BUG: pivot_table with overlapping values (#61293)

* modified:   pandas/tests/reshape/test_pivot_multilevel.py
	- Added two tests, :func:`test_pivot_table_values_in_columns` and :func:`test_pivot_table_values_in_index`, to ensure that the `values` param is still used when the argument is shared between the `columns` and `values` params, and `index` and `values` params.

* modified:   pandas/core/reshape/pivot.py
	- Added condition to :func:`__internal_pivot_table` to aggregate `values` explicitly if `values` were passed, otherwise aggregate all remaining columns. This allows the tests :func:`test_pivot_table_values_in_columns` and :func:`test_pivot_table_values_in_index` in test_pivot_multilevel.py to pass.

* modified:   pandas/tests/reshape/test_pivot.py
	- Added test :func:`test_pivot_table_values_as_two_params` to test that the updates in pivot.py result in expected results, satisfying GH issue #57876.

* modified:   pandas/tests/reshape/test_pivot.py
	- Added GH issue comment to test :func:`test_pivot_table_values_as_two_params`.

* modified:   pandas/tests/reshape/test_pivot_multilevel.py
	- Combined tests :func:`test_pivot_table_values_in_columns` and :func:`test_pivot_table_values_in_index` into a single parametrized test, :func:`test_pivot_table_multiindex_values_as_two_params` to reduce duplicate setup code.

* modified:   pandas/tests/reshape/test_pivot_multilevel.py
	- Added GH issue #61292 as comment to test :func:`test_pivot_table_multiindex_values_as_two_params`.

* modified:   pandas/core/reshape/pivot.py
	- Simplified proposed logic in :func:`__internal_pivot_table`.

* modified:   pandas/core/reshape/pivot.py
	- Added GH issue numbers to new logic in :func:`__internal_pivot_table`.

* modified:   pandas/core/reshape/pivot.py
	- Added ignore-comment to silence mypy error in :func:`__internal_pivot_table`.
	- Added TODO-comment stating that the :meth:`DataFrameGroupBy.__getitem__` should be overloaded to match the pandas-stubs type declarations, informing mypy that the type is correct given `values` is a list.

* modified:   doc/source/whatsnew/v3.0.0.rst
	- Added pivot_table bug to Bugs/Reshaping section referencing issues #57876 and #61292.

* modified:   pandas/core/reshape/pivot.py
	- Moved and simplified mypy comment per feedback.

* modified:   pandas/core/reshape/pivot.py
	- Removed comment about explicit aggregation per feedback.

* modified:   pandas/tests/reshape/test_pivot.py
	- Removed param names and updated `argnames` arg per feedback in parametrized marker.

* modified:   pandas/tests/reshape/test_pivot.py
	- Removed param names in favor of implicit args per feedback.

* modified:   pandas/tests/reshape/test_pivot_multilevel.py
	- Removed param names and updated arg for `argnames` in parametrized marker per feedback.

* modified:   pandas/tests/reshape/test_pivot_multilevel.py
	- Reduced `expected` assignments from two to one per feedback.

* modified:   pandas/tests/reshape/test_pivot_multilevel.py
	- Removed param names in favor of implicit args per feedback.

* modified:   pandas/tests/reshape/test_pivot_multilevel.py
	- Moved e_data, e_index, and e_cols to parametrized marker instead of declaring inside the test :func:`test_pivot_table_multiindex_values_as_two_params`.

* modified:   pandas/tests/reshape/test_pivot.py
	- Moved `expected` setup to parametrized marker instead of in the test :meth:`TestPivotTable.test_pivot_table_values_as_two_params`.

* modified:   pandas/tests/reshape/test_pivot.py
	- Removed walrus operator declarations in parametrized marker for test :meth:TestPivotTable.test_pivot_table_values_as_two_params`. Appears related to this mypy issue -> python/mypy#17377.

* modified:   pandas/tests/reshape/test_pivot_multilevel.py
	- Removed walrus operator declarations as I'm sure mypy would raise an issue with it given that it did in test_pivot.py (see commit 52cf560).

