Adding values to a vector

Dear Matlab forum, I have a vector, T for which I would like to add values to certain indices in a loop. My simplified code is:

T=zeros(10,1)
for iter=1:100
r=[some indices]; % the indices change each loop and are somewhat random
E=[some values for the indices]; % length(E)==length(r)
T(r)=T(r)+E;
end

The issue I am having is that r may contain a multiple occurrences of given index within a single iteration, for example r=[1 4 2 4], and E could be=[2 2 2 2]. I would like to add BOTH values of E to the index 4, but my above code only adds the last one and ignores the first. What is the most efficient way to solve this issue? Thank you very much, -Eli

Answer 1

[Matt Fig]

It has to be done in a loop? You could put a nested loop in there and loop over r...

%

%

EDIT

Here is one way to do it.

T = 1:5;
r = [1 1 1 3 4];
E = [3 3 2 2 5]; 
T = T + accumarray(r.',E.',[5 1]).'

But it might be slower than using a loop... In fact, since you say that T is 20,000 times longer than r, I would bet this was slower than a loop.

%

%

%

%

EDIT2 The timings report...

Have a look for yourself. Of course some of the accumarray solution could be sped of if the r and E could be made column vectors, which would avoid the transposition, but I doubt that will be much faster...

function [] = accum_loop

T = 1:2e7;
rand('twister',33)
tic
for ii = 1:100
    r = ceil(rand(1,1000)*2e7);
    E = ceil(rand(1,1000)*10);
    for jj = 1:length(r)
        T(r(jj)) = T(r(jj)) + E(jj);
    end
end
toc

T2 = 1:2e7;
rand('twister',33)

tic
for ii = 1:100
    r = ceil(rand(1,1000)*2e7);
    E = ceil(rand(1,1000)*10);
    T2 = T2 + accumarray(r.',E.',[2e7 1]).' ;
%     T2 = T2 + accumarray(r.',E.',[2e7 1],@sum,0,true).' ;
end
toc

isequal(T,T2)

I get, as it stands:

Elapsed time is 0.016339 seconds.
Elapsed time is 7.278608 seconds.

And with your modifications (function handles are slow!):

Elapsed time is 0.016107 seconds.
Elapsed time is 23.642409 seconds.

[Eli]

Yes this is a possibility, but I am looking for the most efficient solution because the vectors are VERY large.

-Eli

[Eli]

...by large I mean that T has a length of 2E7 and r has a length of 1000, and the loop may be tens of thousands of iterations. I am trying to minimize the amount of times I call T.

-Eli

[Matt Fig]

See my edit.

[Eli]

that is interesting. accumarray might be the answer I've been looking for, but as you said I should do a speed check. What if I utilized more of the accumarray inputs:

accumarray(r.',E.',[5 1],@sum,0,logical(1))

would the sparse array be more appropriate?

[Sean de Wolski]

You'll have to time test that on your machine since it's system dependent...

[Matt Fig]

I posted results for win 7 64, r2007b.

[Eli]

It turns out the loop is faster, but still not as fast as I would like.

I think the best approach might be to run a loop over the length of r, where I consolidate the the values of E and the indices of r. After this, I could just call T once as before:

T(r*)=T(r*)+E*; % where I r and E have been replaced by r* and E* and no longer have repeated indices. Any ideas of what that loop could look like?

Thanks again,

-Eli

[Eli]

Could I somehow employ the command 'unique'?

[Matt Fig]

Did you look at my timings? Do you get similar values? If you come up with a way to make r* and E* that is more efficient than ACCUMARRAY, post it!

[Eli]

Matt, I don't get similar values, but the order of performance is the same (ie, loop is the best).

Thanks for the help.

[Matt Fig]

I implemented this, in place of the ACCUMARRAY line and the T2 assignment:

ur = unique(r);

uE = zeros(size(ur));

for jj = 1:length(ur)

uE(jj) = sum(E(r==ur(jj)));

end

T2(ur) = T2(ur) + uE;

and found a significant speed increase. But it is still slower than the other loop...

[Eli]

Matt,

your above speed test actually brought to my attention that it was another part of my code that was especially time consuming, rather than adding values t T. I will use the loop that you suggested.

The part of my code that needed adjusting was setting the values of r and E. In my code, r and E are selected each iteration from a subset of a much larger two column array (about the length of T), called trac. I was wondering why your time test was so much faster than mine, and it's because of those lines of code. I was able to split trac into a structure of all the r and E vectors I will need before the loop and then just choose them in the loop. This brings my time to around yours. and I'm happy with the speed now.

Thanks for all the help,

-Eli

[Matt Fig]

You're welcome. In the future you should use the profiler to see where the bottleneck in your code is hiding.

help profile

This is an invaluable tool for helping speed up slow code.

Answer 2

[Jan]

Try to use a LOGICAL vector for r, which has 2 advantages:

1. The vector needs less memory such that the allocation is faster
2. LOGICAL indices do not need a boundary check for each element, such that the copy is faster. The index is applied twice in "T(r)=T(r)+E;"

[Eli]

Jan, I'm not sure I understand how this would work. r can contain multiple occurrences of given index within a single iteration. Therefore I don't see how I can use a logical vector.