better document a technical confusing point in the Hidden Markov Model code

[was]

I was reading the Continuous Hidden Markov Model code and trying to understand how probabilities are defined in a certain context, and got confused. So I added some comments to de-confuse me. Hence this patch.

There is small change in the code itself, where I had checked for "0" instead of checking for smaller than min_sd in one line. This makes the code (1) work much better with actual real world examples, and (2) is consistent with the old ghmm C library from sage-3.x that this code was supposed to replace.

See all #12146 for feature enhancements.

[was]

should apply to any sage since about sage-4.0

[jason]

Thanks for the doc clarifications, and the math changes make sense, though I'm certainly not a HMM expert, so I don't know how to judge the idea that the changes are more useful. However, it does apply and passes tests, so if this "review" is enough, set this to positive review.

[jason]

No one else has looked at this, so I guess my review will stand. Positive review, and thanks for the work!

[jdemeyer]

I get a numerical noise doctest error against sage-5.0.beta1. I lost the exact doctest error, but it's something trivial.

[was]

apply only this; fixes the noise issue (I hope)

[jdemeyer]

There is still numerical noise on 32-bit systems:

sage -t  --long -force_lib devel/sage/sage/stats/hmm/chmm.pyx
**********************************************************************
File "/Users/buildbot/build/sage/moufang-1/moufang_full/build/sage-5.0.beta2/devel/sage-main/sage/stats/hmm/chmm.pyx", line 1354:
    sage: m.baum_welch(v, min_sd=1)
Expected:
    (-12.617885761692419, 1000)
Got:
    (-12.617885761692417, 1000)
**********************************************************************

[was]

apply only this; fixes final numerical noise issue ?

[jason]

All tests in the file still pass for me; positive review. I see that the doctest above is fixed as well so it should pass.