merge.py

"""
SQL-style merge routines
"""

import copy
import string
import warnings

import numpy as np

from pandas._libs import hashtable as libhashtable, join as libjoin, lib
import pandas.compat as compat
from pandas.compat import filter, lzip, map, range, zip
from pandas.errors import MergeError
from pandas.util._decorators import Appender, Substitution

from pandas.core.dtypes.common import (
    ensure_float64, ensure_int64, ensure_object, is_array_like, is_bool,
    is_bool_dtype, is_categorical_dtype, is_datetime64_dtype,
    is_datetime64tz_dtype, is_datetimelike, is_dtype_equal,
    is_extension_array_dtype, is_float_dtype, is_int64_dtype, is_integer,
    is_integer_dtype, is_list_like, is_number, is_numeric_dtype,
    is_object_dtype, needs_i8_conversion)
from pandas.core.dtypes.missing import isnull, na_value_for_dtype

from pandas import Categorical, DataFrame, Index, MultiIndex, Series, Timedelta
import pandas.core.algorithms as algos
from pandas.core.arrays.categorical import _recode_for_categories
import pandas.core.common as com
from pandas.core.frame import _merge_doc
from pandas.core.internals import (
    concatenate_block_managers, items_overlap_with_suffix)
import pandas.core.sorting as sorting
from pandas.core.sorting import is_int64_overflow_possible


@Substitution('\nleft : DataFrame')
@Appender(_merge_doc, indents=0)
def merge(left, right, how='inner', on=None, left_on=None, right_on=None,
          left_index=False, right_index=False, sort=False,
          suffixes=('_x', '_y'), copy=True, indicator=False,
          validate=None):
    op = _MergeOperation(left, right, how=how, on=on, left_on=left_on,
                         right_on=right_on, left_index=left_index,
                         right_index=right_index, sort=sort, suffixes=suffixes,
                         copy=copy, indicator=indicator,
                         validate=validate)
    return op.get_result()


if __debug__:
    merge.__doc__ = _merge_doc % '\nleft : DataFrame'


def _groupby_and_merge(by, on, left, right, _merge_pieces,
                       check_duplicates=True):
    """
    groupby & merge; we are always performing a left-by type operation

    Parameters
    ----------
    by: field to group
    on: duplicates field
    left: left frame
    right: right frame
    _merge_pieces: function for merging
    check_duplicates: boolean, default True
        should we check & clean duplicates
    """

    pieces = []
    if not isinstance(by, (list, tuple)):
        by = [by]

    lby = left.groupby(by, sort=False)

    # if we can groupby the rhs
    # then we can get vastly better perf
    try:

        # we will check & remove duplicates if indicated
        if check_duplicates:
            if on is None:
                on = []
            elif not isinstance(on, (list, tuple)):
                on = [on]

            if right.duplicated(by + on).any():
                right = right.drop_duplicates(by + on, keep='last')
        rby = right.groupby(by, sort=False)
    except KeyError:
        rby = None

    for key, lhs in lby:

        if rby is None:
            rhs = right
        else:
            try:
                rhs = right.take(rby.indices[key])
            except KeyError:
                # key doesn't exist in left
                lcols = lhs.columns.tolist()
                cols = lcols + [r for r in right.columns
                                if r not in set(lcols)]
                merged = lhs.reindex(columns=cols)
                merged.index = range(len(merged))
                pieces.append(merged)
                continue

        merged = _merge_pieces(lhs, rhs)

        # make sure join keys are in the merged
        # TODO, should _merge_pieces do this?
        for k in by:
            try:
                if k in merged:
                    merged[k] = key
            except KeyError:
                pass

        pieces.append(merged)

    # preserve the original order
    # if we have a missing piece this can be reset
    from pandas.core.reshape.concat import concat
    result = concat(pieces, ignore_index=True)
    result = result.reindex(columns=pieces[0].columns, copy=False)
    return result, lby


def merge_ordered(left, right, on=None,
                  left_on=None, right_on=None,
                  left_by=None, right_by=None,
                  fill_method=None, suffixes=('_x', '_y'),
                  how='outer'):
    """Perform merge with optional filling/interpolation designed for ordered
    data like time series data. Optionally perform group-wise merge (see
    examples)

    Parameters
    ----------
    left : DataFrame
    right : DataFrame
    on : label or list
        Field names to join on. Must be found in both DataFrames.
    left_on : label or list, or array-like
        Field names to join on in left DataFrame. Can be a vector or list of
        vectors of the length of the DataFrame to use a particular vector as
        the join key instead of columns
    right_on : label or list, or array-like
        Field names to join on in right DataFrame or vector/list of vectors per
        left_on docs
    left_by : column name or list of column names
        Group left DataFrame by group columns and merge piece by piece with
        right DataFrame
    right_by : column name or list of column names
        Group right DataFrame by group columns and merge piece by piece with
        left DataFrame
    fill_method : {'ffill', None}, default None
        Interpolation method for data
    suffixes : 2-length sequence (tuple, list, ...)
        Suffix to apply to overlapping column names in the left and right
        side, respectively
    how : {'left', 'right', 'outer', 'inner'}, default 'outer'
        * left: use only keys from left frame (SQL: left outer join)
        * right: use only keys from right frame (SQL: right outer join)
        * outer: use union of keys from both frames (SQL: full outer join)
        * inner: use intersection of keys from both frames (SQL: inner join)

        .. versionadded:: 0.19.0

    Returns
    -------
    merged : DataFrame
        The output type will the be same as 'left', if it is a subclass
        of DataFrame.

    See Also
    --------
    merge
    merge_asof

    Examples
    --------
    >>> A                      >>> B
          key  lvalue group        key  rvalue
    0   a       1     a        0     b       1
    1   c       2     a        1     c       2
    2   e       3     a        2     d       3
    3   a       1     b
    4   c       2     b
    5   e       3     b

    >>> merge_ordered(A, B, fill_method='ffill', left_by='group')
      group key  lvalue  rvalue
    0     a   a       1     NaN
    1     a   b       1     1.0
    2     a   c       2     2.0
    3     a   d       2     3.0
    4     a   e       3     3.0
    5     b   a       1     NaN
    6     b   b       1     1.0
    7     b   c       2     2.0
    8     b   d       2     3.0
    9     b   e       3     3.0
    """
    def _merger(x, y):
        # perform the ordered merge operation
        op = _OrderedMerge(x, y, on=on, left_on=left_on, right_on=right_on,
                           suffixes=suffixes, fill_method=fill_method,
                           how=how)
        return op.get_result()

    if left_by is not None and right_by is not None:
        raise ValueError('Can only group either left or right frames')
    elif left_by is not None:
        result, _ = _groupby_and_merge(left_by, on, left, right,
                                       lambda x, y: _merger(x, y),
                                       check_duplicates=False)
    elif right_by is not None:
        result, _ = _groupby_and_merge(right_by, on, right, left,
                                       lambda x, y: _merger(y, x),
                                       check_duplicates=False)
    else:
        result = _merger(left, right)
    return result


def merge_asof(left, right, on=None,
               left_on=None, right_on=None,
               left_index=False, right_index=False,
               by=None, left_by=None, right_by=None,
               suffixes=('_x', '_y'),
               tolerance=None,
               allow_exact_matches=True,
               direction='backward'):
    """Perform an asof merge. This is similar to a left-join except that we
    match on nearest key rather than equal keys.

