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

annotate scripts/polynomial/polyfit.m @ 11918:f2af2233ce7f release-3-0-x

polyfit.m: Fixed tests.

author	Ben Abbott <bpabbott@mac.com>
date	Mon, 12 Jan 2009 12:14:06 +0100
parents	deb777a926ee
children

rev	line source
7017 a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe] jwe parents: 7016 diff changeset	1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2003, 2005, 2006,
a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe] jwe parents: 7016 diff changeset	2 ## 2007 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: 6157 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: 6157 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: 6157 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: 6157 diff changeset	18 ## <http://www.gnu.org/licenses/>.
2303 5cffc4b8de57 [project @ 1996-06-24 09:15:24 by jwe] jwe parents: 2261 diff changeset	19
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3246 diff changeset	20 ## -- texinfo --
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	21 ## @deftypefn {Function File} {[@var{p}, @var{s}, @var{mu}] =} polyfit (@var{x}, @var{y}, @var{n})
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3246 diff changeset	22 ## Return the coefficients of a polynomial @var{p}(@var{x}) of degree
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	23 ## @var{n} that minimizes the least-squares-error of the fit.
3418 ca92c9d3f882 [project @ 2000-01-12 03:07:47 by jwe] jwe parents: 3368 diff changeset	24 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	25 ## The polynomial coefficients are returned in a row vector.
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	26 ##
11917 deb777a926ee style fixes John W. Eaton <jwe@octave.org> parents: 11916 diff changeset	27 ## The second output is a structure containing the following fields:
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3418 diff changeset	28 ##
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	29 ## @table @samp
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	30 ## @item R
11917 deb777a926ee style fixes John W. Eaton <jwe@octave.org> parents: 11916 diff changeset	31 ## Triangular factor R from the QR decomposition.
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	32 ## @item X
11917 deb777a926ee style fixes John W. Eaton <jwe@octave.org> parents: 11916 diff changeset	33 ## The Vandermonde matrix used to compute the polynomial coefficients.
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	34 ## @item df
11917 deb777a926ee style fixes John W. Eaton <jwe@octave.org> parents: 11916 diff changeset	35 ## The degrees of freedom.
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	36 ## @item normr
11917 deb777a926ee style fixes John W. Eaton <jwe@octave.org> parents: 11916 diff changeset	37 ## The norm of the residuals.
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	38 ## @item yf
11917 deb777a926ee style fixes John W. Eaton <jwe@octave.org> parents: 11916 diff changeset	39 ## The values of the polynomial for each value of @var{x}.
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	40 ## @end table
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	41 ##
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	42 ## The second output may be used by @code{polyval} to calculate the
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	43 ## statistical error limits of the predicted values.
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	44 ##
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	45 ## When the third output, @var{mu}, is present the
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	46 ## coefficients, @var{p}, are associated with a polynomial in
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	47 ## @var{xhat} = (@var{x}-@var{mu}(1))/@var{mu}(2).
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	48 ## Where @var{mu}(1) = mean (@var{x}), and @var{mu}(2) = std (@var{x}).
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	49 ## This linear transformation of @var{x} improves the numerical
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	50 ## stability of the fit.
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	51 ## @seealso{polyval, polyconf, residue}
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3246 diff changeset	52 ## @end deftypefn
2311 2b5788792cad [project @ 1996-07-11 20:18:38 by jwe] jwe parents: 2303 diff changeset	53
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5395 diff changeset	54 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
2312 204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	55 ## Created: 13 December 1994
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	56 ## Adapted-By: jwe
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	57
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	58 function [p, s, mu] = polyfit (x, y, n)
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	59
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	60 if (nargin < 3 \|\| nargin > 4)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	61 print_usage ();
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	62 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	63
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	64 if (nargout > 2)
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	65 ## Normalized the x values.
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	66 mu = [mean(x), std(x)];
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	67 x = (x - mu(1)) / mu(2);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	68 endif
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	69
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	70 if (! size_equal (x, y))
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	71 error ("polyfit: x and y must be vectors of the same size");
1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	72 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	73
4030 22bd65326ec1 [project @ 2002-08-09 18:58:13 by jwe] jwe parents: 3426 diff changeset	74 if (! (isscalar (n) && n >= 0 && ! isinf (n) && n == round (n)))
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	75 error ("polyfit: n must be a nonnegative integer");
1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	76 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	77
3091 b06dcbb6b3b1 [project @ 1997-10-10 16:26:47 by jwe] jwe parents: 3069 diff changeset	78 y_is_row_vector = (rows (y) == 1);
