# scale acceleration

**Xi'an's Og » R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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**K**ate Lee pointed me to a rather surprising inefficiency in matlab, exploited in Sylvia Früwirth-Schnatter’s *bayesf* package: running a gamma simulation by rgamma(n,a,b) takes longer and sometimes much longer than rgamma(n,a,1)/b, the latter taking advantage of the scale nature of b. I wanted to check on my own whether or not R faced the same difficulty, so I ran an experiment [while stuck in a Thalys train at Brussels, between Amsterdam and Paris…] Using different values for a [click on the graph] and a range of values of b. To no visible difference between both implementations, at least when using *system.time* for checking.

a=seq(.1,4,le=25) for (t in 1:25) a[t]=system.time( rgamma(10^7,.3,a[t]))[3] a=a/system.time(rgamma(10^7,.3,1))[3]

Once arrived home, I wondered about the relevance of the above comparison, since rgamma(10^7,.3,1) forces R to use 1 as a scale, which may differ from using rgamma(10^7,.3), where 1 is known to be the scale [does this sentence make sense?!]. So I rerun an even bigger experiment as

a=seq(.1,4,le=25) for (t in 1:25) a[t]=system.time( rgamma(10^8,.3,a[t]))[3] a=a/system.time(rgamma(10^7,.3))[3]

and got the graph below. Which is much more interesting because it shows that some values of a are leading to a loss of efficiency of 50%. Indeed. (The most extreme cases correspond to a=0.3, 1.1., 5.8. No clear pattern emerging.)

Filed under: pictures, R, Statistics, Travel, University life Tagged: bayesf, Brussels, R, rgamma, scale, scale parameter, system.time

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