BUG: MultiIndex sort with ascending as list

MultiIndex sorting with `sort_index` would fail when the `ascending`
argument was specified as a list but not all levels of the index were
specified in the `level` argument, or the levels were specified in
a different order to the MultiIndex.

This PR rectifies the issue and introduces a unit test based on pandas-dev#16934

Fixes: pandas-dev#16934

doc/source/whatsnew/v0.21.0.txt

@@ -156,6 +156,7 @@ Indexing
 - When called on an unsorted ``MultiIndex``, the ``loc`` indexer now will raise ``UnsortedIndexError`` only if proper slicing is used on non-sorted levels (:issue:`16734`).
 - Fixes regression in 0.20.3 when indexing with a string on a ``TimedeltaIndex`` (:issue:`16896`).
 - Fixed ``TimedeltaIndex.get_loc`` handling of ``np.timedelta64`` inputs (:issue:`16909`).
+- Fix MultiIndex ``sort_index`` ordering when ``ascending`` argument is a list but not all levels are specified, or are in a different order (:issue:`16934`).
 
 I/O
 ^^^

pandas/core/indexes/multi.py

@@ -1697,7 +1697,8 @@ def sortlevel(self, level=0, ascending=True, sort_remaining=True):
                 raise ValueError("level must have same length as ascending")
 
             from pandas.core.sorting import lexsort_indexer
-            indexer = lexsort_indexer(self.labels, orders=ascending)
+            indexer = lexsort_indexer([self.labels[lev] for lev in level],
+                                      orders=ascending)
 
         # level ordering
         else:

pandas/tests/test_multilevel.py

@@ -2781,3 +2781,20 @@ def test_sort_index_nan(self):
         result = s.sort_index(na_position='first')
         expected = s.iloc[[1, 2, 3, 0]]
         tm.assert_series_equal(result, expected)
+
+    def test_sort_ascending_list(self):
+        # GH: 16934
+
+        # Set up a Series with a three level MultiIndex
+        arrays = [['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux'],
+                  ['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two'],
+                  [4, 3, 2, 1, 4, 3, 2, 1]]
+        tuples = list(zip(*arrays))
+        index = pd.MultiIndex.from_tuples(tuples,
+                                          names=['first', 'second', 'third'])
+        s = pd.Series(range(8), index=index)
+
+        result = s.sort_index(level=['third', 'first'],
+                              ascending=[False, True])
+
+        assert np.array_equal(result, [0, 4, 1, 5, 2, 6, 3, 7])