Re: [Boost-users] math toolkit review

From: John Maddock (john_at_[hidden])
Date: 2007-04-25 12:07:35

Arnaldur Gylfason wrote:
> A few results need comment.
> ->t quantile max diff:           4.07907e-14
> ->t quantile max rel diff:       inf
> Here division by 0 gives inf. max diff is quite acceptable though.
> Some guards should be placed to handle 0 or near 0 but I haven't done
> it. I'm not worried about
> the accuracy but anyone may feel free to remedy this.
> ->cauchy quantile max diff:      2.17426e-12
> ->cauchy quantile max rel diff:  0.104537
> Here we are almost surely again dividing by something near 0. Similar
> comments as above apply.

If you can give me the specific input that causes the difference, we can use 
functions.wolfram.com to check who's right.

> ->lgamma max diff:               1.13687e-13
> ->lgamma max rel diff:           0.211576
> Same old story

Again can you provide the specific values so we can double check?

> R t quantile:             12.88
> boost::math t quantile:   56.15
> R F pdf:                   0.06
> boost::math F pdf:         0.05
> R F cdf:                   0.07
> boost::math F cdf:         0.85
> R F quantile:             18.59
> boost::math F quantile:   54.54
>
> The results vary somewhat but this would be acceptable for my
> applications.
> quantile functions seem to be somewhat slower in boost::math than in
> R. Maybe they're more accurate. More detailed analysis would be
> called for if people are concerned about this.

The longer times are being taken on functions that require the incomplete 
beta to be inverted.  It's possible to do *much* better if you only need a 
couple of digits precision, but what approach R takes I don't know.

> The 2 test programs are attached to this message. If they're somehow
> scrambled,
> anyone can write to me and ask for them.
>
> Last but certainly not the least, my compliments to the authors of
> boost::math ;-)

On behalf of all of us, many thanks!

John.