I need to insert multiple 32x32 arrays into 1024x1024 array at predetermined random locations. How to do this efficiently?

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I need to insert many (10^6) 32x32 arrays into single 1024x1024 array and sum them. Insertion location is random, but predetermined. Simple for loops result in long execution time. How can I optimize? I do have parallel processing and gpu available.
Nx=ceil(rand(1e6,1)*(1024-32)); %avoiding partial arrays at edges
Ny=ceil(rand(1e6,1)*(1024-32));
smallArray=ones(32);
largeArray=zeros(1024);
for ii=1:1e6
largeArray(Nx(ii):Nx(ii)+31,Ny(ii):Ny(ii)+31)=largeArray(Nx(ii):Nx(ii)+31,Ny(ii):Ny(ii)+31)+smallArray;
end

Accepted Answer

Joss Knight
Joss Knight on 8 Jun 2016
Use accumarray (and randi):
N = 1024;
Nx = randi([1 (N-32)], 1e5, 1);
Ny = randi([1 (N-32)], 1e5, 1);
linIndStart = sub2ind([N N], Nx, Ny);
smallArray = gpuArray.ones(32);
[I, J] = ndgrid(1:32);
linOffsets = sub2ind([N N], I(:), J(:)) - 1;
linInd = bsxfun(@plus, linIndStart, linOffsets');
values = repmat(smallArray(:)', numel(Nx), 1); % Replace with actual vals
largeArray = accumarray(linInd(:), values(:), [N*N 1]);
largeArray = reshape(largeArray, N, N);
If your submatrices are genuinely all just ones, then just replace the values(:) with 1.
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More Answers (1)

Ahmet Cecen
Ahmet Cecen on 29 May 2016
If your small array will always be the same, you might be able to do this lightning fast with a convolution. Instead of using the random ok indices as corners, you would use them as centers. Do something like:
LargeArray(randindexvector)=1;
You can separately find repetitions using unique and add them if you happen to get the same center twice. Much smaller for loop.
Then you convolve with a 16x16 ones matrix.
There might be some rough edges in this approach that needs some smoothing, but if you can get it to work, it would be milliseconds.
  2 Comments
Ahmet Cecen
Ahmet Cecen on 29 May 2016
You can cascade on stages of uniqueness and vectorize the fill. Say you created 1000 random values, and say 100 of them are duplicates. You first work on the 900, then 100, then any duplicates within the 100 etc. You do something like:
for i = 1:BiggestNumberofRepetations
WORK HERE
end
Hopefully this is an orders of magnitude smaller iteration. This allows you to iterate over the dimensions of the smaller matrix instead of the number of random numbers. I will burst the memory here but you can work around it. It should look something like:
RandInd = sub2ind([1024 1024],Nx,Ny);
for i = 1:32*32
largeArray(RandInd+floor((i-1)/32)*1024)+mod(i,32)) = largeArray(RandInd+floor((i-1)/32)*1024)+mod(i,32)) + smallArray(i);
end
Now there is some nasty indexing there so double check that. Now your iteration count is MaximumRepetationsCount*numel(smallArray), which in most cases should be still orders of magnitude smaller.

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