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

Answer 2

Sort() returns the index along the dimension you sorted on. You can explicitly construct indexes for the other dimensions that cause the rows to remain stable, and then use linear indexing to rearrange the whole array.

A = rand(3,4);
B = A; %// Start with same values so we can programmatically check result

[A2 ix2] = sort(A,2);
%// ix2 is the index along dimension 2, and we want dimension 1 to remain unchanged
ix1 = repmat([1:size(A,1)]', [1 size(A,2)]); %//'
%// Convert to linear index equivalent of the reordering of the sort() call
ix = sub2ind(size(A), ix1, ix2) 
%// And apply it
B2 = B(ix)
ok = isequal(A2, B2) %// confirm reordering