text: """
  Base and utility classes for pandas objects.
  """
  
  import builtins
  import textwrap
  from typing import Any, Callable, Dict, FrozenSet, List, Optional, Union, cast
  
  import numpy as np
  
  import pandas._libs.lib as lib
  from pandas._typing import AggFuncType, AggFuncTypeBase, IndexLabel, Label
  from pandas.compat import PYPY
  from pandas.compat.numpy import function as nv
  from pandas.errors import AbstractMethodError
  from pandas.util._decorators import cache_readonly, doc
  
  from pandas.core.dtypes.cast import is_nested_object
  from pandas.core.dtypes.common import (
      is_categorical_dtype,
      is_dict_like,
      is_extension_array_dtype,
      is_list_like,
      is_object_dtype,
      is_scalar,
  )
  from pandas.core.dtypes.generic import ABCDataFrame, ABCIndexClass, ABCSeries
  from pandas.core.dtypes.missing import isna
  
  from pandas.core import algorithms, common as com
  from pandas.core.accessor import DirNamesMixin
  from pandas.core.algorithms import duplicated, unique1d, value_counts
  from pandas.core.arrays import ExtensionArray
  from pandas.core.construction import create_series_with_explicit_dtype
  import pandas.core.nanops as nanops
  
  _shared_docs: Dict[str, str] = dict()
  _indexops_doc_kwargs = dict(
      klass="IndexOpsMixin",
      inplace="",
      unique="IndexOpsMixin",
      duplicated="IndexOpsMixin",
  )
  
  
  class PandasObject(DirNamesMixin):
      """
      Baseclass for various pandas objects.
      """
  
      _cache: Dict[str, Any]
  
      @property
      def _constructor(self):
          """
          Class constructor (for this class it's just `__class__`.
          """
          return type(self)
  
      def __repr__(self) -> str:
          """
          Return a string representation for a particular object.
          """
          # Should be overwritten by base classes
          return object.__repr__(self)
  
      def _reset_cache(self, key: Optional[str] = None) -> None:
          """
          Reset cached properties. If ``key`` is passed, only clears that key.
          """
          if getattr(self, "_cache", None) is None:
              return
          if key is None:
              self._cache.clear()
          else:
              self._cache.pop(key, None)
  
      def __sizeof__(self):
          """
          Generates the total memory usage for an object that returns
          either a value or Series of values
          """
          if hasattr(self, "memory_usage"):
              mem = self.memory_usage(deep=True)
              return int(mem if is_scalar(mem) else mem.sum())
  
          # no memory_usage attribute, so fall back to object's 'sizeof'
          return super().__sizeof__()
  
  
  class NoNewAttributesMixin:
      """
      Mixin which prevents adding new attributes.
  
      Prevents additional attributes via xxx.attribute = "something" after a
      call to `self.__freeze()`. Mainly used to prevent the user from using
      wrong attributes on an accessor (`Series.cat/.str/.dt`).
  
      If you really want to add a new attribute at a later time, you need to use
      `object.__setattr__(self, key, value)`.
      """
  
      def _freeze(self):
          """
          Prevents setting additional attributes.
          """
          object.__setattr__(self, "__frozen", True)
  
      # prevent adding any attribute via s.xxx.new_attribute = ...
      def __setattr__(self, key: str, value):
          # _cache is used by a decorator
          # We need to check both 1.) cls.__dict__ and 2.) getattr(self, key)
          # because
          # 1.) getattr is false for attributes that raise errors
          # 2.) cls.__dict__ doesn't traverse into base classes
          if getattr(self, "__frozen", False) and not (
              key == "_cache"
              or key in type(self).__dict__
              or getattr(self, key, None) is not None
          ):
              raise AttributeError(f"You cannot add any new attribute '{key}'")
          object.__setattr__(self, key, value)
  
  
  class DataError(Exception):
      pass
  
  
  class SpecificationError(Exception):
      pass
  
  
  class SelectionMixin:
      """
      mixin implementing the selection & aggregation interface on a group-like
      object sub-classes need to define: obj, exclusions
      """
  
      _selection: Optional[IndexLabel] = None
      _internal_names = ["_cache", "__setstate__"]
      _internal_names_set = set(_internal_names)
  
      _builtin_table = {builtins.sum: np.sum, builtins.max: np.max, builtins.min: np.min}
  
      _cython_table = {
          builtins.sum: "sum",
          builtins.max: "max",
          builtins.min: "min",
          np.all: "all",
          np.any: "any",
          np.sum: "sum",
          np.nansum: "sum",
          np.mean: "mean",
          np.nanmean: "mean",
          np.prod: "prod",
          np.nanprod: "prod",
          np.std: "std",
          np.nanstd: "std",
          np.var: "var",
          np.nanvar: "var",
          np.median: "median",
          np.nanmedian: "median",
          np.max: "max",
          np.nanmax: "max",
          np.min: "min",
          np.nanmin: "min",
          np.cumprod: "cumprod",
          np.nancumprod: "cumprod",
          np.cumsum: "cumsum",
          np.nancumsum: "cumsum",
      }
  
      @property
      def _selection_name(self):
          """
          Return a name for myself;
  
          This would ideally be called the 'name' property,
          but we cannot conflict with the Series.name property which can be set.
          """
          return self._selection
  
