ENH: Implement cross method for Merge Operations

pandas/core/frame.py

@@ -205,12 +205,14 @@
 The join is done on columns or indexes. If joining columns on
 columns, the DataFrame indexes *will be ignored*. Otherwise if joining indexes
 on indexes or indexes on a column or columns, the index will be passed on.
+When performing a cross merge, no column specifications to merge on are
+allowed.
 
 Parameters
 ----------%s
 right : DataFrame or named Series
     Object to merge with.
-how : {'left', 'right', 'outer', 'inner'}, default 'inner'
+how : {'left', 'right', 'outer', 'inner', 'cross'}, default 'inner'
     Type of merge to be performed.
 
     * left: use only keys from left frame, similar to a SQL left outer join;
@@ -221,6 +223,8 @@
       join; sort keys lexicographically.
     * inner: use intersection of keys from both frames, similar to a SQL inner
       join; preserve the order of the left keys.
+    * cross: creates the karthesian product from both frames, preserves the order
+      of the left keys.
 on : label or list
     Column or index level names to join on. These must be found in both
     DataFrames. If `on` is None and not merging on indexes then this defaults

pandas/core/reshape/merge.py

@@ -591,6 +591,8 @@ def __init__(
     ):
         _left = _validate_operand(left)
         _right = _validate_operand(right)
+        if how == "cross":
+            _left, _right, how, on = self._create_cross_configuration(_left, _right, on)
         self.left = self.orig_left = _left
         self.right = self.orig_right = _right
         self.how = how
@@ -690,8 +692,15 @@ def get_result(self):
 
         self._maybe_restore_index_levels(result)
 
+        self._maybe_drop_cross_column(result)
+
         return result.__finalize__(self, method="merge")
 
+    def _maybe_drop_cross_column(self, result: "DataFrame"):
+        cross_col = getattr(self, "_cross", None)
+        if cross_col is not None:
+            result.drop(columns=cross_col, inplace=True)
+
     def _indicator_pre_merge(
         self, left: "DataFrame", right: "DataFrame"
     ) -> Tuple["DataFrame", "DataFrame"]:
@@ -1200,7 +1209,34 @@ def _maybe_coerce_merge_keys(self):
                 typ = rk.categories.dtype if rk_is_cat else object
                 self.right = self.right.assign(**{name: self.right[name].astype(typ)})
 
+    def _create_cross_configuration(
+        self, _left, _right, on
+    ) -> Tuple["DataFrame", "DataFrame", str, str]:
+        if on is not None:
+            raise MergeError(
+                "Can not pass any merge columns when using cross as merge method"
+            )
+        cross_col = f"{max([*_left.columns, *_right.columns])}_cross"
+        _left = _left.copy()
+        _right = _right.copy()
+        _left.insert(loc=0, value=1, column=cross_col)
+        _right.insert(loc=0, value=1, column=cross_col)
+        how = "inner"
+        on = cross_col
+        self._cross = cross_col
+        return _left, _right, how, on
+
     def _validate_specification(self):
+        if hasattr(self, "_cross"):
+            if (
+                self.left_index
+                or self.right_index
+                or self.right_on is not None
+                or self.left_on is not None
+            ):
+                raise MergeError(
+                    "Can not pass any merge columns when using cross as merge method"
+                )
         # Hm, any way to make this logic less complicated??
         if self.on is None and self.left_on is None and self.right_on is None:
 

pandas/tests/reshape/merge/test_merge.py

@@ -2337,3 +2337,34 @@ def test_merge_join_cols_error_reporting_on_and_index(func, kwargs):
     )
     with pytest.raises(MergeError, match=msg):
         getattr(pd, func)(left, right, on="a", **kwargs)
+
+
+@pytest.mark.parametrize(
+    ("input_col", "output_cols"), [("b", ["a", "b"]), ("a", ["a_x", "a_y"])]
+)
+def test_merge_cross(input_col, output_cols):
+    # GH#5401
+    left = DataFrame({"a": [1, 3]})
+    right = DataFrame({input_col: [3, 4]})
+    result = merge(left, right, how="cross")
+    expected = DataFrame({output_cols[0]: [1, 1, 3, 3], output_cols[1]: [3, 4, 3, 4]})
+    tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "kwargs",
+    [
+        {"left_index": True},
+        {"right_index": True},
+        {"on": "a"},
+        {"left_on": "a"},
+        {"right_on": "b"},
+    ],
+)
+def test_merge_cross_error_reporting(kwargs):
+    # GH#5401
+    left = DataFrame({"a": [1, 3]})
+    right = DataFrame({"b": [3, 4]})
+    msg = "Can not pass any merge columns when using cross as merge method"
+    with pytest.raises(MergeError, match=msg):
+        merge(left, right, how="cross", **kwargs)