PERF: concatenation of MultiIndexed objects (MultiIndex.append)

asv_bench/benchmarks/multiindex_object.py

@@ -396,4 +396,30 @@ def time_putmask_all_different(self):
         self.midx.putmask(self.mask, self.midx_values_different)
 
 
+class Append:
+    params = ["datetime64[ns]", "int64", "string"]
+    param_names = ["dtype"]
+
+    def setup(self, dtype):
+        N1 = 1000
+        N2 = 500
+        left_level1 = range(N1)
+        right_level1 = range(N1, N1 + N1)
+
+        if dtype == "datetime64[ns]":
+            level2 = date_range(start="2000-01-01", periods=N2)
+        elif dtype == "int64":
+            level2 = range(N2)
+        elif dtype == "string":
+            level2 = tm.makeStringIndex(N2)
+        else:
+            raise NotImplementedError
+
+        self.left = MultiIndex.from_product([left_level1, level2])
+        self.right = MultiIndex.from_product([right_level1, level2])
+
+    def time_append(self, dtype):
+        self.left.append(self.right)
+
+
 from .pandas_vb_common import setup  # noqa: F401 isort:skip

doc/source/whatsnew/v2.1.0.rst

@@ -321,6 +321,7 @@ Performance improvements
 - Performance improvement accessing :attr:`arrays.IntegerArrays.dtype` & :attr:`arrays.FloatingArray.dtype` (:issue:`52998`)
 - Performance improvement in :class:`Series` reductions (:issue:`52341`)
 - Performance improvement in :func:`concat` when ``axis=1`` and objects have different indexes (:issue:`52541`)
+- Performance improvement in :func:`concat` when the concatenation axis is a :class:`MultiIndex` (:issue:`53574`)
 - Performance improvement in :meth:`.DataFrameGroupBy.groups` (:issue:`53088`)
 - Performance improvement in :meth:`DataFrame.isin` for extension dtypes (:issue:`53514`)
 - Performance improvement in :meth:`DataFrame.loc` when selecting rows and columns (:issue:`53014`)

pandas/core/indexes/multi.py

@@ -88,7 +88,10 @@
     Categorical,
     ExtensionArray,
 )
-from pandas.core.arrays.categorical import factorize_from_iterables
+from pandas.core.arrays.categorical import (
+    factorize_from_iterables,
+    recode_for_categories,
+)
 import pandas.core.common as com
 from pandas.core.construction import sanitize_array
 import pandas.core.indexes.base as ibase
@@ -2145,14 +2148,28 @@ def append(self, other):
         if all(
             (isinstance(o, MultiIndex) and o.nlevels >= self.nlevels) for o in other
         ):
-            arrays, names = [], []
+            codes = []
+            levels = []
+            names = []
             for i in range(self.nlevels):
-                label = self._get_level_values(i)
-                appended = [o._get_level_values(i) for o in other]
-                arrays.append(label.append(appended))
-                single_label_name = all(label.name == x.name for x in appended)
-                names.append(label.name if single_label_name else None)
-            return MultiIndex.from_arrays(arrays, names=names)
+                level_values = self.levels[i]
+                for mi in other:
+                    level_values = level_values.union(mi.levels[i])
+                level_codes = [
+                    recode_for_categories(
+                        mi.codes[i], mi.levels[i], level_values, copy=False
+                    )
+                    for mi in ([self, *other])
+                ]
+                level_name = self.names[i]
+                if any(mi.names[i] != level_name for mi in other):
+                    level_name = None
+                codes.append(np.concatenate(level_codes))
+                levels.append(level_values)
+                names.append(level_name)
+            return MultiIndex(
+                codes=codes, levels=levels, names=names, verify_integrity=False
+            )
 
         to_concat = (self._values,) + tuple(k._values for k in other)
         new_tuples = np.concatenate(to_concat)

pandas/tests/frame/methods/test_combine_first.py

@@ -510,7 +510,7 @@ def test_combine_first_duplicates_rows_for_nan_index_values():
             "y": [12.0, 13.0, np.nan, 14.0],
         },
         index=MultiIndex.from_arrays(
-            [[1, 2, 3, 4], [np.nan, 5.0, 6.0, 7.0]], names=["a", "b"]
+            [[1, 2, 3, 4], [np.nan, 5, 6, 7]], names=["a", "b"]
         ),
     )
     combined = df1.combine_first(df2)

pandas/tests/indexes/multi/test_setops.py

@@ -558,8 +558,6 @@ def test_union_with_missing_values_on_both_sides(nulls_fixture):
     mi2 = MultiIndex.from_arrays([[1, nulls_fixture, 3]])
     result = mi1.union(mi2)
     expected = MultiIndex.from_arrays([[1, 3, nulls_fixture]])
-    # We don't particularly care about having levels[0] be float64, but it is
-    expected = expected.set_levels([expected.levels[0].astype(np.float64)])
     tm.assert_index_equal(result, expected)