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annotate scripts/polynomial/polyval.m @ 14363:f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
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celldisp.m, chop.m, circshift.m, colon.m, common_size.m, cplxpair.m,
cumtrapz.m, curl.m, dblquad.m, deal.m, divergence.m, flipdim.m, fliplr.m,
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get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m,
imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m,
textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m,
duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m,
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hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m,
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wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
findstr.m, hex2dec.m, index.m, isletter.m, mat2str.m, rindex.m, str2num.m,
strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m,
substr.m, validatestring.m, demo.m, example.m, fail.m, speed.m, addtodate.m,
asctime.m, clock.m, ctime.m, date.m, datenum.m, datetick.m, datevec.m,
eomday.m, etime.m, is_leap_year.m, now.m:
Use Octave coding conventions in all m-file %!test blocks
author | Rik <octave@nomad.inbox5.com> |
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date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 72c96de7a403 |
children | 5d3a684236b0 |
rev | line source |
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1 ## Copyright (C) 1994-2012 John W. Eaton |
2313 | 2 ## |
3 ## This file is part of Octave. | |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
2313 | 9 ## |
10 ## Octave is distributed in the hope that it will be useful, but | |
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 ## General Public License for more details. | |
14 ## | |
15 ## You should have received a copy of the GNU General Public License | |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
904 | 18 |
3368 | 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 ## Evaluate the polynomial @var{p} at the specified values of @var{x}. When |
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23 ## @var{mu} is present, evaluate the polynomial for |
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24 ## (@var{x}-@var{mu}(1))/@var{mu}(2). |
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25 ## If @var{x} is a vector or matrix, the polynomial is evaluated for each of |
3368 | 26 ## the elements of @var{x}. |
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27 ## |
7501 | 28 ## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s}) |
29 ## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s}, @var{mu}) | |
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30 ## In addition to evaluating the polynomial, the second output |
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31 ## represents the prediction interval, @var{y} +/- @var{dy}, which |
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32 ## contains at least 50% of the future predictions. To calculate the |
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33 ## prediction interval, the structured variable @var{s}, originating |
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34 ## from @code{polyfit}, must be supplied. |
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35 ## @seealso{polyvalm, polyaffine, polyfit, roots, poly} |
3368 | 36 ## @end deftypefn |
1025 | 37 |
3202 | 38 ## Author: Tony Richardson <arichard@stark.cc.oh.us> |
2312 | 39 ## Created: June 1994 |
40 ## Adapted-By: jwe | |
561 | 41 |
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42 function [y, dy] = polyval (p, x, s = [], mu) |
561 | 43 |
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44 if (nargin < 2 || nargin > 4 || (nargout == 2 && nargin < 3)) |
6046 | 45 print_usage (); |
561 | 46 endif |
47 | |
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48 if (isempty (x)) |
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49 y = []; |
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50 return; |
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51 elseif (isempty (p)) |
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52 y = zeros (size (x)); |
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53 return; |
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54 elseif (! isvector (p)) |
3458 | 55 error ("polyval: first argument must be a vector"); |
561 | 56 endif |
57 | |
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58 if (nargin > 3) |
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59 x = (x - mu(1)) / mu(2); |
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60 endif |
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61 |
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62 n = length (p) - 1; |
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63 y = p(1) * ones (size (x)); |
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64 for i = 2:n+1 |
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65 y = y .* x + p(i); |
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66 endfor |
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67 |
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68 if (nargout == 2) |
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69 ## Note: the F-Distribution is generally considered to be single-sided. |
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70 ## http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm |
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71 ## t = finv (1-alpha, s.df, s.df); |
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72 ## dy = t * sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df) |
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73 ## If my inference is correct, then t must equal 1 for polyval. |
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74 ## This is because finv (0.5, n, n) = 1.0 for any n. |
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75 try |
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76 k = numel (x); |
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77 A = (x(:) * ones (1, n+1)) .^ (ones (k, 1) * (n:-1:0)); |
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78 dy = sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df); |
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79 dy = reshape (dy, size (x)); |
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80 catch |
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81 if (isempty (s)) |
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82 error ("polyval: third input is required.") |
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83 elseif (isstruct (s) |
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84 && all (ismember ({"R", "normr", "df"}, fieldnames (s)))) |
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85 error (lasterr ()) |
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86 elseif (isstruct (s)) |
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87 error ("polyval: third input is missing the required fields."); |
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88 else |
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89 error ("polyval: third input is not a structure."); |
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90 endif |
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91 end_try_catch |
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92 endif |
1025 | 93 |
561 | 94 endfunction |
7411 | 95 |
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96 |
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97 %!fail ("polyval ([1,0;0,1],0:10)") |
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99 %!test |
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100 %! r = 0:10:50; |
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101 %! p = poly (r); |
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102 %! p = p / max (abs (p)); |
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103 %! x = linspace (0,50,11); |
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104 %! y = polyval (p,x) + 0.25*sin (100*x); |
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105 %! [pf, s] = polyfit (x, y, numel (r)); |
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106 %! [y1, delta] = polyval (pf, x, s); |
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107 %! expected = [0.37235, 0.35854, 0.32231, 0.32448, 0.31328, ... |
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108 %! 0.32036, 0.31328, 0.32448, 0.32231, 0.35854, 0.37235]; |
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109 %! assert (delta, expected, 0.00001); |
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111 %!test |
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112 %! x = 10 + (-2:2); |
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113 %! y = [0, 0, 1, 0, 2]; |
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114 %! p = polyfit (x, y, numel (x) - 1); |
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115 %! [pn, s, mu] = polyfit (x, y, numel (x) - 1); |
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116 %! y1 = polyval (p, x); |
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117 %! yn = polyval (pn, x, [], mu); |
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118 %! assert (y1, y, sqrt (eps)); |
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119 %! assert (yn, y, sqrt (eps)); |
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121 %!test |
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122 %! p = [0, 1, 0]; |
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123 %! x = 1:10; |
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124 %! assert (x, polyval (p,x), eps); |
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125 %! x = x(:); |
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126 %! assert (x, polyval (p,x), eps); |
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127 %! x = reshape(x, [2, 5]); |
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128 %! assert (x, polyval (p,x), eps); |
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129 %! x = reshape(x, [5, 2]); |
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130 %! assert (x, polyval (p,x), eps); |
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131 %! x = reshape (x, [1, 1, 5, 2]); |
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132 %! assert (x, polyval (p,x), eps); |
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134 %!test |
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135 %! p = [1]; |
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136 %! x = 1:10; |
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137 %! y = ones (size (x)); |
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138 %! assert (y, polyval (p,x), eps); |
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139 %! x = x(:); |
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140 %! y = ones (size (x)); |
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141 %! assert (y, polyval (p,x), eps); |
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142 %! x = reshape (x, [2, 5]); |
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143 %! y = ones (size (x)); |
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144 %! assert (y, polyval (p,x), eps); |
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145 %! x = reshape (x, [5, 2]); |
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146 %! y = ones (size (x)); |
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147 %! assert (y, polyval (p,x), eps); |
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148 %! x = reshape (x, [1, 1, 5, 2]); |
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149 |
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150 %!assert (zeros (1, 10), polyval ([], 1:10)) |
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151 %!assert ([], polyval (1, [])) |
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152 %!assert ([], polyval ([], [])) |
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153 |