      @property
      def _selection_list(self):
          if not isinstance(
              self._selection, (list, tuple, ABCSeries, ABCIndexClass, np.ndarray)
          ):
              return [self._selection]
          return self._selection
  
      @cache_readonly
      def _selected_obj(self):
          if self._selection is None or isinstance(self.obj, ABCSeries):
              return self.obj
          else:
              return self.obj[self._selection]
  
      @cache_readonly
      def ndim(self) -> int:
          return self._selected_obj.ndim
  
      @cache_readonly
      def _obj_with_exclusions(self):
          if self._selection is not None and isinstance(self.obj, ABCDataFrame):
              return self.obj.reindex(columns=self._selection_list)
  
          if len(self.exclusions) > 0:
              return self.obj.drop(self.exclusions, axis=1)
          else:
              return self.obj
  
      def __getitem__(self, key):
          if self._selection is not None:
              raise IndexError(f"Column(s) {self._selection} already selected")
  
          if isinstance(key, (list, tuple, ABCSeries, ABCIndexClass, np.ndarray)):
              if len(self.obj.columns.intersection(key)) != len(key):
                  bad_keys = list(set(key).difference(self.obj.columns))
                  raise KeyError(f"Columns not found: {str(bad_keys)[1:-1]}")
              return self._gotitem(list(key), ndim=2)
  
          elif not getattr(self, "as_index", False):
              if key not in self.obj.columns:
                  raise KeyError(f"Column not found: {key}")
              return self._gotitem(key, ndim=2)
  
          else:
              if key not in self.obj:
                  raise KeyError(f"Column not found: {key}")
              return self._gotitem(key, ndim=1)
  
      def _gotitem(self, key, ndim: int, subset=None):
          """
          sub-classes to define
          return a sliced object
  
          Parameters
          ----------
          key : str / list of selections
          ndim : 1,2
              requested ndim of result
          subset : object, default None
              subset to act on
          """
          raise AbstractMethodError(self)
  
      def aggregate(self, func, *args, **kwargs):
          raise AbstractMethodError(self)
  
      agg = aggregate
  
      def _try_aggregate_string_function(self, arg: str, *args, **kwargs):
          """
          if arg is a string, then try to operate on it:
          - try to find a function (or attribute) on ourselves
          - try to find a numpy function
          - raise
          """
          assert isinstance(arg, str)
  
          f = getattr(self, arg, None)
          if f is not None:
              if callable(f):
                  return f(*args, **kwargs)
  
              # people may try to aggregate on a non-callable attribute
              # but don't let them think they can pass args to it
              assert len(args) == 0
              assert len([kwarg for kwarg in kwargs if kwarg not in ["axis"]]) == 0
              return f
  
          f = getattr(np, arg, None)
          if f is not None:
              if hasattr(self, "__array__"):
                  # in particular exclude Window
                  return f(self, *args, **kwargs)
  
          raise AttributeError(
              f"'{arg}' is not a valid function for '{type(self).__name__}' object"
          )
  
      def _aggregate(self, arg: AggFuncType, *args, **kwargs):
          """
          provide an implementation for the aggregators
  
          Parameters
          ----------
          arg : string, dict, function
          *args : args to pass on to the function
          **kwargs : kwargs to pass on to the function
  
          Returns
          -------
          tuple of result, how
  
          Notes
          -----
          how can be a string describe the required post-processing, or
          None if not required
          """
          is_aggregator = lambda x: isinstance(x, (list, tuple, dict))
  
          _axis = kwargs.pop("_axis", None)
          if _axis is None:
              _axis = getattr(self, "axis", 0)
  
          if isinstance(arg, str):
              return self._try_aggregate_string_function(arg, *args, **kwargs), None
  
          if isinstance(arg, dict):
              # aggregate based on the passed dict
              if _axis != 0:  # pragma: no cover
                  raise ValueError("Can only pass dict with axis=0")
  
              selected_obj = self._selected_obj
  
              # if we have a dict of any non-scalars
              # eg. {'A' : ['mean']}, normalize all to
              # be list-likes
              if any(is_aggregator(x) for x in arg.values()):
                  new_arg: Dict[Label, Union[AggFuncTypeBase, List[AggFuncTypeBase]]] = {}
                  for k, v in arg.items():
                      if not isinstance(v, (tuple, list, dict)):
                          new_arg[k] = [v]
                      else:
                          new_arg[k] = v
  
                      # the keys must be in the columns
                      # for ndim=2, or renamers for ndim=1
  
                      # ok for now, but deprecated
                      # {'A': { 'ra': 'mean' }}
                      # {'A': { 'ra': ['mean'] }}
                      # {'ra': ['mean']}
  
                      # not ok
                      # {'ra' : { 'A' : 'mean' }}
                      if isinstance(v, dict):
                          raise SpecificationError("nested renamer is not supported")
                      elif isinstance(selected_obj, ABCSeries):
                          raise SpecificationError("nested renamer is not supported")
                      elif (
                          isinstance(selected_obj, ABCDataFrame)
                          and k not in selected_obj.columns
                      ):
                          raise KeyError(f"Column '{k}' does not exist!")
  
