Speedup transfer function calculations #190
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Changed from Roots.jl to SimpleNonlinearSolve.jl to get the time-per-solve down from about 20ms to 2.7ms on well defined problems. An issue that persists is that for small radii on the disc, the solver has a much harder time converging, and sometimes converges badly. This commit attempts to make things a bit more robust, by adding a `best` parameter to track the best solution so far incase the one returned by the root finder projects poorly, and by trying to keep the manifold over which we optimize as smooth as possible. This means, for instance, determining the difference from the projected radius irrespective of disc intersection. The biggest win of this commit however is that calculating a set of interpolated transfer functions has gone from ~20 seconds to about 5, so we get a 4x speedup, with barely any (if any) loss in precision.
Visual inspection of the `impact_parameters_for_target` result shows that there is basically no difference between the two paths, so it's a sort of "good enough" situation.
This was referenced Jun 22, 2024
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