text: from datetime import datetime
  import operator
  from textwrap import dedent
  from typing import Dict, FrozenSet, Hashable, Optional, Union
  import warnings
  
  import numpy as np
  
  from pandas._libs import algos as libalgos, index as libindex, lib
  import pandas._libs.join as libjoin
  from pandas._libs.lib import is_datetime_array
  from pandas._libs.tslibs import OutOfBoundsDatetime, Timestamp
  from pandas._libs.tslibs.period import IncompatibleFrequency
  from pandas._libs.tslibs.timezones import tz_compare
  from pandas.compat import set_function_name
  from pandas.compat.numpy import function as nv
  from pandas.util._decorators import Appender, Substitution, cache_readonly
  
  from pandas.core.dtypes import concat as _concat
  from pandas.core.dtypes.cast import maybe_cast_to_integer_array
  from pandas.core.dtypes.common import (
      ensure_categorical,
      ensure_int64,
      ensure_object,
      ensure_platform_int,
      is_bool,
      is_bool_dtype,
      is_categorical,
      is_categorical_dtype,
      is_datetime64_any_dtype,
      is_datetime64tz_dtype,
      is_dtype_equal,
      is_extension_array_dtype,
      is_float,
      is_float_dtype,
      is_hashable,
      is_integer,
      is_integer_dtype,
      is_interval_dtype,
      is_iterator,
      is_list_like,
      is_object_dtype,
      is_period_dtype,
      is_scalar,
      is_signed_integer_dtype,
      is_timedelta64_dtype,
      is_unsigned_integer_dtype,
  )
  from pandas.core.dtypes.concat import concat_compat
  from pandas.core.dtypes.generic import (
      ABCCategorical,
      ABCDataFrame,
      ABCDatetimeArray,
      ABCDatetimeIndex,
      ABCIndexClass,
      ABCIntervalIndex,
      ABCMultiIndex,
      ABCPandasArray,
      ABCPeriodIndex,
      ABCSeries,
      ABCTimedeltaIndex,
  )
  from pandas.core.dtypes.missing import array_equivalent, isna
  
  from pandas.core import ops
  from pandas.core.accessor import CachedAccessor
  import pandas.core.algorithms as algos
  from pandas.core.arrays import ExtensionArray
  from pandas.core.base import IndexOpsMixin, PandasObject
  import pandas.core.common as com
  from pandas.core.construction import extract_array
  from pandas.core.indexers import maybe_convert_indices
  from pandas.core.indexes.frozen import FrozenList
  import pandas.core.missing as missing
  from pandas.core.ops import get_op_result_name
  from pandas.core.ops.invalid import make_invalid_op
  from pandas.core.strings import StringMethods
  
  from pandas.io.formats.printing import (
      default_pprint,
      format_object_attrs,
      format_object_summary,
      pprint_thing,
  )
  
  __all__ = ["Index"]
  
  _unsortable_types = frozenset(("mixed", "mixed-integer"))
  
  _index_doc_kwargs = dict(
      klass="Index",
      inplace="",
      target_klass="Index",
      raises_section="",
      unique="Index",
      duplicated="np.ndarray",
  )
  _index_shared_docs = dict()
  
  
  def _make_comparison_op(op, cls):
      def cmp_method(self, other):
          if isinstance(other, (np.ndarray, Index, ABCSeries, ExtensionArray)):
              if other.ndim > 0 and len(self) != len(other):
                  raise ValueError("Lengths must match to compare")
  
          if is_object_dtype(self) and isinstance(other, ABCCategorical):
              left = type(other)(self._values, dtype=other.dtype)
              return op(left, other)
          elif is_object_dtype(self) and not isinstance(self, ABCMultiIndex):
              # don't pass MultiIndex
              with np.errstate(all="ignore"):
                  result = ops.comp_method_OBJECT_ARRAY(op, self.values, other)
  
          else:
              with np.errstate(all="ignore"):
                  result = op(self.values, np.asarray(other))
  
          if is_bool_dtype(result):
              return result
          return ops.invalid_comparison(self, other, op)
  
      name = f"__{op.__name__}__"
      return set_function_name(cmp_method, name, cls)
  
  
  def _make_arithmetic_op(op, cls):
      def index_arithmetic_method(self, other):
          if isinstance(other, (ABCSeries, ABCDataFrame, ABCTimedeltaIndex)):
              return NotImplemented
  
          from pandas import Series
  
          result = op(Series(self), other)
          if isinstance(result, tuple):
              return (Index(result[0]), Index(result[1]))
          return Index(result)
  
      name = f"__{op.__name__}__"
      # TODO: docstring?
      return set_function_name(index_arithmetic_method, name, cls)
  
  
  class InvalidIndexError(Exception):
      pass
  
  
  _o_dtype = np.dtype(object)
  _Identity = object
  
  
  def _new_Index(cls, d):
      """
      This is called upon unpickling, rather than the default which doesn't
      have arguments and breaks __new__.
      """
      # required for backward compat, because PI can't be instantiated with
      # ordinals through __new__ GH #13277
      if issubclass(cls, ABCPeriodIndex):
          from pandas.core.indexes.period import _new_PeriodIndex
  
          return _new_PeriodIndex(cls, **d)
  
      if issubclass(cls, ABCMultiIndex):
          if "labels" in d and "codes" not in d:
              # GH#23752 "labels" kwarg has been replaced with "codes"
              d["codes"] = d.pop("labels")
  
      return cls.__new__(cls, **d)
  
  
  class Index(IndexOpsMixin, PandasObject):
      """
      Immutable ndarray implementing an ordered, sliceable set. The basic object
      storing axis labels for all pandas objects.
  
      Parameters
      ----------
      data : array-like (1-dimensional)
      dtype : NumPy dtype (default: object)
          If dtype is None, we find the dtype that best fits the data.
          If an actual dtype is provided, we coerce to that dtype if it's safe.
          Otherwise, an error will be raised.
      copy : bool
          Make a copy of input ndarray.
      name : object
          Name to be stored in the index.
      tupleize_cols : bool (default: True)
          When True, attempt to create a MultiIndex if possible.
  
      See Also
      --------
      RangeIndex : Index implementing a monotonic integer range.
      CategoricalIndex : Index of :class:`Categorical` s.
      MultiIndex : A multi-level, or hierarchical, Index.
      IntervalIndex : An Index of :class:`Interval` s.
      DatetimeIndex, TimedeltaIndex, PeriodIndex
      Int64Index, UInt64Index,  Float64Index
  
      Notes
      -----
      An Index instance can **only** contain hashable objects
  
      Examples
      --------
      >>> pd.Index([1, 2, 3])
      Int64Index([1, 2, 3], dtype='int64')
  
      >>> pd.Index(list('abc'))
      Index(['a', 'b', 'c'], dtype='object')
      """
  
      # tolist is not actually deprecated, just suppressed in the __dir__
      _deprecations: FrozenSet[str] = (
          PandasObject._deprecations
          | IndexOpsMixin._deprecations
          | frozenset(["contains", "set_value"])
      )
  
      # To hand over control to subclasses
      _join_precedence = 1
  
      # Cython methods; see github.com/cython/cython/issues/2647
      #  for why we need to wrap these instead of making them class attributes
      # Moreover, cython will choose the appropriate-dtyped sub-function
      #  given the dtypes of the passed arguments
      def _left_indexer_unique(self, left, right):
          return libjoin.left_join_indexer_unique(left, right)
  
      def _left_indexer(self, left, right):
          return libjoin.left_join_indexer(left, right)
  
      def _inner_indexer(self, left, right):
          return libjoin.inner_join_indexer(left, right)
  
      def _outer_indexer(self, left, right):
          return libjoin.outer_join_indexer(left, right)
  
      _typ = "index"
      _data: Union[ExtensionArray, np.ndarray]
      _id = None
      _name: Optional[Hashable] = None
      # MultiIndex.levels previously allowed setting the index name. We
      # don't allow this anymore, and raise if it happens rather than
      # failing silently.
      _no_setting_name: bool = False
      _comparables = ["name"]
      _attributes = ["name"]
      _is_numeric_dtype = False
      _can_hold_na = True
  
      # would we like our indexing holder to defer to us
      _defer_to_indexing = False
  
      # prioritize current class for _shallow_copy_with_infer,
      # used to infer integers as datetime-likes
      _infer_as_myclass = False
  
      _engine_type = libindex.ObjectEngine
      # whether we support partial string indexing. Overridden
      # in DatetimeIndex and PeriodIndex
      _supports_partial_string_indexing = False
  
      _accessors = {"str"}
  
      str = CachedAccessor("str", StringMethods)
  
      # --------------------------------------------------------------------
      # Constructors
  
      def __new__(
          cls, data=None, dtype=None, copy=False, name=None, tupleize_cols=True, **kwargs,
      ) -> "Index":
  
          from .range import RangeIndex
          from pandas import PeriodIndex, DatetimeIndex, TimedeltaIndex
          from .numeric import Float64Index, Int64Index, UInt64Index
          from .interval import IntervalIndex
          from .category import CategoricalIndex
  
          name = maybe_extract_name(name, data, cls)
  
          if isinstance(data, ABCPandasArray):
              # ensure users don't accidentally put a PandasArray in an index.
              data = data.to_numpy()
  
          # range
          if isinstance(data, RangeIndex):
              return RangeIndex(start=data, copy=copy, dtype=dtype, name=name)
          elif isinstance(data, range):
              return RangeIndex.from_range(data, dtype=dtype, name=name)
  
          # categorical
          elif is_categorical_dtype(data) or is_categorical_dtype(dtype):
              return CategoricalIndex(data, dtype=dtype, copy=copy, name=name, **kwargs)
  
          # interval
          elif is_interval_dtype(data) or is_interval_dtype(dtype):
              closed = kwargs.pop("closed", None)
              if is_dtype_equal(_o_dtype, dtype):
                  return IntervalIndex(
                      data, name=name, copy=copy, closed=closed, **kwargs
                  ).astype(object)
              return IntervalIndex(
                  data, dtype=dtype, name=name, copy=copy, closed=closed, **kwargs
              )
  
          elif (
              is_datetime64_any_dtype(data)
              or is_datetime64_any_dtype(dtype)
              or "tz" in kwargs
          ):
              if is_dtype_equal(_o_dtype, dtype):
                  # GH#23524 passing `dtype=object` to DatetimeIndex is invalid,
                  #  will raise in the where `data` is already tz-aware.  So
                  #  we leave it out of this step and cast to object-dtype after
                  #  the DatetimeIndex construction.
                  # Note we can pass copy=False because the .astype below
                  #  will always make a copy
                  return DatetimeIndex(data, copy=False, name=name, **kwargs).astype(
                      object
                  )
              else:
                  return DatetimeIndex(data, copy=copy, name=name, dtype=dtype, **kwargs)
  
          elif is_timedelta64_dtype(data) or is_timedelta64_dtype(dtype):
              if is_dtype_equal(_o_dtype, dtype):
                  # Note we can pass copy=False because the .astype below
                  #  will always make a copy
                  return TimedeltaIndex(data, copy=False, name=name, **kwargs).astype(
                      object
                  )
              else:
                  return TimedeltaIndex(data, copy=copy, name=name, dtype=dtype, **kwargs)
  
          elif is_period_dtype(data) or is_period_dtype(dtype):
              if is_dtype_equal(_o_dtype, dtype):
                  return PeriodIndex(data, copy=False, name=name, **kwargs).astype(object)
              return PeriodIndex(data, dtype=dtype, copy=copy, name=name, **kwargs)
  
          # extension dtype
          elif is_extension_array_dtype(data) or is_extension_array_dtype(dtype):
              if not (dtype is None or is_object_dtype(dtype)):
                  # coerce to the provided dtype
                  ea_cls = dtype.construct_array_type()
                  data = ea_cls._from_sequence(data, dtype=dtype, copy=False)
              else:
                  data = np.asarray(data, dtype=object)
  
              # coerce to the object dtype
              data = data.astype(object)
              return Index(data, dtype=object, copy=copy, name=name, **kwargs)
  
          # index-like
          elif isinstance(data, (np.ndarray, Index, ABCSeries)):
              if dtype is not None:
                  # we need to avoid having numpy coerce
                  # things that look like ints/floats to ints unless
                  # they are actually ints, e.g. '0' and 0.0
                  # should not be coerced
                  # GH 11836
                  data = _maybe_cast_with_dtype(data, dtype, copy)
                  dtype = data.dtype  # TODO: maybe not for object?
  
              # maybe coerce to a sub-class
              if is_signed_integer_dtype(data.dtype):
                  return Int64Index(data, copy=copy, dtype=dtype, name=name)
              elif is_unsigned_integer_dtype(data.dtype):
                  return UInt64Index(data, copy=copy, dtype=dtype, name=name)
              elif is_float_dtype(data.dtype):
                  return Float64Index(data, copy=copy, dtype=dtype, name=name)
              elif issubclass(data.dtype.type, np.bool) or is_bool_dtype(data):
                  subarr = data.astype("object")
              else:
                  subarr = com.asarray_tuplesafe(data, dtype=object)
  
              # asarray_tuplesafe does not always copy underlying data,
              # so need to make sure that this happens
              if copy:
                  subarr = subarr.copy()
  
              if dtype is None:
                  new_data, new_dtype = _maybe_cast_data_without_dtype(subarr)
                  if new_dtype is not None:
                      return cls(
                          new_data, dtype=new_dtype, copy=False, name=name, **kwargs
                      )
  
              if kwargs:
                  raise TypeError(f"Unexpected keyword arguments {repr(set(kwargs))}")
              return cls._simple_new(subarr, name, **kwargs)
  
          elif hasattr(data, "__array__"):
              return Index(np.asarray(data), dtype=dtype, copy=copy, name=name, **kwargs)
          elif data is None or is_scalar(data):
              raise cls._scalar_data_error(data)
          else:
              if tupleize_cols and is_list_like(data):
                  # GH21470: convert iterable to list before determining if empty
                  if is_iterator(data):
                      data = list(data)
  
                  if data and all(isinstance(e, tuple) for e in data):
                      # we must be all tuples, otherwise don't construct
                      # 10697
                      from .multi import MultiIndex
  
                      return MultiIndex.from_tuples(
                          data, names=name or kwargs.get("names")
                      )
              # other iterable of some kind
              subarr = com.asarray_tuplesafe(data, dtype=object)
              return Index(subarr, dtype=dtype, copy=copy, name=name, **kwargs)
  
      """
      NOTE for new Index creation:
  
      - _simple_new: It returns new Index with the same type as the caller.
        All metadata (such as name) must be provided by caller's responsibility.
        Using _shallow_copy is recommended because it fills these metadata
        otherwise specified.
  
      - _shallow_copy: It returns new Index with the same type (using
        _simple_new), but fills caller's metadata otherwise specified. Passed
        kwargs will overwrite corresponding metadata.
  
      - _shallow_copy_with_infer: It returns new Index inferring its type
        from passed values. It fills caller's metadata otherwise specified as the
        same as _shallow_copy.
  
      See each method's docstring.
      """
  
      @property
      def asi8(self):
          """
          Integer representation of the values.
  
          Returns
          -------
          ndarray
              An ndarray with int64 dtype.
          """
          return None
  
      @classmethod
      def _simple_new(cls, values, name=None, dtype=None):
          """
          We require that we have a dtype compat for the values. If we are passed
          a non-dtype compat, then coerce using the constructor.
  
          Must be careful not to recurse.
          """
          if isinstance(values, (ABCSeries, ABCIndexClass)):
              # Index._data must always be an ndarray.
              # This is no-copy for when _values is an ndarray,
              # which should be always at this point.
              values = np.asarray(values._values)
  
          result = object.__new__(cls)
          result._data = values
          # _index_data is a (temporary?) fix to ensure that the direct data
          # manipulation we do in `_libs/reduction.pyx` continues to work.
          # We need access to the actual ndarray, since we're messing with
          # data buffers and strides. We don't re-use `_ndarray_values`, since
          # we actually set this value too.
          result._index_data = values
          result._name = name
  
          return result._reset_identity()
  
      @cache_readonly
      def _constructor(self):
          return type(self)
  
      # --------------------------------------------------------------------
      # Index Internals Methods
  
      def _get_attributes_dict(self):
          """
          Return an attributes dict for my class.
          """
          return {k: getattr(self, k, None) for k in self._attributes}
  
      _index_shared_docs[
          "_shallow_copy"
      ] = """
          Create a new Index with the same class as the caller, don't copy the
          data, use the same object attributes with passed in attributes taking
          precedence.
  
          *this is an internal non-public method*
  
          Parameters
          ----------
          values : the values to create the new Index, optional
          kwargs : updates the default attributes for this Index
          """
  
      @Appender(_index_shared_docs["_shallow_copy"])
      def _shallow_copy(self, values=None, **kwargs):
          if values is None:
              values = self.values
          attributes = self._get_attributes_dict()
          attributes.update(kwargs)
          if not len(values) and "dtype" not in kwargs:
              attributes["dtype"] = self.dtype
  
          # _simple_new expects an the type of self._data
          values = getattr(values, "_values", values)
          if isinstance(values, ABCDatetimeArray):
              # `self.values` returns `self` for tz-aware, so we need to unwrap
              #  more specifically
              values = values.asi8
  
          return self._simple_new(values, **attributes)
  
      def _shallow_copy_with_infer(self, values, **kwargs):
          """
          Create a new Index inferring the class with passed value, don't copy
          the data, use the same object attributes with passed in attributes
          taking precedence.
  
          *this is an internal non-public method*
  
          Parameters
          ----------
          values : the values to create the new Index, optional
          kwargs : updates the default attributes for this Index
          """
          attributes = self._get_attributes_dict()
          attributes.update(kwargs)
          attributes["copy"] = False
          if not len(values) and "dtype" not in kwargs:
              attributes["dtype"] = self.dtype
          if self._infer_as_myclass:
              try:
                  return self._constructor(values, **attributes)
              except (TypeError, ValueError):
                  pass
          return Index(values, **attributes)
  
      def _update_inplace(self, result, **kwargs):
          # guard when called from IndexOpsMixin
          raise TypeError("Index can't be updated inplace")
  
      def is_(self, other) -> bool:
          """
          More flexible, faster check like ``is`` but that works through views.
  
          Note: this is *not* the same as ``Index.identical()``, which checks
          that metadata is also the same.
  
          Parameters
          ----------
          other : object
              other object to compare against.
  
          Returns
          -------
          True if both have same underlying data, False otherwise : bool
          """
          # use something other than None to be clearer
          return self._id is getattr(other, "_id", Ellipsis) and self._id is not None
  
      def _reset_identity(self):
          """
          Initializes or resets ``_id`` attribute with new object.
          """
          self._id = _Identity()
          return self
  
      def _cleanup(self):
          self._engine.clear_mapping()
  
      @cache_readonly
      def _engine(self):
          # property, for now, slow to look up
  
          # to avoid a reference cycle, bind `_ndarray_values` to a local variable, so
          # `self` is not passed into the lambda.
          _ndarray_values = self._ndarray_values
          return self._engine_type(lambda: _ndarray_values, len(self))
  
      # --------------------------------------------------------------------
      # Array-Like Methods
  
      # ndarray compat
      def __len__(self) -> int:
          """
          Return the length of the Index.
          """
          return len(self._data)
  
      def __array__(self, dtype=None):
          """
          The array interface, return my values.
          """
          return np.asarray(self._data, dtype=dtype)
  
      def __array_wrap__(self, result, context=None):
          """
          Gets called after a ufunc.
          """
          result = lib.item_from_zerodim(result)
          if is_bool_dtype(result) or lib.is_scalar(result):
              return result
  
          attrs = self._get_attributes_dict()
          return Index(result, **attrs)
  
      @cache_readonly
      def dtype(self):
          """
          Return the dtype object of the underlying data.
          """
          return self._data.dtype
  
      def ravel(self, order="C"):
          """
          Return an ndarray of the flattened values of the underlying data.
  
