BUG: construct MultiIndex identically from levels/labels when concatting

closes pandas-dev#15622
closes pandas-dev#15687
closes pandas-dev#14015
closes pandas-dev#13431

asv_bench/benchmarks/timeseries.py

@@ -292,7 +292,10 @@ def setup(self):
         self.rng3 = date_range(start='1/1/2000', periods=1500000, freq='S')
         self.ts3 = Series(1, index=self.rng3)
 
-    def time_sort_index(self):
+    def time_sort_index_monotonic(self):
+        self.ts.sort_index()
+
+    def time_sort_index_non_monotonic(self):
         self.ts.sort_index()
 
     def time_timeseries_slice_minutely(self):

doc/source/whatsnew/v0.20.0.txt

@@ -785,7 +785,7 @@ Performance Improvements
 - Improved performance of ``.rank()`` for categorical data (:issue:`15498`)
 - Improved performance when using ``.unstack()`` (:issue:`15503`)
 - Improved performance of merge/join on ``category`` columns (:issue:`10409`)
-
+- Improved performance of ``Series.sort_index()`` with a monotonic index (:issue:`15694`)
 
 .. _whatsnew_0200.bug_fixes:
 
@@ -818,6 +818,7 @@ Bug Fixes
 - Bug in ``pd.qcut()`` with a single quantile and an array with identical values (:issue:`15431`)
 - Compat with SciPy 0.19.0 for testing on ``.interpolate()`` (:issue:`15662`)
 
+- Bug in ``DataFrame.sort_index()`` that would not sort a lexsorted, but non monotonic ``MultiIndex`` (:issue:`15622`, :issue:`15687`, :issue:`14015`, :issue:`13431`)
 
 - Bug in the display of ``.info()`` where a qualifier (+) would always be displayed with a ``MultiIndex`` that contains only non-strings (:issue:`15245`)
 

pandas/core/frame.py

@@ -3365,6 +3365,10 @@ def sort(self, columns=None, axis=0, ascending=True, inplace=False,
     def sort_index(self, axis=0, level=None, ascending=True, inplace=False,
                    kind='quicksort', na_position='last', sort_remaining=True,
                    by=None):
+
+        # TODO: this can be combined with Series.sort_index impl as
+        # almost identical
+
         inplace = validate_bool_kwarg(inplace, 'inplace')
         # 10726
         if by is not None:
@@ -3378,8 +3382,7 @@ def sort_index(self, axis=0, level=None, ascending=True, inplace=False,
         axis = self._get_axis_number(axis)
         labels = self._get_axis(axis)
 
-        # sort by the index
-        if level is not None:
+        if level:
 
             new_axis, indexer = labels.sortlevel(level, ascending=ascending,
                                                  sort_remaining=sort_remaining)
@@ -3389,17 +3392,15 @@ def sort_index(self, axis=0, level=None, ascending=True, inplace=False,
 
             # make sure that the axis is lexsorted to start
             # if not we need to reconstruct to get the correct indexer
-            if not labels.is_lexsorted():
-                labels = MultiIndex.from_tuples(labels.values)
+            labels = labels._reconstruct_as_sorted()
 
             indexer = lexsort_indexer(labels.labels, orders=ascending,
                                       na_position=na_position)
         else:
             from pandas.core.sorting import nargsort
 
-            # GH11080 - Check monotonic-ness before sort an index
-            # if monotonic (already sorted), return None or copy() according
-            # to 'inplace'
+            # Check monotonic-ness before sort an index
+            # GH11080
             if ((ascending and labels.is_monotonic_increasing) or
                     (not ascending and labels.is_monotonic_decreasing)):
                 if inplace:
@@ -3410,8 +3411,9 @@ def sort_index(self, axis=0, level=None, ascending=True, inplace=False,
             indexer = nargsort(labels, kind=kind, ascending=ascending,
                                na_position=na_position)
 
+        baxis = self._get_block_manager_axis(axis)
         new_data = self._data.take(indexer,
-                                   axis=self._get_block_manager_axis(axis),
+                                   axis=baxis,
                                    convert=False, verify=False)
 
         if inplace:

pandas/core/groupby.py

@@ -1808,6 +1808,13 @@ def get_group_levels(self):
         'ohlc': lambda *args: ['open', 'high', 'low', 'close']
     }
 
