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

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

       Copyright (C) 2008-2024 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.

perl v5.40.0                                       2024-10-20                        Math::GSL::Permutation(3pm)

       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/>

        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";

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

        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