Feat!: new parameter API

[fjebaker]

Closes #58

Still todo:

• Remove all the old binding code
• Try and discover source of the bug below

Documentation still outstanding but that's for another PR. There's one weird bug in test-fit-multi.jl, where before these changes the very last test fitted

┌ MultiFittingResult:
│    Model: CompositeModel[PowerLaw + PowerLaw]
│    . u     : [17.281, 0.28657, 14.935, 3.0998]
│    . χ²    : 2.8628 
│    Model: CompositeModel[(PowerLaw + PowerLaw) + PowerLaw]
│    . u     : [17.281, 3.7090, 42.203, 0.19553, 39.168, 1.9444]
│    . χ²    : 0.24608 
└ Σχ² = 3.1088

and now

┌ MultiFittingResult:
│    Model: CompositeModel[PowerLaw + PowerLaw]
│    . u     : [17.572, 0.29547, 14.557, 3.1249]
│    . χ²    : 2.9777 
│    Model: CompositeModel[(PowerLaw + PowerLaw) + PowerLaw]
│    . u     : [17.572, 1.0, 40.155, 0.20068, 39.196, 3.2011]
│    . χ²    : 11.864 
└ Σχ² = 14.841

I checked the plots and it is an objectively worse fit. I have no idea why this is the only one that is failing though?

[fjebaker]

This is the second time the CI runner has failed to get the data?

[fjebaker]

The fitting bug seems to be that the a power law parameter isn't being fitted when the additive constant is bound... I can't work out why though, since nothing has substantially changed in how the models are invoked...

[fjebaker]

Turning off autodiff gives the right (old) result, so it's some kind of gradient erasure!

[fjebaker]

Between the two model invokes:

# binding :K_1
#         b                     f
Partials(0.1, 3.6, 8.2, 2.0,   0.0, 0.0, 0.0, 0.0, 0.0) # k1
Partials(0.3, 0.0, 0.0, 0.0,   0.0, 0.1, 7.2, 9.1, 7.3) # k2

# we see the gradient does come in though
Partials(0.0, 0.0, 0.0, 0.0,   1.0, 0.0, 0.0, 0.0, 0.0) # parameters

# binding :K_2
#                   b                     f 
Partials(8.2, 2.0, 0.1, 3.6,   0.0, 0.0, 0.0, 0.0, 0.0) # k1 
Partials(0.0, 0.0, 0.3, 0.0,   9.0, 7.3, 0.0, 0.1, 7.2) # k2

There are (4 + 6) 10 model parameters, which it has correctly reduced to 9, but now it has also implicilty managed to pin an additional parameter in the second model.

[fjebaker]

This only happens if the two models being fit have different numbers of model components.

[fjebaker]

Fixed anomalous test condition that was failing 👍

[codecov-commenter]

Codecov Report

Attention: 263 lines in your changes are missing coverage. Please review.

Comparison is base (d8ca4d9) 69.04% compared to head (35d1d7f) 69.09%.
Report is 29 commits behind head on main.

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Additional details and impacted files

@@            Coverage Diff             @@
##             main      #63      +/-   ##
==========================================
+ Coverage   69.04%   69.09%   +0.04%     
==========================================
  Files          34       39       +5     
  Lines        1722     1870     +148     
==========================================
+ Hits         1189     1292     +103     
- Misses        533      578      +45     

Files	Coverage Δ
src/SpectralFitting.jl	100.00% <ø> (ø)
src/ccall-wrapper.jl	71.91% <ø> (ø)
src/fitting/methods.jl	82.85% <100.00%> (-8.38%)	⬇️
src/fitting/multi-cache.jl	100.00% <100.00%> (ø)
src/fitting/statistics.jl	87.50% <100.00%> (+1.78%)	⬆️
src/generation/function-generation.jl	77.33% <100.00%> (-14.34%)	⬇️
src/julia-models/additive.jl	100.00% <100.00%> (ø)
src/julia-models/multiplicative.jl	100.00% <100.00%> (ø)
src/meta-models/table-models.jl	100.00% <100.00%> (ø)
src/param-cache.jl	100.00% <100.00%> (ø)
... and 26 more

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