Benchmarks vs MS_HMMBase & question about messages_backwards_log

[mmattocks]

Just finished benchmarking what I hope is the final commit of MS_HMMBase, where I attempted to add multiple observations to the mle_step function and subfunctions, without compromising performance too much. Here are the results from running https://github.com/mmattocks/MS_HMMBase.jl/blob/master/test/benchmarks.jl:

[ Info: Judging log_likelihoods
BenchmarkTools.TrialJudgement: 
  time:   +14.47% => regression (5.00% tolerance) 
  memory: -19.52% => improvement (1.00% tolerance)

[ Info: Judging messages_forwards_log
BenchmarkTools.TrialJudgement: 
  time:   +1.04% => invariant (5.00% tolerance)
  memory: +0.01% => invariant (1.00% tolerance)

[ Info: Judging messages_backwards_log
BenchmarkTools.TrialJudgement: 
  time:   +1.35% => invariant (5.00% tolerance) 
  memory: +6.46% => regression (1.00% tolerance)

[ Info: Judging mle_step
BenchmarkTools.TrialJudgement: 
  time:   -61.12% => improvement (5.00% tolerance)
  memory: -29.02% => improvement (1.00% tolerance)

If you find any useful lines for HMMBase, please feel free to integrate them, obviously!

Also, if you have time, could you explain how messages_backwards_log works? It seems the views and the temp variable really make this much faster than simpler constructions might suggest- I haven't had much luck with views improving speed in other functions. Thanks very much for your time Max!!