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    }
    return $c / $n;
}

sub recall {
    my $r = shift;
    my $label = shift;
    my ($c, $n) = (0, 0);
    for (@$r) {
        if ($_->[0]->[1] eq $label) {
            my $w = defined($_->[0]->[2]) ? $_->[0]->[2] : 1;
	    $n += $w;
	    $c += $w if $_->[1] eq $label;
	}
    }
    return $c / $n;
}

1;

__END__

=head1 NAME

AI::MaxEntropy::Util - Utilities for doing experiments with ME learners 

=head1 SYNOPSIS

  use AI::MaxEntropy;
  use AI::MaxEntropy::Util qw/:all/;

  my $me = AI::MaxEntropy->new;
  
  my $samples = [
      [['a', 'b', 'c'] => 'x'],
      [['e', 'f'] => 'y' => 1.5],
      ...
  ];

  my ($result, $model) = train_and_test($me, $samples, 'xxxo');

  print precision($result)."\n";
  print recall($result, 'x')."\n";

=head1 DESCRIPTION

This module makes doing experiments with Maximum Entropy learner easier.

Generally, an experiment involves a training set and a testing set
(sometimes also a parameter adjusting set). The learner is trained with
samples in the training set and tested with samples in the testing set.
Usually, 2 measures of performance are concerned.
One is precision, indicating the percentage of samples which are correctly
predicted in the testing set. The other one is recall, indicating the 
precision of samples with a certain label.

=head1 FUNCTIONS

=head2 train_and_test

This function automated the process of training and testing.

    my $me = AI::MaxEntropy->new;
    my $sample = [
        [ ['a', 'b'] => 'x' => 1.5 ],
	...
    ];
    my ($result, $model) = train_and_test($me, $sample, 'xxxo');

First, the whole samples set will be divided into a training set and a
testing set according to the specified pattern. A pattern is a string,
in which each character stands for a part of the samples set.
If the character is C<'x'>, the corresponding part is used for training.
If the character is C<'o'>, the corresponding part is used for testing.
Otherwise, the corresponding part is simply ignored.

For example, the pattern 'xxxo' means the first three forth of the samples
set are used for training while the last one forth is used for testing.

The function returns two values. The first one is an array ref describe
the result of testing, in which each element follows a structure like
C<[sample =E<gt> result]>. The second one is the model learnt from the
training set, which is an L<AI::MaxEntropy::Model> object.

=head2 traverse_partially

This function is the core implementation of L</train_and_test>. It traverse
through some of the elements in an array according to a pattern,
and does some specified actions with each of these elements.
  
  my $arr = [1, 2, 3, 4, 5];

  # print out the first two firth of the array
  traverse_partially { print } $arr, 'xx---';

  # do the same thing, using custom significant character 'o'
  traverse_partially { print } $arr, 'oo---' => 'o';

  my $samples = [
      [['a', 'b'] => 'x'],
      [['c', 'd'] => 'y' => 1.5],
      ...
  ];
  my $me = AI::MaxEntropy->new;

  # see the first one third and the last one third samples
  traverse_partially { $me->see(@$_) } $samples, 'x-x';

=head2 map_partially

This function is similar to L</traverse_partially>. However, it returns an
array ref in which all elements in the original array is mapped according
to the code snippet's return value.

  my $arr = [1, 2, 3, 4, 5];
  
  # increase the last one third of the elements by 1
  $arr = map_partially { $_ + 1 } $arr, '--x';

=head2 precision