full marginaliztion of rotation on SO(3) using Lebedev quadrature

[geoffwoollard]

As in the reference

@Article{Schultze2023,
archivePrefix = {arXiv},
arxivId = {2302.09136},
author = {Schultze, Steffen and Grubm{"{u}}ller, Helmut},
eprint = {2302.09136},
file = {:Users/gw/Documents/work/cyclica/Downloaded/2302.09136v2.pdf:pdf},
title = {{De novo structural ensemble determination from single-molecule X-ray scattering: A Bayesian approach}},
url = {http://arxiv.org/abs/2302.09136},
year = {2023}
}

Ref: https://people.sc.fsu.edu/~jburkardt/datasets/sphere_lebedev_rule/sphere_lebedev_rule.html

CPU performance (on Flatiron cluster rusty)

Number of Poses	Lebedev Quadrature File	Time (s)
24	lebedev_003.txt	0.50
84	lebedev_005.txt	0.49
208	lebedev_007.txt	0.62
380	lebedev_009.txt	0.89
600	lebedev_011.txt	1.0
1036	lebedev_013.txt	1.5
1376	lebedev_015.txt	2.0
1980	lebedev_017.txt	2.6
2920	lebedev_019.txt	3.6
3740	lebedev_021.txt	4.6
4656	lebedev_023.txt	5.4
5980	lebedev_025.txt	6.9
7448	lebedev_027.txt	8.8
9060	lebedev_029.txt	11.0
11200	lebedev_031.txt	12.8
15624	lebedev_035.txt	18.5
24780	lebedev_041.txt	27.6
36960	lebedev_047.txt	42.9
52596	lebedev_053.txt	58.9
72120	lebedev_059.txt	79.5
95964	lebedev_065.txt	106.8
124560	lebedev_071.txt	146.6
158340	lebedev_077.txt	172.4
197736	lebedev_083.txt	220.0
243180	lebedev_089.txt	262.2

[mjo22]

This is in the process of being documented, but we are keeping the cryoJAX main codebase for tools that have demonstrated success in a research setting, with the benchmark that it is actively being used in the community. The intent is to make sure the cryoJAX only comprises the core set of tools for doing cryo-EM research. I’ve been in the process of moving some things downstream myself that don’t fit this bill!

I actually don’t fully understand the method + in what context it’s used, so I’ll defer to @Miro-Astore and @DSilva27 as to whether or not this fits the package. The general principle is that if it’s closer to active research and not currently being used by the community, it should go downstream. Later, it could be added. Note that the AbstractGaussianDistribution is a public class, by design!

Also FYI, cryojax.data is a module that provides tools for different workflows in cryo-EM. The name is a bit confusing I admit.

[geoffwoollard]

I provided the reference in case you'd like to more fully understand. Marginalization (pose, ctf) is also done in cryolike. I think this counts as success in the research setting and active use in the community.

[geoffwoollard]

This is merely a numerical Bayesian treatment of rotation. It can be extended to shift and ctf and other model parameters, and done in all likelihoods (Poisson, others with analytical marginalization). So it's used all over the place. In place of the weighted Lebedev S2 x S1 quadrature there could also other quadratures like uniformly weighted healpix S2 x S1. I tried to make the choice of the quadrature modular.