Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: BinCounts to InterpolatingFunction

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109456] Re: BinCounts to InterpolatingFunction
  • From: dh <dh at metrohm.com>
  • Date: Tue, 27 Apr 2010 08:48:10 -0400 (EDT)
  • References: <hr65uu$jtk$1@smc.vnet.net>

On 27.04.2010 10:06, Kevin J. McCann wrote:
> I am using a Markov Chain Monte Carlo (MCMC) approach to evaluate a
> multidimensional probability density function. The output is a large
> number of multidimensional points {x1,x2,...,xn}. I can use BinCounts to
> gather the points into a PDF (after appropriate normalization). I would
> like to then define a function, p[X_], which is the multidimensional
> interpolation of the BinCounts output, but I can't figure out how to
> automate this for an arbitrary number of dimensions.
>
> Any ideas?
>
> For the 2d case I did the following:
>
> tbl = Partition[
>      Flatten[Table[{xmin + i*\[CapitalDelta]x + \[CapitalDelta]x/2,
>         ymin + j*\[CapitalDelta]y + \[CapitalDelta]y/2,
>         counts[[i + 1,
>          j + 1]]/(\[ScriptCapitalN] \[CapitalDelta]x \
> \[CapitalDelta]y)}, {i, 0, nx - 1}, {j, 0, ny - 1}]], 3];
>
> f=Interpolation[tbl]
>
> But as you can see, this is not easily extended to higher dimensions.
>
> Kevin
>
Hi Kevin,
if I understand correctly, your problem is the generation of a suitable 
grid of data points for "Interpolation".
Assume you have a function bins[{i1,i2,..,in}] of n integer arguments.
The arguments run from 0..ni. The vector of ni is called 
bounds={n1,n2..nn}. We can now define the function "dataGrid" that 
creates a rectangular multidimensional structure for the input to 
Interpolation:

dataGrid[bins_, bounds_] := Module[{iter},
   iter = {x, 0, n - 1} /.
     Table[{x -> Symbol["x" <> ToString[i]], n -> bounds[[i]]}, {i, 1,
       Length[bounds]}];
   Flatten[
    Table[{iter[[All, 1 ]], bins[iter[[All, 1 ]]]},
     Evaluate[Sequence @@ iter]]
    , Length[bounds] - 1]
   ]

If we choose an example for bins:
bins[v : {_ ..}] := Times @@ v;
we can calulation an interpolation:

bins[v : {_ ..}] := Times @@ v;
Interpolation@dataGrid[bins, {4, 4, 4}]

cheers, Daniel

-- 

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>



  • Prev by Date: Re: Precision of calculations
  • Next by Date: Re: Why Return[] does not work?
  • Previous by thread: BinCounts to InterpolatingFunction
  • Next by thread: Re: BinCounts to InterpolatingFunction