MATLAB Matrix Preallocation Slower Than Dynamic Matrix Expansion

Question

In each iteration of a loop, I am calculating a MATLAB matrix. These matrices all must be concatenated together to create one final matrix. I know the dimensions of this fi

Answer 1

I have always assumed preallocation is faster for any array size and never actually tested it. So, I did a simple test timing the population of various array sizes from 1x1x3 up to 20x20x3 using 1000 iterations by both appending and preallocation methods. Here's the code:

arraySize = 1:20;
numIteration = 1000;

timeAppend = zeros(length(arraySize), 1);
timePreAllocate = zeros(length(arraySize), 1);

for ii = 1:length(arraySize); 
    w = [];
    tic;
    for jj = 1:numIteration
        w = [w; rand(arraySize(ii), arraySize(ii), 3)];
    end
    timeAppend(ii) = toc;
end; 

for ii = 1:length(arraySize); 
    w = zeros(arraySize(ii) * numIteration, arraySize(ii), 3);
    tic;
    for jj = 1:numIteration
        indexStart = (jj - 1) * arraySize(ii) + 1;
        indexStop = indexStart + arraySize(ii) - 1;
        w(indexStart:indexStop,:,:) = rand(arraySize(ii), arraySize(ii), 3);
    end
    timePreAllocate(ii) = toc;
end; 

figure;
axes;
plot(timeAppend);
hold on;
plot(timePreAllocate, 'r');
legend('Append', 'Preallocate');

And here are the (as expected) results: