Add post-solve per-process Rosenbrock tendency diagnostics

[haakon-e]

What this adds

This adds post-solve per-process tendency diagnostics for the Rosenbrock averaged-tendency modes, for both the 1-moment and 2-moment + P3 configurations, as a verbose variant of the mode. The substep solve is linear in the tendency, so with the equilibrated system built once per substep each process tendency is pushed through the same linear correction and the per-process realized increments sum exactly to the full increment.

How

The substep kernel is split into a system-build step (equilibration and the system matrix, computed once per substep) and a solve step that is linear in the right-hand side, so the full update and each per-process attribution solve against the same system. The positivity clamp is nonlinear, so it is returned as a separate, non-attributable correction term rather than folded into the per-process sums. The verbose tendency functors regroup the existing process calls instead of recomputing the physics, so the per-process parts sum to the existing instantaneous total.

Testing

Exactness tests confirm that the per-process realized tendencies plus the clamp correction reconstruct the net tendency to roundoff (relative error around 1e-13 in Float64), and that the verbose net equals the non-verbose net, for both schemes and both precisions. The non-verbose hot path is unchanged and still allocation-free, and the verbose entries are JET-clean.

Notes

Draft, builds on the PRs below. One internal helper is intentionally not inlined to sidestep a pre-existing type-inference false report in the P3 state constructor that also affects the non-verbose path; this is documented in the code and has no cost on the hot loop.

[haakon-e]

This change is part of the following stack:

• Make the pointwise 2M+P3 tendencies ForwardDiff-differentiable #725
  • Add a Rosenbrock substepping mode for 2M+P3 #726
    • Add 1M AD-Rosenbrock averaged-tendency mode #731
      • Add post-solve per-process Rosenbrock tendency diagnostics #732 ◀
        • Add implicit-temperature Rosenbrock averaged-tendency mode #733
          • Make the quadrature scheme the configuration choice #728
            • Re-add diagnostic-Nc activation for the 2M scheme #729

_{Change managed by git-spice.}