# ProbDist2D

## PURPOSE

PROBDIST2D

## SYNOPSIS

function [P bins] = ProbDist2D(x, nbins);

## DESCRIPTION

    PROBDIST2D
       Usage: [P bins] = [P bins] = ProbDist2D(x, nbins);

     This function calculates the discrete probability distribution for a
     variable that is in a two dimensional phase space.  Because the variable
     exists in a two dimensional phase space, we have to bin in x^2
     (equivalent to dividing P by x). The function simply calculates a
     normalized histogram using 'hist', so nbins can take any form that hist
     can take, although it does not allow for all the other hist options.

## CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

## SOURCE CODE

    0001 function [P bins] = ProbDist2D(x, nbins);
    0002
    0003 %PROBDIST2D
    0004 %   Usage: [P bins] = [P bins] = ProbDist2D(x, nbins);
    0005 %
    0006 % This function calculates the discrete probability distribution for a
    0007 % variable that is in a two dimensional phase space.  Because the variable
    0008 % exists in a two dimensional phase space, we have to bin in x^2
    0009 % (equivalent to dividing P by x). The function simply calculates a
    0010 % normalized histogram using 'hist', so nbins can take any form that hist
    0011 % can take, although it does not allow for all the other hist options.
    0012
    0013 %Written by Dan Valente
    0014 %September 2007
    0015
    0016 [H bins] = hist(x.^2, nbins);
    0017 N = sum(sum(H));
    0018 binsize = bins(3)-bins(2);
    0019 P = H./(N*binsize);
    0020
    0021 %now transform bins back to the unsquared locations.  This is really only
    0022 %for conviencence, by no means is it necessary.  If this line is commented
    0023 %out, then the plot is simply P vs. x^2 instead of P vs. x
    0024 bins = sqrt(bins);
    0025
    0026 return;