    Both DataFrames must be sorted by the key.

    For each row in the left DataFrame:

      - A "backward" search selects the last row in the right DataFrame whose
        'on' key is less than or equal to the left's key.

      - A "forward" search selects the first row in the right DataFrame whose
        'on' key is greater than or equal to the left's key.

      - A "nearest" search selects the row in the right DataFrame whose 'on'
        key is closest in absolute distance to the left's key.

    The default is "backward" and is compatible in versions below 0.20.0.
    The direction parameter was added in version 0.20.0 and introduces
    "forward" and "nearest".

    Optionally match on equivalent keys with 'by' before searching with 'on'.

    .. versionadded:: 0.19.0

    Parameters
    ----------
    left : DataFrame
    right : DataFrame
    on : label
        Field name to join on. Must be found in both DataFrames.
        The data MUST be ordered. Furthermore this must be a numeric column,
        such as datetimelike, integer, or float. On or left_on/right_on
        must be given.
    left_on : label
        Field name to join on in left DataFrame.
    right_on : label
        Field name to join on in right DataFrame.
    left_index : boolean
        Use the index of the left DataFrame as the join key.

        .. versionadded:: 0.19.2

    right_index : boolean
        Use the index of the right DataFrame as the join key.

        .. versionadded:: 0.19.2

    by : column name or list of column names
        Match on these columns before performing merge operation.
    left_by : column name
        Field names to match on in the left DataFrame.

        .. versionadded:: 0.19.2

    right_by : column name
        Field names to match on in the right DataFrame.

        .. versionadded:: 0.19.2

    suffixes : 2-length sequence (tuple, list, ...)
        Suffix to apply to overlapping column names in the left and right
        side, respectively.
    tolerance : integer or Timedelta, optional, default None
        Select asof tolerance within this range; must be compatible
        with the merge index.
    allow_exact_matches : boolean, default True

        - If True, allow matching with the same 'on' value
          (i.e. less-than-or-equal-to / greater-than-or-equal-to)
        - If False, don't match the same 'on' value
          (i.e., strictly less-than / strictly greater-than)

    direction : 'backward' (default), 'forward', or 'nearest'
        Whether to search for prior, subsequent, or closest matches.

        .. versionadded:: 0.20.0

    Returns
    -------
    merged : DataFrame

    See Also
    --------
    merge
    merge_ordered

    Examples
    --------
    >>> left = pd.DataFrame({'a': [1, 5, 10], 'left_val': ['a', 'b', 'c']})
    >>> left
        a left_val
    0   1        a
    1   5        b
    2  10        c

    >>> right = pd.DataFrame({'a': [1, 2, 3, 6, 7],
    ...                       'right_val': [1, 2, 3, 6, 7]})
    >>> right
       a  right_val
    0  1          1
    1  2          2
    2  3          3
    3  6          6
    4  7          7

    >>> pd.merge_asof(left, right, on='a')
        a left_val  right_val
    0   1        a          1
    1   5        b          3
    2  10        c          7

    >>> pd.merge_asof(left, right, on='a', allow_exact_matches=False)
        a left_val  right_val
    0   1        a        NaN
    1   5        b        3.0
    2  10        c        7.0

    >>> pd.merge_asof(left, right, on='a', direction='forward')
        a left_val  right_val
    0   1        a        1.0
    1   5        b        6.0
    2  10        c        NaN

    >>> pd.merge_asof(left, right, on='a', direction='nearest')
        a left_val  right_val
    0   1        a          1
    1   5        b          6
    2  10        c          7

    We can use indexed DataFrames as well.

    >>> left = pd.DataFrame({'left_val': ['a', 'b', 'c']}, index=[1, 5, 10])
    >>> left
       left_val
    1         a
    5         b
    10        c

    >>> right = pd.DataFrame({'right_val': [1, 2, 3, 6, 7]},
    ...                      index=[1, 2, 3, 6, 7])
    >>> right
       right_val
    1          1
    2          2
    3          3
    6          6
    7          7

    >>> pd.merge_asof(left, right, left_index=True, right_index=True)
       left_val  right_val
    1         a          1
    5         b          3
    10        c          7

    Here is a real-world times-series example

    >>> quotes
                         time ticker     bid     ask
    0 2016-05-25 13:30:00.023   GOOG  720.50  720.93
    1 2016-05-25 13:30:00.023   MSFT   51.95   51.96
    2 2016-05-25 13:30:00.030   MSFT   51.97   51.98
    3 2016-05-25 13:30:00.041   MSFT   51.99   52.00
    4 2016-05-25 13:30:00.048   GOOG  720.50  720.93
    5 2016-05-25 13:30:00.049   AAPL   97.99   98.01
    6 2016-05-25 13:30:00.072   GOOG  720.50  720.88
    7 2016-05-25 13:30:00.075   MSFT   52.01   52.03

    >>> trades
                         time ticker   price  quantity
    0 2016-05-25 13:30:00.023   MSFT   51.95        75
    1 2016-05-25 13:30:00.038   MSFT   51.95       155
    2 2016-05-25 13:30:00.048   GOOG  720.77       100
    3 2016-05-25 13:30:00.048   GOOG  720.92       100
    4 2016-05-25 13:30:00.048   AAPL   98.00       100

    By default we are taking the asof of the quotes

    >>> pd.merge_asof(trades, quotes,
    ...                       on='time',
    ...                       by='ticker')
                         time ticker   price  quantity     bid     ask
    0 2016-05-25 13:30:00.023   MSFT   51.95        75   51.95   51.96
    1 2016-05-25 13:30:00.038   MSFT   51.95       155   51.97   51.98
    2 2016-05-25 13:30:00.048   GOOG  720.77       100  720.50  720.93
    3 2016-05-25 13:30:00.048   GOOG  720.92       100  720.50  720.93
    4 2016-05-25 13:30:00.048   AAPL   98.00       100     NaN     NaN

    We only asof within 2ms between the quote time and the trade time

    >>> pd.merge_asof(trades, quotes,
    ...                       on='time',
    ...                       by='ticker',
    ...                       tolerance=pd.Timedelta('2ms'))
                         time ticker   price  quantity     bid     ask
    0 2016-05-25 13:30:00.023   MSFT   51.95        75   51.95   51.96
    1 2016-05-25 13:30:00.038   MSFT   51.95       155     NaN     NaN
    2 2016-05-25 13:30:00.048   GOOG  720.77       100  720.50  720.93
    3 2016-05-25 13:30:00.048   GOOG  720.92       100  720.50  720.93
    4 2016-05-25 13:30:00.048   AAPL   98.00       100     NaN     NaN

    We only asof within 10ms between the quote time and the trade time
    and we exclude exact matches on time. However *prior* data will
    propagate forward