                  arg = new_arg
  
              else:
                  # deprecation of renaming keys
                  # GH 15931
                  keys = list(arg.keys())
                  if isinstance(selected_obj, ABCDataFrame) and len(
                      selected_obj.columns.intersection(keys)
                  ) != len(keys):
                      cols = sorted(
                          set(keys) - set(selected_obj.columns.intersection(keys))
                      )
                      raise SpecificationError(f"Column(s) {cols} do not exist")
  
              from pandas.core.reshape.concat import concat
  
              def _agg_1dim(name, how, subset=None):
                  """
                  aggregate a 1-dim with how
                  """
                  colg = self._gotitem(name, ndim=1, subset=subset)
                  if colg.ndim != 1:
                      raise SpecificationError(
                          "nested dictionary is ambiguous in aggregation"
                      )
                  return colg.aggregate(how)
  
              def _agg_2dim(how):
                  """
                  aggregate a 2-dim with how
                  """
                  colg = self._gotitem(self._selection, ndim=2, subset=selected_obj)
                  return colg.aggregate(how)
  
              def _agg(arg, func):
                  """
                  run the aggregations over the arg with func
                  return a dict
                  """
                  result = {}
                  for fname, agg_how in arg.items():
                      result[fname] = func(fname, agg_how)
                  return result
  
              # set the final keys
              keys = list(arg.keys())
  
              if self._selection is not None:
  
                  sl = set(self._selection_list)
  
                  # we are a Series like object,
                  # but may have multiple aggregations
                  if len(sl) == 1:
  
                      result = _agg(
                          arg, lambda fname, agg_how: _agg_1dim(self._selection, agg_how)
                      )
  
                  # we are selecting the same set as we are aggregating
                  elif not len(sl - set(keys)):
  
                      result = _agg(arg, _agg_1dim)
  
                  # we are a DataFrame, with possibly multiple aggregations
                  else:
  
                      result = _agg(arg, _agg_2dim)
  
              # no selection
              else:
  
                  try:
                      result = _agg(arg, _agg_1dim)
                  except SpecificationError:
  
                      # we are aggregating expecting all 1d-returns
                      # but we have 2d
                      result = _agg(arg, _agg_2dim)
  
              # combine results
  
              def is_any_series() -> bool:
                  # return a boolean if we have *any* nested series
                  return any(isinstance(r, ABCSeries) for r in result.values())
  
              def is_any_frame() -> bool:
                  # return a boolean if we have *any* nested series
                  return any(isinstance(r, ABCDataFrame) for r in result.values())
  
              if isinstance(result, list):
                  return concat(result, keys=keys, axis=1, sort=True), True
  
              elif is_any_frame():
                  # we have a dict of DataFrames
                  # return a MI DataFrame
  
                  keys_to_use = [k for k in keys if not result[k].empty]
                  # Have to check, if at least one DataFrame is not empty.
                  keys_to_use = keys_to_use if keys_to_use != [] else keys
                  return (
                      concat([result[k] for k in keys_to_use], keys=keys_to_use, axis=1),
                      True,
                  )
  
              elif isinstance(self, ABCSeries) and is_any_series():
  
                  # we have a dict of Series
                  # return a MI Series
                  try:
                      result = concat(result)
                  except TypeError as err:
                      # we want to give a nice error here if
                      # we have non-same sized objects, so
                      # we don't automatically broadcast
  
                      raise ValueError(
                          "cannot perform both aggregation "
                          "and transformation operations "
                          "simultaneously"
                      ) from err
  
                  return result, True
  
              # fall thru
              from pandas import DataFrame, Series
  
              try:
                  result = DataFrame(result)
              except ValueError:
                  # we have a dict of scalars
  
                  # GH 36212 use name only if self is a series
                  if self.ndim == 1:
                      self = cast("Series", self)
                      name = self.name
                  else:
                      name = None
  
                  result = Series(result, name=name)
  
              return result, True
          elif is_list_like(arg):
              # we require a list, but not an 'str'
              return self._aggregate_multiple_funcs(arg, _axis=_axis), None
          else:
              result = None
  
          if callable(arg):
              f = self._get_cython_func(arg)
              if f and not args and not kwargs:
                  return getattr(self, f)(), None
  
          # caller can react
          return result, True
  
      def _aggregate_multiple_funcs(self, arg, _axis):
          from pandas.core.reshape.concat import concat
  
          if _axis != 0:
              raise NotImplementedError("axis other than 0 is not supported")
  
          if self._selected_obj.ndim == 1:
              selected_obj = self._selected_obj
          else:
              selected_obj = self._obj_with_exclusions
  
          results = []
          keys = []
  
          # degenerate case
          if selected_obj.ndim == 1:
              for a in arg:
                  colg = self._gotitem(selected_obj.name, ndim=1, subset=selected_obj)
                  try:
                      new_res = colg.aggregate(a)
  
                  except TypeError:
                      pass
                  else:
                      results.append(new_res)
  
                      # make sure we find a good name
                      name = com.get_callable_name(a) or a
                      keys.append(name)
  
          # multiples
          else:
              for index, col in enumerate(selected_obj):
                  colg = self._gotitem(col, ndim=1, subset=selected_obj.iloc[:, index])
                  try:
                      new_res = colg.aggregate(arg)
                  except (TypeError, DataError):
                      pass
                  except ValueError as err:
                      # cannot aggregate
                      if "Must produce aggregated value" in str(err):
                          # raised directly in _aggregate_named
                          pass
                      elif "no results" in str(err):
                          # raised directly in _aggregate_multiple_funcs
                          pass
                      else:
                          raise
                  else:
                      results.append(new_res)
                      keys.append(col)
  
