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TST: linalg: avoid numerical difficulties in tests involving matrix inversion #469

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Merged
ev-br merged 1 commit into from
Sep 15, 2026
Merged

TST: linalg: avoid numerical difficulties in tests involving matrix inversion #469

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13 changes: 5 additions & 8 deletions array_api_tests/hypothesis_helpers.py
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Original file line number Diff line number Diff line change
Expand Up @@ -428,17 +428,14 @@ def invertible_matrices(draw, dtypes=floating_dtypes, stack_shapes=shapes()):
stack_shape = draw(stack_shapes)
n = draw(integers(0, SQRT_MAX_ARRAY_SIZE // max(math.prod(stack_shape), 1)),)
dtype = draw(dtypes)
elements = one_of(
from_dtype(dtype, min_value=0.5, allow_nan=False, allow_infinity=False),
from_dtype(dtype, max_value=-0.5, allow_nan=False, allow_infinity=False),
elements = one_of( # avoid extreme condition numbers
from_dtype(dtype, min_value=0.5, max_value=50,
allow_nan=False, allow_infinity=False),
from_dtype(dtype, max_value=-0.5, min_value=-50,
allow_nan=False, allow_infinity=False),
)
d = draw(arrays(dtype, shape=(*stack_shape, 1, n), elements=elements))

# Functions that require invertible matrices may do anything when it is
# singular, including raising an exception, so we make sure the diagonals
# are sufficiently nonzero to avoid any numerical issues.
assert xp.all(xp.abs(d) >= 0.5)

@mdhaber mdhaber Sep 15, 2026

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xp.all(xp.abs(d) >= 0.5) was guaranteed by the definition of elements, yet this alone did not avoid numerical issues, so I went ahead and removed it. With the change above, I think the worst condition number possible is 100.


diag_mask = xp.arange(n) == xp.reshape(xp.arange(n), (n, 1))
return xp.where(diag_mask, d, xp.zeros_like(d))

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3 changes: 2 additions & 1 deletion array_api_tests/test_linalg.py
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Expand Up @@ -478,7 +478,8 @@ def test_matrix_norm(x, kw):
_test_stacks(linalg.matrix_norm, x, **kw, dims=2 if keepdims else 0,
res=res)

matrix_power_n = shared(integers(-100, 100), key='matrix_power n')
# use moderate range of `n` to avoid numerical difficulties
matrix_power_n = shared(integers(-10, 10), key='matrix_power n')
@pytest.mark.unvectorized
@pytest.mark.xp_extension('linalg')
@given(
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