+    def _is_builtin_func(self, arg):
+        """
+        if we define an builtin function for this argument, return it,
+        otherwise return the arg
+        """
+        return SelectionMixin._builtin_table.get(arg, arg)
+
     def _get_cython_function(self, kind, how, values, is_numeric):
 
         dtype_str = values.dtype.name
@@ -2033,7 +2040,7 @@ def _aggregate_series_fast(self, obj, func):
         # avoids object / Series creation overhead
         dummy = obj._get_values(slice(None, 0)).to_dense()
         indexer = get_group_index_sorter(group_index, ngroups)
-        obj = obj.take(indexer, convert=False)
+        obj = obj.take(indexer, convert=False).to_dense()
         group_index = algorithms.take_nd(
             group_index, indexer, allow_fill=False)
         grouper = lib.SeriesGrouper(obj, func, group_index, ngroups,

pandas/core/reshape.py

@@ -22,8 +22,8 @@
 from pandas.sparse.libsparse import IntIndex
 
 from pandas.core.categorical import Categorical, _factorize_from_iterable
-from pandas.core.sorting import (get_group_index, compress_group_index,
-                                 decons_obs_group_ids)
+from pandas.core.sorting import (get_group_index, get_compressed_ids,
+                                 compress_group_index, decons_obs_group_ids)
 
 import pandas.core.algorithms as algos
 from pandas._libs import algos as _algos, reshape as _reshape
@@ -494,11 +494,6 @@ def _unstack_frame(obj, level, fill_value=None):
         return unstacker.get_result()
 
 
-def get_compressed_ids(labels, sizes):
-    ids = get_group_index(labels, sizes, sort=True, xnull=False)
-    return compress_group_index(ids, sort=True)
-
-
 def stack(frame, level=-1, dropna=True):
     """
     Convert DataFrame to Series with multi-level Index. Columns become the

pandas/core/series.py

@@ -1756,17 +1756,31 @@ def _try_kind_sort(arr):
     def sort_index(self, axis=0, level=None, ascending=True, inplace=False,
                    kind='quicksort', na_position='last', sort_remaining=True):
 
+        # TODO: this can be combined with DataFrame.sort_index impl as
+        # almost identical
         inplace = validate_bool_kwarg(inplace, 'inplace')
         axis = self._get_axis_number(axis)
         index = self.index
-        if level is not None:
+
+        if level:
             new_index, indexer = index.sortlevel(level, ascending=ascending,
                                                  sort_remaining=sort_remaining)
         elif isinstance(index, MultiIndex):
             from pandas.core.sorting import lexsort_indexer
-            indexer = lexsort_indexer(index.labels, orders=ascending)
+            labels = index._reconstruct_as_sorted()
+            indexer = lexsort_indexer(labels.labels, orders=ascending)
         else:
             from pandas.core.sorting import nargsort
+
+            # Check monotonic-ness before sort an index
+            # GH11080
+            if ((ascending and index.is_monotonic_increasing) or
+                    (not ascending and index.is_monotonic_decreasing)):
+                if inplace:
+                    return
+                else:
+                    return self.copy()
+
             indexer = nargsort(index, kind=kind, ascending=ascending,
                                na_position=na_position)
 

pandas/core/sorting.py

@@ -93,6 +93,11 @@ def maybe_lift(lab, size):  # pormote nan values
     return loop(list(labels), list(shape))
 
 
+def get_compressed_ids(labels, sizes):
+    ids = get_group_index(labels, sizes, sort=True, xnull=False)
+    return compress_group_index(ids, sort=True)
+
+
 def is_int64_overflow_possible(shape):
     the_prod = long(1)
     for x in shape:

pandas/indexes/multi.py

@@ -1175,9 +1175,40 @@ def from_product(cls, iterables, sortorder=None, names=None):
 
         labels, levels = _factorize_from_iterables(iterables)
         labels = cartesian_product(labels)
+        return MultiIndex(levels, labels, sortorder=sortorder, names=names)
 
