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annotate scripts/polynomial/polyval.m @ 20595:c1a6c31ac29a

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eliminate more simple uses of error_state * ov-classdef.cc: Eliminate simple uses of error_state.
author John W. Eaton <jwe@octave.org>
date Tue, 06 Oct 2015 00:20:02 -0400
parents f1d0f506ee78
children
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 1994-2015 John W. Eaton
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{y} =} polyval (@var{p}, @var{x})
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21 ## @deftypefnx {Function File} {@var{y} =} polyval (@var{p}, @var{x}, [], @var{mu})
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22 ## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s})
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23 ## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s}, @var{mu})
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24 ##
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25 ## Evaluate the polynomial @var{p} at the specified values of @var{x}.
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26 ##
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27 ## If @var{x} is a vector or matrix, the polynomial is evaluated for each of
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28 ## the elements of @var{x}.
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29 ##
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30 ## When @var{mu} is present, evaluate the polynomial for
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31 ## (@var{x}-@var{mu}(1))/@var{mu}(2).
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32 ##
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33 ## In addition to evaluating the polynomial, the second output represents the
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34 ## prediction interval, @var{y} +/- @var{dy}, which contains at least 50% of
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35 ## the future predictions. To calculate the prediction interval, the
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36 ## structured variable @var{s}, originating from @code{polyfit}, must be
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37 ## supplied.
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38 ##
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39 ## @seealso{polyvalm, polyaffine, polyfit, roots, poly}
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40 ## @end deftypefn
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41
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42 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
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43 ## Created: June 1994
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44 ## Adapted-By: jwe
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45
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46 function [y, dy] = polyval (p, x, s = [], mu)
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47
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48 if (nargin < 2 || nargin > 4 || (nargout == 2 && nargin < 3))
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49 print_usage ();
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50 endif
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51
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52 if (isempty (x))
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53 y = [];
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54 return;
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55 elseif (isempty (p))
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56 y = zeros (size (x));
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57 return;
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58 elseif (! isvector (p))
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59 error ("polyval: first argument must be a vector");
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60 endif
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61
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62 if (nargin > 3)
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63 x = (x - mu(1)) / mu(2);
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64 endif
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65
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66 n = length (p) - 1;
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67 y = p(1) * ones (size (x));
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68 for i = 2:n+1
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69 y = y .* x + p(i);
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70 endfor
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71
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72 if (nargout == 2)
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73 ## Note: the F-Distribution is generally considered to be single-sided.
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74 ## http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm
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75 ## t = finv (1-alpha, s.df, s.df);
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76 ## dy = t * sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df)
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77 ## If my inference is correct, then t must equal 1 for polyval.
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78 ## This is because finv (0.5, n, n) = 1.0 for any n.
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79 try
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80 k = numel (x);
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81 A = (x(:) * ones (1, n+1)) .^ (ones (k, 1) * (n:-1:0));
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82 dy = sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df);
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83 dy = reshape (dy, size (x));
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84 catch
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85 if (isempty (s))
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86 error ("polyval: third input is required.");
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87 elseif (isstruct (s)
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88 && all (ismember ({"R", "normr", "df"}, fieldnames (s))))
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89 error (lasterr ());
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90 elseif (isstruct (s))
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91 error ("polyval: third input is missing the required fields.");
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92 else
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93 error ("polyval: third input is not a structure.");
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94 endif
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95 end_try_catch
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96 endif
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97
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98 endfunction
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99
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100
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101 %!fail ("polyval ([1,0;0,1],0:10)")
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102
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103 %!test
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104 %! r = 0:10:50;
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105 %! p = poly (r);
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106 %! p = p / max (abs (p));
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107 %! x = linspace (0,50,11);
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108 %! y = polyval (p,x) + 0.25*sin (100*x);
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109 %! [pf, s] = polyfit (x, y, numel (r));
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110 %! [y1, delta] = polyval (pf, x, s);
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111 %! expected = [0.37235, 0.35854, 0.32231, 0.32448, 0.31328, ...
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112 %! 0.32036, 0.31328, 0.32448, 0.32231, 0.35854, 0.37235];
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113 %! assert (delta, expected, 0.00001);
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114
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115 %!test
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116 %! x = 10 + (-2:2);
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117 %! y = [0, 0, 1, 0, 2];
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118 %! p = polyfit (x, y, numel (x) - 1);
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119 %! [pn, s, mu] = polyfit (x, y, numel (x) - 1);
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120 %! y1 = polyval (p, x);
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121 %! yn = polyval (pn, x, [], mu);
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122 %! assert (y1, y, sqrt (eps));
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123 %! assert (yn, y, sqrt (eps));
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124
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125 %!test
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126 %! p = [0, 1, 0];
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127 %! x = 1:10;
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128 %! assert (x, polyval (p,x), eps);
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129 %! x = x(:);
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130 %! assert (x, polyval (p,x), eps);
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131 %! x = reshape (x, [2, 5]);
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132 %! assert (x, polyval (p,x), eps);
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133 %! x = reshape (x, [5, 2]);
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134 %! assert (x, polyval (p,x), eps);
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135 %! x = reshape (x, [1, 1, 5, 2]);
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136 %! assert (x, polyval (p,x), eps);
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83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
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137
12475
009068efc66d Properly evaluate zeroth order polynomials.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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138 %!test
009068efc66d Properly evaluate zeroth order polynomials.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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139 %! p = [1];
009068efc66d Properly evaluate zeroth order polynomials.
Ben Abbott <bpabbott@mac.com>
parents: 11587
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140 %! x = 1:10;
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141 %! y = ones (size (x));
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parents: 14138
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142 %! assert (y, polyval (p,x), eps);
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Ben Abbott <bpabbott@mac.com>
parents: 11587
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143 %! x = x(:);
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parents: 14138
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144 %! y = ones (size (x));
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Rik <octave@nomad.inbox5.com>
parents: 14138
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145 %! assert (y, polyval (p,x), eps);
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Rik <octave@nomad.inbox5.com>
parents: 14138
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146 %! x = reshape (x, [2, 5]);
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parents: 14138
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147 %! y = ones (size (x));
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parents: 14138
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148 %! assert (y, polyval (p,x), eps);
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Rik <octave@nomad.inbox5.com>
parents: 14138
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149 %! x = reshape (x, [5, 2]);
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parents: 14138
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150 %! y = ones (size (x));
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Rik <octave@nomad.inbox5.com>
parents: 14138
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151 %! assert (y, polyval (p,x), eps);
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Rik <octave@nomad.inbox5.com>
parents: 14138
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152 %! x = reshape (x, [1, 1, 5, 2]);
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Ben Abbott <bpabbott@mac.com>
parents: 11587
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153
12982
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Ben Abbott <bpabbott@mac.com>
parents: 12482
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154 %!assert (zeros (1, 10), polyval ([], 1:10))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
Ben Abbott <bpabbott@mac.com>
parents: 12482
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155 %!assert ([], polyval (1, []))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
Ben Abbott <bpabbott@mac.com>
parents: 12482
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156 %!assert ([], polyval ([], []))
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157