From 954d74c21eea942c60456c23fa5d716445b99a4c Mon Sep 17 00:00:00 2001
From: Brock <jbrockmendel@gmail.com>
Date: Sun, 9 Jan 2022 21:59:45 -0800
Subject: [PATCH] BUG: DataFrame[dt64].quantile(axis=1) when empty returning f8

---
 doc/source/whatsnew/v1.5.0.rst              |  2 +-
 pandas/core/frame.py                        | 25 +++++++++++++----
 pandas/tests/frame/methods/test_quantile.py | 31 +++++++++++++++------
 3 files changed, 44 insertions(+), 14 deletions(-)

diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index e723918ad8b4b..1590846218cc7 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -118,7 +118,7 @@ Categorical
 
 Datetimelike
 ^^^^^^^^^^^^
--
+- Bug in :meth:`DataFrame.quantile` with datetime-like dtypes and no rows incorrectly returning ``float64`` dtype instead of retaining datetime-like dtype (:issue:`41544`)
 -
 
 Timedelta
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 8f9294f2c0437..ad6cc6fd93790 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -123,6 +123,7 @@
     is_object_dtype,
     is_scalar,
     is_sequence,
+    needs_i8_conversion,
     pandas_dtype,
 )
 from pandas.core.dtypes.dtypes import ExtensionDtype
@@ -10460,17 +10461,23 @@ def quantile(
         Name: 0.5, dtype: object
         """
         validate_percentile(q)
+        axis = self._get_axis_number(axis)
 
         if not is_list_like(q):
             # BlockManager.quantile expects listlike, so we wrap and unwrap here
-            res = self.quantile(
+            res_df = self.quantile(
                 [q], axis=axis, numeric_only=numeric_only, interpolation=interpolation
             )
-            return res.iloc[0]
+            res = res_df.iloc[0]
+            if axis == 1 and len(self) == 0:
+                # GH#41544 try to get an appropriate dtype
+                dtype = find_common_type(list(self.dtypes))
+                if needs_i8_conversion(dtype):
+                    return res.astype(dtype)
+            return res
 
         q = Index(q, dtype=np.float64)
         data = self._get_numeric_data() if numeric_only else self
-        axis = self._get_axis_number(axis)
 
         if axis == 1:
             data = data.T
@@ -10478,9 +10485,17 @@ def quantile(
         if len(data.columns) == 0:
             # GH#23925 _get_numeric_data may have dropped all columns
             cols = Index([], name=self.columns.name)
+
+            dtype = np.float64
+            if axis == 1:
+                # GH#41544 try to get an appropriate dtype
+                cdtype = find_common_type(list(self.dtypes))
+                if needs_i8_conversion(cdtype):
+                    dtype = cdtype
+
             if is_list_like(q):
-                return self._constructor([], index=q, columns=cols)
-            return self._constructor_sliced([], index=cols, name=q, dtype=np.float64)
+                return self._constructor([], index=q, columns=cols, dtype=dtype)
+            return self._constructor_sliced([], index=cols, name=q, dtype=dtype)
 
         res = data._mgr.quantile(qs=q, axis=1, interpolation=interpolation)
 
diff --git a/pandas/tests/frame/methods/test_quantile.py b/pandas/tests/frame/methods/test_quantile.py
index 8ff1b211c0db1..d60fe7d4f316d 100644
--- a/pandas/tests/frame/methods/test_quantile.py
+++ b/pandas/tests/frame/methods/test_quantile.py
@@ -293,6 +293,28 @@ def test_quantile_datetime(self):
         expected = DataFrame(index=[0.5])
         tm.assert_frame_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "dtype",
+        [
+            "datetime64[ns]",
+            "datetime64[ns, US/Pacific]",
+            "timedelta64[ns]",
+            "Period[D]",
+        ],
+    )
+    def test_quantile_dt64_empty(self, dtype):
+        # GH#41544
+        df = DataFrame(columns=["a", "b"], dtype=dtype)
+
+        res = df.quantile(0.5, axis=1, numeric_only=False)
+        expected = Series([], index=[], name=0.5, dtype=dtype)
+        tm.assert_series_equal(res, expected)
+
+        # no columns in result, so no dtype preservation
+        res = df.quantile([0.5], axis=1, numeric_only=False)
+        expected = DataFrame(index=[0.5])
+        tm.assert_frame_equal(res, expected)
+
     def test_quantile_invalid(self, datetime_frame):
         msg = "percentiles should all be in the interval \\[0, 1\\]"
         for invalid in [-1, 2, [0.5, -1], [0.5, 2]]:
@@ -722,14 +744,7 @@ def test_empty_numeric(self, dtype, expected_data, expected_index, axis):
     @pytest.mark.parametrize(
         "dtype, expected_data, expected_index, axis, expected_dtype",
         [
-            pytest.param(
-                "datetime64[ns]",
-                [],
-                [],
-                1,
-                "datetime64[ns]",
-                marks=pytest.mark.xfail(reason="#GH 41544"),
-            ),
+            ["datetime64[ns]", [], [], 1, "datetime64[ns]"],
             ["datetime64[ns]", [pd.NaT, pd.NaT], ["a", "b"], 0, "datetime64[ns]"],
         ],
     )