Return a fixed frequency IntervalIndex

    Parameters
    ----------
    start : numeric or datetime-like, default None
        Left bound for generating intervals
    end : numeric or datetime-like, default None
        Right bound for generating intervals
    periods : integer, default None
        Number of periods to generate
    freq : numeric, string, or DateOffset, default None
        The length of each interval. Must be consistent with the type of start
        and end, e.g. 2 for numeric, or '5H' for datetime-like.  Default is 1
        for numeric and 'D' for datetime-like.
    name : string, default None
        Name of the resulting IntervalIndex
    closed : {'left', 'right', 'both', 'neither'}, default 'right'
        Whether the intervals are closed on the left-side, right-side, both
        or neither.

    Returns
    -------
    rng : IntervalIndex

    See Also
    --------
    IntervalIndex : An Index of intervals that are all closed on the same side.

    Notes
    -----
    Of the four parameters ``start``, ``end``, ``periods``, and ``freq``,
    exactly three must be specified. If ``freq`` is omitted, the resulting
    ``IntervalIndex`` will have ``periods`` linearly spaced elements between
    ``start`` and ``end``, inclusively.

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

    Examples
    --------
    Numeric ``start`` and  ``end`` is supported.

    >>> pd.interval_range(start=0, end=5)
    IntervalIndex([(0, 1], (1, 2], (2, 3], (3, 4], (4, 5]],
                  closed='right', dtype='interval[int64]')

    Additionally, datetime-like input is also supported.

    >>> pd.interval_range(start=pd.Timestamp('2017-01-01'),
    ...                   end=pd.Timestamp('2017-01-04'))
    IntervalIndex([(2017-01-01, 2017-01-02], (2017-01-02, 2017-01-03],
                   (2017-01-03, 2017-01-04]],
                  closed='right', dtype='interval[datetime64[ns]]')

    The ``freq`` parameter specifies the frequency between the left and right.
    endpoints of the individual intervals within the ``IntervalIndex``.  For
    numeric ``start`` and ``end``, the frequency must also be numeric.

    >>> pd.interval_range(start=0, periods=4, freq=1.5)
    IntervalIndex([(0.0, 1.5], (1.5, 3.0], (3.0, 4.5], (4.5, 6.0]],
                  closed='right', dtype='interval[float64]')

    Similarly, for datetime-like ``start`` and ``end``, the frequency must be
    convertible to a DateOffset.

    >>> pd.interval_range(start=pd.Timestamp('2017-01-01'),
    ...                   periods=3, freq='MS')
    IntervalIndex([(2017-01-01, 2017-02-01], (2017-02-01, 2017-03-01],
                   (2017-03-01, 2017-04-01]],
                  closed='right', dtype='interval[datetime64[ns]]')

    Specify ``start``, ``end``, and ``periods``; the frequency is generated
    automatically (linearly spaced).

    >>> pd.interval_range(start=0, end=6, periods=4)
    IntervalIndex([(0.0, 1.5], (1.5, 3.0], (3.0, 4.5], (4.5, 6.0]],
              closed='right',
              dtype='interval[float64]')

    The ``closed`` parameter specifies which endpoints of the individual
    intervals within the ``IntervalIndex`` are closed.

    >>> pd.interval_range(end=5, periods=4, closed='both')
    IntervalIndex([[1, 2], [2, 3], [3, 4], [4, 5]],
                  closed='both', dtype='interval[int64]')

def interval_range(start=None, end=None, periods=None, freq=None,
                   name=None, closed='right'):
    """
    Return a fixed frequency IntervalIndex

    Parameters
    ----------
    start : numeric or datetime-like, default None
        Left bound for generating intervals
    end : numeric or datetime-like, default None
        Right bound for generating intervals
    periods : integer, default None
        Number of periods to generate
    freq : numeric, string, or DateOffset, default None
        The length of each interval. Must be consistent with the type of start
        and end, e.g. 2 for numeric, or '5H' for datetime-like.  Default is 1
        for numeric and 'D' for datetime-like.
    name : string, default None
        Name of the resulting IntervalIndex
    closed : {'left', 'right', 'both', 'neither'}, default 'right'
        Whether the intervals are closed on the left-side, right-side, both
        or neither.

    Returns
    -------
    rng : IntervalIndex

    See Also
    --------
    IntervalIndex : An Index of intervals that are all closed on the same side.

    Notes
    -----
    Of the four parameters ``start``, ``end``, ``periods``, and ``freq``,
    exactly three must be specified. If ``freq`` is omitted, the resulting
    ``IntervalIndex`` will have ``periods`` linearly spaced elements between
    ``start`` and ``end``, inclusively.

