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package Data::Pareto; |
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use warnings; |
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use strict; |
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use Scalar::Util qw( reftype ); |
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use Carp; |
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=head1 NAME |
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Data::Pareto - Computing Pareto sets in Perl |
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=head1 VERSION |
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Version 0.05 |
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=cut |
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our $VERSION = '0.05'; |
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=head1 SYNOPSIS |
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use Data::Pareto; |
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# only first and third columns are used in comparison |
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# the others are simply descriptive |
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my $set = new Data::Pareto( { columns => [0, 2] } ); |
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$set->add( |
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[ 5, "pareto", 10, 11 ], |
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[ 5, "dominated", 11, 9 ], |
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[ 4, "pareto2", 12, 12 ] |
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); |
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# this returns [ [ 5, "pareto", 10, 11 ], [ 4, "pareto2", 12, 12 ] ], |
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# the other one is dominated on selected columns |
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$set->get_pareto_ref; |
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=head1 DESCRIPTION |
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This module makes calculation of Pareto set. Given a set of vectors |
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(i.e. arrays of simple scalars), Pareto set is all the vectors from the given |
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set which are not dominated by any other vector of the set. A vector C is |
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said to be dominated by C, iff C<< X[i] >= Y[i] >> for all C and |
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C<< X[i] > Y[i] >> for at least one C. |
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Pareto sets play an important role in multiobjective optimization, where |
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each non-dominated (i.e. Pareto) vector describes objectives value of |
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"optimal" solution to the given problem. |
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This module allows occurrence of duplicates in the set - this makes it |
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rather a bag than a set, but is useful in practice (e.g. when we want to |
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preserve two solutions giving the same objectives value, but structurally |
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different). This assumption influences dominance definition given above: |
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two duplicates never dominate each other and hence can be present in the Pareto |
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set. This is controlled by C option passed to L: if set |
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to C value, duplicates are allowed in Pareto set; otherwise, only the |
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first found element of the subset of duplicated vectors is preserved in Pareto |
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set. |
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The values are allowed to be invalid. The meaning of 'invalid' is 'the worst |
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possible'. It's different concept than 'unknown'; unknown value make the |
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definition of domination less clear. |
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By default, the comparison of column values is numerical and the smaller |
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value dominates the larger one. If you want to override this behaviour, pass |
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your own dominator sub in arguments to L. |
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=head1 FUNCTIONS |
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By default, a vector is passed around as a ref to array of consecutive column |
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values. This means you shouldn't mess with it after passing to C method. |
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=cut |
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=head2 new |
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Creates a new object for calculating Pareto set. |
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The first argument passed is a hashref with options; the recognized options are: |
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=over |
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=item * C |
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Arrayref containing column numbers which should be used for determining |
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domination and duplication. Column numbers are C<0>-based array indexes to |
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data vectors. |
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Only values at those positions will be ever compared between vectors. |
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Any other data in the vectors may be present and is not used in any way. |
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At least one column number should be passed, for obvious reasons. |
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=item * C |
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If set to C value, duplicated vectors are all put in Pareto set (if they |
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are Pareto, of course). If set to C, duplicates of vectors already |
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in the Pareto set are discarded. |
