octave: scripts/polynomial/polyfit.m annotate

annotate scripts/polynomial/polyfit.m @ 29359:7854d5752dd2

maint: merge stable to default.

author	John W. Eaton <jwe@octave.org>
date	Wed, 10 Feb 2021 10:10:40 -0500
parents	90fea9cc9caa 0a5b15007766
children	796f54d4ddbf

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
29358 0a5b15007766 update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 27985 diff changeset	3 ## Copyright (C) 1996-2021 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	7 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	8 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## (at your option) any later version.
2313 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 ## 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	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	18 ## GNU General Public License for more details.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	19 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	20 ## 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	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
2303 5cffc4b8de57 [project @ 1996-06-24 09:15:24 by jwe] jwe parents: 2261 diff changeset	25
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3246 diff changeset	26 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20165 diff changeset	27 ## @deftypefn {} {@var{p} =} polyfit (@var{x}, @var{y}, @var{n})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20165 diff changeset	28 ## @deftypefnx {} {[@var{p}, @var{s}] =} polyfit (@var{x}, @var{y}, @var{n})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20165 diff changeset	29 ## @deftypefnx {} {[@var{p}, @var{s}, @var{mu}] =} polyfit (@var{x}, @var{y}, @var{n})
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	30 ## Return the coefficients of a polynomial @var{p}(@var{x}) of degree @var{n}
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	31 ## that minimizes the least-squares-error of the fit to the points
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	32 ## @code{[@var{x}(:), @var{y}(:)]}.
20165 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	33 ##
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	34 ## @var{n} is typically an integer @geq{} 0 specifying the degree of the
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	35 ## approximating polynomial. If @var{n} is a logical vector, it is used as a
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	36 ## mask to selectively force the corresponding polynomial coefficients to be
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	37 ## used or ignored.
3418 ca92c9d3f882 [project @ 2000-01-12 03:07:47 by jwe] jwe parents: 3368 diff changeset	38 ##
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	39 ## The polynomial coefficients are returned in the row vector @var{p}. The
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	40 ## output @var{p} may be directly used with @code{polyval} to estimate values
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	41 ## using the fitted polynomial.
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	42 ##
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 14062 diff changeset	43 ## 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	44 ##
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	45 ## @table @samp
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	46 ##
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	47 ## @item yf
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	48 ## The values of the polynomial for each value of @var{x}.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	49 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	50 ## @item X
25003 2365c2661b3c doc: Spellcheck documentation ahead of 4.4 release. Rik <rik@octave.org> parents: 24534 diff changeset	51 ## The @nospell{Vandermonde} matrix used to compute the polynomial
2365c2661b3c doc: Spellcheck documentation ahead of 4.4 release. Rik <rik@octave.org> parents: 24534 diff changeset	52 ## coefficients.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	53 ##
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	54 ## @item R
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	55 ## Triangular factor R from the QR@tie{}decomposition.
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	56 ##
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	57 ## @item C
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	58 ## 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	59 ## @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	60 ## propagation.
19593 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	61 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	62 ## @item df
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	63 ## The degrees of freedom.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	64 ##
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	65 ## @item normr
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	66 ## The norm of the residuals.
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	67 ## @end table
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	68 ##
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	69 ## The second output may be used by @code{polyval} to calculate the statistical
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	70 ## error limits of the predicted values. In particular, the standard deviation
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	71 ## of @var{p} coefficients is given by
20165 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	72 ##
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	73 ## @code{sqrt (diag (@var{s.C})/@var{s.df}) * @var{s.normr}}.
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	74 ##
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	75 ## When the third output, @var{mu}, is present the original data is centered
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	76 ## and scaled which can improve the numerical stability of the fit. The
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	77 ## coefficients @var{p} are associated with a polynomial in
20165 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	78 ##
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	79 ## @code{@var{xhat} = (@var{x} - @var{mu}(1)) / @var{mu}(2)} @*
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	80 ## where @var{mu}(1) = mean (@var{x}), and @var{mu}(2) = std (@var{x}).