    >>> pd.merge_asof(trades, quotes,
    ...                       on='time',
    ...                       by='ticker',
    ...                       tolerance=pd.Timedelta('10ms'),
    ...                       allow_exact_matches=False)
                         time ticker   price  quantity     bid     ask
    0 2016-05-25 13:30:00.023   MSFT   51.95        75     NaN     NaN
    1 2016-05-25 13:30:00.038   MSFT   51.95       155   51.97   51.98
    2 2016-05-25 13:30:00.048   GOOG  720.77       100     NaN     NaN
    3 2016-05-25 13:30:00.048   GOOG  720.92       100     NaN     NaN
    4 2016-05-25 13:30:00.048   AAPL   98.00       100     NaN     NaN
    """
    op = _AsOfMerge(left, right,
                    on=on, left_on=left_on, right_on=right_on,
                    left_index=left_index, right_index=right_index,
                    by=by, left_by=left_by, right_by=right_by,
                    suffixes=suffixes,
                    how='asof', tolerance=tolerance,
                    allow_exact_matches=allow_exact_matches,
                    direction=direction)
    return op.get_result()


# TODO: transformations??
# TODO: only copy DataFrames when modification necessary
class _MergeOperation(object):
    """
    Perform a database (SQL) merge operation between two DataFrame objects
    using either columns as keys or their row indexes
    """
    _merge_type = 'merge'

    def __init__(self, left, right, how='inner', on=None,
                 left_on=None, right_on=None, axis=1,
                 left_index=False, right_index=False, sort=True,
                 suffixes=('_x', '_y'), copy=True, indicator=False,
                 validate=None):
        left = validate_operand(left)
        right = validate_operand(right)
        self.left = self.orig_left = left
        self.right = self.orig_right = right
        self.how = how
        self.axis = axis

        self.on = com.maybe_make_list(on)
        self.left_on = com.maybe_make_list(left_on)
        self.right_on = com.maybe_make_list(right_on)

        self.copy = copy
        self.suffixes = suffixes
        self.sort = sort

        self.left_index = left_index
        self.right_index = right_index

        self.indicator = indicator

        if isinstance(self.indicator, compat.string_types):
            self.indicator_name = self.indicator
        elif isinstance(self.indicator, bool):
            self.indicator_name = '_merge' if self.indicator else None
        else:
            raise ValueError(
                'indicator option can only accept boolean or string arguments')

        if not is_bool(left_index):
            raise ValueError(
                'left_index parameter must be of type bool, not '
                '{left_index}'.format(left_index=type(left_index)))
        if not is_bool(right_index):
            raise ValueError(
                'right_index parameter must be of type bool, not '
                '{right_index}'.format(right_index=type(right_index)))

        # warn user when merging between different levels
        if left.columns.nlevels != right.columns.nlevels:
            msg = ('merging between different levels can give an unintended '
                   'result ({left} levels on the left, {right} on the right)'
                   ).format(left=left.columns.nlevels,
                            right=right.columns.nlevels)
            warnings.warn(msg, UserWarning)

        self._validate_specification()

        # note this function has side effects
        (self.left_join_keys,
         self.right_join_keys,
         self.join_names) = self._get_merge_keys()

        # validate the merge keys dtypes. We may need to coerce
        # to avoid incompat dtypes
        self._maybe_coerce_merge_keys()

        # If argument passed to validate,
        # check if columns specified as unique
        # are in fact unique.
        if validate is not None:
            self._validate(validate)

    def get_result(self):
        if self.indicator:
            self.left, self.right = self._indicator_pre_merge(
                self.left, self.right)

        join_index, left_indexer, right_indexer = self._get_join_info()

        ldata, rdata = self.left._data, self.right._data
        lsuf, rsuf = self.suffixes

        llabels, rlabels = items_overlap_with_suffix(ldata.items, lsuf,
                                                     rdata.items, rsuf)

        lindexers = {1: left_indexer} if left_indexer is not None else {}
        rindexers = {1: right_indexer} if right_indexer is not None else {}

        result_data = concatenate_block_managers(
            [(ldata, lindexers), (rdata, rindexers)],
            axes=[llabels.append(rlabels), join_index],
            concat_axis=0, copy=self.copy)

        typ = self.left._constructor
        result = typ(result_data).__finalize__(self, method=self._merge_type)

        if self.indicator:
            result = self._indicator_post_merge(result)

        self._maybe_add_join_keys(result, left_indexer, right_indexer)

        self._maybe_restore_index_levels(result)

        return result

    def _indicator_pre_merge(self, left, right):

        columns = left.columns.union(right.columns)

        for i in ['_left_indicator', '_right_indicator']:
            if i in columns:
                raise ValueError("Cannot use `indicator=True` option when "
                                 "data contains a column named {name}"
                                 .format(name=i))
        if self.indicator_name in columns:
            raise ValueError(
                "Cannot use name of an existing column for indicator column")

        left = left.copy()
        right = right.copy()

        left['_left_indicator'] = 1
        left['_left_indicator'] = left['_left_indicator'].astype('int8')

        right['_right_indicator'] = 2
        right['_right_indicator'] = right['_right_indicator'].astype('int8')

        return left, right

    def _indicator_post_merge(self, result):

        result['_left_indicator'] = result['_left_indicator'].fillna(0)
        result['_right_indicator'] = result['_right_indicator'].fillna(0)

        result[self.indicator_name] = Categorical((result['_left_indicator'] +
                                                   result['_right_indicator']),
                                                  categories=[1, 2, 3])
        result[self.indicator_name] = (
            result[self.indicator_name]
            .cat.rename_categories(['left_only', 'right_only', 'both']))

        result = result.drop(labels=['_left_indicator', '_right_indicator'],
                             axis=1)
        return result

    def _maybe_restore_index_levels(self, result):
        """
        Restore index levels specified as `on` parameters

        Here we check for cases where `self.left_on` and `self.right_on` pairs
        each reference an index level in their respective DataFrames. The
        joined columns corresponding to these pairs are then restored to the
        index of `result`.

        **Note:** This method has side effects. It modifies `result` in-place

        Parameters
        ----------
        result: DataFrame
            merge result

        Returns
        -------
        None
        """
        names_to_restore = []
        for name, left_key, right_key in zip(self.join_names,
                                             self.left_on,
                                             self.right_on):
            if (self.orig_left._is_level_reference(left_key) and
                    self.orig_right._is_level_reference(right_key) and
                    name not in result.index.names):

                names_to_restore.append(name)

        if names_to_restore:
            result.set_index(names_to_restore, inplace=True)

    def _maybe_add_join_keys(self, result, left_indexer, right_indexer):

        left_has_missing = None
        right_has_missing = None

        keys = zip(self.join_names, self.left_on, self.right_on)
        for i, (name, lname, rname) in enumerate(keys):
            if not _should_fill(lname, rname):
                continue

            take_left, take_right = None, None

            if name in result:

                if left_indexer is not None and right_indexer is not None:
                    if name in self.left:

                        if left_has_missing is None:
                            left_has_missing = (left_indexer == -1).any()

                        if left_has_missing:
                            take_right = self.right_join_keys[i]

