text: #
  # Copyright (C) 2019 Databricks, Inc.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  #
  
  """
  An internal immutable DataFrame with some metadata to manage indexes.
  """
  from distutils.version import LooseVersion
  import re
  from typing import Dict, List, Optional, Tuple, Union, TYPE_CHECKING
  from itertools import accumulate
  import py4j
  
  import numpy as np
  import pandas as pd
  from pandas.api.types import CategoricalDtype, is_datetime64_dtype, is_datetime64tz_dtype
  import pyspark
  from pyspark import sql as spark
  from pyspark._globals import _NoValue, _NoValueType
  from pyspark.sql import functions as F, Window
  from pyspark.sql.functions import PandasUDFType, pandas_udf
  from pyspark.sql.types import BooleanType, DataType, IntegralType, StructField, StructType, LongType
  
  try:
      from pyspark.sql.types import to_arrow_type
  except ImportError:
      from pyspark.sql.pandas.types import to_arrow_type  # noqa: F401
  
  # For running doctests and reference resolution in PyCharm.
  from databricks import koalas as ks  # noqa: F401
  
  if TYPE_CHECKING:
      # This is required in old Python 3.5 to prevent circular reference.
      from databricks.koalas.series import Series
  from databricks.koalas.config import get_option
  from databricks.koalas.typedef import (
      Dtype,
      DtypeDataTypes,
      as_spark_type,
      extension_dtypes,
      infer_pd_series_spark_type,
      spark_type_to_pandas_dtype,
  )
  from databricks.koalas.utils import (
      column_labels_level,
      default_session,
      is_name_like_tuple,
      is_testing,
      lazy_property,
      name_like_string,
      scol_for,
      verify_temp_column_name,
  )
  
  
  # A function to turn given numbers to Spark columns that represent Koalas index.
  SPARK_INDEX_NAME_FORMAT = "__index_level_{}__".format
  SPARK_DEFAULT_INDEX_NAME = SPARK_INDEX_NAME_FORMAT(0)
  # A pattern to check if the name of a Spark column is a Koalas index name or not.
  SPARK_INDEX_NAME_PATTERN = re.compile(r"__index_level_[0-9]+__")
  
  NATURAL_ORDER_COLUMN_NAME = "__natural_order__"
  
  HIDDEN_COLUMNS = {NATURAL_ORDER_COLUMN_NAME}
  
  DEFAULT_SERIES_NAME = 0
  SPARK_DEFAULT_SERIES_NAME = str(DEFAULT_SERIES_NAME)
  
  
  class InternalFrame(object):
      """
      The internal immutable DataFrame which manages Spark DataFrame and column names and index
      information.
  
      .. note:: this is an internal class. It is not supposed to be exposed to users and users
          should not directly access to it.
  
      The internal immutable DataFrame represents the index information for a DataFrame it belongs to.
      For instance, if we have a Koalas DataFrame as below, pandas DataFrame does not store the index
      as columns.
  
      >>> kdf = ks.DataFrame({
      ...     'A': [1, 2, 3, 4],
      ...     'B': [5, 6, 7, 8],
      ...     'C': [9, 10, 11, 12],
      ...     'D': [13, 14, 15, 16],
      ...     'E': [17, 18, 19, 20]}, columns = ['A', 'B', 'C', 'D', 'E'])
      >>> kdf  # doctest: +NORMALIZE_WHITESPACE
         A  B   C   D   E
      0  1  5   9  13  17
      1  2  6  10  14  18
      2  3  7  11  15  19
      3  4  8  12  16  20
  
      However, all columns including index column are also stored in Spark DataFrame internally
      as below.
  
      >>> kdf._internal.to_internal_spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE
      +-----------------+---+---+---+---+---+
      |__index_level_0__|  A|  B|  C|  D|  E|
      +-----------------+---+---+---+---+---+
      |                0|  1|  5|  9| 13| 17|
      |                1|  2|  6| 10| 14| 18|
      |                2|  3|  7| 11| 15| 19|
      |                3|  4|  8| 12| 16| 20|
      +-----------------+---+---+---+---+---+
  
      In order to fill this gap, the current metadata is used by mapping Spark's internal column
      to Koalas' index. See the method below:
  
      * `spark_frame` represents the internal Spark DataFrame
  
      * `data_spark_column_names` represents non-indexing Spark column names
  
      * `data_spark_columns` represents non-indexing Spark columns
  
      * `data_dtypes` represents external non-indexing dtypes
  
      * `index_spark_column_names` represents internal index Spark column names
  
      * `index_spark_columns` represents internal index Spark columns
  
      * `index_dtypes` represents external index dtypes
  
      * `spark_column_names` represents all columns
  
      * `index_names` represents the external index name as a label
  
      * `to_internal_spark_frame` represents Spark DataFrame derived by the metadata. Includes index.
  
      * `to_pandas_frame` represents pandas DataFrame derived by the metadata
  
      >>> internal = kdf._internal
      >>> internal.spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS
      +-----------------+---+---+---+---+---+-----------------+
      |__index_level_0__|  A|  B|  C|  D|  E|__natural_order__|
      +-----------------+---+---+---+---+---+-----------------+
      |                0|  1|  5|  9| 13| 17|              ...|
      |                1|  2|  6| 10| 14| 18|              ...|
      |                2|  3|  7| 11| 15| 19|              ...|
      |                3|  4|  8| 12| 16| 20|              ...|
      +-----------------+---+---+---+---+---+-----------------+
      >>> internal.data_spark_column_names
      ['A', 'B', 'C', 'D', 'E']
      >>> internal.index_spark_column_names
      ['__index_level_0__']
      >>> internal.spark_column_names
      ['__index_level_0__', 'A', 'B', 'C', 'D', 'E']
      >>> internal.index_names
      [None]
      >>> internal.data_dtypes
      [dtype('int64'), dtype('int64'), dtype('int64'), dtype('int64'), dtype('int64')]
      >>> internal.index_dtypes
      [dtype('int64')]
      >>> internal.to_internal_spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE
      +-----------------+---+---+---+---+---+
      |__index_level_0__|  A|  B|  C|  D|  E|
      +-----------------+---+---+---+---+---+
      |                0|  1|  5|  9| 13| 17|
      |                1|  2|  6| 10| 14| 18|
      |                2|  3|  7| 11| 15| 19|
      |                3|  4|  8| 12| 16| 20|
      +-----------------+---+---+---+---+---+
      >>> internal.to_pandas_frame
         A  B   C   D   E
      0  1  5   9  13  17
      1  2  6  10  14  18
      2  3  7  11  15  19
      3  4  8  12  16  20
  
      In case that index is set to one of the existing column as below:
  
