address comments

dpnp/linalg/dpnp_iface_linalg.py

@@ -1073,7 +1073,7 @@ def matrix_rank(A, tol=None, hermitian=False, *, rtol=None):
     ----------
     A : {(M,), (..., M, N)} {dpnp.ndarray, usm_ndarray}
         Input vector or stack of matrices.
-    tol : (...) {float, dpnp.ndarray, usm_ndarray}, optional
+    tol : (...) {None, float, dpnp.ndarray, usm_ndarray}, optional
         Threshold below which SVD values are considered zero. Only `tol` or
         `rtol` can be set at a time. If none of them are provided, defaults
         to ``S.max() * max(M, N) * eps`` where `S` is an array with singular
@@ -1083,7 +1083,7 @@ def matrix_rank(A, tol=None, hermitian=False, *, rtol=None):
         If ``True``, `A` is assumed to be Hermitian (symmetric if real-valued),
         enabling a more efficient method for finding singular values.
         Default: ``False``.
-    rtol : (...) {float, dpnp.ndarray, usm_ndarray}, optional
+    rtol : (...) {None, float, dpnp.ndarray, usm_ndarray}, optional
         Parameter for the relative tolerance component. Only `tol` or `rtol`
         can be set at a time. If none of them are provided, defaults to
         ``max(M, N) * eps`` where `eps` is the epsilon value for datatype
@@ -1479,7 +1479,7 @@ def pinv(a, rcond=None, hermitian=False, *, rtol=None):
     ----------
     a : (..., M, N) {dpnp.ndarray, usm_ndarray}
         Matrix or stack of matrices to be pseudo-inverted.
-    rcond : (...) {float, dpnp.ndarray, usm_ndarray}, optional
+    rcond : (...) {None, float, dpnp.ndarray, usm_ndarray}, optional
         Cutoff for small singular values.
         Singular values less than or equal to ``rcond * largest_singular_value``
         are set to zero. Broadcasts against the stack of matrices.
@@ -1490,7 +1490,7 @@ def pinv(a, rcond=None, hermitian=False, *, rtol=None):
         If ``True``, a is assumed to be Hermitian (symmetric if real-valued),
         enabling a more efficient method for finding singular values.
         Default: ``False``.
-    rtol : (...) {float, dpnp.ndarray, usm_ndarray}, optional
+    rtol : (...) {None, float, dpnp.ndarray, usm_ndarray}, optional
         Same as `rcond`, but it's an Array API compatible parameter name.
         Only `rcond` or `rtol` can be set at a time. If none of them are
         provided, defaults to ``max(M, N) * dpnp.finfo(a.dtype).eps``.

dpnp/linalg/dpnp_utils_linalg.py

@@ -2234,10 +2234,13 @@ def dpnp_matrix_rank(A, tol=None, hermitian=False, rtol=None):
         if rtol is None:
             rtol = max(A.shape[-2:]) * dpnp.finfo(S.dtype).eps
         elif not dpnp.isscalar(rtol):
+            # Add a new axis to make it broadcastable against S
+            # needed for S > tol comparison below
             rtol = rtol[..., None]
         tol = S.max(axis=-1, keepdims=True) * rtol
     elif not dpnp.isscalar(tol):
-        # Add a new axis to match NumPy's output
+        # Add a new axis to make it broadcastable against S,
+        # needed for S > tol comparison below
         tol = tol[..., None]
 
     return dpnp.count_nonzero(S > tol, axis=-1)

tests/test_linalg.py

@@ -2100,25 +2100,28 @@ def test_matrix_rank_tolerance(self, high_tol, low_tol):
     # rtol kwarg was added in numpy 2.0
     @testing.with_requires("numpy>=2.0")
     @pytest.mark.parametrize(
-        "rtol",
-        [0.99e-6, numpy.array(1.01e-6), numpy.array([0.99e-6])],
+        "tol",
+        [0.99e-6, numpy.array(1.01e-6), numpy.ones(4) * [0.99e-6]],
         ids=["float", "0-D array", "1-D array"],
     )
-    def test_matrix_rank_rtol(self, rtol):
-        a = numpy.eye(4)
-        a[-1, -1] = 1e-6
+    def test_matrix_rank_tol(self, tol):
+        a = numpy.zeros((4, 3, 2))
         a_dp = inp.array(a)
 
-        if isinstance(rtol, numpy.ndarray):
-            dp_rtol = inp.array(
-                rtol, usm_type=a_dp.usm_type, sycl_queue=a_dp.sycl_queue
+        if isinstance(tol, numpy.ndarray):
+            dp_tol = inp.array(
+                tol, usm_type=a_dp.usm_type, sycl_queue=a_dp.sycl_queue
             )
         else:
-            dp_rtol = rtol
+            dp_tol = tol
 
-        expected = numpy.linalg.matrix_rank(a, rtol=rtol)
-        result = inp.linalg.matrix_rank(a_dp, rtol=dp_rtol)
-        assert expected == result
+        expected = numpy.linalg.matrix_rank(a, rtol=tol)
+        result = inp.linalg.matrix_rank(a_dp, rtol=dp_tol)
+        assert_dtype_allclose(result, expected)
+
+        expected = numpy.linalg.matrix_rank(a, tol=tol)
+        result = inp.linalg.matrix_rank(a_dp, tol=dp_tol)
+        assert_dtype_allclose(result, expected)
 
     def test_matrix_rank_errors(self):
         a_dp = inp.array([[1, 2], [3, 4]], dtype="float32")