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BUG: np.linalg.svd(..., hermitian=True) returns non-unitary vh #31347

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BUG: np.linalg.svd(..., hermitian=True) returns non-unitary vh #31347

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36c4b52
BUG: avoid sign 0
EarlMilktea Apr 28, 2026
3ae7f1d
TST: Add Hermitian SVD test
EarlMilktea Apr 28, 2026
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2 changes: 2 additions & 0 deletions numpy/linalg/_linalg.py
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Expand Up @@ -1810,6 +1810,8 @@ def svd(a, full_matrices=True, compute_uv=True, hermitian=False):
if compute_uv:
s, u = eigh(a)
sgn = sign(s)
# avoid zero sign
sgn = np.where(sgn == 0, 1, sgn)
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@seberg seberg Apr 28, 2026

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Thanks, can we assume that -0 isn't a thing and just use signbit instead of sign?

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@EarlMilktea EarlMilktea Apr 28, 2026

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I personally prefer my approach to make the result predictable...

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@jorenham jorenham Apr 28, 2026

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well, there's a performance penalty with this approach

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@seberg seberg Apr 28, 2026

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Yeah, but if we aren't sure (I dunno yet), there is already sorting, etc. going on, so it shouldn't actually matter (where just always feels slightly awkward to me, I guess).

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@seberg seberg Apr 28, 2026

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Anyway, I think it's probably good. But @WarrenWeckesser might have a quick thought and know this a bit better.

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@EarlMilktea EarlMilktea Apr 30, 2026

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Thank you all for comments. Let me know if there are any updates.

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@EarlMilktea EarlMilktea May 14, 2026

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@WarrenWeckesser Could you kindly review this PR for me? Thank you in advance!

s = abs(s)
sidx = argsort(s)[..., ::-1]
sgn = np.take_along_axis(sgn, sidx, axis=-1)
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6 changes: 6 additions & 0 deletions numpy/linalg/tests/test_linalg.py
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Expand Up @@ -745,6 +745,12 @@ def hermitian(mat):
class TestSVDHermitian(SVDHermitianCases, SVDBaseTests):
hermitian = True

def test_singular(self):
x = np.array([[1, 0], [0, 0]])
u, _, vh = linalg.svd(x, hermitian=self.hermitian)
assert_almost_equal(u @ u.T.conj(), np.eye(2))
assert_almost_equal(vh @ vh.T.conj(), np.eye(2))


class CondCases(LinalgSquareTestCase, LinalgGeneralizedSquareTestCase):
# cond(x, p) for p in (None, 2, -2)
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