Evaluate all possible combinations of subarrays in an array

Hi everyone,

I have an algorithm which is not exactly fast, due to 4 for loops, and I am wondering if the same result can be achieved much faster by using the power of Matlab.

I want to evaluate all possible subarray sizes, each at all possible positions in the main array. The output result is the position and size of a single subarray, which gives the maximum value (critMax) based on the "merit function" (in the example below, the sum over the subarray components, divided by the size)

nx = 100;
ny = 50;
array = rand(nx,ny);                                  %some data array, random numbers are just an example

crit = [0 0 0 0];
critMax = 0;

for Dx = 1:nx                                         %defines width x
    for Dy = 1:ny                                     %defines width y
        for x0 = 1:nx-Dx                              %defines start index x
            for y0 = 1:ny-Dy                          %defines start index y
                x1 = x0 + Dx - 1;                     %defines end index x
                y1 = y0 + Dy - 1;                     %defines end index y
                subarray = array(x0:x1,y0:y1);            %takes the subarray
                total = sum(subarray(:));             %sum over whole subarray
                res = total/(Dx+Dy);                  %apply some function, this is just an example, result is a 1x1 double
                if res > critMax                      %compare whether the value in the current subarray is the "best" so far
                    crit = [x0 y0 x1 y1];
                    critMax = res;
                end
            end           
        end
    end
end

crit
critMax

I hope the problem became clear, otherwise I will add more infos.

Thanks a lot in advance.

PS: Matlab R2018a, no additional toolboxes available.

[KSSV]

Have a look on nchoosek./ perms