[Haskell-cafe] monte carlo trouble

[Paul Johnson]

Chad Scherrer wrote:
> There's a problem I've been struggling with for a long time...
>
> I need to build a function
> buildSample :: [A] -> State StdGen [(A,B,C)]
>   
> given lookup functions
> f :: A -> [B]
> g :: A -> [C]
>
> The idea is to first draw randomly form the [A], then apply each
> lookup function and draw randomly from the result of each.
>   
I don't understand why this returns a list of triples instead of a 
single triple.  Your description below seems to imply the latter.

You should probably look at the "Gen" monad in Test.QuickCheck, which is 
basically a nice implementation of what you are doing with "State 
StdGen" below.  Its "elements" function gets a single random element, 
and you can combine it with replicateM to get a list of defined length.

(BTW, are you sure want multiple random samples rather than a shuffle?  
A shuffle has each element exactly once whereas multiple random samples 
can pick any element an arbitrary number of times.  I ask because 
shuffles are a more common requirement.  For the code below I'll assume 
you meant what you said.)

Using Test.QuickCheck I think you want something like this (which I have 
not tested):

   buildSample :: [A] -> Gen (A,B,C)
   buildSample xs = do
      x <- elements xs
      f1 <- elements $ f x
      g1 <- elements $ g x
      return

If you want n such samples then I would suggest

   samples <- replicateM n $ buildSample xs
> It's actually slightly more complicated than this, since for the real
> problem I start with type [[A]], and want to map buildSample over
> these, and sample from the results.
>
> There seem to be so many ways to deal with random numbers in Haskell.
>   
Indeed.
> After some false starts, I ended up doing something like
>
> sample :: [a] -> State StdGen [a]
> sample [] = return []
> sample xs = do
>   g <- get
>   let (g', g'') = split g
>       bds = (1, length xs)
>       xArr = listArray bds xs
>   put g''
>   return . map (xArr !) $ randomRs bds g'
>   
Not bad, although you could instead have a sample function that returns 
a single element and then use replicateM to get a list.
> buildSample xs = sample $ do
>   x <- xs
>   y <- f x
>   z <- g x
>   return (x,y,z)
>
> This is really bad, since it builds a huge array of all the
> possibilities and then draws from that. Memory is way leaky right now.
> I'd like to be able to just have it apply the lookup functions as
> needed.
>
> Also, I'm still using GHC 6.6, so I don't have
> Control.Monad.State.Strict. Not sure how much difference this makes,
> but I guess I could just copy the source for that module if I need to.
>   
Strictness won't help.  In fact you would be better with laziness if 
that were possible (which it isn't here).  The entire array has to be 
constructed before you can look up any elements in it.  That forces the 
entire computation.   But compare your implementation of buildSample to 
mine.

Paul.