Clarify dpnp.linalg.cond() behavior with singular matrices (#2460)

This PR suggests clarifying the behavior and updating
`dpnp.linalg.cond()` tests for singular matrices.
It adds `Notes` section to the docs explaining the difference with NumPy
when handling singular input and updates tests to avoid crashes while
testing

Author: vlad-perevezentsev

CHANGELOG.md

@@ -41,6 +41,7 @@ This release achieves 100% compliance with Python Array API specification (revis
 * Updated FFT module to ensure an input array is Hermitian before calling complex-to-real FFT [#2444](https://github.com/IntelPython/dpnp/pull/2444)
 * Aligned `black` configuration with the list of supported python versions [#2457](https://github.com/IntelPython/dpnp/pull/2457)
 * Use `pyproject.toml` instead of `setup.py` aligning with current packaging best practices [#2462](https://github.com/IntelPython/dpnp/pull/2462)
+* Added a clarification to `dpnp.linalg.cond` docstring about its behavior with singular matrices [#2500] (https://github.com/IntelPython/dpnp/pull/2500)
 
 ### Fixed
 

dpnp/linalg/dpnp_iface_linalg.py

@@ -195,6 +195,14 @@ def cond(x, p=None):
     --------
     :obj:`dpnp.linalg.norm` : Matrix or vector norm.
 
+    Notes
+    -----
+    This function will raise :class:`dpnp.linalg.LinAlgError` on singular input
+    when using any of the norm: ``1``, ``-1``, ``inf``, ``-inf``, or ``'fro'``.
+    In contrast, :obj:`numpy.linalg.cond` will fill the result array with
+    ``inf`` values for each 2D batch in the input array that is singular
+    when using these norms.
+
     Examples
     --------
     >>> import dpnp as np

dpnp/tests/test_linalg.py

@@ -326,29 +326,22 @@ def test_bool(self, p):
     @pytest.mark.parametrize(
         "p", [None, -dpnp.inf, -2, -1, 1, 2, dpnp.inf, "fro"]
     )
-    def test_nan(self, p):
-        # dpnp.linalg.cond uses dpnp.linalg.inv()
-        # for the case when p is not None or p != -2 or p != 2
-        # For singular matrices cuSolver raises an error
-        # while OneMKL returns nans
-        if is_cuda_device() and p in [-dpnp.inf, -1, 1, dpnp.inf, "fro"]:
-            pytest.skip("Different behavior on CUDA")
-        elif requires_intel_mkl_version("2025.2") and p in [
-            -dpnp.inf,
-            -1,
-            1,
-            dpnp.inf,
-            "fro",
-        ]:
-            pytest.skip("SAT-7966")
-        a = generate_random_numpy_array((2, 2, 2, 2))
-        a[0, 0] = 0
-        a[1, 1] = 0
+    def test_nan_to_inf(self, p):
+        a = numpy.zeros((2, 2))
         ia = dpnp.array(a)
 
-        result = dpnp.linalg.cond(ia, p=p)
-        expected = numpy.linalg.cond(a, p=p)
-        assert_dtype_allclose(result, expected)
+        # NumPy does not raise LinAlgError on singular matrices.
+        # It returns `inf`, `0`, or large/small finite values
+        # depending on the norm and the matrix content.
+        # DPNP raises LinAlgError for 1, -1, inf, -inf, and 'fro'
+        # due to use of gesv in the 2D case.
+        # For [None, 2, -2], DPNP does not raise.
+        if p in [None, 2, -2]:
+            result = dpnp.linalg.cond(ia, p=p)
+            expected = numpy.linalg.cond(a, p=p)
+            assert_dtype_allclose(result, expected)
+        else:
+            assert_raises(dpnp.linalg.LinAlgError, dpnp.linalg.cond, ia, p=p)
 
     @pytest.mark.parametrize(
         "p", [None, -dpnp.inf, -2, -1, 1, 2, dpnp.inf, "fro"]