0:.6f}"  # limit the printed precision to 6 digits
    >>> print(fmt.format(scipy.stats.kurtosis(arr[:-1], bias=False)))
    -1.200000
    >>> print(fmt.format(scipy.stats.kurtosis(arr, bias=False)))
    4.999874
    >>> s = pd.Series(arr)
    >>> s.expanding(4).kurt()
    0         NaN
    1         NaN
    2         NaN
    3   -1.200000
    4    4.999874
    dtype: float64
    """
    )

    @Appender(_agg_doc)
    @Substitution(name="expanding")
    @Appender(_shared_docs["kurt"])
    def kurt(self, **kwargs):
        return super().kurt(**kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["quantile"])
    def quantile(self, quantile, interpolation="linear", **kwargs):
        return super().quantile(
            quantile=quantile, interpolation=interpolation, **kwargs
        )

    @Substitution(name="expanding")
    @Appender(_doc_template)
    @Appender(_shared_docs["cov"])
    def cov(self, other=None, pairwise=None, ddof=1, **kwargs):
        return super().cov(other=other, pairwise=pairwise, ddof=ddof, **kwargs)

    @Substitution(name="expanding")
    @Appender(_shared_docs["corr"])
    def corr(self, other=None, pairwise=None, **kwargs):
        return super().corr(other=other, pairwise=pairwise, **kwargs)


class ExpandingGroupby(_GroupByMixin, Expanding):
    """
    Provide a expanding groupby implementation.
    """

    @property
    def _constructor(self):
        return Expanding


_bias_template = """
        Parameters
        ----------
        bias : bool, default False
            Use a standard estimation bias correction.
        *args, **kwargs
            Arguments and keyword arguments to be passed into func.
"""

_pairwise_template = """
        Parameters
        ----------
        other : Series, DataFrame, or ndarray, optional
            If not supplied then will default to self and produce pairwise
            output.
        pairwise : bool, default None
            If False then only matching columns between self and other will be
            used and the output will be a DataFrame.
            If True then all pairwise combinations will be calculated and the
            output will be a MultiIndex DataFrame in the case of DataFrame
            inputs. In the case of missing elements, only complete pairwise
            observations will be used.
        bias : bool, default False
           Use a standard estimation bias correction.
        **kwargs
           Keyword arguments to be passed into func.
"""


class EWM(_Rolling):
    r"""
    Provide exponential weighted functions.

    Parameters
    ----------
    com : float, optional
        Specify decay in terms of center of mass,
        :math:`\alpha = 1 / (1 + com),\text{ for } com \geq 0`.
    span : float, optional
        Specify decay in terms of span,
        :math:`\alpha = 2 / (span + 1),\text{ for } span \geq 1`.
    halflife : float, optional
        Specify decay in terms of half-life,
        :math:`\alpha = 1 - exp(log(0.5) / halflife),\text{for} halflife > 0`.
    alpha : float, optional
        Specify smoothing factor :math:`\alpha` directly,
        :math:`0 < \alpha \leq 1`.
    min_periods : int, default 0
        Minimum number of observations in window required to have a value
        (otherwise result is NA).
    adjust : bool, default True
        Divide by decaying adjustment factor in beginning periods to account
        for imbalance in relative weightings
        (viewing EWMA as a moving average).
    ignore_na : bool, default False
        Ignore missing values when calculating weights;
        specify True to reproduce pre-0.15.0 behavior.
    axis : {0 or 'index', 1 or 'columns'}, default 0
        The axis to use. The value 0 identifies the rows, and 1
        identifies the columns.

    Returns
    -------
    DataFrame
        A Window sub-classed for the particular operation.

    See Also
    --------
    rolling : Provides rolling window calculations.
    expanding : Provides expanding transformations.

    Notes
    -----
    Exactly one of center of mass, span, half-life, and alpha must be provided.
    Allowed values and relationship between the parameters are specified in the
    parameter descriptions above; see the link at the end of this section for
    a detailed explanation.