                            if not is_dtype_equal(result[name].dtype,
                                                  self.left[name].dtype):
                                take_left = self.left[name]._values

                    elif name in self.right:

                        if right_has_missing is None:
                            right_has_missing = (right_indexer == -1).any()

                        if right_has_missing:
                            take_left = self.left_join_keys[i]

                            if not is_dtype_equal(result[name].dtype,
                                                  self.right[name].dtype):
                                take_right = self.right[name]._values

            elif left_indexer is not None \
                    and is_array_like(self.left_join_keys[i]):
                take_left = self.left_join_keys[i]
                take_right = self.right_join_keys[i]

            if take_left is not None or take_right is not None:

                if take_left is None:
                    lvals = result[name]._values
                else:
                    lfill = na_value_for_dtype(take_left.dtype)
                    lvals = algos.take_1d(take_left, left_indexer,
                                          fill_value=lfill)

                if take_right is None:
                    rvals = result[name]._values
                else:
                    rfill = na_value_for_dtype(take_right.dtype)
                    rvals = algos.take_1d(take_right, right_indexer,
                                          fill_value=rfill)

                # if we have an all missing left_indexer
                # make sure to just use the right values
                mask = left_indexer == -1
                if mask.all():
                    key_col = rvals
                else:
                    key_col = Index(lvals).where(~mask, rvals)

                if result._is_label_reference(name):
                    result[name] = key_col
                elif result._is_level_reference(name):
                    if isinstance(result.index, MultiIndex):
                        key_col.name = name
                        idx_list = [result.index.get_level_values(level_name)
                                    if level_name != name else key_col
                                    for level_name in result.index.names]

                        result.set_index(idx_list, inplace=True)
                    else:
                        result.index = Index(key_col, name=name)
                else:
                    result.insert(i, name or 'key_{i}'.format(i=i), key_col)

    def _get_join_indexers(self):
        """ return the join indexers """
        return _get_join_indexers(self.left_join_keys,
                                  self.right_join_keys,
                                  sort=self.sort,
                                  how=self.how)

    def _get_join_info(self):
        left_ax = self.left._data.axes[self.axis]
        right_ax = self.right._data.axes[self.axis]

        if self.left_index and self.right_index and self.how != 'asof':
            join_index, left_indexer, right_indexer = \
                left_ax.join(right_ax, how=self.how, return_indexers=True,
                             sort=self.sort)
        elif self.right_index and self.how == 'left':
            join_index, left_indexer, right_indexer = \
                _left_join_on_index(left_ax, right_ax, self.left_join_keys,
                                    sort=self.sort)

        elif self.left_index and self.how == 'right':
            join_index, right_indexer, left_indexer = \
                _left_join_on_index(right_ax, left_ax, self.right_join_keys,
                                    sort=self.sort)
        else:
            (left_indexer,
             right_indexer) = self._get_join_indexers()

            if self.right_index:
                if len(self.left) > 0:
                    join_index = self.left.index.take(left_indexer)
                else:
                    join_index = self.right.index.take(right_indexer)
                    left_indexer = np.array([-1] * len(join_index))
            elif self.left_index:
                if len(self.right) > 0:
                    join_index = self.right.index.take(right_indexer)
                else:
                    join_index = self.left.index.take(left_indexer)
                    right_indexer = np.array([-1] * len(join_index))
            else:
                join_index = Index(np.arange(len(left_indexer)))

        if len(join_index) == 0:
            join_index = join_index.astype(object)
        return join_index, left_indexer, right_indexer

    def _get_merge_keys(self):
        """
        Note: has side effects (copy/delete key columns)

        Parameters
        ----------
        left
        right
        on

        Returns
        -------
        left_keys, right_keys
        """
        left_keys = []
        right_keys = []
        join_names = []
        right_drop = []
        left_drop = []

        left, right = self.left, self.right

        is_lkey = lambda x: is_array_like(x) and len(x) == len(left)
        is_rkey = lambda x: is_array_like(x) and len(x) == len(right)

        # Note that pd.merge_asof() has separate 'on' and 'by' parameters. A
        # user could, for example, request 'left_index' and 'left_by'. In a
        # regular pd.merge(), users cannot specify both 'left_index' and
        # 'left_on'. (Instead, users have a MultiIndex). That means the
        # self.left_on in this function is always empty in a pd.merge(), but
        # a pd.merge_asof(left_index=True, left_by=...) will result in a
        # self.left_on array with a None in the middle of it. This requires
        # a work-around as designated in the code below.
        # See _validate_specification() for where this happens.

        # ugh, spaghetti re #733
        if _any(self.left_on) and _any(self.right_on):
            for lk, rk in zip(self.left_on, self.right_on):
                if is_lkey(lk):
                    left_keys.append(lk)
                    if is_rkey(rk):
                        right_keys.append(rk)
                        join_names.append(None)  # what to do?
                    else:
                        if rk is not None:
                            right_keys.append(
                                right._get_label_or_level_values(rk))
                            join_names.append(rk)
                        else:
                            # work-around for merge_asof(right_index=True)
                            right_keys.append(right.index)
                            join_names.append(right.index.name)
                else:
                    if not is_rkey(rk):
                        if rk is not None:
                            right_keys.append(
                                right._get_label_or_level_values(rk))
                        else:
                            # work-around for merge_asof(right_index=True)
                            right_keys.append(right.index)
                        if lk is not None and lk == rk:
                            # avoid key upcast in corner case (length-0)
                            if len(left) > 0:
                                right_drop.append(rk)
                            else:
                                left_drop.append(lk)
                    else:
                        right_keys.append(rk)
                    if lk is not None:
                        left_keys.append(left._get_label_or_level_values(lk))
                        join_names.append(lk)
                    else:
                        # work-around for merge_asof(left_index=True)
                        left_keys.append(left.index)
                        join_names.append(left.index.name)
        elif _any(self.left_on):
            for k in self.left_on:
                if is_lkey(k):
                    left_keys.append(k)
                    join_names.append(None)
                else:
                    left_keys.append(left._get_label_or_level_values(k))
                    join_names.append(k)
            if isinstance(self.right.index, MultiIndex):
                right_keys = [lev._values.take(lev_codes) for lev, lev_codes
                              in zip(self.right.index.levels,
                                     self.right.index.codes)]
            else:
                right_keys = [self.right.index._values]
        elif _any(self.right_on):
            for k in self.right_on:
                if is_rkey(k):
                    right_keys.append(k)
                    join_names.append(None)
                else:
                    right_keys.append(right._get_label_or_level_values(k))
                    join_names.append(k)
            if isinstance(self.left.index, MultiIndex):
                left_keys = [lev._values.take(lev_codes) for lev, lev_codes
                             in zip(self.left.index.levels,
                                    self.left.index.codes)]
            else:
                left_keys = [self.left.index.values]

        if left_drop:
            self.left = self.left._drop_labels_or_levels(left_drop)

        if right_drop:
            self.right = self.right._drop_labels_or_levels(right_drop)

        return left_keys, right_keys, join_names

    def _maybe_coerce_merge_keys(self):
        # we have valid mergees but we may have to further
        # coerce these if they are originally incompatible types
        #
        # for example if these are categorical, but are not dtype_equal
        # or if we have object and integer dtypes

        for lk, rk, name in zip(self.left_join_keys,
                                self.right_join_keys,
                                self.join_names):
            if (len(lk) and not len(rk)) or (not len(lk) and len(rk)):
                continue

            lk_is_cat = is_categorical_dtype(lk)
            rk_is_cat = is_categorical_dtype(rk)
            lk_is_object = is_object_dtype(lk)
            rk_is_object = is_object_dtype(rk)

