Return unitary vh from dpnp.linalg.svd for singular Hermitian inputs

CHANGELOG.md

@@ -43,6 +43,7 @@ This release is compatible with NumPy 2.5.
 * Fixed incorrect `dpnp.tensor.expm1` result for `complex(±0, 0)` special case on CPU to match the Python Array API specification [#2926](https://github.com/IntelPython/dpnp/pull/2926)
 * Fixed tests which expected lists from `dpctl` functions which now return tuples (i.e., `dpctl.SyclDevice.create_sub_devices`) [#2945](https://github.com/IntelPython/dpnp/pull/2945)
 * Fixed `PytestRemovedIn10Warning` raised by `pytest` 9.1.0 by converting class-scoped fixtures to class methods [#2952](https://github.com/IntelPython/dpnp/pull/2952)
+* Fixed `dpnp.linalg.svd(..., hermitian=True)` returning a non-unitary `vh` for singular input arrays due to a zero sign appearing [#2954](https://github.com/IntelPython/dpnp/pull/2954)
 
 ### Security
 

dpnp/linalg/dpnp_utils_linalg.py

@@ -914,7 +914,8 @@ def _hermitian_svd(a, compute_uv):
     # the eigenvalues and related arrays to have the correct order
     if compute_uv:
         s, u = dpnp_eigh(a, eigen_mode="V")
-        sgn = dpnp.sign(s)
+        # avoid zero sign
+        sgn = dpnp.copysign(1.0, s)
         s = dpnp.abs(s, out=s)
         sidx = dpnp.argsort(s)[..., ::-1]
         # Rearrange the signs according to sorted indices

dpnp/tests/test_linalg.py

@@ -27,6 +27,8 @@
 from .qr_helper import check_qr
 from .third_party.cupy import testing
 
+ALL_DTYPES_NO_BOOL = get_all_dtypes(no_none=True, no_bool=True)
+
 
 def vvsort(val, vec, size, xp):
     val_kwargs = {}
@@ -464,8 +466,6 @@ def test_det_errors(self):
 
 
 class TestEigenvalue:
-    ALL_DTYPES_NO_BOOL = get_all_dtypes(no_none=True, no_bool=True)
-
     # Eigenvalue decomposition of a matrix or a batch of matrices
     # by checking if the eigen equation A*v=w*v holds for given eigenvalues(w)
     # and eigenvectors(v).
@@ -3974,7 +3974,7 @@ def get_tol(self, dtype):
     # Additionally checks for equality of singular values
     # between dpnp and numpy decompositions
     def check_decomposition(
-        self, dp_a, dp_u, dp_s, dp_vt, np_u, np_s, np_vt, compute_vt
+        self, dp_a, dp_u, dp_s, dp_vt, np_u, np_s, np_vt, compute_vt=False
     ):
         tol = self._tol
         if compute_vt:
@@ -4006,13 +4006,13 @@ def check_decomposition(
                     atol=tol,
                 )
 
-    @pytest.mark.parametrize("dtype", get_all_dtypes(no_bool=True))
+    @pytest.mark.parametrize("dtype", ALL_DTYPES_NO_BOOL)
     @pytest.mark.parametrize(
         "shape",
         [(2, 2), (3, 4), (5, 3), (16, 16)],
         ids=["(2, 2)", "(3, 4)", "(5, 3)", "(16, 16)"],
     )
-    def test_svd(self, dtype, shape):
+    def test_basic(self, dtype, shape):
         a = numpy.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
         dp_a = dpnp.array(a)
 
@@ -4030,7 +4030,7 @@ def test_svd(self, dtype, shape):
     @pytest.mark.parametrize(
         "shape", [(2, 2), (16, 16)], ids=["(2, 2)", "(16, 16)"]
     )
-    def test_svd_hermitian(self, dtype, compute_vt, shape):
+    def test_hermitian(self, dtype, compute_vt, shape):
         a = generate_random_numpy_array(shape, dtype, hermitian=True)
         dp_a = dpnp.array(a)
 
@@ -4053,6 +4053,16 @@ def test_svd_hermitian(self, dtype, compute_vt, shape):
             dp_a, dp_u, dp_s, dp_vh, np_u, np_s, np_vh, compute_vt
         )
 
+    @testing.with_requires("numpy>=2.5")
+    def test_hermitian_singular(self):
+        a = numpy.array([[1, 0], [0, 0]])
+        dp_a = dpnp.array(a)
+
+        np_u, _, np_vh = numpy.linalg.svd(a, hermitian=True)
+        u, _, vh = dpnp.linalg.svd(dp_a, hermitian=True)
+        assert_allclose(u, np_u)
+        assert_allclose(vh, np_vh)
+
     def test_svd_errors(self):
         a_dp = dpnp.array([[1, 2], [3, 4]], dtype="float32")