Improve algorithm in GetEnergyLossesFromReach & GetEnergyLossesInTransit

[mdunphy]

Addressing a Problem?

The calculation in GetEnergyLossesFromReach & GetEnergyLossesInTransit is cubic complexity in N=_nMlatHist[p]. First the k loop, then the m loop, and then inside of FunkyEnergyIntegral again a loop over m, yields O(N^3) work

Potential Solution

It should be possible to reduce this to quadratic complexity through using a prefix-sum recurrence to replace the summation in FunkyTemperatureIntegral, which will save a lot of calls to exp()

Additional context

i think #76 needs resolution before working up the prefix sum part.

Contribution

• I would be willing/able to open a Pull Request to contribute this feature.

[mdunphy]

OK, the case we are running has N=20 (so N^3=8000) and it was completely dominating the runtime. I made an attempt at reworking the calculation and got it down to O(N), so it's 400x faster for this particular case

The code is perhaps more complex now than before (it makes use of prefix sums and tail sums to cache calculations instead of repeating them), so not sure if this is mergable as-is, but dropping it here for input

Branch with direct algo replacement: https://github.com/mdunphy/RavenHydroFramework/tree/fast_temperatureintegral_nocheck

Branch with the new code added instead, as to allow for comparing with the original while running: https://github.com/mdunphy/RavenHydroFramework/tree/fast_temperatureintegral_withcheck