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

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Hancheng Zhu
Hancheng Zhu 2025-2-25
回答： Deepak 2025-3-26
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?

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回答（1 个）

Deepak
Deepak 2025-3-26
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.

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