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Add optional high order moments to the HSM output file. #142
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Hi @rmjarvis - Thanks for pointing this out. I feel like we have touched on this a few times verbally but never written something down. I just took a look at
As in the name, I agree T4 and e4 are much easier to understand. I would still suggest adding a parenthesis, i.e., T^(4) and e^(4) to avoid confusion with the power of the second moments. I am open to suggestions too. |
I agree that the naming scheme for the M's in calculate_moments is a bit non-standard. I think the notation came from @aaronroodman. But it's trying to hew closer to the "spin" combinations. Here is the logic of it. For p>=q: So M_20 is aka e_1. M_02 is e_2. M11 is T. |
Credit Chris Davis for this scheme
…_________________________________________________________________________
Prof. Aaron Roodman
Deputy Director Vera C. Rubin Observatory
Dept. of Particle Physics & Astrophysics
Kavli Institute for Particle Astrophysics & Cosmology
SLAC National Accelerator Laboratory
Stanford University
SLAC National Accelerator Laboratory E-mail: ***@***.******@***.***>
2575 Sand Hill Rd. Phone: 650-926-2705
MS 29
Menlo Park, CA 94025 URL: http://www.slac.stanford.edu/~roodman
_________________________________________________________________________
From: Mike Jarvis ***@***.***>
Date: Monday, February 6, 2023 at 7:46 AM
To: rmjarvis/Piff ***@***.***>
Cc: Roodman, Aaron ***@***.***>, Mention ***@***.***>
Subject: Re: [rmjarvis/Piff] Add optional high order moments to the HSM output file. (Issue #142)
I agree that the naming scheme for the M's in calculate_moments is a bit non-standard. I think the notation came from @aaronroodman<https://github.com/aaronroodman>. But it's trying to hew closer to the "spin" combinations. Here is the logic of it.
For p>=q:
M_pq = Re(<(u+iv)^p (u-iv)^q>)
M_qp = Im(<(u+iv)^p (u-iv)^q>)
So M_20 is aka e_1. M_02 is e_2. M11 is T.
At fourth order, M_22 is the spin-0 quantity. M_31 + iM_13 is spin-2. And M_40 + iM04 is spin-4.
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PR here: #144 |
@ztq1996 has made a convincing case that we should look at the high-order moments of the PSF to look for potential biases in the PSF models leading to biased galaxy shapes.
This would be especially easy for many use cases if we add these moment measurements to the standard hsm output catalog we make in Piff. My proposal is to add a
fourth_order=True
option to the HSMCatalog statistic type, which would turn on these measurements.To make these more directly useful to galaxy shape error diagnostics, I propose that we output these in terms of the spin-0, spin-2 and spin-4 combinations:
spin-0: M_40 + 2M_22 + M_04.
spin-2: (M_40 − M_04) + i(2M_31 + 2M_13)
spin-4: (M_40 - 6M_22 + M_04) + i(4M_31 - 4M_13)
The spin-4 one probably isn't too useful (e.g. there is no spin-4 quantity in TreeCorr to do proper correlations with it), but the other two definitely are.
TQ calls the first two rho and M^(4)_PSF, respectively, which I don't love as names for these. They are kind of the 4-th order T and e quantities, so maybe T4 and e4 would be more accessible to most users? I'm open to suggestions here.
We also need some name for the spin-4 quantity (TQ didn't name it AFAICT).
There is already a function in Piff to calculate the high-order moments, so I think this will be easy to add. Just call that function if fourth_order is set to true and add those columns to the output file. So the implementation should be pretty straightforward.
Refs:
https://ui.adsabs.harvard.edu/abs/2022MNRAS.510.1978Z/abstract
https://ui.adsabs.harvard.edu/abs/2022arXiv221203257Z/abstract
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