Parfor in Matlab

Question

I'm trying to run this loop as a parfor-loop:

correlations = zeros(1,N);   
parfor i = 1:(size(timestamps,1)-1)
    j = i+1;
    dts = timestamps(j) - timestamps(i);
    while (dts < T) && (j <= size(timestamps,1))
        if dts == 0 && detectors(i) ~= detectors(j)
            correlations(1) = correlations(1) + 2;
        elseif detectors(i) ~= detectors(j)
            dts = floor(dts/binning)+1;
            correlations(dts) = correlations(dts) + 1;
        end
        j = j + 1;
        if j <= size(timestamps,1)
            dts = timestamps(j) - timestamps(i);
        end
    end
end

Matlab gives me the following error:

Error: File: correlate_xcorr.m Line: 18 Column: 17
The variable correlations in a parfor cannot be classified.
See Parallel for Loops in MATLAB, "Overview".

Line 18 is the following:

correlations(1) = correlations(1) + 2;

I can not understand why this shouldn'n be possible. The final value of correlations doesn't depend on the order in which the loop is executed, but only dts and detectors. I found similar examples in the documentation which work fine.

Why can't Matlab execute this code and how can I fix it?

Answer 1

I found the following solution and it seems to work. The program looks a litte different, but it has the same shape. This way Matlab is forced to think x/correlations is a reduction variable.

X = zeros(1,5);
parfor i= 1:1000
    a = zeros(1,5);
    dts = randi(10)-1;
    if dts == 0
        a(1) = (a(1) + 2);
    elseif dts <= 5
        a(dts) = a(dts) +1;
    end
    X = X + a;
end

Answer 2

MATLAB cannot determine that your loop is order independent because of the way you're accessing correlations(1) from multiple iterations of the PARFOR loop. It looks like this value is in some way 'special', it should work to make a 'reduction' variable, i.e. replace correlations(1) with correlations_1 or something.

The next problem you'll encounter is that you are not correctly 'slicing' the remainder of correlations. For MATLAB to analyse a PARFOR loop, it needs to be able to tell that each loop iteration is writing only to its 'slice' of the output variables. In practice, this means that you must index the outputs using literally the loop index.

More about PARFOR variable classification here: http://www.mathworks.com/help/distcomp/advanced-topics.html#bq_of7_-1

EDIT:

If you want correlations to behave strictly as a reduction variable as I believe you imply in your comments, you need to give PARFOR a clue that's what you mean: in particular, you need to add to the whole variable each time you need to. In other words, something more like:

parfor ...
    dummyVec = zeros(1, N);
    dummyVec(elementToIncrement) = 1;
    correlations = correlations + dummyVec;
end

I agree this is non-obvious. See http://blogs.mathworks.com/cleve/2012/11/26/magic-squares-meet-supercomputing/ for more.