      >>> kdf1 = kdf.set_index("A")
      >>> kdf1  # doctest: +NORMALIZE_WHITESPACE
         B   C   D   E
      A
      1  5   9  13  17
      2  6  10  14  18
      3  7  11  15  19
      4  8  12  16  20
  
      >>> kdf1._internal.to_internal_spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE
      +---+---+---+---+---+
      |  A|  B|  C|  D|  E|
      +---+---+---+---+---+
      |  1|  5|  9| 13| 17|
      |  2|  6| 10| 14| 18|
      |  3|  7| 11| 15| 19|
      |  4|  8| 12| 16| 20|
      +---+---+---+---+---+
  
      >>> internal = kdf1._internal
      >>> internal.spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS
      +-----------------+---+---+---+---+---+-----------------+
      |__index_level_0__|  A|  B|  C|  D|  E|__natural_order__|
      +-----------------+---+---+---+---+---+-----------------+
      |                0|  1|  5|  9| 13| 17|              ...|
      |                1|  2|  6| 10| 14| 18|              ...|
      |                2|  3|  7| 11| 15| 19|              ...|
      |                3|  4|  8| 12| 16| 20|              ...|
      +-----------------+---+---+---+---+---+-----------------+
      >>> internal.data_spark_column_names
      ['B', 'C', 'D', 'E']
      >>> internal.index_spark_column_names
      ['A']
      >>> internal.spark_column_names
      ['A', 'B', 'C', 'D', 'E']
      >>> internal.index_names
      [('A',)]
      >>> internal.data_dtypes
      [dtype('int64'), dtype('int64'), dtype('int64'), dtype('int64')]
      >>> internal.index_dtypes
      [dtype('int64')]
      >>> internal.to_internal_spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE
      +---+---+---+---+---+
      |  A|  B|  C|  D|  E|
      +---+---+---+---+---+
      |  1|  5|  9| 13| 17|
      |  2|  6| 10| 14| 18|
      |  3|  7| 11| 15| 19|
      |  4|  8| 12| 16| 20|
      +---+---+---+---+---+
      >>> internal.to_pandas_frame  # doctest: +NORMALIZE_WHITESPACE
         B   C   D   E
      A
      1  5   9  13  17
      2  6  10  14  18
      3  7  11  15  19
      4  8  12  16  20
  
      In case that index becomes a multi index as below:
  
      >>> kdf2 = kdf.set_index("A", append=True)
      >>> kdf2  # doctest: +NORMALIZE_WHITESPACE
           B   C   D   E
        A
      0 1  5   9  13  17
      1 2  6  10  14  18
      2 3  7  11  15  19
      3 4  8  12  16  20
  
      >>> kdf2._internal.to_internal_spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE
      +-----------------+---+---+---+---+---+
      |__index_level_0__|  A|  B|  C|  D|  E|
      +-----------------+---+---+---+---+---+
      |                0|  1|  5|  9| 13| 17|
      |                1|  2|  6| 10| 14| 18|
      |                2|  3|  7| 11| 15| 19|
      |                3|  4|  8| 12| 16| 20|
      +-----------------+---+---+---+---+---+
  
      >>> internal = kdf2._internal
      >>> internal.spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS
      +-----------------+---+---+---+---+---+-----------------+
      |__index_level_0__|  A|  B|  C|  D|  E|__natural_order__|
      +-----------------+---+---+---+---+---+-----------------+
      |                0|  1|  5|  9| 13| 17|              ...|
      |                1|  2|  6| 10| 14| 18|              ...|
      |                2|  3|  7| 11| 15| 19|              ...|
      |                3|  4|  8| 12| 16| 20|              ...|
      +-----------------+---+---+---+---+---+-----------------+
      >>> internal.data_spark_column_names
      ['B', 'C', 'D', 'E']
      >>> internal.index_spark_column_names
      ['__index_level_0__', 'A']
      >>> internal.spark_column_names
      ['__index_level_0__', 'A', 'B', 'C', 'D', 'E']
      >>> internal.index_names
      [None, ('A',)]
      >>> internal.data_dtypes
      [dtype('int64'), dtype('int64'), dtype('int64'), dtype('int64')]
      >>> internal.index_dtypes
      [dtype('int64'), dtype('int64')]
      >>> internal.to_internal_spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE
      +-----------------+---+---+---+---+---+
      |__index_level_0__|  A|  B|  C|  D|  E|
      +-----------------+---+---+---+---+---+
      |                0|  1|  5|  9| 13| 17|
      |                1|  2|  6| 10| 14| 18|
      |                2|  3|  7| 11| 15| 19|
      |                3|  4|  8| 12| 16| 20|
      +-----------------+---+---+---+---+---+
      >>> internal.to_pandas_frame  # doctest: +NORMALIZE_WHITESPACE
           B   C   D   E
        A
      0 1  5   9  13  17
      1 2  6  10  14  18
      2 3  7  11  15  19
      3 4  8  12  16  20
  
      For multi-level columns, it also holds column_labels
  
      >>> columns = pd.MultiIndex.from_tuples([('X', 'A'), ('X', 'B'),
      ...                                      ('Y', 'C'), ('Y', 'D')])
      >>> kdf3 = ks.DataFrame([
      ...     [1, 2, 3, 4],
      ...     [5, 6, 7, 8],
      ...     [9, 10, 11, 12],
      ...     [13, 14, 15, 16],
      ...     [17, 18, 19, 20]], columns = columns)
      >>> kdf3  # doctest: +NORMALIZE_WHITESPACE
          X       Y
          A   B   C   D
      0   1   2   3   4
      1   5   6   7   8
      2   9  10  11  12
      3  13  14  15  16
      4  17  18  19  20
  
      >>> internal = kdf3._internal
      >>> internal.spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS
      +-----------------+------+------+------+------+-----------------+
      |__index_level_0__|(X, A)|(X, B)|(Y, C)|(Y, D)|__natural_order__|
      +-----------------+------+------+------+------+-----------------+
      |                0|     1|     2|     3|     4|              ...|
      |                1|     5|     6|     7|     8|              ...|
      |                2|     9|    10|    11|    12|              ...|
      |                3|    13|    14|    15|    16|              ...|
      |                4|    17|    18|    19|    20|              ...|
      +-----------------+------+------+------+------+-----------------+
      >>> internal.data_spark_column_names
      ['(X, A)', '(X, B)', '(Y, C)', '(Y, D)']
      >>> internal.column_labels
      [('X', 'A'), ('X', 'B'), ('Y', 'C'), ('Y', 'D')]
  
      For Series, it also holds scol to represent the column.
  