    When adjust is True (default), weighted averages are calculated using
    weights (1-alpha)**(n-1), (1-alpha)**(n-2), ..., 1-alpha, 1.

    When adjust is False, weighted averages are calculated recursively as:
       weighted_average[0] = arg[0];
       weighted_average[i] = (1-alpha)*weighted_average[i-1] + alpha*arg[i].

    When ignore_na is False (default), weights are based on absolute positions.
    For example, the weights of x and y used in calculating the final weighted
    average of [x, None, y] are (1-alpha)**2 and 1 (if adjust is True), and
    (1-alpha)**2 and alpha (if adjust is False).

    When ignore_na is True (reproducing pre-0.15.0 behavior), weights are based
    on relative positions. For example, the weights of x and y used in
    calculating the final weighted average of [x, None, y] are 1-alpha and 1
    (if adjust is True), and 1-alpha and alpha (if adjust is False).

    More details can be found at
    http://pandas.pydata.org/pandas-docs/stable/user_guide/computation.html#exponentially-weighted-windows

    Examples
    --------

    >>> df = pd.DataFrame({'B': [0, 1, 2, np.nan, 4]})
    >>> df
         B
    0  0.0
    1  1.0
    2  2.0
    3  NaN
    4  4.0

    >>> df.ewm(com=0.5).mean()
              B
    0  0.000000
    1  0.750000
    2  1.615385
    3  1.615385
    4  3.670213
    """
    _attributes = ["com", "min_periods", "adjust", "ignore_na", "axis"]

    def __init__(
        self,
        obj,
        com=None,
        span=None,
        halflife=None,
        alpha=None,
        min_periods=0,
        adjust=True,
        ignore_na=False,
        axis=0,
    ):
        self.obj = obj
        self.com = _get_center_of_mass(com, span, halflife, alpha)
        self.min_periods = min_periods
        self.adjust = adjust
        self.ignore_na = ignore_na
        self.axis = axis
        self.on = None

    @property
    def _constructor(self):
        return EWM

    _agg_see_also_doc = dedent(
        """
    See Also
    --------
    pandas.DataFrame.rolling.aggregate
    """
    )

    _agg_examples_doc = dedent(
        """
    Examples
    --------

    >>> df = pd.DataFrame(np.random.randn(10, 3), columns=['A', 'B', 'C'])
    >>> df
              A         B         C
    0 -2.385977 -0.102758  0.438822
    1 -1.004295  0.905829 -0.954544
    2  0.735167 -0.165272 -1.619346
    3 -0.702657 -1.340923 -0.706334
    4 -0.246845  0.211596 -0.901819
    5  2.463718  3.157577 -1.380906
    6 -1.142255  2.340594 -0.039875
    7  1.396598 -1.647453  1.677227
    8 -0.543425  1.761277 -0.220481
    9 -0.640505  0.289374 -1.550670

    >>> df.ewm(alpha=0.5).mean()
              A         B         C
    0 -2.385977 -0.102758  0.438822
    1 -1.464856  0.569633 -0.490089
    2 -0.207700  0.149687 -1.135379
    3 -0.471677 -0.645305 -0.906555
    4 -0.355635 -0.203033 -0.904111
    5  1.076417  1.503943 -1.146293
    6 -0.041654  1.925562 -0.588728
    7  0.680292  0.132049  0.548693
    8  0.067236  0.948257  0.163353
    9 -0.286980  0.618493 -0.694496
    """
    )

    @Substitution(
        see_also=_agg_see_also_doc,
        examples=_agg_examples_doc,
        versionadded="",
        klass="Series/Dataframe",
        axis="",
    )
    @Appender(_shared_docs["aggregate"])
    def aggregate(self, arg, *args, **kwargs):
        return super().aggregate(arg, *args, **kwargs)

    agg = aggregate

    def _apply(self, func, **kwargs):
        """
        Rolling statistical measure using supplied function. Designed to be
        used with passed-in Cython array-based functions.

