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

annotate scripts/polynomial/polyfit.m @ 14377:c87f927d047d

polyfit.m: add the ability to specify the polynomial template.

author	Pascal Dupuis <Pascal.Dupuis@uclouvain.be>
date	Sun, 05 Feb 2012 15:07:45 +0100
parents	f3d52523cde1
children	2bce551c85b6

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 14110 diff changeset	1 ## Copyright (C) 1996-2012 John W. Eaton
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	2 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	3 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	4 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	5 ## 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	6 ## 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	7 ## 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	8 ## your option) any later version.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	9 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	10 ## 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	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	12 ## 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	13 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	14 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	15 ## 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	16 ## 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	17 ## <http://www.gnu.org/licenses/>.
2303 5cffc4b8de57 [project @ 1996-06-24 09:15:24 by jwe] jwe parents: 2261 diff changeset	18
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3246 diff changeset	19 ## -- texinfo --
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 9290 diff changeset	20 ## @deftypefn {Function File} {@var{p} =} polyfit (@var{x}, @var{y}, @var{n})
a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 9290 diff changeset	21 ## @deftypefnx {Function File} {[@var{p}, @var{s}] =} polyfit (@var{x}, @var{y}, @var{n})
a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 9290 diff changeset	22 ## @deftypefnx {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	23 ## Return the coefficients of a polynomial @var{p}(@var{x}) of degree
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 14062 diff changeset	24 ## @var{n} that minimizes the least-squares-error of the fit to the points
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	25 ## @code{[@var{x}, @var{y}]}. If @var{n} is a logical vector, it is used
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	26 ## as a mask to selectivelly force the corresponding polynomial
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	27 ## coefficients to be used or ignored.
3418 ca92c9d3f882 [project @ 2000-01-12 03:07:47 by jwe] jwe parents: 3368 diff changeset	28 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	29 ## The polynomial coefficients are returned in a row vector.
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	30 ##
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 14062 diff changeset	31 ## The optional output @var{s} is a structure containing the following fields:
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3418 diff changeset	32 ##
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	33 ## @table @samp
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	34 ## @item R
11593 1577c6f80926 Use non-breaking spaces between certain adjectives and their nouns in docstrings. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	35 ## Triangular factor R from the QR@tie{}decomposition.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	36 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	37 ## @item X
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	38 ## The Vandermonde matrix used to compute the polynomial coefficients.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	39 ##
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	40 ## @item C
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	41 ## The unscaled covariance matrix, formally equal to the inverse of
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	42 ## @var{x'}*@var{x}, but computed in a way minimizing roundoff error
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	43 ## propagation.
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	44 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	45 ## @item df
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	46 ## The degrees of freedom.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	47 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	48 ## @item normr
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	49 ## The norm of the residuals.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	50 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	51 ## @item yf
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	52 ## 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	53 ## @end table
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	54 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	55 ## The second output may be used by @code{polyval} to calculate the
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	56 ## statistical error limits of the predicted values. In particular, the
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	57 ## standard deviation of @var{p} coefficients is given by @*
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	58 ## @code{sqrt (diag (s.C)/s.df)*s.normr}.
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	59 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	60 ## When the third output, @var{mu}, is present the
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	61 ## 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	62 ## @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	63 ## 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	64 ## 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	65 ## stability of the fit.
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 14062 diff changeset	66 ## @seealso{polyval, polyaffine, roots, vander, zscore}
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3246 diff changeset	67 ## @end deftypefn
2311 2b5788792cad [project @ 1996-07-11 20:18:38 by jwe] jwe parents: 2303 diff changeset	68
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5395 diff changeset	69 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
2312 204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	70 ## Created: 13 December 1994
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	71 ## Adapted-By: jwe
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	72 ## Modified on 20120204 by P. Dupuis; added the ability to specify a
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	73 ## polynomial mask instead of a polynomial degree.
2312 204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	74
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	75 function [p, s, mu] = polyfit (x, y, n)
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	76
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	77 if (nargin < 3 \|\| nargin > 4)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	78 print_usage ();
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	79 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	80
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	81 if (nargout > 2)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	82 ## Normalized the x values.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	83 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	84 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	85 endif
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	86
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	87 if (! size_equal (x, y))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	88 error ("polyfit: X and Y must be vectors of the same size");
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	89 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	90
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	91 if (islogical (n))
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	92 polymask = n;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	93 ## n is the polynomial degree as given the polymask size; m is the
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	94 ## effective number of used coefficients.
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	95 n = length (polymask) - 1; m = sum (polymask) - 1;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	96 else
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	97 if (! (isscalar (n) && n >= 0 && ! isinf (n) && n == fix (n)))
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	98 error ("polyfit: N must be a non-negative integer");
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	99 endif
