How to linearize the nested parfor loop?

I have two variables i,j, where j index start depends on i index.

n = 3;
for i = 1:n
    for j = i+1:n
        % Feature matching
        matches = getMatches(input, allDescriptors{i}, allDescriptors{j});
        nf = size(matches, 2);
        numMatches(i,j) = nf;
    end   
end

I am trying to linearize it using the below code:

n = 3;
M = n;
N = n;
parfor i = 1:M*N
    % IND2SUB converts from a "linear" index into individual
    % subscripts
    [ii,jj] = ind2sub([M,N], i);
    
    if (ii~=jj)
        matches = getMatches(input, allDescriptors{ii}, allDescriptors{jj});
        nf = size(matches, 2);
        numMatches(i) = nf;
    end
end

But have some entries on the lower part of the square matrix.

Any help is appreciated!

Answer 1

[Jeff Miller]

One approach is to set out all the desired pairs in advance. A crude way to do that is

pairs = zeros(0,2);
n = 3;
for i = 1:n  % or reallyl just to n-1?
    for j = i+1:n
        pairs(end+1,:) = [i, j];
    end   
end

Then your parfor loop can just go through the preset pairs:

npairs = size(pairs,1);
parfor i = 1:npairs
    ii = pairs(i,1);
    jj = pairs(i,2);
        matches = getMatches(input, allDescriptors{ii}, allDescriptors{jj});
        nf = size(matches, 2);
        numMatches(i) = nf;
end

[Preetham Manjunatha]

It should fill-in the upper triangular matirx (except i,j = 1,1), but the first column in

numMatches

is getting filled up.

[Jeff Miller]

Maybe change

 numMatches(i) = nf;

to

 numMatches(ii,jj) = nf;

I don't see your definition of numMatches so I'm not sure what you want

[Preetham Manjunatha]

If it is

numMatches(ii,jj) = nf;

MATLAB thows an error:

Unable to classify the variable 'numMatches' in the body of the parfor-loop.

[Jeff Miller]

OK, then I guess you have to store the parfor results in a temporary vector and put them into numMatches after the parfor loop is done.

pairs = zeros(0,2);
n = 3;
for i = 1:n  % or reallyl just to n-1?
    for j = i+1:n
        pairs(end+1,:) = [i, j];
    end   
end

npairs = size(pairs,1);
temp = zeros(npairs,1);
parfor i = 1:npairs
    ii = pairs(i,1);
    jj = pairs(i,2);
    matches = getMatches(input, allDescriptors{ii}, allDescriptors{jj});
    nf = size(matches, 2);
    temp(i) = nf;
end

numMatches = zeros(n,n);
for i=1:npairs
    ii = pairs(i,1);
    jj = pairs(i,2);
    numMatches(ii,jj) = temp(i);
end

[Preetham Manjunatha]

Thanks, it works! But there are way too many for loops, which I was trying to avoid.