      >>> kseries = kdf1.B
      >>> kseries
      A
      1    5
      2    6
      3    7
      4    8
      Name: B, dtype: int64
  
      >>> internal = kseries._internal
      >>> internal.spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS
      +-----------------+---+---+---+---+---+-----------------+
      |__index_level_0__|  A|  B|  C|  D|  E|__natural_order__|
      +-----------------+---+---+---+---+---+-----------------+
      |                0|  1|  5|  9| 13| 17|              ...|
      |                1|  2|  6| 10| 14| 18|              ...|
      |                2|  3|  7| 11| 15| 19|              ...|
      |                3|  4|  8| 12| 16| 20|              ...|
      +-----------------+---+---+---+---+---+-----------------+
      >>> internal.data_spark_column_names
      ['B']
      >>> internal.index_spark_column_names
      ['A']
      >>> internal.spark_column_names
      ['A', 'B']
      >>> internal.index_names
      [('A',)]
      >>> internal.data_dtypes
      [dtype('int64')]
      >>> internal.index_dtypes
      [dtype('int64')]
      >>> internal.to_internal_spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE
      +---+---+
      |  A|  B|
      +---+---+
      |  1|  5|
      |  2|  6|
      |  3|  7|
      |  4|  8|
      +---+---+
      >>> internal.to_pandas_frame  # doctest: +NORMALIZE_WHITESPACE
         B
      A
      1  5
      2  6
      3  7
      4  8
      """
  
      def __init__(
          self,
          spark_frame: spark.DataFrame,
          index_spark_columns: Optional[List[spark.Column]],
          index_names: Optional[List[Optional[Tuple]]] = None,
          index_dtypes: Optional[List[Dtype]] = None,
          column_labels: Optional[List[Tuple]] = None,
          data_spark_columns: Optional[List[spark.Column]] = None,
          data_dtypes: Optional[List[Dtype]] = None,
          column_label_names: Optional[List[Optional[Tuple]]] = None,
      ) -> None:
          """
          Create a new internal immutable DataFrame to manage Spark DataFrame, column fields and
          index fields and names.
  
          :param spark_frame: Spark DataFrame to be managed.
          :param index_spark_columns: list of Spark Column
                                      Spark Columns for the index.
          :param index_names: list of tuples
                              the index names.
          :param index_dtypes: list of dtypes
                               the index dtypes.
          :param column_labels: list of tuples with the same length
                                The multi-level values in the tuples.
          :param data_spark_columns: list of Spark Column
                                     Spark Columns to appear as columns. If this is None, calculated
                                     from spark_frame.
          :param data_dtypes: list of dtypes.
                              the data dtypes.
          :param column_label_names: Names for each of the column index levels.
  
          See the examples below to refer what each parameter means.
  
          >>> column_labels = pd.MultiIndex.from_tuples(
          ...     [('a', 'x'), ('a', 'y'), ('b', 'z')], names=["column_labels_a", "column_labels_b"])
          >>> row_index = pd.MultiIndex.from_tuples(
          ...     [('foo', 'bar'), ('foo', 'bar'), ('zoo', 'bar')],
          ...     names=["row_index_a", "row_index_b"])
          >>> kdf = ks.DataFrame(
          ...     [[1, 2, 3], [4, 5, 6], [7, 8, 9]], index=row_index, columns=column_labels)
          >>> kdf.set_index(('a', 'x'), append=True, inplace=True)
          >>> kdf  # doctest: +NORMALIZE_WHITESPACE
          column_labels_a                  a  b
          column_labels_b                  y  z
          row_index_a row_index_b (a, x)
          foo         bar         1       2  3
                                  4       5  6
          zoo         bar         7       8  9
  
          >>> internal = kdf._internal
  
          >>> internal.spark_frame.show()  # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS
          +-----------------+-----------------+------+------+------+...
          |__index_level_0__|__index_level_1__|(a, x)|(a, y)|(b, z)|...
          +-----------------+-----------------+------+------+------+...
          |              foo|              bar|     1|     2|     3|...
          |              foo|              bar|     4|     5|     6|...
          |              zoo|              bar|     7|     8|     9|...
          +-----------------+-----------------+------+------+------+...
  
          >>> internal.index_spark_columns  # doctest: +SKIP
          [Column<'__index_level_0__'>, Column<'__index_level_1__'>, Column<'(a, x)'>]
  
          >>> internal.index_names
          [('row_index_a',), ('row_index_b',), ('a', 'x')]
  
          >>> internal.index_dtypes
          [dtype('O'), dtype('O'), dtype('int64')]
  
          >>> internal.column_labels
          [('a', 'y'), ('b', 'z')]
  
          >>> internal.data_spark_columns  # doctest: +SKIP
          [Column<'(a, y)'>, Column<'(b, z)'>]
  
          >>> internal.data_dtypes
          [dtype('int64'), dtype('int64')]
  
          >>> internal.column_label_names
          [('column_labels_a',), ('column_labels_b',)]
          """
  
          assert isinstance(spark_frame, spark.DataFrame)
          assert not spark_frame.isStreaming, "Koalas does not support Structured Streaming."
  
          if not index_spark_columns:
              if data_spark_columns is not None:
                  if column_labels is not None:
                      data_spark_columns = [
                          scol.alias(name_like_string(label))
                          for scol, label in zip(data_spark_columns, column_labels)
                      ]
                  spark_frame = spark_frame.select(data_spark_columns)
  
              assert not any(SPARK_INDEX_NAME_PATTERN.match(name) for name in spark_frame.columns), (
                  "Index columns should not appear in columns of the Spark DataFrame. Avoid "
                  "index column names [%s]." % SPARK_INDEX_NAME_PATTERN
              )
  
              # Create default index.
              spark_frame = InternalFrame.attach_default_index(spark_frame)
              index_spark_columns = [scol_for(spark_frame, SPARK_DEFAULT_INDEX_NAME)]
  
              if data_spark_columns is not None:
                  data_spark_columns = [
                      scol_for(spark_frame, col)
                      for col in spark_frame.columns
                      if col != SPARK_DEFAULT_INDEX_NAME
                  ]
  
          if NATURAL_ORDER_COLUMN_NAME not in spark_frame.columns:
              spark_frame = spark_frame.withColumn(
                  NATURAL_ORDER_COLUMN_NAME, F.monotonically_increasing_id()
              )
  
          self._sdf = spark_frame  # type: spark.DataFrame
  
          # index_spark_columns
          assert all(
              isinstance(index_scol, spark.Column) for index_scol in index_spark_columns
          ), index_spark_columns
  
          self._index_spark_columns = index_spark_columns  # type: List[spark.Column]
  
          # index_names
          if not index_names:
              index_names = [None] * len(index_spark_columns)
  
          assert len(index_spark_columns) == len(index_names), (
              len(index_spark_columns),
              len(index_names),
          )
          assert all(
              is_name_like_tuple(index_name, check_type=True) for index_name in index_names
          ), index_names
  
          self._index_names = index_names  # type: List[Optional[Tuple]]
  