        Parameters
        ----------
        func : str/callable to apply

        Returns
        -------
        y : same type as input argument
        """
        blocks, obj = self._create_blocks()
        block_list = list(blocks)

        results = []
        exclude = []
        for i, b in enumerate(blocks):
            try:
                values = self._prep_values(b.values)

            except (TypeError, NotImplementedError):
                if isinstance(obj, ABCDataFrame):
                    exclude.extend(b.columns)
                    del block_list[i]
                    continue
                else:
                    raise DataError("No numeric types to aggregate")

            if values.size == 0:
                results.append(values.copy())
                continue

            # if we have a string function name, wrap it
            if isinstance(func, str):
                cfunc = getattr(libwindow, func, None)
                if cfunc is None:
                    raise ValueError(
                        "we do not support this function "
                        "in libwindow.{func}".format(func=func)
                    )

                def func(arg):
                    return cfunc(
                        arg,
                        self.com,
                        int(self.adjust),
                        int(self.ignore_na),
                        int(self.min_periods),
                    )

            results.append(np.apply_along_axis(func, self.axis, values))

        return self._wrap_results(results, block_list, obj, exclude)

    @Substitution(name="ewm")
    @Appender(_doc_template)
    def mean(self, *args, **kwargs):
        """
        Exponential weighted moving average.

        Parameters
        ----------
        *args, **kwargs
            Arguments and keyword arguments to be passed into func.
        """
        nv.validate_window_func("mean", args, kwargs)
        return self._apply("ewma", **kwargs)

    @Substitution(name="ewm")
    @Appender(_doc_template)
    @Appender(_bias_template)
    def std(self, bias=False, *args, **kwargs):
        """
        Exponential weighted moving stddev.
        """
        nv.validate_window_func("std", args, kwargs)
        return _zsqrt(self.var(bias=bias, **kwargs))

    vol = std

    @Substitution(name="ewm")
    @Appender(_doc_template)
    @Appender(_bias_template)
    def var(self, bias=False, *args, **kwargs):
        """
        Exponential weighted moving variance.
        """
        nv.validate_window_func("var", args, kwargs)

        def f(arg):
            return libwindow.ewmcov(
                arg,
                arg,
                self.com,
                int(self.adjust),
                int(self.ignore_na),
                int(self.min_periods),
                int(bias),
            )

        return self._apply(f, **kwargs)

    @Substitution(name="ewm")
    @Appender(_doc_template)
    @Appender(_pairwise_template)
    def cov(self, other=None, pairwise=None, bias=False, **kwargs):
        """
        Exponential weighted sample covariance.
        """
        if other is None:
            other = self._selected_obj
            # only default unset
            pairwise = True if pairwise is None else pairwise
        other = self._shallow_copy(other)

        def _get_cov(X, Y):
            X = self._shallow_copy(X)
            Y = self._shallow_copy(Y)
            cov = libwindow.ewmcov(
                X._prep_values(),
                Y._prep_values(),
                self.com,
                int(self.adjust),
                int(self.ignore_na),
                int(self.min_periods),
                int(bias),
            )
            return X._wrap_result(cov)

        return _flex_binary_moment(
            self._selected_obj, other._selected_obj, _get_cov, pairwise=bool(pairwise)
        )

    @Substitution(name="ewm")
    @Appender(_doc_template)
    @Appender(_pairwise_template)
    def corr(self, other=None, pairwise=None, **kwargs):
        """
        Exponential weighted sample correlation.
        """
        if other is None:
            other = self._selected_obj
            # only default unset
            pairwise = True if pairwise is None else pairwise
        other = self._shallow_copy(other)

        def _get_corr(X, Y):
            X = self._shallow_copy(X)
            Y = self._shallow_copy(Y)

            def _cov(x, y):
                return libwindow.ewmcov(
                    x,
                    y,
                    self.com,
                    int(self.adjust),
                    int(self.ignore_na),
                    int(self.min_periods),
                    1,
                )

            x_values = X._prep_values()
            y_values = Y._prep_values()
            with np.errstate(all="ignore"):
                cov = _cov(x_values, y_values)
                x_var = _cov(x_values, x_values)
                y_var = _cov(y_values, y_values)
                corr = cov / _zsqrt(x_var * y_var)
            return X._wrap_result(corr)

        return _flex_binary_moment(
            self._selected_obj, other._selected_obj, _get_corr, pairwise=bool(pairwise)
        )


