BUG: IntervalIndex set op bugs for empty results

doc/source/whatsnew/v0.23.0.txt

@@ -405,6 +405,7 @@ Indexing
 - Bug in :func:`MultiIndex.__contains__` where non-tuple keys would return ``True`` even if they had been dropped (:issue:`19027`)
 - Bug in :func:`MultiIndex.set_labels` which would cause casting (and potentially clipping) of the new labels if the ``level`` argument is not 0 or a list like [0, 1, ... ]  (:issue:`19057`)
 - Bug in ``str.extractall`` when there were no matches empty :class:`Index` was returned instead of appropriate :class:`MultiIndex` (:issue:`19034`)
+- Bug in :class:`IntervalIndex` where set operations that returned an empty ``IntervalIndex`` had the wrong dtype (:issue:`19101`)
 
 I/O
 ^^^

pandas/core/indexes/interval.py

@@ -5,7 +5,7 @@
 from pandas.core.dtypes.missing import notna, isna
 from pandas.core.dtypes.generic import ABCDatetimeIndex, ABCPeriodIndex
 from pandas.core.dtypes.dtypes import IntervalDtype
-from pandas.core.dtypes.cast import maybe_convert_platform
+from pandas.core.dtypes.cast import maybe_convert_platform, find_common_type
 from pandas.core.dtypes.common import (
     _ensure_platform_int,
     is_list_like,
@@ -16,6 +16,7 @@
     is_integer_dtype,
     is_float_dtype,
     is_interval_dtype,
+    is_object_dtype,
     is_scalar,
     is_float,
     is_number,
@@ -1289,9 +1290,25 @@ def func(self, other):
             msg = ('can only do set operations between two IntervalIndex '
                    'objects that are closed on the same side')
             other = self._as_like_interval_index(other, msg)
+
+            # GH 19016: ensure set op will not return a prohibited dtype
+            subtypes = [self.dtype.subtype, other.dtype.subtype]
+            common_subtype = find_common_type(subtypes)
+            if is_object_dtype(common_subtype):
+                msg = ('can only do {op} between two IntervalIndex '
+                       'objects that have compatible dtypes')
+                raise TypeError(msg.format(op=op_name))
+
             result = getattr(self._multiindex, op_name)(other._multiindex)
             result_name = self.name if self.name == other.name else None
-            return type(self).from_tuples(result.values, closed=self.closed,
+
+            # GH 19101: ensure empty results have correct dtype
+            if result.empty:
+                result = result.values.astype(self.dtype.subtype)
+            else:
+                result = result.values
+
+            return type(self).from_tuples(result, closed=self.closed,
                                           name=result_name)
         return func
 

pandas/tests/indexes/interval/test_interval.py

@@ -880,6 +880,16 @@ def test_union(self, closed):
         tm.assert_index_equal(index.union(index), index)
         tm.assert_index_equal(index.union(index[:1]), index)
 
+        # GH 19101: empty result, same dtype
+        index = IntervalIndex(np.array([], dtype='int64'), closed=closed)
+        result = index.union(index)
+        tm.assert_index_equal(result, index)
+
+        # GH 19101: empty result, different dtypes
+        other = IntervalIndex(np.array([], dtype='float64'), closed=closed)
+        result = index.union(other)
+        tm.assert_index_equal(result, index)
+
     def test_intersection(self, closed):
         index = self.create_index(closed=closed)
         other = IntervalIndex.from_breaks(range(5, 13), closed=closed)
@@ -893,14 +903,48 @@ def test_intersection(self, closed):
 
         tm.assert_index_equal(index.intersection(index), index)
 
+        # GH 19101: empty result, same dtype
+        other = IntervalIndex.from_breaks(range(300, 314), closed=closed)
+        expected = IntervalIndex(np.array([], dtype='int64'), closed=closed)
+        result = index.intersection(other)
+        tm.assert_index_equal(result, expected)
+
+        # GH 19101: empty result, different dtypes
+        breaks = np.arange(300, 314, dtype='float64')
+        other = IntervalIndex.from_breaks(breaks, closed=closed)
+        result = index.intersection(other)
+        tm.assert_index_equal(result, expected)
+
     def test_difference(self, closed):
         index = self.create_index(closed=closed)
         tm.assert_index_equal(index.difference(index[:1]), index[1:])
 
+        # GH 19101: empty result, same dtype
+        result = index.difference(index)
+        expected = IntervalIndex(np.array([], dtype='int64'), closed=closed)
+        tm.assert_index_equal(result, expected)
+
+        # GH 19101: empty result, different dtypes
+        other = IntervalIndex.from_arrays(index.left.astype('float64'),
+                                          index.right, closed=closed)
+        result = index.difference(other)
+        tm.assert_index_equal(result, expected)
+
     def test_symmetric_difference(self, closed):
-        idx = self.create_index(closed=closed)
-        result = idx[1:].symmetric_difference(idx[:-1])
-        expected = IntervalIndex([idx[0], idx[-1]])
+        index = self.create_index(closed=closed)
+        result = index[1:].symmetric_difference(index[:-1])
+        expected = IntervalIndex([index[0], index[-1]])
+        tm.assert_index_equal(result, expected)
+
+        # GH 19101: empty result, same dtype
+        result = index.symmetric_difference(index)
+        expected = IntervalIndex(np.array([], dtype='int64'), closed=closed)
+        tm.assert_index_equal(result, expected)
+
+        # GH 19101: empty result, different dtypes
+        other = IntervalIndex.from_arrays(index.left.astype('float64'),
+                                          index.right, closed=closed)
+        result = index.symmetric_difference(other)
         tm.assert_index_equal(result, expected)
 
     @pytest.mark.parametrize('op_name', [
@@ -909,17 +953,25 @@ def test_set_operation_errors(self, closed, op_name):
         index = self.create_index(closed=closed)
         set_op = getattr(index, op_name)
 
-        # test errors
+        # non-IntervalIndex
         msg = ('can only do set operations between two IntervalIndex objects '
                'that are closed on the same side')
         with tm.assert_raises_regex(ValueError, msg):
             set_op(Index([1, 2, 3]))
 
+        # mixed closed
         for other_closed in {'right', 'left', 'both', 'neither'} - {closed}:
             other = self.create_index(closed=other_closed)
             with tm.assert_raises_regex(ValueError, msg):
                 set_op(other)
 
+        # GH 19016: incompatible dtypes
+        other = interval_range(Timestamp('20180101'), periods=9, closed=closed)
+        msg = ('can only do {op} between two IntervalIndex objects that have '
+               'compatible dtypes').format(op=op_name)
+        with tm.assert_raises_regex(TypeError, msg):
+            set_op(other)
+
     def test_isin(self, closed):
         index = self.create_index(closed=closed)