          # if we are empty
          if not len(results):
              raise ValueError("no results")
  
          try:
              return concat(results, keys=keys, axis=1, sort=False)
          except TypeError as err:
  
              # we are concatting non-NDFrame objects,
              # e.g. a list of scalars
  
              from pandas import Series
  
              result = Series(results, index=keys, name=self.name)
              if is_nested_object(result):
                  raise ValueError(
                      "cannot combine transform and aggregation operations"
                  ) from err
              return result
  
      def _get_cython_func(self, arg: Callable) -> Optional[str]:
          """
          if we define an internal function for this argument, return it
          """
          return self._cython_table.get(arg)
  
      def _is_builtin_func(self, arg):
          """
          if we define an builtin function for this argument, return it,
          otherwise return the arg
          """
          return self._builtin_table.get(arg, arg)
  
  
  class IndexOpsMixin:
      """
      Common ops mixin to support a unified interface / docs for Series / Index
      """
  
      # ndarray compatibility
      __array_priority__ = 1000
      _deprecations: FrozenSet[str] = frozenset(
          ["tolist"]  # tolist is not deprecated, just suppressed in the __dir__
      )
  
      @property
      def _values(self) -> Union[ExtensionArray, np.ndarray]:
          # must be defined here as a property for mypy
          raise AbstractMethodError(self)
  
      def transpose(self, *args, **kwargs):
          """
          Return the transpose, which is by definition self.
  
          Returns
          -------
          %(klass)s
          """
          nv.validate_transpose(args, kwargs)
          return self
  
      T = property(
          transpose,
          doc="""
          Return the transpose, which is by definition self.
          """,
      )
  
      @property
      def shape(self):
          """
          Return a tuple of the shape of the underlying data.
          """
          return self._values.shape
  
      def __len__(self) -> int:
          # We need this defined here for mypy
          raise AbstractMethodError(self)
  
      @property
      def ndim(self) -> int:
          """
          Number of dimensions of the underlying data, by definition 1.
          """
          return 1
  
      def item(self):
          """
          Return the first element of the underlying data as a python scalar.
  
          Returns
          -------
          scalar
              The first element of %(klass)s.
  
          Raises
          ------
          ValueError
              If the data is not length-1.
          """
          if len(self) == 1:
              return next(iter(self))
          raise ValueError("can only convert an array of size 1 to a Python scalar")
  
      @property
      def nbytes(self) -> int:
          """
          Return the number of bytes in the underlying data.
          """
          return self._values.nbytes
  
      @property
      def size(self) -> int:
          """
          Return the number of elements in the underlying data.
          """
          return len(self._values)
  
      @property
      def array(self) -> ExtensionArray:
          """
          The ExtensionArray of the data backing this Series or Index.
  
          .. versionadded:: 0.24.0
  
          Returns
          -------
          ExtensionArray
              An ExtensionArray of the values stored within. For extension
              types, this is the actual array. For NumPy native types, this
              is a thin (no copy) wrapper around :class:`numpy.ndarray`.
  
              ``.array`` differs ``.values`` which may require converting the
              data to a different form.
  
          See Also
          --------
          Index.to_numpy : Similar method that always returns a NumPy array.
          Series.to_numpy : Similar method that always returns a NumPy array.
  
          Notes
          -----
          This table lays out the different array types for each extension
          dtype within pandas.
  
          ================== =============================
          dtype              array type
          ================== =============================
          category           Categorical
          period             PeriodArray
          interval           IntervalArray
          IntegerNA          IntegerArray
          string             StringArray
          boolean            BooleanArray
          datetime64[ns, tz] DatetimeArray
          ================== =============================
  
          For any 3rd-party extension types, the array type will be an
          ExtensionArray.
  
          For all remaining dtypes ``.array`` will be a
          :class:`arrays.NumpyExtensionArray` wrapping the actual ndarray
          stored within. If you absolutely need a NumPy array (possibly with
          copying / coercing data), then use :meth:`Series.to_numpy` instead.
  
          Examples
          --------
          For regular NumPy types like int, and float, a PandasArray
          is returned.
  
          >>> pd.Series([1, 2, 3]).array
          <PandasArray>
          [1, 2, 3]
          Length: 3, dtype: int64
  
          For extension types, like Categorical, the actual ExtensionArray
          is returned
  
          >>> ser = pd.Series(pd.Categorical(['a', 'b', 'a']))
          >>> ser.array
          ['a', 'b', 'a']
          Categories (2, object): ['a', 'b']
          """
          raise AbstractMethodError(self)
  
      def to_numpy(self, dtype=None, copy=False, na_value=lib.no_default, **kwargs):
          """
          A NumPy ndarray representing the values in this Series or Index.
  
          .. versionadded:: 0.24.0
  
          Parameters
          ----------
          dtype : str or numpy.dtype, optional
              The dtype to pass to :meth:`numpy.asarray`.
          copy : bool, default False
              Whether to ensure that the returned value is not a view on
              another array. Note that ``copy=False`` does not *ensure* that
              ``to_numpy()`` is no-copy. Rather, ``copy=True`` ensure that
              a copy is made, even if not strictly necessary.
          na_value : Any, optional
              The value to use for missing values. The default value depends
              on `dtype` and the type of the array.
  
