Row sums by vector indices without for loop?

Best illustrated by example

M=rand(5,10);
s=[1 3; 5 8; 9 10];
for i=1:size(s,1)
sm(:,i)=sum(M(:,s(i,1):s(i,2)),2);
end

Is there a one-liner or short-cut for the for loop? I do not know how large M or s is ahead of time, or their values. Above code shown only for illustration of problem trying to solve.

Thanks!

edit: Corrected typo of 'm' in for-loop to 'M'

Answer 1

[Walter Roberson]

If your accuracy requirements are not high and your values are not extreme, you can use cumsum(), after which it becomes the difference of the cumsum indexed at two positions -- a transformation that gets around the problem that your indices do not always designate the same number of elements to be summed per row.

If I recall collectly, Bruno, and Matt Fig, both have posted non-cumsum() versions of this task in the past (it has come up before in cssm discussions.)

[Oleg Komarov]

There's a submission by Bruno, mcolon, which will allow you to create the indexes and use accumarray avoiding the multiple call to sum.

[Mike Sheppard]

I like the cumsum solution for its simplicity.

cm=cumsum([zeros(size(M,1),1) M],2);

sm2=cm(:,s(:,2)+1)-cm(:,s(:,1))

Just had to add a column of zeros; but I like the calculus F(b)-F(a)intuitive solution. Thanks!

Answer 2

[Bruno Luong]

Yes, to be more specific my mcolon on FEX

http://www.mathworks.com/matlabcentral/fileexchange/29854-multiple-colon

can be used like this:

% Data
M = ceil(10*rand(5,10))
s = [1 3; 5 8; 9 10];

% Engine
[a i] = mcolon(s(:,1),s(:,2));
[r c] = ndgrid(1:size(M,1),i);
Ma = M(:,a);
sm = accumarray([r(:) c(:)], Ma(:))

Bruno

[Jan]

Did you compare the speed with the OP's FOR loop method with adding a pre-allocation?

[Bruno Luong]

Following Jan's question: I make the following test and I get the 25% acceleration by using MCOLON

Time relative for-loop/mcol = 1.26013/1

% Code

ntest = 10;

t = zeros(2,ntest);

for n=1:ntest

s = ceil(10*rand(1,2*10000));

s = cumsum(s);

s = reshape(s, 2, [])';

M=rand(5,s(end));

% for loop Engine

tic

sm = zeros(size(M,1),size(s,1));

for i=1:size(s,1)

sm(:,i)=sum(M(:,s(i,1):s(i,2)),2);

end

t(1,n) = toc;

% mcolon Engine

tic

[a c] = mcolon(s(:,1),s(:,2));

[r c] = ndgrid(1:size(M,1),c);

Ma = M(:,a);

sm = accumarray([r(:) c(:)], Ma(:));

t(2,n) = toc;

end

t = min(t,[],2);

t = t/min(t);

fprintf('Time relative for-loop/mcol = %g/%g\n', t);