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# permutes

## PURPOSE

PERMUTES All N! permutations of 1:N + signatures [P,S]=(N)

## SYNOPSIS

function [p,s]=permutes(n)

## DESCRIPTION

```PERMUTES All N! permutations of 1:N + signatures [P,S]=(N)
The output P is a matrix of size (N!,N) where each row
contains a permutation of the numbers 1:N. The rows are in
lexically sorted order.

To permute the elements of an arbitrary vector V use
V(PERMUTES(LENGTH(V))).```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
• mintrace MINTRACE find row permutation to minimize the trace p=(x)

## SOURCE CODE

```0001 function [p,s]=permutes(n)
0002 %PERMUTES All N! permutations of 1:N + signatures [P,S]=(N)
0003 % The output P is a matrix of size (N!,N) where each row
0004 % contains a permutation of the numbers 1:N. The rows are in
0005 % lexically sorted order.
0006 %
0007 % To permute the elements of an arbitrary vector V use
0008 % V(PERMUTES(LENGTH(V))).
0009
0010 % PERMUTES(N) is the same as SORTROWS(PERMS(1:N)) but much faster.
0011
0012 % Thanks to Peter J Acklam for several improvements.
0013
0014 %      Copyright (c) 1998 Mike Brookes,  mike.brookes@ic.ac.uk
0015 %      Version: \$Id: permutes.m 713 2011-10-16 14:45:43Z dmb \$
0016 %
0017 %   VOICEBOX is a MATLAB toolbox for speech processing.
0019 %
0020 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0021 %   This program is free software; you can redistribute it and/or modify
0023 %   the Free Software Foundation; either version 2 of the License, or
0024 %   (at your option) any later version.
0025 %
0026 %   This program is distributed in the hope that it will be useful,
0027 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0028 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0029 %   GNU General Public License for more details.
0030 %
0031 %   You can obtain a copy of the GNU General Public License from
0032 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0033 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0034 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0035
0036 p=1;
0037 m=1;
0038 if n>1
0039   for a=2:n
0040     q=zeros(a*m,a);
0041     r=2:a+1;
0042        ix=1:m;
0043     for b=1:a
0044        q(ix,1)=b;
0045       q(ix,2:a)=r(p);
0046       r(b)=b;
0047       ix=ix+m;
0048     end
0049     m=m*a;
0050     p=q;
0051   end
0052 end
0053 if nargout>1 s=1-2*rem(fix((1:m)'/2),2); end```

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