          # index_dtypes
          if not index_dtypes:
              index_dtypes = [None] * len(index_spark_columns)
  
          assert len(index_spark_columns) == len(index_dtypes), (
              len(index_spark_columns),
              len(index_dtypes),
          )
  
          index_dtypes = [
              spark_type_to_pandas_dtype(spark_frame.select(scol).schema[0].dataType)
              if dtype is None or dtype == np.dtype("object")
              else dtype
              for dtype, scol in zip(index_dtypes, index_spark_columns)
          ]
  
          assert all(
              isinstance(dtype, DtypeDataTypes)
              and (dtype == np.dtype("object") or as_spark_type(dtype, raise_error=False) is not None)
              for dtype in index_dtypes
          ), index_dtypes
  
          self._index_dtypes = index_dtypes
  
          # data_spark-columns
          if data_spark_columns is None:
              data_spark_columns = [
                  scol_for(spark_frame, col)
                  for col in spark_frame.columns
                  if all(
                      not scol_for(spark_frame, col)._jc.equals(index_scol._jc)
                      for index_scol in index_spark_columns
                  )
                  and col not in HIDDEN_COLUMNS
              ]
              self._data_spark_columns = data_spark_columns
          else:
              assert all(isinstance(scol, spark.Column) for scol in data_spark_columns)
              self._data_spark_columns = data_spark_columns
  
          # column_labels
          if column_labels is None:
              self._column_labels = [
                  (col,) for col in spark_frame.select(self._data_spark_columns).columns
              ]  # type: List[Tuple]
          else:
              assert len(column_labels) == len(self._data_spark_columns), (
                  len(column_labels),
                  len(self._data_spark_columns),
              )
              if len(column_labels) == 1:
                  column_label = column_labels[0]
                  assert is_name_like_tuple(column_label, check_type=True), column_label
              else:
                  assert all(
                      is_name_like_tuple(column_label, check_type=True)
                      for column_label in column_labels
                  ), column_labels
                  assert len(set(len(label) for label in column_labels)) <= 1, column_labels
              self._column_labels = column_labels
  
          # data_dtypes
          if not data_dtypes:
              data_dtypes = [None] * len(data_spark_columns)
  
          assert len(data_spark_columns) == len(data_dtypes), (
              len(data_spark_columns),
              len(data_dtypes),
          )
  
          data_dtypes = [
              spark_type_to_pandas_dtype(spark_frame.select(scol).schema[0].dataType)
              if dtype is None or dtype == np.dtype("object")
              else dtype
              for dtype, scol in zip(data_dtypes, data_spark_columns)
          ]
  
          assert all(
              isinstance(dtype, DtypeDataTypes)
              and (dtype == np.dtype("object") or as_spark_type(dtype, raise_error=False) is not None)
              for dtype in data_dtypes
          ), data_dtypes
  
          self._data_dtypes = data_dtypes
  
          # column_label_names
          if column_label_names is None:
              self._column_label_names = [None] * column_labels_level(
                  self._column_labels
              )  # type: List[Optional[Tuple]]
          else:
              if len(self._column_labels) > 0:
                  assert len(column_label_names) == column_labels_level(self._column_labels), (
                      len(column_label_names),
                      column_labels_level(self._column_labels),
                  )
              else:
                  assert len(column_label_names) > 0, len(column_label_names)
              assert all(
                  is_name_like_tuple(column_label_name, check_type=True)
                  for column_label_name in column_label_names
              ), column_label_names
              self._column_label_names = column_label_names
  
      @staticmethod
      def attach_default_index(sdf, default_index_type=None):
          """
          This method attaches a default index to Spark DataFrame. Spark does not have the index
          notion so corresponding column should be generated.
          There are several types of default index can be configured by `compute.default_index_type`.
  
          >>> spark_frame = ks.range(10).to_spark()
          >>> spark_frame
          DataFrame[id: bigint]
  
          It adds the default index column '__index_level_0__'.
  
          >>> spark_frame = InternalFrame.attach_default_index(spark_frame)
          >>> spark_frame
          DataFrame[__index_level_0__: bigint, id: bigint]
  
          It throws an exception if the given column name already exists.
  
          >>> InternalFrame.attach_default_index(spark_frame)
          ... # doctest: +ELLIPSIS
          Traceback (most recent call last):
            ...
          AssertionError: '__index_level_0__' already exists...
          """
          index_column = SPARK_DEFAULT_INDEX_NAME
          assert (
              index_column not in sdf.columns
          ), "'%s' already exists in the Spark column names '%s'" % (index_column, sdf.columns)
  
          if default_index_type is None:
              default_index_type = get_option("compute.default_index_type")
  
          if default_index_type == "sequence":
              return InternalFrame.attach_sequence_column(sdf, column_name=index_column)
          elif default_index_type == "distributed-sequence":
              return InternalFrame.attach_distributed_sequence_column(sdf, column_name=index_column)
          elif default_index_type == "distributed":
              return InternalFrame.attach_distributed_column(sdf, column_name=index_column)
          else:
              raise ValueError(
                  "'compute.default_index_type' should be one of 'sequence',"
                  " 'distributed-sequence' and 'distributed'"
              )
  
      @staticmethod
      def attach_sequence_column(sdf, column_name):
          scols = [scol_for(sdf, column) for column in sdf.columns]
          sequential_index = (
              F.row_number().over(Window.orderBy(F.monotonically_increasing_id())).cast("long") - 1
          )
          return sdf.select(sequential_index.alias(column_name), *scols)
  
      @staticmethod
      def attach_distributed_column(sdf, column_name):
          scols = [scol_for(sdf, column) for column in sdf.columns]
          return sdf.select(F.monotonically_increasing_id().alias(column_name), *scols)
  
      @staticmethod
      def attach_distributed_sequence_column(sdf, column_name):
          """
          This method attaches a Spark column that has a sequence in a distributed manner.
          This is equivalent to the column assigned when default index type 'distributed-sequence'.
  
