how to sum the elements specified by a cell in matlab? - matlab

Question

I have a big matrix M (nxm). I am going to sum some elements which are specified by index stored in vector as cell elements. There are many groups of indices so the cell has more than one element. For example
M = rand(2103, 2030);
index{1} = [1 3 2 4 53 5 23 3];
index{2} = [2 3 1 3 23 10234 2032];
% ...
index{2032} = ...;
I am going to sum up all elements at index{1}, sum up all elements at index{2} ..., now I am using a loop
sums = zeros(1, 2032);
for n=1:2032
sums(n) = sum(M(index{n}));
end
I am wondering if there is any way to use one-line command instead of a loop to do that. Using a loop is pretty slow.

Answer 1

Probably a classic use of cellfun
sums = cellfun(#(idx) sum(M(idx)), index);
EDIT: here is a benchmarking for a large case that shows that this approach is slightly slower than a for loop but faster than Eitan T's method
M = rand(2103, 2030);
index = cell(1, 2032);
index{1} = [1 3 2 4 53 5 23 3];
index{2} = [2 3 1 3 23 10234 2032];
for n=3:2032
index{n} = randi(numel(M), 1, randi(10000));
end
N = 1e1;
sums = zeros(1, 2032);
tic
for kk = 1:N
for n=1:2032
sums(n) = sum(M(index{n}));
end
end
toc
tic
for kk = 1:N
sums = cellfun(#(idx) sum(M(idx)), index);
end
toc
tic
for kk = 1:N
sums = cumsum(M([index{:}]));
sums = diff([0, sums(cumsum(cellfun('length', index)))]);
end
toc
results in
Elapsed time is 2.072292 seconds.
Elapsed time is 2.139882 seconds.
Elapsed time is 2.669894 seconds.

Answer 2

Perhaps not as elegant as a cellfun one-liner, but runs more than an order of magnitude faster:
sums = cumsum(M([index{:}]));
sums = diff([0, sums(cumsum(cellfun('length', index)))]);
It even runs approximately 4 or 5 times faster than a JIT-accelerated loop for large inputs. Note that when each cell in index contains a vector with more than ~2000 elements, the performance of this approach begins to deteriorate in comparison with a loop (and cellfun).
Benchmark
M = rand(2103, 2030);
I = ceil(numel(M) * rand(2032, 10));
index = mat2cell(I, ones(size(I, 1), 1), size(I, 2));
N = 100;
tic
for k = 1:N
sums = zeros(1, numel(index));
for n = 1:numel(sums)
sums(n) = sum(M(index{n}));
end
end
toc
tic
for k = 1:N
sums = cellfun(#(idx) sum(M(idx)), index);
end
toc
tic
for k = 1:N
sums = cumsum(M([index{:}]));
sums2 = diff([0, sums(cumsum(cellfun('length', index)))]);
end
toc
When executing this in MATLAB 2012a (Windows Server 2008 R2 running on a 2.27GHz 16-core Intel Xeon processor), I got:
Elapsed time is 0.579783 seconds.
Elapsed time is 1.789809 seconds.
Elapsed time is 0.111455 seconds.