```
# Copyright 2006, 2007, 2009, 2010 Kevin Ryde
# This file is part of Chart.
#
# Chart is free software; you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation; either version 3, or (at your option) any later version.
#
# Chart is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
# details.
#
# You should have received a copy of the GNU General Public License along
# with Chart. If not, see <http://www.gnu.org/licenses/>.
package App::Chart::Series::Derived::DEMA;
use 5.010;
use strict;
use warnings;
use Carp;
use Locale::TextDomain 1.17; # for __p()
use Locale::TextDomain ('App-Chart');
use base 'App::Chart::Series::Indicator';
use App::Chart::Series::Derived::EMA;
use App::Chart::Series::Derived::EMAx2;
# http://www.stockworm.com/help/manual/double-ema.html
# Example graph PFE (what year?).
#
# http://trader.online.pl/ELZ/t-i-Double_Smoothed_Exponential_Moving_Average.html
# Tradestation example ^SPC 2001.
#
# http://store.traders.com/-v12-c01-smoothi-pdf.html
# Intro of TA S&C magazine, describing as faster.
#
# http://www.fmlabs.com/reference/DEMA.htm
# Formula only.
#
sub longname { __('DEMA - Double EMA') }
sub shortname { __('DEMA') }
sub manual { __p('manual-node','Double and Triple Exponential Moving Average') }
use constant
{ type => 'average',
priority => -10,
parameter_info => [ { name => __('Days'),
key => 'dema_days',
type => 'integer',
minimum => 0,
default => 20 } ],
};
sub new {
my ($class, $parent, $N) = @_;
$N //= parameter_info()->[0]->{'default'};
($N > 0) or croak "DEMA bad N: $N";
return $class->SUPER::new
(parent => $parent,
parameters => [ $N ],
N => $N,
arrays => { values => [] },
array_aliases => { });
}
sub proc {
my ($class_or_self, $N) = @_;
my $ema_proc = App::Chart::Series::Derived::EMA->proc($N);
my $ema2_proc = App::Chart::Series::Derived::EMA->proc($N);
return sub {
my ($value) = @_;
my $e = $ema_proc->($value);
my $e2 = $ema2_proc->($e);
return 2*$e - $e2;
};
}
# A DEMA is in theory influenced by all preceding data, but warmup_count()
# is designed to determine a warmup count. The next point will have an
# omitted weight of no more than 0.1% of the total. Omitting 0.1% should be
# negligable, unless past values are ridiculously bigger than recent ones.
#
# The implementation here does a binary search for the first i satisfying
# Omitted(i)<=0.001, so it's only moderately fast.
#
sub warmup_count {
my ($self_or_class, $N) = @_;
if ($N <= 1) { return 0; }
my $f = App::Chart::Series::Derived::EMA::N_to_f ($N);
return App::Chart::Series::Derived::EMAx2::bsearch_first_true
(sub {
my ($i) = @_;
return (dema_omitted($N,$f,$i)
<= App::Chart::Series::Derived::EMA::WARMUP_OMITTED_FRACTION) },
$N);
}
# dema-omitted() returns the fraction (between 0 and 1) of absolute weight
# omitted by stopping a DEMA at the f^k term, which means the first k+1
# terms.
#
# The EMA and EMAofEMA omitted totals are
#
# Q(k) = f^(k+1)
# R(k) = f^(k+1) * (k+2 - f * (k+1))
#
# thus for the DEMA the net signed amount, implemented in
# dema_omitted_signed(), is
#
# S(k) = 2*Q(k) - R(k)
# = f^(k+1) * (f*(k+1) - k)
#
# This grows above 1 up to the f^N term, then the terms go negative and it
# decreases towards 1.
#
# The position of the negative/positive transition is always at f^N. The
# coefficient of that f^N term is
#
# 2 - (1-f)*(N+1) = 2 - (1-(N-1)/(N+1))*(N+1)
# = 2 - (N+1-(N-1))
# = 2 - N - 1 + N - 1
# = 0
#
# An absolute omitted weight is calculated from the signed omitted amount.
# When k>N we can just negate the signed omitted. When k<N we add the
# negative terms past N in twice, first to cancel the negative then to add
# in as positive.
#
# The total of all the negatives beyond N is -S(N),
#
# tail = -S(N) = f^(N+1) * (f*(N+1) - N)
# = f^(N+1) * ((N-1)/(N+1) * (N+1) - N)
# = f^(N+1) * (N-1 - N)
# = f^(N+1)
#
# Thus the absolute omitted,
#
# T(k) = / - S(k) if k >= N
# \ S(k) + 2*f^(N+1) if k < N
#
# This is out of a total which is the positive and negative parts added as
# abolute values. Knowing pos+neg=1 and neg=-f^(N+1),
#
# total absolute weight = 1 + 2*f(N+1)
#
# And that total is applied as a divisor, so the return from `dema-omitted'
# is between 0 and 1. (It works to call it with k=-1 for no terms omitted,
# the result is 1.0.)
#
sub dema_omitted {
my ($N, $f, $k) = @_;
my $tail = $f ** ($N + 1);
my $num = dema_omitted_signed ($f, $k);
if ($k >= $N) {
$num = -$num;
} else {
$num += 2 * $tail;
}
return $num / (2*$tail + 1);
}
sub dema_omitted_signed {
my ($f, $k) = @_;
return $f**($k+1) * ($f*($k+1) - $k);
}
1;
__END__
# =head1 NAME
#
# App::Chart::Series::Derived::DEMA -- double-exponential moving average
#
# =head1 SYNOPSIS
#
# my $series = $parent->DEMA($N);
#
# =head1 DESCRIPTION
#
# ...
#
# =head1 SEE ALSO
#
# L<App::Chart::Series>, L<App::Chart::Series::Derived::EMA>
#
# =cut
```