            # if either left or right is a categorical
            # then the must match exactly in categories & ordered
            if lk_is_cat and rk_is_cat:
                if lk.is_dtype_equal(rk):
                    continue

            elif lk_is_cat or rk_is_cat:
                pass

            elif is_dtype_equal(lk.dtype, rk.dtype):
                continue

            msg = ("You are trying to merge on {lk_dtype} and "
                   "{rk_dtype} columns. If you wish to proceed "
                   "you should use pd.concat".format(lk_dtype=lk.dtype,
                                                     rk_dtype=rk.dtype))

            # if we are numeric, then allow differing
            # kinds to proceed, eg. int64 and int8, int and float
            # further if we are object, but we infer to
            # the same, then proceed
            if is_numeric_dtype(lk) and is_numeric_dtype(rk):
                if lk.dtype.kind == rk.dtype.kind:
                    continue

                # check whether ints and floats
                elif is_integer_dtype(rk) and is_float_dtype(lk):
                    if not (lk == lk.astype(rk.dtype))[~np.isnan(lk)].all():
                        warnings.warn('You are merging on int and float '
                                      'columns where the float values '
                                      'are not equal to their int '
                                      'representation', UserWarning)
                    continue

                elif is_float_dtype(rk) and is_integer_dtype(lk):
                    if not (rk == rk.astype(lk.dtype))[~np.isnan(rk)].all():
                        warnings.warn('You are merging on int and float '
                                      'columns where the float values '
                                      'are not equal to their int '
                                      'representation', UserWarning)
                    continue

                # let's infer and see if we are ok
                elif (lib.infer_dtype(lk, skipna=False)
                      == lib.infer_dtype(rk, skipna=False)):
                    continue

            # Check if we are trying to merge on obviously
            # incompatible dtypes GH 9780, GH 15800

            # bool values are coerced to object
            elif ((lk_is_object and is_bool_dtype(rk)) or
                  (is_bool_dtype(lk) and rk_is_object)):
                pass

            # object values are allowed to be merged
            elif ((lk_is_object and is_numeric_dtype(rk)) or
                  (is_numeric_dtype(lk) and rk_is_object)):
                inferred_left = lib.infer_dtype(lk, skipna=False)
                inferred_right = lib.infer_dtype(rk, skipna=False)
                bool_types = ['integer', 'mixed-integer', 'boolean', 'empty']
                string_types = ['string', 'unicode', 'mixed', 'bytes', 'empty']

                # inferred bool
                if (inferred_left in bool_types and
                        inferred_right in bool_types):
                    pass

                # unless we are merging non-string-like with string-like
                elif ((inferred_left in string_types and
                       inferred_right not in string_types) or
                      (inferred_right in string_types and
                       inferred_left not in string_types)):
                    raise ValueError(msg)

            # datetimelikes must match exactly
            elif is_datetimelike(lk) and not is_datetimelike(rk):
                raise ValueError(msg)
            elif not is_datetimelike(lk) and is_datetimelike(rk):
                raise ValueError(msg)
            elif is_datetime64tz_dtype(lk) and not is_datetime64tz_dtype(rk):
                raise ValueError(msg)
            elif not is_datetime64tz_dtype(lk) and is_datetime64tz_dtype(rk):
                raise ValueError(msg)

            elif lk_is_object and rk_is_object:
                continue

            # Houston, we have a problem!
            # let's coerce to object if the dtypes aren't
            # categorical, otherwise coerce to the category
            # dtype. If we coerced categories to object,
            # then we would lose type information on some
            # columns, and end up trying to merge
            # incompatible dtypes. See GH 16900.
            if name in self.left.columns:
                typ = lk.categories.dtype if lk_is_cat else object
                self.left = self.left.assign(
                    **{name: self.left[name].astype(typ)})
            if name in self.right.columns:
                typ = rk.categories.dtype if rk_is_cat else object
                self.right = self.right.assign(
                    **{name: self.right[name].astype(typ)})

    def _validate_specification(self):
        # Hm, any way to make this logic less complicated??
        if self.on is None and self.left_on is None and self.right_on is None:

            if self.left_index and self.right_index:
                self.left_on, self.right_on = (), ()
            elif self.left_index:
                if self.right_on is None:
                    raise MergeError('Must pass right_on or right_index=True')
            elif self.right_index:
                if self.left_on is None:
                    raise MergeError('Must pass left_on or left_index=True')
            else:
                # use the common columns
                common_cols = self.left.columns.intersection(
                    self.right.columns)
                if len(common_cols) == 0:
                    raise MergeError(
                        'No common columns to perform merge on. '
                        'Merge options: left_on={lon}, right_on={ron}, '
                        'left_index={lidx}, right_index={ridx}'
                        .format(lon=self.left_on, ron=self.right_on,
                                lidx=self.left_index, ridx=self.right_index))
                if not common_cols.is_unique:
                    raise MergeError("Data columns not unique: {common!r}"
                                     .format(common=common_cols))
                self.left_on = self.right_on = common_cols
        elif self.on is not None:
            if self.left_on is not None or self.right_on is not None:
                raise MergeError('Can only pass argument "on" OR "left_on" '
                                 'and "right_on", not a combination of both.')
            self.left_on = self.right_on = self.on
        elif self.left_on is not None:
            n = len(self.left_on)
            if self.right_index:
                if len(self.left_on) != self.right.index.nlevels:
                    raise ValueError('len(left_on) must equal the number '
                                     'of levels in the index of "right"')
                self.right_on = [None] * n
        elif self.right_on is not None:
            n = len(self.right_on)
            if self.left_index:
                if len(self.right_on) != self.left.index.nlevels:
                    raise ValueError('len(right_on) must equal the number '
                                     'of levels in the index of "left"')
                self.left_on = [None] * n
        if len(self.right_on) != len(self.left_on):
            raise ValueError("len(right_on) must equal len(left_on)")

    def _validate(self, validate):

        # Check uniqueness of each
        if self.left_index:
            left_unique = self.orig_left.index.is_unique
        else:
            left_unique = MultiIndex.from_arrays(self.left_join_keys
                                                 ).is_unique

        if self.right_index:
            right_unique = self.orig_right.index.is_unique
        else:
            right_unique = MultiIndex.from_arrays(self.right_join_keys
                                                  ).is_unique