-        return MultiIndex(levels=levels, labels=labels, sortorder=sortorder,
-                          names=names)
+    def _reconstruct_as_sorted(self):
+        """
+        reconstruct the MultiIndex, such that we are
+        monotonically sorted; this will also ensure that
+        we are lexsorted
+        """
+        if self.is_lexsorted() and self.is_monotonic:
+            return self
+
+        new_levels = []
+        new_labels = []
+        for lev, lab in zip(self.levels, self.labels):
+
+            if lev.is_monotonic:
+                new_levels.append(lev)
+                new_labels.append(lab)
+                continue
+
+            # indexer to reorder the levels
+            indexer = lev.argsort()
+            lev = lev.take(indexer)
+
+            # indexer to reorder the labels
+            ri = lib.get_reverse_indexer(indexer, len(indexer))
+            lab = algos.take_1d(ri, lab)
+
+            new_levels.append(lev)
+            new_labels.append(lab)
+
+        return MultiIndex(new_levels, new_labels,
+                          names=self.names, sortorder=self.sortorder,
+                          verify_integrity=False)
 
     @property
     def nlevels(self):

pandas/tests/indexes/test_multi.py

@@ -2411,6 +2411,51 @@ def test_is_monotonic(self):
 
         self.assertFalse(i.is_monotonic)
 
+    def test_reconstruct_as_sorted(self):
+
+        # starts off lexsorted & monotonic
+        mi = MultiIndex.from_arrays([
+            ['A', 'A', 'B', 'B', 'B'], [1, 2, 1, 2, 3]
+        ])
+        assert mi.is_lexsorted()
+        assert mi.is_monotonic
+
+        recons = mi._reconstruct_as_sorted()
+        assert recons.is_lexsorted()
+        assert recons.is_monotonic
+        assert mi is recons
+
+        assert mi.equals(recons)
+        assert Index(mi.values).equals(Index(recons.values))
+
+        # cannot convert to lexsorted
+        mi = pd.MultiIndex.from_tuples([('z', 'a'), ('x', 'a'), ('y', 'b'),
+                                        ('x', 'b'), ('y', 'a'), ('z', 'b')],
+                                       names=['one', 'two'])
+        assert not mi.is_lexsorted()
+        assert not mi.is_monotonic
+
+        recons = mi._reconstruct_as_sorted()
+        assert not recons.is_lexsorted()
+        assert not recons.is_monotonic
+
+        assert mi.equals(recons)
+        assert Index(mi.values).equals(Index(recons.values))
+
+        # cannot convert to lexsorted
+        mi = MultiIndex(levels=[['b', 'd', 'a'], [1, 2, 3]],
+                        labels=[[0, 1, 0, 2], [2, 0, 0, 1]],
+                        names=['col1', 'col2'])
+        assert not mi.is_lexsorted()
+        assert not mi.is_monotonic
+
+        recons = mi._reconstruct_as_sorted()
+        assert not recons.is_lexsorted()
+        assert not recons.is_monotonic
+
+        assert mi.equals(recons)
+        assert Index(mi.values).equals(Index(recons.values))
+
     def test_isin(self):
         values = [('foo', 2), ('bar', 3), ('quux', 4)]
 

pandas/tests/series/test_analytics.py

@@ -1632,7 +1632,7 @@ def test_unstack(self):
                                labels=[[0, 1, 2, 0, 1, 2], [0, 1, 0, 1, 0, 1]])
         expected = DataFrame({'bar': s.values},
                              index=exp_index).sort_index(level=0)
-        unstacked = s.unstack(0)
+        unstacked = s.unstack(0).sort_index()
         assert_frame_equal(unstacked, expected)
 
         # GH5873

pandas/tests/test_multilevel.py

@@ -2449,6 +2449,30 @@ def test_getitem_slice_not_sorted(self):
         expected = df.reindex(columns=df.columns[:3])
         tm.assert_frame_equal(result, expected)
 
