BUG: astype not casting values for dictionary dtype correctly (pandas-dev#58479)

* BUG: astype not casting values for dictionary dtype correctly

* Fixup

Author: phofl

pandas/core/arrays/arrow/array.py

@@ -525,6 +525,8 @@ def _box_pa_array(
         if pa_type is not None and pa_array.type != pa_type:
             if pa.types.is_dictionary(pa_type):
                 pa_array = pa_array.dictionary_encode()
+                if pa_array.type != pa_type:
+                    pa_array = pa_array.cast(pa_type)
             else:
                 try:
                     pa_array = pa_array.cast(pa_type)

pandas/tests/extension/test_arrow.py

@@ -3498,6 +3498,14 @@ def test_to_numpy_timestamp_to_int():
     tm.assert_numpy_array_equal(result, expected)
 
 
+@pytest.mark.parametrize("arrow_type", [pa.large_string(), pa.string()])
+def test_cast_dictionary_different_value_dtype(arrow_type):
+    df = pd.DataFrame({"a": ["x", "y"]}, dtype="string[pyarrow]")
+    data_type = ArrowDtype(pa.dictionary(pa.int32(), arrow_type))
+    result = df.astype({"a": data_type})
+    assert result.dtypes.iloc[0] == data_type
+
+
 def test_map_numeric_na_action():
     ser = pd.Series([32, 40, None], dtype="int64[pyarrow]")
     result = ser.map(lambda x: 42, na_action="ignore")