Vectorizing three nested loops

Dear All,

How can I vectorize the following three nested loops? I tried using arrayfun but I did not succeed in doing it.

    % Range of random number for x and y.
    L = 8;
    H = 6;

    % The number of random numbers.
    n = 100;  

    % Randomly spaced data.
    x = rand( n, 1 )*L;
    y = rand( n, 1 )*H;

    d = .01;
    [ X, Y ] = meshgrid( 0:d:L, 0:d:H );

    TOL = .01;
    I = zeros(size(X));

    for i=1:size(X,1)
        for j=1:size(X,2)
            for k=1:numel(x)
                dist = (X(i,j)-x(k))^2+(Y(i,j)-y(k))^2;
                if( dist<TOL)
                    I(i,j) = 1;
                end
            end
        end
    end

Thanks,

Ahmad

Answer 1

[Matt Fig]

I2 = any((bsxfun(@minus,X,reshape(x,1,1,n)).^2 +...
        bsxfun(@minus,Y,reshape(y,1,1,n)).^2)<TOL,3) ;

[AP]

Matt, it does not give me the correct result.

[Matt Fig]

The code above does give the same result here.....

isequal(I,I2)
ans =

       1

I ran it 10 times, and every time I get the same thing. Here is the code I used to test that I and I2 are equal. So what are you doing that says they are not equal? Did you run something other than what you posted?

% Range of random number for x and y.
L = 8;
H = 6;
% The number of random numbers.
n = 100;
% Randomly spaced data.
x = rand( n, 1 )*L;
y = rand( n, 1 )*H;
d = .01;
[ X, Y ] = meshgrid( 0:d:L, 0:d:H );
TOL = .01;
tic
I = zeros(size(X));

for i=1:size(X,1)
    for j=1:size(X,2)
        for k=1:numel(x)
            dist = (X(i,j)-x(k))^2+(Y(i,j)-y(k))^2;
            if( dist<TOL)
                I(i,j) = 1;
            end
        end
    end
end
toc

tic 
I2 = any((bsxfun(@minus,X,reshape(x,1,1,n)).^2 +...
          bsxfun(@minus,Y,reshape(y,1,1,n)).^2)<TOL,3) ;   
toc

isequal(I,I2)

[AP]

Sorry, I did not noticed one of the statements had been changed. I get the same results too. Thanks so much.