          Returns
          -------
          numpy.ndarray
              Flattened array.
  
          See Also
          --------
          numpy.ndarray.ravel
          """
          return self._ndarray_values.ravel(order=order)
  
      def view(self, cls=None):
  
          # we need to see if we are subclassing an
          # index type here
          if cls is not None and not hasattr(cls, "_typ"):
              result = self._data.view(cls)
          else:
              result = self._shallow_copy()
          if isinstance(result, Index):
              result._id = self._id
          return result
  
      _index_shared_docs[
          "astype"
      ] = """
          Create an Index with values cast to dtypes. The class of a new Index
          is determined by dtype. When conversion is impossible, a ValueError
          exception is raised.
  
          Parameters
          ----------
          dtype : numpy dtype or pandas type
              Note that any signed integer `dtype` is treated as ``'int64'``,
              and any unsigned integer `dtype` is treated as ``'uint64'``,
              regardless of the size.
          copy : bool, default True
              By default, astype always returns a newly allocated object.
              If copy is set to False and internal requirements on dtype are
              satisfied, the original data is used to create a new Index
              or the original Index is returned.
  
          Returns
          -------
          Index
              Index with values cast to specified dtype.
          """
  
      @Appender(_index_shared_docs["astype"])
      def astype(self, dtype, copy=True):
          if is_dtype_equal(self.dtype, dtype):
              return self.copy() if copy else self
  
          elif is_categorical_dtype(dtype):
              from .category import CategoricalIndex
  
              return CategoricalIndex(self.values, name=self.name, dtype=dtype, copy=copy)
  
          elif is_extension_array_dtype(dtype):
              return Index(np.asarray(self), dtype=dtype, copy=copy)
  
          try:
              return Index(
                  self.values.astype(dtype, copy=copy), name=self.name, dtype=dtype
              )
          except (TypeError, ValueError):
              raise TypeError(f"Cannot cast {type(self).__name__} to dtype {dtype}")
  
      _index_shared_docs[
          "take"
      ] = """
          Return a new %(klass)s of the values selected by the indices.
  
          For internal compatibility with numpy arrays.
  
          Parameters
          ----------
          indices : list
              Indices to be taken.
          axis : int, optional
              The axis over which to select values, always 0.
          allow_fill : bool, default True
          fill_value : bool, default None
              If allow_fill=True and fill_value is not None, indices specified by
              -1 is regarded as NA. If Index doesn't hold NA, raise ValueError.
  
          Returns
          -------
          numpy.ndarray
              Elements of given indices.
  
          See Also
          --------
          numpy.ndarray.take
          """
  
      @Appender(_index_shared_docs["take"] % _index_doc_kwargs)
      def take(self, indices, axis=0, allow_fill=True, fill_value=None, **kwargs):
          if kwargs:
              nv.validate_take(tuple(), kwargs)
          indices = ensure_platform_int(indices)
          if self._can_hold_na:
              taken = self._assert_take_fillable(
                  self.values,
                  indices,
                  allow_fill=allow_fill,
                  fill_value=fill_value,
                  na_value=self._na_value,
              )
          else:
              if allow_fill and fill_value is not None:
                  cls_name = type(self).__name__
                  raise ValueError(
                      f"Unable to fill values because {cls_name} cannot contain NA"
                  )
              taken = self.values.take(indices)
          return self._shallow_copy(taken)
  
      def _assert_take_fillable(
          self, values, indices, allow_fill=True, fill_value=None, na_value=np.nan
      ):
          """
          Internal method to handle NA filling of take.
          """
          indices = ensure_platform_int(indices)
  
          # only fill if we are passing a non-None fill_value
          if allow_fill and fill_value is not None:
              if (indices < -1).any():
                  raise ValueError(
                      "When allow_fill=True and fill_value is not None, "
                      "all indices must be >= -1"
                  )
              taken = algos.take(
                  values, indices, allow_fill=allow_fill, fill_value=na_value
              )
          else:
              taken = values.take(indices)
          return taken
  
      _index_shared_docs[
          "repeat"
      ] = """
          Repeat elements of a %(klass)s.
  
          Returns a new %(klass)s where each element of the current %(klass)s
          is repeated consecutively a given number of times.
  
          Parameters
          ----------
          repeats : int or array of ints
              The number of repetitions for each element. This should be a
              non-negative integer. Repeating 0 times will return an empty
              %(klass)s.
          axis : None
              Must be ``None``. Has no effect but is accepted for compatibility
              with numpy.
  
          Returns
          -------
          repeated_index : %(klass)s
              Newly created %(klass)s with repeated elements.
  
          See Also
          --------
          Series.repeat : Equivalent function for Series.
          numpy.repeat : Similar method for :class:`numpy.ndarray`.
  
          Examples
          --------
          >>> idx = pd.Index(['a', 'b', 'c'])
          >>> idx
          Index(['a', 'b', 'c'], dtype='object')
          >>> idx.repeat(2)
          Index(['a', 'a', 'b', 'b', 'c', 'c'], dtype='object')
          >>> idx.repeat([1, 2, 3])
          Index(['a', 'b', 'b', 'c', 'c', 'c'], dtype='object')
          """
  
      @Appender(_index_shared_docs["repeat"] % _index_doc_kwargs)
      def repeat(self, repeats, axis=None):
          repeats = ensure_platform_int(repeats)
          nv.validate_repeat(tuple(), dict(axis=axis))
          return self._shallow_copy(self._values.repeat(repeats))
  
      # --------------------------------------------------------------------
      # Copying Methods
  
      _index_shared_docs[
          "copy"
      ] = """
          Make a copy of this object.  Name and dtype sets those attributes on
          the new object.
  
          Parameters
          ----------
          name : str, optional
          deep : bool, default False
          dtype : numpy dtype or pandas type
  
          Returns
          -------
          copy : Index
  
          Notes
          -----
          In most cases, there should be no functional difference from using
          ``deep``, but if ``deep`` is passed it will attempt to deepcopy.
          """
  
      @Appender(_index_shared_docs["copy"])
      def copy(self, name=None, deep=False, dtype=None, **kwargs):
          if deep:
              new_index = self._shallow_copy(self._data.copy())
          else:
              new_index = self._shallow_copy()
  
          names = kwargs.get("names")
          names = self._validate_names(name=name, names=names, deep=deep)
          new_index = new_index.set_names(names)
  
          if dtype:
              new_index = new_index.astype(dtype)
          return new_index
  
      def __copy__(self, **kwargs):
          return self.copy(**kwargs)
  
      def __deepcopy__(self, memo=None):
          """
          Parameters
          ----------
          memo, default None
              Standard signature. Unused
          """
          return self.copy(deep=True)
  
      # --------------------------------------------------------------------
      # Rendering Methods
  
      def __repr__(self):
          """
          Return a string representation for this object.
          """
          klass_name = type(self).__name__
          data = self._format_data()
          attrs = self._format_attrs()
          space = self._format_space()
          attrs_str = [f"{k}={v}" for k, v in attrs]
          prepr = f",{space}".join(attrs_str)
  
          # no data provided, just attributes
          if data is None:
              data = ""
  
          res = f"{klass_name}({data}{prepr})"
  
          return res
  
      def _format_space(self):
  
          # using space here controls if the attributes
          # are line separated or not (the default)
  
          # max_seq_items = get_option('display.max_seq_items')
          # if len(self) > max_seq_items:
          #    space = "\n%s" % (' ' * (len(klass) + 1))
          return " "
  
      @property
      def _formatter_func(self):
          """
          Return the formatter function.
          """
          return default_pprint
  
      def _format_data(self, name=None):
          """
          Return the formatted data as a unicode string.
          """
  
          # do we want to justify (only do so for non-objects)
          is_justify = not (
              self.inferred_type in ("string", "unicode")
              or (
                  self.inferred_type == "categorical" and is_object_dtype(self.categories)
              )
          )
  
          return format_object_summary(
              self, self._formatter_func, is_justify=is_justify, name=name
          )
  
      def _format_attrs(self):
          """
          Return a list of tuples of the (attr,formatted_value).
          """
          return format_object_attrs(self)
  
      def _mpl_repr(self):
          # how to represent ourselves to matplotlib
          return self.values
  
      def format(self, name=False, formatter=None, **kwargs):
          """
          Render a string representation of the Index.
          """
          header = []
          if name:
              header.append(
                  pprint_thing(self.name, escape_chars=("\t", "\r", "\n"))
                  if self.name is not None
                  else ""
              )
  
          if formatter is not None:
              return header + list(self.map(formatter))
  
          return self._format_with_header(header, **kwargs)
  
      def _format_with_header(self, header, na_rep="NaN", **kwargs):
          values = self.values
  
          from pandas.io.formats.format import format_array
  
          if is_categorical_dtype(values.dtype):
              values = np.array(values)
  
          elif is_object_dtype(values.dtype):
              values = lib.maybe_convert_objects(values, safe=1)
  
          if is_object_dtype(values.dtype):
              result = [pprint_thing(x, escape_chars=("\t", "\r", "\n")) for x in values]
  
              # could have nans
              mask = isna(values)
              if mask.any():
                  result = np.array(result)
                  result[mask] = na_rep
                  result = result.tolist()
  
          else:
              result = _trim_front(format_array(values, None, justify="left"))
          return header + result
  
      def to_native_types(self, slicer=None, **kwargs):
          """
          Format specified values of `self` and return them.
  
          Parameters
          ----------
          slicer : int, array-like
              An indexer into `self` that specifies which values
              are used in the formatting process.
          kwargs : dict
              Options for specifying how the values should be formatted.
              These options include the following:
  
              1) na_rep : str
                  The value that serves as a placeholder for NULL values
              2) quoting : bool or None
                  Whether or not there are quoted values in `self`
              3) date_format : str
                  The format used to represent date-like values.
  
          Returns
          -------
          numpy.ndarray
              Formatted values.
          """
  
          values = self
          if slicer is not None:
              values = values[slicer]
          return values._format_native_types(**kwargs)
  
      def _format_native_types(self, na_rep="", quoting=None, **kwargs):
          """
          Actually format specific types of the index.
          """
          mask = isna(self)
          if not self.is_object() and not quoting:
              values = np.asarray(self).astype(str)
          else:
              values = np.array(self, dtype=object, copy=True)
  
          values[mask] = na_rep
          return values
  
      def _summary(self, name=None):
          """
          Return a summarized representation.
  
          Parameters
          ----------
          name : str
              name to use in the summary representation
  
          Returns
          -------
          String with a summarized representation of the index
          """
          if len(self) > 0:
              head = self[0]
              if hasattr(head, "format") and not isinstance(head, str):
                  head = head.format()
              tail = self[-1]
              if hasattr(tail, "format") and not isinstance(tail, str):
                  tail = tail.format()
              index_summary = f", {head} to {tail}"
          else:
              index_summary = ""
  
          if name is None:
              name = type(self).__name__
          return f"{name}: {len(self)} entries{index_summary}"
  
      # --------------------------------------------------------------------
      # Conversion Methods
  
      def to_flat_index(self):
          """
          Identity method.
  
          .. versionadded:: 0.24.0
  
          This is implemented for compatibility with subclass implementations
          when chaining.
  
          Returns
          -------
          pd.Index
              Caller.
  
          See Also
          --------
          MultiIndex.to_flat_index : Subclass implementation.
          """
          return self
  
      def to_series(self, index=None, name=None):
          """
          Create a Series with both index and values equal to the index keys.
  
          Useful with map for returning an indexer based on an index.
  
          Parameters
          ----------
          index : Index, optional
              Index of resulting Series. If None, defaults to original index.
          name : str, optional
              Dame of resulting Series. If None, defaults to name of original
              index.
  
          Returns
          -------
          Series
              The dtype will be based on the type of the Index values.
          """
  
          from pandas import Series
  
          if index is None:
              index = self._shallow_copy()
          if name is None:
              name = self.name
  
          return Series(self.values.copy(), index=index, name=name)
  
      def to_frame(self, index=True, name=None):
          """
          Create a DataFrame with a column containing the Index.
  
          .. versionadded:: 0.24.0
  
          Parameters
          ----------
          index : bool, default True
              Set the index of the returned DataFrame as the original Index.
  
          name : object, default None
              The passed name should substitute for the index name (if it has
              one).
  
          Returns
          -------
          DataFrame
              DataFrame containing the original Index data.
  
          See Also
          --------
          Index.to_series : Convert an Index to a Series.
          Series.to_frame : Convert Series to DataFrame.
  
          Examples
          --------
          >>> idx = pd.Index(['Ant', 'Bear', 'Cow'], name='animal')
          >>> idx.to_frame()
                 animal
          animal
          Ant       Ant
          Bear     Bear
          Cow       Cow
  
          By default, the original Index is reused. To enforce a new Index:
  
          >>> idx.to_frame(index=False)
              animal
          0   Ant
          1  Bear
          2   Cow
  
          To override the name of the resulting column, specify `name`:
  
          >>> idx.to_frame(index=False, name='zoo')
              zoo
          0   Ant
          1  Bear
          2   Cow
          """
  
          from pandas import DataFrame
  
          if name is None:
              name = self.name or 0
          result = DataFrame({name: self._values.copy()})
  
          if index:
              result.index = self
          return result
  
      # --------------------------------------------------------------------
      # Name-Centric Methods
  
      @property
      def name(self):
          return self._name
  
      @name.setter
      def name(self, value):
          if self._no_setting_name:
              # Used in MultiIndex.levels to avoid silently ignoring name updates.
              raise RuntimeError(
                  "Cannot set name on a level of a MultiIndex. Use "
                  "'MultiIndex.set_names' instead."
              )
          maybe_extract_name(value, None, type(self))
          self._name = value
  
      def _validate_names(self, name=None, names=None, deep=False):
          """
          Handles the quirks of having a singular 'name' parameter for general
          Index and plural 'names' parameter for MultiIndex.
          """
          from copy import deepcopy
  
          if names is not None and name is not None:
              raise TypeError("Can only provide one of `names` and `name`")
          elif names is None and name is None:
              return deepcopy(self.names) if deep else self.names
          elif names is not None:
              if not is_list_like(names):
                  raise TypeError("Must pass list-like as `names`.")
              return names
          else:
              if not is_list_like(name):
                  return [name]
              return name
  
      def _get_names(self):
          return FrozenList((self.name,))
  
      def _set_names(self, values, level=None):
          """
          Set new names on index. Each name has to be a hashable type.
  
          Parameters
          ----------
          values : str or sequence
              name(s) to set
          level : int, level name, or sequence of int/level names (default None)
              If the index is a MultiIndex (hierarchical), level(s) to set (None
              for all levels).  Otherwise level must be None
  
          Raises
          ------
          TypeError if each name is not hashable.
          """
          if not is_list_like(values):
              raise ValueError("Names must be a list-like")
          if len(values) != 1:
              raise ValueError(f"Length of new names must be 1, got {len(values)}")
  
          # GH 20527
          # All items in 'name' need to be hashable:
          for name in values:
              if not is_hashable(name):
                  raise TypeError(f"{type(self).__name__}.name must be a hashable type")
          self._name = values[0]
  
      names = property(fset=_set_names, fget=_get_names)
  
      def set_names(self, names, level=None, inplace=False):
          """
          Set Index or MultiIndex name.
  
          Able to set new names partially and by level.
  
          Parameters
          ----------
          names : label or list of label
              Name(s) to set.
          level : int, label or list of int or label, optional
              If the index is a MultiIndex, level(s) to set (None for all
              levels). Otherwise level must be None.
          inplace : bool, default False
              Modifies the object directly, instead of creating a new Index or
              MultiIndex.
  
          Returns
          -------
          Index
              The same type as the caller or None if inplace is True.
  
          See Also
          --------
          Index.rename : Able to set new names without level.
  
          Examples
          --------
          >>> idx = pd.Index([1, 2, 3, 4])
          >>> idx
          Int64Index([1, 2, 3, 4], dtype='int64')
          >>> idx.set_names('quarter')
          Int64Index([1, 2, 3, 4], dtype='int64', name='quarter')
  
          >>> idx = pd.MultiIndex.from_product([['python', 'cobra'],
          ...                                   [2018, 2019]])
          >>> idx
          MultiIndex([('python', 2018),
                      ('python', 2019),
                      ( 'cobra', 2018),
                      ( 'cobra', 2019)],
                     )
          >>> idx.set_names(['kind', 'year'], inplace=True)
          >>> idx
          MultiIndex([('python', 2018),
                      ('python', 2019),
                      ( 'cobra', 2018),
                      ( 'cobra', 2019)],
                     names=['kind', 'year'])
          >>> idx.set_names('species', level=0)
          MultiIndex([('python', 2018),
                      ('python', 2019),
                      ( 'cobra', 2018),
                      ( 'cobra', 2019)],
                     names=['species', 'year'])
          """
  
          if level is not None and not isinstance(self, ABCMultiIndex):
              raise ValueError("Level must be None for non-MultiIndex")
  
          if level is not None and not is_list_like(level) and is_list_like(names):
              raise TypeError("Names must be a string when a single level is provided.")
  
          if not is_list_like(names) and level is None and self.nlevels > 1:
              raise TypeError("Must pass list-like as `names`.")
  
          if not is_list_like(names):
              names = [names]
          if level is not None and not is_list_like(level):
              level = [level]
  
          if inplace:
              idx = self
          else:
              idx = self._shallow_copy()
          idx._set_names(names, level=level)
          if not inplace:
              return idx
  
      def rename(self, name, inplace=False):
          """
          Alter Index or MultiIndex name.
  
          Able to set new names without level. Defaults to returning new index.
          Length of names must match number of levels in MultiIndex.
  
          Parameters
          ----------
          name : label or list of labels
              Name(s) to set.
          inplace : bool, default False
              Modifies the object directly, instead of creating a new Index or
              MultiIndex.
  
          Returns
          -------
          Index
              The same type as the caller or None if inplace is True.
  
          See Also
          --------
          Index.set_names : Able to set new names partially and by level.
  
          Examples
          --------
          >>> idx = pd.Index(['A', 'C', 'A', 'B'], name='score')
          >>> idx.rename('grade')
          Index(['A', 'C', 'A', 'B'], dtype='object', name='grade')
  
          >>> idx = pd.MultiIndex.from_product([['python', 'cobra'],
          ...                                   [2018, 2019]],
          ...                                   names=['kind', 'year'])
          >>> idx
          MultiIndex([('python', 2018),
                      ('python', 2019),
                      ( 'cobra', 2018),
                      ( 'cobra', 2019)],
                     names=['kind', 'year'])
          >>> idx.rename(['species', 'year'])
          MultiIndex([('python', 2018),
                      ('python', 2019),
                      ( 'cobra', 2018),
                      ( 'cobra', 2019)],
                     names=['species', 'year'])
          >>> idx.rename('species')
          Traceback (most recent call last):
          TypeError: Must pass list-like as `names`.
          """
          return self.set_names([name], inplace=inplace)
  
      # --------------------------------------------------------------------
      # Level-Centric Methods
  
      @property
      def nlevels(self) -> int:
          """
          Number of levels.
          """
          return 1
  
      def _sort_levels_monotonic(self):
          """
          Compat with MultiIndex.
          """
          return self
  
      def _validate_index_level(self, level):
          """
          Validate index level.
  