          >>> sdf = ks.DataFrame(['a', 'b', 'c']).to_spark()
          >>> sdf = InternalFrame.attach_distributed_sequence_column(sdf, column_name="sequence")
          >>> sdf.show()  # doctest: +NORMALIZE_WHITESPACE
          +--------+---+
          |sequence|  0|
          +--------+---+
          |       0|  a|
          |       1|  b|
          |       2|  c|
          +--------+---+
          """
          if len(sdf.columns) > 0:
              try:
                  jdf = sdf._jdf.toDF()
  
                  sql_ctx = sdf.sql_ctx
                  encoders = sql_ctx._jvm.org.apache.spark.sql.Encoders
                  encoder = encoders.tuple(jdf.exprEnc(), encoders.scalaLong())
  
                  jrdd = jdf.localCheckpoint(False).rdd().zipWithIndex()
  
                  df = spark.DataFrame(
                      sql_ctx.sparkSession._jsparkSession.createDataset(jrdd, encoder).toDF(), sql_ctx
                  )
                  columns = df.columns
                  return df.selectExpr(
                      "`{}` as `{}`".format(columns[1], column_name), "`{}`.*".format(columns[0])
                  )
              except py4j.protocol.Py4JError:
                  if is_testing():
                      raise
                  return InternalFrame._attach_distributed_sequence_column(sdf, column_name)
          else:
              cnt = sdf.count()
              if cnt > 0:
                  return default_session().range(cnt).toDF(column_name)
              else:
                  return default_session().createDataFrame(
                      [], schema=StructType().add(column_name, data_type=LongType(), nullable=False)
                  )
  
      @staticmethod
      def _attach_distributed_sequence_column(sdf, column_name):
          """
          >>> sdf = ks.DataFrame(['a', 'b', 'c']).to_spark()
          >>> sdf = InternalFrame._attach_distributed_sequence_column(sdf, column_name="sequence")
          >>> sdf.sort("sequence").show()  # doctest: +NORMALIZE_WHITESPACE
          +--------+---+
          |sequence|  0|
          +--------+---+
          |       0|  a|
          |       1|  b|
          |       2|  c|
          +--------+---+
          """
          scols = [scol_for(sdf, column) for column in sdf.columns]
  
          spark_partition_column = verify_temp_column_name(sdf, "__spark_partition_id__")
          offset_column = verify_temp_column_name(sdf, "__offset__")
          row_number_column = verify_temp_column_name(sdf, "__row_number__")
  
          # 1. Calculates counts per each partition ID. `counts` here is, for instance,
          #     {
          #         1: 83,
          #         6: 83,
          #         3: 83,
          #         ...
          #     }
          sdf = sdf.withColumn(spark_partition_column, F.spark_partition_id())
  
          # Checkpoint the DataFrame to fix the partition ID.
          sdf = sdf.localCheckpoint(eager=False)
  
          counts = map(
              lambda x: (x["key"], x["count"]),
              sdf.groupby(sdf[spark_partition_column].alias("key")).count().collect(),
          )
  
          # 2. Calculates cumulative sum in an order of partition id.
          #     Note that it does not matter if partition id guarantees its order or not.
          #     We just need a one-by-one sequential id.
  
          # sort by partition key.
          sorted_counts = sorted(counts, key=lambda x: x[0])
          # get cumulative sum in an order of partition key.
          cumulative_counts = [0] + list(accumulate(map(lambda count: count[1], sorted_counts)))
          # zip it with partition key.
          sums = dict(zip(map(lambda count: count[0], sorted_counts), cumulative_counts))
  
          # 3. Attach offset for each partition.
          @pandas_udf(LongType(), PandasUDFType.SCALAR)
          def offset(id):
              current_partition_offset = sums[id.iloc[0]]
              return pd.Series(current_partition_offset).repeat(len(id))
  
          sdf = sdf.withColumn(offset_column, offset(spark_partition_column))
  
          # 4. Calculate row_number in each partition.
          w = Window.partitionBy(spark_partition_column).orderBy(F.monotonically_increasing_id())
          row_number = F.row_number().over(w)
          sdf = sdf.withColumn(row_number_column, row_number)
  
          # 5. Calculate the index.
          return sdf.select(
              (sdf[offset_column] + sdf[row_number_column] - 1).alias(column_name), *scols
          )
  
      def spark_column_for(self, label: Tuple) -> spark.Column:
          """ Return Spark Column for the given column label. """
          column_labels_to_scol = dict(zip(self.column_labels, self.data_spark_columns))
          if label in column_labels_to_scol:
              return column_labels_to_scol[label]
          else:
              raise KeyError(name_like_string(label))
  
      def spark_column_name_for(self, label_or_scol: Union[Tuple, spark.Column]) -> str:
          """ Return the actual Spark column name for the given column label. """
          if isinstance(label_or_scol, spark.Column):
              scol = label_or_scol
          else:
              scol = self.spark_column_for(label_or_scol)
          return self.spark_frame.select(scol).columns[0]
  
      def spark_type_for(self, label_or_scol: Union[Tuple, spark.Column]) -> DataType:
          """ Return DataType for the given column label. """
          if isinstance(label_or_scol, spark.Column):
              scol = label_or_scol
          else:
              scol = self.spark_column_for(label_or_scol)
          return self.spark_frame.select(scol).schema[0].dataType
  
      def spark_column_nullable_for(self, label_or_scol: Union[Tuple, spark.Column]) -> bool:
          """ Return nullability for the given column label. """
          if isinstance(label_or_scol, spark.Column):
              scol = label_or_scol
          else:
              scol = self.spark_column_for(label_or_scol)
          return self.spark_frame.select(scol).schema[0].nullable
  
      def dtype_for(self, label: Tuple) -> Dtype:
          """ Return dtype for the given column label. """
          column_labels_to_dtype = dict(zip(self.column_labels, self.data_dtypes))
          if label in column_labels_to_dtype:
              return column_labels_to_dtype[label]
          else:
              raise KeyError(name_like_string(label))
  
      @property
      def spark_frame(self) -> spark.DataFrame:
          """ Return the managed Spark DataFrame. """
          return self._sdf
  
      @lazy_property
      def data_spark_column_names(self) -> List[str]:
          """ Return the managed column field names. """
          return self.spark_frame.select(self.data_spark_columns).columns
  
      @property
      def data_spark_columns(self) -> List[spark.Column]:
          """ Return Spark Columns for the managed data columns. """
          return self._data_spark_columns
  
      @property
      def index_spark_column_names(self) -> List[str]:
          """ Return the managed index field names. """
          return self.spark_frame.select(self.index_spark_columns).columns
  
      @property
      def index_spark_columns(self) -> List[spark.Column]:
          """ Return Spark Columns for the managed index columns. """
          return self._index_spark_columns
  
      @lazy_property
      def spark_column_names(self) -> List[str]:
          """ Return all the field names including index field names. """
          return self.spark_frame.select(self.spark_columns).columns
  
      @lazy_property
      def spark_columns(self) -> List[spark.Column]:
          """ Return Spark Columns for the managed columns including index columns. """
          index_spark_columns = self.index_spark_columns
          return index_spark_columns + [
              spark_column
              for spark_column in self.data_spark_columns
              if all(not spark_column._jc.equals(scol._jc) for scol in index_spark_columns)
          ]
  
      @property
      def index_names(self) -> List[Optional[Tuple]]:
          """ Return the managed index names. """
          return self._index_names
  
      @lazy_property
      def index_level(self) -> int:
          """ Return the level of the index. """
          return len(self._index_names)
  
      @property
      def column_labels(self) -> List[Tuple]:
          """ Return the managed column index. """
          return self._column_labels
  
