how to use accumarray over a matrix avoiding a loop?

Question

Fernando 2013-2-12

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编辑： Jasper van Casteren 2022-2-8

Hi,

I want to sum elements of a matrix according to an index. If instead of the matrix I had a vector, I could use accumarray. However, accumarray does not accept matrices as second argument. Any ideas on how to do this avoiding a loop to sum for each vector separately?

For example:

A=[1;1;2;3;3;3];
B=rand(6,10);
C=accumarray(A,B);

gives the output ??? Error using ==> accumarray Second input VAL must be a vector with one element for each row in SUBS, or a scalar.

I could do this by columns of B

C=zeros(size(unique(A),1),10);
for i=1:10,
C(:,i)=accumarray(A,B(:,i));
end

But if the number of columns of B is large, this will be quite slow and I would like this step to be done quickly as it has to be done as part of a minimization routine, so it is done every time the objective function is evaluated.

Thanks,

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Answer 1

Sean de Wolski 2013-2-12

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编辑：Sean de Wolski 2013-2-12

在 MATLAB Online 中打开

You could always use accumarray with two dimensions of subs rather than vals:

A=[1;1;2;3;3;3];
B=rand(6,10);
[xx, yy] = ndgrid(A,1:size(B,2));
C=accumarray([xx(:) yy(:)],B(:));

Frankly, I'll bet the for-loop will be fastest.

More And my suspicions are right depending on how big A and B actually are. I am seeing the for-loop be faster with small arrays and accumarray with two-dimensional subs being faster for larger ones.

arrayfun/cell2mat etc are really slow since they require the conversion to cells which are slow and arrayfun is just slower than a for-loop anyway.

function timeAccumarray
A=[1;1;2;3;3;3];
B=rand(6,10);
[t1,t2,t3] = deal(0);
for ii = 1:100
    tic
    [xx, yy] = ndgrid(A,1:size(B,2));
    C=accumarray([xx(:) yy(:)],B(:));
    t1 = t1+toc;
    tic    
    for jj=size(B,2):-1:1   %dynamically preallocate, avoiding slow unique()
        C2(:,jj)=accumarray(A,B(:,jj));
    end
    t2=t2+toc;
    tic
    C3=cell2mat(arrayfun(@(x) accumarray(A,B(:,x)),1:size(B,2),'un',0));
    t3 = t3+toc;
end
isequal(C,C2,C3)
[t1 t2 t3]

ans = 0.0072 0.0289 0.1381

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Baris Gecer 2017-2-24

编辑：Baris Gecer 2017-2-24

This helped me a lot.Thanks! The first code was quite fast in my case where the matrix is 4096*128.

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Answer 2

Azzi Abdelmalek 2013-2-12

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在 MATLAB Online 中打开

C=cell2mat(arrayfun(@(x) accumarray(A,B(:,x)),1:size(B,2),'un',0));

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Answer 3

Fernando 2013-2-12

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Thanks for your help. I will check which of the three alternatives is better for my data.

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Answer 4

Jasper van Casteren 2022-2-8

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编辑：Jasper van Casteren 2022-2-8

在 MATLAB Online 中打开

I have the following problem and solution:

for instance, I have a set of nodes of which I have the indices in A, and a set of measured injections at these nodes. I have multiple injections at the same node. B thus contains the same indices as A, but in random order and non-unique.

How to accumulate the injections in B per node in A?

A = unique node indices for which I need the matrix of injections

B = non-unique node indices for which I have a matrix of injections. All indices in B are also in A

V = matrix of injections for the nodes in B.

I use,

A = unique(randi([1,1000], 300, 1));  % few hundred random node indices
B = A(randi([1, numel(A)], 1000, 1)); % 1000 random measurement locations
nA = numel(A); % for convenience
nB = numel(B); % for convenience
V = randi([10,100], nB, 8760); % 8760 random measurements at 1000 locations
[~, B2A] = ismember(B,A);
printf('%d', any(B2A<1)); % should be zero
tic;
C = full(sparse(B2A, 1:nB, 1, nA, nB) * V);
toc