Add optional high order moments to the HSM output file. about piff HOT 4 CLOSED

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 piff.util.calculate_moments(). It looks pretty good to me for setting up higher moments measurement. I just have a few questions and comments:

1. I have a hard time lining up the index of M_{pq} in piff with its mathematical meaning: for example, for second moments, M11=trace, M20=e1, M02=e2. I don't think we need to change how the indices are done here, as that could break some other code, but maybe we need some explanation for the indices.
2. Here du and dv are coordinated from the centroid. So the higher moments will be correlated to second moments (larger PSF = larger higher radial moments, for example). This is slightly different from the definition that I have been using, which erases the second moment's information. I think both definitions are probably fine for capturing additive biases in shear, but I need to look at their difference with a certain dataset to say that for sure.

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.

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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:
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

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