      @lazy_property
      def column_labels_level(self) -> int:
          """ Return the level of the column index. """
          return len(self._column_label_names)
  
      @property
      def column_label_names(self) -> List[Optional[Tuple]]:
          """ Return names of the index levels. """
          return self._column_label_names
  
      @property
      def index_dtypes(self) -> List[Dtype]:
          """ Return dtypes for the managed index columns. """
          return self._index_dtypes
  
      @property
      def data_dtypes(self) -> List[Dtype]:
          """ Return dtypes for the managed columns. """
          return self._data_dtypes
  
      @lazy_property
      def to_internal_spark_frame(self) -> spark.DataFrame:
          """
          Return as Spark DataFrame. This contains index columns as well
          and should be only used for internal purposes.
          """
          index_spark_columns = self.index_spark_columns
          data_columns = []
          for spark_column in self.data_spark_columns:
              if all(not spark_column._jc.equals(scol._jc) for scol in index_spark_columns):
                  data_columns.append(spark_column)
          return self.spark_frame.select(index_spark_columns + data_columns)
  
      @lazy_property
      def to_pandas_frame(self) -> pd.DataFrame:
          """ Return as pandas DataFrame. """
          sdf = self.to_internal_spark_frame
          pdf = sdf.toPandas()
          if len(pdf) == 0 and len(sdf.schema) > 0:
              pdf = pdf.astype(
                  {field.name: spark_type_to_pandas_dtype(field.dataType) for field in sdf.schema}
              )
          elif LooseVersion(pyspark.__version__) < LooseVersion("3.0"):
              for field in sdf.schema:
                  if field.nullable and pdf[field.name].isnull().all():
                      if isinstance(field.dataType, BooleanType):
                          pdf[field.name] = pdf[field.name].astype(np.object)
                      elif isinstance(field.dataType, IntegralType):
                          pdf[field.name] = pdf[field.name].astype(np.float64)
                      else:
                          pdf[field.name] = pdf[field.name].astype(
                              spark_type_to_pandas_dtype(field.dataType)
                          )
  
          return InternalFrame.restore_index(pdf, **self.arguments_for_restore_index)
  
      @lazy_property
      def arguments_for_restore_index(self) -> Dict:
          """ Create arguments for `restore_index`. """
          column_names = []
          ext_dtypes = {
              col: dtype
              for col, dtype in zip(self.index_spark_column_names, self.index_dtypes)
              if isinstance(dtype, extension_dtypes)
          }
          categorical_dtypes = {
              col: dtype
              for col, dtype in zip(self.index_spark_column_names, self.index_dtypes)
              if isinstance(dtype, CategoricalDtype)
          }
          for spark_column, column_name, dtype in zip(
              self.data_spark_columns, self.data_spark_column_names, self.data_dtypes
          ):
              for index_spark_column_name, index_spark_column in zip(
                  self.index_spark_column_names, self.index_spark_columns
              ):
                  if spark_column._jc.equals(index_spark_column._jc):
                      column_names.append(index_spark_column_name)
                      break
              else:
                  column_names.append(column_name)
                  if isinstance(dtype, extension_dtypes):
                      ext_dtypes[column_name] = dtype
                  elif isinstance(dtype, CategoricalDtype):
                      categorical_dtypes[column_name] = dtype
  
          return dict(
              index_columns=self.index_spark_column_names,
              index_names=self.index_names,
              data_columns=column_names,
              column_labels=self.column_labels,
              column_label_names=self.column_label_names,
              ext_dtypes=ext_dtypes,
              categorical_dtypes=categorical_dtypes,
          )
  
      @staticmethod
      def restore_index(
          pdf: pd.DataFrame,
          *,
          index_columns: List[str],
          index_names: List[Tuple],
          data_columns: List[str],
          column_labels: List[Tuple],
          column_label_names: List[Tuple],
          ext_dtypes: Dict[str, Dtype] = None,
          categorical_dtypes: Dict[str, CategoricalDtype] = None
      ) -> pd.DataFrame:
          """
          Restore pandas DataFrame indices using the metadata.
  
          :param pdf: the pandas DataFrame to be processed.
          :param index_columns: the original column names for index columns.
          :param index_names: the index names after restored.
          :param data_columns: the original column names for data columns.
          :param column_labels: the column labels after restored.
          :param column_label_names: the column label names after restored.
          :param ext_dtypes: the map from the original column names to extension data types.
          :param categorical_dtypes: the map from the original column names to categorical types.
          :return: the restored pandas DataFrame
  
          >>> pdf = pd.DataFrame({"index": [10, 20, 30], "a": ['a', 'b', 'c'], "b": [0, 2, 1]})
          >>> InternalFrame.restore_index(
          ...     pdf,
          ...     index_columns=["index"],
          ...     index_names=[("idx",)],
          ...     data_columns=["a", "b", "index"],
          ...     column_labels=[("x",), ("y",), ("z",)],
          ...     column_label_names=[("lv1",)],
          ...     ext_dtypes=None,
          ...     categorical_dtypes={"b": CategoricalDtype(categories=["i", "j", "k"])}
          ... )  # doctest: +NORMALIZE_WHITESPACE
          lv1  x  y   z
          idx
          10   a  i  10
          20   b  k  20
          30   c  j  30
          """
          if ext_dtypes is not None and len(ext_dtypes) > 0:
              pdf = pdf.astype(ext_dtypes, copy=True)
  
          if categorical_dtypes is not None:
              for col, dtype in categorical_dtypes.items():
                  pdf[col] = pd.Categorical.from_codes(
                      pdf[col], categories=dtype.categories, ordered=dtype.ordered
                  )
  
          append = False
          for index_field in index_columns:
              drop = index_field not in data_columns
              pdf = pdf.set_index(index_field, drop=drop, append=append)
              append = True
          pdf = pdf[data_columns]
  
          pdf.index.names = [
              name if name is None or len(name) > 1 else name[0] for name in index_names
          ]
  
          names = [name if name is None or len(name) > 1 else name[0] for name in column_label_names]
          if len(column_label_names) > 1:
              pdf.columns = pd.MultiIndex.from_tuples(column_labels, names=names)
          else:
              pdf.columns = pd.Index(
                  [None if label is None else label[0] for label in column_labels], name=names[0],
              )
  
          return pdf
  
      @lazy_property
      def resolved_copy(self) -> "InternalFrame":
          """ Copy the immutable InternalFrame with the updates resolved. """
          sdf = self.spark_frame.select(self.spark_columns + list(HIDDEN_COLUMNS))
          return self.copy(
              spark_frame=sdf,
              index_spark_columns=[scol_for(sdf, col) for col in self.index_spark_column_names],
              data_spark_columns=[scol_for(sdf, col) for col in self.data_spark_column_names],
          )
  
      def with_new_sdf(
          self,
          spark_frame: spark.DataFrame,
          *,
          index_dtypes: Optional[List[Dtype]] = None,
          data_columns: Optional[List[str]] = None,
          data_dtypes: Optional[List[Dtype]] = None
      ) -> "InternalFrame":
          """ Copy the immutable InternalFrame with the updates by the specified Spark DataFrame.
  
