math - Apparent error in Matlab's perms function -

 p = perms([0:2]) 

p =

 2     1     0  2     0     1  1     2     0  1     0     2  0     1     2  0     2     1 

this function supposed display permutations of vector in reverse lexicographical order. hence, expect last row of output contain elements 0 1 2; however, contains 0 2 1. other rows displayed correctly.

in short, order of last 2 rows interchanged. going on here?

yes, seems bug. catch! bug in documentation, rather in function.

if type open perms see source code, you'll see following description in first lines:

%perms  possible permutations. %   perms(1:n), or perms(v) v vector of length n, creates %   matrix n! rows , n columns containing possible %   permutations of n elements. % %   function practical situations n less %   10 (for n=11, output takes on 3 gigabytes). % %   class support input v: %      float: double, single %      integer: uint8, int8, uint16, int16, uint32, int32, uint64, int64 %      logical, char 

in no reference made reverse lexicographical order.

the actual job done recursive, local function permsr. if @ code, it's not obvious @ first how works (as usual recursion), line

t(t == i) = n 

gives clue no particular order sought in result.

if try larger vector you'll see discrepancies reverse lexicographical order in more rows:

>> perms(0:3) ans =      3     2     1     0      3     2     0     1      3     1     2     0      3     1     0     2      3     0     1     2      3     0     2     1   %// here. affects cols 1 , 2      2     3     1     0      2     3     0     1      2     1     3     0      2     1     0     3      2     0     1     3      2     0     3     1   %// here. affects cols 1 , 2      1     2     3     0      1     2     0     3      1     3     2     0   %// here. affects cols 2 , 3      ... 

in summary, function seems have been designed without regard order. documentation wrong in claiming order.