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Simulator.ZGSA not made for d != 2n? #135

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ludopulles opened this issue Dec 2, 2024 · 0 comments
Open

Simulator.ZGSA not made for d != 2n? #135

ludopulles opened this issue Dec 2, 2024 · 0 comments

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@ludopulles
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I was looking at the output of the ZGSA simulator, and it gives rather strange results, e.g.:

> from estimator import *
> Simulator.ZGSA(d=100,n=95, q=1e20, beta=100, tau=None)[0:12]

[1.18044705041897e20,
 1.13772205086816e20,
 1.09654343629579e20,
 1.05685523697626e20,
 1.01860350894742e20,
 9.81736260690248e19,
 9.46203382462363e19,
 9.11956578189076e19,
 8.78949299819696e19,
 8.47136684059716e19,
 1.00000000000000,
 1.00000000000000]

The basis profile shouldn't drop to 1 already at the 10th basis vector, and perhaps the average should be far lower.

On the other hand, Simulator.GSA gives a decreasing slope, which does seem like the intended output:

> Simulator.GSA(d=100,n=95, q=1e20, beta=100, tau=None)[ 0::99]

[620.150571793365, 16.1251161489407]

So it seems to me that the ZGSA here is wrong. If Heuristic 2.8 from [DucvWo21] is used, it seems it works for dimension d=2n where indeed Vol(L)/d ~ sqrt(q), but not beyond d != 2n.

Perhaps the best way forward is to first use the profile from the GSA, and "clamp" the output square norms in the range [xi^2, q^2].

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