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	81 ##
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	82 ## Example 1 : logical @var{n} and integer @var{n}
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	83 ##
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	84 ## @example
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	85 ## @group
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	86 ## f = @@(x) x.^2 + 5; # data-generating function
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	87 ## x = 0:5;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	88 ## y = f (x);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	89 ## ## Fit data to polynomial Ax^3 + Bx^1
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	90 ## p = polyfit (x, y, logical ([1, 0, 1, 0]))
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	91 ## @result{} p = [ 0.0680, 0, 4.2444, 0 ]
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	92 ## ## Fit data to polynomial using all terms up to x^3
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	93 ## p = polyfit (x, y, 3)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	94 ## @result{} p = [ -4.9608e-17, 1.0000e+00, -3.3813e-15, 5.0000e+00 ]
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	95 ## @end group
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	96 ## @end example
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	97 ##
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 14062 diff changeset	98 ## @seealso{polyval, polyaffine, roots, vander, zscore}
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3246 diff changeset	99 ## @end deftypefn
2311 2b5788792cad [project @ 1996-07-11 20:18:38 by jwe] jwe parents: 2303 diff changeset	100
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	101 function [p, s, mu] = polyfit (x, y, n)
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	102
28789 28de41192f3c Eliminate unneeded verification of nargin, nargout in m-files. Rik <rik@octave.org> parents: 28693 diff changeset	103 if (nargin < 3)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	104 print_usage ();
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	105 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	106
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	107 y_is_row_vector = isrow (y);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	108
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	109 ## Reshape x & y into column vectors.
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	110 x = x(:);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	111 y = y(:);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	112
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	113 nx = numel (x);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	114 ny = numel (y);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	115 if (nx != ny)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	116 error ("polyfit: X and Y must have the same number of points");
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	117 endif
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	118
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	119 if (nargout > 2)
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	120 ## Center and scale the x values.
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	121 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	122 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	123 endif
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	124
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	125 ## n is the polynomial degree (an input, or deduced from the polymask size)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	126 ## m is the effective number of coefficients.
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	127 if (islogical (n))
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	128 polymask = n(:).'; # force to row vector
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	129 n = numel (polymask) - 1;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	130 m = sum (polymask) - 1;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	131 pad_output = true;
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	132 else
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	133 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	134 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	135 endif
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	136 polymask = true (1, n+1);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	137 m = n;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	138 pad_output = false;
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	139 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	140
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	141 if (m >= nx)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	142 warning ("polyfit: degree of polynomial N is >= number of data points; solution is not unique");
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	143 m = nx;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	144 pad_output = true;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	145 ## Keep the lowest m entries in polymask
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	146 idx = find (polymask);
28693 2bb050267d74 maint: Remove trailing spaces from code base. Rik <rik@octave.org> parents: 28502 diff changeset	147 idx((end-m+1):end) = [];
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	148 polymask(idx) = false;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	149 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	150
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	151 ## Construct the Vandermonde matrix.
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	152 X = vander (x, n+1);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	153 v = X(:, polymask);
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	154
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	155 ## Solve by QR decomposition.
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	156 [q, r, k] = qr (v, 0);
9138 436b498b0506 simplify polyfit Jaroslav Hajek <highegg@gmail.com> parents: 8920 diff changeset	157 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	158 p(k) = p;
19593 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	159
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	160 if (isargout (2))
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	161 yf = v*p;
14110 b8d9530e940e undo non-documentation changes in changeset 614505385171 John W. Eaton <jwe@octave.org> parents: 14104 diff changeset	162 if (y_is_row_vector)
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	163 s.yf = yf.';
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	164 else
96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	165 s.yf = yf;
3105 f936c7f5074f [project @ 1997-11-19 04:36:17 by jwe] jwe parents: 3092 diff changeset	166 endif
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	167
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	168 s.X = X;
3091 b06dcbb6b3b1 [project @ 1997-10-10 16:26:47 by jwe] jwe parents: 3069 diff changeset	169
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	170 ## r.'*r is positive definite if matrix v is of full rank. Invert it by
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	171 ## cholinv to avoid taking the square root of squared quantities.
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	172 ## If cholinv fails, then v is rank deficient and not invertible.
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	173 try
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	174 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	175 catch
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	176 C = NaN (m, m);
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	177 end_try_catch
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	178
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	179 if (pad_output)
20955 77f5591878bf maint: Use '! expr' rather than '!expr' to conform to coding guidelines. Rik <rik@octave.org> parents: 20852 diff changeset	180 s.X(:, ! polymask) = 0;
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	181 s.R = zeros (rows (r), n+1); s.R(:, polymask) = r;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	182 s.C = zeros (rows (C), n+1); s.C(:, polymask) = C;
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	183 else
19593 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	184 s.R = r;
14377 c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	185 s.C = C;
c87f927d047d polyfit.m: add the ability to specify the polynomial template. Pascal Dupuis <Pascal.Dupuis@uclouvain.be> parents: 14363 diff changeset	186 endif
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	187
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	188 s.df = max (0, nx - m - 1);
4491 96a25f032846 [project @ 2003-08-28 21:01:21 by jwe] jwe parents: 4030 diff changeset	189 s.normr = norm (yf - y);
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	190 endif
1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	191
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	192 if (pad_output)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	193 ## Zero pad output
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	194 q = p;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	195 p = zeros (n+1, 1);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	196 p(polymask) = q;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	197 endif
28693 2bb050267d74 maint: Remove trailing spaces from code base. Rik <rik@octave.org> parents: 28502 diff changeset	198 p = p.'; # Return a row vector.