          For single-level Index getting level number is a no-op, but some
          verification must be done like in MultiIndex.
  
          """
          if isinstance(level, int):
              if level < 0 and level != -1:
                  raise IndexError(
                      "Too many levels: Index has only 1 level, "
                      f"{level} is not a valid level number"
                  )
              elif level > 0:
                  raise IndexError(
                      f"Too many levels: Index has only 1 level, not {level + 1}"
                  )
          elif level != self.name:
              raise KeyError(
                  f"Requested level ({level}) does not match index name ({self.name})"
              )
  
      def _get_level_number(self, level):
          self._validate_index_level(level)
          return 0
  
      def sortlevel(self, level=None, ascending=True, sort_remaining=None):
          """
          For internal compatibility with with the Index API.
  
          Sort the Index. This is for compat with MultiIndex
  
          Parameters
          ----------
          ascending : bool, default True
              False to sort in descending order
  
          level, sort_remaining are compat parameters
  
          Returns
          -------
          Index
          """
          return self.sort_values(return_indexer=True, ascending=ascending)
  
      def _get_level_values(self, level):
          """
          Return an Index of values for requested level.
  
          This is primarily useful to get an individual level of values from a
          MultiIndex, but is provided on Index as well for compatibility.
  
          Parameters
          ----------
          level : int or str
              It is either the integer position or the name of the level.
  
          Returns
          -------
          Index
              Calling object, as there is only one level in the Index.
  
          See Also
          --------
          MultiIndex.get_level_values : Get values for a level of a MultiIndex.
  
          Notes
          -----
          For Index, level should be 0, since there are no multiple levels.
  
          Examples
          --------
  
          >>> idx = pd.Index(list('abc'))
          >>> idx
          Index(['a', 'b', 'c'], dtype='object')
  
          Get level values by supplying `level` as integer:
  
          >>> idx.get_level_values(0)
          Index(['a', 'b', 'c'], dtype='object')
          """
          self._validate_index_level(level)
          return self
  
      get_level_values = _get_level_values
  
      def droplevel(self, level=0):
          """
          Return index with requested level(s) removed.
  
          If resulting index has only 1 level left, the result will be
          of Index type, not MultiIndex.
  
          .. versionadded:: 0.23.1 (support for non-MultiIndex)
  
          Parameters
          ----------
          level : int, str, or list-like, default 0
              If a string is given, must be the name of a level
              If list-like, elements must be names or indexes of levels.
  
          Returns
          -------
          Index or MultiIndex
          """
          if not isinstance(level, (tuple, list)):
              level = [level]
  
          levnums = sorted(self._get_level_number(lev) for lev in level)[::-1]
  
          if len(level) == 0:
              return self
          if len(level) >= self.nlevels:
              raise ValueError(
                  f"Cannot remove {len(level)} levels from an index with {self.nlevels} "
                  "levels: at least one level must be left."
              )
          # The two checks above guarantee that here self is a MultiIndex
  
          new_levels = list(self.levels)
          new_codes = list(self.codes)
          new_names = list(self.names)
  
          for i in levnums:
              new_levels.pop(i)
              new_codes.pop(i)
              new_names.pop(i)
  
          if len(new_levels) == 1:
  
              # set nan if needed
              mask = new_codes[0] == -1
              result = new_levels[0].take(new_codes[0])
              if mask.any():
                  result = result.putmask(mask, np.nan)
  
              result._name = new_names[0]
              return result
          else:
              from .multi import MultiIndex
  
              return MultiIndex(
                  levels=new_levels,
                  codes=new_codes,
                  names=new_names,
                  verify_integrity=False,
              )
  
      _index_shared_docs[
          "_get_grouper_for_level"
      ] = """
          Get index grouper corresponding to an index level
  
          Parameters
          ----------
          mapper: Group mapping function or None
              Function mapping index values to groups
          level : int or None
              Index level
  
          Returns
          -------
          grouper : Index
              Index of values to group on.
          labels : ndarray of int or None
              Array of locations in level_index.
          uniques : Index or None
              Index of unique values for level.
          """
  
      @Appender(_index_shared_docs["_get_grouper_for_level"])
      def _get_grouper_for_level(self, mapper, level=None):
          assert level is None or level == 0
          if mapper is None:
              grouper = self
          else:
              grouper = self.map(mapper)
  
          return grouper, None, None
  
      # --------------------------------------------------------------------
      # Introspection Methods
  
      @property
      def is_monotonic(self) -> bool:
          """
          Alias for is_monotonic_increasing.
          """
          return self.is_monotonic_increasing
  
      @property
      def is_monotonic_increasing(self):
          """
          Return if the index is monotonic increasing (only equal or
          increasing) values.
  
          Examples
          --------
          >>> Index([1, 2, 3]).is_monotonic_increasing
          True
          >>> Index([1, 2, 2]).is_monotonic_increasing
          True
          >>> Index([1, 3, 2]).is_monotonic_increasing
          False
          """
          return self._engine.is_monotonic_increasing
  
      @property
      def is_monotonic_decreasing(self) -> bool:
          """
          Return if the index is monotonic decreasing (only equal or
          decreasing) values.
  
          Examples
          --------
          >>> Index([3, 2, 1]).is_monotonic_decreasing
          True
          >>> Index([3, 2, 2]).is_monotonic_decreasing
          True
          >>> Index([3, 1, 2]).is_monotonic_decreasing
          False
          """
          return self._engine.is_monotonic_decreasing
  
      @property
      def _is_strictly_monotonic_increasing(self) -> bool:
          """
          Return if the index is strictly monotonic increasing
          (only increasing) values.
  
          Examples
          --------
          >>> Index([1, 2, 3])._is_strictly_monotonic_increasing
          True
          >>> Index([1, 2, 2])._is_strictly_monotonic_increasing
          False
          >>> Index([1, 3, 2])._is_strictly_monotonic_increasing
          False
          """
          return self.is_unique and self.is_monotonic_increasing
  
      @property
      def _is_strictly_monotonic_decreasing(self) -> bool:
          """
          Return if the index is strictly monotonic decreasing
          (only decreasing) values.
  
          Examples
          --------
          >>> Index([3, 2, 1])._is_strictly_monotonic_decreasing
          True
          >>> Index([3, 2, 2])._is_strictly_monotonic_decreasing
          False
          >>> Index([3, 1, 2])._is_strictly_monotonic_decreasing
          False
          """
          return self.is_unique and self.is_monotonic_decreasing
  
      @cache_readonly
      def is_unique(self) -> bool:
          """
          Return if the index has unique values.
          """
          return self._engine.is_unique
  
      @property
      def has_duplicates(self) -> bool:
          return not self.is_unique
  
      def is_boolean(self) -> bool:
          return self.inferred_type in ["boolean"]
  
      def is_integer(self) -> bool:
          return self.inferred_type in ["integer"]
  
      def is_floating(self) -> bool:
          return self.inferred_type in ["floating", "mixed-integer-float", "integer-na"]
  
      def is_numeric(self) -> bool:
          return self.inferred_type in ["integer", "floating"]
  
      def is_object(self) -> bool:
          return is_object_dtype(self.dtype)
  
      def is_categorical(self) -> bool:
          """
          Check if the Index holds categorical data.
  
          Returns
          -------
          boolean
              True if the Index is categorical.
  
          See Also
          --------
          CategoricalIndex : Index for categorical data.
  
          Examples
          --------
          >>> idx = pd.Index(["Watermelon", "Orange", "Apple",
          ...                 "Watermelon"]).astype("category")
          >>> idx.is_categorical()
          True
  
          >>> idx = pd.Index([1, 3, 5, 7])
          >>> idx.is_categorical()
          False
  
          >>> s = pd.Series(["Peter", "Victor", "Elisabeth", "Mar"])
          >>> s
          0        Peter
          1       Victor
          2    Elisabeth
          3          Mar
          dtype: object
          >>> s.index.is_categorical()
          False
          """
          return self.inferred_type in ["categorical"]
  
      def is_interval(self) -> bool:
          return self.inferred_type in ["interval"]
  
      def is_mixed(self) -> bool:
          return self.inferred_type in ["mixed"]
  
      def holds_integer(self):
          """
          Whether the type is an integer type.
          """
          return self.inferred_type in ["integer", "mixed-integer"]
  
      @cache_readonly
      def inferred_type(self):
          """
          Return a string of the type inferred from the values.
          """
          return lib.infer_dtype(self, skipna=False)
  
      @cache_readonly
      def is_all_dates(self) -> bool:
          return is_datetime_array(ensure_object(self.values))
  
      # --------------------------------------------------------------------
      # Pickle Methods
  
      def __reduce__(self):
          d = dict(data=self._data)
          d.update(self._get_attributes_dict())
          return _new_Index, (type(self), d), None
  
      def __setstate__(self, state):
          """
          Necessary for making this object picklable.
          """
  
          if isinstance(state, dict):
              self._data = state.pop("data")
              for k, v in state.items():
                  setattr(self, k, v)
  
          elif isinstance(state, tuple):
  
              if len(state) == 2:
                  nd_state, own_state = state
                  data = np.empty(nd_state[1], dtype=nd_state[2])
                  np.ndarray.__setstate__(data, nd_state)
                  self._name = own_state[0]
  
              else:  # pragma: no cover
                  data = np.empty(state)
                  np.ndarray.__setstate__(data, state)
  
              self._data = data
              self._reset_identity()
          else:
              raise Exception("invalid pickle state")
  
      _unpickle_compat = __setstate__
  
      # --------------------------------------------------------------------
      # Null Handling Methods
  
      _na_value = np.nan
      """The expected NA value to use with this index."""
  
      @cache_readonly
      def _isnan(self):
          """
          Return if each value is NaN.
          """
          if self._can_hold_na:
              return isna(self)
          else:
              # shouldn't reach to this condition by checking hasnans beforehand
              values = np.empty(len(self), dtype=np.bool_)
              values.fill(False)
              return values
  
      @cache_readonly
      def _nan_idxs(self):
          if self._can_hold_na:
              return self._isnan.nonzero()[0]
          else:
              return np.array([], dtype=np.int64)
  
      @cache_readonly
      def hasnans(self):
          """
          Return if I have any nans; enables various perf speedups.
          """
          if self._can_hold_na:
              return bool(self._isnan.any())
          else:
              return False
  
      def isna(self):
          """
          Detect missing values.
  
          Return a boolean same-sized object indicating if the values are NA.
          NA values, such as ``None``, :attr:`numpy.NaN` or :attr:`pd.NaT`, get
          mapped to ``True`` values.
          Everything else get mapped to ``False`` values. Characters such as
          empty strings `''` or :attr:`numpy.inf` are not considered NA values
          (unless you set ``pandas.options.mode.use_inf_as_na = True``).
  
          Returns
          -------
          numpy.ndarray
              A boolean array of whether my values are NA.
  
          See Also
          --------
          Index.notna : Boolean inverse of isna.
          Index.dropna : Omit entries with missing values.
          isna : Top-level isna.
          Series.isna : Detect missing values in Series object.
  
          Examples
          --------
          Show which entries in a pandas.Index are NA. The result is an
          array.
  
          >>> idx = pd.Index([5.2, 6.0, np.NaN])
          >>> idx
          Float64Index([5.2, 6.0, nan], dtype='float64')
          >>> idx.isna()
          array([False, False,  True], dtype=bool)
  
          Empty strings are not considered NA values. None is considered an NA
          value.
  
          >>> idx = pd.Index(['black', '', 'red', None])
          >>> idx
          Index(['black', '', 'red', None], dtype='object')
          >>> idx.isna()
          array([False, False, False,  True], dtype=bool)
  
          For datetimes, `NaT` (Not a Time) is considered as an NA value.
  
          >>> idx = pd.DatetimeIndex([pd.Timestamp('1940-04-25'),
          ...                         pd.Timestamp(''), None, pd.NaT])
          >>> idx
          DatetimeIndex(['1940-04-25', 'NaT', 'NaT', 'NaT'],
                        dtype='datetime64[ns]', freq=None)
          >>> idx.isna()
          array([False,  True,  True,  True], dtype=bool)
          """
          return self._isnan
  
      isnull = isna
  
      def notna(self):
          """
          Detect existing (non-missing) values.
  
          Return a boolean same-sized object indicating if the values are not NA.
          Non-missing values get mapped to ``True``. Characters such as empty
          strings ``''`` or :attr:`numpy.inf` are not considered NA values
          (unless you set ``pandas.options.mode.use_inf_as_na = True``).
          NA values, such as None or :attr:`numpy.NaN`, get mapped to ``False``
          values.
  
          Returns
          -------
          numpy.ndarray
              Boolean array to indicate which entries are not NA.
  
          See Also
          --------
          Index.notnull : Alias of notna.
          Index.isna: Inverse of notna.
          notna : Top-level notna.
  
          Examples
          --------
          Show which entries in an Index are not NA. The result is an
          array.
  
          >>> idx = pd.Index([5.2, 6.0, np.NaN])
          >>> idx
          Float64Index([5.2, 6.0, nan], dtype='float64')
          >>> idx.notna()
          array([ True,  True, False])
  
          Empty strings are not considered NA values. None is considered a NA
          value.
  
          >>> idx = pd.Index(['black', '', 'red', None])
          >>> idx
          Index(['black', '', 'red', None], dtype='object')
          >>> idx.notna()
          array([ True,  True,  True, False])
          """
          return ~self.isna()
  
      notnull = notna
  
      _index_shared_docs[
          "fillna"
      ] = """
          Fill NA/NaN values with the specified value.
  
          Parameters
          ----------
          value : scalar
              Scalar value to use to fill holes (e.g. 0).
              This value cannot be a list-likes.
          downcast : dict, default is None
              a dict of item->dtype of what to downcast if possible,
              or the string 'infer' which will try to downcast to an appropriate
              equal type (e.g. float64 to int64 if possible).
  
          Returns
          -------
          filled : Index
          """
  
      @Appender(_index_shared_docs["fillna"])
      def fillna(self, value=None, downcast=None):
          self._assert_can_do_op(value)
          if self.hasnans:
              result = self.putmask(self._isnan, value)
              if downcast is None:
                  # no need to care metadata other than name
                  # because it can't have freq if
                  return Index(result, name=self.name)
          return self._shallow_copy()
  
      _index_shared_docs[
          "dropna"
      ] = """
          Return Index without NA/NaN values.
  
          Parameters
          ----------
          how : {'any', 'all'}, default 'any'
              If the Index is a MultiIndex, drop the value when any or all levels
              are NaN.
  
          Returns
          -------
          valid : Index
          """
  
      @Appender(_index_shared_docs["dropna"])
      def dropna(self, how="any"):
          if how not in ("any", "all"):
              raise ValueError(f"invalid how option: {how}")
  
          if self.hasnans:
              return self._shallow_copy(self.values[~self._isnan])
          return self._shallow_copy()
  
      # --------------------------------------------------------------------
      # Uniqueness Methods
  
      _index_shared_docs[
          "index_unique"
      ] = """
          Return unique values in the index. Uniques are returned in order
          of appearance, this does NOT sort.
  
          Parameters
          ----------
          level : int or str, optional, default None
              Only return values from specified level (for MultiIndex).
  
              .. versionadded:: 0.23.0
  
          Returns
          -------
          Index without duplicates
  
          See Also
          --------
          unique
          Series.unique
          """
  
      @Appender(_index_shared_docs["index_unique"] % _index_doc_kwargs)
      def unique(self, level=None):
          if level is not None:
              self._validate_index_level(level)
          result = super().unique()
          return self._shallow_copy(result)
  
      def drop_duplicates(self, keep="first"):
          """
          Return Index with duplicate values removed.
  
          Parameters
          ----------
          keep : {'first', 'last', ``False``}, default 'first'
              - 'first' : Drop duplicates except for the first occurrence.
              - 'last' : Drop duplicates except for the last occurrence.
              - ``False`` : Drop all duplicates.
  
          Returns
          -------
          deduplicated : Index
  
          See Also
          --------
          Series.drop_duplicates : Equivalent method on Series.
          DataFrame.drop_duplicates : Equivalent method on DataFrame.
          Index.duplicated : Related method on Index, indicating duplicate
              Index values.
  
          Examples
          --------
          Generate an pandas.Index with duplicate values.
  
          >>> idx = pd.Index(['lama', 'cow', 'lama', 'beetle', 'lama', 'hippo'])
  
          The `keep` parameter controls  which duplicate values are removed.
          The value 'first' keeps the first occurrence for each
          set of duplicated entries. The default value of keep is 'first'.
  
          >>> idx.drop_duplicates(keep='first')
          Index(['lama', 'cow', 'beetle', 'hippo'], dtype='object')
  
          The value 'last' keeps the last occurrence for each set of duplicated
          entries.
  
          >>> idx.drop_duplicates(keep='last')
          Index(['cow', 'beetle', 'lama', 'hippo'], dtype='object')
  
          The value ``False`` discards all sets of duplicated entries.
  
          >>> idx.drop_duplicates(keep=False)
          Index(['cow', 'beetle', 'hippo'], dtype='object')
          """
          return super().drop_duplicates(keep=keep)
  
      def duplicated(self, keep="first"):
          """
          Indicate duplicate index values.
  
          Duplicated values are indicated as ``True`` values in the resulting
          array. Either all duplicates, all except the first, or all except the
          last occurrence of duplicates can be indicated.
  
          Parameters
          ----------
          keep : {'first', 'last', False}, default 'first'
              The value or values in a set of duplicates to mark as missing.
  
              - 'first' : Mark duplicates as ``True`` except for the first
                occurrence.
              - 'last' : Mark duplicates as ``True`` except for the last
                occurrence.
              - ``False`` : Mark all duplicates as ``True``.
  
          Returns
          -------
          numpy.ndarray
  
          See Also
          --------
          Series.duplicated : Equivalent method on pandas.Series.
          DataFrame.duplicated : Equivalent method on pandas.DataFrame.
          Index.drop_duplicates : Remove duplicate values from Index.
  
          Examples
          --------
          By default, for each set of duplicated values, the first occurrence is
          set to False and all others to True:
  
          >>> idx = pd.Index(['lama', 'cow', 'lama', 'beetle', 'lama'])
          >>> idx.duplicated()
          array([False, False,  True, False,  True])
  
          which is equivalent to
  
          >>> idx.duplicated(keep='first')
          array([False, False,  True, False,  True])
  
          By using 'last', the last occurrence of each set of duplicated values
          is set on False and all others on True:
  
          >>> idx.duplicated(keep='last')
          array([ True, False,  True, False, False])
  
          By setting keep on ``False``, all duplicates are True:
  
          >>> idx.duplicated(keep=False)
          array([ True, False,  True, False,  True])
          """
          return super().duplicated(keep=keep)
  
      def _get_unique_index(self, dropna=False):
          """
          Returns an index containing unique values.
  
          Parameters
          ----------
          dropna : bool
              If True, NaN values are dropped.
  
