BUG: `array_api.argsort(descending=True)` respects relative sort order (#20788)

* BUG: `array_api.argsort(descending=True)` respects relative order

* Regression test for stable descending `array_api.argsort()`

2 files changed, 37 insertions, 3 deletions

diff --git a/numpy/array_api/_sorting_functions.py b/numpy/array_api/_sorting_functions.py
index 9cd49786c..b2a11872f 100644
--- a/numpy/array_api/_sorting_functions.py
+++ b/numpy/array_api/_sorting_functions.py
@@ -15,9 +15,20 @@ def argsort(
     """
     # Note: this keyword argument is different, and the default is different.
     kind = "stable" if stable else "quicksort"
-    res = np.argsort(x._array, axis=axis, kind=kind)
-    if descending:
-        res = np.flip(res, axis=axis)
+    if not descending:
+        res = np.argsort(x._array, axis=axis, kind=kind)
+    else:
+        # As NumPy has no native descending sort, we imitate it here. Note that
+        # simply flipping the results of np.argsort(x._array, ...) would not
+        # respect the relative order like it would in native descending sorts.
+        res = np.flip(
+            np.argsort(np.flip(x._array, axis=axis), axis=axis, kind=kind),
+            axis=axis,
+        )
+        # Rely on flip()/argsort() to validate axis
+        normalised_axis = axis if axis >= 0 else x.ndim + axis
+        max_i = x.shape[normalised_axis] - 1
+        res = max_i - res
     return Array._new(res)
 
 
diff --git a/numpy/array_api/tests/test_sorting_functions.py b/numpy/array_api/tests/test_sorting_functions.py
new file mode 100644
index 000000000..9848bbfeb
--- /dev/null
+++ b/numpy/array_api/tests/test_sorting_functions.py
@@ -0,0 +1,23 @@
+import pytest
+
+from numpy import array_api as xp
+
+
+@pytest.mark.parametrize(
+    "obj, axis, expected",
+    [
+        ([0, 0], -1, [0, 1]),
+        ([0, 1, 0], -1, [1, 0, 2]),
+        ([[0, 1], [1, 1]], 0, [[1, 0], [0, 1]]),
+        ([[0, 1], [1, 1]], 1, [[1, 0], [0, 1]]),
+    ],
+)
+def test_stable_desc_argsort(obj, axis, expected):
+    """
+    Indices respect relative order of a descending stable-sort
+
+    See https://github.com/numpy/numpy/issues/20778
+    """
+    x = xp.asarray(obj)
+    out = xp.argsort(x, axis=axis, stable=True, descending=True)
+    assert xp.all(out == xp.asarray(expected))