Re: [boost] [math distributions]

Subject: Re: [boost] [math distributions]
From: Paul A. Bristow (pbristow_at_[hidden])
Date: 2008-11-29 11:16:54

> -----Original Message-----
> From: boost-bounces_at_[hidden] [mailto:boost-bounces_at_[hidden]] On
> Behalf Of Thijs van den Berg
> Sent: 29 November 2008 14:15
> To: boost_at_[hidden]
> Subject: Re: [boost] [math distributions]
> 
> Paul A. Bristow wrote:
> >
> >> -----Original Message-----
> >> From: boost-bounces_at_[hidden]
> >> [mailto:boost-bounces_at_[hidden]] On Behalf Of Thijs van den
> >> Berg
> >> Sent: 29 November 2008 09:59
> >> To: boost_at_[hidden]
> >> Subject: Re: [boost] [math distributions]
> >>
> >>>>> PS, I see no LambertW function in math::special_function. I'm sure
> >>>>> Knuth is going to be very upset! :)
> > But I'm sure you are right - Knuth will be very, very disappointed.
> >
> > Anyone with nothing better to do fancy implementing this? :-))
> >
> > Paul
> >
> well I was thinking about implementing it using this ref

> http://www.whim.org/nebula/math/lambertw.html
> 
> but I'm not sure about the complex number version (which is very important, because
> it's needed for the colorplots!)

A Friday afternoon project? ;-)
 
> Another thing is that the multivariate Gaussian has higher priority on my list. It's
> something I actually need to do quite soon (in- or out-side boost), plus the fact that
> adding a new function is *way* more work than just implementing a simple formula.
> 
> Essentially lapalace is nothing more than
> 
> T function pdf_lapace(const T& x, const T& a, const T& b) return exp(-abs(x-
> a)/b)/b/2;
> 
> so I thought, I can do that in 10 minutes!
> ..but I ended up writing an additional 800 lines. aagghh. A little think I could try to do is
> decompose the unit test into a distribution invariant part (which is reusable) and a
> laplace specific part. How about common_test.hpp, as an analogy to
> common_error_handling.hpp? That would make adding a test other as simple as
> adding a single line. Your idea on testing all non-member functions for the way they
> handle infinity could e.g. be done like this:

> 
> // The centralized part. Testing various values, is a bit configurable with a couple of
> boolean
> 
> template <class DistributionType>
> template distribution_check_throw_on_inf(const DistributionType dist, bool x_neg_inf,
> bool x_pos_inf, ...) {
>    typedef DistributionType::RealType realtype;
> 
>    if (x_neg_inf) //check if an error gets thrown on x ==  -inf
>    {
>       BOOST_CHECK_THROW(pdf(dist,
> -std::numeric_limits<RealType>::infinity()), std::domain_error);
>       BOOST_CHECK_THROW(cdf(dist,
> -std::numeric_limits<RealType>::infinity()), std::domain_error);
> 
>       ... other non-member functions...
> 
>    }
> 
>    if (x_pos_inf)
>    {
>       ...
>    }
> 
>    ... other tests ..., e.g. p=0, p=1 in quantile }
> 
> And then have a test that uses it like this:
> 
> BOOST_AUTO_TEST_CASE( dist_test )
> {
>    distribution_check_throw_on_inf(normal<float>(0,1), true, true, ..
>    distribution_check_throw_on_inf(normal<double>(0,1), true, true, ..
>    distribution_check_throw_on_inf(normal<long double>(0,1), true, true, ..
> }
> 
> we could even make a single centralized test for *all* distributions! A author of a new
> distribution will have to add a couple of lines to this
> 
> BOOST_AUTO_TEST_CASE( dist_throw_test )
> {
>    distribution_check_throw_on_inf(normal<float>(0,1), true, true, ..
>    distribution_check_throw_on_inf(normal<double>(0,1), true, true, ..
>    ...
> 
>    distribution_check_throw_on_inf(laplace<float>(0,1), true, true, ..
>    ...
> }
> 
> something like this would make me much more confident that all tests are performed
> on all distribution (nothing forgotten). What do you think? It also makes the burden of
> thinking about all possible cases much less, as the test cases are centralized...

Well if we had known what we do now, we might well have done it this clearly better way. 

- but having done most of the distributions, I fear it is easier to keep using what we have as boilerplate.

And the tolerance are too variable to handle this way easily - Laplace is rather accurate because only using exp.

And the multivariate will be pretty different too.

Reminds me of a quote "Why spend five years of your life automating something that you can do in a day or two?" :-)

Paul

---
Paul A. Bristow
Prizet Farmhouse
Kendal, UK   LA8 8AB
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pbristow_at_[hidden]