          Returns
          -------
          uniques : index
          """
          if self.is_unique and not dropna:
              return self
  
          values = self.values
  
          if not self.is_unique:
              values = self.unique()
  
          if dropna:
              try:
                  if self.hasnans:
                      values = values[~isna(values)]
              except NotImplementedError:
                  pass
  
          return self._shallow_copy(values)
  
      # --------------------------------------------------------------------
      # Arithmetic & Logical Methods
  
      def __add__(self, other):
          if isinstance(other, (ABCSeries, ABCDataFrame)):
              return NotImplemented
          from pandas import Series
  
          return Index(Series(self) + other)
  
      def __radd__(self, other):
          from pandas import Series
  
          return Index(other + Series(self))
  
      def __iadd__(self, other):
          # alias for __add__
          return self + other
  
      def __sub__(self, other):
          return Index(np.array(self) - other)
  
      def __rsub__(self, other):
          # wrap Series to ensure we pin name correctly
          from pandas import Series
  
          return Index(other - Series(self))
  
      def __and__(self, other):
          return self.intersection(other)
  
      def __or__(self, other):
          return self.union(other)
  
      def __xor__(self, other):
          return self.symmetric_difference(other)
  
      def __nonzero__(self):
          raise ValueError(
              f"The truth value of a {type(self).__name__} is ambiguous. "
              "Use a.empty, a.bool(), a.item(), a.any() or a.all()."
          )
  
      __bool__ = __nonzero__
  
      # --------------------------------------------------------------------
      # Set Operation Methods
  
      def _get_reconciled_name_object(self, other):
          """
          If the result of a set operation will be self,
          return self, unless the name changes, in which
          case make a shallow copy of self.
          """
          name = get_op_result_name(self, other)
          if self.name != name:
              return self._shallow_copy(name=name)
          return self
  
      def _union_incompatible_dtypes(self, other, sort):
          """
          Casts this and other index to object dtype to allow the formation
          of a union between incompatible types.
  
          Parameters
          ----------
          other : Index or array-like
          sort : False or None, default False
              Whether to sort the resulting index.
  
              * False : do not sort the result.
              * None : sort the result, except when `self` and `other` are equal
                or when the values cannot be compared.
  
          Returns
          -------
          Index
          """
          this = self.astype(object, copy=False)
          # cast to Index for when `other` is list-like
          other = Index(other).astype(object, copy=False)
          return Index.union(this, other, sort=sort).astype(object, copy=False)
  
      def _is_compatible_with_other(self, other):
          """
          Check whether this and the other dtype are compatible with each other.
          Meaning a union can be formed between them without needing to be cast
          to dtype object.
  
          Parameters
          ----------
          other : Index or array-like
  
          Returns
          -------
          bool
          """
          return type(self) is type(other) and is_dtype_equal(self.dtype, other.dtype)
  
      def _validate_sort_keyword(self, sort):
          if sort not in [None, False]:
              raise ValueError(
                  "The 'sort' keyword only takes the values of "
                  f"None or False; {sort} was passed."
              )
  
      def union(self, other, sort=None):
          """
          Form the union of two Index objects.
  
          If the Index objects are incompatible, both Index objects will be
          cast to dtype('object') first.
  
              .. versionchanged:: 0.25.0
  
          Parameters
          ----------
          other : Index or array-like
          sort : bool or None, default None
              Whether to sort the resulting Index.
  
              * None : Sort the result, except when
  
                1. `self` and `other` are equal.
                2. `self` or `other` has length 0.
                3. Some values in `self` or `other` cannot be compared.
                   A RuntimeWarning is issued in this case.
  
              * False : do not sort the result.
  
              .. versionadded:: 0.24.0
  
              .. versionchanged:: 0.24.1
  
                 Changed the default value from ``True`` to ``None``
                 (without change in behaviour).
  
          Returns
          -------
          union : Index
  
          Examples
          --------
  
          Union matching dtypes
  
          >>> idx1 = pd.Index([1, 2, 3, 4])
          >>> idx2 = pd.Index([3, 4, 5, 6])
          >>> idx1.union(idx2)
          Int64Index([1, 2, 3, 4, 5, 6], dtype='int64')
  
          Union mismatched dtypes
  
          >>> idx1 = pd.Index(['a', 'b', 'c', 'd'])
          >>> idx2 = pd.Index([1, 2, 3, 4])
          >>> idx1.union(idx2)
          Index(['a', 'b', 'c', 'd', 1, 2, 3, 4], dtype='object')
          """
          self._validate_sort_keyword(sort)
          self._assert_can_do_setop(other)
  
          if not self._is_compatible_with_other(other):
              return self._union_incompatible_dtypes(other, sort=sort)
  
          return self._union(other, sort=sort)
  
      def _union(self, other, sort):
          """
          Specific union logic should go here. In subclasses, union behavior
          should be overwritten here rather than in `self.union`.
  
          Parameters
          ----------
          other : Index or array-like
          sort : False or None, default False
              Whether to sort the resulting index.
  
              * False : do not sort the result.
              * None : sort the result, except when `self` and `other` are equal
                or when the values cannot be compared.
  
          Returns
          -------
          Index
          """
  
          if not len(other) or self.equals(other):
              return self._get_reconciled_name_object(other)
  
          if not len(self):
              return other._get_reconciled_name_object(self)
  
          # TODO(EA): setops-refactor, clean all this up
          if is_period_dtype(self) or is_datetime64tz_dtype(self):
              lvals = self._ndarray_values
          else:
              lvals = self._values
          if is_period_dtype(other) or is_datetime64tz_dtype(other):
              rvals = other._ndarray_values
          else:
              rvals = other._values
  
          if sort is None and self.is_monotonic and other.is_monotonic:
              try:
                  result = self._outer_indexer(lvals, rvals)[0]
              except TypeError:
                  # incomparable objects
                  result = list(lvals)
  
                  # worth making this faster? a very unusual case
                  value_set = set(lvals)
                  result.extend([x for x in rvals if x not in value_set])
          else:
              # find indexes of things in "other" that are not in "self"
              if self.is_unique:
                  indexer = self.get_indexer(other)
                  indexer = (indexer == -1).nonzero()[0]
              else:
                  indexer = algos.unique1d(self.get_indexer_non_unique(other)[1])
  
              if len(indexer) > 0:
                  other_diff = algos.take_nd(rvals, indexer, allow_fill=False)
                  result = concat_compat((lvals, other_diff))
  
              else:
                  result = lvals
  
              if sort is None:
                  try:
                      result = algos.safe_sort(result)
                  except TypeError as err:
                      warnings.warn(
                          f"{err}, sort order is undefined for incomparable objects",
                          RuntimeWarning,
                          stacklevel=3,
                      )
  
          # for subclasses
          return self._wrap_setop_result(other, result)
  
      def _wrap_setop_result(self, other, result):
          return self._constructor(result, name=get_op_result_name(self, other))
  
      _index_shared_docs[
          "intersection"
      ] = """
          Form the intersection of two Index objects.
  
          This returns a new Index with elements common to the index and `other`.
  
          Parameters
          ----------
          other : Index or array-like
          sort : False or None, default False
              Whether to sort the resulting index.
  
              * False : do not sort the result.
              * None : sort the result, except when `self` and `other` are equal
                or when the values cannot be compared.
  
              .. versionadded:: 0.24.0
  
              .. versionchanged:: 0.24.1
  
                 Changed the default from ``True`` to ``False``, to match
                 the behaviour of 0.23.4 and earlier.
  
          Returns
          -------
          intersection : Index
  
          Examples
          --------
  
          >>> idx1 = pd.Index([1, 2, 3, 4])
          >>> idx2 = pd.Index([3, 4, 5, 6])
          >>> idx1.intersection(idx2)
          Int64Index([3, 4], dtype='int64')
          """
  
      # TODO: standardize return type of non-union setops type(self vs other)
      @Appender(_index_shared_docs["intersection"])
      def intersection(self, other, sort=False):
          self._validate_sort_keyword(sort)
          self._assert_can_do_setop(other)
          other = ensure_index(other)
  
          if self.equals(other):
              return self._get_reconciled_name_object(other)
  
          if not is_dtype_equal(self.dtype, other.dtype):
              this = self.astype("O")
              other = other.astype("O")
              return this.intersection(other, sort=sort)
  
          # TODO(EA): setops-refactor, clean all this up
          lvals = self._values
          rvals = other._values
  
          if self.is_monotonic and other.is_monotonic:
              try:
                  result = self._inner_indexer(lvals, rvals)[0]
                  return self._wrap_setop_result(other, result)
              except TypeError:
                  pass
  
          try:
              indexer = Index(rvals).get_indexer(lvals)
              indexer = indexer.take((indexer != -1).nonzero()[0])
          except (InvalidIndexError, IncompatibleFrequency):
              # InvalidIndexError raised by get_indexer if non-unique
              # IncompatibleFrequency raised by PeriodIndex.get_indexer
              indexer = algos.unique1d(Index(rvals).get_indexer_non_unique(lvals)[0])
              indexer = indexer[indexer != -1]
  
          taken = other.take(indexer)
          res_name = get_op_result_name(self, other)
  
          if sort is None:
              taken = algos.safe_sort(taken.values)
              return self._shallow_copy(taken, name=res_name)
  
          taken.name = res_name
          return taken
  
      def difference(self, other, sort=None):
          """
          Return a new Index with elements from the index that are not in
          `other`.
  
          This is the set difference of two Index objects.
  
          Parameters
          ----------
          other : Index or array-like
          sort : False or None, default None
              Whether to sort the resulting index. By default, the
              values are attempted to be sorted, but any TypeError from
              incomparable elements is caught by pandas.
  
              * None : Attempt to sort the result, but catch any TypeErrors
                from comparing incomparable elements.
              * False : Do not sort the result.
  
              .. versionadded:: 0.24.0
  
              .. versionchanged:: 0.24.1
  
                 Changed the default value from ``True`` to ``None``
                 (without change in behaviour).
  
          Returns
          -------
          difference : Index
  
          Examples
          --------
  
          >>> idx1 = pd.Index([2, 1, 3, 4])
          >>> idx2 = pd.Index([3, 4, 5, 6])
          >>> idx1.difference(idx2)
          Int64Index([1, 2], dtype='int64')
          >>> idx1.difference(idx2, sort=False)
          Int64Index([2, 1], dtype='int64')
          """
          self._validate_sort_keyword(sort)
          self._assert_can_do_setop(other)
  
          if self.equals(other):
              # pass an empty np.ndarray with the appropriate dtype
              return self._shallow_copy(self._data[:0])
  
          other, result_name = self._convert_can_do_setop(other)
  
          this = self._get_unique_index()
  
          indexer = this.get_indexer(other)
          indexer = indexer.take((indexer != -1).nonzero()[0])
  
          label_diff = np.setdiff1d(np.arange(this.size), indexer, assume_unique=True)
          the_diff = this.values.take(label_diff)
          if sort is None:
              try:
                  the_diff = algos.safe_sort(the_diff)
              except TypeError:
                  pass
  
          return this._shallow_copy(the_diff, name=result_name)
  
      def symmetric_difference(self, other, result_name=None, sort=None):
          """
          Compute the symmetric difference of two Index objects.
  
          Parameters
          ----------
          other : Index or array-like
          result_name : str
          sort : False or None, default None
              Whether to sort the resulting index. By default, the
              values are attempted to be sorted, but any TypeError from
              incomparable elements is caught by pandas.
  
              * None : Attempt to sort the result, but catch any TypeErrors
                from comparing incomparable elements.
              * False : Do not sort the result.
  
              .. versionadded:: 0.24.0
  
              .. versionchanged:: 0.24.1
  
                 Changed the default value from ``True`` to ``None``
                 (without change in behaviour).
  
          Returns
          -------
          symmetric_difference : Index
  
          Notes
          -----
          ``symmetric_difference`` contains elements that appear in either
          ``idx1`` or ``idx2`` but not both. Equivalent to the Index created by
          ``idx1.difference(idx2) | idx2.difference(idx1)`` with duplicates
          dropped.
  
          Examples
          --------
          >>> idx1 = pd.Index([1, 2, 3, 4])
          >>> idx2 = pd.Index([2, 3, 4, 5])
          >>> idx1.symmetric_difference(idx2)
          Int64Index([1, 5], dtype='int64')
  
          You can also use the ``^`` operator:
  
          >>> idx1 ^ idx2
          Int64Index([1, 5], dtype='int64')
          """
          self._validate_sort_keyword(sort)
          self._assert_can_do_setop(other)
          other, result_name_update = self._convert_can_do_setop(other)
          if result_name is None:
              result_name = result_name_update
  
          this = self._get_unique_index()
          other = other._get_unique_index()
          indexer = this.get_indexer(other)
  
          # {this} minus {other}
          common_indexer = indexer.take((indexer != -1).nonzero()[0])
          left_indexer = np.setdiff1d(
              np.arange(this.size), common_indexer, assume_unique=True
          )
          left_diff = this.values.take(left_indexer)
  
          # {other} minus {this}
          right_indexer = (indexer == -1).nonzero()[0]
          right_diff = other.values.take(right_indexer)
  
          the_diff = concat_compat([left_diff, right_diff])
          if sort is None:
              try:
                  the_diff = algos.safe_sort(the_diff)
              except TypeError:
                  pass
  
          attribs = self._get_attributes_dict()
          attribs["name"] = result_name
          if "freq" in attribs:
              attribs["freq"] = None
          return self._shallow_copy_with_infer(the_diff, **attribs)
  
      def _assert_can_do_setop(self, other):
          if not is_list_like(other):
              raise TypeError("Input must be Index or array-like")
          return True
  
      def _convert_can_do_setop(self, other):
          if not isinstance(other, Index):
              other = Index(other, name=self.name)
              result_name = self.name
          else:
              result_name = get_op_result_name(self, other)
          return other, result_name
  
      # --------------------------------------------------------------------
      # Indexing Methods
  
      _index_shared_docs[
          "get_loc"
      ] = """
          Get integer location, slice or boolean mask for requested label.
  
          Parameters
          ----------
          key : label
          method : {None, 'pad'/'ffill', 'backfill'/'bfill', 'nearest'}, optional
              * default: exact matches only.
              * pad / ffill: find the PREVIOUS index value if no exact match.
              * backfill / bfill: use NEXT index value if no exact match
              * nearest: use the NEAREST index value if no exact match. Tied
                distances are broken by preferring the larger index value.
          tolerance : int or float, optional
              Maximum distance from index value for inexact matches. The value of
              the index at the matching location most satisfy the equation
              ``abs(index[loc] - key) <= tolerance``.
  
              .. versionadded:: 0.21.0 (list-like tolerance)
  
          Returns
          -------
          loc : int if unique index, slice if monotonic index, else mask
  
          Examples
          --------
          >>> unique_index = pd.Index(list('abc'))
          >>> unique_index.get_loc('b')
          1
  
          >>> monotonic_index = pd.Index(list('abbc'))
          >>> monotonic_index.get_loc('b')
          slice(1, 3, None)
  
          >>> non_monotonic_index = pd.Index(list('abcb'))
          >>> non_monotonic_index.get_loc('b')
          array([False,  True, False,  True], dtype=bool)
          """
  
      @Appender(_index_shared_docs["get_loc"])
      def get_loc(self, key, method=None, tolerance=None):
          if method is None:
              if tolerance is not None:
                  raise ValueError(
                      "tolerance argument only valid if using pad, "
                      "backfill or nearest lookups"
                  )
              try:
                  return self._engine.get_loc(key)
              except KeyError:
                  return self._engine.get_loc(self._maybe_cast_indexer(key))
          indexer = self.get_indexer([key], method=method, tolerance=tolerance)
          if indexer.ndim > 1 or indexer.size > 1:
              raise TypeError("get_loc requires scalar valued input")
          loc = indexer.item()
          if loc == -1:
              raise KeyError(key)
          return loc
  
      _index_shared_docs[
          "get_indexer"
      ] = """
          Compute indexer and mask for new index given the current index. The
          indexer should be then used as an input to ndarray.take to align the
          current data to the new index.
  
          Parameters
          ----------
          target : %(target_klass)s
          method : {None, 'pad'/'ffill', 'backfill'/'bfill', 'nearest'}, optional
              * default: exact matches only.
              * pad / ffill: find the PREVIOUS index value if no exact match.
              * backfill / bfill: use NEXT index value if no exact match
              * nearest: use the NEAREST index value if no exact match. Tied
                distances are broken by preferring the larger index value.
          limit : int, optional
              Maximum number of consecutive labels in ``target`` to match for
              inexact matches.
          tolerance : optional
              Maximum distance between original and new labels for inexact
              matches. The values of the index at the matching locations most
              satisfy the equation ``abs(index[indexer] - target) <= tolerance``.
  
              Tolerance may be a scalar value, which applies the same tolerance
              to all values, or list-like, which applies variable tolerance per
              element. List-like includes list, tuple, array, Series, and must be
              the same size as the index and its dtype must exactly match the
              index's type.
  
              .. versionadded:: 0.21.0 (list-like tolerance)
  
          Returns
          -------
          indexer : ndarray of int
              Integers from 0 to n - 1 indicating that the index at these
              positions matches the corresponding target values. Missing values
              in the target are marked by -1.
          %(raises_section)s
          Examples
          --------
          >>> index = pd.Index(['c', 'a', 'b'])
          >>> index.get_indexer(['a', 'b', 'x'])
          array([ 1,  2, -1])
  
          Notice that the return value is an array of locations in ``index``
          and ``x`` is marked by -1, as it is not in ``index``.
          """
  
      @Appender(_index_shared_docs["get_indexer"] % _index_doc_kwargs)
      def get_indexer(self, target, method=None, limit=None, tolerance=None):
          method = missing.clean_reindex_fill_method(method)
          target = ensure_index(target)
          if tolerance is not None:
              tolerance = self._convert_tolerance(tolerance, target)
  
          # Treat boolean labels passed to a numeric index as not found. Without
          # this fix False and True would be treated as 0 and 1 respectively.
          # (GH #16877)
          if target.is_boolean() and self.is_numeric():
              return ensure_platform_int(np.repeat(-1, target.size))
  
          pself, ptarget = self._maybe_promote(target)
          if pself is not self or ptarget is not target:
              return pself.get_indexer(
                  ptarget, method=method, limit=limit, tolerance=tolerance
              )
  
          if not is_dtype_equal(self.dtype, target.dtype):
              this = self.astype(object)
              target = target.astype(object)
              return this.get_indexer(
                  target, method=method, limit=limit, tolerance=tolerance
              )
  
          if not self.is_unique:
              raise InvalidIndexError(
                  "Reindexing only valid with uniquely valued Index objects"
              )
  
          if method == "pad" or method == "backfill":
              indexer = self._get_fill_indexer(target, method, limit, tolerance)
          elif method == "nearest":
              indexer = self._get_nearest_indexer(target, limit, tolerance)
          else:
              if tolerance is not None:
                  raise ValueError(
                      "tolerance argument only valid if doing pad, "
                      "backfill or nearest reindexing"
                  )
              if limit is not None:
                  raise ValueError(
                      "limit argument only valid if doing pad, "
                      "backfill or nearest reindexing"
                  )
  
              indexer = self._engine.get_indexer(target._ndarray_values)
  
          return ensure_platform_int(indexer)
  
      def _convert_tolerance(self, tolerance, target):
          # override this method on subclasses
          tolerance = np.asarray(tolerance)
          if target.size != tolerance.size and tolerance.size > 1:
              raise ValueError("list-like tolerance size must match target index size")
          return tolerance
  
      def _get_fill_indexer(self, target, method, limit=None, tolerance=None):
          if self.is_monotonic_increasing and target.is_monotonic_increasing:
              method = (
                  self._engine.get_pad_indexer
                  if method == "pad"
                  else self._engine.get_backfill_indexer
              )
              indexer = method(target._ndarray_values, limit)
          else:
              indexer = self._get_fill_indexer_searchsorted(target, method, limit)
          if tolerance is not None:
              indexer = self._filter_indexer_tolerance(
                  target._ndarray_values, indexer, tolerance
              )
          return indexer
  
      def _get_fill_indexer_searchsorted(self, target, method, limit=None):
          """
          Fallback pad/backfill get_indexer that works for monotonic decreasing
          indexes and non-monotonic targets.
          """
          if limit is not None:
              raise ValueError(
                  f"limit argument for {repr(method)} method only well-defined "
                  "if index and target are monotonic"
              )
  
          side = "left" if method == "pad" else "right"
  
          # find exact matches first (this simplifies the algorithm)
          indexer = self.get_indexer(target)
          nonexact = indexer == -1
          indexer[nonexact] = self._searchsorted_monotonic(target[nonexact], side)
          if side == "left":
              # searchsorted returns "indices into a sorted array such that,
              # if the corresponding elements in v were inserted before the
              # indices, the order of a would be preserved".
              # Thus, we need to subtract 1 to find values to the left.
              indexer[nonexact] -= 1
              # This also mapped not found values (values of 0 from
              # np.searchsorted) to -1, which conveniently is also our
              # sentinel for missing values
          else:
              # Mark indices to the right of the largest value as not found
              indexer[indexer == len(self)] = -1
          return indexer
  
      def _get_nearest_indexer(self, target, limit, tolerance):
          """
          Get the indexer for the nearest index labels; requires an index with
          values that can be subtracted from each other (e.g., not strings or
          tuples).
          """
          left_indexer = self.get_indexer(target, "pad", limit=limit)
          right_indexer = self.get_indexer(target, "backfill", limit=limit)
  
          target = np.asarray(target)
          left_distances = abs(self.values[left_indexer] - target)
          right_distances = abs(self.values[right_indexer] - target)
  
          op = operator.lt if self.is_monotonic_increasing else operator.le
          indexer = np.where(
              op(left_distances, right_distances) | (right_indexer == -1),
              left_indexer,
              right_indexer,
          )
          if tolerance is not None:
              indexer = self._filter_indexer_tolerance(target, indexer, tolerance)
          return indexer
  
      def _filter_indexer_tolerance(self, target, indexer, tolerance):
          distance = abs(self.values[indexer] - target)
          indexer = np.where(distance <= tolerance, indexer, -1)
          return indexer
  
      # --------------------------------------------------------------------
      # Indexer Conversion Methods
  
      _index_shared_docs[
          "_convert_scalar_indexer"
      ] = """
          Convert a scalar indexer.
  