          :param spark_frame: the new Spark DataFrame
          :param index_dtypes: the index dtypes. If None, the original dtyeps are used.
          :param data_columns: the new column names. If None, the original one is used.
          :param data_dtypes: the data dtypes. If None, the original dtyeps are used.
          :return: the copied InternalFrame.
          """
          if index_dtypes is None:
              index_dtypes = self.index_dtypes
          else:
              assert len(index_dtypes) == len(self.index_dtypes), (
                  len(index_dtypes),
                  len(self.index_dtypes),
              )
  
          if data_columns is None:
              data_columns = self.data_spark_column_names
          else:
              assert len(data_columns) == len(self.column_labels), (
                  len(data_columns),
                  len(self.column_labels),
              )
  
          if data_dtypes is None:
              data_dtypes = self.data_dtypes
          else:
              assert len(data_dtypes) == len(self.column_labels), (
                  len(data_dtypes),
                  len(self.column_labels),
              )
  
          sdf = spark_frame.drop(NATURAL_ORDER_COLUMN_NAME)
          return self.copy(
              spark_frame=sdf,
              index_spark_columns=[scol_for(sdf, col) for col in self.index_spark_column_names],
              index_dtypes=index_dtypes,
              data_spark_columns=[scol_for(sdf, col) for col in data_columns],
              data_dtypes=data_dtypes,
          )
  
      def with_new_columns(
          self,
          scols_or_ksers: List[Union[spark.Column, "Series"]],
          *,
          column_labels: Optional[List[Tuple]] = None,
          data_dtypes: Optional[List[Dtype]] = None,
          column_label_names: Optional[Union[List[Optional[Tuple]], _NoValueType]] = _NoValue,
          keep_order: bool = True
      ) -> "InternalFrame":
          """
          Copy the immutable InternalFrame with the updates by the specified Spark Columns or Series.
  
          :param scols_or_ksers: the new Spark Columns or Series.
          :param column_labels: the new column index.
              If None, the column_labels of the corresponding `scols_or_ksers` is used if it is
              Series; otherwise the original one is used.
          :param data_dtypes: the new dtypes.
              If None, the dtypes of the corresponding `scols_or_ksers` is used if it is Series;
              otherwise the dtypes will be inferred from the corresponding `scols_or_ksers`.
          :param column_label_names: the new names of the column index levels.
          :return: the copied InternalFrame.
          """
          from databricks.koalas.series import Series
  
          if column_labels is None:
              if all(isinstance(scol_or_kser, Series) for scol_or_kser in scols_or_ksers):
                  column_labels = [kser._column_label for kser in scols_or_ksers]
              else:
                  assert len(scols_or_ksers) == len(self.column_labels), (
                      len(scols_or_ksers),
                      len(self.column_labels),
                  )
                  column_labels = []
                  for scol_or_kser, label in zip(scols_or_ksers, self.column_labels):
                      if isinstance(scol_or_kser, Series):
                          column_labels.append(scol_or_kser._column_label)
                      else:
                          column_labels.append(label)
          else:
              assert len(scols_or_ksers) == len(column_labels), (
                  len(scols_or_ksers),
                  len(column_labels),
              )
  
          data_spark_columns = []
          for scol_or_kser in scols_or_ksers:
              if isinstance(scol_or_kser, Series):
                  scol = scol_or_kser.spark.column
              else:
                  scol = scol_or_kser
              data_spark_columns.append(scol)
  
          if data_dtypes is None:
              data_dtypes = []
              for scol_or_kser in scols_or_ksers:
                  if isinstance(scol_or_kser, Series):
                      data_dtypes.append(scol_or_kser.dtype)
                  else:
                      data_dtypes.append(None)
          else:
              assert len(scols_or_ksers) == len(data_dtypes), (
                  len(scols_or_ksers),
                  len(data_dtypes),
              )
  
          sdf = self.spark_frame
          if not keep_order:
              sdf = self.spark_frame.select(self.index_spark_columns + data_spark_columns)
              index_spark_columns = [scol_for(sdf, col) for col in self.index_spark_column_names]
              data_spark_columns = [
                  scol_for(sdf, col) for col in self.spark_frame.select(data_spark_columns).columns
              ]
          else:
              index_spark_columns = self.index_spark_columns
  
          if column_label_names is _NoValue:
              column_label_names = self._column_label_names
  
          return self.copy(
              spark_frame=sdf,
              index_spark_columns=index_spark_columns,
              column_labels=column_labels,
              data_spark_columns=data_spark_columns,
              data_dtypes=data_dtypes,
              column_label_names=column_label_names,
          )
  
      def with_filter(self, pred: Union[spark.Column, "Series"]) -> "InternalFrame":
          """ Copy the immutable InternalFrame with the updates by the predicate.
  
          :param pred: the predicate to filter.
          :return: the copied InternalFrame.
          """
          from databricks.koalas.series import Series
  
          if isinstance(pred, Series):
              assert isinstance(pred.spark.data_type, BooleanType), pred.spark.data_type
              pred = pred.spark.column
          else:
              spark_type = self.spark_frame.select(pred).schema[0].dataType
              assert isinstance(spark_type, BooleanType), spark_type
  
          return self.with_new_sdf(self.spark_frame.filter(pred).select(self.spark_columns))
  
      def with_new_spark_column(
          self,
          column_label: Tuple,
          scol: spark.Column,
          *,
          dtype: Optional[Dtype] = None,
          keep_order: bool = True
      ) -> "InternalFrame":
          """
          Copy the immutable InternalFrame with the updates by the specified Spark Column.
  
          :param column_label: the column label to be updated.
          :param scol: the new Spark Column
          :param dtype: the new dtype.
              If not specified, the dtypes will be inferred from the spark Column.
          :return: the copied InternalFrame.
          """
          assert column_label in self.column_labels, column_label
  
          idx = self.column_labels.index(column_label)
          data_spark_columns = self.data_spark_columns.copy()
          data_spark_columns[idx] = scol
          data_dtypes = self.data_dtypes.copy()
          data_dtypes[idx] = dtype
          return self.with_new_columns(
              data_spark_columns, data_dtypes=data_dtypes, keep_order=keep_order
          )
  
      def select_column(self, column_label: Tuple) -> "InternalFrame":
          """
          Copy the immutable InternalFrame with the specified column.
  
