File Coverage

blib/lib/App/Chart/Series/Derived/DEMA.pm
Criterion Covered Total %
statement 20 20 100.0
branch n/a
condition n/a
subroutine 7 7 100.0
pod n/a
total 27 27 100.0


line stmt bran cond sub pod time code
1             # Copyright 2006, 2007, 2009, 2010 Kevin Ryde
2              
3             # This file is part of Chart.
4             #
5             # Chart is free software; you can redistribute it and/or modify it under the
6             # terms of the GNU General Public License as published by the Free Software
7             # Foundation; either version 3, or (at your option) any later version.
8             #
9             # Chart is distributed in the hope that it will be useful, but WITHOUT ANY
10             # WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
11             # FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
12             # details.
13             #
14             # You should have received a copy of the GNU General Public License along
15             # with Chart. If not, see <http://www.gnu.org/licenses/>.
16              
17             package App::Chart::Series::Derived::DEMA;
18 1     1   390 use 5.010;
  1         3  
19 1     1   5 use strict;
  1         2  
  1         16  
20 1     1   4 use warnings;
  1         2  
  1         19  
21 1     1   4 use Carp;
  1         2  
  1         48  
22 1     1   331 use Locale::TextDomain 1.17; # for __p()
  1         17155  
  1         5  
23 1     1   5354 use Locale::TextDomain ('App-Chart');
  1         2  
  1         3  
24              
25 1     1   25 use base 'App::Chart::Series::Indicator';
  1         2  
  1         308  
26             use App::Chart::Series::Derived::EMA;
27             use App::Chart::Series::Derived::EMAx2;
28              
29             # http://www.stockworm.com/help/manual/double-ema.html
30             # Example graph PFE (what year?).
31             #
32             # http://trader.online.pl/ELZ/t-i-Double_Smoothed_Exponential_Moving_Average.html
33             # Tradestation example ^SPC 2001.
34             #
35             # http://store.traders.com/-v12-c01-smoothi-pdf.html
36             # Intro of TA S&C magazine, describing as faster.
37             #
38             # http://www.fmlabs.com/reference/DEMA.htm
39             # Formula only.
40             #
41              
42              
43             sub longname { __('DEMA - Double EMA') }
44             sub shortname { __('DEMA') }
45             sub manual { __p('manual-node','Double and Triple Exponential Moving Average') }
46              
47             use constant
48             { type => 'average',
49             priority => -10,
50             parameter_info => [ { name => __('Days'),
51             key => 'dema_days',
52             type => 'integer',
53             minimum => 0,
54             default => 20 } ],
55             };
56              
57             sub new {
58             my ($class, $parent, $N) = @_;
59              
60             $N //= parameter_info()->[0]->{'default'};
61             ($N > 0) or croak "DEMA bad N: $N";
62              
63             return $class->SUPER::new
64             (parent => $parent,
65             parameters => [ $N ],
66             N => $N,
67             arrays => { values => [] },
68             array_aliases => { });
69             }
70             sub proc {
71             my ($class_or_self, $N) = @_;
72             my $ema_proc = App::Chart::Series::Derived::EMA->proc($N);
73             my $ema2_proc = App::Chart::Series::Derived::EMA->proc($N);
74             return sub {
75             my ($value) = @_;
76             my $e = $ema_proc->($value);
77             my $e2 = $ema2_proc->($e);
78             return 2*$e - $e2;
79             };
80             }
81             # A DEMA is in theory influenced by all preceding data, but warmup_count()
82             # is designed to determine a warmup count. The next point will have an
83             # omitted weight of no more than 0.1% of the total. Omitting 0.1% should be
84             # negligable, unless past values are ridiculously bigger than recent ones.
85             #
86             # The implementation here does a binary search for the first i satisfying
87             # Omitted(i)<=0.001, so it's only moderately fast.
88             #
89             sub warmup_count {
90             my ($self_or_class, $N) = @_;
91              
92             if ($N <= 1) { return 0; }
93             my $f = App::Chart::Series::Derived::EMA::N_to_f ($N);
94             return App::Chart::Series::Derived::EMAx2::bsearch_first_true
95             (sub {
96             my ($i) = @_;
97             return (dema_omitted($N,$f,$i)
98             <= App::Chart::Series::Derived::EMA::WARMUP_OMITTED_FRACTION) },
99             $N);
100             }
101              
102             # dema-omitted() returns the fraction (between 0 and 1) of absolute weight
103             # omitted by stopping a DEMA at the f^k term, which means the first k+1
104             # terms.
105             #
106             # The EMA and EMAofEMA omitted totals are
107             #
108             # Q(k) = f^(k+1)
109             # R(k) = f^(k+1) * (k+2 - f * (k+1))
110             #
111             # thus for the DEMA the net signed amount, implemented in
112             # dema_omitted_signed(), is
113             #
114             # S(k) = 2*Q(k) - R(k)
115             # = f^(k+1) * (f*(k+1) - k)
116             #
117             # This grows above 1 up to the f^N term, then the terms go negative and it
118             # decreases towards 1.
119             #
120             # The position of the negative/positive transition is always at f^N. The
121             # coefficient of that f^N term is
122             #
123             # 2 - (1-f)*(N+1) = 2 - (1-(N-1)/(N+1))*(N+1)
124             # = 2 - (N+1-(N-1))
125             # = 2 - N - 1 + N - 1
126             # = 0
127             #
128             # An absolute omitted weight is calculated from the signed omitted amount.
129             # When k>N we can just negate the signed omitted. When k<N we add the
130             # negative terms past N in twice, first to cancel the negative then to add
131             # in as positive.
132             #
133             # The total of all the negatives beyond N is -S(N),
134             #
135             # tail = -S(N) = f^(N+1) * (f*(N+1) - N)
136             # = f^(N+1) * ((N-1)/(N+1) * (N+1) - N)
137             # = f^(N+1) * (N-1 - N)
138             # = f^(N+1)
139             #
140             # Thus the absolute omitted,
141             #
142             # T(k) = / - S(k) if k >= N
143             # \ S(k) + 2*f^(N+1) if k < N
144             #
145             # This is out of a total which is the positive and negative parts added as
146             # abolute values. Knowing pos+neg=1 and neg=-f^(N+1),
147             #
148             # total absolute weight = 1 + 2*f(N+1)
149             #
150             # And that total is applied as a divisor, so the return from `dema-omitted'
151             # is between 0 and 1. (It works to call it with k=-1 for no terms omitted,
152             # the result is 1.0.)
153             #
154              
155             sub dema_omitted {
156             my ($N, $f, $k) = @_;
157             my $tail = $f ** ($N + 1);
158             my $num = dema_omitted_signed ($f, $k);
159             if ($k >= $N) {
160             $num = -$num;
161             } else {
162             $num += 2 * $tail;
163             }
164             return $num / (2*$tail + 1);
165             }
166              
167             sub dema_omitted_signed {
168             my ($f, $k) = @_;
169             return $f**($k+1) * ($f*($k+1) - $k);
170             }
171              
172             1;
173             __END__
174              
175             # =head1 NAME
176             #
177             # App::Chart::Series::Derived::DEMA -- double-exponential moving average
178             #
179             # =head1 SYNOPSIS
180             #
181             # my $series = $parent->DEMA($N);
182             #
183             # =head1 DESCRIPTION
184             #
185             # ...
186             #
187             # =head1 SEE ALSO
188             #
189             # L<App::Chart::Series>, L<App::Chart::Series::Derived::EMA>
190             #
191             # =cut