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=item * C |
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The value considered invalid in pareto set. Such value is dominated by |
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any value and dominates only invalid value. |
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However, computations of domination in presence of invalid values can be |
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considerably slower, as much as 5 times. So it probably will be faster to first |
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parse the data and replace invalid markers with some huge-and-surely-dominated |
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values. |
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=item * C |
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The sub(s) used to compare specific column values and determining domination |
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between them. Scalar, sub ref or hash ref. If not set, the default is that |
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the numerically smaller value dominates the other one. |
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When the scalar is passed, it is assumed to be the name of a predefined |
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dominator. This is a much faster option to specifying the sub of your own. |
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Recognized dominators are: |
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=over |
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=item * C numerically smaller value dominates |
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=item * C numerically greater value dominates |
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=item * C earlier in collation order value dominates (lexicographical |
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order) |
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=item * C later in collation order value dominates (reversed |
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lexicographical order) |
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=item * C standard, i.e. C dominator |
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=back |
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During creation of Pareto set, the dominator sub is called with three arguments: |
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column number, first vector's value, second vector's value, and should return |
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C, when the second value dominates the first one, assuming they appeared |
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in the specified column. |
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142
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Make sure that your sub returns C when two passed values are the same. |
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This is necessary to obey the whole Pareto set domination contract. |
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145
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There are two approaches possible when the values in different columns are of |
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different types, in the sense of domination. First, you can use passed column |
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number to decide the domination check function. Alternatively, you can pass a |
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hash ref with mapping from the column number to the sub ref used to compare the |
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given column: |
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151
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my $lexi_dominator = sub { |
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my ($col, $dominated, $by) = @_; |
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return ($dominated ge $by); |
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}; |
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my $min_dominator = sub { |
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my ($col, $dominated, $by) = @_; |
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return ($dominated >= $by); |
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} |
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160
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my $set = new Data::Pareto({ |
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columns => [0, 2], |
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column_dominator => { |
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0 => $lexi_dominator, |
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2 => $min_dominator |
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} |
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}); |
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$set->add(['a', 'label 1', 12], ['b', 'label 2', 9]); |
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169
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=back |
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171
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The rest of arguments are assumed to be vectors, and passed to L |
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method. |
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174
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=cut |
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177
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sub new { |
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my ($class, $attrs) = (shift, shift); |
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my $self = bless { |
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pareto => [ ], |
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vectorStatus => { }, |
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%$attrs |
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}, $class; |
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$self->_construct_subs; |
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$self->add(@_) if @_; |
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return $self; |
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} |
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190
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=head2 add |
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192