Author: it176131

doc/source/whatsnew/v3.0.0.rst

@@ -835,6 +835,7 @@ Reshaping
 - Bug in :meth:`DataFrame.unstack` producing incorrect results when ``sort=False`` (:issue:`54987`, :issue:`55516`)
 - Bug in :meth:`DataFrame.merge` when merging two :class:`DataFrame` on ``intc`` or ``uintc`` types on Windows (:issue:`60091`, :issue:`58713`)
 - Bug in :meth:`DataFrame.pivot_table` incorrectly subaggregating results when called without an ``index`` argument (:issue:`58722`)
+- Bug in :meth:`DataFrame.pivot_table` incorrectly ignoring the ``values`` argument when also supplied to the ``index`` or ``columns`` parameters (:issue:`57876`, :issue:`61292`)
 - Bug in :meth:`DataFrame.stack` with the new implementation where ``ValueError`` is raised when ``level=[]`` (:issue:`60740`)
 - Bug in :meth:`DataFrame.unstack` producing incorrect results when manipulating empty :class:`DataFrame` with an :class:`ExtentionDtype` (:issue:`59123`)
 - Bug in :meth:`concat` where concatenating DataFrame and Series with ``ignore_index = True`` drops the series name (:issue:`60723`, :issue:`56257`)

pandas/core/reshape/pivot.py

@@ -336,6 +336,11 @@ def __internal_pivot_table(
         values = list(values)
 
     grouped = data.groupby(keys, observed=observed, sort=sort, dropna=dropna)
+    if values_passed:
+        # GH#57876 and GH#61292
+        # mypy is not aware `grouped[values]` will always be a DataFrameGroupBy
+        grouped = grouped[values]  # type: ignore[assignment]
+
     agged = grouped.agg(aggfunc, **kwargs)
 
     if dropna and isinstance(agged, ABCDataFrame) and len(agged.columns):

pandas/tests/reshape/test_pivot.py

@@ -2554,6 +2554,46 @@ def test_pivot_table_index_and_column_keys_with_nan(self, dropna):
 
         tm.assert_frame_equal(left=result, right=expected)
 
+    @pytest.mark.parametrize(
+        "index, columns, e_data, e_index, e_cols",
+        [
+            (
+                "Category",
+                "Value",
+                [
+                    [1.0, np.nan, 1.0, np.nan],
+                    [np.nan, 1.0, np.nan, 1.0],
+                ],
+                Index(data=["A", "B"], name="Category"),
+                Index(data=[10, 20, 40, 50], name="Value"),
+            ),
+            (
+                "Value",
+                "Category",
+                [
+                    [1.0, np.nan],
+                    [np.nan, 1.0],
+                    [1.0, np.nan],
+                    [np.nan, 1.0],
+                ],
+                Index(data=[10, 20, 40, 50], name="Value"),
+                Index(data=["A", "B"], name="Category"),
+            ),
+        ],
+        ids=["values-and-columns", "values-and-index"],
+    )
+    def test_pivot_table_values_as_two_params(
+        self, index, columns, e_data, e_index, e_cols
+    ):
+        # GH#57876
+        data = {"Category": ["A", "B", "A", "B"], "Value": [10, 20, 40, 50]}
+        df = DataFrame(data)
+        result = df.pivot_table(
+            index=index, columns=columns, values="Value", aggfunc="count"
+        )
+        expected = DataFrame(data=e_data, index=e_index, columns=e_cols)
+        tm.assert_frame_equal(result, expected)
+
 
 class TestPivot:
     def test_pivot(self):

pandas/tests/reshape/test_pivot_multilevel.py

@@ -250,3 +250,52 @@ def test_pivot_df_multiindex_index_none():
         columns=Index(["label1", "label2"], name="label"),
     )
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "index, columns, e_data, e_index, e_cols",
+    [
+        (
+            "index",
+            ["col", "value"],
+            [
+                [50.0, np.nan, 100.0, np.nan],
+                [np.nan, 100.0, np.nan, 200.0],
+            ],
+            Index(data=["A", "B"], name="index"),
+            MultiIndex.from_arrays(
+                arrays=[[1, 1, 2, 2], [50, 100, 100, 200]], names=["col", "value"]
+            ),
+        ),
+        (
+            ["index", "value"],
+            "col",
+            [
+                [50.0, np.nan],
+                [np.nan, 100.0],
+                [100.0, np.nan],
+                [np.nan, 200.0],
+            ],
+            MultiIndex.from_arrays(
+                arrays=[["A", "A", "B", "B"], [50, 100, 100, 200]],
+                names=["index", "value"],
+            ),
+            Index(data=[1, 2], name="col"),
+        ),
+    ],
+    ids=["values-and-columns", "values-and-index"],
+)
+def test_pivot_table_multiindex_values_as_two_params(
+    index, columns, e_data, e_index, e_cols
+):
+    # GH#61292
+    data = [
+        ["A", 1, 50, -1],
+        ["B", 1, 100, -2],
+        ["A", 2, 100, -2],
+        ["B", 2, 200, -4],
+    ]
+    df = pd.DataFrame(data=data, columns=["index", "col", "value", "extra"])
+    result = df.pivot_table(values="value", index=index, columns=columns)
+    expected = pd.DataFrame(data=e_data, index=e_index, columns=e_cols)
+    tm.assert_frame_equal(result, expected)