input:
% ~~~~~~
% switchVal - operation of the finction
% initialize=0;
% sample=1;
% results=2;
% plot = 3;
%
% gR - the output struct contaning the histogram
% (shuold be created with "gR = struct;" before initialization
%
% coords - x,y coordinates of partical centers
% first row x, second row y
%
% Lx - x size of area to calculate
% Ly - y size of area to calculate
%
% NumOfBins - number of bins in the final histogram
%
% output:
% ~~~~~~~
% gR is a histogram struct contaning:
% gR.count - total number of object counted
% gR.range - x axis range for the histogram
% gR.increment - increment of x axis
% gR.saveFileName - name of saved dat file
%
% method:
% ~~~~~~~
% the RDF is calculated by binnig all pair partical distances into
% a histogram, and normalizing each bin with it's Ideal gas number of
% particals.
% when binning the pair distances, we take into acount Periodic
% Boudary Conditions (PBC)
% finaly, to ansure that when r->infinity : RDF ->1 , we
% normalize by multiplying RDF*2/(N-1) where N is the number of
% particals.
% for more information http://www2.msm.ctw.utwente.nl/sluding/TEACHING/APiE_Script_v2011.pdf
% page 48 - "Radial distribution function"

-------
|important|
-------
this function uses the functions "histogram", "distPBC2D"
"histogram" can be found here: http://www.cchem.berkeley.edu/chem195/histogram_8m.html#aedd379efd57ae78820ad8787bfab0cce
"distPBC2D" can be found here: http://www.mathworks.com/matlabcentral/fileexchange/46575-distpbc2d-m
%% example %%
example for the code above. please note that "radialDistribution2D" uses the functions "histogram" and "distPBC2D":
"histogram" can be found here: http://www.cchem.berkeley.edu/chem195/histogram_8m.html#aedd379efd57ae78820ad8787bfab0cce
"distPBC2D" can be found here: http://www.mathworks.com/matlabcentral/fileexchange/46575-distpbc2d-m

make sure these functions are in your path before you run this code.

coords = [rand(1,100); rand(1,100)]; % in this example we will calculate
% the RDF for a random sett of 100 coordinates. first row is x coordinates,
% second row is y coordinates.

Lx = 1; % board size
Ly = 1;

NumOfBins = 100; % How many bins you want in your RDF histogram. this is
% the RDF's resolution.

gR = struct; % create a struct, this is where our RDF
%(radial distribution function) will be at the end of this calculation.

% initialize gR struct
gR = radialDistribution2D(0,gR,coords,Lx,Ly,NumOfBins);

% Loop over pairs and determine the distribution of distances
gR = radialDistribution2D(1,gR,coords,Lx,Ly,NumOfBins);

% Normalize distance distribution histogram to get the RDF
gR = radialDistribution2D(2,gR,coords,Lx,Ly,NumOfBins);

% plot Result
gR = radialDistribution2D(3,gR,coords,Lx,Ly,NumOfBins);

your results are saved in "gR" struct. "gR.values" has the bins (x axis) of the RDF. "gR.histo" has the histogram (y axis) of the RDF.