code: """ define the IntervalIndex """
  import textwrap
  import warnings
  
  import numpy as np
  
  from pandas.compat import add_metaclass
  from pandas.core.dtypes.missing import isna
  from pandas.core.dtypes.cast import find_common_type, maybe_downcast_to_dtype
  from pandas.core.dtypes.common import (
      ensure_platform_int,
      is_list_like,
      is_datetime_or_timedelta_dtype,
      is_datetime64tz_dtype,
      is_integer_dtype,
      is_float_dtype,
      is_interval_dtype,
      is_object_dtype,
      is_scalar,
      is_float,
      is_number,
      is_integer)
  from pandas.core.indexes.base import (
      Index, ensure_index,
      default_pprint, _index_shared_docs)
  
  from pandas._libs import Timestamp, Timedelta
  from pandas._libs.interval import (
      Interval, IntervalMixin, IntervalTree,
  )
  
  from pandas.core.indexes.datetimes import date_range
  from pandas.core.indexes.timedeltas import timedelta_range
  from pandas.core.indexes.multi import MultiIndex
  import pandas.core.common as com
  from pandas.util._decorators import cache_readonly, Appender
  from pandas.util._doctools import _WritableDoc
  from pandas.util._exceptions import rewrite_exception
  from pandas.core.config import get_option
  from pandas.tseries.frequencies import to_offset
  from pandas.tseries.offsets import DateOffset
  
  import pandas.core.indexes.base as ibase
  from pandas.core.arrays.interval import (IntervalArray,
                                           _interval_shared_docs)
  
  _VALID_CLOSED = {'left', 'right', 'both', 'neither'}
  _index_doc_kwargs = dict(ibase._index_doc_kwargs)
  _index_doc_kwargs.update(
      dict(klass='IntervalIndex',
           target_klass='IntervalIndex or list of Intervals',
           name=textwrap.dedent("""\
           name : object, optional
                to be stored in the index.
           """),
           ))
  
  
  def _get_next_label(label):
      dtype = getattr(label, 'dtype', type(label))
      if isinstance(label, (Timestamp, Timedelta)):
          dtype = 'datetime64'
      if is_datetime_or_timedelta_dtype(dtype) or is_datetime64tz_dtype(dtype):
          return label + np.timedelta64(1, 'ns')
      elif is_integer_dtype(dtype):
          return label + 1
      elif is_float_dtype(dtype):
          return np.nextafter(label, np.infty)
      else:
          raise TypeError('cannot determine next label for type {typ!r}'
                          .format(typ=type(label)))
  
  
  def _get_prev_label(label):
      dtype = getattr(label, 'dtype', type(label))
      if isinstance(label, (Timestamp, Timedelta)):
          dtype = 'datetime64'
      if is_datetime_or_timedelta_dtype(dtype) or is_datetime64tz_dtype(dtype):
          return label - np.timedelta64(1, 'ns')
      elif is_integer_dtype(dtype):
          return label - 1
      elif is_float_dtype(dtype):
          return np.nextafter(label, -np.infty)
      else:
          raise TypeError('cannot determine next label for type {typ!r}'
                          .format(typ=type(label)))
  
  
  def _get_interval_closed_bounds(interval):
      """
      Given an Interval or IntervalIndex, return the corresponding interval with
      closed bounds.
      """
      left, right = interval.left, interval.right
      if interval.open_left:
          left = _get_next_label(left)
      if interval.open_right:
          right = _get_prev_label(right)
      return left, right
  
  
  def _new_IntervalIndex(cls, d):
      """
      This is called upon unpickling, rather than the default which doesn't have
      arguments and breaks __new__
      """
      return cls.from_arrays(**d)
  
  
  @Appender(_interval_shared_docs['class'] % dict(
      klass="IntervalIndex",
      summary="Immutable index of intervals that are closed on the same side.",
      name=_index_doc_kwargs['name'],
      versionadded="0.20.0",
      extra_methods="contains\n",
      examples=textwrap.dedent("""\
  
      Examples
      --------
      A new ``IntervalIndex`` is typically constructed using
      :func:`interval_range`:
  
      >>> pd.interval_range(start=0, end=5)
      IntervalIndex([(0, 1], (1, 2], (2, 3], (3, 4], (4, 5]]
                    closed='right', dtype='interval[int64]')
  
      It may also be constructed using one of the constructor
      methods: :meth:`IntervalIndex.from_arrays`,
      :meth:`IntervalIndex.from_breaks`, and :meth:`IntervalIndex.from_tuples`.
  
