Question

I’m trying to index a large matrix in MATLAB that contains numbers monotonically increasing across rows, and across columns, i.e. if the matrix is called A, for every (i,j), A(i+1,j) > A(i,j) and A(i,j+1) > A(i,j).

I need to create a random number n and compare it with the values of the matrix A, to see where that random number should be placed in the matrix A. In other words, the value of n may not equal any of the contents of the matrix, but it may lie in between any two rows and any two columns, and that determines a “bin” that identifies its position in A. Once I find this position, I increment the corresponding index in a new matrix of the same size as A.

The problem is that I want to do this 1,000,000 times. I need to create a random number a million times and do the index-checking for each of these numbers. It’s a Monte Carlo Simulation of a million photons coming from a point landing on a screen; the matrix A consists of angles in spherical coordinates, and the random number is the solid angle of each incident photon.

My code so far goes something like this (I haven’t copy-pasted it here because the details aren’t important):

for k = 1:1000000  
    n = rand(1,1)*pi;  
    for i = length(A(:,1))  
        for j = length(A(1,:))  
            if (n > A(i-1,j)) && (n < A(i+1,j)) && (n > A(i,j-1)) && (n < A(i,j+1))  

                new_img(i,j) = new_img(i,j) + 1;   % new_img defined previously as zeros

            end
        end
    end
end

The “if” statement is just checking to find the indices of A that form the bounds of n.

This works perfectly fine, but it takes ridiculously long, especially since my matrix A is an image of dimensions 11856 x 11000. is there a quicker / cleverer / easier way of doing this?

Thanks in advance.

Answer 1

You can get rid of the inner loops by performing the calculation on all elements of A at once. Also, you can create the random numbers all at once, instead of one at a time. Note that the outermost pixels of new_img can never be different from zero.

randomNumbers = rand(1,1000000)*pi;
new_img = zeros(size(A));
tmp_img = zeros(size(A)-2);

for r = randomNumbers
    tmp_img = tmp_img + A(:,1:end-2)<r & A(:,3:end)>r & A(1:end-1,:)<r & A(3:end,:)>r;
end

new_img(2:end-1,2:end-1) = tmp_img;

/aside: If the arrays were smaller, I’d have used bsxfun for the comparison, but with the array sizes in the OP, the approach would run out of memory.