1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
|
<html lang="en">
<head>
<title>Permutations - GNU Scientific Library -- Reference Manual</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="GNU Scientific Library -- Reference Manual">
<meta name="generator" content="makeinfo 4.8">
<link title="Top" rel="start" href="index.html#Top">
<link rel="prev" href="Vectors-and-Matrices.html" title="Vectors and Matrices">
<link rel="next" href="Combinations.html" title="Combinations">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<!--
Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 The GSL Team.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2 or
any later version published by the Free Software Foundation; with the
Invariant Sections being ``GNU General Public License'' and ``Free Software
Needs Free Documentation'', the Front-Cover text being ``A GNU Manual'',
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled ``GNU Free Documentation
License''.
(a) The Back-Cover Text is: ``You have freedom to copy and modify this
GNU Manual, like GNU software.''-->
<meta http-equiv="Content-Style-Type" content="text/css">
<style type="text/css"><!--
pre.display { font-family:inherit }
pre.format { font-family:inherit }
pre.smalldisplay { font-family:inherit; font-size:smaller }
pre.smallformat { font-family:inherit; font-size:smaller }
pre.smallexample { font-size:smaller }
pre.smalllisp { font-size:smaller }
span.sc { font-variant:small-caps }
span.roman { font-family:serif; font-weight:normal; }
span.sansserif { font-family:sans-serif; font-weight:normal; }
--></style>
</head>
<body>
<div class="node">
<p>
<a name="Permutations"></a>
Next: <a rel="next" accesskey="n" href="Combinations.html">Combinations</a>,
Previous: <a rel="previous" accesskey="p" href="Vectors-and-Matrices.html">Vectors and Matrices</a>,
Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<hr>
</div>
<h2 class="chapter">9 Permutations</h2>
<p><a name="index-permutations-992"></a>
This chapter describes functions for creating and manipulating
permutations. A permutation p is represented by an array of
n integers in the range 0 to n-1, where each value
p_i occurs once and only once. The application of a permutation
p to a vector v yields a new vector v' where
<!-- {$v'_i = v_{p_i}$} -->
v'_i = v_{p_i}.
For example, the array (0,1,3,2) represents a permutation
which exchanges the last two elements of a four element vector.
The corresponding identity permutation is (0,1,2,3).
<p>Note that the permutations produced by the linear algebra routines
correspond to the exchange of matrix columns, and so should be considered
as applying to row-vectors in the form v' = v P rather than
column-vectors, when permuting the elements of a vector.
<p>The functions described in this chapter are defined in the header file
<samp><span class="file">gsl_permutation.h</span></samp>.
<ul class="menu">
<li><a accesskey="1" href="The-Permutation-struct.html">The Permutation struct</a>
<li><a accesskey="2" href="Permutation-allocation.html">Permutation allocation</a>
<li><a accesskey="3" href="Accessing-permutation-elements.html">Accessing permutation elements</a>
<li><a accesskey="4" href="Permutation-properties.html">Permutation properties</a>
<li><a accesskey="5" href="Permutation-functions.html">Permutation functions</a>
<li><a accesskey="6" href="Applying-Permutations.html">Applying Permutations</a>
<li><a accesskey="7" href="Reading-and-writing-permutations.html">Reading and writing permutations</a>
<li><a accesskey="8" href="Permutations-in-cyclic-form.html">Permutations in cyclic form</a>
<li><a accesskey="9" href="Permutation-Examples.html">Permutation Examples</a>
<li><a href="Permutation-References-and-Further-Reading.html">Permutation References and Further Reading</a>
</ul>
<hr>The GNU Scientific Library - a free numerical library licensed under the GNU GPL<br>Back to the <a href="/software/gsl/">GNU Scientific Library Homepage</a></body></html>
|
