creating and using correlated uncertainties uvars

[newville]

I've been working on some analyses, where I'm fitting data with a background and two peaks, not unlike the NistGauss2 example. Once the fits were done, I wanted to calculate the centroid and total area of the two "non-background" peaks and the uncertainties in these values. The peaks overlap, so the amplitudes of the two peaks are highly correlated. That means that adding the uncertainties for the amplitudes in quadrature greatly overestimates the uncertainty in the total area (by like 5x as it turns out).

If I define derived parameters of 'centroid' and 'amp_sum' for these, for example adding to that example:

pars.add('centroid', expr='(g2_amplitude*g2_center+g1_amplitude*g1_center)/(g2_amplitude+g1_amplitude)')
pars.add('area', expr='(g2_amplitude+g1_amplitude)')

which will then give good values for uncertainties in centroid and area.

But: it would be nice to do this after the fit. In fact, a one-line change in Minimzer.py (around line 870)

            try:
                uvars = uncertainties.correlated_values(vbest, self.result.covar)
            except (LinAlgError, ValueError):
                uvars = None
            self.result.upars = {name: uv for name, uv in zip(self.result.var_names, uvars)}    # <- add this

would give a dict result.upars with each value being the correlated 'uncertainties uvar'. That would allow such derived quantities could be found after the fact with

     print(f"Total area =  {result.upars['g1_amplitude']+result.upars['g2_amplitude']}")

and without having to actually add them to Parameters before the fit is done. I propose we add this. Any objections to that?

And also: We could change many of the derived values like "fwhm" and "height" for the built-in models to be calculated after the fact. That would mean they are not calculated at each iteration. There have been a few concerns about the overhead of these calculations, and we do not use them at each iteration.

We could do this either by adding a post_fit method to Model that each sub-class can overwrite to put these values into the results.params immediately after the fit is done.

Or we could add a flag to Parameter to indicate that constraint expressions are "post fit, derived values".
Or, we could leave it as is.

At this point, I think the post_fit method might be the cleanest and most flexible, but I could be persuaded otherwise.
Any preferences on this part?

[newville]

I started a PR for this at #888.