Why does SORT outperform SORTROWS?

Any theories as to why SORT + row re-ordering outperforms SORTROWS when sorting with respect to a single column:

x=rand(18e6,7);

tic;
  [~,idx]=sort(x(:,1)); 
  y1=x(idx,:);   
toc
%Elapsed time is 3.589928 seconds.

   tic; 
    y2=sortrows(x,1);
   toc
   %Elapsed time is 14.869106 seconds.

Answer 1

[Jan]

The profile shows, that the additional time is spent in the C-Mex function sortrowsc.mexw64. At least in R2009a the source code has been shipped with Matlab. Inside the C-Mex, the not stable qsort is called, which is obviously slower than Matlab's sort algorithm.

Copy sortrows.m and change the line 74 of from:

ndx = sortrowsc(x_sub, col);

to:

ndx = sort_back_to_front(x_sub, col);

to let the main work be done by sort. For a productive use, cells must be considered also, see some lines later for the general case in the else branch. It is ironic, that this is the "old Matlab 6.0" fallback, which has been obviously much faster.

Please send an enhancement request to TMW.