5395 8db4eb48f546 [project @ 2005-06-16 20:19:18 by jwe] jwe parents: 5307 diff changeset	199
2261 1b6e1629fb91 [project @ 1996-05-23 00:52:07 by jwe] jwe parents: diff changeset	200 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	201
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	202
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	203 %!shared x
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	204 %! x = [-2, -1, 0, 1, 2];
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	205
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	206 %!assert (polyfit (x, 3x.^2 + 2x + 1, 2), [3, 2, 1], 10*eps)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	207 %!assert (polyfit (x, 3x.^2 + 2x + 1, logical ([1 1 1])), [3, 2, 1], 10*eps)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	208 %!assert (polyfit (x, x.^2 + 2x + 3, 3), [0, 1, 2, 3], 10eps)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	209 %!assert (polyfit (x, x.^2 + 2x + 3, logical ([0 1 1 1])), [0 1 2 3], 10eps)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	210
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	211 ## Test logical input N
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	212 %!test
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	213 %! x = [0:5];
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	214 %! y = 3x.^3 + 2x.^2 + 4;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	215 %! [p, s] = polyfit (x, y, logical ([1, 0, 1, 1]));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	216 %! assert (p(2), 0);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	217 %! assert (all (p([1, 3, 4])));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	218 %! assert (s.df, 3);
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	219
21751 b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 20955 diff changeset	220 ## Test difficult case where scaling is really needed. This example
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	221 ## 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	222 ## 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	223 ## 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	224 %!test
19670 e5facc6eec13 Silence warning messages in %!test code. Rik <rik@octave.org> parents: 19593 diff changeset	225 %! warning ("off", "Octave:nearly-singular-matrix", "local");
17245 7babcdb9bc13 Use ... instead of \ for line continuation marker. Stefan Mahr <dac922@gmx.de> parents: 14620 diff changeset	226 %! x = [ -1196.4, -1195.2, -1194, -1192.8, -1191.6, -1190.4, -1189.2, -1188, ...
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	227 %! -1186.8, -1185.6, -1184.4, -1183.2, -1182];
17245 7babcdb9bc13 Use ... instead of \ for line continuation marker. Stefan Mahr <dac922@gmx.de> parents: 14620 diff changeset	228 %! y = [ 315571.7086, 315575.9618, 315579.4195, 315582.6206, 315585.4966, ...
7babcdb9bc13 Use ... instead of \ for line continuation marker. Stefan Mahr <dac922@gmx.de> parents: 14620 diff changeset	229 %! 315588.3172, 315590.9326, 315593.5934, 315596.0455, 315598.4201, ...
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	230 %! 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	231 %! [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	232 %! [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	233 %! 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	234
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	235 %!test
19670 e5facc6eec13 Silence warning messages in %!test code. Rik <rik@octave.org> parents: 19593 diff changeset	236 %! warning ("off", "Octave:nearly-singular-matrix", "local");
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	237 %! x = 1000 + (-5:5);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	238 %! 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	239 %! pn = ones (1,5);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	240 %! y = polyval (pn, xn);
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	241 %! n = numel (pn) - 1;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	242 %! [p, s, mu] = polyfit (x, y, n);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	243 %! [p2, s2] = polyfit (x, y, n);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	244 %! 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	245 %! 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	246 %! 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	247 %! 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	248
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	249 ## Complex polynomials
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	250 %!test
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	251 %! x = 1:4;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	252 %! p0 = [1i, 0, 2i, 4];
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	253 %! y = polyval (p0, x);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	254 %! n = numel (p0) - 1;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	255 %! p = polyfit (x, y, n);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	256 %! assert (p, p0, 1000*eps);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	257
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	258 ## Matrix input
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	259 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	260 %! 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	261 %! 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	262 %! 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	263 %! 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	264 %! 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	265
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	266 ## Orientation of output
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	267 %!test
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	268 %! x = 0:5;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	269 %! y = x.^4 + 2*x + 5;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	270 %! [p, s] = polyfit (x, y, 3);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	271 %! assert (isrow (s.yf));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	272 %! [p, s] = polyfit (x, y.', 3);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	273 %! assert (iscolumn (s.yf));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	274
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	275 ## Insufficient data for fit
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	276 %!test
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	277 %! x = [1, 2];
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	278 %! y = [3, 4];
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	279 %! ## Disable warnings entirely because there is not a specific ID to disable.
