Purposefully Slow MATLAB Function?

Question

I want to write a really, really, slow program for MATLAB. I'm talking like, O(2^n) or worse. It has to finish, and it has to be deterministically slow, so no "if rand() = 123,123, exit!" This sounds crazy, but it's actually for a distributed systems test. I need to create a .m file, compile it (with MCC), and then run it on my distributed system to perform some debugging operations.

The program must constantly be doing work, so sleep() is not a valid option.

I tried making a random large matrix and finding its inverse, but this was completing too quickly. Any ideas?

Answer 1

This naive implementation of the Discrete Fourier Transform takes ~ 9 seconds for a 2048 long input vector x on my 1.86 GHz single core machine. Going to 4096 inputs extends the time to ~ 35 seconds, close to the 4x I would expect for O(N^2). I don't have the patience to try longer inputs :)

function y = SlowDFT(x)

t = cputime;
y = zeros(size(x));
for c1=1:length(x)
    for c2=1:length(x)
        y(c1) = y(c1) + x(c2)*(cos((c1-1)*(c2-1)*2*pi/length(x)) - ...
                            1j*sin((c1-1)*(c2-1)*2*pi/length(x)));
    end
end
disp(cputime-t);

EDIT: Or if you're looking to stress memory more than CPU:

function y = SlowDFT_MemLookup(x)

t = cputime;
y = zeros(size(x));
cosbuf = cos((0:1:(length(x)-1))*2*pi/length(x));
for c1=1:length(x)
    cosctr = 1;
    sinctr = round(3*length(x)/4)+1;
    for c2=1:length(x)
         y(c1) = y(c1) + x(c2)*(cosbuf(cosctr) ...
                            -1j*cosbuf(sinctr));
         cosctr = cosctr + (c1-1);
         if cosctr > length(x), cosctr = cosctr - length(x); end
         sinctr = sinctr + (c1-1);
         if sinctr > length(x), sinctr = sinctr - length(x); end
    end
end
disp(cputime-t);

This is faster than calculating sin and cos on each iteration. A 2048 long input took ~ 3 seconds, and a 16384 long input took ~ 180 seconds.

Answer 2

Count to 2ⁿ. Optionally, make a slow function call in each iteration.