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

    Examples
    --------
    Numeric ``start`` and  ``end`` is supported.

    >>> pd.interval_range(start=0, end=5)
    IntervalIndex([(0, 1], (1, 2], (2, 3], (3, 4], (4, 5]],
                  closed='right', dtype='interval[int64]')

    Additionally, datetime-like input is also supported.

    >>> pd.interval_range(start=pd.Timestamp('2017-01-01'),
    ...                   end=pd.Timestamp('2017-01-04'))
    IntervalIndex([(2017-01-01, 2017-01-02], (2017-01-02, 2017-01-03],
                   (2017-01-03, 2017-01-04]],
                  closed='right', dtype='interval[datetime64[ns]]')

    The ``freq`` parameter specifies the frequency between the left and right.
    endpoints of the individual intervals within the ``IntervalIndex``.  For
    numeric ``start`` and ``end``, the frequency must also be numeric.

    >>> pd.interval_range(start=0, periods=4, freq=1.5)
    IntervalIndex([(0.0, 1.5], (1.5, 3.0], (3.0, 4.5], (4.5, 6.0]],
                  closed='right', dtype='interval[float64]')

    Similarly, for datetime-like ``start`` and ``end``, the frequency must be
    convertible to a DateOffset.

    >>> pd.interval_range(start=pd.Timestamp('2017-01-01'),
    ...                   periods=3, freq='MS')
    IntervalIndex([(2017-01-01, 2017-02-01], (2017-02-01, 2017-03-01],
                   (2017-03-01, 2017-04-01]],
                  closed='right', dtype='interval[datetime64[ns]]')

    Specify ``start``, ``end``, and ``periods``; the frequency is generated
    automatically (linearly spaced).

    >>> pd.interval_range(start=0, end=6, periods=4)
    IntervalIndex([(0.0, 1.5], (1.5, 3.0], (3.0, 4.5], (4.5, 6.0]],
              closed='right',
              dtype='interval[float64]')

    The ``closed`` parameter specifies which endpoints of the individual
    intervals within the ``IntervalIndex`` are closed.

    >>> pd.interval_range(end=5, periods=4, closed='both')
    IntervalIndex([[1, 2], [2, 3], [3, 4], [4, 5]],
                  closed='both', dtype='interval[int64]')
    """
    start = com.maybe_box_datetimelike(start)
    end = com.maybe_box_datetimelike(end)
    endpoint = start if start is not None else end

    if freq is None and com._any_none(periods, start, end):
        freq = 1 if is_number(endpoint) else 'D'

    if com.count_not_none(start, end, periods, freq) != 3:
        raise ValueError('Of the four parameters: start, end, periods, and '
                         'freq, exactly three must be specified')

    if not _is_valid_endpoint(start):
        msg = 'start must be numeric or datetime-like, got {start}'
        raise ValueError(msg.format(start=start))
    elif not _is_valid_endpoint(end):
        msg = 'end must be numeric or datetime-like, got {end}'
        raise ValueError(msg.format(end=end))

    if is_float(periods):
        periods = int(periods)
    elif not is_integer(periods) and periods is not None:
        msg = 'periods must be a number, got {periods}'
        raise TypeError(msg.format(periods=periods))

    if freq is not None and not is_number(freq):
        try:
            freq = to_offset(freq)
        except ValueError:
            raise ValueError('freq must be numeric or convertible to '
                             'DateOffset, got {freq}'.format(freq=freq))

    # verify type compatibility
    if not all([_is_type_compatible(start, end),
                _is_type_compatible(start, freq),
                _is_type_compatible(end, freq)]):
        raise TypeError("start, end, freq need to be type compatible")

    # +1 to convert interval count to breaks count (n breaks = n-1 intervals)
    if periods is not None:
        periods += 1

    if is_number(endpoint):
        # force consistency between start/end/freq (lower end if freq skips it)
        if com._all_not_none(start, end, freq):
            end -= (end - start) % freq

        # compute the period/start/end if unspecified (at most one)
        if periods is None:
            periods = int((end - start) // freq) + 1
        elif start is None:
            start = end - (periods - 1) * freq
        elif end is None:
            end = start + (periods - 1) * freq

        breaks = np.linspace(start, end, periods)
        if all(is_integer(x) for x in com._not_none(start, end, freq)):
            # np.linspace always produces float output
            breaks = maybe_downcast_to_dtype(breaks, 'int64')
    else:
        # delegate to the appropriate range function
        if isinstance(endpoint, Timestamp):
            range_func = date_range
        else:
            range_func = timedelta_range

        breaks = range_func(start=start, end=end, periods=periods, freq=freq)

    return IntervalIndex.from_breaks(breaks, name=name, closed=closed)