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Tests vectors passed as arguments and adds the non-dominated ones to the |
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Pareto set. |
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195
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=cut |
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197
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sub add { |
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my $self = shift; |
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$self->_update_pareto($_) for @_; |
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} |
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202
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=head2 get_pareto |
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204
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Returns the current content of Pareto set as a list of vectors. |
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206
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=cut |
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208
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sub get_pareto { |
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my ($self) = @_; |
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return (@{$self->{pareto}}); |
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} |
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213
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=head2 get_pareto_ref |
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215
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Returns the current content of Pareto set as a ref to array with vectors. |
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The return value references the original array, so treat it as read-only! |
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218
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=cut |
219
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220
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sub get_pareto_ref { |
221
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my ($self) = @_; |
222
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return $self->{pareto}; |
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} |
224
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225
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# update (potentially) the set with a new vector: |
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# check if it is Pareto, if so, remove dominated vectors |
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sub _update_pareto { |
228
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my ($self, $NV) = @_; |
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230
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# check if we already have a duplicate? |
231
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# if so, handle it gently, so there are no mind-cracking |
232
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# algorithm variations after that |
233
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234
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43
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100
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72
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if ($self->_has_duplicates($NV)) { |
235
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# ...then it depends on the policy |
236
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4
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100
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8
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if ($self->{duplicates}) { |
237
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# add the duplicated vector to the pareto set |
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3
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4
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push @{$self->{pareto}}, $NV; |
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5
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} else { |
240
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# simply disgard the new vector |
241
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} |
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4
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12
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return; |
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} |
244
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39
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45
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my @newP = ( ); |
246
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39
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62
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my $surePareto = 0; |
247
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248
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# check with every vector considered pareto so far |
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for my $o (@{$self->{pareto}}) { |
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66
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250
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27
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100
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40
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if ($surePareto) { |
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# preserve the current vector only if it is not dominated by new (now Pareto) vector |
252
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1
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50
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20
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if ($self->{_sub_is_dominated}($self, $o, $NV)) { |
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1
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3
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$self->_ban_vector($o); |
254
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} else { |
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0
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0
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push @newP, $o; |
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} |
257
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} else { |
258
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# stop processing with unchanged Pareto set if the new vector is dominated by the current one |
259
