# Why is sum(f,1) slower than sum(g,2) for g=f'?

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Kutsop on 15 Feb 2023
Commented: Kutsop on 15 Feb 2023
So I'm trying to optimize my code and I came across something that doesn't immediately make sense to me but I think is INCREDIBLY important for me to understand.
In the sample code below I found that summing the transpose of my matrix along the second dimmension is 3 times faster than summing the original matrix. Why is this?
f = rand(3,10000);
g = f';
tic
for k = 1:1000000
sum(f,1);
end
toc
%Elapsed time is 28.528823 seconds.
tic
for k = 1:1000000
sum(g,2);
end
toc
%Elapsed time is 9.325141 seconds.
##### 2 CommentsShow 1 older commentHide 1 older comment
Kutsop on 15 Feb 2023
Edited: Kutsop on 15 Feb 2023
I disagree, I only need to tranpose the matrix once. If you're referring to the title of the post, yes it was misleading, but I was trying to keep things simple. The code accuretly describes the things I'm curios about which is, why is the sum the tranpose of a matrix along 1 dimmension, faster than summing the original matrix along the other dimmension. I updated the title.

Rik on 15 Feb 2023
I expect this has to do with how a matrix is stored in memory. If I recall correctly, this is column major, so summing along row requires jumping around in the list, while summing along the columns is just following the raw data.
If you had put the conjugate in the test, I expect the result to flip.
Kutsop on 15 Feb 2023
Thank you! I think you are corrrect! I had never heard "column-major" before so i did some more searching and found supporting evidence on StackOverflow which I've included below for any future folks interested in this topic:
https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order

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