# Vectorise or Parallel Computing

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Mingzhi Shihua on 20 Nov 2019
Commented: Mingzhi Shihua on 24 Nov 2019
Can this for loop be vectorized or use parfor instead? If so, how should I do it?
for edgeID = 1:size(IE,1)
self = selfs(edgeID);
sdl(self) = sdl(self)+sdl_edge(edgeID); % add frac to self
res(:,self) = res(:,self)+flux_edge(:,edgeID); % add flux to self residual
end % internal edge iteration ends
"selfs" is an array with some order. That means I want to loop over this "order array" and fill in some value according to that order (not in the order of 12345).
I have tried several ways but failed...

Jan on 20 Nov 2019
Some example data would be nice, because then we can test the suggestions without needing to invent inputs. self is not unqiue, isn't it?
Mingzhi Shihua on 21 Nov 2019
self is something like [2,4,7,8,5,9,1,0,3,6,8,2,5,6]. When I loop over index = 1,2,3,... I need an array in that order 2,4,7,... to update accordingly. Exact variables are uploaded. Initialize sdl and res
sdl = zeros(1,7219);
res = zeros(5,7219);
This indicates that all element in self will not exceed 7219.

Jan on 21 Nov 2019
This loop cannot be parallelized. If flux_edge is a vector and not a matrix, accumarray would solve the problem efficiently. Try this:
% UNTESTED and most likey BUGGY!
sdl(selfs) = accumarray(selfs, sdl_edge);
resCell = splitapply(@(c) {sum(c, 2)}, flux_edge, selfs);
res(:, selfs) = cat(2, resCell{:});
The values of selfs are missing. Therefore I cannot test the code and I assume, it contains serious bugs. I assume you can find the remaining problems and modify the code until it solves your needs.
If the problem is time-critical (the bottleneck of the total program), I'd write a C-mex function. Accumulating in cells and joining them afterwards is not efficient for the memory consumption.
The size of selfs matters. It might be more efficient to collect the equal values at first by unique and run the loop over this list:
% UNTESTED
v = unique(selfs);
sdl = zeros(1, 7219);
res = zeros(5, 7219);
for iv = 1:numel(v)
av = v(iv);
res(:, av) = sum(flux_edge(:, mask), 2);
end
If this has a fair speed, you can parallelize it with parfor.
% UNTESTED
v = unique(selfs);
nv = numel(v);
A = zeros(1, nv);
B = zeros(5, nv);
parfor iv = 1:nv
av = v(iv);
B(:, iv) = sum(flux_edge(:, mask), 2);
end
sdl = zeros(1, 7219);
sdl(v) = A;
res = zeros(5, 7219);
res(:, v) = B;

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Jan on 22 Nov 2019
I assume this explains the problem, why sdl(selfs) = sdl(selfs)+sdl_edge does not work as expected:
index = [1, 2, 2];
x = ones(1, 2);
x(index) = x(index) + 1
This replies [2, 2] and not [2,3], because this is calculated internally:
x = [1, 1]
y = x(index) + 1; % A data copy! Result: [2, 2, 2]
x(1) = y(1)
x(2) = y(2)
x(2) = y(2)
I'll check the computations on the weekend with the provided data.
Jan on 23 Nov 2019
Sorry, the original code needs 0.002 seconds on my R2018b system. I do not see a way to accelerate this substantially, because this very fast already. My suggestion solutions are ways slower than the original approach.
Do you work with much larger problems than the posted data?
Mingzhi Shihua on 24 Nov 2019
Actually the whole code involves more than 20000 times repetition of that part. Of course, self_edge and flux_edge changes each time. But I think, yes, you are right, the most time consuming part should be updating those two.