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26
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100
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524
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return if $self->{_sub_is_dominated}($self, $NV, $o); |
260
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261
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# mark new vector as "sure Pareto" only if it dominates the current vector |
262
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21
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100
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426
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if ($self->{_sub_is_dominated}($self, $o, $NV)) { |
263
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5
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7
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$surePareto = 1; |
264
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# ...and hence we don't preserve the dominated current vector |
265
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5
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10
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$self->_ban_vector($o); |
266
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5
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9
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next; |
267
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} |
268
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269
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# otherwise, the current vector is for sure Pareto still, so preserve it |
270
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16
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33
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push @newP, $o; |
271
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} |
272
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} |
273
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274
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34
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46
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push @newP, $NV; |
275
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34
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65
|
$self->_mark_vector($NV); |
276
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34
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134
|
$self->{pareto} = \@newP; |
277
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} |
278
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279
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=head2 is_dominated |
280
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281
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Checks if the first vector passed is dominated by the second one. |
282
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The comparison is made based on the values in vectors' columns, which |
283
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were passed to L. |
284
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285
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The vectors passed are never duplicates of each other when this method is |
286
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called from inside this module. |
287
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288
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Returns C, when the first vector from arguments list |
289
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is dominated by the other one, and C otherwise. |
290
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291
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=cut |
292
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293
|
22
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22
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1
|
745
|
sub is_dominated { $_[0]->{_sub_is_dominated}(@_); } # pass the whole @_, as the sub thinks it is a method |
294
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295
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# these are is_dominated() parts which will be composed into the function, |
296
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|
# depending on the constructor options. |
297
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|
my %_is_dominated_parts = ( |
298
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invalid => <<'_EOT_', |
299
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|
next if $self->{_sub_is_invalid}($dominated->[$col]); # invalid dominated by anything |
300
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|
return 0 if $self->{_sub_is_invalid}($by->[$col]); # invalid can't dominate valid |
301
|
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|
|
_EOT_ |
302
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|
|
dominator_min => '($dominated->[$col] >= $by->[$col])', |
303
|
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|
|
dominator_max => '($dominated->[$col] <= $by->[$col])', |
304
|
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|
|
dominator_lexi => '($dominated->[$col] ge $by->[$col])', |
305
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|
|
dominator_lexi_rev => '($dominated->[$col] le $by->[$col])', |
306
|
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307
|
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|
|
_dominator_custom => <<'_EOT_', |
308
|
|
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|
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|
|
$self->{column_dominator}($col, $dominated->[$col], $by->[$col]) |
309
|
|
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|
|
_EOT_ |
310
|
|
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|
|
_dominator_custom_hash => <<'_EOT_', |
311
|
|
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|
|
|
$self->{column_dominator}{$col}($col, $dominated->[$col], $by->[$col]) |
312
|
|
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|
|
|
_EOT_ |
313
|
|
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|
|
|
|
|
314
|
|
|
|
|
|
|
); |
315
|
|
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|
|
|
|
$_is_dominated_parts{dominator_std} = $_is_dominated_parts{dominator_min}; |
316
|
|
|
|
|
|
|
|
317
|
|
|
|
|
|
|
sub _construct_subs { |
318
|
32
|
|
|
32
|
|
39
|
my ($self) = @_; |
319
|
|
|
|
|
|
|
|
320
|
32
|
|
|
|
|
29
|
my $invalid_part; |
321
|
32
|
100
|
|
|
|
66
|
if (exists $self->{invalid}) { |
322
|
4
|
|
|
|
|
5
|
my $inv = $self->{invalid}; |
323
|
4
|
|
|
23
|
|
14
|
