How to accelerate the running speed of this code for calculate a matrix?

function [ M ] = fun(X,A,B)
%% Calculate M from X
%% the size of X is A*B
    M = zeros(A,B);
    for a = 1:A
        Z = X - X(a,:);
        Z(a,:) = X(a,:);
        M(a,:) = prod(X,1)./prod(Z,1);
    end
end

Here X is a real number matrix with dimensional , and the resulting matrix M is also a real number matrix with dimensional and is derived from the above "fun" function. Is there any way to optimize the running speed of these codes since i need to use it many times?

[Steven Lord]

Why did you ask this as a separate question rather than following up on this post, which I believe is strongly related?

https://www.mathworks.com/matlabcentral/answers/2174487-how-to-fastly-calculate-this-real-number-matrix-manipulation?s_tid=srchtitle

Answer 1

[Deepak]

Hi @Hancheng Zhu,

We can optimize the running speed of the code by avoiding redundant calculations inside the loop. Instead of recalculating the column-wise product prod(X, 1) for each iteration, we precompute it once before the loop starts.

Additionally, we eliminate the need to repeatedly modify the matrix Z by directly subtracting the a-th row from all other rows in X, and then replacing the a-th row of Z with X(a,:). By performing these operations outside the loop and focusing on matrix-based calculations, we reduce the computational overhead and take advantage of optimized matrix operations of MATLAB, leading to faster execution.

Below is the sample MATLAB code to achieve the same:

function [ M ] = fun(X,A,B)
%% Optimized calculation of M from X
%% the size of X is A*B
    prodX = prod(X, 1);  % Pre-compute the product of each column of X
    M = zeros(A, B);     % Initialize the result matrix M

    % Vectorized computation of M
    for a = 1:A
        % Construct Z by subtracting X(a,:) from each row of X
        Z = X - X(a, :);
        Z(a, :) = X(a, :);  % Replace the a-th row of Z with X(a,:)
        
        % Compute element-wise product ratio
        M(a, :) = prodX ./ prod(Z, 1); 
    end
end

Please find attached the documentation of functions used for reference:

Array Indexing: https://www.mathworks.com/help/matlab/math/array-indexing.html

I hope this helps.