Account for integral of underlying distributions when sampling Mixture

[paulromano]

Description

The Mixture distribution type allows you to sample a mixture of multiple distributions at specified probabilities. We used to assume that the underlying distributions always integrated to one, but now we have distributions which are allowed to integrate to non-unity values to represent intensities (e.g., line spectra from a decay photon source). On the Python side, when sampling the Mixture distribution, the probabilities are weighted by the integrals of the underlying distributions, but we missed this on the C++ side. This PR fixes this so that the integrals of the distributions are accounted for when choosing which distribution to sampling from.

Checklist

• I have performed a self-review of my own code
• I have run clang-format on any C++ source files (if applicable)
• I have followed the style guidelines for Python source files (if applicable)
• [ ] I have made corresponding changes to the documentation (if applicable)
• I have added tests that prove my fix is effective or that my feature works (if applicable)

[shimwell]

oh wow good find, wondering if this will change the results of an R2S simulation slightly?

[paulromano]

@shimwell Yes, this is actually how I found this bug in the first place. It affects results if you are using a chain file generated from ENDF/B-VIII.0 (which results in Mixture distributions for some decay photon spectra).

[shimwell]

My c++ skills are not good enough to review this PR but I have been using the branch to run R2S simulations and can confirm that it ran without error if that helps :-)

[eepeterson]

Thanks for the fix @paulromano! The only thing I'm slightly concerned about is the meaning of the integral() of the distribution. It's a little hard to know what the meaning is when the actual integral of the probability density gives 1, but the integral() property does not. I know this is used to encode a sort of relative strength into probability mixtures when the integral of a distribution represents something like particles/cc/second, but I'm wondering if there is a better more consistent way.

[eepeterson]

Good find and thanks for the fix @paulromano!