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	100 polymask = logical (ones (1, n+1)); m = n;
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	101 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	102
14110 b8d9530e940e undo non-documentation changes in changeset 614505385171 John W. Eaton <jwe@octave.org> parents: 14104 diff changeset	103 y_is_row_vector = (rows (y) == 1);
b8d9530e940e undo non-documentation changes in changeset 614505385171 John W. Eaton <jwe@octave.org> parents: 14104 diff changeset	104
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	105 ## 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	106 l = numel (x);
9138 436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	107 x = x(:);
436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	108 y = y(:);
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	109
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	110 ## Construct the Vandermonde matrix.
9138 436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	111 v = vander (x, n+1);
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	112
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	113 ## Solve by QR decomposition.
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	114 [q, r, k] = qr (v(:, polymask), 0);
9138 436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	115 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	116 p(k) = p;
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	117
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	118 if (n ~= m)
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	119 q = p; p = zeros (n+1, 1);
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	120 p(polymask) = q;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	121 endif
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	122
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	123 if (nargout > 1)
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	124 yf = v*p;
3105 f936c7f5074f [project @ 1997-11-19 04:36:17 by jwe] jwe parents: 3092 diff changeset	125
14110 b8d9530e940e undo non-documentation changes in changeset 614505385171 John W. Eaton <jwe@octave.org> parents: 14104 diff changeset	126 if (y_is_row_vector)
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	127 s.yf = yf.';
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	128 else
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	129 s.yf = yf;
3105 f936c7f5074f [project @ 1997-11-19 04:36:17 by jwe] jwe parents: 3092 diff changeset	130 endif
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	131 s.X = v;
3091 b06dcbb6b3b1 [project @ 1997-10-10 16:26:47 by jwe] jwe parents: 3069 diff changeset	132
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	133 ## r.'*r is positive definite if X(:, polymask) is of full rank.
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	134 ## Invert it by cholinv to avoid taking the square root of squared
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	135 ## quantities. If cholinv fails, then X(:, polymask) is rank
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	136 ## deficient and not invertible.
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	137 try
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	138 C = cholinv (r.'*r)(k, k);
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	139 catch
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	140 C = NaN * ones (m+1, m+1);
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	141 end_try_catch
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	142
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	143 if (n ~= m)
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	144 ## fill matrices if required
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	145 s.X(:, ~polymask) = 0;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	146 s.R = zeros (n+1, n+1); s.R(polymask, polymask) = r;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	147 s.C = zeros (n+1, n+1); s.C(polymask, polymask) = C;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	148 else
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	149 s.R = r;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	150 s.C = C;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	151 endif
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	152 s.df = l - m - 1;
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	153 s.normr = norm (yf - y);
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	154 endif
1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	155
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	156 ## Return a row vector.
5395 8db4eb48f546 [project @ 2005-06-16 20:19:18 by jwe] jwe parents: 5307 diff changeset	157 p = p.';
8db4eb48f546 [project @ 2005-06-16 20:19:18 by jwe] jwe parents: 5307 diff changeset	158
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	159 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	160
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	161
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	162 %!shared x
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	163 %! x = [-2, -1, 0, 1, 2];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	164 %!assert (polyfit (x, x.^2+x+1, 2), [1, 1, 1], sqrt (eps))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	165 %!assert (polyfit (x, x.^2+x+1, 3), [0, 1, 1, 1], sqrt (eps))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	166 %!fail ("polyfit (x, x.^2+x+1)")
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	167 %!fail ("polyfit (x, x.^2+x+1, [])")
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	168
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	169 ## 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	170 ## 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	171 ## 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	172 ## 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	173 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	174 %! 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	175 %! -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	176 %! 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	177 %! 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	178 %! 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	179 %! [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	180 %! [p2, s2, mu] = polyfit (x, y, 10);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	181 %! 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	182
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	183 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	184 %! x = 1:4;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	185 %! 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	186 %! y0 = polyval (p0, x);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	187 %! p = polyfit (x, y0, numel (p0) - 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	188 %! assert (p, p0, 1000*eps);
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	189
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	190 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	191 %! x = 1000 + (-5:5);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	192 %! 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	193 %! pn = ones (1,5);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	194 %! y = polyval (pn, xn);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	195 %! [p, s, mu] = polyfit (x, y, numel (pn) - 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	196 %! [p2, s2] = polyfit (x, y, numel (pn) - 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	197 %! assert (p, pn, s.normr);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	198 %! assert (s.yf, y, s.normr);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	199 %! assert (mu, [mean(x), std(x)]);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	200 %! 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	201
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	202 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	203 %! 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	204 %! 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	205 %! p = polyfit (x, y, 5);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	206 %! expected = [0, 1, -14, 65, -112, 60] / 12;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	207 %! assert (p, expected, sqrt (eps));
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	208
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	209 %!error <vectors of the same size> polyfit ([1, 2; 3, 4], [1, 2, 3, 4], 2)
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	210

Mercurial > octave-nkf

annotate scripts/polynomial/polyfit.m @ 14377:c87f927d047d