              .. versionadded:: 1.0.0
  
          **kwargs
              Additional keywords passed through to the ``to_numpy`` method
              of the underlying array (for extension arrays).
  
              .. versionadded:: 1.0.0
  
          Returns
          -------
          numpy.ndarray
  
          See Also
          --------
          Series.array : Get the actual data stored within.
          Index.array : Get the actual data stored within.
          DataFrame.to_numpy : Similar method for DataFrame.
  
          Notes
          -----
          The returned array will be the same up to equality (values equal
          in `self` will be equal in the returned array; likewise for values
          that are not equal). When `self` contains an ExtensionArray, the
          dtype may be different. For example, for a category-dtype Series,
          ``to_numpy()`` will return a NumPy array and the categorical dtype
          will be lost.
  
          For NumPy dtypes, this will be a reference to the actual data stored
          in this Series or Index (assuming ``copy=False``). Modifying the result
          in place will modify the data stored in the Series or Index (not that
          we recommend doing that).
  
          For extension types, ``to_numpy()`` *may* require copying data and
          coercing the result to a NumPy type (possibly object), which may be
          expensive. When you need a no-copy reference to the underlying data,
          :attr:`Series.array` should be used instead.
  
          This table lays out the different dtypes and default return types of
          ``to_numpy()`` for various dtypes within pandas.
  
          ================== ================================
          dtype              array type
          ================== ================================
          category[T]        ndarray[T] (same dtype as input)
          period             ndarray[object] (Periods)
          interval           ndarray[object] (Intervals)
          IntegerNA          ndarray[object]
          datetime64[ns]     datetime64[ns]
          datetime64[ns, tz] ndarray[object] (Timestamps)
          ================== ================================
  
          Examples
          --------
          >>> ser = pd.Series(pd.Categorical(['a', 'b', 'a']))
          >>> ser.to_numpy()
          array(['a', 'b', 'a'], dtype=object)
  
          Specify the `dtype` to control how datetime-aware data is represented.
          Use ``dtype=object`` to return an ndarray of pandas :class:`Timestamp`
          objects, each with the correct ``tz``.
  
          >>> ser = pd.Series(pd.date_range('2000', periods=2, tz="CET"))
          >>> ser.to_numpy(dtype=object)
          array([Timestamp('2000-01-01 00:00:00+0100', tz='CET', freq='D'),
                 Timestamp('2000-01-02 00:00:00+0100', tz='CET', freq='D')],
                dtype=object)
  
          Or ``dtype='datetime64[ns]'`` to return an ndarray of native
          datetime64 values. The values are converted to UTC and the timezone
          info is dropped.
  
          >>> ser.to_numpy(dtype="datetime64[ns]")
          ... # doctest: +ELLIPSIS
          array(['1999-12-31T23:00:00.000000000', '2000-01-01T23:00:00...'],
                dtype='datetime64[ns]')
          """
          if is_extension_array_dtype(self.dtype):
              return self.array.to_numpy(dtype, copy=copy, na_value=na_value, **kwargs)
          elif kwargs:
              bad_keys = list(kwargs.keys())[0]
              raise TypeError(
                  f"to_numpy() got an unexpected keyword argument '{bad_keys}'"
              )
  
          result = np.asarray(self._values, dtype=dtype)
          # TODO(GH-24345): Avoid potential double copy
          if copy or na_value is not lib.no_default:
              result = result.copy()
              if na_value is not lib.no_default:
                  result[self.isna()] = na_value
          return result
  
      @property
      def empty(self):
          return not self.size
  
      def max(self, axis=None, skipna=True, *args, **kwargs):
          """
          Return the maximum value of the Index.
  
          Parameters
          ----------
          axis : int, optional
              For compatibility with NumPy. Only 0 or None are allowed.
          skipna : bool, default True
              Exclude NA/null values when showing the result.
          *args, **kwargs
              Additional arguments and keywords for compatibility with NumPy.
  
          Returns
          -------
          scalar
              Maximum value.
  
          See Also
          --------
          Index.min : Return the minimum value in an Index.
          Series.max : Return the maximum value in a Series.
          DataFrame.max : Return the maximum values in a DataFrame.
  
          Examples
          --------
          >>> idx = pd.Index([3, 2, 1])
          >>> idx.max()
          3
  
          >>> idx = pd.Index(['c', 'b', 'a'])
          >>> idx.max()
          'c'
  
          For a MultiIndex, the maximum is determined lexicographically.
  
          >>> idx = pd.MultiIndex.from_product([('a', 'b'), (2, 1)])
          >>> idx.max()
          ('b', 2)
          """
          nv.validate_minmax_axis(axis)
          nv.validate_max(args, kwargs)
          return nanops.nanmax(self._values, skipna=skipna)
  
      @doc(op="max", oppose="min", value="largest")
      def argmax(self, axis=None, skipna=True, *args, **kwargs):
          """
          Return int position of the {value} value in the Series.
  
          If the {op}imum is achieved in multiple locations,
          the first row position is returned.
  
          Parameters
          ----------
          axis : {{None}}
              Dummy argument for consistency with Series.
          skipna : bool, default True
              Exclude NA/null values when showing the result.
          *args, **kwargs
              Additional arguments and keywords for compatibility with NumPy.
  