+    def test_frame_getitem_not_sorted2(self):
+        # 13431
+        df = DataFrame({'col1': ['b', 'd', 'b', 'a'],
+                        'col2': [3, 1, 1, 2],
+                        'data': ['one', 'two', 'three', 'four']})
+
+        df2 = df.set_index(['col1', 'col2'])
+        df2_original = df2.copy()
+
+        df2.index.set_levels(['b', 'd', 'a'], level='col1', inplace=True)
+        df2.index.set_labels([0, 1, 0, 2], level='col1', inplace=True)
+        assert not df2.index.is_lexsorted()
+        assert not df2.index.is_monotonic
+
+        assert df2_original.index.equals(df2.index)
+        expected = df2.sort_index()
+        assert not expected.index.is_lexsorted()
+        assert expected.index.is_monotonic
+
+        result = df2.sort_index(level=0)
+        assert not result.index.is_lexsorted()
+        assert result.index.is_monotonic
+        tm.assert_frame_equal(result, expected)
+
     def test_frame_getitem_not_sorted(self):
         df = self.frame.T
         df['foo', 'four'] = 'foo'
@@ -2485,3 +2509,89 @@ def test_series_getitem_not_sorted(self):
         expected.index = expected.index.droplevel(0)
         tm.assert_series_equal(result, expected)
         tm.assert_series_equal(result2, expected)
+
+    def test_sort_index_and_reconstruction(self):
+
+        # 15622
+        # lexsortedness should be identical
+        # across MultiIndex consruction methods
+
+        df = DataFrame([[1, 1], [2, 2]], index=list('ab'))
+        expected = DataFrame([[1, 1], [2, 2], [1, 1], [2, 2]],
+                             index=MultiIndex.from_tuples([(0.5, 'a'),
+                                                           (0.5, 'b'),
+                                                           (0.8, 'a'),
+                                                           (0.8, 'b')]))
+        assert expected.index.is_lexsorted()
+
+        result = DataFrame(
+            [[1, 1], [2, 2], [1, 1], [2, 2]],
+            index=MultiIndex.from_product([[0.5, 0.8], list('ab')]))
+        result = result.sort_index()
+        assert result.index.is_lexsorted()
+        assert result.index.is_monotonic
+
+        tm.assert_frame_equal(result, expected)
+
+        result = DataFrame(
+            [[1, 1], [2, 2], [1, 1], [2, 2]],
+            index=MultiIndex(levels=[[0.5, 0.8], ['a', 'b']],
+                             labels=[[0, 0, 1, 1], [0, 1, 0, 1]]))
+        result = result.sort_index()
+        assert result.index.is_lexsorted()
+
+        tm.assert_frame_equal(result, expected)
+
+        concatted = pd.concat([df, df], keys=[0.8, 0.5])
+        result = concatted.sort_index()
+
+        # this will be monotonic, but not lexsorted!
+        assert not result.index.is_lexsorted()
+        assert result.index.is_monotonic
+
+        tm.assert_frame_equal(result, expected)
+
+        # 14015
+        df = DataFrame([[1, 2], [6, 7]],
+                       columns=MultiIndex.from_tuples(
+                           [(0, '20160811 12:00:00'),
+                            (0, '20160809 12:00:00')],
+                           names=['l1', 'Date']))
+
+        df.columns.set_levels(pd.to_datetime(df.columns.levels[1]),
+                              level=1,
+                              inplace=True)
+        assert not df.columns.is_lexsorted()
+        assert not df.columns.is_monotonic
+        result = df.sort_index(axis=1)
+        assert result.columns.is_lexsorted()
+        assert result.columns.is_monotonic
+        result = df.sort_index(axis=1, level=1)
+        assert result.columns.is_lexsorted()
+        assert result.columns.is_monotonic
+
+    def test_sort_index_reorder_on_ops(self):
+        # 15687
+        df = pd.DataFrame(
+            np.random.randn(8, 2),
+            index=MultiIndex.from_product(
+                [['a', 'b'],
+                 ['big', 'small'],
+                 ['red', 'blu']],
+                names=['letter', 'size', 'color']),
+            columns=['near', 'far'])
+        df = df.sort_index()
+
+        def my_func(group):
+            group.index = ['newz', 'newa']
+            return group
+
+        result = df.groupby(level=['letter', 'size']).apply(
+            my_func).sort_index()
+        expected = MultiIndex.from_product(
+            [['a', 'b'],
+             ['big', 'small'],
+             ['newa', 'newz']],
+            names=['letter', 'size', None])
+
+        tm.assert_index_equal(result.index, expected)