Incrementing array within parfor? - matlab

Question

I am calculating sort of a histogram based on the distance between a pair of points in 3d space:
numBins = 20;
binWidth = 2.5;
pop = zeros(1,numBins);
parfor j=1:particles
r1 = coords(j,:);
for k=j+1:particles
r2 = coords(k,:);
d = norm(r1-r2);
ind = ceil(d/binWidth);
pop(ind) = pop(ind) + 1;
end
end
This, expectedly, results in
Error: The variable pop in a parfor cannot be classified.
I understand the problem, but I am confused as to how can I solve it.
In principle, what could be done is to have n copies of pop = zeroes(1,numBins) be sent to each of n workers, and joined by adding each copy together at the end of computation. How can I do this here? Or is there another, more standard way of solving the problem?

Answer 1

There is two things that don't work in your code:
1) for k = j+1:particles
In a parfor a nested loop should have fixed bound.
2) pop(ind)
Matlab is afraid that the for-loop order matters and display an error message. Even if, in your specific case, the order doesn't matters (But matlab is not smart enough to know that).
The solution, Linearization:
%Dummy data
numBins = 20;
binWidth = 2.5;
particles = 10;
coords = rand(10,2)*40;
%Initialization
pop = zeros(1,numBins);
parfor j=1:particles
r1 = coords(j,:)
r2 = coords((j+1):end,:)
d = sqrt(sum([r1-r2].^2,2)) % compute each norm at the same time !
pop = pop + histcounts(ceil(d/binWidth),0:numBins)
end

Answer 2

You can create a function that computes the inner loop and use a handle to it in the parfor (I didn't tested it but I think it should work according to the documentation):
function pop = hist_comp(pop,j,particles,coords,binWidth)
r1 = coords(j,:);
for k=j+1:particles
r2 = coords(k,:);
d = norm(r1-r2);
ind = ceil(d/binWidth);
pop(ind) = pop(ind) + 1;
end
end
numBins = 20;
binWidth = 2.5;
particles = 10;
coords = rand(10,2)*5;
pop = zeros(1,numBins);
f = #(pop,j) hist_comp(pop,j,particles,coords,binWidth);
parfor j=1:particles
pop = f(pop,j);
end