annotate scripts/signal/arma_rnd.m @ 27923:bd51beb6205e

update formatting of copyright notices * Use <https://octave.org/copyright/> instead of <https://octave.org/COPYRIGHT.html/>. * For consistency with other comments in the Octave sources, use C++-style comments for copyright blocks in C and C++ files. * Use delimiters above and below copyright blocks that are appropriate for the language used in the file. * Eliminate extra spacing inside copyright blocks. * lex.ll (looks_like_copyright): Also allow newlines and carriage returns before the word "Copyright". * scripts/mk-doc.pl (gethelp): Also skip empty comment lines. * bp-table.cc, type.m: Adjust tests.
author John W. Eaton <jwe@octave.org>
date Wed, 08 Jan 2020 11:59:41 -0500
parents 1891570abac8
children b09432b20a84
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 1995-2020 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {} arma_rnd (@var{a}, @var{b}, @var{v}, @var{t}, @var{n})
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28 ## Return a simulation of the ARMA model.
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29 ##
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30 ## The ARMA model is defined by
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31 ##
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32 ## @example
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33 ## @group
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34 ## x(n) = a(1) * x(n-1) + @dots{} + a(k) * x(n-k)
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35 ## + e(n) + b(1) * e(n-1) + @dots{} + b(l) * e(n-l)
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36 ## @end group
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37 ## @end example
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38 ##
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39 ## @noindent
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40 ## in which @var{k} is the length of vector @var{a}, @var{l} is the length of
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41 ## vector @var{b} and @var{e} is Gaussian white noise with variance @var{v}.
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42 ## The function returns a vector of length @var{t}.
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43 ##
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44 ## The optional parameter @var{n} gives the number of dummy @var{x}(@var{i})
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45 ## used for initialization, i.e., a sequence of length @var{t}+@var{n} is
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46 ## generated and @var{x}(@var{n}+1:@var{t}+@var{n}) is returned. If @var{n}
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47 ## is omitted, @var{n} = 100 is used.
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48 ## @end deftypefn
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50 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
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51 ## Description: Simulate an ARMA process
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52
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53 function x = arma_rnd (a, b, v, t, n)
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54
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55 if (nargin == 4)
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56 n = 100;
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57 elseif (nargin == 5)
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58 if (! isscalar (n))
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59 error ("arma_rnd: N must be a scalar");
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60 endif
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61 else
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62 print_usage ();
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63 endif
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64
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65 if ((min (size (a)) > 1) || (min (size (b)) > 1))
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66 error ("arma_rnd: A and B must not be matrices");
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67 endif
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68
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69 if (! isscalar (t))
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70 error ("arma_rnd: T must be a scalar");
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71 endif
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72
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73 ar = length (a);
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74 br = length (b);
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75
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76 a = reshape (a, ar, 1);
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77 b = reshape (b, br, 1);
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78
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79 ## Apply our notational convention.
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80 a = [1; -a];
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81 b = [1; b];
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82
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83 n = min (n, ar + br);
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84
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85 e = sqrt (v) * randn (t + n, 1);
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86
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87 x = filter (b, a, e);
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88 x = x(n + 1 : t + n);
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89
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90 endfunction