          Parameters
          ----------
          key : label of the slice bound
          kind : {'ix', 'loc', 'getitem', 'iloc'} or None
      """
  
      @Appender(_index_shared_docs["_convert_scalar_indexer"])
      def _convert_scalar_indexer(self, key, kind=None):
          assert kind in ["ix", "loc", "getitem", "iloc", None]
  
          if kind == "iloc":
              return self._validate_indexer("positional", key, kind)
  
          if len(self) and not isinstance(self, ABCMultiIndex):
  
              # we can raise here if we are definitive that this
              # is positional indexing (eg. .ix on with a float)
              # or label indexing if we are using a type able
              # to be represented in the index
  
              if kind in ["getitem", "ix"] and is_float(key):
                  if not self.is_floating():
                      return self._invalid_indexer("label", key)
  
              elif kind in ["loc"] and is_float(key):
  
                  # we want to raise KeyError on string/mixed here
                  # technically we *could* raise a TypeError
                  # on anything but mixed though
                  if self.inferred_type not in [
                      "floating",
                      "mixed-integer-float",
                      "integer-na",
                      "string",
                      "unicode",
                      "mixed",
                  ]:
                      self._invalid_indexer("label", key)
  
              elif kind in ["loc"] and is_integer(key):
                  if not self.holds_integer():
                      self._invalid_indexer("label", key)
  
          return key
  
      _index_shared_docs[
          "_convert_slice_indexer"
      ] = """
          Convert a slice indexer.
  
          By definition, these are labels unless 'iloc' is passed in.
          Floats are not allowed as the start, step, or stop of the slice.
  
          Parameters
          ----------
          key : label of the slice bound
          kind : {'ix', 'loc', 'getitem', 'iloc'} or None
      """
  
      @Appender(_index_shared_docs["_convert_slice_indexer"])
      def _convert_slice_indexer(self, key: slice, kind=None):
          assert kind in ["ix", "loc", "getitem", "iloc", None]
  
          # validate iloc
          if kind == "iloc":
              return slice(
                  self._validate_indexer("slice", key.start, kind),
                  self._validate_indexer("slice", key.stop, kind),
                  self._validate_indexer("slice", key.step, kind),
              )
  
          # potentially cast the bounds to integers
          start, stop, step = key.start, key.stop, key.step
  
          # figure out if this is a positional indexer
          def is_int(v):
              return v is None or is_integer(v)
  
          is_null_slicer = start is None and stop is None
          is_index_slice = is_int(start) and is_int(stop)
          is_positional = is_index_slice and not (
              self.is_integer() or self.is_categorical()
          )
  
          if kind == "getitem":
              """
              called from the getitem slicers, validate that we are in fact
              integers
              """
              if self.is_integer() or is_index_slice:
                  return slice(
                      self._validate_indexer("slice", key.start, kind),
                      self._validate_indexer("slice", key.stop, kind),
                      self._validate_indexer("slice", key.step, kind),
                  )
  
          # convert the slice to an indexer here
  
          # if we are mixed and have integers
          try:
              if is_positional and self.is_mixed():
                  # Validate start & stop
                  if start is not None:
                      self.get_loc(start)
                  if stop is not None:
                      self.get_loc(stop)
                  is_positional = False
          except KeyError:
              if self.inferred_type in ["mixed-integer-float", "integer-na"]:
                  raise
  
          if is_null_slicer:
              indexer = key
          elif is_positional:
              indexer = key
          else:
              indexer = self.slice_indexer(start, stop, step, kind=kind)
  
          return indexer
  
      def _convert_listlike_indexer(self, keyarr, kind=None):
          """
          Parameters
          ----------
          keyarr : list-like
              Indexer to convert.
  
          Returns
          -------
          indexer : numpy.ndarray or None
              Return an ndarray or None if cannot convert.
          keyarr : numpy.ndarray
              Return tuple-safe keys.
          """
          if isinstance(keyarr, Index):
              keyarr = self._convert_index_indexer(keyarr)
          else:
              keyarr = self._convert_arr_indexer(keyarr)
  
          indexer = self._convert_list_indexer(keyarr, kind=kind)
          return indexer, keyarr
  
      _index_shared_docs[
          "_convert_arr_indexer"
      ] = """
          Convert an array-like indexer to the appropriate dtype.
  
          Parameters
          ----------
          keyarr : array-like
              Indexer to convert.
  
          Returns
          -------
          converted_keyarr : array-like
      """
  
      @Appender(_index_shared_docs["_convert_arr_indexer"])
      def _convert_arr_indexer(self, keyarr):
          keyarr = com.asarray_tuplesafe(keyarr)
          return keyarr
  
      _index_shared_docs[
          "_convert_index_indexer"
      ] = """
          Convert an Index indexer to the appropriate dtype.
  
          Parameters
          ----------
          keyarr : Index (or sub-class)
              Indexer to convert.
  
          Returns
          -------
          converted_keyarr : Index (or sub-class)
      """
  
      @Appender(_index_shared_docs["_convert_index_indexer"])
      def _convert_index_indexer(self, keyarr):
          return keyarr
  
      _index_shared_docs[
          "_convert_list_indexer"
      ] = """
          Convert a list-like indexer to the appropriate dtype.
  
          Parameters
          ----------
          keyarr : Index (or sub-class)
              Indexer to convert.
          kind : iloc, ix, loc, optional
  
          Returns
          -------
          positional indexer or None
      """
  
      @Appender(_index_shared_docs["_convert_list_indexer"])
      def _convert_list_indexer(self, keyarr, kind=None):
          if (
              kind in [None, "iloc", "ix"]
              and is_integer_dtype(keyarr)
              and not self.is_floating()
              and not isinstance(keyarr, ABCPeriodIndex)
          ):
  
              if self.inferred_type == "mixed-integer":
                  indexer = self.get_indexer(keyarr)
                  if (indexer >= 0).all():
                      return indexer
                  # missing values are flagged as -1 by get_indexer and negative
                  # indices are already converted to positive indices in the
                  # above if-statement, so the negative flags are changed to
                  # values outside the range of indices so as to trigger an
                  # IndexError in maybe_convert_indices
                  indexer[indexer < 0] = len(self)
  
                  return maybe_convert_indices(indexer, len(self))
  
              elif not self.inferred_type == "integer":
                  keyarr = np.where(keyarr < 0, len(self) + keyarr, keyarr)
                  return keyarr
  
          return None
  
      def _invalid_indexer(self, form, key):
          """
          Consistent invalid indexer message.
          """
          raise TypeError(
              f"cannot do {form} indexing on {type(self)} with these "
              f"indexers [{key}] of {type(key)}"
          )
  
      # --------------------------------------------------------------------
      # Reindex Methods
  
      def _can_reindex(self, indexer):
          """
          Check if we are allowing reindexing with this particular indexer.
  
          Parameters
          ----------
          indexer : an integer indexer
  
          Raises
          ------
          ValueError if its a duplicate axis
          """
  
          # trying to reindex on an axis with duplicates
          if not self.is_unique and len(indexer):
              raise ValueError("cannot reindex from a duplicate axis")
  
      def reindex(self, target, method=None, level=None, limit=None, tolerance=None):
          """
          Create index with target's values (move/add/delete values
          as necessary).
  
          Parameters
          ----------
          target : an iterable
  
          Returns
          -------
          new_index : pd.Index
              Resulting index.
          indexer : np.ndarray or None
              Indices of output values in original index.
          """
          # GH6552: preserve names when reindexing to non-named target
          # (i.e. neither Index nor Series).
          preserve_names = not hasattr(target, "name")
  
          # GH7774: preserve dtype/tz if target is empty and not an Index.
          target = _ensure_has_len(target)  # target may be an iterator
  
          if not isinstance(target, Index) and len(target) == 0:
              attrs = self._get_attributes_dict()
              attrs.pop("freq", None)  # don't preserve freq
              values = self._data[:0]  # appropriately-dtyped empty array
              target = self._simple_new(values, dtype=self.dtype, **attrs)
          else:
              target = ensure_index(target)
  
          if level is not None:
              if method is not None:
                  raise TypeError("Fill method not supported if level passed")
              _, indexer, _ = self._join_level(
                  target, level, how="right", return_indexers=True
              )
          else:
              if self.equals(target):
                  indexer = None
              else:
                  # check is_overlapping for IntervalIndex compat
                  if self.is_unique and not getattr(self, "is_overlapping", False):
                      indexer = self.get_indexer(
                          target, method=method, limit=limit, tolerance=tolerance
                      )
                  else:
                      if method is not None or limit is not None:
                          raise ValueError(
                              "cannot reindex a non-unique index "
                              "with a method or limit"
                          )
                      indexer, missing = self.get_indexer_non_unique(target)
  
          if preserve_names and target.nlevels == 1 and target.name != self.name:
              target = target.copy()
              target.name = self.name
  
          return target, indexer
  
      def _reindex_non_unique(self, target):
          """
          Create a new index with target's values (move/add/delete values as
          necessary) use with non-unique Index and a possibly non-unique target.
  
          Parameters
          ----------
          target : an iterable
  
          Returns
          -------
          new_index : pd.Index
              Resulting index.
          indexer : np.ndarray or None
              Indices of output values in original index.
  
          """
  
          target = ensure_index(target)
          indexer, missing = self.get_indexer_non_unique(target)
          check = indexer != -1
          new_labels = self.take(indexer[check])
          new_indexer = None
  
          if len(missing):
              length = np.arange(len(indexer))
  
              missing = ensure_platform_int(missing)
              missing_labels = target.take(missing)
              missing_indexer = ensure_int64(length[~check])
              cur_labels = self.take(indexer[check]).values
              cur_indexer = ensure_int64(length[check])
  
              new_labels = np.empty(tuple([len(indexer)]), dtype=object)
              new_labels[cur_indexer] = cur_labels
              new_labels[missing_indexer] = missing_labels
  
              # a unique indexer
              if target.is_unique:
  
                  # see GH5553, make sure we use the right indexer
                  new_indexer = np.arange(len(indexer))
                  new_indexer[cur_indexer] = np.arange(len(cur_labels))
                  new_indexer[missing_indexer] = -1
  
              # we have a non_unique selector, need to use the original
              # indexer here
              else:
  
                  # need to retake to have the same size as the indexer
                  indexer[~check] = -1
  
                  # reset the new indexer to account for the new size
                  new_indexer = np.arange(len(self.take(indexer)))
                  new_indexer[~check] = -1
  
          new_index = self._shallow_copy_with_infer(new_labels)
          return new_index, indexer, new_indexer
  
      # --------------------------------------------------------------------
      # Join Methods
  
      _index_shared_docs[
          "join"
      ] = """
          Compute join_index and indexers to conform data
          structures to the new index.
  
          Parameters
          ----------
          other : Index
          how : {'left', 'right', 'inner', 'outer'}
          level : int or level name, default None
          return_indexers : bool, default False
          sort : bool, default False
              Sort the join keys lexicographically in the result Index. If False,
              the order of the join keys depends on the join type (how keyword).
  
          Returns
          -------
          join_index, (left_indexer, right_indexer)
          """
  
      @Appender(_index_shared_docs["join"])
      def join(self, other, how="left", level=None, return_indexers=False, sort=False):
          self_is_mi = isinstance(self, ABCMultiIndex)
          other_is_mi = isinstance(other, ABCMultiIndex)
  
          # try to figure out the join level
          # GH3662
          if level is None and (self_is_mi or other_is_mi):
  
              # have the same levels/names so a simple join
              if self.names == other.names:
                  pass
              else:
                  return self._join_multi(other, how=how, return_indexers=return_indexers)
  
          # join on the level
          if level is not None and (self_is_mi or other_is_mi):
              return self._join_level(
                  other, level, how=how, return_indexers=return_indexers
              )
  
          other = ensure_index(other)
  
          if len(other) == 0 and how in ("left", "outer"):
              join_index = self._shallow_copy()
              if return_indexers:
                  rindexer = np.repeat(-1, len(join_index))
                  return join_index, None, rindexer
              else:
                  return join_index
  
          if len(self) == 0 and how in ("right", "outer"):
              join_index = other._shallow_copy()
              if return_indexers:
                  lindexer = np.repeat(-1, len(join_index))
                  return join_index, lindexer, None
              else:
                  return join_index
  
          if self._join_precedence < other._join_precedence:
              how = {"right": "left", "left": "right"}.get(how, how)
              result = other.join(
                  self, how=how, level=level, return_indexers=return_indexers
              )
              if return_indexers:
                  x, y, z = result
                  result = x, z, y
              return result
  
          if not is_dtype_equal(self.dtype, other.dtype):
              this = self.astype("O")
              other = other.astype("O")
              return this.join(other, how=how, return_indexers=return_indexers)
  
          _validate_join_method(how)
  
          if not self.is_unique and not other.is_unique:
              return self._join_non_unique(
                  other, how=how, return_indexers=return_indexers
              )
          elif not self.is_unique or not other.is_unique:
              if self.is_monotonic and other.is_monotonic:
                  return self._join_monotonic(
                      other, how=how, return_indexers=return_indexers
                  )
              else:
                  return self._join_non_unique(
                      other, how=how, return_indexers=return_indexers
                  )
          elif self.is_monotonic and other.is_monotonic:
              try:
                  return self._join_monotonic(
                      other, how=how, return_indexers=return_indexers
                  )
              except TypeError:
                  pass
  
          if how == "left":
              join_index = self
          elif how == "right":
              join_index = other
          elif how == "inner":
              # TODO: sort=False here for backwards compat. It may
              # be better to use the sort parameter passed into join
              join_index = self.intersection(other, sort=False)
          elif how == "outer":
              # TODO: sort=True here for backwards compat. It may
              # be better to use the sort parameter passed into join
              join_index = self.union(other)
  
          if sort:
              join_index = join_index.sort_values()
  
          if return_indexers:
              if join_index is self:
                  lindexer = None
              else:
                  lindexer = self.get_indexer(join_index)
              if join_index is other:
                  rindexer = None
              else:
                  rindexer = other.get_indexer(join_index)
              return join_index, lindexer, rindexer
          else:
              return join_index
  
      def _join_multi(self, other, how, return_indexers=True):
          from .multi import MultiIndex
          from pandas.core.reshape.merge import _restore_dropped_levels_multijoin
  
          # figure out join names
          self_names = set(com.not_none(*self.names))
          other_names = set(com.not_none(*other.names))
          overlap = self_names & other_names
  
          # need at least 1 in common
          if not overlap:
              raise ValueError("cannot join with no overlapping index names")
  
          self_is_mi = isinstance(self, MultiIndex)
          other_is_mi = isinstance(other, MultiIndex)
  
          if self_is_mi and other_is_mi:
  
              # Drop the non-matching levels from left and right respectively
              ldrop_names = list(self_names - overlap)
              rdrop_names = list(other_names - overlap)
  
              # if only the order differs
              if not len(ldrop_names + rdrop_names):
                  self_jnlevels = self
                  other_jnlevels = other.reorder_levels(self.names)
              else:
                  self_jnlevels = self.droplevel(ldrop_names)
                  other_jnlevels = other.droplevel(rdrop_names)
  
              # Join left and right
              # Join on same leveled multi-index frames is supported
              join_idx, lidx, ridx = self_jnlevels.join(
                  other_jnlevels, how, return_indexers=True
              )
  
              # Restore the dropped levels
              # Returned index level order is
              # common levels, ldrop_names, rdrop_names
              dropped_names = ldrop_names + rdrop_names
  
              levels, codes, names = _restore_dropped_levels_multijoin(
                  self, other, dropped_names, join_idx, lidx, ridx
              )
  
              # Re-create the multi-index
              multi_join_idx = MultiIndex(
                  levels=levels, codes=codes, names=names, verify_integrity=False
              )
  
              multi_join_idx = multi_join_idx.remove_unused_levels()
  
              return multi_join_idx, lidx, ridx
  
          jl = list(overlap)[0]
  
          # Case where only one index is multi
          # make the indices into mi's that match
          flip_order = False
          if self_is_mi:
              self, other = other, self
              flip_order = True
              # flip if join method is right or left
              how = {"right": "left", "left": "right"}.get(how, how)
  
          level = other.names.index(jl)
          result = self._join_level(
              other, level, how=how, return_indexers=return_indexers
          )
  
          if flip_order:
              if isinstance(result, tuple):
                  return result[0], result[2], result[1]
          return result
  
      def _join_non_unique(self, other, how="left", return_indexers=False):
          from pandas.core.reshape.merge import _get_join_indexers
  
          left_idx, right_idx = _get_join_indexers(
              [self._ndarray_values], [other._ndarray_values], how=how, sort=True
          )
  
          left_idx = ensure_platform_int(left_idx)
          right_idx = ensure_platform_int(right_idx)
  
          join_index = np.asarray(self._ndarray_values.take(left_idx))
          mask = left_idx == -1
          np.putmask(join_index, mask, other._ndarray_values.take(right_idx))
  
          join_index = self._wrap_joined_index(join_index, other)
  
          if return_indexers:
              return join_index, left_idx, right_idx
          else:
              return join_index
  
      def _join_level(
          self, other, level, how="left", return_indexers=False, keep_order=True
      ):
          """
          The join method *only* affects the level of the resulting
          MultiIndex. Otherwise it just exactly aligns the Index data to the
          labels of the level in the MultiIndex.
  