      See further examples in the doc strings of ``interval_range`` and the
      mentioned constructor methods.
      """),
  
  ))
  @add_metaclass(_WritableDoc)
  class IntervalIndex(IntervalMixin, Index):
      _typ = 'intervalindex'
      _comparables = ['name']
      _attributes = ['name', 'closed']
  
      # we would like our indexing holder to defer to us
      _defer_to_indexing = True
  
      # Immutable, so we are able to cache computations like isna in '_mask'
      _mask = None
  
      def __new__(cls, data, closed=None, dtype=None, copy=False,
                  name=None, verify_integrity=True):
  
          if name is None and hasattr(data, 'name'):
              name = data.name
  
          with rewrite_exception("IntervalArray", cls.__name__):
              array = IntervalArray(data, closed=closed, copy=copy, dtype=dtype,
                                    verify_integrity=verify_integrity)
  
          return cls._simple_new(array, name)
  
      @classmethod
      def _simple_new(cls, array, name, closed=None):
          """
          Construct from an IntervalArray
  
          Parameters
          ----------
          array : IntervalArray
          name : str
              Attached as result.name
          closed : Any
              Ignored.
          """
          result = IntervalMixin.__new__(cls)
          result._data = array
          result.name = name
          result._reset_identity()
          return result
  
      @Appender(_index_shared_docs['_shallow_copy'])
      def _shallow_copy(self, left=None, right=None, **kwargs):
          result = self._data._shallow_copy(left=left, right=right)
          attributes = self._get_attributes_dict()
          attributes.update(kwargs)
          return self._simple_new(result, **attributes)
  
      @cache_readonly
      def _isnan(self):
          """Return a mask indicating if each value is NA"""
          if self._mask is None:
              self._mask = isna(self.left)
          return self._mask
  
      @cache_readonly
      def _engine(self):
          return IntervalTree(self.left, self.right, closed=self.closed)
  
      def __contains__(self, key):
          """
          return a boolean if this key is IN the index
          We *only* accept an Interval
  
          Parameters
          ----------
          key : Interval
  
          Returns
          -------
          boolean
          """
          if not isinstance(key, Interval):
              return False
  
          try:
              self.get_loc(key)
              return True
          except KeyError:
              return False
  
      def contains(self, key):
          """
          Return a boolean indicating if the key is IN the index
  
          We accept / allow keys to be not *just* actual
          objects.
  
          Parameters
          ----------
          key : int, float, Interval
  
          Returns
          -------
          boolean
          """
          try:
              self.get_loc(key)
              return True
          except KeyError:
              return False
  
      @classmethod
      @Appender(_interval_shared_docs['from_breaks'] % _index_doc_kwargs)
      def from_breaks(cls, breaks, closed='right', name=None, copy=False,
                      dtype=None):
          with rewrite_exception("IntervalArray", cls.__name__):
              array = IntervalArray.from_breaks(breaks, closed=closed, copy=copy,
                                                dtype=dtype)
          return cls._simple_new(array, name=name)
  
      @classmethod
      @Appender(_interval_shared_docs['from_arrays'] % _index_doc_kwargs)
      def from_arrays(cls, left, right, closed='right', name=None, copy=False,
                      dtype=None):
          with rewrite_exception("IntervalArray", cls.__name__):
              array = IntervalArray.from_arrays(left, right, closed, copy=copy,
                                                dtype=dtype)
          return cls._simple_new(array, name=name)
  
      @classmethod
      @Appender(_interval_shared_docs['from_intervals'] % _index_doc_kwargs)
      def from_intervals(cls, data, closed=None, name=None, copy=False,
                         dtype=None):
          msg = ('IntervalIndex.from_intervals is deprecated and will be '
                 'removed in a future version; Use IntervalIndex(...) instead')
          warnings.warn(msg, FutureWarning, stacklevel=2)
          with rewrite_exception("IntervalArray", cls.__name__):
              array = IntervalArray(data, closed=closed, copy=copy, dtype=dtype)
  
          if name is None and isinstance(data, cls):
              name = data.name
  
          return cls._simple_new(array, name=name)
  
