Mercurial > octave-nkf
annotate scripts/polynomial/polyval.m @ 14868:5d3a684236b0
maint: Use Octave coding conventions for cuddling parentheses in scripts directory
* lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m,
colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m,
int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m,
__isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m,
rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m,
inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m,
gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m,
ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m,
compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m,
getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m,
__xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m,
fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m,
copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m,
installed_packages.m, is_architecture_dependent.m, load_package_dirs.m,
print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m,
allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m,
comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m,
fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m,
mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m,
polar.m, print.m, __add_datasource__.m, __add_default_menu__.m,
__axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m,
__errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m,
__ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m,
__go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m,
__pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m,
__stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m,
__uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m,
ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m,
surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m,
mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m,
addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m,
arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m,
hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m,
stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m,
__sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m,
treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m,
magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m,
quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m,
bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m,
kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m,
z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m,
strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m,
test.m, now.m: Use Octave coding conventions for cuddling parentheses in
scripts directory.
author | Rik <octave@nomad.inbox5.com> |
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date | Tue, 17 Jul 2012 07:08:39 -0700 |
parents | f3d52523cde1 |
children | f3b5cadfd6d5 |
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)") |
7411 | 98 |
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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 |