$self->{_sub_is_invalid} = sub { $_[0] eq $inv }; |
|
23
|
|
|
|
|
378
|
|
324
|
4
|
|
|
|
|
9
|
$invalid_part = $_is_dominated_parts{invalid}; |
325
|
|
|
|
|
|
|
} else { |
326
|
28
|
|
|
2
|
|
91
|
$self->{_sub_is_invalid} = sub { 0 }; |
|
2
|
|
|
|
|
11
|
|
327
|
28
|
|
|
|
|
36
|
$invalid_part = ''; |
328
|
|
|
|
|
|
|
} |
329
|
|
|
|
|
|
|
|
330
|
32
|
|
|
|
|
32
|
my $cmp_part; |
331
|
32
|
100
|
|
|
|
69
|
if (exists $self->{column_dominator}) { |
332
|
10
|
|
50
|
|
|
26
|
my $dom = $self->{column_dominator} || ''; |
333
|
10
|
|
|
|
|
25
|
my $type = reftype $dom; |
334
|
10
|
100
|
66
|
|
|
25
|
if (!defined $type) { |
|
|
100
|
|
|
|
|
|
335
|
|
|
|
|
|
|
# builtin |
336
|
8
|
|
|
|
|
18
|
$cmp_part = $_is_dominated_parts{"dominator_$dom"}; |
337
|
8
|
50
|
|
|
|
18
|
croak "Unrecognized dominator builtin '$dom'" unless $cmp_part; |
338
|
|
|
|
|
|
|
} elsif ($type && $type eq 'HASH') { |
339
|
1
|
|
|
|
|
2
|
$cmp_part = $_is_dominated_parts{_dominator_custom_hash}; |
340
|
|
|
|
|
|
|
} else { |
341
|
1
|
|
|
|
|
3
|
$cmp_part = $_is_dominated_parts{_dominator_custom}; |
342
|
|
|
|
|
|
|
} |
343
|
|
|
|
|
|
|
} else { |
344
|
22
|
|
|
|
|
36
|
$cmp_part = $_is_dominated_parts{dominator_std}; |
345
|
|
|
|
|
|
|
} |
346
|
|
|
|
|
|
|
|
347
|
32
|
|
|
|
|
77
|
my $sub_str = <<'_EOT_' |
348
|
|
|
|
|
|
|
sub { |
349
|
|
|
|
|
|
|
my ($self, $dominated, $by) = @_; |
350
|
|
|
|
|
|
|
for my $col (@{$self->{columns}}) { |
351
|
|
|
|
|
|
|
_EOT_ |
352
|
|
|
|
|
|
|
. <<_EOT_ |
353
|
|
|
|
|
|
|
$invalid_part |
354
|
|
|
|
|
|
|
return 0 unless $cmp_part; |
355
|
|
|
|
|
|
|
} |
356
|
|
|
|
|
|
|
1; |
357
|
|
|
|
|
|
|
} |
358
|
|
|
|
|
|
|
_EOT_ |
359
|
|
|
|
|
|
|
; |
360
|
32
|
|
|
|
|
3282
|
$self->{_sub_is_dominated} = eval $sub_str; |
361
|
|
|
|
|
|
|
} |
362
|
|
|
|
|
|
|
|
363
|
|
|
|
|
|
|
=head2 is_invalid |
364
|
|
|
|
|
|
|
|
365
|
|
|
|
|
|
|
Checks if the given value is considered invalid for the current object. |
366
|
|
|
|
|
|
|
Every value is valid by default. |
367
|
|
|
|
|
|
|
|
368
|
|
|
|
|
|
|
=cut |
369
|
|
|
|
|
|
|
|
370
|
6
|
|
|
6
|
1
|
51
|
sub is_invalid { return $_[0]->{_sub_is_invalid}($_[1]); } |
371
|
|
|
|
|
|
|
|
372
|
|
|
|
|
|
|
# calculate the string repr. of a vector; to be used as a hash key |
373
|
|
|
|
|
|
|
sub _vector_key { |
374
|
83
|
|
|
83
|
|
86
|
my ($self, $v) = @_; |
375
|
83
|
|
|
|
|
94
|
my @cols = ( ); |
376
|
83
|
|
|
|
|
71
|
for my $c (@{$self->{columns}}) { |
|
83
|
|
|
|
|
146
|
|
377
|
191
|
|
|
|
|
273
|
push @cols, $v->[$c]; |
378
|
|
|
|
|
|
|
} |
379
|
|
|
|
|
|
|
|
380
|
83
|
|
|
|
|
267
|
return join ';', @cols; |
381
|
|
|
|
|
|
|
} |
382
|
|
|
|
|
|
|
|
383
|
|
|
|
|
|
|
# checks if the given vector has duplicates in Pareto |
384
|
|
|
|
|
|
|
sub _has_duplicates { |
385
|
43
|
|
|
43
|
|
44
|
my ($self, $v) = @_; |
386
|
43
|
|
|
|
|
73
|
my $key = $self->_vector_key($v); |
387
|
43
|
|
100
|
|
|
169
|
return (exists $self->{vectorStatus}{$key} && $self->{vectorStatus}{$key} > 0); |
388
|
|
|
|
|
|
|
} |
389
|
|
|
|
|
|
|
|
390
|
|
|
|
|
|
|
# mark the vector as not present in Pareto. |
391
|
|
|
|
|
|
|
# In the future it can be used to ban the vector from trying to return |
392
|
|
|
|
|
|
|
# to the Pareto set. |
393
|
|
|
|
|
|
|
sub _ban_vector { |
394
|
6
|
|
|
6
|
|
8
|
my ($self, $v) = @_; |
395
|
6
|
|
|
|
|
10
|
my $key = $self->_vector_key($v); |
396
|
6
|
|
|
|
|
11
|
$self->{vectorStatus}{$key} = 0; |
397
|
|
|
|
|
|
|
} |
398
|
|
|
|
|
|
|
|
399
|
|
|
|
|
|
|
# mark vector as present in the Pareto set. |
400
|
|
|
|
|
|
|
sub _mark_vector { |
401
|
34
|
|
|
34
|
|
38
|
my ($self, $v) = @_; |
402
|
34
|
|
|
|
|
56
|
my $key = $self->_vector_key($v); |
403
|
34
|
|
|
|
|
84
|
$self->{vectorStatus}{$key} = 1; |
404
|
|
|
|
|
|
|
} |
405
|
|
|
|
|
|
|
|
406
|
|
|
|
|
|
|
=head1 TODO |
407
|
|
|
|
|
|
|
|
408
|
|
|
|
|
|
|
Allow specifying built-in dominators inside dominator hash. |
409
|
|
|
|
|
|
|
|
410
|
|
|
|
|
|
|
For large data sets calculations become time-intensive. There are a couple |
411
|
|
|
|
|
|
|
of techniques which might be applied to improve the performance: |
412
|
|
|
|
|
|
|
|
413
|
|
|
|
|
|
|
=over |
414
|
|
|
|
|
|
|
|
415
|
|
|
|
|
|
|
=item * defer the phase of removing vectors dominated by newly added vectors |
416
|
|
|
|
|
|
|
to L call; this results in smaller number of arrays |
417
|
|
|
|
|
|
|
rewritings. |
418
|
|
|
|
|
|
|
|
419
|
|
|
|
|
|
|
=item * split the set of vectors being added into smaller subsets, calculate |
420
|
|
|
|
|
|
|
Pareto sets for such subsets, and then apply insertion of resulting Pareto |
421
|
|
|
|
|
|
|
subsets to the main set; this results in smaller number of useless tries of |
422
|
|
|
|
|
|
|
adding dominated vectors into the set. |
423
|
|
|
|
|
|
|
|
424
|
|
|
|
|
|
|
=back |
425
|
|
|
|
|
|
|
|
426
|
|
|
|
|
|
|
=head1 AUTHOR |
427
|
|
|
|
|
|
|
|
428
|
|
|
|
|
|
|
Przemyslaw Wesolek, C<< >> |
429
|
|
|
|
|
|
|
|
430
|
|
|
|
|
|
|
=head1 BUGS |
431
|
|
|
|
|
|
|
|
432
|
|
|
|
|
|
|
Please report any bugs or feature requests to C, or through |
433
|
|
|
|
|
|
|
the web interface at L. I will be notified, and then you'll |
434
|
|
|
|
|
|
|
automatically be notified of progress on your bug as I make changes. |
435
|
|
|
|
|
|
|
|
436
|
|
|
|
|
|
|
=head1 SUPPORT |
437
|
|
|
|
|
|
|
|
438
|
|
|
|
|
|
|
You can find documentation for this module with the perldoc command. |
439
|
|
|
|
|
|
|
|
440
|
|
|
|
|
|
|
perldoc Data::Pareto |
441
|
|
|
|
|
|
|
|
442
|
|
|
|
|
|
|
|
443
|
|
|
|
|
|
|
You can also look for information at: |
444
|
|
|
|
|
|
|
|
445
|
|
|
|
|
|
|
=over 4 |
446
|
|
|
|
|
|
|
|
447
|
|
|
|
|
|
|
=item * RT: CPAN's request tracker |
448
|
|
|
|
|
|
|
|
449
|
|
|
|
|
|
|
L |
450
|
|
|
|
|
|
|
|
451
|
|
|
|
|
|
|
=item * AnnoCPAN: Annotated CPAN documentation |
452
|
|
|
|
|
|
|
|
453
|
|
|
|
|
|
|
L |
454
|
|
|
|
|
|
|
|
455
|
|
|
|
|
|
|
=item * CPAN Ratings |
456
|
|
|
|
|
|
|
|
457
|
|
|
|
|
|
|
L |
458
|
|
|
|
|
|
|
|
459
|
|
|
|
|
|
|
=item * Search CPAN |
460
|
|
|
|
|
|
|
|
461
|
|
|
|
|
|
|
L |
462
|
|
|
|
|
|
|
|
463
|
|
|
|
|
|
|
=back |
464
|
|
|
|
|
|
|
|
465
|
|
|
|
|
|
|
=head1 COPYRIGHT & LICENSE |
466
|
|
|
|
|
|
|
|
467
|
|
|
|
|
|
|
|
468
|
|
|
|
|
|
|
Copyright 2009 Przemyslaw Wesolek |
469
|
|
|
|
|
|
|
|
470
|
|
|
|
|
|
|
This program is free software; you can redistribute it and/or modify it |
471
|
|
|
|
|
|
|
under the terms of the Artistic License 2.0. For details, see the full |
472
|
|
|
|
|
|
|
text of the license in the file LICENSE. |
473
|
|
|
|
|
|
|
|
474
|
|
|
|
|
|
|
=cut |
475
|
|
|
|
|
|
|
|
476
|
|
|
|
|
|
|
1; # End of Data::Pareto |