      @classmethod
      @Appender(_interval_shared_docs['from_tuples'] % _index_doc_kwargs)
      def from_tuples(cls, data, closed='right', name=None, copy=False,
                      dtype=None):
          with rewrite_exception("IntervalArray", cls.__name__):
              arr = IntervalArray.from_tuples(data, closed=closed, copy=copy,
                                              dtype=dtype)
          return cls._simple_new(arr, name=name)
  
      @Appender(_interval_shared_docs['to_tuples'] % dict(
          return_type="Index",
          examples="""
          Examples
          --------
          >>>  idx = pd.IntervalIndex.from_arrays([0, np.nan, 2], [1, np.nan, 3])
          >>>  idx.to_tuples()
          Index([(0.0, 1.0), (nan, nan), (2.0, 3.0)], dtype='object')
          >>>  idx.to_tuples(na_tuple=False)
          Index([(0.0, 1.0), nan, (2.0, 3.0)], dtype='object')""",
      ))
      def to_tuples(self, na_tuple=True):
          tuples = self._data.to_tuples(na_tuple=na_tuple)
          return Index(tuples)
  
      @cache_readonly
      def _multiindex(self):
          return MultiIndex.from_arrays([self.left, self.right],
                                        names=['left', 'right'])
  
      @property
      def left(self):
          """
          Return the left endpoints of each Interval in the IntervalIndex as
          an Index
          """
          return self._data._left
  
      @property
      def right(self):
          """
          Return the right endpoints of each Interval in the IntervalIndex as
          an Index
          """
          return self._data._right
  
      @property
      def closed(self):
          """
          Whether the intervals are closed on the left-side, right-side, both or
          neither
          """
          return self._data._closed
  
      @Appender(_interval_shared_docs['set_closed'] % _index_doc_kwargs)
      def set_closed(self, closed):
          if closed not in _VALID_CLOSED:
              msg = "invalid option for 'closed': {closed}"
              raise ValueError(msg.format(closed=closed))
  
          # return self._shallow_copy(closed=closed)
          array = self._data.set_closed(closed)
          return self._simple_new(array, self.name)
  
      @property
      def length(self):
          """
          Return an Index with entries denoting the length of each Interval in
          the IntervalIndex
          """
          return self._data.length
  
      @property
      def size(self):
          # Avoid materializing ndarray[Interval]
          return self._data.size
  
      @property
      def shape(self):
          # Avoid materializing ndarray[Interval]
          return self._data.shape
  
      @property
      def itemsize(self):
          msg = ('IntervalIndex.itemsize is deprecated and will be removed in '
                 'a future version')
          warnings.warn(msg, FutureWarning, stacklevel=2)
  
          # supress the warning from the underlying left/right itemsize
          with warnings.catch_warnings():
              warnings.simplefilter('ignore')
              return self.left.itemsize + self.right.itemsize
  
      def __len__(self):
          return len(self.left)
  
      @cache_readonly
      def values(self):
          """
          Return the IntervalIndex's data as an IntervalArray.
          """
          return self._data
  
      @cache_readonly
      def _values(self):
          return self._data
  
      @cache_readonly
      def _ndarray_values(self):
          return np.array(self._data)
  
      def __array__(self, result=None):
          """ the array interface, return my values """
          return self._ndarray_values
  
      def __array_wrap__(self, result, context=None):
          # we don't want the superclass implementation
          return result
  
      def __reduce__(self):
          d = dict(left=self.left,
                   right=self.right)
          d.update(self._get_attributes_dict())
          return _new_IntervalIndex, (self.__class__, d), None
  
      @Appender(_index_shared_docs['copy'])
      def copy(self, deep=False, name=None):
          array = self._data.copy(deep=deep)
          attributes = self._get_attributes_dict()
          if name is not None:
              attributes.update(name=name)
  
          return self._simple_new(array, **attributes)
  
