How to compare two numbers in two different vectors and save without using for loop?

I have the below code

nodeMat = zeros(size(mainNodes,1),3); count = 0;
for i=1:size(allNodes,1)
    for j=1:size(mainNodes,1)
        if isalmost(mainNodes(j,2),allNodes(i,1),1e-4) && ...
           isalmost(mainNodes(j,3),allNodes(i,2),1e-4)
            count = count + 1;
            nodeMat(count,:) = [i mainNodes(j,2) mainNodes(j,3)];
        end
    end
end

wher allNodes, mainNodes are given vectors containing float numbers. i have to run this code many times and to make it faster i dont want ot use cluster for loop.

Can someone please help?

Thanks in advance

[Jan]

Should we assume that the function isalmost is coming from here: https://www.mathworks.com/matlabcentral/fileexchange/15816-isalmost ?

[Akash Bhuwal]

yes

Answer 1

[Jan]

The implementation of isalmost is not efficient. It is faster to check the values directly:

nodeMat = zeros(size(mainNodes,1),3);
count = 0;
for i = 1:size(allNodes,1)
    for j = 1:size(mainNodes,1)
        if abs(mainNodes(j,2) - allNodes(i,1)) <= 1e-4 && ...
           abs(mainNodes(j,3) - allNodes(i,2)) <= 1e-4
             count = count + 1;
             nodeMat(count,:) = [i mainNodes(j,2) mainNodes(j,3)];
        end
    end
end
nodeMat = nodeMat(1:count, :);

For this input:

mainNodes = randi([1, 10], 1000, 3);
allNodes  = randi([1, 10], 1000, 2);

my Matlab R2018b runs the code in 0.039 seconds instead of 2.11 seconds with isalmost. 53 times faster.

Now lets check, if a vectorization is useful...

nodeMat = zeros(size(mainNodes,1),3);
count = 0;
for i = 1:size(allNodes,1)
    match = abs(mainNodes(:,2) - allNodes(i,1)) <= 1e-4 & ...
            abs(mainNodes(:,3) - allNodes(i,2)) <= 1e-4;
    n = sum(match);
    if n ~= 0
       nodeMat(count + 1:count + n, 1) = i;
       nodeMat(count + 1:count + n, 2) = mainNodes(match, 2);
       nodeMat(count + 1:count + n, 3) = mainNodes(match, 3);
       count = count + n;
    end
end
nodeMat = nodeMat(1:count, :);
% 0.015610 seconds

My trials for a fully vectorized methods are not faster.