How to speed-up this matlab loops

Question

I hope you can help me out here, I have a speed problem in matlab with the following code:

%Example Definition
bf = 80;
sam = 10000;
dim = 300;
a = rand(bf, sam, dim);
T = rand(bf, sam, dim);
x = repmat(rand(1, sam, dim), [bf 1 1]);

%Calculation
E = zeros(size(T, ndims(T)));
dist = zeros(bf, sam);
a = repmat( a, [ 1 1 dim ]);
for i = 1:dim
    for j = 1:dim
        dist = x(:,:,j) .* T(:,:,i);
         E(i,j) = sum(sum(a(:,:,i) .* (0.5 * dist), 2), 1);
    end        
end

These 3 diminsional arrays are quite big (like 80x10000x300), so that there is a high computation time to calculate this 'E' matrix. I've already tried to vectorize it, but i have no a good idea how to do that without going into the memory limit (16 GB).

Any idea how to speed this up ?

Could you make a small complete sample code by defining `T` `bf` `sam` `a` `dim` and `x`? — Yvon, Mar 05 '17 at 20:11
Running loops will slow the computation. Convert formula into direct matrix operations and/or use parallel for loops. First one is preferred and viable as you've large data. Also consider data partitioning and processing in parallel loops (one for each partition). — SACn, Mar 05 '17 at 20:40

score 0 · Answer 1 · answered Mar 05 '17 at 20:02

0

I don't see why it should be more than 16GB.

You store each pixel as 8B. 80*10K*300=240M, so each matrix is close to 2GB. You have for matrices, in total 8GB.

Your code is quite efficient, one simple suggestion to decrease memory usage is make everything single; i.e. single(zeros(size(T)))

Another suggestion is if you are using more matrices, clear variables when you are done.

Also, don't create dist variable, it is used only once.

answered Mar 05 '17 at 20:02

smttsp

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I tried to vectorize it with repmat and reshape. So I created the same values for 'X' times and run over the 16GB. Not with this code that i posted here :) – yoshiii90 Mar 05 '17 at 20:23

score 0 · Answer 2 · edited May 23 '17 at 12:25

0

First of all, using i and j for loops slow things down. See: Using i and j as variables in Matlab

The out-of-memory problem occurs in a = repmat( a, [ 1 1 dim ]); which expands a by bf x sam x dim times. However the only place you access a is a(:,:,ii) and ii goes from 1 to dim. Therefore in the 300x300 elements in the 3rd dimension, only the first 300 are used.

One possible answer: You don't need to repmat and leave a as-is.

Another possible answer: a = repmat(rand(bf, sam, 1), [ 1 1 dim ]);

edited May 23 '17 at 12:25

Community

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answered Mar 05 '17 at 20:10

Yvon

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You are right! This was my fault, I forgot to delete this `repmat a`. Thanks :) – yoshiii90 Mar 05 '17 at 22:05

score 0 · Accepted Answer · answered Mar 05 '17 at 20:54

0

If you reshape 3D matrices to 2D matrices,nested loop will be converted to a matrix multiplication:

x = reshape(x,[],dim).';
a = reshape(a,[],dim);
T = reshape(T,[],dim);
E = x * (a.*T*.5);

answered Mar 05 '17 at 20:54

rahnema1

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Yeah this is what I was looking for! Thank you :) – yoshiii90 Mar 05 '17 at 22:15

score 0 · Answer 4 · answered Mar 05 '17 at 21:50

Sometimes just updating your nested loop from the following

for i=1:m
    for j=1:n
        out(i,j) = something;
    end
end

to

for j=1:n
    for i=1:m
        out(i,j) = something;         %first rows fill
    end
end

would improve the performance significantly:

How to speed-up this matlab loops

4 Answers4