Vectorising a for loop that creates a 2-D surface for each point in a Domain

Hi, I'm having a bit of difficulty optimising the following piece of code:

x = [-2:0.1:2]
y = x'

for i = 1:numel(x)
    for j = 1:numel(x)
        z(:,:,i,j) = 0.5*exp(-(((x(i)-x).^2)/0.2 + ((x(j)-y).^2)/0.2));
    end
end

The code creates a surface at each point in a domain. I would like know whether it would be possible to vectorise this for loop since I would like to be able to do this for larger domains and hence need a faster way of doing this. Any help is much appreciated.

[per isakson]

"for larger domains and hence need a faster " How large and how fast do you aim at?

Answer 1

[per isakson]

Matlab loops are faster than their reputation. I believe it's difficult to significantly outperform this function

function  z = cssm( )
    x = -2:0.05:2;
    y = x';
    n = numel(x);
    z = nan(n,n,n,n);   % pre-allocation is a must!
    %    
    f = nan(n,n);
    for kk = 1:n
        f(kk,:) = exp(-((x(kk)-x).^2)/0.2); 
    end
    for ii = 1:n
        for jj = 1:n
            z(:,:,ii,jj) = 0.5 .* f(ii,:) .* f(jj,:)';
        end
    end
end