Add Minuit optimiser and update NRSource

[CristianAntochi]

In this pull request I have added the Minuit optimiser and updated the NRSource for SR1.

Further more as discussed in issue #36 I have taken out the scaling of the parameters in the optimiser since it seemed to give problems with the error computation.

The Minuit optimiser needs some polishing but from testing seems to work very well and the computation time penalty doesn't seem to be too great (roughly a factor 2) with respect to the tensorflow optimiser.

The main advantage of Minuit comes from the fact that bounds can be given to the parameters and this avoids the useless stepping into negative parameter values and nan-s from the objective function.

Possible improvements to this implementation are:

• give automatic bounds to the parameters and not leave them as keyword arguments
• give initial step size as a percentage of the guess params
• figure out how the precision of migrad works and give an appropriate value as default (and not necessarily use the internal migrad precision)
• compute and return the Hesse errors of Minuit and compare with our implementation

[CristianAntochi]

I know why the tests don't pass. Tomorrow I will change the objective function to make it work!

[jonas-eschle]

Hey, that looks nice! About minuit:

• Minuit does a minimal amount of steps. If the minimum is found trivially, minuit will in general be slower (but this should not be a problem)
• limits: they should not be used if possible, only to find good starting values, since they perform a transformation. If a value is close to the bounds, the fit result is not reliable in general. In general, since Minuit is a local optimizer, a successful fit should start with good initial values.

On another note, I've opened #41 to discuss the broader scope of minimizers and their implementation

[CristianAntochi]

Hey, that looks nice! About minuit:

• Minuit does a minimal amount of steps. If the minimum is found trivially, minuit will in general be slower (but this should not be a problem)
• limits: they should not be used if possible, only to find good starting values, since they perform a transformation. If a value is close to the bounds, the fit result is not reliable in general. In general, since Minuit is a local optimizer, a successful fit should start with good initial values.

On another note, I've opened #41 to discuss the broader scope of minimizers and their implementation

Thanks for the input! I will take that into consideration! 😄

[pelssers]

Thanks for adding iminuit!
I've added a few comments on inference.py where there are a few places where things can be simplified and cleaned up.
We have to see how to make the bestfit arguments the same for different optimizers (tolerance specification and options such as use_hessian) and make sure it returns the same output for different optimizers, but its great that we can now compare different optimizers and error estimators.
Do you know if the tutorial notebook also runs with iminuit?

[JelleAalbers]

Thanks for adding minuit Christian! I hope the optimizer will now be more stable with the scaling removed -- let's see how it works.