Vectorizing code to calculate radial distance for all points

Hi all!

I have currently written this code to calculate the radial distance for all points with their x, y and z coordinates.

 for x = xmin:step:xmax
    for y = ymin:step:ymax
        for z = zmin:step:zmax
            r((x-xmin)/step+1,(y-ymin)/step+1,(z-zmin)/step+1) = sqrt(x^2 + y^2 + z^2);

        end
    end
end

I am wondering if there is a way to vectorize this code so that I don't have to run the nested loops and hence speed up my calculation time, because I have to run the code for quite a number of times to analyze different data sets.

I am new to matlab so this question may seem quite trivial but please do help me :) Thank you in advance.

[Roger Stafford]

Aside from the question of vectorizing code, it is unwise to set up for-loops in the way you show here. The problem is that expressions such as (x-xmin)/step+1 used as indices may not turn out to be exact positive integers due to tiny round-off errors and thereby would produce error messages. For example, with xmin = 0, step = 0.1, and xmax = 1, my machine produces a non-integer for (x-xmin)/step+1 at the seventh step and would complain if I used it as an index. With for-loops you should instead do something like the following so that you are guaranteed to have integer values for your indices:

 x = xmin:step:xmax;
 y = ymin:step:ymax;
 z = zmin:step:zmax;
 for kx = 1:length(x)
   for ky = 1:length(y)
     for kz = 1:length(z)
       r(kx,ky,kz) = sqrt(x(kx)^2 + y(ky)^2 + z(kz)^2);
     end
   end
 end

Answer 1

[Matt J]

 x = (xmin:step:xmax).';
 y = ymin:step:ymax;
 z = reshape(zmin:step:zmax,1,1,[]);

 r=sqrt(bsxfun(@plus, bsxfun(@plus,x.^2,y.^2),z.^2 ));

Answer 2

[Roger Stafford]

You can also do:

 [X,Y,Z] = ndgrid(xmin:step:xmax,ymin:step:ymax,zmin:step:zmax);
 r = sqrt(X.^2+Y.^2+Z.^2);