      @Appender(_index_shared_docs['astype'])
      def astype(self, dtype, copy=True):
          with rewrite_exception('IntervalArray', self.__class__.__name__):
              new_values = self.values.astype(dtype, copy=copy)
          if is_interval_dtype(new_values):
              return self._shallow_copy(new_values.left, new_values.right)
          return super(IntervalIndex, self).astype(dtype, copy=copy)
  
      @cache_readonly
      def dtype(self):
          """Return the dtype object of the underlying data"""
          return self._data.dtype
  
      @property
      def inferred_type(self):
          """Return a string of the type inferred from the values"""
          return 'interval'
  
      @Appender(Index.memory_usage.__doc__)
      def memory_usage(self, deep=False):
          # we don't use an explicit engine
          # so return the bytes here
          return (self.left.memory_usage(deep=deep) +
                  self.right.memory_usage(deep=deep))
  
      @cache_readonly
      def mid(self):
          """
          Return the midpoint of each Interval in the IntervalIndex as an Index
          """
          return self._data.mid
  
      @cache_readonly
      def is_monotonic(self):
          """
          Return True if the IntervalIndex is monotonic increasing (only equal or
          increasing values), else False
          """
          return self._multiindex.is_monotonic
  
      @cache_readonly
      def is_monotonic_increasing(self):
          """
          Return True if the IntervalIndex is monotonic increasing (only equal or
          increasing values), else False
          """
          return self._multiindex.is_monotonic_increasing
  
      @cache_readonly
      def is_monotonic_decreasing(self):
          """
          Return True if the IntervalIndex is monotonic decreasing (only equal or
          decreasing values), else False
          """
          return self._multiindex.is_monotonic_decreasing
  
      @cache_readonly
      def is_unique(self):
          """
          Return True if the IntervalIndex contains unique elements, else False
          """
          return self._multiindex.is_unique
  
      @cache_readonly
      def is_non_overlapping_monotonic(self):
          return self._data.is_non_overlapping_monotonic
  
      @Appender(_index_shared_docs['_convert_scalar_indexer'])
      def _convert_scalar_indexer(self, key, kind=None):
          if kind == 'iloc':
              return super(IntervalIndex, self)._convert_scalar_indexer(
                  key, kind=kind)
          return key
  
      def _maybe_cast_slice_bound(self, label, side, kind):
          return getattr(self, side)._maybe_cast_slice_bound(label, side, kind)
  
      @Appender(_index_shared_docs['_convert_list_indexer'])
      def _convert_list_indexer(self, keyarr, kind=None):
          """
          we are passed a list-like indexer. Return the
          indexer for matching intervals.
          """
          locs = self.get_indexer_for(keyarr)
  
          # we have missing values
          if (locs == -1).any():
              raise KeyError
  
          return locs
  
      def _maybe_cast_indexed(self, key):
          """
          we need to cast the key, which could be a scalar
          or an array-like to the type of our subtype
          """
          if isinstance(key, IntervalIndex):
              return key
  
          subtype = self.dtype.subtype
          if is_float_dtype(subtype):
              if is_integer(key):
                  key = float(key)
              elif isinstance(key, (np.ndarray, Index)):
                  key = key.astype('float64')
          elif is_integer_dtype(subtype):
              if is_integer(key):
                  key = int(key)
  
          return key
  
      def _check_method(self, method):
          if method is None:
              return
  
          if method in ['bfill', 'backfill', 'pad', 'ffill', 'nearest']:
              msg = 'method {method} not yet implemented for IntervalIndex'
              raise NotImplementedError(msg.format(method=method))
  
          raise ValueError("Invalid fill method")
  
      def _searchsorted_monotonic(self, label, side, exclude_label=False):
          if not self.is_non_overlapping_monotonic:
              raise KeyError('can only get slices from an IntervalIndex if '
                             'bounds are non-overlapping and all monotonic '
                             'increasing or decreasing')
  
          if isinstance(label, IntervalMixin):
              raise NotImplementedError
  
          # GH 20921: "not is_monotonic_increasing" for the second condition
          # instead of "is_monotonic_decreasing" to account for single element
          # indexes being both increasing and decreasing
          if ((side == 'left' and self.left.is_monotonic_increasing) or
                  (side == 'right' and not self.left.is_monotonic_increasing)):
              sub_idx = self.right
              if self.open_right or exclude_label:
                  label = _get_next_label(label)
          else:
              sub_idx = self.left
              if self.open_left or exclude_label:
                  label = _get_prev_label(label)
  
          return sub_idx._searchsorted_monotonic(label, side)
  
      def _get_loc_only_exact_matches(self, key):
          if isinstance(key, Interval):
  
              if not self.is_unique:
                  raise ValueError("cannot index with a slice Interval"
                                   " and a non-unique index")
  
