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package Statistics::DEA; |
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use vars qw($VERSION); |
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$VERSION = '0.04'; |
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use strict; |
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# use warnings; requires 5.6.0 |
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use Carp; |
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=head1 NAME |
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Statistics::DEA - Discontiguous Exponential Averaging |
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=head1 SYNOPSIS |
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use Statistics::DEA; |
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my $dea = Statistics::DEA->new($alpha, $max_gap); |
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while (($data, $time) = some_data_source(...)) { |
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... |
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$dea->update($data, $time); |
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print $dea->average(), "\n"; |
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print $dea->standard_deviation(), "\n"; |
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print $dea->completeness($time), "\n"; |
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... |
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} |
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=head1 DESCRIPTION |
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The Statistics::DEA module can be used to compute exponentially |
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decaying averages and standard deviations even when the data has |
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gaps. The algorithm also avoids initial value bias and postgap bias. |
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=head2 new |
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my $dea = Statistics::DEA->new($alpha, $max_gap); |
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Creates a new (potentially discontiguous) exponential average object. |
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The I<$alpha> is the exponential decay of I: from zero (inclusive) |
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to one (exclusive): the lower values cause the effect of data to decay |
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more quickly, the higher values cause the effect of data to decay more |
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slowly . Specifically, weights on older data decay exponentially with a |
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characteristic time of I<-1/log(alpha)> (I being the natural logarithm). |
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The I<$max_gap> is the maximum I |
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considered lost. If the time interval between updates is I, |
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using a I<$max_gap> of I will cause each update to fill in up to |
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I of any preceeding skipped updates with the current data value. |
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Use a I<$max_gap> of I to prevent such filling. |
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=head2 update |
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$dea->update($data, $time); |
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Update the average with new data at a particular point in time. |
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The time parameter is how you can indicate gaps in the data; |
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if you don't have gaps in your data, just monotonously increase it, |
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for example C<$time++>. |
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=head2 average |
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my $avg = $dea->average(); |
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Return the current average. |
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Functionally equivalent alias avg() is also available. |
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=head2 standard_deviation |
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my $std_dev = $dea->standard_deviation(); |
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Return the current standard deviation. |
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Functionally equivalent alias std_dev() is also available. |
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=head2 completeness |
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my $completeness = $dea->completeness($time); |
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Return the current I: how well based the current average |
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and standard deviation are on actual data. Any time intervals between |
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updates greater than I<$max_gap> reduce this value. A series of updates |
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at time intervals of less than I<$max_gap> will gradually increase this |
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value from its initial, minimum, value of 0 to its maximum value of 1. |
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The $time should represent the current time. It must be >= the time of |
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the last update. |
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=head2 alpha |
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my $alpha = $dea->alpha(); |
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Return the current exponential decay of data. |
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$dea->alpha($alpha); |
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Set the exponential decay of data. |
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=head2 max_gap |
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my $alpha = $dea->max_gap(); |
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Return the current maximum time gap. |
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$dea->max_gap($max_gap); |
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Set the maximum time gap. |
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=head1 AUTHOR |
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Jarkko Hietaniemi |
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=head1 LICENSE |
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120
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This library is free software; you can redistribute it and/or modify |
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it under the same terms as Perl itself. |
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=head1 ACKNOWLEDGEMENT |
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The idea and the code are from the September 1998 Doctor Dobb's |
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Journal Algorithm Alley article "Discontiguous Exponential Averaging" |
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by John C. Gunther, used with permission. JCG also provided valuable |
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feedback for the documentation -- and even fixed a bug in the code |
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without knowing Perl as such. This is just a Perlification of the |
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pseudocode in the article, all errors in transcription are solely mine. |
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=cut |
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sub alpha { |
