Fix DataFrame.apply to support additional dtypes. (#2125)

Fix `DataFrame.apply` to support additional dtypes.

After this, additional dtypes can be specified in the return type annotation of the UDFs for `DataFrame.apply`.

```py
>>> kdf = ks.DataFrame(
...     {"a": ["a", "b", "c", "a", "b", "c"], "b": ["b", "a", "c", "c", "b", "a"]}
... )
>>> dtype = pd.CategoricalDtype(categories=["a", "b", "c"])
>>> def categorize(ser) -> ks.Series[dtype]:
...     return ser.astype(dtype)
...
>>> applied = kdf.apply(categorize)
>>> applied
   a  b
0  a  b
1  b  a
2  c  c
3  a  c
4  b  b
5  c  a
>>> applied.dtypes
a    category
b    category
```

FYI: without the fix:

```py
>>> applied
   a  b
0  0  1
1  1  0
2  2  2
3  0  2
4  1  1
5  2  0
>>> applied.dtypes
a    int64
b    int64
dtype: object
```

databricks/koalas/frame.py

@@ -2588,6 +2588,7 @@ def apply_func(pdf):
                     self_applied.columns, [return_schema] * len(self_applied.columns)
                 )
                 return_schema = StructType([StructField(c, t) for c, t in fields_types])
+                data_dtypes = [cast(SeriesType, return_type).dtype] * len(self_applied.columns)
             elif require_column_axis:
                 if axis != 1:
                     raise TypeError(
@@ -2596,11 +2597,13 @@ def apply_func(pdf):
                         "was %s" % return_sig
                     )
                 return_schema = cast(DataFrameType, return_type).spark_type
+                data_dtypes = cast(DataFrameType, return_type).dtypes
             else:
                 # any axis is fine.
                 should_return_series = True
                 return_schema = cast(ScalarType, return_type).spark_type
                 return_schema = StructType([StructField(SPARK_DEFAULT_SERIES_NAME, return_schema)])
+                data_dtypes = [cast(ScalarType, return_type).dtype]
                 column_labels = [None]
 
             if should_use_map_in_pandas:
@@ -2621,7 +2624,10 @@ def apply_func(pdf):
 
             # Otherwise, it loses index.
             internal = InternalFrame(
-                spark_frame=sdf, index_spark_columns=None, column_labels=column_labels
+                spark_frame=sdf,
+                index_spark_columns=None,
+                column_labels=column_labels,
+                data_dtypes=data_dtypes,
             )
 
         result = DataFrame(internal)  # type: "DataFrame"

databricks/koalas/tests/test_categorical.py

@@ -40,7 +40,7 @@ def kdf(self):
 
     @property
     def df_pair(self):
-        return (self.pdf, self.kdf)
+        return self.pdf, self.kdf
 
     def test_categorical_frame(self):
         pdf, kdf = self.df_pair
@@ -106,6 +106,33 @@ def test_factorize(self):
         self.assert_eq(kcodes.tolist(), pcodes.tolist())
         self.assert_eq(kuniques, puniques)
 
+    def test_frame_apply(self):
+        pdf, kdf = self.df_pair
+
+        self.assert_eq(kdf.apply(lambda x: x).sort_index(), pdf.apply(lambda x: x).sort_index())
+        self.assert_eq(
+            kdf.apply(lambda x: x, axis=1).sort_index(), pdf.apply(lambda x: x, axis=1).sort_index()
+        )
+
+    def test_frame_apply_without_shortcut(self):
+        with ks.option_context("compute.shortcut_limit", 0):
+            self.test_frame_apply()
+
+        pdf = pd.DataFrame(
+            {"a": ["a", "b", "c", "a", "b", "c"], "b": ["b", "a", "c", "c", "b", "a"]}
+        )
+        kdf = ks.from_pandas(pdf)
+
+        dtype = CategoricalDtype(categories=["a", "b", "c"])
+
+        def categorize(ser) -> ks.Series[dtype]:
+            return ser.astype(dtype)
+
+        self.assert_eq(
+            kdf.apply(categorize).sort_values(["a", "b"]).reset_index(drop=True),
+            pdf.apply(categorize).sort_values(["a", "b"]).reset_index(drop=True),
+        )
+
     def test_groupby_apply(self):
         pdf, kdf = self.df_pair