octave-nkf: scripts/polynomial/polyval.m annotate

annotate scripts/polynomial/polyval.m @ 11110:0be2d25700a7

polynomial/polyval.m: Use Horner's method.

author	Marco Caliari <marco.caliari@univr.it>
date	Mon, 18 Oct 2010 20:13:45 +0200
parents	a8ce6bdecce5
children	fd0a3ac60b0e

rev	line source
7017 a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe] jwe parents: 7016 diff changeset	1 ## Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2004,
9245 16f53d29049f update copyright notices John W. Eaton <jwe@octave.org> parents: 9051 diff changeset	2 ## 2005, 2006, 2007, 2008, 2009 John W. Eaton
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	3 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	4 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	5 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	7 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	9 ## your option) any later version.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	10 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	14 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	15 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	16 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	18 ## <http://www.gnu.org/licenses/>.
904 3470f1e25a79 [project @ 1994-11-09 21:22:15 by jwe] jwe parents: 561 diff changeset	19
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3202 diff changeset	20 ## -- texinfo --
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10224 diff changeset	21 ## @deftypefn {Function File} {@var{y} =} polyval (@var{p}, @var{x})
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	22 ## @deftypefnx {Function File} {@var{y} =} polyval (@var{p}, @var{x}, [], @var{mu})
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10224 diff changeset	23 ## Evaluate the polynomial @var{p} at the specified values of @var{x}. When
a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10224 diff changeset	24 ## @var{mu} is present evaluate the polynomial for
a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10224 diff changeset	25 ## (@var{x}-@var{mu}(1))/@var{mu}(2).
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	26 ## If @var{x} is a vector or matrix, the polynomial is evaluated for each of
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3202 diff changeset	27 ## the elements of @var{x}.
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	28 ## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s})
83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	29 ## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s}, @var{mu})
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	30 ## In addition to evaluating the polynomial, the second output
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	31 ## represents the prediction interval, @var{y} +/- @var{dy}, which
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	32 ## contains at least 50% of the future predictions. To calculate the
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	33 ## prediction interval, the structured variable @var{s}, originating
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	34 ## form `polyfit', must be present.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	35 ## @seealso{polyfit, polyvalm, poly, roots, conv, deconv, residue, filter,
10224 f6e0404421f4 point to polyint in @seealso, not polyinteg John W. Eaton <jwe@octave.org> parents: 9245 diff changeset	36 ## polyderiv, polyint}
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3202 diff changeset	37 ## @end deftypefn
1025 f558749713f1 [project @ 1995-01-11 20:52:10 by jwe] jwe parents: 904 diff changeset	38
3202 44d82b369c78 [project @ 1998-10-29 20:27:57 by jwe] jwe parents: 3085 diff changeset	39 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
2312 204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	40 ## Created: June 1994
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	41 ## Adapted-By: jwe
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	42
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	43 function [y, dy] = polyval (p, x, s, mu)
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	44
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	45 if (nargin < 2 \|\| nargin > 4 \|\| (nargout == 2 && nargin < 3))
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5642 diff changeset	46 print_usage ();
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	47 endif
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	48
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	49 if (nargin < 3)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	50 s = [];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	51 endif
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	52
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	53 if (! (isvector (p) \|\| isempty (p)))
3458 d25bc039237b [project @ 2000-01-19 09:36:14 by jwe] jwe parents: 3457 diff changeset	54 error ("polyval: first argument must be a vector");
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	55 endif
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	56
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	57 if (nargin < 4)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	58 mu = [0, 1];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	59 endif
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	60
2716 2b5c27299cde [project @ 1997-02-22 08:40:55 by jwe] jwe parents: 2325 diff changeset	61 if (isempty (x))
2b5c27299cde [project @ 1997-02-22 08:40:55 by jwe] jwe parents: 2325 diff changeset	62 y = [];
2b5c27299cde [project @ 1997-02-22 08:40:55 by jwe] jwe parents: 2325 diff changeset	63 return;
2b5c27299cde [project @ 1997-02-22 08:40:55 by jwe] jwe parents: 2325 diff changeset	64 endif
2b5c27299cde [project @ 1997-02-22 08:40:55 by jwe] jwe parents: 2325 diff changeset	65