          Returns
          -------
          int
              Row position of the {op}imum value.
  
          See Also
          --------
          Series.arg{op} : Return position of the {op}imum value.
          Series.arg{oppose} : Return position of the {oppose}imum value.
          numpy.ndarray.arg{op} : Equivalent method for numpy arrays.
          Series.idxmax : Return index label of the maximum values.
          Series.idxmin : Return index label of the minimum values.
  
          Examples
          --------
          Consider dataset containing cereal calories
  
          >>> s = pd.Series({{'Corn Flakes': 100.0, 'Almond Delight': 110.0,
          ...                'Cinnamon Toast Crunch': 120.0, 'Cocoa Puff': 110.0}})
          >>> s
          Corn Flakes              100.0
          Almond Delight           110.0
          Cinnamon Toast Crunch    120.0
          Cocoa Puff               110.0
          dtype: float64
  
          >>> s.argmax()
          2
          >>> s.argmin()
          0
  
          The maximum cereal calories is the third element and
          the minimum cereal calories is the first element,
          since series is zero-indexed.
          """
          nv.validate_minmax_axis(axis)
          nv.validate_argmax_with_skipna(skipna, args, kwargs)
          return nanops.nanargmax(self._values, skipna=skipna)
  
      def min(self, axis=None, skipna=True, *args, **kwargs):
          """
          Return the minimum value of the Index.
  
          Parameters
          ----------
          axis : {None}
              Dummy argument for consistency with Series.
          skipna : bool, default True
              Exclude NA/null values when showing the result.
          *args, **kwargs
              Additional arguments and keywords for compatibility with NumPy.
  
          Returns
          -------
          scalar
              Minimum value.
  
          See Also
          --------
          Index.max : Return the maximum value of the object.
          Series.min : Return the minimum value in a Series.
          DataFrame.min : Return the minimum values in a DataFrame.
  
          Examples
          --------
          >>> idx = pd.Index([3, 2, 1])
          >>> idx.min()
          1
  
          >>> idx = pd.Index(['c', 'b', 'a'])
          >>> idx.min()
          'a'
  
          For a MultiIndex, the minimum is determined lexicographically.
  
          >>> idx = pd.MultiIndex.from_product([('a', 'b'), (2, 1)])
          >>> idx.min()
          ('a', 1)
          """
          nv.validate_minmax_axis(axis)
          nv.validate_min(args, kwargs)
          return nanops.nanmin(self._values, skipna=skipna)
  
      @doc(argmax, op="min", oppose="max", value="smallest")
      def argmin(self, axis=None, skipna=True, *args, **kwargs):
          nv.validate_minmax_axis(axis)
          nv.validate_argmax_with_skipna(skipna, args, kwargs)
          return nanops.nanargmin(self._values, skipna=skipna)
  
      def tolist(self):
          """
          Return a list of the values.
  
          These are each a scalar type, which is a Python scalar
          (for str, int, float) or a pandas scalar
          (for Timestamp/Timedelta/Interval/Period)
  
          Returns
          -------
          list
  
          See Also
          --------
          numpy.ndarray.tolist : Return the array as an a.ndim-levels deep
              nested list of Python scalars.
          """
          if not isinstance(self._values, np.ndarray):
              # check for ndarray instead of dtype to catch DTA/TDA
              return list(self._values)
          return self._values.tolist()
  
      to_list = tolist
  
      def __iter__(self):
          """
          Return an iterator of the values.
  
          These are each a scalar type, which is a Python scalar
          (for str, int, float) or a pandas scalar
          (for Timestamp/Timedelta/Interval/Period)
  
          Returns
          -------
          iterator
          """
          # We are explicitly making element iterators.
          if not isinstance(self._values, np.ndarray):
              # Check type instead of dtype to catch DTA/TDA
              return iter(self._values)
          else:
              return map(self._values.item, range(self._values.size))
  
      @cache_readonly
      def hasnans(self):
          """
          Return if I have any nans; enables various perf speedups.
          """
          return bool(isna(self).any())
  
      def _reduce(
          self,
          op,
          name: str,
          axis=0,
          skipna=True,
          numeric_only=None,
          filter_type=None,
          **kwds,
      ):
          """
          Perform the reduction type operation if we can.
          """
          func = getattr(self, name, None)
          if func is None:
              raise TypeError(
                  f"{type(self).__name__} cannot perform the operation {name}"
              )
          return func(skipna=skipna, **kwds)
  
      def _map_values(self, mapper, na_action=None):
          """
          An internal function that maps values using the input
          correspondence (which can be a dict, Series, or function).
  
