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annotate scripts/polynomial/polyval.m @ 19790:446c46af4b42 stable

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strip trailing whitespace from most source files * Makefile.am, NEWS, build-aux/common.mk, configure.ac, doc/Makefile.am, doc/doxyhtml/Makefile.am, doc/interpreter/Makefile.am, doc/interpreter/arith.txi, doc/interpreter/audio.txi, doc/interpreter/basics.txi, doc/interpreter/bugs.txi, doc/interpreter/container.txi, doc/interpreter/cp-idx.txi, doc/interpreter/data.txi, doc/interpreter/debug.txi, doc/interpreter/diagperm.txi, doc/interpreter/diffeq.txi, doc/interpreter/doccheck/README, doc/interpreter/doccheck/spellcheck, doc/interpreter/emacs.txi, doc/interpreter/errors.txi, doc/interpreter/eval.txi, doc/interpreter/expr.txi, doc/interpreter/external.txi, doc/interpreter/fn-idx.txi, doc/interpreter/func.txi, doc/interpreter/geometry.txi, doc/interpreter/geometryimages.m, doc/interpreter/gpl.txi, doc/interpreter/grammar.txi, doc/interpreter/gui.txi, doc/interpreter/image.txi, doc/interpreter/install.txi, doc/interpreter/interp.txi, doc/interpreter/interpimages.m, 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scripts/statistics/distributions/frnd.m, scripts/statistics/distributions/gamrnd.m, scripts/statistics/distributions/geornd.m, scripts/statistics/distributions/hygernd.m, scripts/statistics/distributions/kolmogorov_smirnov_cdf.m, scripts/statistics/distributions/laplace_cdf.m, scripts/statistics/distributions/laplace_pdf.m, scripts/statistics/distributions/logistic_cdf.m, scripts/statistics/distributions/logistic_pdf.m, scripts/statistics/distributions/lognrnd.m, scripts/statistics/distributions/nbincdf.m, scripts/statistics/distributions/nbininv.m, scripts/statistics/distributions/nbinpdf.m, scripts/statistics/distributions/nbinrnd.m, scripts/statistics/distributions/normrnd.m, scripts/statistics/distributions/poissinv.m, scripts/statistics/distributions/poissrnd.m, scripts/statistics/distributions/tinv.m, scripts/statistics/distributions/trnd.m, scripts/statistics/distributions/unidcdf.m, scripts/statistics/distributions/unidpdf.m, scripts/statistics/distributions/unidrnd.m, scripts/statistics/distributions/unifrnd.m, scripts/statistics/distributions/wblrnd.m, scripts/statistics/models/module.mk, scripts/statistics/tests/kruskal_wallis_test.m, scripts/strings/base2dec.m, scripts/strings/deblank.m, scripts/strings/dec2base.m, scripts/strings/dec2bin.m, scripts/strings/dec2hex.m, scripts/strings/mat2str.m, scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m, scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strjoin.m, scripts/strings/strsplit.m, scripts/strings/strtok.m, scripts/strings/strtrim.m, scripts/strings/strtrunc.m, scripts/strings/substr.m, scripts/testfun/__run_test_suite__.m, scripts/testfun/speed.m, scripts/testfun/test.m, scripts/time/asctime.m, scripts/time/datenum.m, scripts/time/datevec.m, scripts/time/weekday.m, src/Makefile.am, test/Makefile.am, test/build-bc-overload-tests.sh, test/build-sparse-tests.sh, test/jit.tst, test/line-continue.tst: Strip trailing whitespace.
author John W. Eaton <jwe@octave.org>
date Tue, 20 Jan 2015 08:26:57 -0500
parents d63878346099
children 4197fc428c7d
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1 ## Copyright (C) 1994-2013 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
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
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8 ## your option) any later version.
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9 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
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10 ## Octave is distributed in the hope that it will be useful, but
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
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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}. When
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26 ## @var{mu} is present, evaluate the polynomial for
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27 ## (@var{x}-@var{mu}(1))/@var{mu}(2).
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28 ## If @var{x} is a vector or matrix, the polynomial is evaluated for each of
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29 ## the elements of @var{x}.
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30 ##
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31 ## In addition to evaluating the polynomial, the second output
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32 ## represents the prediction interval, @var{y} +/- @var{dy}, which
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33 ## contains at least 50% of the future predictions. To calculate the
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34 ## prediction interval, the structured variable @var{s}, originating
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614505385171 doc: Overhaul docstrings for polynomial functions.
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35 ## from @code{polyfit}, must be supplied.
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36 ##
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37 ## @seealso{polyvalm, polyaffine, polyfit, roots, poly}
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38 ## @end deftypefn
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39
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40 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
2312
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe]
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41 ## Created: June 1994
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe]
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42 ## Adapted-By: jwe
561
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43
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44 function [y, dy] = polyval (p, x, s = [], mu)
561
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe]
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45
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46 if (nargin < 2 || nargin > 4 || (nargout == 2 && nargin < 3))
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47 print_usage ();
561
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48 endif
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe]
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49
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50 if (isempty (x))
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51 y = [];
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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52 return;
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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53 elseif (isempty (p))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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54 y = zeros (size (x));
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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55 return;
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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56 elseif (! isvector (p))
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57 error ("polyval: first argument must be a vector");
561
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe]
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58 endif
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe]
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59
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60 if (nargin > 3)
3244c6e0af4a polynomial/polyval.m: Compute offset/normalization only when needed.
