Minor optimizations

[vandenman]

Profiling shows that the majority of the time is spend in the gradient computation, which is to be expected. Sadly I wasn't able to improve this much for this PR.

I think that in principle a lot more optimization is possible, but that would require much more changes to the code. Basically, instead of separate log_p and gradient functions we'd need a class. That way, things like total_len can be easily computed once and cached, and the gradient vector grad can also be reused. In general, it should make memory reuse easier.

For now, this PR implements:

• fewer allocations in bgmCompare
• replace strings with enums, because comparing strings is more expensive than ints.
• small tweak to the progress bar: the finish() method ensures that all progress bars are completely filled at the end of the loop. Now it no longer does this if there was a user interrupt.

Let's see if the R CMD CHECK runtime decreases (I doubt it though).

[MaartenMarsman]

I ran the following tests on the code and spotted differences in the bgmCompare output with and without these updates.

#run this with old software
fit_bgm = bgm(Wenchuan[, 1:5], seed = 1234)
x = Boredom[Boredom$language == "fr", 2:6][1:50,]
y = Boredom[Boredom$language != "fr", 2:6][1:50,]
z = Boredom[Boredom$language != "fr", 2:6][51:90, ]
group = c(rep(1, 50), rep(2, 50), rep(3, 40))
x = rbind(x,y,z)
fit_compare <- bgmCompare(x, group = group, seed = 1234)

#run this with new software
fit_bgm2 = bgm(Wenchuan[, 1:5], seed = 1234)
x = Boredom[Boredom$language == "fr", 2:6][1:50,]
y = Boredom[Boredom$language != "fr", 2:6][1:50,]
z = Boredom[Boredom$language != "fr", 2:6][51:90, ]
group = c(rep(1, 50), rep(2, 50), rep(3, 40))
x = rbind(x,y,z)
fit_compare2 <- bgmCompare(x, group = group, seed = 1234)

#tests

all.equal(fit_bgm$raw_samples, fit_bgm2$raw_samples)
[1] TRUE

all.equal(fit_compare$raw_samples, fit_compare2$raw_samples)
[1] "Component “main”: Component 1: Mean relative difference: 0.1814449"
[2] "Component “main”: Component 2: Mean relative difference: 0.1823261"
[3] "Component “main”: Component 3: Mean relative difference: 0.1826248"
[4] "Component “main”: Component 4: Mean relative difference: 0.1847298"
[5] "Component “pairwise”: Component 1: Mean relative difference: 0.4530948"
[6] "Component “pairwise”: Component 2: Mean relative difference: 0.4708279"
[7] "Component “pairwise”: Component 3: Mean relative difference: 0.4671137"
[8] "Component “pairwise”: Component 4: Mean relative difference: 0.4657075"
[9] "Component “indicator”: Component 1: Mean relative difference: 1.882105"
[10] "Component “indicator”: Component 2: Mean relative difference: 2.010225"
[11] "Component “indicator”: Component 3: Mean relative difference: 1.995624"
[12] "Component “indicator”: Component 4: Mean relative difference: 1.880952"

[vandenman]

I'll double check where the change comes from! Also Windows is now down to 1h 20m from 2h 30m 🎉