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

annotate scripts/polynomial/polyfit.m @ 9290:40ba43a4745f

fix too optimistic polyfit test

author	Jaroslav Hajek <highegg@gmail.com>
date	Wed, 03 Jun 2009 07:38:17 +0200
parents	16f53d29049f
children	a8ce6bdecce5

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,
9245 16f53d29049f update copyright notices John W. Eaton <jwe@octave.org> parents: 9138 diff changeset	2 ## 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: 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 --
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 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
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 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 ##
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 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 ##
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	29 ## @table @samp
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	30 ## @item R
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 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
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 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
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 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
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 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
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 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
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	41 ##
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	42 ## The second output may be used by @code{polyval} to calculate the
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	43 ## statistical error limits of the predicted values.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	44 ##
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	45 ## When the third output, @var{mu}, is present the
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	46 ## coefficients, @var{p}, are associated with a polynomial in
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	47 ## @var{xhat} = (@var{x}-@var{mu}(1))/@var{mu}(2).
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	48 ## Where @var{mu}(1) = mean (@var{x}), and @var{mu}(2) = std (@var{x}).
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	49 ## This linear transformation of @var{x} improves the numerical
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	50 ## stability of the fit.
8286 6f2d95255911 fix @seealso references to point to existing anchors Thorsten Meyer <thorsten.meyier@gmx.de> parents: 7547 diff changeset	51 ## @seealso{polyval, 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
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 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
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	64 if (nargout > 2)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	65 ## Normalized the x values.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	66 mu = [mean(x), std(x)];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	67 x = (x - mu(1)) / mu(2);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	68 endif
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	69
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 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
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	80 ## Reshape x & y into column vectors.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	81 l = numel (x);
9138 436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	82 x = x(:);
436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	83 y = y(:);
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	84
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	85 ## Construct the Vandermonde matrix.
9138 436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	86 v = vander (x, n+1);
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	87
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	88 ## Solve by QR decomposition.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	89 [q, r, k] = qr (v, 0);
9138 436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	90 p = r \ (q' * y);
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 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)
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 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
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	102 s.R = r;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 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
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 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
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	111 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	112
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	113 %!test
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	114 %! x = [-2, -1, 0, 1, 2];
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	115 %! assert(all (all (abs (polyfit (x, x.^2+x+1, 2) - [1, 1, 1]) < sqrt (eps))));
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	116
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	117 %!error(polyfit ([1, 2; 3, 4], [1, 2, 3, 4], 2))
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	118
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	119 %!test
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	120 %! x = [-2, -1, 0, 1, 2];
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	121 %! assert(all (all (abs (polyfit (x, x.^2+x+1, 3) - [0, 1, 1, 1]) < sqrt (eps))));
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	122
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	123 %!test
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	124 %! x = [-2, -1, 0, 1, 2];
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	125 %! fail("polyfit (x, x.^2+x+1)");
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	126
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	127 %!test
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	128 %! x = [-2, -1, 0, 1, 2];
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	129 %! fail("polyfit (x, x.^2+x+1, [])");
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	130
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	131 ## Test difficult case where scaling is really needed. This example
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	132 ## demonstrates the rather poor result which occurs when the dependent
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	133 ## variable is not normalized properly.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	134 ## Also check the usage of 2nd & 3rd output arguments.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	135 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	136 %! x = [ -1196.4, -1195.2, -1194, -1192.8, -1191.6, -1190.4, -1189.2, -1188, \
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	137 %! -1186.8, -1185.6, -1184.4, -1183.2, -1182];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	138 %! y = [ 315571.7086, 315575.9618, 315579.4195, 315582.6206, 315585.4966, \
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	139 %! 315588.3172, 315590.9326, 315593.5934, 315596.0455, 315598.4201, \
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	140 %! 315600.7143, 315602.9508, 315605.1765 ];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	141 %! [p1, s1] = polyfit (x, y, 10);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	142 %! [p2, s2, mu] = polyfit (x, y, 10);
9290 40ba43a4745f fix too optimistic polyfit test Jaroslav Hajek <highegg@gmail.com> parents: 9245 diff changeset	143 %! assert (s2.normr < s1.normr)
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	144
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	145 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	146 %! x = 1:4;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	147 %! p0 = [1i, 0, 2i, 4];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	148 %! y0 = polyval (p0, x);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	149 %! p = polyfit (x, y0, numel(p0)-1);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	150 %! assert (p, p0, 1000*eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	151
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	152 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	153 %! x = 1000 + (-5:5);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	154 %! xn = (x - mean (x)) / std (x);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	155 %! pn = ones (1,5);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	156 %! y = polyval (pn, xn);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	157 %! [p, s, mu] = polyfit (x, y, numel(pn)-1);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	158 %! [p2, s2] = polyfit (x, y, numel(pn)-1);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	159 %! assert (p, pn, s.normr)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	160 %! assert (s.yf, y, s.normr)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	161 %! assert (mu, [mean(x), std(x)])
7547 40ca9fb9a314 polyfit.m: Fixed tests. Ben Abbott <bpabbott@mac.com> parents: 7501 diff changeset	162 %! assert (s.normr/s2.normr < sqrt(eps))
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	163
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	164 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	165 %! x = [1, 2, 3; 4, 5, 6];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	166 %! y = [0, 0, 1; 1, 0, 0];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	167 %! p = polyfit (x, y, 5);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	168 %! expected = [0, 1, -14, 65, -112, 60]/12;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	169 %! assert (p, expected, sqrt(eps))
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	170
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	171

Mercurial > hg > octave-nkf

annotate scripts/polynomial/polyfit.m @ 9290:40ba43a4745f