IMAP-Lo systematic error calculation fixes

[vineetbansal]

Closes #3314

Overview

• Updated uncertainty values in geometric factor csvs (v4) to be 1/1000th of previous values (which were in [eV]).
• calculate_intensities and calculate_backgrounds now propagate the asymmetric GF uncertainty with the exact reciprocal relation (J·G/(G ∓ dG), emit _sys_err_plus / _sys_err_minus bounds, and store the geometric mean sqrt(minus·plus) in the existing _sys_err variable. Applied to ena_intensity, bg_rate, and bg_intensity.
• Made changes to tests to match the correct formulas.

EDIT: Removed the GF correction for bg_rate_sys_err since it is independent of GF, as per the second commit (and comment below).

[vineetbansal]

Please wait on merging this PR till @frahmanif has had a chance to sign off on this ...

[vineetbansal]

Also tagging @mitchellshen and @hi1011

[frahmanif]

As we discussed, background rates and associated uncertainty (systematic uncertainty) are read from the hydrogen-background ancillary file. GF values are not involved in the rates calculations and thus the asymmetry in the systematic uncertainty error bars do not affect the bg rates uncertainties. In the next step, when we calculate bg flux and systematic uncertainty, the GF values and uncertainties are then used and we expect the asymmetry to be considered.

[vineetbansal]

@frahmanif, @mitchellshen, @hi1011 - As per Fatemeh's input as well as what I could understand from the algorithm document, I've tweaked the calculation of bg_rate_sys_err (as we're calling it in the code) to match eq 64 of the algorithm document, which calls it systematic uncertainty:

$$\langle \sigma R^B \rangle_{\text{pxl}} = \frac{\sum_i \sigma R^B_i , \tau_i}{\sum_i \tau_i}$$

The delta term = $\langle (\delta R^B)^2 \rangle_{\text{pxl}}$ is bg_rate_stat_uncert in the code/CDFs.

So the terms we're using in the code do have the "stat" or "sys" prefix, but call it the "statistical uncertainty" and "systematic error" respectively, while the document calls the latter "systematic uncertainty". This is a carryover from when the code was written and attributes in the CDF created, so hopefully it is not a big deal.

So the sigma row in files like imap_lo_H_background.csv corresponds to bg_rate_stat_uncert in the product CDFs. The fact that the bg_rate_sys_err in all CDFs is all 0 is because the dropbox pipeline doesn't put the actual values anywhere (ideally there would be a 3rd row after each pair of "rate" and "sigma" row), so the SDC pipeline doesn't have it either.

In fact an existing test even asserts this:

imap_processing/imap_processing/tests/lo/test_lo_l1c.py

Line 586 in 9c089f6

# Systematic error is always zero

    # Systematic error is always zero
    np.testing.assert_array_equal(err.values, 0)

But that's a separate issue and we can tackle it in another PR. This PR is now done.

[tmplummer]

This all looks fine to me.