          If ```keep_order == True```, the order of the data indexed by the
          MultiIndex will not be changed; otherwise, it will tie out
          with `other`.
          """
          from .multi import MultiIndex
  
          def _get_leaf_sorter(labels):
              """
              Returns sorter for the inner most level while preserving the
              order of higher levels.
              """
              if labels[0].size == 0:
                  return np.empty(0, dtype="int64")
  
              if len(labels) == 1:
                  lab = ensure_int64(labels[0])
                  sorter, _ = libalgos.groupsort_indexer(lab, 1 + lab.max())
                  return sorter
  
              # find indexers of beginning of each set of
              # same-key labels w.r.t all but last level
              tic = labels[0][:-1] != labels[0][1:]
              for lab in labels[1:-1]:
                  tic |= lab[:-1] != lab[1:]
  
              starts = np.hstack(([True], tic, [True])).nonzero()[0]
              lab = ensure_int64(labels[-1])
              return lib.get_level_sorter(lab, ensure_int64(starts))
  
          if isinstance(self, MultiIndex) and isinstance(other, MultiIndex):
              raise TypeError("Join on level between two MultiIndex objects is ambiguous")
  
          left, right = self, other
  
          flip_order = not isinstance(self, MultiIndex)
          if flip_order:
              left, right = right, left
              how = {"right": "left", "left": "right"}.get(how, how)
  
          level = left._get_level_number(level)
          old_level = left.levels[level]
  
          if not right.is_unique:
              raise NotImplementedError(
                  "Index._join_level on non-unique index is not implemented"
              )
  
          new_level, left_lev_indexer, right_lev_indexer = old_level.join(
              right, how=how, return_indexers=True
          )
  
          if left_lev_indexer is None:
              if keep_order or len(left) == 0:
                  left_indexer = None
                  join_index = left
              else:  # sort the leaves
                  left_indexer = _get_leaf_sorter(left.codes[: level + 1])
                  join_index = left[left_indexer]
  
          else:
              left_lev_indexer = ensure_int64(left_lev_indexer)
              rev_indexer = lib.get_reverse_indexer(left_lev_indexer, len(old_level))
  
              new_lev_codes = algos.take_nd(
                  rev_indexer, left.codes[level], allow_fill=False
              )
  
              new_codes = list(left.codes)
              new_codes[level] = new_lev_codes
  
              new_levels = list(left.levels)
              new_levels[level] = new_level
  
              if keep_order:  # just drop missing values. o.w. keep order
                  left_indexer = np.arange(len(left), dtype=np.intp)
                  mask = new_lev_codes != -1
                  if not mask.all():
                      new_codes = [lab[mask] for lab in new_codes]
                      left_indexer = left_indexer[mask]
  
              else:  # tie out the order with other
                  if level == 0:  # outer most level, take the fast route
                      ngroups = 1 + new_lev_codes.max()
                      left_indexer, counts = libalgos.groupsort_indexer(
                          new_lev_codes, ngroups
                      )
  
                      # missing values are placed first; drop them!
                      left_indexer = left_indexer[counts[0] :]
                      new_codes = [lab[left_indexer] for lab in new_codes]
  
                  else:  # sort the leaves
                      mask = new_lev_codes != -1
                      mask_all = mask.all()
                      if not mask_all:
                          new_codes = [lab[mask] for lab in new_codes]
  
                      left_indexer = _get_leaf_sorter(new_codes[: level + 1])
                      new_codes = [lab[left_indexer] for lab in new_codes]
  
                      # left_indexers are w.r.t masked frame.
                      # reverse to original frame!
                      if not mask_all:
                          left_indexer = mask.nonzero()[0][left_indexer]
  
              join_index = MultiIndex(
                  levels=new_levels,
                  codes=new_codes,
                  names=left.names,
                  verify_integrity=False,
              )
  
          if right_lev_indexer is not None:
              right_indexer = algos.take_nd(
                  right_lev_indexer, join_index.codes[level], allow_fill=False
              )
          else:
              right_indexer = join_index.codes[level]
  
          if flip_order:
              left_indexer, right_indexer = right_indexer, left_indexer
  
          if return_indexers:
              left_indexer = (
                  None if left_indexer is None else ensure_platform_int(left_indexer)
              )
              right_indexer = (
                  None if right_indexer is None else ensure_platform_int(right_indexer)
              )
              return join_index, left_indexer, right_indexer
          else:
              return join_index
  
      def _join_monotonic(self, other, how="left", return_indexers=False):
          if self.equals(other):
              ret_index = other if how == "right" else self
              if return_indexers:
                  return ret_index, None, None
              else:
                  return ret_index
  
          sv = self._ndarray_values
          ov = other._ndarray_values
  
          if self.is_unique and other.is_unique:
              # We can perform much better than the general case
              if how == "left":
                  join_index = self
                  lidx = None
                  ridx = self._left_indexer_unique(sv, ov)
              elif how == "right":
                  join_index = other
                  lidx = self._left_indexer_unique(ov, sv)
                  ridx = None
              elif how == "inner":
                  join_index, lidx, ridx = self._inner_indexer(sv, ov)
                  join_index = self._wrap_joined_index(join_index, other)
              elif how == "outer":
                  join_index, lidx, ridx = self._outer_indexer(sv, ov)
                  join_index = self._wrap_joined_index(join_index, other)
          else:
              if how == "left":
                  join_index, lidx, ridx = self._left_indexer(sv, ov)
              elif how == "right":
                  join_index, ridx, lidx = self._left_indexer(ov, sv)
              elif how == "inner":
                  join_index, lidx, ridx = self._inner_indexer(sv, ov)
              elif how == "outer":
                  join_index, lidx, ridx = self._outer_indexer(sv, ov)
              join_index = self._wrap_joined_index(join_index, other)
  
          if return_indexers:
              lidx = None if lidx is None else ensure_platform_int(lidx)
              ridx = None if ridx is None else ensure_platform_int(ridx)
              return join_index, lidx, ridx
          else:
              return join_index
  
      def _wrap_joined_index(self, joined, other):
          name = get_op_result_name(self, other)
          return Index(joined, name=name)
  
      # --------------------------------------------------------------------
      # Uncategorized Methods
  
      @property
      def values(self):
          """
          Return an array representing the data in the Index.
  
          .. warning::
  
             We recommend using :attr:`Index.array` or
             :meth:`Index.to_numpy`, depending on whether you need
             a reference to the underlying data or a NumPy array.
  
          Returns
          -------
          array: numpy.ndarray or ExtensionArray
  
          See Also
          --------
          Index.array : Reference to the underlying data.
          Index.to_numpy : A NumPy array representing the underlying data.
          """
          return self._data.view(np.ndarray)
  
      @property
      def _values(self) -> Union[ExtensionArray, ABCIndexClass, np.ndarray]:
          # TODO(EA): remove index types as they become extension arrays
          """
          The best array representation.
  
          This is an ndarray, ExtensionArray, or Index subclass. This differs
          from ``_ndarray_values``, which always returns an ndarray.
  
          Both ``_values`` and ``_ndarray_values`` are consistent between
          ``Series`` and ``Index``.
  
          It may differ from the public '.values' method.
  
          index             | values          | _values       | _ndarray_values |
          ----------------- | --------------- | ------------- | --------------- |
          Index             | ndarray         | ndarray       | ndarray         |
          CategoricalIndex  | Categorical     | Categorical   | ndarray[int]    |
          DatetimeIndex     | ndarray[M8ns]   | ndarray[M8ns] | ndarray[M8ns]   |
          DatetimeIndex[tz] | ndarray[M8ns]   | DTI[tz]       | ndarray[M8ns]   |
          PeriodIndex       | ndarray[object] | PeriodArray   | ndarray[int]    |
          IntervalIndex     | IntervalArray   | IntervalArray | ndarray[object] |
  
          See Also
          --------
          values
          _ndarray_values
          """
          return self._data
  
      def _internal_get_values(self):
          """
          Return `Index` data as an `numpy.ndarray`.
  
          Returns
          -------
          numpy.ndarray
              A one-dimensional numpy array of the `Index` values.
  
          See Also
          --------
          Index.values : The attribute that _internal_get_values wraps.
  
          Examples
          --------
          Getting the `Index` values of a `DataFrame`:
  
          >>> df = pd.DataFrame([[1, 2, 3], [4, 5, 6], [7, 8, 9]],
          ...                    index=['a', 'b', 'c'], columns=['A', 'B', 'C'])
          >>> df
             A  B  C
          a  1  2  3
          b  4  5  6
          c  7  8  9
          >>> df.index._internal_get_values()
          array(['a', 'b', 'c'], dtype=object)
  
          Standalone `Index` values:
  
          >>> idx = pd.Index(['1', '2', '3'])
          >>> idx._internal_get_values()
          array(['1', '2', '3'], dtype=object)
  
          `MultiIndex` arrays also have only one dimension:
  
          >>> midx = pd.MultiIndex.from_arrays([[1, 2, 3], ['a', 'b', 'c']],
          ...                                  names=('number', 'letter'))
          >>> midx._internal_get_values()
          array([(1, 'a'), (2, 'b'), (3, 'c')], dtype=object)
          >>> midx._internal_get_values().ndim
          1
          """
          return self.values
  
      @Appender(IndexOpsMixin.memory_usage.__doc__)
      def memory_usage(self, deep=False):
          result = super().memory_usage(deep=deep)
  
          # include our engine hashtable
          result += self._engine.sizeof(deep=deep)
          return result
  
      _index_shared_docs[
          "where"
      ] = """
          Return an Index of same shape as self and whose corresponding
          entries are from self where cond is True and otherwise are from
          other.
  
          Parameters
          ----------
          cond : bool array-like with the same length as self
          other : scalar, or array-like
  
          Returns
          -------
          Index
          """
  
      @Appender(_index_shared_docs["where"])
      def where(self, cond, other=None):
          if other is None:
              other = self._na_value
  
          dtype = self.dtype
          values = self.values
  
          if is_bool(other) or is_bool_dtype(other):
  
              # bools force casting
              values = values.astype(object)
              dtype = None
  
          values = np.where(cond, values, other)
  
          if self._is_numeric_dtype and np.any(isna(values)):
              # We can't coerce to the numeric dtype of "self" (unless
              # it's float) if there are NaN values in our output.
              dtype = None
  
          return self._shallow_copy_with_infer(values, dtype=dtype)
  
      # construction helpers
      @classmethod
      def _scalar_data_error(cls, data):
          # We return the TypeError so that we can raise it from the constructor
          #  in order to keep mypy happy
          return TypeError(
              f"{cls.__name__}(...) must be called with a collection of some "
              f"kind, {repr(data)} was passed"
          )
  
      @classmethod
      def _string_data_error(cls, data):
          raise TypeError(
              "String dtype not supported, you may need "
              "to explicitly cast to a numeric type"
          )
  
      def _coerce_scalar_to_index(self, item):
          """
          We need to coerce a scalar to a compat for our index type.
  
          Parameters
          ----------
          item : scalar item to coerce
          """
          dtype = self.dtype
  
          if self._is_numeric_dtype and isna(item):
              # We can't coerce to the numeric dtype of "self" (unless
              # it's float) if there are NaN values in our output.
              dtype = None
  
          return Index([item], dtype=dtype, **self._get_attributes_dict())
  
      def _to_safe_for_reshape(self):
          """
          Convert to object if we are a categorical.
          """
          return self
  
      def _convert_for_op(self, value):
          """
          Convert value to be insertable to ndarray.
          """
          return value
  
      def _assert_can_do_op(self, value):
          """
          Check value is valid for scalar op.
          """
          if not is_scalar(value):
              raise TypeError(f"'value' must be a scalar, passed: {type(value).__name__}")
  
      def _is_memory_usage_qualified(self) -> bool:
          """
          Return a boolean if we need a qualified .info display.
          """
          return self.is_object()
  
      def is_type_compatible(self, kind) -> bool:
          """
          Whether the index type is compatible with the provided type.
          """
          return kind == self.inferred_type
  
      _index_shared_docs[
          "contains"
      ] = """
          Return a boolean indicating whether the provided key is in the index.
  
          Parameters
          ----------
          key : label
              The key to check if it is present in the index.
  
          Returns
          -------
          bool
              Whether the key search is in the index.
  
          See Also
          --------
          Index.isin : Returns an ndarray of boolean dtype indicating whether the
              list-like key is in the index.
  
          Examples
          --------
          >>> idx = pd.Index([1, 2, 3, 4])
          >>> idx
          Int64Index([1, 2, 3, 4], dtype='int64')
  
          >>> 2 in idx
          True
          >>> 6 in idx
          False
          """
  
      @Appender(_index_shared_docs["contains"] % _index_doc_kwargs)
      def __contains__(self, key) -> bool:
          hash(key)
          try:
              return key in self._engine
          except (OverflowError, TypeError, ValueError):
              return False
  
      def __hash__(self):
          raise TypeError(f"unhashable type: {repr(type(self).__name__)}")
  
      def __setitem__(self, key, value):
          raise TypeError("Index does not support mutable operations")
  
      def __getitem__(self, key):
          """
          Override numpy.ndarray's __getitem__ method to work as desired.
  
          This function adds lists and Series as valid boolean indexers
          (ndarrays only supports ndarray with dtype=bool).
  
          If resulting ndim != 1, plain ndarray is returned instead of
          corresponding `Index` subclass.
  
          """
          # There's no custom logic to be implemented in __getslice__, so it's
          # not overloaded intentionally.
          getitem = self._data.__getitem__
          promote = self._shallow_copy
  
          if is_scalar(key):
              key = com.cast_scalar_indexer(key)
              return getitem(key)
  
          if isinstance(key, slice):
              # This case is separated from the conditional above to avoid
              # pessimization of basic indexing.
              return promote(getitem(key))
  
          if com.is_bool_indexer(key):
              key = np.asarray(key, dtype=bool)
  
          key = com.values_from_object(key)
          result = getitem(key)
          if not is_scalar(result):
              return promote(result)
          else:
              return result
  
      def _can_hold_identifiers_and_holds_name(self, name) -> bool:
          """
          Faster check for ``name in self`` when we know `name` is a Python
          identifier (e.g. in NDFrame.__getattr__, which hits this to support
          . key lookup). For indexes that can't hold identifiers (everything
          but object & categorical) we just return False.
  
          https://github.com/pandas-dev/pandas/issues/19764
          """
          if self.is_object() or self.is_categorical():
              return name in self
          return False
  
      def append(self, other):
          """
          Append a collection of Index options together.
  
          Parameters
          ----------
          other : Index or list/tuple of indices
  
          Returns
          -------
          appended : Index
          """
  
          to_concat = [self]
  
          if isinstance(other, (list, tuple)):
              to_concat = to_concat + list(other)
          else:
              to_concat.append(other)
  
          for obj in to_concat:
              if not isinstance(obj, Index):
                  raise TypeError("all inputs must be Index")
  
          names = {obj.name for obj in to_concat}
          name = None if len(names) > 1 else self.name
  
          return self._concat(to_concat, name)
  
      def _concat(self, to_concat, name):
  
          typs = _concat.get_dtype_kinds(to_concat)
  
          if len(typs) == 1:
              return self._concat_same_dtype(to_concat, name=name)
          return Index._concat_same_dtype(self, to_concat, name=name)
  
      def _concat_same_dtype(self, to_concat, name):
          """
          Concatenate to_concat which has the same class.
          """
          # must be overridden in specific classes
          klasses = (
              ABCDatetimeIndex,
              ABCTimedeltaIndex,
              ABCPeriodIndex,
              ExtensionArray,
              ABCIntervalIndex,
          )
          to_concat = [
              x.astype(object) if isinstance(x, klasses) else x for x in to_concat
          ]
  
          self = to_concat[0]
          attribs = self._get_attributes_dict()
          attribs["name"] = name
  
          to_concat = [x._values if isinstance(x, Index) else x for x in to_concat]
  
          return self._shallow_copy_with_infer(np.concatenate(to_concat), **attribs)
  
      def putmask(self, mask, value):
          """
          Return a new Index of the values set with the mask.
  
          Returns
          -------
          Index
  
          See Also
          --------
          numpy.ndarray.putmask
          """
          values = self.values.copy()
          try:
              np.putmask(values, mask, self._convert_for_op(value))
              return self._shallow_copy(values)
          except (ValueError, TypeError) as err:
              if is_object_dtype(self):
                  raise err
  
              # coerces to object
              return self.astype(object).putmask(mask, value)
  
      def equals(self, other) -> bool:
          """
          Determine if two Index objects contain the same elements.
  
          Returns
          -------
          bool
              True if "other" is an Index and it has the same elements as calling
              index; False otherwise.
          """
          if self.is_(other):
              return True
  
          if not isinstance(other, Index):
              return False
  
          if is_object_dtype(self) and not is_object_dtype(other):
              # if other is not object, use other's logic for coercion
              return other.equals(self)
  
          if isinstance(other, ABCMultiIndex):
              # d-level MultiIndex can equal d-tuple Index
              if not is_object_dtype(self.dtype):
                  if self.nlevels != other.nlevels:
                      return False
  
          return array_equivalent(
              com.values_from_object(self), com.values_from_object(other)
          )
  
      def identical(self, other) -> bool:
          """
          Similar to equals, but check that other comparable attributes are
          also equal.
  
          Returns
          -------
          bool
              If two Index objects have equal elements and same type True,
              otherwise False.
          """
          return (
              self.equals(other)
              and all(
                  (
                      getattr(self, c, None) == getattr(other, c, None)
                      for c in self._comparables
                  )
              )
              and type(self) == type(other)
          )
  
      def asof(self, label):
          """
          Return the label from the index, or, if not present, the previous one.
  
          Assuming that the index is sorted, return the passed index label if it
          is in the index, or return the previous index label if the passed one
          is not in the index.
  
          Parameters
          ----------
          label : object
              The label up to which the method returns the latest index label.
  
          Returns
          -------
          object
              The passed label if it is in the index. The previous label if the
              passed label is not in the sorted index or `NaN` if there is no
              such label.
  
          See Also
          --------
          Series.asof : Return the latest value in a Series up to the
              passed index.
          merge_asof : Perform an asof merge (similar to left join but it
              matches on nearest key rather than equal key).
          Index.get_loc : An `asof` is a thin wrapper around `get_loc`
              with method='pad'.
  
          Examples
          --------
          `Index.asof` returns the latest index label up to the passed label.
  
          >>> idx = pd.Index(['2013-12-31', '2014-01-02', '2014-01-03'])
          >>> idx.asof('2014-01-01')
          '2013-12-31'
  
          If the label is in the index, the method returns the passed label.
  
          >>> idx.asof('2014-01-02')
          '2014-01-02'
  
          If all of the labels in the index are later than the passed label,
          NaN is returned.
  
          >>> idx.asof('1999-01-02')
          nan
  
          If the index is not sorted, an error is raised.
  
          >>> idx_not_sorted = pd.Index(['2013-12-31', '2015-01-02',
          ...                            '2014-01-03'])
          >>> idx_not_sorted.asof('2013-12-31')
          Traceback (most recent call last):
          ValueError: index must be monotonic increasing or decreasing
          """
          try:
              loc = self.get_loc(label, method="pad")
          except KeyError:
              return self._na_value
          else:
              if isinstance(loc, slice):
                  loc = loc.indices(len(self))[-1]
              return self[loc]
  
      def asof_locs(self, where, mask):
          """
          Find the locations (indices) of the labels from the index for
          every entry in the `where` argument.
  
          As in the `asof` function, if the label (a particular entry in
          `where`) is not in the index, the latest index label up to the
          passed label is chosen and its index returned.
  
          If all of the labels in the index are later than a label in `where`,
          -1 is returned.
  
          `mask` is used to ignore NA values in the index during calculation.
  
          Parameters
          ----------
          where : Index
              An Index consisting of an array of timestamps.
          mask : array-like
              Array of booleans denoting where values in the original
              data are not NA.
  