          Parameters
          ----------
          mapper : function, dict, or Series
              The input correspondence object
          na_action : {None, 'ignore'}
              If 'ignore', propagate NA values, without passing them to the
              mapping function
  
          Returns
          -------
          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.
          """
          # we can fastpath dict/Series to an efficient map
          # as we know that we are not going to have to yield
          # python types
          if is_dict_like(mapper):
              if isinstance(mapper, dict) and hasattr(mapper, "__missing__"):
                  # If a dictionary subclass defines a default value method,
                  # convert mapper to a lookup function (GH #15999).
                  dict_with_default = mapper
                  mapper = lambda x: dict_with_default[x]
              else:
                  # Dictionary does not have a default. Thus it's safe to
                  # convert to an Series for efficiency.
                  # we specify the keys here to handle the
                  # possibility that they are tuples
  
                  # The return value of mapping with an empty mapper is
                  # expected to be pd.Series(np.nan, ...). As np.nan is
                  # of dtype float64 the return value of this method should
                  # be float64 as well
                  mapper = create_series_with_explicit_dtype(
                      mapper, dtype_if_empty=np.float64
                  )
  
          if isinstance(mapper, ABCSeries):
              # Since values were input this means we came from either
              # a dict or a series and mapper should be an index
              if is_categorical_dtype(self.dtype):
                  # use the built in categorical series mapper which saves
                  # time by mapping the categories instead of all values
                  return self._values.map(mapper)
  
              values = self._values
  
              indexer = mapper.index.get_indexer(values)
              new_values = algorithms.take_1d(mapper._values, indexer)
  
              return new_values
  
          # we must convert to python types
          if is_extension_array_dtype(self.dtype) and hasattr(self._values, "map"):
              # GH#23179 some EAs do not have `map`
              values = self._values
              if na_action is not None:
                  raise NotImplementedError
              map_f = lambda values, f: values.map(f)
          else:
              values = self.astype(object)._values
              if na_action == "ignore":
  
                  def map_f(values, f):
                      return lib.map_infer_mask(values, f, isna(values).view(np.uint8))
  
              elif na_action is None:
                  map_f = lib.map_infer
              else:
                  msg = (
                      "na_action must either be 'ignore' or None, "
                      f"{na_action} was passed"
                  )
                  raise ValueError(msg)
  
          # mapper is a function
          new_values = map_f(values, mapper)
  
          return new_values
  
      def value_counts(
          self, normalize=False, sort=True, ascending=False, bins=None, dropna=True
      ):
          """
          Return a Series containing counts of unique values.
  
          The resulting object will be in descending order so that the
          first element is the most frequently-occurring element.
          Excludes NA values by default.
  
          Parameters
          ----------
          normalize : bool, default False
              If True then the object returned will contain the relative
              frequencies of the unique values.
          sort : bool, default True
              Sort by frequencies.
          ascending : bool, default False
              Sort in ascending order.
          bins : int, optional
              Rather than count values, group them into half-open bins,
              a convenience for ``pd.cut``, only works with numeric data.
          dropna : bool, default True
              Don't include counts of NaN.
  
          Returns
          -------
          Series
  
          See Also
          --------
          Series.count: Number of non-NA elements in a Series.
          DataFrame.count: Number of non-NA elements in a DataFrame.
          DataFrame.value_counts: Equivalent method on DataFrames.
  
          Examples
          --------
          >>> index = pd.Index([3, 1, 2, 3, 4, np.nan])
          >>> index.value_counts()
          3.0    2
          4.0    1
          2.0    1
          1.0    1
          dtype: int64
  
          With `normalize` set to `True`, returns the relative frequency by
          dividing all values by the sum of values.
  
          >>> s = pd.Series([3, 1, 2, 3, 4, np.nan])
          >>> s.value_counts(normalize=True)
          3.0    0.4
          4.0    0.2
          2.0    0.2
          1.0    0.2
          dtype: float64
  
          **bins**
  
          Bins can be useful for going from a continuous variable to a
          categorical variable; instead of counting unique
          apparitions of values, divide the index in the specified
          number of half-open bins.
  
          >>> s.value_counts(bins=3)
          (2.0, 3.0]      2
          (0.996, 2.0]    2
          (3.0, 4.0]      1
          dtype: int64
  
          **dropna**
  
          With `dropna` set to `False` we can also see NaN index values.
  
          >>> s.value_counts(dropna=False)
          3.0    2
          NaN    1
          4.0    1
          2.0    1
          1.0    1
          dtype: int64
          """
          result = value_counts(
              self,
              sort=sort,
              ascending=ascending,
              normalize=normalize,
              bins=bins,
              dropna=dropna,
          )
          return result
  
      def unique(self):
          values = self._values
  
          if not isinstance(values, np.ndarray):
              result = values.unique()
              if self.dtype.kind in ["m", "M"] and isinstance(self, ABCSeries):
                  # GH#31182 Series._values returns EA, unpack for backward-compat
                  if getattr(self.dtype, "tz", None) is None:
                      result = np.asarray(result)
          else:
              result = unique1d(values)
  
          return result
  
      def nunique(self, dropna: bool = True) -> int:
          """
          Return number of unique elements in the object.
  
          Excludes NA values by default.
  
          Parameters
          ----------
          dropna : bool, default True
              Don't include NaN in the count.
  
          Returns
          -------
          int
  
          See Also
          --------
          DataFrame.nunique: Method nunique for DataFrame.
          Series.count: Count non-NA/null observations in the Series.
  
          Examples
          --------
          >>> s = pd.Series([1, 3, 5, 7, 7])
          >>> s
          0    1
          1    3
          2    5
          3    7
          4    7
          dtype: int64
  
          >>> s.nunique()
          4
          """
          uniqs = self.unique()
          n = len(uniqs)
          if dropna and isna(uniqs).any():
              n -= 1
          return n
  
      @property
      def is_unique(self) -> bool:
          """
          Return boolean if values in the object are unique.
  
          Returns
          -------
          bool
          """
          return self.nunique(dropna=False) == len(self)
  
      @property
      def is_monotonic(self) -> bool:
          """
          Return boolean if values in the object are
          monotonic_increasing.
  