# Helper Funcs


def _flex_binary_moment(arg1, arg2, f, pairwise=False):

    if not (
        isinstance(arg1, (np.ndarray, ABCSeries, ABCDataFrame))
        and isinstance(arg2, (np.ndarray, ABCSeries, ABCDataFrame))
    ):
        raise TypeError(
            "arguments to moment function must be of type "
            "np.ndarray/Series/DataFrame"
        )

    if isinstance(arg1, (np.ndarray, ABCSeries)) and isinstance(
        arg2, (np.ndarray, ABCSeries)
    ):
        X, Y = _prep_binary(arg1, arg2)
        return f(X, Y)

    elif isinstance(arg1, ABCDataFrame):
        from pandas import DataFrame

        def dataframe_from_int_dict(data, frame_template):
            result = DataFrame(data, index=frame_template.index)
            if len(result.columns) > 0:
                result.columns = frame_template.columns[result.columns]
            return result

        results = {}
        if isinstance(arg2, ABCDataFrame):
            if pairwise is False:
                if arg1 is arg2:
                    # special case in order to handle duplicate column names
                    for i, col in enumerate(arg1.columns):
                        results[i] = f(arg1.iloc[:, i], arg2.iloc[:, i])
                    return dataframe_from_int_dict(results, arg1)
                else:
                    if not arg1.columns.is_unique:
                        raise ValueError("'arg1' columns are not unique")
                    if not arg2.columns.is_unique:
                        raise ValueError("'arg2' columns are not unique")
                    with warnings.catch_warnings(record=True):
                        warnings.simplefilter("ignore", RuntimeWarning)
                        X, Y = arg1.align(arg2, join="outer")
                    X = X + 0 * Y
                    Y = Y + 0 * X

                    with warnings.catch_warnings(record=True):
                        warnings.simplefilter("ignore", RuntimeWarning)
                        res_columns = arg1.columns.union(arg2.columns)
                    for col in res_columns:
                        if col in X and col in Y:
                            results[col] = f(X[col], Y[col])
                    return DataFrame(results, index=X.index, columns=res_columns)
            elif pairwise is True:
                results = defaultdict(dict)
                for i, k1 in enumerate(arg1.columns):
                    for j, k2 in enumerate(arg2.columns):
                        if j < i and arg2 is arg1:
                            # Symmetric case
                            results[i][j] = results[j][i]
                        else:
                            results[i][j] = f(
                                *_prep_binary(arg1.iloc[:, i], arg2.iloc[:, j])
                            )

                from pandas import concat

                result_index = arg1.index.union(arg2.index)
                if len(result_index):

                    # construct result frame
                    result = concat(
                        [
                            concat(
                                [results[i][j] for j, c in enumerate(arg2.columns)],
                                ignore_index=True,
                            )
                            for i, c in enumerate(arg1.columns)
                        ],
                        ignore_index=True,
                        axis=1,
                    )
                    result.columns = arg1.columns

                    # set the index and reorder
                    if arg2.columns.nlevels > 1:
                        result.index = MultiIndex.from_product(
                            arg2.columns.levels + [result_index]
                        )
                        result = result.reorder_levels([2, 0, 1]).sort_index()
                    else:
                        result.index = MultiIndex.from_product(
                            [range(len(arg2.columns)), range(len(result_index))]
                        )
                        result = result.swaplevel(1, 0).sort_index()
                        result.index = MultiIndex.from_product(
                            [result_index] + [arg2.columns]
                        )
                else:

