Correct use of arrayfun

Suppose that I have a matrix a, and I want to do an operation on it, e.g. subtracting the mean of its columns from each element of the matrix. How can i do that by using the command arrayfun?

a = [ 3 6 ; 6 5 ]
arrayfun(@(x) a(i,j)-mean(a(i,:)),a,'UniformOutput',false)

Answer 1

[Matt J]

Well first of all, arrayfun should be a last resort. There are much more optimal ways of doing the mean subtraction you describe as well as many other operations like it. In R2016b or higher,

a-mean(a,1),

else if older than R2016b,

 bsxfun(@minus, a, mean(a,1))

But, if you really must use arrayfun, it can be done, for example, as follows

cell2mat( arrayfun(@(i) a(:,i)-mean(a(:,i)),  1:size(a,2), 'uni',0) )

[Jan]

+1. The bsxfun approach is not only useful for older Matlab versions. [EDITED: Removed "but it is faster also"].

[Matt J]

but it is faster also.

Faster, you mean, than implicit scalar expansion? Very strange!

[Jan]

I test the speed under R2016b, in which the implicit expansion was still new. Maybe this is the cause for my observation, that it is sometimes slower than an explicit bsxfun. The effects are not consistent, see:

function AutoExpandTest

X = rand(1000, 1000);
n  = size(X, 1);

tic
dx = zeros(n, n);
for j = 1:n
   dx(j+1:n, j) = sqrt(sum(bsxfun(@minus, X(:, j+1:n), X(:, j)) .^ 2, 1));
   dx(j, j+1:n) = dx(j+1:n, j);
end
toc

tic
dx = zeros(n, n);
for j = 1:n
   dx(j+1:n, j) = sqrt(sum((X(:, j+1:n) - X(:, j)) .^ 2, 1));
   dx(j, j+1:n) = dx(j+1:n, j);
end
toc

tic
for k = 1:1000
   Y = bsxfun(@minus, X, mean(X, 2));
end
toc

tic
for k = 1:1000
   Y = X - mean(X, 2);
end
toc

end

Under R2016b/Win7:

 Elapsed time is 7.603560 seconds.    BSXFUN
 Elapsed time is 10.218603 seconds.   Auto Expand
 Elapsed time is 9.134871 seconds.    BSXFUN
 Elapsed time is 6.894594 seconds.    Auto Expand

This is interesting, because in the first example the subtraction is a small part of the computation only and the summation and square root should damp the effects.