          Returns
          -------
          bool
          """
          from pandas import Index
  
          return Index(self).is_monotonic
  
      @property
      def is_monotonic_increasing(self) -> bool:
          """
          Alias for is_monotonic.
          """
          # mypy complains if we alias directly
          return self.is_monotonic
  
      @property
      def is_monotonic_decreasing(self) -> bool:
          """
          Return boolean if values in the object are
          monotonic_decreasing.
  
          Returns
          -------
          bool
          """
          from pandas import Index
  
          return Index(self).is_monotonic_decreasing
  
      def memory_usage(self, deep=False):
          """
          Memory usage of the values.
  
          Parameters
          ----------
          deep : bool, default False
              Introspect the data deeply, interrogate
              `object` dtypes for system-level memory consumption.
  
          Returns
          -------
          bytes used
  
          See Also
          --------
          numpy.ndarray.nbytes : Total bytes consumed by the elements of the
              array.
  
          Notes
          -----
          Memory usage does not include memory consumed by elements that
          are not components of the array if deep=False or if used on PyPy
          """
          if hasattr(self.array, "memory_usage"):
              return self.array.memory_usage(deep=deep)
  
          v = self.array.nbytes
          if deep and is_object_dtype(self) and not PYPY:
              v += lib.memory_usage_of_objects(self._values)
          return v
  
      @doc(
          algorithms.factorize,
          values="",
          order="",
          size_hint="",
          sort=textwrap.dedent(
              """\
              sort : bool, default False
                  Sort `uniques` and shuffle `codes` to maintain the
                  relationship.
              """
          ),
      )
      def factorize(self, sort: bool = False, na_sentinel: Optional[int] = -1):
          return algorithms.factorize(self, sort=sort, na_sentinel=na_sentinel)
  
      _shared_docs[
          "searchsorted"
      ] = """
          Find indices where elements should be inserted to maintain order.
  
          Find the indices into a sorted {klass} `self` such that, if the
          corresponding elements in `value` were inserted before the indices,
          the order of `self` would be preserved.
  
          .. note::
  
              The {klass} *must* be monotonically sorted, otherwise
              wrong locations will likely be returned. Pandas does *not*
              check this for you.
  
          Parameters
          ----------
          value : array_like
              Values to insert into `self`.
          side : {{'left', 'right'}}, optional
              If 'left', the index of the first suitable location found is given.
              If 'right', return the last such index.  If there is no suitable
              index, return either 0 or N (where N is the length of `self`).
          sorter : 1-D array_like, optional
              Optional array of integer indices that sort `self` into ascending
              order. They are typically the result of ``np.argsort``.
  
          Returns
          -------
          int or array of int
              A scalar or array of insertion points with the
              same shape as `value`.
  
              .. versionchanged:: 0.24.0
                  If `value` is a scalar, an int is now always returned.
                  Previously, scalar inputs returned an 1-item array for
                  :class:`Series` and :class:`Categorical`.
  
          See Also
          --------
          sort_values : Sort by the values along either axis.
          numpy.searchsorted : Similar method from NumPy.
  
          Notes
          -----
          Binary search is used to find the required insertion points.
  
          Examples
          --------
          >>> ser = pd.Series([1, 2, 3])
          >>> ser
          0    1
          1    2
          2    3
          dtype: int64
  
          >>> ser.searchsorted(4)
          3
  
          >>> ser.searchsorted([0, 4])
          array([0, 3])
  
          >>> ser.searchsorted([1, 3], side='left')
          array([0, 2])
  
          >>> ser.searchsorted([1, 3], side='right')
          array([1, 3])
  
          >>> ser = pd.Categorical(
          ...     ['apple', 'bread', 'bread', 'cheese', 'milk'], ordered=True
          ... )
          >>> ser
          ['apple', 'bread', 'bread', 'cheese', 'milk']
          Categories (4, object): ['apple' < 'bread' < 'cheese' < 'milk']
  
          >>> ser.searchsorted('bread')
          1
  
          >>> ser.searchsorted(['bread'], side='right')
          array([3])
  
          If the values are not monotonically sorted, wrong locations
          may be returned:
  
          >>> ser = pd.Series([2, 1, 3])
          >>> ser
          0    2
          1    1
          2    3
          dtype: int64
  
          >>> ser.searchsorted(1)  # doctest: +SKIP
          0  # wrong result, correct would be 1
          """
  
      @doc(_shared_docs["searchsorted"], klass="Index")
      def searchsorted(self, value, side="left", sorter=None) -> np.ndarray:
          return algorithms.searchsorted(self._values, value, side=side, sorter=sorter)
  
      def drop_duplicates(self, keep="first"):
          if isinstance(self, ABCIndexClass):
              if self.is_unique:
                  return self._shallow_copy()
  
          duplicated = self.duplicated(keep=keep)
          result = self[np.logical_not(duplicated)]
          return result
  
      def duplicated(self, keep="first"):
          if isinstance(self, ABCIndexClass):
              if self.is_unique:
                  return np.zeros(len(self), dtype=bool)
              return duplicated(self, keep=keep)
          else:
              return self._constructor(
                  duplicated(self, keep=keep), index=self.index
              ).__finalize__(self, method="duplicated")
  