          :param column_label: the column label to use.
          :return: the copied InternalFrame.
          """
          assert column_label in self.column_labels, column_label
  
          return self.copy(
              column_labels=[column_label],
              data_spark_columns=[self.spark_column_for(column_label)],
              data_dtypes=[self.dtype_for(column_label)],
              column_label_names=None,
          )
  
      def copy(
          self,
          *,
          spark_frame: Union[spark.DataFrame, _NoValueType] = _NoValue,
          index_spark_columns: Union[List[spark.Column], _NoValueType] = _NoValue,
          index_names: Union[List[Optional[Tuple]], _NoValueType] = _NoValue,
          index_dtypes: Optional[Union[List[Dtype], _NoValueType]] = _NoValue,
          column_labels: Optional[Union[List[Tuple], _NoValueType]] = _NoValue,
          data_spark_columns: Optional[Union[List[spark.Column], _NoValueType]] = _NoValue,
          data_dtypes: Optional[Union[List[Dtype], _NoValueType]] = _NoValue,
          column_label_names: Optional[Union[List[Optional[Tuple]], _NoValueType]] = _NoValue
      ) -> "InternalFrame":
          """ Copy the immutable InternalFrame.
  
          :param spark_frame: the new Spark DataFrame. If not specified, the original one is used.
          :param index_spark_columns: the list of Spark Column.
                                      If not specified, the original ones are used.
          :param index_names: the index names. If not specified, the original ones are used.
          :param index_dtypes: the index dtypes. If not specified, the original dtyeps are used.
          :param column_labels: the new column labels. If not specified, the original ones are used.
          :param data_spark_columns: the new Spark Columns.
                                     If not specified, the original ones are used.
          :param data_dtypes: the data dtypes. If not specified, the original dtyeps are used.
          :param column_label_names: the new names of the column index levels.
                                     If not specified, the original ones are used.
          :return: the copied immutable InternalFrame.
          """
          if spark_frame is _NoValue:
              spark_frame = self.spark_frame
          if index_spark_columns is _NoValue:
              index_spark_columns = self.index_spark_columns
          if index_names is _NoValue:
              index_names = self.index_names
          if index_dtypes is _NoValue:
              index_dtypes = self.index_dtypes
          if column_labels is _NoValue:
              column_labels = self.column_labels
          if data_spark_columns is _NoValue:
              data_spark_columns = self.data_spark_columns
          if data_dtypes is _NoValue:
              data_dtypes = self.data_dtypes
          if column_label_names is _NoValue:
              column_label_names = self.column_label_names
          return InternalFrame(
              spark_frame=spark_frame,
              index_spark_columns=index_spark_columns,
              index_names=index_names,
              index_dtypes=index_dtypes,
              column_labels=column_labels,
              data_spark_columns=data_spark_columns,
              data_dtypes=data_dtypes,
              column_label_names=column_label_names,
          )
  
      @staticmethod
      def from_pandas(pdf: pd.DataFrame) -> "InternalFrame":
          """ Create an immutable DataFrame from pandas DataFrame.
  
          :param pdf: :class:`pd.DataFrame`
          :return: the created immutable DataFrame
          """
  
          index_names = [
              name if name is None or isinstance(name, tuple) else (name,) for name in pdf.index.names
          ]
  
          columns = pdf.columns
          if isinstance(columns, pd.MultiIndex):
              column_labels = columns.tolist()
          else:
              column_labels = [(col,) for col in columns]
          column_label_names = [
              name if name is None or isinstance(name, tuple) else (name,) for name in columns.names
          ]
  
          (
              pdf,
              index_columns,
              index_dtypes,
              data_columns,
              data_dtypes,
          ) = InternalFrame.prepare_pandas_frame(pdf)
  
          schema = StructType(
              [
                  StructField(
                      name, infer_pd_series_spark_type(col, dtype), nullable=bool(col.isnull().any()),
                  )
                  for (name, col), dtype in zip(pdf.iteritems(), index_dtypes + data_dtypes)
              ]
          )
  
          sdf = default_session().createDataFrame(pdf, schema=schema)
          return InternalFrame(
              spark_frame=sdf,
              index_spark_columns=[scol_for(sdf, col) for col in index_columns],
              index_names=index_names,
              index_dtypes=index_dtypes,
              column_labels=column_labels,
              data_spark_columns=[scol_for(sdf, col) for col in data_columns],
              data_dtypes=data_dtypes,
              column_label_names=column_label_names,
          )
  
      @staticmethod
      def prepare_pandas_frame(
          pdf: pd.DataFrame, *, retain_index: bool = True
      ) -> Tuple[pd.DataFrame, List[str], List[Dtype], List[str], List[Dtype]]:
          """
          Prepare pandas DataFrame for creating Spark DataFrame.
  
          :param pdf: the pandas DataFrame to be prepared.
          :param retain_index: whether the indices should be retained.
          :return: the tuple of
              - the prepared pandas dataFrame
              - index column names for Spark DataFrame
              - index dtypes of the given pandas DataFrame
              - data column names for Spark DataFrame
              - data dtypes of the given pandas DataFrame
  
          >>> pdf = pd.DataFrame(
          ...    {("x", "a"): ['a', 'b', 'c'],
          ...     ("y", "b"): pd.Categorical(["i", "k", "j"], categories=["i", "j", "k"])},
          ...    index=[10, 20, 30])
          >>> prepared, index_columns, index_dtypes, data_columns, data_dtypes = (
          ...     InternalFrame.prepare_pandas_frame(pdf))
          >>> prepared
             __index_level_0__ (x, a)  (y, b)
          0                 10      a       0
          1                 20      b       2
          2                 30      c       1
          >>> index_columns
          ['__index_level_0__']
          >>> index_dtypes
          [dtype('int64')]
          >>> data_columns
          ['(x, a)', '(y, b)']
          >>> data_dtypes
          [dtype('O'), CategoricalDtype(categories=['i', 'j', 'k'], ordered=False)]
          """
          pdf = pdf.copy()
  
          data_columns = [name_like_string(col) for col in pdf.columns]
          pdf.columns = data_columns
  
          if retain_index:
              index_nlevels = pdf.index.nlevels
              index_columns = [SPARK_INDEX_NAME_FORMAT(i) for i in range(index_nlevels)]
              pdf.index.names = index_columns
              reset_index = pdf.reset_index()
          else:
              index_nlevels = 0
              index_columns = []
              reset_index = pdf
  
          index_dtypes = list(reset_index.dtypes)[:index_nlevels]
          data_dtypes = list(reset_index.dtypes)[index_nlevels:]
  
          for name, col in reset_index.iteritems():
              dt = col.dtype
              if is_datetime64_dtype(dt) or is_datetime64tz_dtype(dt):
                  continue
              elif isinstance(dt, CategoricalDtype):
                  col = col.cat.codes
              reset_index[name] = col.replace({np.nan: None})
  
          return reset_index, index_columns, index_dtypes, data_columns, data_dtypes
  