b06dcbb6b3b1 [project @ 1997-10-10 16:26:47 by jwe] jwe parents: 3069 diff changeset	79
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	80 ## Reshape x & y into column vectors.
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	81 l = numel (x);
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	82 x = reshape (x, l, 1);
1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	83 y = reshape (y, l, 1);
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	84
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	85 ## Construct the Vandermonde matrix.
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	86 v = (x * ones (1, n+1)) .^ (ones (l, 1) * (n : -1 : 0));
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	87
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	88 ## Solve by QR decomposition.
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	89 [q, r, k] = qr (v, 0);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	90 p = r \ (y' * q)';
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	91 p(k) = p;
3091 b06dcbb6b3b1 [project @ 1997-10-10 16:26:47 by jwe] jwe parents: 3069 diff changeset	92
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	93 if (nargout > 1)
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	94 yf = v*p;
3105 f936c7f5074f [project @ 1997-11-19 04:36:17 by jwe] jwe parents: 3092 diff changeset	95
f936c7f5074f [project @ 1997-11-19 04:36:17 by jwe] jwe parents: 3092 diff changeset	96 if (y_is_row_vector)
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	97 s.yf = yf.';
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	98 else
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	99 s.yf = yf;
3105 f936c7f5074f [project @ 1997-11-19 04:36:17 by jwe] jwe parents: 3092 diff changeset	100 endif
3091 b06dcbb6b3b1 [project @ 1997-10-10 16:26:47 by jwe] jwe parents: 3069 diff changeset	101
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	102 s.R = r;
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	103 s.X = v;
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	104 s.df = l - n - 1;
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	105 s.normr = norm (yf - y);
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	106 endif
1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	107
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	108 ## Return a row vector.
5395 8db4eb48f546 [project @ 2005-06-16 20:19:18 by jwe] jwe parents: 5307 diff changeset	109 p = p.';
8db4eb48f546 [project @ 2005-06-16 20:19:18 by jwe] jwe parents: 5307 diff changeset	110
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	111 ## Test difficult case where scaling is really needed. This example
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	112 ## demonstrates the rather poor result which occurs when the dependent
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	113 ## variable is not normalized properly.
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	114 ## Also check the usage of 2nd & 3rd output arguments.
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	115 %!test
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	116 %! x = [ -1196.4, -1195.2, -1194, -1192.8, -1191.6, -1190.4, -1189.2, -1188, \
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	117 %! -1186.8, -1185.6, -1184.4, -1183.2, -1182];
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	118 %! y = [ 315571.7086, 315575.9618, 315579.4195, 315582.6206, 315585.4966, \
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	119 %! 315588.3172, 315590.9326, 315593.5934, 315596.0455, 315598.4201, \
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	120 %! 315600.7143, 315602.9508, 315605.1765 ];
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	121 %! [p1, s1] = polyfit (x, y, 10);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	122 %! [p2, s2, mu] = polyfit (x, y, 10);
11918 f2af2233ce7f polyfit.m: Fixed tests. Ben Abbott <bpabbott@mac.com> parents: 11917 diff changeset	123 %! assert (2*s2.normr < s1.normr)
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	124
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	125 %!test
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	126 %! x = 1:4;
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	127 %! p0 = [1i, 0, 2i, 4];
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	128 %! y0 = polyval (p0, x);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	129 %! p = polyfit (x, y0, numel(p0)-1);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	130 %! assert (p, p0, 1000*eps)
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	131
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	132 %!test
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	133 %! x = 1000 + (-5:5);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	134 %! xn = (x - mean (x)) / std (x);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	135 %! pn = ones (1,5);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	136 %! y = polyval (pn, xn);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	137 %! [p, s, mu] = polyfit (x, y, numel(pn)-1);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	138 %! [p2, s2] = polyfit (x, y, numel(pn)-1);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	139 %! assert (p, pn, s.normr)
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	140 %! assert (s.yf, y, s.normr)
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	141 %! assert (mu, [mean(x), std(x)])
11918 f2af2233ce7f polyfit.m: Fixed tests. Ben Abbott <bpabbott@mac.com> parents: 11917 diff changeset	142 %! assert (s.normr/s2.normr < sqrt(eps))
11916 377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	143
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	144 %!test
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	145 %! x = [1, 2, 3; 4, 5, 6];
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	146 %! y = [0, 0, 1; 1, 0, 0];
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	147 %! p = polyfit (x, y, 5);
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	148 %! expected = [0, 1, -14, 65, -112, 60]/12;
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	149 %! assert (p, expected, sqrt(eps))
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	150
377d908f7e40 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7017 diff changeset	151
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	152 endfunction

Mercurial > octave-nkf

annotate scripts/polynomial/polyfit.m @ 11918:f2af2233ce7f release-3-0-x