Output arrayfun into trid dimension of the matrix in MATLAB

Question

Assume that I have a matrix A = rand(n,m). I want to compute matrix B with size n x n x m, where B(:,:,i) = A(:,i)*A(:,i)'; The code that can produce this is quite simple:

A = rand(n,m); B = zeros(n,n,m);
for i=1:m
B(:,:,i) = A(:,i)*A(:,i)'
end

However, I am concerned about speed and would like to ask you help to tell me how to implement it without using loops. Very likely that I need to use either bsxfun, arrayfun or rowfun, but I am not sure. All answers are appreciated.

I know that it is fine, my question is, is there a method to speed it up by not using loops — Mykola Servetnyk, Mar 17 '18 at 14:12

Hossein Kashiani · Answer 1 · 2018-03-17T15:26:09.677

1

arrayfun and bsxfun does not speed up the calculations in my attempt as below:

clc;close all;
clear all;
m=300;n=400;

A = rand(n,m); B = zeros(n,n,m);
tic
for i=1:m
    B(:,:,i) = A(:,i)*A(:,i)';
end
t1=toc

C = reshape(cell2mat(arrayfun(@(k) bsxfun(@times, A(:,k), A(:,k)'), ...
    1:m, 'UniformOutput',false)),n,n,m);
 %C=reshape(C,n,n,m);
t2=toc-t1

 % t1 =0.3079
 % t2 =0.5112

edited Mar 17 '18 at 15:26

answered Mar 17 '18 at 15:07

Hossein Kashiani

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I think that's because you use `cell2mat` function. My question was exactly bout this, how can I output array fun in third dimension of the matrix. – Mykola Servetnyk Mar 18 '18 at 02:34

score 1 · Accepted Answer · answered Mar 17 '18 at 16:35

I don't have MATLAB at hand right now, but I think this code should produce the same result as your loop:

A1 = reshape(A,n,1,m);
A2 = reshape(A,1,n,m);
B = bsxfun(@times,A1,A2);

If you have a newer version of MATLAB, you don't need bsxfun any more, you can just write

B = A1 .* A2;

On older versions this last line will give an error message.

Whether any of this is faster than your loop depends also on the version of MATLAB. Newer MATLAB versions are not slow any more with loops. I think the loop is more readable, it's worth using more readable code, or at least keep the loop in a comment to clarify what the vectorized code does.

Exactly as you said: `A1 .* A2` won't work in R2015b, but works in R2017a.Thank you! — Mykola Servetnyk, Mar 18 '18 at 03:34

Output arrayfun into trid dimension of the matrix in MATLAB

2 Answers2