          Returns
          -------
          numpy.ndarray
              An array of locations (indices) of the labels from the Index
              which correspond to the return values of the `asof` function
              for every element in `where`.
          """
          locs = self.values[mask].searchsorted(where.values, side="right")
          locs = np.where(locs > 0, locs - 1, 0)
  
          result = np.arange(len(self))[mask].take(locs)
  
          first = mask.argmax()
          result[(locs == 0) & (where.values < self.values[first])] = -1
  
          return result
  
      def sort_values(self, return_indexer=False, ascending=True):
          """
          Return a sorted copy of the index.
  
          Return a sorted copy of the index, and optionally return the indices
          that sorted the index itself.
  
          Parameters
          ----------
          return_indexer : bool, default False
              Should the indices that would sort the index be returned.
          ascending : bool, default True
              Should the index values be sorted in an ascending order.
  
          Returns
          -------
          sorted_index : pandas.Index
              Sorted copy of the index.
          indexer : numpy.ndarray, optional
              The indices that the index itself was sorted by.
  
          See Also
          --------
          Series.sort_values : Sort values of a Series.
          DataFrame.sort_values : Sort values in a DataFrame.
  
          Examples
          --------
          >>> idx = pd.Index([10, 100, 1, 1000])
          >>> idx
          Int64Index([10, 100, 1, 1000], dtype='int64')
  
          Sort values in ascending order (default behavior).
  
          >>> idx.sort_values()
          Int64Index([1, 10, 100, 1000], dtype='int64')
  
          Sort values in descending order, and also get the indices `idx` was
          sorted by.
  
          >>> idx.sort_values(ascending=False, return_indexer=True)
          (Int64Index([1000, 100, 10, 1], dtype='int64'), array([3, 1, 0, 2]))
          """
          _as = self.argsort()
          if not ascending:
              _as = _as[::-1]
  
          sorted_index = self.take(_as)
  
          if return_indexer:
              return sorted_index, _as
          else:
              return sorted_index
  
      def sort(self, *args, **kwargs):
          """
          Use sort_values instead.
          """
          raise TypeError("cannot sort an Index object in-place, use sort_values instead")
  
      def shift(self, periods=1, freq=None):
          """
          Shift index by desired number of time frequency increments.
  
          This method is for shifting the values of datetime-like indexes
          by a specified time increment a given number of times.
  
          Parameters
          ----------
          periods : int, default 1
              Number of periods (or increments) to shift by,
              can be positive or negative.
          freq : pandas.DateOffset, pandas.Timedelta or str, optional
              Frequency increment to shift by.
              If None, the index is shifted by its own `freq` attribute.
              Offset aliases are valid strings, e.g., 'D', 'W', 'M' etc.
  
          Returns
          -------
          pandas.Index
              Shifted index.
  
          See Also
          --------
          Series.shift : Shift values of Series.
  
          Notes
          -----
          This method is only implemented for datetime-like index classes,
          i.e., DatetimeIndex, PeriodIndex and TimedeltaIndex.
  
          Examples
          --------
          Put the first 5 month starts of 2011 into an index.
  
          >>> month_starts = pd.date_range('1/1/2011', periods=5, freq='MS')
          >>> month_starts
          DatetimeIndex(['2011-01-01', '2011-02-01', '2011-03-01', '2011-04-01',
                         '2011-05-01'],
                        dtype='datetime64[ns]', freq='MS')
  
          Shift the index by 10 days.
  
          >>> month_starts.shift(10, freq='D')
          DatetimeIndex(['2011-01-11', '2011-02-11', '2011-03-11', '2011-04-11',
                         '2011-05-11'],
                        dtype='datetime64[ns]', freq=None)
  
          The default value of `freq` is the `freq` attribute of the index,
          which is 'MS' (month start) in this example.
  
          >>> month_starts.shift(10)
          DatetimeIndex(['2011-11-01', '2011-12-01', '2012-01-01', '2012-02-01',
                         '2012-03-01'],
                        dtype='datetime64[ns]', freq='MS')
          """
          raise NotImplementedError(f"Not supported for type {type(self).__name__}")
  
      def argsort(self, *args, **kwargs):
          """
          Return the integer indices that would sort the index.
  
          Parameters
          ----------
          *args
              Passed to `numpy.ndarray.argsort`.
          **kwargs
              Passed to `numpy.ndarray.argsort`.
  
          Returns
          -------
          numpy.ndarray
              Integer indices that would sort the index if used as
              an indexer.
  
          See Also
          --------
          numpy.argsort : Similar method for NumPy arrays.
          Index.sort_values : Return sorted copy of Index.
  
          Examples
          --------
          >>> idx = pd.Index(['b', 'a', 'd', 'c'])
          >>> idx
          Index(['b', 'a', 'd', 'c'], dtype='object')
  
          >>> order = idx.argsort()
          >>> order
          array([1, 0, 3, 2])
  
          >>> idx[order]
          Index(['a', 'b', 'c', 'd'], dtype='object')
          """
          result = self.asi8
          if result is None:
              result = np.array(self)
          return result.argsort(*args, **kwargs)
  
      _index_shared_docs[
          "get_value"
      ] = """
          Fast lookup of value from 1-dimensional ndarray. Only use this if you
          know what you're doing.
  
          Returns
          -------
          scalar
              A value in the Series with the index of the key value in self.
          """
  
      @Appender(_index_shared_docs["get_value"] % _index_doc_kwargs)
      def get_value(self, series, key):
  
          # if we have something that is Index-like, then
          # use this, e.g. DatetimeIndex
          # Things like `Series._get_value` (via .at) pass the EA directly here.
          s = extract_array(series, extract_numpy=True)
          if isinstance(s, ExtensionArray):
              if is_scalar(key):
                  # GH 20882, 21257
                  # First try to convert the key to a location
                  # If that fails, raise a KeyError if an integer
                  # index, otherwise, see if key is an integer, and
                  # try that
                  try:
                      iloc = self.get_loc(key)
                      return s[iloc]
                  except KeyError:
                      if len(self) > 0 and (self.holds_integer() or self.is_boolean()):
                          raise
                      elif is_integer(key):
                          return s[key]
              else:
                  # if key is not a scalar, directly raise an error (the code below
                  # would convert to numpy arrays and raise later any way) - GH29926
                  raise InvalidIndexError(key)
  
          s = com.values_from_object(series)
          k = com.values_from_object(key)
  
          k = self._convert_scalar_indexer(k, kind="getitem")
          try:
              return self._engine.get_value(s, k, tz=getattr(series.dtype, "tz", None))
          except KeyError as e1:
              if len(self) > 0 and (self.holds_integer() or self.is_boolean()):
                  raise
  
              try:
                  return libindex.get_value_at(s, key)
              except IndexError:
                  raise
              except TypeError:
                  # generator/iterator-like
                  if is_iterator(key):
                      raise InvalidIndexError(key)
                  else:
                      raise e1
              except Exception:
                  raise e1
          except TypeError:
              # e.g. "[False] is an invalid key"
              if is_scalar(key):
                  raise IndexError(key)
              raise InvalidIndexError(key)
  
      def set_value(self, arr, key, value):
          """
          Fast lookup of value from 1-dimensional ndarray.
  
          .. deprecated:: 1.0
  
          Notes
          -----
          Only use this if you know what you're doing.
          """
          warnings.warn(
              (
                  "The 'set_value' method is deprecated, and "
                  "will be removed in a future version."
              ),
              FutureWarning,
              stacklevel=2,
          )
          self._engine.set_value(
              com.values_from_object(arr), com.values_from_object(key), value
          )
  
      _index_shared_docs[
          "get_indexer_non_unique"
      ] = """
          Compute indexer and mask for new index given the current index. The
          indexer should be then used as an input to ndarray.take to align the
          current data to the new index.
  
          Parameters
          ----------
          target : %(target_klass)s
  
          Returns
          -------
          indexer : ndarray of int
              Integers from 0 to n - 1 indicating that the index at these
              positions matches the corresponding target values. Missing values
              in the target are marked by -1.
          missing : ndarray of int
              An indexer into the target of the values not found.
              These correspond to the -1 in the indexer array.
          """
  
      @Appender(_index_shared_docs["get_indexer_non_unique"] % _index_doc_kwargs)
      def get_indexer_non_unique(self, target):
          target = ensure_index(target)
          pself, ptarget = self._maybe_promote(target)
          if pself is not self or ptarget is not target:
              return pself.get_indexer_non_unique(ptarget)
  
          if is_categorical(target):
              tgt_values = np.asarray(target)
          elif self.is_all_dates and target.is_all_dates:  # GH 30399
              tgt_values = target.asi8
          else:
              tgt_values = target._ndarray_values
  
          indexer, missing = self._engine.get_indexer_non_unique(tgt_values)
          return ensure_platform_int(indexer), missing
  
      def get_indexer_for(self, target, **kwargs):
          """
          Guaranteed return of an indexer even when non-unique.
  
          This dispatches to get_indexer or get_indexer_non_unique
          as appropriate.
  
          Returns
          -------
          numpy.ndarray
              List of indices.
          """
          if self.is_unique:
              return self.get_indexer(target, **kwargs)
          indexer, _ = self.get_indexer_non_unique(target, **kwargs)
          return indexer
  
      def _maybe_promote(self, other):
          # A hack, but it works
  
          if self.inferred_type == "date" and isinstance(other, ABCDatetimeIndex):
              return type(other)(self), other
          elif self.inferred_type == "boolean":
              if not is_object_dtype(self.dtype):
                  return self.astype("object"), other.astype("object")
          return self, other
  
      def groupby(self, values) -> Dict[Hashable, np.ndarray]:
          """
          Group the index labels by a given array of values.
  
          Parameters
          ----------
          values : array
              Values used to determine the groups.
  
          Returns
          -------
          dict
              {group name -> group labels}
          """
  
          # TODO: if we are a MultiIndex, we can do better
          # that converting to tuples
          if isinstance(values, ABCMultiIndex):
              values = values.values
          values = ensure_categorical(values)
          result = values._reverse_indexer()
  
          # map to the label
          result = {k: self.take(v) for k, v in result.items()}
  
          return result
  
      def map(self, mapper, na_action=None):
          """
          Map values using input correspondence (a dict, Series, or function).
  
          Parameters
          ----------
          mapper : function, dict, or Series
              Mapping correspondence.
          na_action : {None, 'ignore'}
              If 'ignore', propagate NA values, without passing them to the
              mapping correspondence.
  
          Returns
          -------
          applied : Union[Index, MultiIndex], inferred
              The output of the mapping function applied to the index.
              If the function returns a tuple with more than one element
              a MultiIndex will be returned.
          """
  
          from .multi import MultiIndex
  
          new_values = super()._map_values(mapper, na_action=na_action)
  
          attributes = self._get_attributes_dict()
  
          # we can return a MultiIndex
          if new_values.size and isinstance(new_values[0], tuple):
              if isinstance(self, MultiIndex):
                  names = self.names
              elif attributes.get("name"):
                  names = [attributes.get("name")] * len(new_values[0])
              else:
                  names = None
              return MultiIndex.from_tuples(new_values, names=names)
  
          attributes["copy"] = False
          if not new_values.size:
              # empty
              attributes["dtype"] = self.dtype
  
          return Index(new_values, **attributes)
  
      def isin(self, values, level=None):
          """
          Return a boolean array where the index values are in `values`.
  
          Compute boolean array of whether each index value is found in the
          passed set of values. The length of the returned boolean array matches
          the length of the index.
  
          Parameters
          ----------
          values : set or list-like
              Sought values.
          level : str or int, optional
              Name or position of the index level to use (if the index is a
              `MultiIndex`).
  
          Returns
          -------
          is_contained : ndarray
              NumPy array of boolean values.
  
          See Also
          --------
          Series.isin : Same for Series.
          DataFrame.isin : Same method for DataFrames.
  
          Notes
          -----
          In the case of `MultiIndex` you must either specify `values` as a
          list-like object containing tuples that are the same length as the
          number of levels, or specify `level`. Otherwise it will raise a
          ``ValueError``.
  
          If `level` is specified:
  
          - if it is the name of one *and only one* index level, use that level;
          - otherwise it should be a number indicating level position.
  
          Examples
          --------
          >>> idx = pd.Index([1,2,3])
          >>> idx
          Int64Index([1, 2, 3], dtype='int64')
  
          Check whether each index value in a list of values.
          >>> idx.isin([1, 4])
          array([ True, False, False])
  
          >>> midx = pd.MultiIndex.from_arrays([[1,2,3],
          ...                                  ['red', 'blue', 'green']],
          ...                                  names=('number', 'color'))
          >>> midx
          MultiIndex(levels=[[1, 2, 3], ['blue', 'green', 'red']],
                     codes=[[0, 1, 2], [2, 0, 1]],
                     names=['number', 'color'])
  
          Check whether the strings in the 'color' level of the MultiIndex
          are in a list of colors.
  
          >>> midx.isin(['red', 'orange', 'yellow'], level='color')
          array([ True, False, False])
  
          To check across the levels of a MultiIndex, pass a list of tuples:
  
          >>> midx.isin([(1, 'red'), (3, 'red')])
          array([ True, False, False])
  
          For a DatetimeIndex, string values in `values` are converted to
          Timestamps.
  
          >>> dates = ['2000-03-11', '2000-03-12', '2000-03-13']
          >>> dti = pd.to_datetime(dates)
          >>> dti
          DatetimeIndex(['2000-03-11', '2000-03-12', '2000-03-13'],
          dtype='datetime64[ns]', freq=None)
  
          >>> dti.isin(['2000-03-11'])
          array([ True, False, False])
          """
          if level is not None:
              self._validate_index_level(level)
          return algos.isin(self, values)
  
      def _get_string_slice(self, key, use_lhs=True, use_rhs=True):
          # this is for partial string indexing,
          # overridden in DatetimeIndex, TimedeltaIndex and PeriodIndex
          raise NotImplementedError
  
      def slice_indexer(self, start=None, end=None, step=None, kind=None):
          """
          For an ordered or unique index, compute the slice indexer for input
          labels and step.
  
          Parameters
          ----------
          start : label, default None
              If None, defaults to the beginning.
          end : label, default None
              If None, defaults to the end.
          step : int, default None
          kind : str, default None
  
          Returns
          -------
          indexer : slice
  
          Raises
          ------
          KeyError : If key does not exist, or key is not unique and index is
              not ordered.
  
          Notes
          -----
          This function assumes that the data is sorted, so use at your own peril
  
          Examples
          --------
          This is a method on all index types. For example you can do:
  
          >>> idx = pd.Index(list('abcd'))
          >>> idx.slice_indexer(start='b', end='c')
          slice(1, 3)
  
          >>> idx = pd.MultiIndex.from_arrays([list('abcd'), list('efgh')])
          >>> idx.slice_indexer(start='b', end=('c', 'g'))
          slice(1, 3)
          """
          start_slice, end_slice = self.slice_locs(start, end, step=step, kind=kind)
  
          # return a slice
          if not is_scalar(start_slice):
              raise AssertionError("Start slice bound is non-scalar")
          if not is_scalar(end_slice):
              raise AssertionError("End slice bound is non-scalar")
  
          return slice(start_slice, end_slice, step)
  
      def _maybe_cast_indexer(self, key):
          """
          If we have a float key and are not a floating index, then try to cast
          to an int if equivalent.
          """
  
          if is_float(key) and not self.is_floating():
              try:
                  ckey = int(key)
                  if ckey == key:
                      key = ckey
              except (OverflowError, ValueError, TypeError):
                  pass
          return key
  
      def _validate_indexer(self, form, key, kind):
          """
          If we are positional indexer, validate that we have appropriate
          typed bounds must be an integer.
          """
          assert kind in ["ix", "loc", "getitem", "iloc"]
  
          if key is None:
              pass
          elif is_integer(key):
              pass
          elif kind in ["iloc", "getitem"]:
              self._invalid_indexer(form, key)
          return key
  
      _index_shared_docs[
          "_maybe_cast_slice_bound"
      ] = """
          This function should be overloaded in subclasses that allow non-trivial
          casting on label-slice bounds, e.g. datetime-like indices allowing
          strings containing formatted datetimes.
  
          Parameters
          ----------
          label : object
          side : {'left', 'right'}
          kind : {'ix', 'loc', 'getitem'}
  
          Returns
          -------
          label : object
  
          Notes
          -----
          Value of `side` parameter should be validated in caller.
          """
  
      @Appender(_index_shared_docs["_maybe_cast_slice_bound"])
      def _maybe_cast_slice_bound(self, label, side, kind):
          assert kind in ["ix", "loc", "getitem", None]
  
          # We are a plain index here (sub-class override this method if they
          # wish to have special treatment for floats/ints, e.g. Float64Index and
          # datetimelike Indexes
          # reject them
          if is_float(label):
              if not (kind in ["ix"] and (self.holds_integer() or self.is_floating())):
                  self._invalid_indexer("slice", label)
  
          # we are trying to find integer bounds on a non-integer based index
          # this is rejected (generally .loc gets you here)
          elif is_integer(label):
              self._invalid_indexer("slice", label)
  
          return label
  
      def _searchsorted_monotonic(self, label, side="left"):
          if self.is_monotonic_increasing:
              return self.searchsorted(label, side=side)
          elif self.is_monotonic_decreasing:
              # np.searchsorted expects ascending sort order, have to reverse
              # everything for it to work (element ordering, search side and
              # resulting value).
              pos = self[::-1].searchsorted(
                  label, side="right" if side == "left" else "left"
              )
              return len(self) - pos
  
          raise ValueError("index must be monotonic increasing or decreasing")
  
      def get_slice_bound(self, label, side, kind):
          """
          Calculate slice bound that corresponds to given label.
  
          Returns leftmost (one-past-the-rightmost if ``side=='right'``) position
          of given label.
  
          Parameters
          ----------
          label : object
          side : {'left', 'right'}
          kind : {'ix', 'loc', 'getitem'}
  
          Returns
          -------
          int
              Index of label.
          """
          assert kind in ["ix", "loc", "getitem", None]
  
          if side not in ("left", "right"):
              raise ValueError(
                  f"Invalid value for side kwarg, must be either"
                  f" 'left' or 'right': {side}"
              )
  
          original_label = label
  
          # For datetime indices label may be a string that has to be converted
          # to datetime boundary according to its resolution.
          label = self._maybe_cast_slice_bound(label, side, kind)
  
          # we need to look up the label
          try:
              slc = self.get_loc(label)
          except KeyError as err:
              try:
                  return self._searchsorted_monotonic(label, side)
              except ValueError:
                  # raise the original KeyError
                  raise err
  
          if isinstance(slc, np.ndarray):
              # get_loc may return a boolean array or an array of indices, which
              # is OK as long as they are representable by a slice.
              if is_bool_dtype(slc):
                  slc = lib.maybe_booleans_to_slice(slc.view("u1"))
              else:
                  slc = lib.maybe_indices_to_slice(slc.astype("i8"), len(self))
              if isinstance(slc, np.ndarray):
                  raise KeyError(
                      f"Cannot get {side} slice bound for non-unique "
                      f"label: {repr(original_label)}"
                  )
  
          if isinstance(slc, slice):
              if side == "left":
                  return slc.start
              else:
                  return slc.stop
          else:
              if side == "right":
                  return slc + 1
              else:
                  return slc
  
      def slice_locs(self, start=None, end=None, step=None, kind=None):
          """
          Compute slice locations for input labels.
  