              # TODO: this expands to a tuple index, see if we can
              # do better
              return Index(self._multiindex.values).get_loc(key)
          raise KeyError
  
      def _find_non_overlapping_monotonic_bounds(self, key):
          if isinstance(key, IntervalMixin):
              start = self._searchsorted_monotonic(
                  key.left, 'left', exclude_label=key.open_left)
              stop = self._searchsorted_monotonic(
                  key.right, 'right', exclude_label=key.open_right)
          elif isinstance(key, slice):
              # slice
              start, stop = key.start, key.stop
              if (key.step or 1) != 1:
                  raise NotImplementedError("cannot slice with a slice step")
              if start is None:
                  start = 0
              else:
                  start = self._searchsorted_monotonic(start, 'left')
              if stop is None:
                  stop = len(self)
              else:
                  stop = self._searchsorted_monotonic(stop, 'right')
          else:
              # scalar or index-like
  
              start = self._searchsorted_monotonic(key, 'left')
              stop = self._searchsorted_monotonic(key, 'right')
          return start, stop
  
      def get_loc(self, key, method=None):
          """Get integer location, slice or boolean mask for requested label.
  
          Parameters
          ----------
          key : label
          method : {None}, optional
              * default: matches where the label is within an interval only.
  
          Returns
          -------
          loc : int if unique index, slice if monotonic index, else mask
  
          Examples
          ---------
          >>> i1, i2 = pd.Interval(0, 1), pd.Interval(1, 2)
          >>> index = pd.IntervalIndex([i1, i2])
          >>> index.get_loc(1)
          0
  
          You can also supply an interval or an location for a point inside an
          interval.
  
          >>> index.get_loc(pd.Interval(0, 2))
          array([0, 1], dtype=int64)
          >>> index.get_loc(1.5)
          1
  
          If a label is in several intervals, you get the locations of all the
          relevant intervals.
  
          >>> i3 = pd.Interval(0, 2)
          >>> overlapping_index = pd.IntervalIndex([i2, i3])
          >>> overlapping_index.get_loc(1.5)
          array([0, 1], dtype=int64)
          """
          self._check_method(method)
  
          original_key = key
          key = self._maybe_cast_indexed(key)
  
          if self.is_non_overlapping_monotonic:
              if isinstance(key, Interval):
                  left = self._maybe_cast_slice_bound(key.left, 'left', None)
                  right = self._maybe_cast_slice_bound(key.right, 'right', None)
                  key = Interval(left, right, key.closed)
              else:
                  key = self._maybe_cast_slice_bound(key, 'left', None)
  
              start, stop = self._find_non_overlapping_monotonic_bounds(key)
  
              if start is None or stop is None:
                  return slice(start, stop)
              elif start + 1 == stop:
                  return start
              elif start < stop:
                  return slice(start, stop)
              else:
                  raise KeyError(original_key)
  
          else:
              # use the interval tree
              if isinstance(key, Interval):
                  left, right = _get_interval_closed_bounds(key)
                  return self._engine.get_loc_interval(left, right)
              else:
                  return self._engine.get_loc(key)
  
      def get_value(self, series, key):
          if com.is_bool_indexer(key):
              loc = key
          elif is_list_like(key):
              loc = self.get_indexer(key)
          elif isinstance(key, slice):
  
              if not (key.step is None or key.step == 1):
                  raise ValueError("cannot support not-default step in a slice")
  
              try:
                  loc = self.get_loc(key)
              except TypeError:
                  # we didn't find exact intervals or are non-unique
                  msg = "unable to slice with this key: {key}".format(key=key)
                  raise ValueError(msg)
  
          else:
              loc = self.get_loc(key)
          return series.iloc[loc]
  