                    # empty result
                    result = DataFrame(
                        index=MultiIndex(
                            levels=[arg1.index, arg2.columns], codes=[[], []]
                        ),
                        columns=arg2.columns,
                        dtype="float64",
                    )

                # reset our index names to arg1 names
                # reset our column names to arg2 names
                # careful not to mutate the original names
                result.columns = result.columns.set_names(arg1.columns.names)
                result.index = result.index.set_names(
                    result_index.names + arg2.columns.names
                )

                return result

            else:
                raise ValueError("'pairwise' is not True/False")
        else:
            results = {
                i: f(*_prep_binary(arg1.iloc[:, i], arg2))
                for i, col in enumerate(arg1.columns)
            }
            return dataframe_from_int_dict(results, arg1)

    else:
        return _flex_binary_moment(arg2, arg1, f)


def _get_center_of_mass(comass, span, halflife, alpha):
    valid_count = com.count_not_none(comass, span, halflife, alpha)
    if valid_count > 1:
        raise ValueError("comass, span, halflife, and alpha are mutually exclusive")

    # Convert to center of mass; domain checks ensure 0 < alpha <= 1
    if comass is not None:
        if comass < 0:
            raise ValueError("comass must satisfy: comass >= 0")
    elif span is not None:
        if span < 1:
            raise ValueError("span must satisfy: span >= 1")
        comass = (span - 1) / 2.0
    elif halflife is not None:
        if halflife <= 0:
            raise ValueError("halflife must satisfy: halflife > 0")
        decay = 1 - np.exp(np.log(0.5) / halflife)
        comass = 1 / decay - 1
    elif alpha is not None:
        if alpha <= 0 or alpha > 1:
            raise ValueError("alpha must satisfy: 0 < alpha <= 1")
        comass = (1.0 - alpha) / alpha
    else:
        raise ValueError("Must pass one of comass, span, halflife, or alpha")

    return float(comass)


def _offset(window, center):
    if not is_integer(window):
        window = len(window)
    offset = (window - 1) / 2.0 if center else 0
    try:
        return int(offset)
    except TypeError:
        return offset.astype(int)


def _require_min_periods(p):
    def _check_func(minp, window):
        if minp is None:
            return window
        else:
            return max(p, minp)

    return _check_func


def _use_window(minp, window):
    if minp is None:
        return window
    else:
        return minp


def _zsqrt(x):
    with np.errstate(all="ignore"):
        result = np.sqrt(x)
        mask = x < 0

    if isinstance(x, ABCDataFrame):
        if mask.values.any():
            result[mask] = 0
    else:
        if mask.any():
            result[mask] = 0

    return result


def _prep_binary(arg1, arg2):
    if not isinstance(arg2, type(arg1)):
        raise Exception("Input arrays must be of the same type!")

    # mask out values, this also makes a common index...
    X = arg1 + 0 * arg2
    Y = arg2 + 0 * arg1

    return X, Y


# Top-level exports


def rolling(obj, win_type=None, **kwds):
    if not isinstance(obj, (ABCSeries, ABCDataFrame)):
        raise TypeError("invalid type: %s" % type(obj))

    if win_type is not None:
        return Window(obj, win_type=win_type, **kwds)

    return Rolling(obj, **kwds)


rolling.__doc__ = Window.__doc__


def expanding(obj, **kwds):
    if not isinstance(obj, (ABCSeries, ABCDataFrame)):
        raise TypeError("invalid type: %s" % type(obj))

    return Expanding(obj, **kwds)


expanding.__doc__ = Expanding.__doc__


def ewm(obj, **kwds):
    if not isinstance(obj, (ABCSeries, ABCDataFrame)):
        raise TypeError("invalid type: %s" % type(obj))

    return EWM(obj, **kwds)


ewm.__doc__ = EWM.__doc__