        # Check data integrity
        if validate in ["one_to_one", "1:1"]:
            if not left_unique and not right_unique:
                raise MergeError("Merge keys are not unique in either left"
                                 " or right dataset; not a one-to-one merge")
            elif not left_unique:
                raise MergeError("Merge keys are not unique in left dataset;"
                                 " not a one-to-one merge")
            elif not right_unique:
                raise MergeError("Merge keys are not unique in right dataset;"
                                 " not a one-to-one merge")

        elif validate in ["one_to_many", "1:m"]:
            if not left_unique:
                raise MergeError("Merge keys are not unique in left dataset;"
                                 " not a one-to-many merge")

        elif validate in ["many_to_one", "m:1"]:
            if not right_unique:
                raise MergeError("Merge keys are not unique in right dataset;"
                                 " not a many-to-one merge")

        elif validate in ['many_to_many', 'm:m']:
            pass

        else:
            raise ValueError("Not a valid argument for validate")


def _get_join_indexers(left_keys, right_keys, sort=False, how='inner',
                       **kwargs):
    """

    Parameters
    ----------
    left_keys: ndarray, Index, Series
    right_keys: ndarray, Index, Series
    sort: boolean, default False
    how: string {'inner', 'outer', 'left', 'right'}, default 'inner'

    Returns
    -------
    tuple of (left_indexer, right_indexer)
        indexers into the left_keys, right_keys

    """
    from functools import partial

    assert len(left_keys) == len(right_keys), \
        'left_key and right_keys must be the same length'

    # bind `sort` arg. of _factorize_keys
    fkeys = partial(_factorize_keys, sort=sort)

    # get left & right join labels and num. of levels at each location
    llab, rlab, shape = map(list, zip(* map(fkeys, left_keys, right_keys)))

    # get flat i8 keys from label lists
    lkey, rkey = _get_join_keys(llab, rlab, shape, sort)

    # factorize keys to a dense i8 space
    # `count` is the num. of unique keys
    # set(lkey) | set(rkey) == range(count)
    lkey, rkey, count = fkeys(lkey, rkey)

    # preserve left frame order if how == 'left' and sort == False
    kwargs = copy.copy(kwargs)
    if how == 'left':
        kwargs['sort'] = sort
    join_func = _join_functions[how]

    return join_func(lkey, rkey, count, **kwargs)


def _restore_dropped_levels_multijoin(left, right, dropped_level_names,
                                      join_index, lindexer, rindexer):
    """
    *this is an internal non-public method*

    Returns the levels, labels and names of a multi-index to multi-index join.
    Depending on the type of join, this method restores the appropriate
    dropped levels of the joined multi-index.
    The method relies on lidx, rindexer which hold the index positions of
    left and right, where a join was feasible

    Parameters
    ----------
    left : MultiIndex
        left index
    right : MultiIndex
        right index
    dropped_level_names : str array
        list of non-common level names
    join_index : MultiIndex
        the index of the join between the
        common levels of left and right
    lindexer : intp array
        left indexer
    rindexer : intp array
        right indexer

    Returns
    -------
    levels : list of Index
        levels of combined multiindexes
    labels : intp array
        labels of combined multiindexes
    names : str array
        names of combined multiindexes

    """

    def _convert_to_mulitindex(index):
        if isinstance(index, MultiIndex):
            return index
        else:
            return MultiIndex.from_arrays([index.values],
                                          names=[index.name])

    # For multi-multi joins with one overlapping level,
    # the returned index if of type Index
    # Assure that join_index is of type MultiIndex
    # so that dropped levels can be appended
    join_index = _convert_to_mulitindex(join_index)

    join_levels = join_index.levels
    join_codes = join_index.codes
    join_names = join_index.names

    # lindexer and rindexer hold the indexes where the join occurred
    # for left and right respectively. If left/right is None then
    # the join occurred on all indices of left/right
    if lindexer is None:
        lindexer = range(left.size)

    if rindexer is None:
        rindexer = range(right.size)

    # Iterate through the levels that must be restored
    for dropped_level_name in dropped_level_names:
        if dropped_level_name in left.names:
            idx = left
            indexer = lindexer
        else:
            idx = right
            indexer = rindexer

        # The index of the level name to be restored
        name_idx = idx.names.index(dropped_level_name)

        restore_levels = idx.levels[name_idx]
        # Inject -1 in the codes list where a join was not possible
        # IOW indexer[i]=-1
        codes = idx.codes[name_idx]
        restore_codes = algos.take_nd(codes, indexer, fill_value=-1)

        join_levels = join_levels + [restore_levels]
        join_codes = join_codes + [restore_codes]
        join_names = join_names + [dropped_level_name]

    return join_levels, join_codes, join_names


class _OrderedMerge(_MergeOperation):
    _merge_type = 'ordered_merge'

    def __init__(self, left, right, on=None, left_on=None, right_on=None,
                 left_index=False, right_index=False, axis=1,
                 suffixes=('_x', '_y'), copy=True,
                 fill_method=None, how='outer'):

        self.fill_method = fill_method
        _MergeOperation.__init__(self, left, right, on=on, left_on=left_on,
                                 left_index=left_index,
                                 right_index=right_index,
                                 right_on=right_on, axis=axis,
                                 how=how, suffixes=suffixes,
                                 sort=True  # factorize sorts
                                 )

    def get_result(self):
        join_index, left_indexer, right_indexer = self._get_join_info()

        # this is a bit kludgy
        ldata, rdata = self.left._data, self.right._data
        lsuf, rsuf = self.suffixes

        llabels, rlabels = items_overlap_with_suffix(ldata.items, lsuf,
                                                     rdata.items, rsuf)

        if self.fill_method == 'ffill':
            left_join_indexer = libjoin.ffill_indexer(left_indexer)
            right_join_indexer = libjoin.ffill_indexer(right_indexer)
        else:
            left_join_indexer = left_indexer
            right_join_indexer = right_indexer

        lindexers = {
            1: left_join_indexer} if left_join_indexer is not None else {}
        rindexers = {
            1: right_join_indexer} if right_join_indexer is not None else {}

        result_data = concatenate_block_managers(
            [(ldata, lindexers), (rdata, rindexers)],
            axes=[llabels.append(rlabels), join_index],
            concat_axis=0, copy=self.copy)

        typ = self.left._constructor
        result = typ(result_data).__finalize__(self, method=self._merge_type)

        self._maybe_add_join_keys(result, left_indexer, right_indexer)

        return result


def _asof_function(direction):
    name = 'asof_join_{dir}'.format(dir=direction)
    return getattr(libjoin, name, None)


def _asof_by_function(direction):
    name = 'asof_join_{dir}_on_X_by_Y'.format(dir=direction)
    return getattr(libjoin, name, None)


_type_casters = {
    'int64_t': ensure_int64,
    'double': ensure_float64,
    'object': ensure_object,
}


def _get_cython_type_upcast(dtype):
    """ Upcast a dtype to 'int64_t', 'double', or 'object' """
    if is_integer_dtype(dtype):
        return 'int64_t'
    elif is_float_dtype(dtype):
        return 'double'
    else:
        return 'object'


class _AsOfMerge(_OrderedMerge):
    _merge_type = 'asof_merge'

    def __init__(self, left, right, on=None, left_on=None, right_on=None,
                 left_index=False, right_index=False,
                 by=None, left_by=None, right_by=None,
                 axis=1, suffixes=('_x', '_y'), copy=True,
                 fill_method=None,
                 how='asof', tolerance=None,
                 allow_exact_matches=True,
                 direction='backward'):

        self.by = by
        self.left_by = left_by
        self.right_by = right_by
        self.tolerance = tolerance
        self.allow_exact_matches = allow_exact_matches
        self.direction = direction

