# NAME

Math::GSL::Permutation - functions for creating and manipulating permutations

# SYNOPSIS

```
use Math::GSL::Permutation qw/:all/;
my $permutation = Math::GSL::Permutation->new(30); # allocate and initialize a permutation of size 30
my $lenght = $permutation->lenght; # returns the lenght of the permutation object, here it is 30
gsl_permutation_swap($permutation->raw, 2,7);
# the raw method is made to use the underlying permutation structure of the permutation object
my $value = $permutation->get(2); # returns the third value (starting from 0) of the permutation
my @values = $permutation->as_list; # returns all the values of the permutation
my @set = $permutation->get([0,1,2,3]); # returns the four first values of the permutation
```

# DESCRIPTION

Here is a list of all the functions included in this module :

- gsl_permutation_alloc($n) - return a newly allocated permutation of size $n
- gsl_permutation_calloc($n) - return a newly allocated permutation of size $n which is initialized to the identity
- gsl_permutation_init($p) - initialize the permutation $p to the identity i.e. (0,1,2, ..., n-1)
- gsl_permutation_free($p) - free all the memory use by the permutaion $p
- gsl_permutation_memcpy($dest, $src) - copy the permutation $src into the permutation $dest, the two permutations must have the same lenght and return 0 if the operation suceeded, 1 otherwise
- gsl_permutation_fread($stream, $p) - This function reads into the permutation $p from the open stream $stream (opened with the gsl_fopen function from the Math::GSL module) in binary format. The permutation $p must be preallocated with the correct length since the function uses the size of $p to determine how many bytes to read. The function returns 1 if there was a problem reading from the file. The data is assumed to have been written in the native binary format on the same architecture.
- gsl_permutation_fwrite($stream, $p) - This function writes the elements of the permutation $p to the stream $stream (opened with the gsl_fopen function from the Math::GSL module) in binary format. The function returns 1 if there was a problem writing to the file. Since the data is written in the native binary format it may not be portable between different architectures.
- gsl_permutation_fscanf($stream, $p) - This function reads formatted data from the stream $stream (opened with the gsl_fopen function from the Math::GSL module) into the permutation $p. The permutation $p must be preallocated with the correct length since the function uses the size of $p to determine how many numbers to read. The function returns 1 if there was a problem reading from the file.
- gsl_permutation_fprintf($stream, $p, $format) - This function writes the elements of the permutation $p line-by-line to the stream $stream (opened with the gsl_fopen function from the Math::GSL module) using the format specifier $format, which should be suitable. "%zu\n" is a suitable format. The function returns 1 if there was a problem writing to the file.
- gsl_permutation_size($p) - return the size of the permutation $p
- gsl_permutation_data
- gsl_permutation_get($p, $i) - return the $i-th element of the permutation $p, return 0 if $i is outside the range of 0 to n-1
- gsl_permutation_swap($p, $i, $j) - exchange the $i-th position and the $j-th position of the permutation $p and return 0 if the operation suceeded, 1 otherwise
- gsl_permutation_valid($p) - return 0 if the permutation $p is valid (if the n elements contain each of the numbers 0 to n-1 once and only once), 1 otherwise
- gsl_permutation_reverse($p) - reverse the elements of the permutation $p
- gsl_permutation_inverse($inv, $p) - compute the inverse of the permutation $p, storing it in $inv and return 0 if the operation succeeded, 1 otherwise
- gsl_permutation_next($p) - advance the permutation $p to the next permutation in lexicographic order and return 0 if the operation succeeded, 1 otherwise
- gsl_permutation_prev($p) - step backward from the permutation $p to the previous permutation in lexicographic order and return 0 if the operation suceeded, 1 otherwise
- gsl_permutation_mul($p, $pa, $pb) - combine the two permutation $pa and $pb into a single permutation $p and return 0 if the operation suceeded, 1 otherwise
- gsl_permutation_linear_to_canonical($q, $p) - compute the canonical form the permutation $p and store it in $q and return 0 if the operation suceeded, 1 otherwise
- gsl_permutation_canonical_to_linear($p, $q) - convert a canonical permutation $q back into linear form and store it in $p and return 0 if the operation suceeded, 1 otherwise
- gsl_permutation_inversions($p) - return the number of inversions in the permutation $p
- gsl_permutation_linear_cycles($p) - return the number of cycles in the permutation $p, given a linear form
- gsl_permute_vector_int_inversegsl_permutation_canonical_cycles($p) - return the number of cycles in the permutation $p, given a canonical form
- gsl_permute
- gsl_permute_inverse
- gsl_permute_int
- gsl_permute_int_inverse
- gsl_permute_vector
- gsl_permute_vector_inverse
- gsl_permute_vector_int

```
You have to add the functions you want to use inside the qw/put_funtion_here/ with spaces between each function.
You can also write use Math::GSL::CDF qw/:all/ to use all avaible functions of the module.
Other tags are also avaible, here is a complete list of all tags for this module.
For more informations on the functions, we refer you to the GSL offcial documentation:
L<http://www.gnu.org/software/gsl/manual/html_node/>
```

# EXAMPLES

```
use Math::GSL::Permutation qw/:all/;
$p->{permutation} = gsl_permutation_calloc(5);
print "The permutation contains [";
map { print gsl_permutation_get($p->{permutation}, $_) . ", " } (0..3);
print gsl_permutation_get($p->{permutation}, 4);
print "] \n";
print "We'll then swap the first and last elements of the permutation...\n";
gsl_permutation_swap($p->{permutation}, 0, 4);
print "The permutation now contains [";
map { print gsl_permutation_get($p->{permutation},$_) . ", " } (0..3);
print gsl_permutation_get($p->{permutation}, 4);
print "] \n";
use Math::GSL::Permutation qw/:all/;
use Math::GSL::Vector qw/:all/;
my $p->{permutation} = gsl_permutation_calloc(6);
gsl_permutation_init($p->{permutation});
gsl_permutation_swap($p->{permutation}, 0, 1);
print "The permutation has his first and second elements swapped : [";
map { print gsl_permutation_get($p->{permutation}, $_) . "," } (0..4);
print gsl_permutation_get($p->{permutation}, 5) . "] \n";
my $vec->{vector} = gsl_vector_alloc(6);
map { gsl_vector_set($vec->{vector}, $_, $_) } (0..5);
print "We will now apply the permutation to this vector : [";
map { print gsl_vector_get($vec->{vector}, $_) . "," } (0..4);
print gsl_vector_get($vec->{vector}, 5) . "] \n";
gsl_permute_vector($p->{permutation}, $vec->{vector});
print "The vector is now : [";
map { print gsl_vector_get($vec->{vector}, $_) . "," } (0..4);
print gsl_vector_get($vec->{vector}, 5) . "] \n";
```

# AUTHORS

Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>

# COPYRIGHT AND LICENSE

Copyright (C) 2008-2011 Jonathan "Duke" Leto and Thierry Moisan

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.