How to add two probability density functions efficiently

Hello,       I have a simple problem but I need to improve the execution efficiency when I have thousands of data in a probability density function, a small example:

close all
clear
%example
x =[ 1 3 5 9 15];
y =[ 4 7 8 12 6];
xn=[ 3 9 16]; 
yn=[ 10 3 4];
[xnew,ynew]=add2pdf(x,y,xn,yn);
xnew
ynew

% function
function [xnew,ynew]=add2pdf(x,y,xn,yn)
% sum two probability density function
[nf,nc]=size(xn);
xold=x;
yold=y;
    xx=[x xn];
    [xv,xp]=sort(xx,'ascend');
    dxv=diff(xv);
    xnew=[xv(1) xv(find(dxv>0)+1)];
    ynew=zeros(1,length(xnew));
    for i=1:size(y,2),
        pynew=find(xnew==xold(i)); % <====this instruction it's very slow (find), but I need the pointers
        ynew(pynew)=y(i); 
    end
    for i=1:length(xn), 
        px=find(xnew==xn(i));
        ynew(px)=ynew(px)+yn(i); 
    end
return

Answer 1

[David Goodmanson]

Hi Juan,

Here is one way. It takes advantage of the fact that when you make a sparse matrix with repeated indices, the corresponding values get added. Here M is a one-row matrix.

M = full(sparse([x xn],1,[y yn]))';
xnew = find(M);
ynew = M(xnew);

[Juan Pablo Segovia]

David, Thanks so much. I will test the code to evaluate the efficiency in the problem.

[Juan Pablo Segovia]

David, Great solution for integers numbers, fast, efficient and elegant. Thank you very much.

[David Goodmanson]

Juan, you're welcome, thank you for your comment. The sparse function has useful properties and did most of the work here.