Gradus spectral models

[fjebaker]

Added the Gradus additive line profile model to the fit.

There's a few outstanding problems here:

• [x] Parameter binding is broken when freezing parameters https://github.com/fjebaker/SpectralFitting.jl/issues/114
• [x] AD doesn't work with the Gradus models yet because of all the interpolating it's doing https://github.com/astro-group-bristol/Gradus.jl/issues/199

Additionally the example transfer function table I've included in the data directory only has a 10x10 grid of parameters (done for brevity). Let's chat about what kind of models we want to fit, and the parameter ranges for the transfer function tables and then compute some new (denser) tables for the actual fitting.

I also ran JuliaFormatter over the script, so apologies for some unnecessary diffs!

[fjebaker]

The good news is for some of the XMM data (specifically index 2 and 3) we get fairly sensible fits. Both are along the lines of:

┌ CompositeModel with 2 model components:
│      a2 + a1
│ Model key and parameters:
│    a1 => LineProfile
│         K_1 ->  0.000139 ± 0.1  ∈ [ 0, Inf   ]   FREE
│         a_1 ->     0.963 ± 0.1  ∈ [ 0, 0.998 ]   FREE
│         θ_1 ->      33.6 ± 4    ∈ [ 0, Inf   ]   FREE
│       rin_1 ->         1                              FROZEN
│      rout_1 ->       100                              FROZEN
│        E₀_1 ->       6.4                              FROZEN
│    a2 => PowerLaw
│         K_2 ->   0.00796 ± 0.1  ∈ [ 0, Inf   ]   FREE
│         a_2 ->      1.83 ± 0.2  ∈ [ 0, Inf   ]   FREE
└ 

┌ FittingResult:
│   Model: CompositeModel[PowerLaw + LineProfile]
│   . u     : [0.00013859, 0.96276, 33.614, 0.0079636, 1.8282]
│   . σᵤ    : [1.2338e-05, 0.075803, 1.4552, 0.00018689, 0.015545]
│   . χ²    : 114.32 
└ 

[fjebaker]

AD now works! 🎉 we can remove the autodiff = :finite argument.

[fjebaker]

With your fix for the frozen parameter binding, we can now fit the whole thing with the Gradus models! Here's a preliminary attempt:

┌ MultiFittingResult:
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [0.00018873, 0.95716, 34.729, 0.018017, 1.9156]
│    . σᵤ    : [9.3231e-06, 0.023654, 0.46583, 8.7455e-05, 0.0028567]
│    . χ²    : 200.40 
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [0.00011664, 0.95716, 34.729, 0.011149, 1.9156]
│    . σᵤ    : [7.1866e-06, 0.023654, 0.46583, 5.9531e-05, 0.0028567]
│    . χ²    : 163.38 
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [0.00016146, 0.95716, 34.729, 0.0090218, 1.9156]
│    . σᵤ    : [1.1121e-05, 0.023654, 0.46583, 6.7429e-05, 0.0028567]
│    . χ²    : 145.19 
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [0.00024576, 0.95716, 34.729, 0.016804, 1.9156]
│    . σᵤ    : [3.0203e-05, 0.023654, 0.46583, 0.00017771, 0.0028567]
│    . χ²    : 348.35 
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [0.00026623, 0.95716, 34.729, 0.016361, 1.9156]
│    . σᵤ    : [3.0455e-05, 0.023654, 0.46583, 0.00017768, 0.0028567]
│    . χ²    : 337.94 
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [0.00020407, 0.95716, 34.729, 0.017525, 1.9156]
│    . σᵤ    : [1.2407e-05, 0.023654, 0.46583, 0.00012182, 0.0028567]
│    . χ²    : 1152.3 
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [0.00020958, 0.95716, 34.729, 0.017174, 1.9156]
│    . σᵤ    : [1.2456e-05, 0.023654, 0.46583, 0.00012002, 0.0028567]
│    . χ²    : 1074.3 
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [0.00011123, 0.95716, 34.729, 0.011953, 1.9156]
│    . σᵤ    : [2.1734e-05, 0.023654, 0.46583, 0.00012733, 0.0028567]
│    . χ²    : 703.13 
│    Model: CompositeModel[PowerLaw + AutoCache]
│    . u     : [9.6993e-05, 0.95716, 34.729, 0.011836, 1.9156]
│    . σᵤ    : [2.2030e-05, 0.023654, 0.46583, 0.00012830, 0.0028567]
│    . χ²    : 542.06 
└ Σχ² = 4667.1

[fjebaker]

Performance leaves a little to be desired:

result = @time fit(prob, LevenbergMarquadt(); verbose = true)
# looking to improve on
#  78.044531 seconds (9.23 M allocations: 1.073 GiB, 0.23% gc time, 28.93% compilation time)
#  55.780932 seconds (38.87 k allocations: 513.027 MiB, 0.24% gc time)

[phajy]

This looks great. I'll run through this locally and then get back to you with any comments (if any) before merging. Should we close and merge this one before looking at PR https://github.com/phajy/Sesto2024/pull/3?

[fjebaker]

3 is merging into this branch. But the order is unimportant, as we can change which branch to merge into. Probably makes more sense to resolve this one first, then look at #3