Sum variable size chunks in array

Hello,

I am looking for a vectorized way of summing variable size chunks in a matrix, for example I have some matrix

A = [1 2 3 4 5 6 7 8
     3 4 2 2 8 4 2 9]

and I want to do a rowwise summation using some vector as a rule, for example

 v = [2 3 3]

In this case the result would be a 2x3 where the first column would be the summation of the first 2 columns in A (according to v),

the second column would be the summation of the next 3 columns in A etc. I can think of various ways of doing this using loops

but I am wondering if there is a faster vectorized way of doing it ?

Thank you!

Answer 1

[Stephen23]

Avoiding duplicating the data in memory (i.e. avoid mat2cell) will probably be faster for larger matrices:

fun = @(c){sum(A(:,c),2)};
G = repelem(1:numel(V),V);
C = 1:numel(G);
Z = accumarray(G(:),C(:),[],fun);
Z = horzcat(Z{:});

If your matrix only has two (or a fixed, small number) of rows, then this is much faster:

G = repelem(1:numel(V),V);
Y = [accumarray(G(:),A(1,:).'),...
     accumarray(G(:),A(2,:).')].';

Here are some timing tests (1e4 iterations):

Elapsed time is 9.600425 seconds.  % single ACCUMARRAY call.
Elapsed time is 0.208772 seconds.  % dual ACCUMARRAY call.
Elapsed time is 11.146120 seconds. % Fangjun Jiang's answer.

[Tudorel Afilipoae]

Thank you so much, the accumarray function is exactly what I was looking for. This is so much faster !!

[Stephen23]

@Tudorel Afilipoae: you can show your appreciation by accepting my answer.

[Tudorel Afilipoae]

Sorry, I wasn't aware that I could do this after already having accepted another answer..

Anyaway, my pleasure and thanks again!

Answer 2

[Fangjun Jiang]

B=mat2cell(A,size(A,1),v);
C=cellfun(@(x) sum(x(:)),B)

or should be this

B=mat2cell(A,size(A,1),v);
C=cell2mat(cellfun(@(x) sum(x,2),B,'uni',0));

[Tudorel Afilipoae]

Thank you very much for your answer, indeed this was the only way I could do it without using loops. Unfortunately, the use of the mat2cell function makes the speed of the entire process comparable with the one of a loop.