How to construct a Sliced Reduction Variable in MALTAB parallel for loop

Hello all, I am having a code with the following construction. In this code, I need to extract K (M x M) from the parfor as this will save much time. Currently, I am working on it using ordinary for loop.

...    % code
K = zeros(M,M);
parfor i = 1:N
    k = ...    % k is a matrix of dimensions (m x m) created in each pafor iteration.
    u = ...    % u is a vector of integers (n x 1) created in each pafor iteration.
    K(u,u) = K(u,u) + k;    % This line returns back an error message.
end
...    % code

Is there anyway to re-write the code to be accepted in parfor loop without changing the calculation methodology. In a more general form, how can I involve a sliced reduction variable (K in this case) in parfor loop?

Thanks all and best Ahmad

Answer 1

[Jeff Miller]

Maybe something like this?

k = cell(N,1);
u = cell(N,1);
parfor i = 1:N
    k{i} = ...    % k is a matrix of dimensions (m x m) created in each pafor iteration.
    u{i} = ...    % u is a vector of integers (n x 1) created in each pafor iteration.
end

K = zeros(M,M);
for i = 1:N
    K(u{i},u{i}) = K(u{i},u{i}) + k{i};
end

[Ahmad Gad]

Hi Jeff, thanks for the answer.

I already isolated them in two different loops as you said. But my question was how to combine them all in a one parallel loop.

Thanks and best Ahmad

Answer 2

[Edric Ellis]

parfor doesn't support the notion of a variable that is both sliced and reduced. You need to recast things so that you have either a pure sliced or a pure reduced output. Here's one way that you might be able to achieve that - I'm not sure if I've completely understood your example, but perhaps this should give you sufficient information to continue:

m = 4;
n = 3;
K = zeros(m, m);
parfor idx = 1:n
    % build 'k' and 'u' as per the example
    k = idx .* ones(m, m);
    u = (1:n)';
    % Build an m-by-m increment
    increment = zeros(m, m);
    increment(u, u) = k(u, u);
    % Ensure 'K' is a pure reduction variable
    K = K + increment;
end

[Ahmad Gad]

Hello Edric;

I had previously implemented a similar method, but for very big matrices (such as my cases), adding matrices many times always kills MATLAB. I am trying my best to avoid your final line

K = K + increment;

From my main example, M = 300k, N = 100k, m = n = 450

Thank you!