Efficiently finding equal neigbors in arrays.

I project I'm currently working on requires me to check if arrays (contained in cell arrays ) contain neighboring elements that are equal, and if they are pass the position of the first of these two elements to some nested function. I noticed that my naive approach to doing this is one of the bottlenecks of my code currently (because this piece of code is being called extremely often during my simulations). What is the most efficient way to handle this?

Here are some more details about my code:

My code needs to deal with a cell array X, each cell of which is itself a cell array, containing a (d,2) double array where the value of d can vary. For example, X could look as follows:

X = cell(N,1);
for i=1:N
    X{i}=cell(1,10);
    for j=1:10
        d = randi(50);
        X{i}{j} = randi(10, d,2); %each cell contains a double array of size (5,2)
    end
end

I need check if any array X{i}{j} contains two rows where the first collumn is equal, and pass the position of the first row of each such pair to some function. I do this as follows:

for i=1:N
    Xi = X{i}
    for j=1:10
        for k = 1:size(Xi{j},1)-1
            if Xi{j}(k,1) == Xi{j}(k+1)
                MyNestedFunction(i,j,k); % a nested function that modifies X
            end
        end
    end
end

While profiling my code, I noticed that most time is spent on the line containing the inner most forloop for k=1:size(X{i}{j},1)-1. Is there a way to make this more efficient?

I also tried using

for i=1:N
    Xi = X{i}
    for j=1:10        
        for k = find(diff(Xi{j}(1:size(Xi{j},1)))==0)
            MyNestedFunction(i,j,k); % a nested function that modifies X
        end
    end
end

but this is actually slower than my first attempt.

Answer 1

[David Hill]

for i=1:N
    Xi = X{i}
    for j=1:9
        m=min([size(X{i}{j},1),size(X{i}{j+1},1)]);
        k=find(X{i}{j}(1:m,1)]),1)-X{i}{j+1}(1:m,1)==0);
        MyNestedFunction(i,j,k);
    end
end

[AS]

Thanks for taking your time to reply, I fear I haven't been entirely clear about my question though. I only need to compare neighboring elements inside X{i}{j} (for any i and j). So I need to find all triplets (i,j,k) such that X{i}{j}(k,1)==X{i}{j}(k+1,1).

Maybe I should not have included the whole thing about the cells containing cells, but I thought it might be relevant in the sense that maybe the loops over i and j can be done more efficiently too (I have no clue if they can, but maybe someone here does).

[David Hill]

Is that not what I did? Does the code I provided not do what you wanted?

[AS]

No, you are comparing X{i}{j}(m,1) with X{i}{j+1}(m,1) instead of comparing X{i}{j}(m,1) with X{i}{j}(m+1,1).

[David Hill]

for i=1:N
    Xi = X{i};
    for j=1:10
        k=find(diff(X{i}{j}(:,1))==0);
        MyNestedFunction(i,j,k);
    end
end