MATLAB: Saving (in a matrix) the elapsed time and number of iterations for a large number of cases

matrixtime

I have a program that outputs the *number of iterations* and a *test value*, given inputs *A1,A2,A3,A4*.
I want to run through 5 values each of A1, A2, A3, A4, thus making 625 runs. In the process, I want to save the *time elapsed* for each run, the *number of iterations*, and *test value* in 3 separate matrices.
I have tried using 4 nested *for* loops, and made progress, but need some help on indexing the elements of the matrices. The iterator variables in the for loops don't match the indexing variables…
The code for the 4 nested loops is below:
    m = logspace(-4,4,5);
    n = logspace(0,8,5);
    eltime = zeros(5,length(m)*length(m)*length(m));
    for A1 = m
        for A2 = m
            for A3 = m
                for A4 = n
                    tic
                    SmallMAX(A1,A2,A3,A4)
                    toc;
                    for i=1:numel(eltime)
                        for j = 1:length(n)
                            eltime(j,i) = toc;
                        end
                    end
                end
            end
        end
    end
The code for the main program is excerpted below:
    function [k,test] = OC(A1,A2,A3,A4)
    ...
    end
Thanks for any help.

Best Answer

Use this kind of code framework
mvals = logspace(-4,4,5);
numm = length(mvals);
nvals = logspace(0,8,5);
numn = length(nvals);
for A1idx = 1 : numm
  A1 = mvals(A1idx);
  for A2idx = 1 : numm
    A2 = mvals(A2idx);
    for A3idx = 1 : numm
      A3 = mvals(A3idx);
      for A4idx = 1 : numn
        A4 = nvals(A4idx);
        ....
         eltime(A4idx, A3idx, A2idx, A1idx) = ....
       end
     end
   end
 end
You might notice that I reversed the indices from the obvious, that I did not index eltime(A1idx, A2idx, A3idx, A4idx) . You can use that order, but it is less efficient than the order I used. That is because in MATLAB memory is arranged "down columns", so A(1,1) is immediately adjacent to A(2,1) then A(3,1) rather than A(1,1) being immediately adjacent to A(1,2) then A(1,3) . It is more efficient to assign to adjacent memory.
You should also examine your code to determine whether you can vectorize it, calculating on a matrix basis instead of one value at a time. For example, A1 + A2 * A3^A4 can be vectorized as A1 + A2 .* A3 .^ A4 so now if you feed in arrays of the same size, the expression would calculate for each corresponding element. This can end up being quite a lot faster.
If your code can be vectorized, then you can use ndgrid to build the appropriate matrices:
[A1, A2, A3, A4] = ndgrid(mvals, mvals, mvals, nvals);
result = OC(A1, A2, A3, A4);   %do everything at once, no loops at all!
this will not give you the individual elapsed times, but you might find that it is no longer important compared to the speedup.
Related Question