Sort a matrix with another matrix

Question

Suppose I have a matrix A and I sort the rows of this matrix. How do I replicate the same ordering on a matrix B (same size of course)?

E.g.

A = rand(3,4);
[val ind] = sort(A,2);
B = rand(3,4);
%// Reorder the elements of B according to the reordering of A

This is the best I've come up with

m = size(A,1);
B = B(bsxfun(@plus,(ind-1)*m,(1:m)'));

Out of curiosity, any alternatives?

Update: Jonas' excellent solution profiled on 2008a (XP):

n = n

0.048524       1.4632       1.4791        1.195       1.0662        1.108       1.0082      0.96335      0.93155      0.90532      0.88976

n = 2m

0.63202       1.3029       1.1112       1.0501      0.94703      0.92847      0.90411       0.8849       0.8667      0.92098      0.85569

It just goes to show that loops aren't anathema to MATLAB programmers anymore thanks to JITA (perhaps).

Answer 1

A somewhat clearer way to do this is to use a loop

A = rand(3,4);
B = rand(3,4);
[sortedA,ind] = sort(A,2);

for r = 1:size(A,1)
   B(r,:) = B(r,ind(r,:));
end

Interestingly, the loop version is faster for small (<12 rows) and large (>~700 rows) square arrays (r2010a, OS X). The more columns there are relative to rows, the better the loop performs.

Here's the code I quickly hacked up for testing:

siz = 10:100:1010;
tt = zeros(100,2,length(siz));

for s = siz
    for k = 1:100

        A = rand(s,1*s);
        B = rand(s,1*s);
        [sortedA,ind] = sort(A,2);

        tic;
        for r = 1:size(A,1)
            B(r,:) = B(r,ind(r,:));
        end,tt(k,1,s==siz) = toc;

        tic;
        m = size(A,1);
        B = B(bsxfun(@plus,(ind-1)*m,(1:m).'));
        tt(k,2,s==siz) = toc;

    end
end

m = squeeze(mean(tt,1));

m(1,:)./m(2,:)

For square arrays

ans =

    0.7149    2.1508    1.2203    1.4684    1.2339    1.1855    1.0212    1.0201    0.8770       0.8584    0.8405

For twice as many columns as there are rows (same number of rows)

ans =

    0.8431    1.2874    1.3550    1.1311    0.9979    0.9921    0.8263    0.7697    0.6856    0.7004    0.7314