MATLAB: Using a matrix as an index to another matrix

loops are fasterMATLABusing a matrix as an index to another matrix

Simple case:
>> x = [ 10 8 ; 4 3 ]
x =
      10     8
       4     3
>> [y,i] = sort(x,2 )
y =
       8    10
       3     4
i =
       2     1
       2     1
>> x(i)
ans =
       4    10
       4    10
We see x(i) is not equiv. to y. Can I use x & i to derive y … ?

Best Answer

3 versions with a speed comparison:
function speedtest
x = rand(2000, 1000);
tic;
for k = 1:5
  % Method 1: SUB2IND:
  [y, idx2] = sort(x, 2);
  sx        = size(x);
  index     = sub2ind(sx, repmat((1:sx(1)).', 1, sx(2)), idx2);
  y2        = x(index);
end
toc
tic;
for k = 1:5
  % Method 2: Simplified loop, row-wise
  [y, idx2] = sort(x, 2);
  y3 = zeros(size(x));
  for r = 1:size(x,1) 
    y3(r, :) = x(r, idx2(r, :));
  end
end
toc
tic;
for k = 1:5
  % Method 3: Simplified loop, column-wise
  xt         = x.';
  [yt, idx1] = sort(xt, 1);
  y4         = zeros(size(xt));
  for r = 1:size(x,1)
     y4(:, r) = xt(idx1(:, r), r);
  end
  y4 = y4.';
end
toc
isequal(y, y2, y3, y4)
Matlab 2009a/64, Win7, 2 cores of an i5 in a VM:
 Elapsed time is 2.174286 seconds.  % SUB2IND
 Elapsed time is 2.512037 seconds.  % Loop, rowwise
 Elapsed time is 0.706579 seconds.  % Loop, columnwise
The cloumn-wise loop method is faster for [200, 10000] and [10000, 200] inputs also.
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