Provide a function to give initial temperature guesses for PTE

[jdolence]

PR Summary

This PR introduces a function that solves $u_0 = \sum_m \rho_m \alpha_m \epsilon_m(\rho_m, T)$ for the temperature $T$, for fixed input $u_0$ (total material energy density, i.e. $erg/cm^{3}$), $\alpha_m$ (material volume fractions), and $\rho_m$ (material physical densities). The intent of the function is to be used to provide an initial guess for the PTE solver, so the hard coded tolerance of the solver is quite loose. Bisection is used because it's better behaved for EOSs that have only a weak dependence of $\epsilon$ on $T$ at cold temperatures.

To go along with this, the PTE solvers have been augmented to allow an initial temperature guess to be (optionally) provided. If a guess is not provided, or the guess is zero, the solver tries to guess a temperature as before.

PR Checklist

• Adds a test for any bugs fixed. Adds tests for new features.
• Format your changes by using the make format command after configuring with cmake.
• Document any new features, update documentation for changes made.
• Make sure the copyright notice on any files you modified is up to date.
• After creating a pull request, note it in the CHANGELOG.md file

[jhp-lanl]

The changes look good to me, but can we add a dead simple unit test to cover the behavior?

[Yurlungur]

I like this. Also nice use of not-quite-transcendental functions. :D

I do think we should have some kind of test. What about just using this initial guess machinery in test_pte.cpp to generate initial guesses for the solver?

[Yurlungur]

Should we allow zero temperature? I assume not?

[jdolence]

thanks for the quick review @jhp-lanl and @Yurlungur. I've added a call to this function in the test_pte code, as @Yurlungur suggested. If the tests pass, is this good to go?

[Yurlungur]

Yep, I'd say so. I'll trigger tests on Darwin and then let's get it merged in.

[Yurlungur]

Ah, actually Darwin CI currently in-repair. I'll just merge when github tests pass.