Simplification of "for" loop MATLAB R2018a

I want to perform the following procedure:

I have two vectors x=[1,2,3] and y=[5,7,9]

I want to take first element of x and then add each element from y to it, then I want to take second element from x and add each element from y to it and so on... Finally, I want to save each result from each step of this procedure in a vector of the corresponding size. I know in advance that I will get the following vector r =[6,8,10,7,9,11,8,10,12].

In order to perform the following procedure I have written the following script:

clear
a = 1;
b = 3;
c = 5;
d = 2;
e = 9;
x = [a:b];
y = [c:d:e];
[rx,cx] = size(x);
[ry,cy] = size(y);
r = zeros((cx*cy),1);

for ii = x
for jj = y
xi = find(x==ii)    
yi = find(y==jj)
row = xi*cy-(cy-yi)
r(row) = ii + jj
end
end

Finally, I got the result but I spent about 2 hours to come up with that. (well, I am just beginner in programming). I would be happy to know if there is any simpler and more efficient way to do that. I am especially concerned about this step, since it took the most of my time. Or should I give up coding since I took for so long for so simple problem?

xi = find(x==ii)    
yi = find(y==jj)
row = xi*cy-(cy-yi)
r(row) = ii + jj

Answer 1

[Birdman]

By the power of implicit expansion starting from R2016b in MATLAB, your desire can be achieved in one line of code:

 r=reshape((x.'+y).',1,[])

Read the following blog to understand implicit expansion:

https://blogs.mathworks.com/loren/2016/10/24/matlab-arithmetic-expands-in-r2016b/

Note that (x.'+y).' part refers to implicit expansion. Since they have a dimension mismatch, MATLAB internally adjusts their dimensions to allow them to be summed.

[GIorgi Tsutskiridze]

This is amazing. Thanks!