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	66 if (length (p) == 0)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	67 y = p;
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	68 return;
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	69 endif
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	70
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	71 n = length (p) - 1;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	72 x = (x - mu(1)) / mu(2);
11110 0be2d25700a7 polynomial/polyval.m: Use Horner's method. Marco Caliari <marco.caliari@univr.it> parents: 10687 diff changeset	73 y = p(1);
0be2d25700a7 polynomial/polyval.m: Use Horner's method. Marco Caliari <marco.caliari@univr.it> parents: 10687 diff changeset	74 for i = 2:n+1
0be2d25700a7 polynomial/polyval.m: Use Horner's method. Marco Caliari <marco.caliari@univr.it> parents: 10687 diff changeset	75 y = y .* x(:) + p(i);
0be2d25700a7 polynomial/polyval.m: Use Horner's method. Marco Caliari <marco.caliari@univr.it> parents: 10687 diff changeset	76 endfor
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	77 y = reshape (y, size (x));
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	78
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	79 if (nargout == 2)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	80 ## Note: the F-Distribution is generally considered to be single-sided.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	81 ## http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	82 ## t = finv (1-alpha, s.df, s.df);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	83 ## dy = t * sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	84 ## If my inference is correct, then t must equal 1 for polyval.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	85 ## This is because finv (0.5, n, n) = 1.0 for any n.
11110 0be2d25700a7 polynomial/polyval.m: Use Horner's method. Marco Caliari <marco.caliari@univr.it> parents: 10687 diff changeset	86 k = numel (x);
0be2d25700a7 polynomial/polyval.m: Use Horner's method. Marco Caliari <marco.caliari@univr.it> parents: 10687 diff changeset	87 A = (x(:) * ones (1, n+1)) .^ (ones (k, 1) * (n:-1:0));
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	88 dy = sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	89 dy = reshape (dy, size (x));
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	90 endif
1025 f558749713f1 [project @ 1995-01-11 20:52:10 by jwe] jwe parents: 904 diff changeset	91
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	92 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	93
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	94 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	95 %! fail("polyval([1,0;0,1],0:10)");
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	96
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	97 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	98 %! r = 0:10:50;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	99 %! p = poly (r);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	100 %! p = p / max(abs(p));
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	101 %! x = linspace(0,50,11);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	102 %! y = polyval(p,x) + 0.25sin(100x);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	103 %! [pf, s] = polyfit (x, y, numel(r));
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	104 %! [y1, delta] = polyval (pf, x, s);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	105 %! expected = [0.37235, 0.35854, 0.32231, 0.32448, 0.31328, ...
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	106 %! 0.32036, 0.31328, 0.32448, 0.32231, 0.35854, 0.37235];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	107 %! assert (delta, expected, 0.00001)
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	108
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	109 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	110 %! x = 10 + (-2:2);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	111 %! y = [0, 0, 1, 0, 2];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	112 %! p = polyfit (x, y, numel (x) - 1);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	113 %! [pn, s, mu] = polyfit (x, y, numel (x) - 1);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	114 %! y1 = polyval (p, x);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	115 %! yn = polyval (pn, x, [], mu);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	116 %! assert (y1, y, sqrt(eps))
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	117 %! assert (yn, y, sqrt(eps))
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	118
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	119 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	120 %! p = [0, 1, 0];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	121 %! x = 1:10;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	122 %! assert (x, polyval(p,x), eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	123 %! x = x(:);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	124 %! assert (x, polyval(p,x), eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	125 %! x = reshape(x, [2, 5]);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	126 %! assert (x, polyval(p,x), eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	127 %! x = reshape(x, [5, 2]);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	128 %! assert (x, polyval(p,x), eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	129 %! x = reshape(x, [1, 1, 5, 2]);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	130 %! assert (x, polyval(p,x), eps)
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	131

Mercurial > octave-nkf

annotate scripts/polynomial/polyval.m @ 11110:0be2d25700a7