        _OrderedMerge.__init__(self, left, right, on=on, left_on=left_on,
                               right_on=right_on, left_index=left_index,
                               right_index=right_index, axis=axis,
                               how=how, suffixes=suffixes,
                               fill_method=fill_method)

    def _validate_specification(self):
        super(_AsOfMerge, self)._validate_specification()

        # we only allow on to be a single item for on
        if len(self.left_on) != 1 and not self.left_index:
            raise MergeError("can only asof on a key for left")

        if len(self.right_on) != 1 and not self.right_index:
            raise MergeError("can only asof on a key for right")

        if self.left_index and isinstance(self.left.index, MultiIndex):
            raise MergeError("left can only have one index")

        if self.right_index and isinstance(self.right.index, MultiIndex):
            raise MergeError("right can only have one index")

        # set 'by' columns
        if self.by is not None:
            if self.left_by is not None or self.right_by is not None:
                raise MergeError('Can only pass by OR left_by '
                                 'and right_by')
            self.left_by = self.right_by = self.by
        if self.left_by is None and self.right_by is not None:
            raise MergeError('missing left_by')
        if self.left_by is not None and self.right_by is None:
            raise MergeError('missing right_by')

        # add 'by' to our key-list so we can have it in the
        # output as a key
        if self.left_by is not None:
            if not is_list_like(self.left_by):
                self.left_by = [self.left_by]
            if not is_list_like(self.right_by):
                self.right_by = [self.right_by]

            if len(self.left_by) != len(self.right_by):
                raise MergeError('left_by and right_by must be same length')

            self.left_on = self.left_by + list(self.left_on)
            self.right_on = self.right_by + list(self.right_on)

        # check 'direction' is valid
        if self.direction not in ['backward', 'forward', 'nearest']:
            raise MergeError('direction invalid: {direction}'
                             .format(direction=self.direction))

    @property
    def _asof_key(self):
        """ This is our asof key, the 'on' """
        return self.left_on[-1]

    def _get_merge_keys(self):

        # note this function has side effects
        (left_join_keys,
         right_join_keys,
         join_names) = super(_AsOfMerge, self)._get_merge_keys()

        # validate index types are the same
        for i, (lk, rk) in enumerate(zip(left_join_keys, right_join_keys)):
            if not is_dtype_equal(lk.dtype, rk.dtype):
                raise MergeError("incompatible merge keys [{i}] {lkdtype} and "
                                 "{rkdtype}, must be the same type"
                                 .format(i=i, lkdtype=lk.dtype,
                                         rkdtype=rk.dtype))

        # validate tolerance; must be a Timedelta if we have a DTI
        if self.tolerance is not None:

            if self.left_index:
                lt = self.left.index
            else:
                lt = left_join_keys[-1]

            msg = ("incompatible tolerance {tolerance}, must be compat "
                   "with type {lkdtype}".format(
                       tolerance=type(self.tolerance),
                       lkdtype=lt.dtype))

            if is_datetime64_dtype(lt) or is_datetime64tz_dtype(lt):
                if not isinstance(self.tolerance, Timedelta):
                    raise MergeError(msg)
                if self.tolerance < Timedelta(0):
                    raise MergeError("tolerance must be positive")

            elif is_int64_dtype(lt):
                if not is_integer(self.tolerance):
                    raise MergeError(msg)
                if self.tolerance < 0:
                    raise MergeError("tolerance must be positive")

            elif is_float_dtype(lt):
                if not is_number(self.tolerance):
                    raise MergeError(msg)
                if self.tolerance < 0:
                    raise MergeError("tolerance must be positive")

            else:
                raise MergeError("key must be integer, timestamp or float")

        # validate allow_exact_matches
        if not is_bool(self.allow_exact_matches):
            msg = "allow_exact_matches must be boolean, passed {passed}"
            raise MergeError(msg.format(passed=self.allow_exact_matches))

        return left_join_keys, right_join_keys, join_names

    def _get_join_indexers(self):
        """ return the join indexers """

        def flip(xs):
            """ unlike np.transpose, this returns an array of tuples """
            labels = list(string.ascii_lowercase[:len(xs)])
            dtypes = [x.dtype for x in xs]
            labeled_dtypes = list(zip(labels, dtypes))
            return np.array(lzip(*xs), labeled_dtypes)

        # values to compare
        left_values = (self.left.index.values if self.left_index else
                       self.left_join_keys[-1])
        right_values = (self.right.index.values if self.right_index else
                        self.right_join_keys[-1])
        tolerance = self.tolerance

        # we require sortedness and non-null values in the join keys
        msg_sorted = "{side} keys must be sorted"
        msg_missings = "Merge keys contain null values on {side} side"

        if not Index(left_values).is_monotonic:
            if isnull(left_values).any():
                raise ValueError(msg_missings.format(side='left'))
            else:
                raise ValueError(msg_sorted.format(side='left'))

        if not Index(right_values).is_monotonic:
            if isnull(right_values).any():
                raise ValueError(msg_missings.format(side='right'))
            else:
                raise ValueError(msg_sorted.format(side='right'))

        # initial type conversion as needed
        if needs_i8_conversion(left_values):
            left_values = left_values.view('i8')
            right_values = right_values.view('i8')
            if tolerance is not None:
                tolerance = tolerance.value

        # a "by" parameter requires special handling
        if self.left_by is not None:
            # remove 'on' parameter from values if one existed
            if self.left_index and self.right_index:
                left_by_values = self.left_join_keys
                right_by_values = self.right_join_keys
            else:
                left_by_values = self.left_join_keys[0:-1]
                right_by_values = self.right_join_keys[0:-1]

            # get tuple representation of values if more than one
            if len(left_by_values) == 1:
                left_by_values = left_by_values[0]
                right_by_values = right_by_values[0]
            else:
                left_by_values = flip(left_by_values)
                right_by_values = flip(right_by_values)

            # upcast 'by' parameter because HashTable is limited
            by_type = _get_cython_type_upcast(left_by_values.dtype)
            by_type_caster = _type_casters[by_type]
            left_by_values = by_type_caster(left_by_values)
            right_by_values = by_type_caster(right_by_values)

            # choose appropriate function by type
            func = _asof_by_function(self.direction)
            return func(left_values,
                        right_values,
                        left_by_values,
                        right_by_values,
                        self.allow_exact_matches,
                        tolerance)
        else:
            # choose appropriate function by type
            func = _asof_function(self.direction)
            return func(left_values,
                        right_values,
                        self.allow_exact_matches,
                        tolerance)


def _get_multiindex_indexer(join_keys, index, sort):
    from functools import partial

