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definition of relative error #154
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The suggested definition doesn't work when
v = v_ref = 0(most likely happens for integers), so we should check it first.what about:
rel_diff = (v - v_ref) / max(|v|, |v_ref|, |eps|)?It covers the corner case I mentioned above, but why do we introduce a user-defined and hard-coded variable?
In the mentioned wiki article all relative difference definitions are not defined when the
f(x,y)is equal to zero. IMHO this is the special case which should be treated separately.- locked and limited conversation to collaborators
on Apr 1, 2022
Currently the relative error when the reference value is zero is defined using an epsilon to avoid division by zero; see https://github.com/ROCmSoftwarePlatform/composable_kernel/blob/313bbea5886850acab286f45e9d9816cf0b0dca0/library/include/ck/library/host_tensor/host_tensor.hpp#L327
The problem is that this approve results in very large relative error even if the absolute error is small. For example,
(v = 1e-8, v_ref = 0, eps = 1e-10), thenref_diff = 100. We can use more reasonable definition, for example:rel_diff = (v - v_ref) / max(|v|, |v_ref|). See https://en.wikipedia.org/wiki/Relative_change_and_difference for other alternatives.