      @Appender(_index_shared_docs['get_indexer'] % _index_doc_kwargs)
      def get_indexer(self, target, method=None, limit=None, tolerance=None):
  
          self._check_method(method)
          target = ensure_index(target)
          target = self._maybe_cast_indexed(target)
  
          if self.equals(target):
              return np.arange(len(self), dtype='intp')
  
          if self.is_non_overlapping_monotonic:
              start, stop = self._find_non_overlapping_monotonic_bounds(target)
  
              start_plus_one = start + 1
              if not ((start_plus_one < stop).any()):
                  return np.where(start_plus_one == stop, start, -1)
  
          if not self.is_unique:
              raise ValueError("cannot handle non-unique indices")
  
          # IntervalIndex
          if isinstance(target, IntervalIndex):
              indexer = self._get_reindexer(target)
  
          # non IntervalIndex
          else:
              indexer = np.concatenate([self.get_loc(i) for i in target])
  
          return ensure_platform_int(indexer)
  
      def _get_reindexer(self, target):
          """
          Return an indexer for a target IntervalIndex with self
          """
  
          # find the left and right indexers
          lindexer = self._engine.get_indexer(target.left.values)
          rindexer = self._engine.get_indexer(target.right.values)
  
          # we want to return an indexer on the intervals
          # however, our keys could provide overlapping of multiple
          # intervals, so we iterate thru the indexers and construct
          # a set of indexers
  
          indexer = []
          n = len(self)
  
          for i, (lhs, rhs) in enumerate(zip(lindexer, rindexer)):
  
              target_value = target[i]
  
              # matching on the lhs bound
              if (lhs != -1 and
                      self.closed == 'right' and
                      target_value.left == self[lhs].right):
                  lhs += 1
  
              # matching on the lhs bound
              if (rhs != -1 and
                      self.closed == 'left' and
                      target_value.right == self[rhs].left):
                  rhs -= 1
  
              # not found
              if lhs == -1 and rhs == -1:
                  indexer.append(np.array([-1]))
  
              elif rhs == -1:
  
                  indexer.append(np.arange(lhs, n))
  
              elif lhs == -1:
  
                  # care about left/right closed here
                  value = self[i]
  
                  # target.closed same as self.closed
                  if self.closed == target.closed:
                      if target_value.left < value.left:
                          indexer.append(np.array([-1]))
                          continue
  
                  # target.closed == 'left'
                  elif self.closed == 'right':
                      if target_value.left <= value.left:
                          indexer.append(np.array([-1]))
                          continue
  
                  # target.closed == 'right'
                  elif self.closed == 'left':
                      if target_value.left <= value.left:
                          indexer.append(np.array([-1]))
                          continue
  
                  indexer.append(np.arange(0, rhs + 1))
  
              else:
                  indexer.append(np.arange(lhs, rhs + 1))
  
          return np.concatenate(indexer)
  
      @Appender(_index_shared_docs['get_indexer_non_unique'] % _index_doc_kwargs)
      def get_indexer_non_unique(self, target):
          target = self._maybe_cast_indexed(ensure_index(target))
          return super(IntervalIndex, self).get_indexer_non_unique(target)
  
      @Appender(_index_shared_docs['where'])
      def where(self, cond, other=None):
          if other is None:
              other = self._na_value
          values = np.where(cond, self.values, other)
          return self._shallow_copy(values)
  
      def delete(self, loc):
          """
          Return a new IntervalIndex with passed location(-s) deleted
  
          Returns
          -------
          new_index : IntervalIndex
          """
          new_left = self.left.delete(loc)
          new_right = self.right.delete(loc)
          return self._shallow_copy(new_left, new_right)
  
      def insert(self, loc, item):
          """
          Return a new IntervalIndex inserting new item at location. Follows
          Python list.append semantics for negative values.  Only Interval
          objects and NA can be inserted into an IntervalIndex
  