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61 x = (x - mu(1)) / mu(2);
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62 endif
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63
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64 n = length (p) - 1;
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diff changeset
65 y = p(1) * ones (size (x));
11110
0be2d25700a7 polynomial/polyval.m: Use Horner's method.
Marco Caliari <marco.caliari@univr.it>
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diff changeset
66 for i = 2:n+1
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67 y = y .* x + p(i);
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diff changeset
68 endfor
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69
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70 if (nargout == 2)
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71 ## Note: the F-Distribution is generally considered to be single-sided.
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72 ## http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm
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73 ## t = finv (1-alpha, s.df, s.df);
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74 ## dy = t * sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df)
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75 ## If my inference is correct, then t must equal 1 for polyval.
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76 ## This is because finv (0.5, n, n) = 1.0 for any n.
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77 try
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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78 k = numel (x);
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diff changeset
79 A = (x(:) * ones (1, n+1)) .^ (ones (k, 1) * (n:-1:0));
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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80 dy = sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df);
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81 dy = reshape (dy, size (x));
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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diff changeset
82 catch
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility).
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83 if (isempty (s))
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84 error ("polyval: third input is required.");
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85 elseif (isstruct (s)
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86 && all (ismember ({"R", "normr", "df"}, fieldnames (s))))
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diff changeset
87 error (lasterr ());
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88 elseif (isstruct (s))
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diff changeset
89 error ("polyval: third input is missing the required fields.");
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90 else
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91 error ("polyval: third input is not a structure.");
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92 endif
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93 end_try_catch
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94 endif
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95
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96 endfunction
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97
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98
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99 %!fail ("polyval ([1,0;0,1],0:10)")
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100
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101 %!test
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102 %! r = 0:10:50;
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103 %! p = poly (r);
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104 %! p = p / max (abs (p));
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105 %! x = linspace (0,50,11);
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106 %! y = polyval (p,x) + 0.25*sin (100*x);
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107 %! [pf, s] = polyfit (x, y, numel (r));
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108 %! [y1, delta] = polyval (pf, x, s);
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109 %! expected = [0.37235, 0.35854, 0.32231, 0.32448, 0.31328, ...
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diff changeset
110 %! 0.32036, 0.31328, 0.32448, 0.32231, 0.35854, 0.37235];
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111 %! assert (delta, expected, 0.00001);
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112
7500
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113 %!test
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114 %! x = 10 + (-2:2);
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115 %! y = [0, 0, 1, 0, 2];
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116 %! p = polyfit (x, y, numel (x) - 1);
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117 %! [pn, s, mu] = polyfit (x, y, numel (x) - 1);
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118 %! y1 = polyval (p, x);
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119 %! yn = polyval (pn, x, [], mu);
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120 %! assert (y1, y, sqrt (eps));
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121 %! assert (yn, y, sqrt (eps));
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122
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123 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval
Ben Abbott <bpabbott@mac.com>
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124 %! p = [0, 1, 0];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval
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125 %! x = 1:10;
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126 %! assert (x, polyval (p,x), eps);
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127 %! x = x(:);
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128 %! assert (x, polyval (p,x), eps);
14868
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129 %! x = reshape (x, [2, 5]);
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130 %! assert (x, polyval (p,x), eps);
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131 %! x = reshape (x, [5, 2]);
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132 %! assert (x, polyval (p,x), eps);
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133 %! x = reshape (x, [1, 1, 5, 2]);
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134 %! assert (x, polyval (p,x), eps);
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135
12475
009068efc66d Properly evaluate zeroth order polynomials.
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136 %!test
009068efc66d Properly evaluate zeroth order polynomials.
Ben Abbott <bpabbott@mac.com>
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137 %! p = [1];
009068efc66d Properly evaluate zeroth order polynomials.
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138 %! x = 1:10;
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139 %! y = ones (size (x));
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140 %! assert (y, polyval (p,x), eps);
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141 %! x = x(:);
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142 %! y = ones (size (x));
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143 %! assert (y, polyval (p,x), eps);
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144 %! x = reshape (x, [2, 5]);
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145 %! y = ones (size (x));
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146 %! assert (y, polyval (p,x), eps);
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147 %! x = reshape (x, [5, 2]);
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148 %! y = ones (size (x));
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149 %! assert (y, polyval (p,x), eps);
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150 %! x = reshape (x, [1, 1, 5, 2]);
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diff changeset
151
12982
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152 %!assert (zeros (1, 10), polyval ([], 1:10))
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153 %!assert ([], polyval (1, []))
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154 %!assert ([], polyval ([], []))
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diff changeset
155