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my $dea = shift; |
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$dea->{alpha} = shift if @_; |
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$dea->_max_weight(); |
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return $dea->{alpha}; |
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} |
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sub max_gap { |
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my $dea = shift; |
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$dea->{max_gap} = shift if @_; |
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$dea->_max_weight(); |
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return $dea->{max_gap}; |
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} |
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sub _max_weight { # Internal use only. |
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my $dea = shift; |
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return unless defined $dea->{alpha} && defined $dea->{max_gap}; |
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$dea->{max_weight} = 1 - $dea->{alpha} ** $dea->{max_gap}; |
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} |
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sub new { |
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my $class = shift; |
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croak __PACKAGE__, "::new: need two arguments: alpha, max_gap" |
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unless @_ == 2; |
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my ($alpha, $max_gap) = @_; |
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croak __PACKAGE__, "::new: Not 0 <= alpha $alpha < 1" |
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unless 0 <= $alpha && $alpha < 1; |
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croak __PACKAGE__, "::new: Not max_gap $max_gap > 0" |
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unless $max_gap > 0; |
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my $dea = bless {}, $class; |
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$dea->{sum_of_weights} = 0; |
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$dea->{sum_of_data} = 0; |
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$dea->{sum_of_squared_data} = 0; |
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$dea->{previous_time} = -1e38; # about IEEE -Infinity |
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$dea->alpha($alpha); |
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$dea->max_gap($max_gap); |
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return $dea; |
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} |
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sub update { |
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my ($dea, $new_data, $time) = @_; |
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croak __PACKAGE__, "::update: Not previous_time $dea->{previous_time} < time $time" |
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unless $dea->{previous_time} < $time; |
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my $weight_reduction_factor = |
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$dea->{alpha} ** ($time - $dea->{previous_time}); |
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my $new_data_weight_a = 1 - $weight_reduction_factor; |
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my $new_data_weight_b = $dea->{max_weight}; |
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my $new_data_weight = |
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$new_data_weight_a < $new_data_weight_b ? |
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$new_data_weight_a : $new_data_weight_b; |
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$dea->{sum_of_weights} = |
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$weight_reduction_factor * $dea->{sum_of_weights} + |
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$new_data_weight; |
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$dea->{sum_of_data} = |
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$weight_reduction_factor * $dea->{sum_of_data} + |
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$new_data_weight * $new_data; |
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$dea->{sum_of_squared_data} = |
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$weight_reduction_factor * $dea->{sum_of_squared_data} + |
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$new_data_weight * $new_data * $new_data; |
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$dea->{previous_time} = $time; |
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} |
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sub _average { # Internal use only. |
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my $dea = shift; |
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return $dea->{sum_of_data} / $dea->{sum_of_weights}; |
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} |
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201
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sub average { |
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2
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2
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1
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my $dea = shift; |
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2
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croak __PACKAGE__, "::average: Not sum_of_weights > 0" |
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unless $dea->{sum_of_weights} > 0; |
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2
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return $dea->_average(); |
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} |
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208
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*avg = \&average; |
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210
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sub standard_deviation { |
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2
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2
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1
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my $dea = shift; |
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2
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10
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croak __PACKAGE__, "::standard_deviation: Not sum_of_weights > 0" |
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unless $dea->{sum_of_weights} > 0; |
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2
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my $average = $dea->_average(); |
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2
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24
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return sqrt($dea->{sum_of_squared_data} / $dea->{sum_of_weights} - |
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$average * $average); |
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} |
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|
|
|
219
|
|
|
|
|
|
|
*std_dev = \&standard_deviation; |
220
|
|
|
|
|
|
|
|
221
|
|
|
|
|
|
|
sub completeness { |
222
|
2
|
|
|
2
|
1
|
5
|
my $dea = shift; |
223
|
2
|
50
|
|
|
|
9
|
croak __PACKAGE__, "::completeness: need one argument: time" |
224
|
|
|
|
|
|
|
unless @_ == 1; |
225
|
2
|
|
|
|
|
4
|
my $time = shift; |
226
|
2
|
50
|
|
|
|
8
|
croak __PACKAGE__, "::completeness: Not previous_time $dea->{previous_time} <= time $time" |
227
|
|
|
|
|
|
|
unless $dea->{previous_time} <= $time; |
228
|
|
|
|
|
|
|
return |
229
|
2
|
|
|
|
|
14
|
$dea->{alpha} ** ($time - $dea->{previous_time}) * |
230
|
|
|
|
|
|
|
$dea->{sum_of_weights}; |
231
|
|
|
|
|
|
|
} |
232
|
|
|
|
|
|
|
|
233
|
|
|
|
|
|
|
1; |