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

annotate scripts/polynomial/polyfit.m @ 15063:36cbcc37fdb8

Refactor configure.ac to make it more understandable. Use common syntax for messages in config.h Correct typos, refer to libraries in all caps, use two spaces after period. Follow Autoconf guidelines and place general tests before specific tests. * configure.ac, m4/acinclude.m4: Use common syntax for messages in config.h Correct typos, refer to libraries in all caps, use two spaces after period. Follow Autoconf guidelines and place general tests before specific tests.

author	Rik <rik@octave.org>
date	Tue, 31 Jul 2012 10:28:51 -0700
parents	cd375519eab0
children	7babcdb9bc13

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
14620 cd375519eab0 doc: Periodic grammar check of documentation Rik <octave@nomad.inbox5.com> parents: 14401 diff changeset	25 ## @code{[@var{x}, @var{y}]}. If @var{n} is a logical vector, it is used
14401 2bce551c85b6 doc: Correct typo in polyfit docstring. Rik <octave@nomad.inbox5.com> parents: 14377 diff changeset	26 ## as a mask to selectively force the corresponding polynomial
14377 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
14620 cd375519eab0 doc: Periodic grammar check of documentation Rik <octave@nomad.inbox5.com> parents: 14401 diff changeset	56 ## statistical error limits of the predicted values. In particular, the
14377 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 > hg > octave-nkf

annotate scripts/polynomial/polyfit.m @ 15063:36cbcc37fdb8