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 $length = $permutation->length; # returns the length of the permutation object, here it is 30
        gsl_permutation_swap($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
       $dest, the two permutations must have the same length and return 0 if the operation
       succeeded, 1 otherwise
       gsl_permutation_fread($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 $p and return 0 if the operation succeeded, 1 otherwise
       gsl_permutation_valid($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 $p to the previous
       permutation in lexicographic order and return 0 if the operation succeeded, 1 otherwise
       gsl_permutation_mul($p, $pa, $pb) - combine the two permutation $pa and $pb into a single
       permutation $p and return 0 if the operation succeeded, 1 otherwise
       gsl_permutation_linear_to_canonical($q, $p) - compute the canonical form the permutation
       $p and store it in $q and return 0 if the operation succeeded, 1 otherwise
       gsl_permutation_canonical_to_linear($p, $q) - convert a canonical permutation $q back into
       linear form and store it in $p and return 0 if the operation succeeded, 1 otherwise
       gsl_permutation_inversions($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_function_here/ with spaces between each function.
        You can also write use Math::GSL::CDF qw/:all/ to use all available functions of the module.
        Other tags are also available, here is a complete list of all tags for this module.
       For more information on the functions, we refer you to the GSL official 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) 2008-2021 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.