Tolerance defaults differ: np.allclose, math.isclose, assert_allclose

Checked on NumPy 2.5 / Python 3.12. np.isclose and np.allclose default to rtol=1e-5, atol=1e-8, so for small-magnitude data the atol dominates and the check passes trivially: np.allclose(1e-9, 2e-9) is True although the values differ by 100%. math.isclose defaults to rel_tol=1e-9, abs_tol=0, so math.isclose(1e-17, 0.0) is False and nothing except 0.0 is close to zero. numpy.testing.assert_allclose uses rtol=1e-7, atol=0, the opposite convention from np.allclose: assert_allclose(1e-9, 2e-9) fails. np.isclose is also asymmetric, |a-b| <= atol + rtol*|b|: np.isclose(1e6, 1e6+10.00005) is True and the swapped call is False. math.isclose is symmetric. Set atol to the scale of your data instead of relying on defaults.