Lowering bug?

[ioannisPApapadopoulos]

@dlfivefifty The lowering Zernike(0,1) \ Weighted(Zernike(0,1)) is a factor of 2 off. This also seems to be confirmed in the tests..?

MultivariateOrthogonalPolynomials.jl/test/test_disk.jl

Line 303 in cb0fb24

@test 2w*Zernike(1)[xy,Block.(1:5)]' ≈ Zernike(1)[xy,Block.(1:7)]'*L[Block.(1:7),Block.(1:5)]

Is there a reason for this?

[dlfivefifty]

No clue... maybe the weight has that factor of 2 in it?

[TSGut]

There's a factor 2 to some power in the polynomials defined im FastTransforms, see https://mikaelslevinsky.github.io/FastTransforms/transforms.html#disk2cxf

Maybe that's where this originates, some difference in conventions?

[ioannisPApapadopoulos]

Convenctions in Weighted vs. what the weighted is defined as? Should we change this to be consistent?

[TSGut]

I think so. This can lead to really nasty untraceable errors and doesn't make sense syntax wise.

[dlfivefifty]

I think we should really focus on making things less consistent, not more

[MikaelSlevinsky]

Was gonna propose random complex phases to improve stability with a seed based on the SHA256 checksum of the user's System folder, but maybe that's still too consistent.

[DanielVandH]

There's a factor 2 to some power in the polynomials defined im FastTransforms, see https://mikaelslevinsky.github.io/FastTransforms/transforms.html#disk2cxf

Maybe that's where this originates, some difference in conventions?

Are the polynomials in this package supposed to be the same as those at that link? The weights aren't the same ($r^{2\alpha+1}(1-r^2)^\beta$ vs $r^{2\alpha}(1-r^2)^\beta$, a factor $r$ difference), unless this package is assuming the differential to be $r dr d\theta$ already and the current ZernikeWeight() definition in this package is fine.

[dlfivefifty]

No I don't think it's different: we are using $r^{2α} (1-r^2)^β dxdy = r^{2α} (1-r^2)^β r dr dθ$