          Parameters
          ----------
          loc : int
          item : object
  
          Returns
          -------
          new_index : IntervalIndex
          """
          if isinstance(item, Interval):
              if item.closed != self.closed:
                  raise ValueError('inserted item must be closed on the same '
                                   'side as the index')
              left_insert = item.left
              right_insert = item.right
          elif is_scalar(item) and isna(item):
              # GH 18295
              left_insert = right_insert = item
          else:
              raise ValueError('can only insert Interval objects and NA into '
                               'an IntervalIndex')
  
          new_left = self.left.insert(loc, left_insert)
          new_right = self.right.insert(loc, right_insert)
          return self._shallow_copy(new_left, new_right)
  
      def _as_like_interval_index(self, other):
          self._assert_can_do_setop(other)
          other = ensure_index(other)
          if not isinstance(other, IntervalIndex):
              msg = ('the other index needs to be an IntervalIndex too, but '
                     'was type {}').format(other.__class__.__name__)
              raise TypeError(msg)
          elif self.closed != other.closed:
              msg = ('can only do set operations between two IntervalIndex '
                     'objects that are closed on the same side')
              raise ValueError(msg)
          return other
  
      def _concat_same_dtype(self, to_concat, name):
          """
          assert that we all have the same .closed
          we allow a 0-len index here as well
          """
          if not len({i.closed for i in to_concat if len(i)}) == 1:
              msg = ('can only append two IntervalIndex objects '
                     'that are closed on the same side')
              raise ValueError(msg)
          return super(IntervalIndex, self)._concat_same_dtype(to_concat, name)
  
      @Appender(_index_shared_docs['take'] % _index_doc_kwargs)
      def take(self, indices, axis=0, allow_fill=True,
               fill_value=None, **kwargs):
          result = self._data.take(indices, axis=axis, allow_fill=allow_fill,
                                   fill_value=fill_value, **kwargs)
          attributes = self._get_attributes_dict()
          return self._simple_new(result, **attributes)
  
      def __getitem__(self, value):
          result = self._data[value]
          if isinstance(result, IntervalArray):
              return self._shallow_copy(result)
          else:
              # scalar
              return result
  
      # __repr__ associated methods are based on MultiIndex
  
      def _format_with_header(self, header, **kwargs):
          return header + list(self._format_native_types(**kwargs))
  
      def _format_native_types(self, na_rep='', quoting=None, **kwargs):
          """ actually format my specific types """
          from pandas.io.formats.format import IntervalArrayFormatter
          return IntervalArrayFormatter(values=self,
                                        na_rep=na_rep,
                                        justify='all').get_result()
  
      def _format_data(self, name=None):
  
          # TODO: integrate with categorical and make generic
          # name argument is unused here; just for compat with base / categorical
          n = len(self)
          max_seq_items = min((get_option(
              'display.max_seq_items') or n) // 10, 10)
  
          formatter = str
  
          if n == 0:
              summary = '[]'
          elif n == 1:
              first = formatter(self[0])
              summary = '[{first}]'.format(first=first)
          elif n == 2:
              first = formatter(self[0])
              last = formatter(self[-1])
              summary = '[{first}, {last}]'.format(first=first, last=last)
          else:
  
              if n > max_seq_items:
                  n = min(max_seq_items // 2, 10)
                  head = [formatter(x) for x in self[:n]]
                  tail = [formatter(x) for x in self[-n:]]
                  summary = '[{head} ... {tail}]'.format(
                      head=', '.join(head), tail=', '.join(tail))
              else:
                  tail = [formatter(x) for x in self]
                  summary = '[{tail}]'.format(tail=', '.join(tail))
  
          return summary + ',' + self._format_space()
  
      def _format_attrs(self):
          attrs = [('closed', repr(self.closed))]
          if self.name is not None:
              attrs.append(('name', default_pprint(self.name)))
          attrs.append(('dtype', "'{dtype}'".format(dtype=self.dtype)))
          return attrs
  
      def _format_space(self):
          space = ' ' * (len(self.__class__.__name__) + 1)
          return "\n{space}".format(space=space)
  
      def argsort(self, *args, **kwargs):
          return np.lexsort((self.right, self.left))
  
      def equals(self, other):
          """
          Determines if two IntervalIndex objects contain the same elements
          """
          if self.is_(other):
              return True
  