          Parameters
          ----------
          start : label, default None
              If None, defaults to the beginning.
          end : label, default None
              If None, defaults to the end.
          step : int, defaults None
              If None, defaults to 1.
          kind : {'ix', 'loc', 'getitem'} or None
  
          Returns
          -------
          start, end : int
  
          See Also
          --------
          Index.get_loc : Get location for a single label.
  
          Notes
          -----
          This method only works if the index is monotonic or unique.
  
          Examples
          --------
          >>> idx = pd.Index(list('abcd'))
          >>> idx.slice_locs(start='b', end='c')
          (1, 3)
          """
          inc = step is None or step >= 0
  
          if not inc:
              # If it's a reverse slice, temporarily swap bounds.
              start, end = end, start
  
          # GH 16785: If start and end happen to be date strings with UTC offsets
          # attempt to parse and check that the offsets are the same
          if isinstance(start, (str, datetime)) and isinstance(end, (str, datetime)):
              try:
                  ts_start = Timestamp(start)
                  ts_end = Timestamp(end)
              except (ValueError, TypeError):
                  pass
              else:
                  if not tz_compare(ts_start.tzinfo, ts_end.tzinfo):
                      raise ValueError("Both dates must have the same UTC offset")
  
          start_slice = None
          if start is not None:
              start_slice = self.get_slice_bound(start, "left", kind)
          if start_slice is None:
              start_slice = 0
  
          end_slice = None
          if end is not None:
              end_slice = self.get_slice_bound(end, "right", kind)
          if end_slice is None:
              end_slice = len(self)
  
          if not inc:
              # Bounds at this moment are swapped, swap them back and shift by 1.
              #
              # slice_locs('B', 'A', step=-1): s='B', e='A'
              #
              #              s='A'                 e='B'
              # AFTER SWAP:    |                     |
              #                v ------------------> V
              #           -----------------------------------
              #           | | |A|A|A|A| | | | | |B|B| | | | |
              #           -----------------------------------
              #              ^ <------------------ ^
              # SHOULD BE:   |                     |
              #           end=s-1              start=e-1
              #
              end_slice, start_slice = start_slice - 1, end_slice - 1
  
              # i == -1 triggers ``len(self) + i`` selection that points to the
              # last element, not before-the-first one, subtracting len(self)
              # compensates that.
              if end_slice == -1:
                  end_slice -= len(self)
              if start_slice == -1:
                  start_slice -= len(self)
  
          return start_slice, end_slice
  
      def delete(self, loc):
          """
          Make new Index with passed location(-s) deleted.
  
          Returns
          -------
          new_index : Index
          """
          return self._shallow_copy(np.delete(self._data, loc))
  
      def insert(self, loc, item):
          """
          Make new Index inserting new item at location.
  
          Follows Python list.append semantics for negative values.
  
          Parameters
          ----------
          loc : int
          item : object
  
          Returns
          -------
          new_index : Index
          """
          _self = np.asarray(self)
          item = self._coerce_scalar_to_index(item)._ndarray_values
          idx = np.concatenate((_self[:loc], item, _self[loc:]))
          return self._shallow_copy_with_infer(idx)
  
      def drop(self, labels, errors="raise"):
          """
          Make new Index with passed list of labels deleted.
  
          Parameters
          ----------
          labels : array-like
          errors : {'ignore', 'raise'}, default 'raise'
              If 'ignore', suppress error and existing labels are dropped.
  
          Returns
          -------
          dropped : Index
  
          Raises
          ------
          KeyError
              If not all of the labels are found in the selected axis
          """
          arr_dtype = "object" if self.dtype == "object" else None
          labels = com.index_labels_to_array(labels, dtype=arr_dtype)
          indexer = self.get_indexer(labels)
          mask = indexer == -1
          if mask.any():
              if errors != "ignore":
                  raise KeyError(f"{labels[mask]} not found in axis")
              indexer = indexer[~mask]
          return self.delete(indexer)
  
      # --------------------------------------------------------------------
      # Generated Arithmetic, Comparison, and Unary Methods
  
      @classmethod
      def _add_comparison_methods(cls):
          """
          Add in comparison methods.
          """
          cls.__eq__ = _make_comparison_op(operator.eq, cls)
          cls.__ne__ = _make_comparison_op(operator.ne, cls)
          cls.__lt__ = _make_comparison_op(operator.lt, cls)
          cls.__gt__ = _make_comparison_op(operator.gt, cls)
          cls.__le__ = _make_comparison_op(operator.le, cls)
          cls.__ge__ = _make_comparison_op(operator.ge, cls)
  
      @classmethod
      def _add_numeric_methods_add_sub_disabled(cls):
          """
          Add in the numeric add/sub methods to disable.
          """
          cls.__add__ = make_invalid_op("__add__")
          cls.__radd__ = make_invalid_op("__radd__")
          cls.__iadd__ = make_invalid_op("__iadd__")
          cls.__sub__ = make_invalid_op("__sub__")
          cls.__rsub__ = make_invalid_op("__rsub__")
          cls.__isub__ = make_invalid_op("__isub__")
  
      @classmethod
      def _add_numeric_methods_disabled(cls):
          """
          Add in numeric methods to disable other than add/sub.
          """
          cls.__pow__ = make_invalid_op("__pow__")
          cls.__rpow__ = make_invalid_op("__rpow__")
          cls.__mul__ = make_invalid_op("__mul__")
          cls.__rmul__ = make_invalid_op("__rmul__")
          cls.__floordiv__ = make_invalid_op("__floordiv__")
          cls.__rfloordiv__ = make_invalid_op("__rfloordiv__")
          cls.__truediv__ = make_invalid_op("__truediv__")
          cls.__rtruediv__ = make_invalid_op("__rtruediv__")
          cls.__mod__ = make_invalid_op("__mod__")
          cls.__divmod__ = make_invalid_op("__divmod__")
          cls.__neg__ = make_invalid_op("__neg__")
          cls.__pos__ = make_invalid_op("__pos__")
          cls.__abs__ = make_invalid_op("__abs__")
          cls.__inv__ = make_invalid_op("__inv__")
  
      @classmethod
      def _add_numeric_methods_binary(cls):
          """
          Add in numeric methods.
          """
          cls.__add__ = _make_arithmetic_op(operator.add, cls)
          cls.__radd__ = _make_arithmetic_op(ops.radd, cls)
          cls.__sub__ = _make_arithmetic_op(operator.sub, cls)
          cls.__rsub__ = _make_arithmetic_op(ops.rsub, cls)
          cls.__rpow__ = _make_arithmetic_op(ops.rpow, cls)
          cls.__pow__ = _make_arithmetic_op(operator.pow, cls)
  
          cls.__truediv__ = _make_arithmetic_op(operator.truediv, cls)
          cls.__rtruediv__ = _make_arithmetic_op(ops.rtruediv, cls)
  
          # TODO: rmod? rdivmod?
          cls.__mod__ = _make_arithmetic_op(operator.mod, cls)
          cls.__floordiv__ = _make_arithmetic_op(operator.floordiv, cls)
          cls.__rfloordiv__ = _make_arithmetic_op(ops.rfloordiv, cls)
          cls.__divmod__ = _make_arithmetic_op(divmod, cls)
          cls.__mul__ = _make_arithmetic_op(operator.mul, cls)
          cls.__rmul__ = _make_arithmetic_op(ops.rmul, cls)
  
      @classmethod
      def _add_numeric_methods_unary(cls):
          """
          Add in numeric unary methods.
          """
  
          def _make_evaluate_unary(op, opstr):
              def _evaluate_numeric_unary(self):
  
                  attrs = self._get_attributes_dict()
                  return Index(op(self.values), **attrs)
  
              _evaluate_numeric_unary.__name__ = opstr
              return _evaluate_numeric_unary
  
          cls.__neg__ = _make_evaluate_unary(operator.neg, "__neg__")
          cls.__pos__ = _make_evaluate_unary(operator.pos, "__pos__")
          cls.__abs__ = _make_evaluate_unary(np.abs, "__abs__")
          cls.__inv__ = _make_evaluate_unary(lambda x: -x, "__inv__")
  
      @classmethod
      def _add_numeric_methods(cls):
          cls._add_numeric_methods_unary()
          cls._add_numeric_methods_binary()
  
      @classmethod
      def _add_logical_methods(cls):
          """
          Add in logical methods.
          """
          _doc = """
          %(desc)s
  
          Parameters
          ----------
          *args
              These parameters will be passed to numpy.%(outname)s.
          **kwargs
              These parameters will be passed to numpy.%(outname)s.
  
          Returns
          -------
          %(outname)s : bool or array_like (if axis is specified)
              A single element array_like may be converted to bool."""
  
          _index_shared_docs["index_all"] = dedent(
              """
  
          See Also
          --------
          Index.any : Return whether any element in an Index is True.
          Series.any : Return whether any element in a Series is True.
          Series.all : Return whether all elements in a Series are True.
  
          Notes
          -----
          Not a Number (NaN), positive infinity and negative infinity
          evaluate to True because these are not equal to zero.
  
          Examples
          --------
          **all**
  
          True, because nonzero integers are considered True.
  
          >>> pd.Index([1, 2, 3]).all()
          True
  
          False, because ``0`` is considered False.
  
          >>> pd.Index([0, 1, 2]).all()
          False
  
          **any**
  
          True, because ``1`` is considered True.
  
          >>> pd.Index([0, 0, 1]).any()
          True
  
          False, because ``0`` is considered False.
  
          >>> pd.Index([0, 0, 0]).any()
          False
          """
          )
  
          _index_shared_docs["index_any"] = dedent(
              """
  
          See Also
          --------
          Index.all : Return whether all elements are True.
          Series.all : Return whether all elements are True.
  
          Notes
          -----
          Not a Number (NaN), positive infinity and negative infinity
          evaluate to True because these are not equal to zero.
  
          Examples
          --------
          >>> index = pd.Index([0, 1, 2])
          >>> index.any()
          True
  
          >>> index = pd.Index([0, 0, 0])
          >>> index.any()
          False
          """
          )
  
          def _make_logical_function(name, desc, f):
              @Substitution(outname=name, desc=desc)
              @Appender(_index_shared_docs["index_" + name])
              @Appender(_doc)
              def logical_func(self, *args, **kwargs):
                  result = f(self.values)
                  if (
                      isinstance(result, (np.ndarray, ABCSeries, Index))
                      and result.ndim == 0
                  ):
                      # return NumPy type
                      return result.dtype.type(result.item())
                  else:  # pragma: no cover
                      return result
  
              logical_func.__name__ = name
              return logical_func
  
          cls.all = _make_logical_function(
              "all", "Return whether all elements are True.", np.all
          )
          cls.any = _make_logical_function(
              "any", "Return whether any element is True.", np.any
          )
  
      @classmethod
      def _add_logical_methods_disabled(cls):
          """
          Add in logical methods to disable.
          """
          cls.all = make_invalid_op("all")
          cls.any = make_invalid_op("any")
  
      @property
      def shape(self):
          """
          Return a tuple of the shape of the underlying data.
          """
          # not using "(len(self), )" to return "correct" shape if the values
          # consists of a >1 D array (see GH-27775)
          # overridden in MultiIndex.shape to avoid materializing the values
          return self._values.shape
  
  
  Index._add_numeric_methods_disabled()
  Index._add_logical_methods()
  Index._add_comparison_methods()
  
  
  def ensure_index_from_sequences(sequences, names=None):
      """
      Construct an index from sequences of data.
  
      A single sequence returns an Index. Many sequences returns a
      MultiIndex.
  
      Parameters
      ----------
      sequences : sequence of sequences
      names : sequence of str
  
      Returns
      -------
      index : Index or MultiIndex
  
      Examples
      --------
      >>> ensure_index_from_sequences([[1, 2, 3]], names=['name'])
      Int64Index([1, 2, 3], dtype='int64', name='name')
  
      >>> ensure_index_from_sequences([['a', 'a'], ['a', 'b']],
                                      names=['L1', 'L2'])
      MultiIndex([('a', 'a'),
                  ('a', 'b')],
                 names=['L1', 'L2'])
  
      See Also
      --------
      ensure_index
      """
      from .multi import MultiIndex
  
      if len(sequences) == 1:
          if names is not None:
              names = names[0]
          return Index(sequences[0], name=names)
      else:
          return MultiIndex.from_arrays(sequences, names=names)
  
  
  def ensure_index(index_like, copy=False):
      """
      Ensure that we have an index from some index-like object.
  
      Parameters
      ----------
      index : sequence
          An Index or other sequence
      copy : bool
  
      Returns
      -------
      index : Index or MultiIndex
  
      Examples
      --------
      >>> ensure_index(['a', 'b'])
      Index(['a', 'b'], dtype='object')
  
      >>> ensure_index([('a', 'a'),  ('b', 'c')])
      Index([('a', 'a'), ('b', 'c')], dtype='object')
  
      >>> ensure_index([['a', 'a'], ['b', 'c']])
      MultiIndex([('a', 'b'),
                  ('a', 'c')],
                 dtype='object')
                 )
  
      See Also
      --------
      ensure_index_from_sequences
      """
      if isinstance(index_like, Index):
          if copy:
              index_like = index_like.copy()
          return index_like
      if hasattr(index_like, "name"):
          return Index(index_like, name=index_like.name, copy=copy)
  
      if is_iterator(index_like):
          index_like = list(index_like)
  
      # must check for exactly list here because of strict type
      # check in clean_index_list
      if isinstance(index_like, list):
          if type(index_like) != list:
              index_like = list(index_like)
  
          converted, all_arrays = lib.clean_index_list(index_like)
  
          if len(converted) > 0 and all_arrays:
              from .multi import MultiIndex
  
              return MultiIndex.from_arrays(converted)
          else:
              index_like = converted
      else:
          # clean_index_list does the equivalent of copying
          # so only need to do this if not list instance
          if copy:
              from copy import copy
  
              index_like = copy(index_like)
  
      return Index(index_like)
  
  
  def _ensure_has_len(seq):
      """
      If seq is an iterator, put its values into a list.
      """
      try:
          len(seq)
      except TypeError:
          return list(seq)
      else:
          return seq
  
  
  def _trim_front(strings):
      """
      Trims zeros and decimal points.
      """
      trimmed = strings
      while len(strings) > 0 and all(x[0] == " " for x in trimmed):
          trimmed = [x[1:] for x in trimmed]
      return trimmed
  
  
  def _validate_join_method(method):
      if method not in ["left", "right", "inner", "outer"]:
          raise ValueError(f"do not recognize join method {method}")
  
  
  def default_index(n):
      from pandas.core.indexes.range import RangeIndex
  
      return RangeIndex(0, n, name=None)
  
  
  def maybe_extract_name(name, obj, cls) -> Optional[Hashable]:
      """
      If no name is passed, then extract it from data, validating hashability.
      """
      if name is None and isinstance(obj, (Index, ABCSeries)):
          # Note we don't just check for "name" attribute since that would
          #  pick up e.g. dtype.name
          name = obj.name
  
      # GH#29069
      if not is_hashable(name):
          raise TypeError(f"{cls.__name__}.name must be a hashable type")
  
      return name
  
  
  def _maybe_cast_with_dtype(data: np.ndarray, dtype: np.dtype, copy: bool) -> np.ndarray:
      """
      If a dtype is passed, cast to the closest matching dtype that is supported
      by Index.
  
      Parameters
      ----------
      data : np.ndarray
      dtype : np.dtype
      copy : bool
  
      Returns
      -------
      np.ndarray
      """
      # we need to avoid having numpy coerce
      # things that look like ints/floats to ints unless
      # they are actually ints, e.g. '0' and 0.0
      # should not be coerced
      # GH 11836
      if is_integer_dtype(dtype):
          inferred = lib.infer_dtype(data, skipna=False)
          if inferred == "integer":
              data = maybe_cast_to_integer_array(data, dtype, copy=copy)
          elif inferred in ["floating", "mixed-integer-float"]:
              if isna(data).any():
                  raise ValueError("cannot convert float NaN to integer")
  
              if inferred == "mixed-integer-float":
                  data = maybe_cast_to_integer_array(data, dtype)
  
              # If we are actually all equal to integers,
              # then coerce to integer.
              try:
                  data = _try_convert_to_int_array(data, copy, dtype)
              except ValueError:
                  data = np.array(data, dtype=np.float64, copy=copy)
  
          elif inferred == "string":
              pass
          else:
              data = data.astype(dtype)
      elif is_float_dtype(dtype):
          inferred = lib.infer_dtype(data, skipna=False)
          if inferred == "string":
              pass
          else:
              data = data.astype(dtype)
      else:
          data = np.array(data, dtype=dtype, copy=copy)
  
      return data
  
  
  def _maybe_cast_data_without_dtype(subarr):
      """
      If we have an arraylike input but no passed dtype, try to infer
      a supported dtype.
  
      Parameters
      ----------
      subarr : np.ndarray, Index, or Series
  
      Returns
      -------
      converted : np.ndarray or ExtensionArray
      dtype : np.dtype or ExtensionDtype
      """
      # Runtime import needed bc IntervalArray imports Index
      from pandas.core.arrays import (
          IntervalArray,
          PeriodArray,
          DatetimeArray,
          TimedeltaArray,
      )
  
      inferred = lib.infer_dtype(subarr, skipna=False)
  
      if inferred == "integer":
          try:
              data = _try_convert_to_int_array(subarr, False, None)
              return data, data.dtype
          except ValueError:
              pass
  
          return subarr, object
  
      elif inferred in ["floating", "mixed-integer-float", "integer-na"]:
          # TODO: Returns IntegerArray for integer-na case in the future
          return subarr, np.float64
  
      elif inferred == "interval":
          try:
              data = IntervalArray._from_sequence(subarr, copy=False)
              return data, data.dtype
          except ValueError:
              # GH27172: mixed closed Intervals --> object dtype
              pass
      elif inferred == "boolean":
          # don't support boolean explicitly ATM
          pass
      elif inferred != "string":
          if inferred.startswith("datetime"):
              try:
                  data = DatetimeArray._from_sequence(subarr, copy=False)
                  return data, data.dtype
              except (ValueError, OutOfBoundsDatetime):
                  # GH 27011
                  # If we have mixed timezones, just send it
                  # down the base constructor
                  pass
  
          elif inferred.startswith("timedelta"):
              data = TimedeltaArray._from_sequence(subarr, copy=False)
              return data, data.dtype
          elif inferred == "period":
              try:
                  data = PeriodArray._from_sequence(subarr)
                  return data, data.dtype
              except IncompatibleFrequency:
                  pass
  
      return subarr, subarr.dtype
  
  
  def _try_convert_to_int_array(
      data: np.ndarray, copy: bool, dtype: np.dtype
  ) -> np.ndarray:
      """
      Attempt to convert an array of data into an integer array.
  
      Parameters
      ----------
      data : The data to convert.
      copy : bool
          Whether to copy the data or not.
      dtype : np.dtype
  
      Returns
      -------
      int_array : data converted to either an ndarray[int64] or ndarray[uint64]
  
      Raises
      ------
      ValueError if the conversion was not successful.
      """
  
      if not is_unsigned_integer_dtype(dtype):
          # skip int64 conversion attempt if uint-like dtype is passed, as
          # this could return Int64Index when UInt64Index is what's desired
          try:
              res = data.astype("i8", copy=False)
              if (res == data).all():
                  return res  # TODO: might still need to copy
          except (OverflowError, TypeError, ValueError):
              pass
  
      # Conversion to int64 failed (possibly due to overflow) or was skipped,
      # so let's try now with uint64.
      try:
          res = data.astype("u8", copy=False)
          if (res == data).all():
              return res  # TODO: might still need to copy
      except (OverflowError, TypeError, ValueError):
          pass
  
      raise ValueError
  