X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;f=octave_packages%2Fm%2Fpolynomial%2Fpolyval.m;fp=octave_packages%2Fm%2Fpolynomial%2Fpolyval.m;h=cb4895c783028eaebd024955bfba3afa3b1f19ac;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git
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+## Copyright (C) 1994-2012 John W. Eaton
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING. If not, see
+## .
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{y} =} polyval (@var{p}, @var{x})
+## @deftypefnx {Function File} {@var{y} =} polyval (@var{p}, @var{x}, [], @var{mu})
+## Evaluate the polynomial @var{p} at the specified values of @var{x}. When
+## @var{mu} is present, evaluate the polynomial for
+## (@var{x}-@var{mu}(1))/@var{mu}(2).
+## If @var{x} is a vector or matrix, the polynomial is evaluated for each of
+## the elements of @var{x}.
+##
+## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s})
+## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s}, @var{mu})
+## In addition to evaluating the polynomial, the second output
+## represents the prediction interval, @var{y} +/- @var{dy}, which
+## contains at least 50% of the future predictions. To calculate the
+## prediction interval, the structured variable @var{s}, originating
+## from @code{polyfit}, must be supplied.
+## @seealso{polyvalm, polyaffine, polyfit, roots, poly}
+## @end deftypefn
+
+## Author: Tony Richardson
+## Created: June 1994
+## Adapted-By: jwe
+
+function [y, dy] = polyval (p, x, s = [], mu)
+
+ if (nargin < 2 || nargin > 4 || (nargout == 2 && nargin < 3))
+ print_usage ();
+ endif
+
+ if (isempty (x))
+ y = [];
+ return;
+ elseif (isempty (p))
+ y = zeros (size (x));
+ return;
+ elseif (! isvector (p))
+ error ("polyval: first argument must be a vector");
+ endif
+
+ if (nargin > 3)
+ x = (x - mu(1)) / mu(2);
+ endif
+
+ n = length (p) - 1;
+ y = p(1) * ones (size (x));
+ for i = 2:n+1
+ y = y .* x + p(i);
+ endfor
+
+ if (nargout == 2)
+ ## Note: the F-Distribution is generally considered to be single-sided.
+ ## http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm
+ ## t = finv (1-alpha, s.df, s.df);
+ ## dy = t * sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df)
+ ## If my inference is correct, then t must equal 1 for polyval.
+ ## This is because finv (0.5, n, n) = 1.0 for any n.
+ try
+ k = numel (x);
+ A = (x(:) * ones (1, n+1)) .^ (ones (k, 1) * (n:-1:0));
+ dy = sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df);
+ dy = reshape (dy, size (x));
+ catch
+ if (isempty (s))
+ error ("polyval: third input is required.")
+ elseif (isstruct (s)
+ && all (ismember ({"R", "normr", "df"}, fieldnames (s))))
+ error (lasterr ())
+ elseif (isstruct (s))
+ error ("polyval: third input is missing the required fields.");
+ else
+ error ("polyval: third input is not a structure.");
+ endif
+ end_try_catch
+ endif
+
+endfunction
+
+%!test
+%! fail("polyval([1,0;0,1],0:10)");
+
+%!test
+%! r = 0:10:50;
+%! p = poly (r);
+%! p = p / max(abs(p));
+%! x = linspace(0,50,11);
+%! y = polyval(p,x) + 0.25*sin(100*x);
+%! [pf, s] = polyfit (x, y, numel(r));
+%! [y1, delta] = polyval (pf, x, s);
+%! expected = [0.37235, 0.35854, 0.32231, 0.32448, 0.31328, ...
+%! 0.32036, 0.31328, 0.32448, 0.32231, 0.35854, 0.37235];
+%! assert (delta, expected, 0.00001)
+
+%!test
+%! x = 10 + (-2:2);
+%! y = [0, 0, 1, 0, 2];
+%! p = polyfit (x, y, numel (x) - 1);
+%! [pn, s, mu] = polyfit (x, y, numel (x) - 1);
+%! y1 = polyval (p, x);
+%! yn = polyval (pn, x, [], mu);
+%! assert (y1, y, sqrt(eps))
+%! assert (yn, y, sqrt(eps))
+
+%!test
+%! p = [0, 1, 0];
+%! x = 1:10;
+%! assert (x, polyval(p,x), eps)
+%! x = x(:);
+%! assert (x, polyval(p,x), eps)
+%! x = reshape(x, [2, 5]);
+%! assert (x, polyval(p,x), eps)
+%! x = reshape(x, [5, 2]);
+%! assert (x, polyval(p,x), eps)
+%! x = reshape(x, [1, 1, 5, 2]);
+%! assert (x, polyval(p,x), eps)
+
+%!test
+%! p = [1];
+%! x = 1:10;
+%! y = ones(size(x));
+%! assert (y, polyval(p,x), eps)
+%! x = x(:);
+%! y = ones(size(x));
+%! assert (y, polyval(p,x), eps)
+%! x = reshape(x, [2, 5]);
+%! y = ones(size(x));
+%! assert (y, polyval(p,x), eps)
+%! x = reshape(x, [5, 2]);
+%! y = ones(size(x));
+%! assert (y, polyval(p,x), eps)
+%! x = reshape(x, [1, 1, 5, 2]);
+
+%!assert (zeros (1, 10), polyval ([], 1:10))
+%!assert ([], polyval (1, []))
+%!assert ([], polyval ([], []))