    # bind `sort` argument
    fkeys = partial(_factorize_keys, sort=sort)

    # left & right join labels and num. of levels at each location
    rcodes, lcodes, shape = map(list, zip(* map(fkeys,
                                                index.levels,
                                                join_keys)))
    if sort:
        rcodes = list(map(np.take, rcodes, index.codes))
    else:
        i8copy = lambda a: a.astype('i8', subok=False, copy=True)
        rcodes = list(map(i8copy, index.codes))

    # fix right labels if there were any nulls
    for i in range(len(join_keys)):
        mask = index.codes[i] == -1
        if mask.any():
            # check if there already was any nulls at this location
            # if there was, it is factorized to `shape[i] - 1`
            a = join_keys[i][lcodes[i] == shape[i] - 1]
            if a.size == 0 or not a[0] != a[0]:
                shape[i] += 1

            rcodes[i][mask] = shape[i] - 1

    # get flat i8 join keys
    lkey, rkey = _get_join_keys(lcodes, rcodes, shape, sort)

    # factorize keys to a dense i8 space
    lkey, rkey, count = fkeys(lkey, rkey)

    return libjoin.left_outer_join(lkey, rkey, count, sort=sort)


def _get_single_indexer(join_key, index, sort=False):
    left_key, right_key, count = _factorize_keys(join_key, index, sort=sort)

    left_indexer, right_indexer = libjoin.left_outer_join(
        ensure_int64(left_key),
        ensure_int64(right_key),
        count, sort=sort)

    return left_indexer, right_indexer


def _left_join_on_index(left_ax, right_ax, join_keys, sort=False):
    if len(join_keys) > 1:
        if not ((isinstance(right_ax, MultiIndex) and
                 len(join_keys) == right_ax.nlevels)):
            raise AssertionError("If more than one join key is given then "
                                 "'right_ax' must be a MultiIndex and the "
                                 "number of join keys must be the number of "
                                 "levels in right_ax")

        left_indexer, right_indexer = \
            _get_multiindex_indexer(join_keys, right_ax, sort=sort)
    else:
        jkey = join_keys[0]

        left_indexer, right_indexer = \
            _get_single_indexer(jkey, right_ax, sort=sort)

    if sort or len(left_ax) != len(left_indexer):
        # if asked to sort or there are 1-to-many matches
        join_index = left_ax.take(left_indexer)
        return join_index, left_indexer, right_indexer

    # left frame preserves order & length of its index
    return left_ax, None, right_indexer


def _right_outer_join(x, y, max_groups):
    right_indexer, left_indexer = libjoin.left_outer_join(y, x, max_groups)
    return left_indexer, right_indexer


_join_functions = {
    'inner': libjoin.inner_join,
    'left': libjoin.left_outer_join,
    'right': _right_outer_join,
    'outer': libjoin.full_outer_join,
}


def _factorize_keys(lk, rk, sort=True):
    # Some pre-processing for non-ndarray lk / rk
    if is_datetime64tz_dtype(lk) and is_datetime64tz_dtype(rk):
        lk = lk._data
        rk = rk._data

    elif (is_categorical_dtype(lk) and
            is_categorical_dtype(rk) and
            lk.is_dtype_equal(rk)):
        if lk.categories.equals(rk.categories):
            # if we exactly match in categories, allow us to factorize on codes
            rk = rk.codes
        else:
            # Same categories in different orders -> recode
            rk = _recode_for_categories(rk.codes, rk.categories, lk.categories)

        lk = ensure_int64(lk.codes)
        rk = ensure_int64(rk)

    elif (is_extension_array_dtype(lk.dtype) and
          is_extension_array_dtype(rk.dtype) and
          lk.dtype == rk.dtype):
        lk, _ = lk._values_for_factorize()
        rk, _ = rk._values_for_factorize()

    if is_integer_dtype(lk) and is_integer_dtype(rk):
        # GH#23917 TODO: needs tests for case where lk is integer-dtype
        #  and rk is datetime-dtype
        klass = libhashtable.Int64Factorizer
        lk = ensure_int64(com.values_from_object(lk))
        rk = ensure_int64(com.values_from_object(rk))
    elif (issubclass(lk.dtype.type, (np.timedelta64, np.datetime64)) and
          issubclass(rk.dtype.type, (np.timedelta64, np.datetime64))):
        # GH#23917 TODO: Needs tests for non-matching dtypes
        klass = libhashtable.Int64Factorizer
        lk = ensure_int64(com.values_from_object(lk))
        rk = ensure_int64(com.values_from_object(rk))
    else:
        klass = libhashtable.Factorizer
        lk = ensure_object(lk)
        rk = ensure_object(rk)

    rizer = klass(max(len(lk), len(rk)))

    llab = rizer.factorize(lk)
    rlab = rizer.factorize(rk)

    count = rizer.get_count()

    if sort:
        uniques = rizer.uniques.to_array()
        llab, rlab = _sort_labels(uniques, llab, rlab)

    # NA group
    lmask = llab == -1
    lany = lmask.any()
    rmask = rlab == -1
    rany = rmask.any()

    if lany or rany:
        if lany:
            np.putmask(llab, lmask, count)
        if rany:
            np.putmask(rlab, rmask, count)
        count += 1

    return llab, rlab, count


def _sort_labels(uniques, left, right):
    if not isinstance(uniques, np.ndarray):
        # tuplesafe
        uniques = Index(uniques).values

    llength = len(left)
    labels = np.concatenate([left, right])

    _, new_labels = sorting.safe_sort(uniques, labels, na_sentinel=-1)
    new_labels = ensure_int64(new_labels)
    new_left, new_right = new_labels[:llength], new_labels[llength:]

    return new_left, new_right


def _get_join_keys(llab, rlab, shape, sort):

    # how many levels can be done without overflow
    pred = lambda i: not is_int64_overflow_possible(shape[:i])
    nlev = next(filter(pred, range(len(shape), 0, -1)))

    # get keys for the first `nlev` levels
    stride = np.prod(shape[1:nlev], dtype='i8')
    lkey = stride * llab[0].astype('i8', subok=False, copy=False)
    rkey = stride * rlab[0].astype('i8', subok=False, copy=False)

    for i in range(1, nlev):
        with np.errstate(divide='ignore'):
            stride //= shape[i]
        lkey += llab[i] * stride
        rkey += rlab[i] * stride

    if nlev == len(shape):  # all done!
        return lkey, rkey

    # densify current keys to avoid overflow
    lkey, rkey, count = _factorize_keys(lkey, rkey, sort=sort)

    llab = [lkey] + llab[nlev:]
    rlab = [rkey] + rlab[nlev:]
    shape = [count] + shape[nlev:]

    return _get_join_keys(llab, rlab, shape, sort)


def _should_fill(lname, rname):
    if (not isinstance(lname, compat.string_types) or
            not isinstance(rname, compat.string_types)):
        return True
    return lname == rname


def _any(x):
    return x is not None and com._any_not_none(*x)


def validate_operand(obj):
    if isinstance(obj, DataFrame):
        return obj
    elif isinstance(obj, Series):
        if obj.name is None:
            raise ValueError('Cannot merge a Series without a name')
        else:
            return obj.to_frame()
    else:
        raise TypeError('Can only merge Series or DataFrame objects, '
                        'a {obj} was passed'.format(obj=type(obj)))