          # if we can coerce to an II
          # then we can compare
          if not isinstance(other, IntervalIndex):
              if not is_interval_dtype(other):
                  return False
              other = Index(getattr(other, '.values', other))
  
          return (self.left.equals(other.left) and
                  self.right.equals(other.right) and
                  self.closed == other.closed)
  
      def _setop(op_name):
          def func(self, other):
              other = self._as_like_interval_index(other)
  
              # GH 19016: ensure set op will not return a prohibited dtype
              subtypes = [self.dtype.subtype, other.dtype.subtype]
              common_subtype = find_common_type(subtypes)
              if is_object_dtype(common_subtype):
                  msg = ('can only do {op} between two IntervalIndex '
                         'objects that have compatible dtypes')
                  raise TypeError(msg.format(op=op_name))
  
              result = getattr(self._multiindex, op_name)(other._multiindex)
              result_name = self.name if self.name == other.name else None
  
              # GH 19101: ensure empty results have correct dtype
              if result.empty:
                  result = result.values.astype(self.dtype.subtype)
              else:
                  result = result.values
  
              return type(self).from_tuples(result, closed=self.closed,
                                            name=result_name)
          return func
  
      union = _setop('union')
      intersection = _setop('intersection')
      difference = _setop('difference')
      symmetric_difference = _setop('symmetric_difference')
  
      # TODO: arithmetic operations
  
  
  IntervalIndex._add_logical_methods_disabled()
  
  
  def _is_valid_endpoint(endpoint):
      """helper for interval_range to check if start/end are valid types"""
      return any([is_number(endpoint),
                  isinstance(endpoint, Timestamp),
                  isinstance(endpoint, Timedelta),
                  endpoint is None])
  
  
  def _is_type_compatible(a, b):
      """helper for interval_range to check type compat of start/end/freq"""
      is_ts_compat = lambda x: isinstance(x, (Timestamp, DateOffset))
      is_td_compat = lambda x: isinstance(x, (Timedelta, DateOffset))
      return ((is_number(a) and is_number(b)) or
              (is_ts_compat(a) and is_ts_compat(b)) or
              (is_td_compat(a) and is_td_compat(b)) or
              com._any_none(a, b))
  
  
  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.
  
      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>`__.
  
      Returns
      -------
      rng : IntervalIndex
  
      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]')
  
      See Also
      --------
      IntervalIndex : an Index of intervals that are all closed on the same side.
      """
      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)
  
apis: pandas.core.dtypes.common.is_number pandas.core.indexes.base.default_pprint pandas.core.dtypes.common.is_float_dtype pandas.core.arrays.interval.IntervalArray numpy.nextafter pandas.core.arrays.interval.IntervalArray.from_breaks pandas.core.dtypes.common.is_integer pandas.core.dtypes.common.is_list_like pandas.core.common._all_not_none pandas.core.dtypes.common.is_float pandas.core.config.get_option pandas.core.arrays.interval.IntervalArray.from_arrays pandas.core.common.count_not_none numpy.timedelta64 pandas._libs.interval.IntervalTree pandas.core.indexes.base.ensure_index pandas.core.dtypes.cast.maybe_downcast_to_dtype numpy.where pandas.core.common.maybe_box_datetimelike numpy.linspace pandas.core.common._not_none pandas.core.indexes.base.Index pandas.util._exceptions.rewrite_exception pandas.tseries.frequencies.to_offset pandas.core.dtypes.common.is_interval_dtype numpy.lexsort pandas.io.formats.format.IntervalArrayFormatter numpy.arange pandas.core.common.is_bool_indexer pandas.core.dtypes.cast.find_common_type pandas._libs.interval.IntervalMixin.__new__ pandas.core.indexes.multi.MultiIndex.from_arrays pandas.core.dtypes.common.ensure_platform_int pandas.core.common._any_none pandas.core.dtypes.missing.isna pandas.core.dtypes.common.is_scalar pandas.util._decorators.Appender pandas.core.dtypes.common.is_datetime_or_timedelta_dtype pandas.compat.add_metaclass pandas.core.dtypes.common.is_datetime64tz_dtype pandas.core.arrays.interval.IntervalArray.from_tuples pandas.core.dtypes.common.is_object_dtype pandas._libs.interval.Interval numpy.array numpy.concatenate pandas.core.dtypes.common.is_integer_dtype