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	280 %! wstate = warning ();
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	281 %! unwind_protect
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	282 %! warning ("off", "all");
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	283 %! p0 = polyfit (x, y, 4);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	284 %! [p1, s, mu] = polyfit (x, y, 4);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	285 %! unwind_protect_cleanup
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	286 %! warning (wstate);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	287 %! end_unwind_protect
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	288 %! assert (p0, [0, 0, 0, 1, 2], 10*eps);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	289 %! assert (p1, [0, 0, 0, sqrt(2)/2, 3.5], 10*eps);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	290 %! assert (size (s.X), [2, 5]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	291 %! assert (s.X(:,1:3), zeros (2,3));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	292 %! assert (size (s.R), [2, 5]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	293 %! assert (s.R(:,1:3), zeros (2,3));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	294 %! assert (size (s.C), [2, 5]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	295 %! assert (s.C(:,1:3), zeros (2,3));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	296 %! assert (s.df, 0);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	297 %! assert (mu, [1.5, sqrt(2)/2]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	298
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	299 %!test
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	300 %! x = [1, 2, 3];
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	301 %! y = 2*x + 1;
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	302 %! ## Disable warnings entirely because there is not a specific ID to disable.
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	303 %! wstate = warning ();
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	304 %! unwind_protect
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	305 %! warning ("off", "all");
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	306 %! p0 = polyfit (x, y, logical ([1, 1, 1, 0 1]));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	307 %! [p1, s, mu] = polyfit (x, y, logical ([1, 1, 1, 0 1]));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	308 %! unwind_protect_cleanup
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	309 %! warning (wstate);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	310 %! end_unwind_protect
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	311 %! assert (p0, [0, -2/11, 12/11, 0, 23/11], 10*eps);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	312 %! assert (p1, [0, 2, 0, 0, 5], 10*eps);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	313 %! assert (size (s.X), [3, 5]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	314 %! assert (s.X(:,[1,4]), zeros (3,2));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	315 %! assert (size (s.R), [3, 5]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	316 %! assert (s.R(:,[1,4]), zeros (3,2));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	317 %! assert (size (s.C), [3, 5]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	318 %! assert (s.C(:,[1,4]), zeros (3,2));
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	319 %! assert (s.df, 0);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	320 %! assert (mu, [2, 1]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	321
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	322 %!test <*57964>
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	323 %! ## Disable warnings entirely because there is not a specific ID to disable.
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	324 %! wstate = warning ();
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	325 %! unwind_protect
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	326 %! warning ("off", "all");
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	327 %! [p, s] = polyfit ([1,2], [3,4], 2);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	328 %! unwind_protect_cleanup
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	329 %! warning (wstate);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	330 %! end_unwind_protect
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	331 %! assert (size (p), [1, 3]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	332 %! assert (size (s.X), [2, 3]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	333 %! assert (s.X(:,1), [0; 0]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	334 %! assert (size (s.R), [2, 3]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	335 %! assert (s.R(:,1), [0; 0]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	336 %! assert (size (s.C), [2, 3]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	337 %! assert (s.C(:,1), [0; 0]);
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	338
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	339 ## Test input validation
28896 90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 28789 diff changeset	340 %!error <Invalid call> polyfit ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 28789 diff changeset	341 %!error <Invalid call> polyfit (1)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 28789 diff changeset	342 %!error <Invalid call> polyfit (1,2)
28502 39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	343 %!error <X and Y must have the same number of points> polyfit ([1, 2], 1, 1)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	344 %!error <X and Y must have the same number of points> polyfit (1, [1, 2], 1)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	345 %!error <N must be a non-negative integer> polyfit (1, 2, [1,2])
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	346 %!error <N must be a non-negative integer> polyfit (1, 2, -1)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	347 %!error <N must be a non-negative integer> polyfit (1, 2, Inf)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	348 %!error <N must be a non-negative integer> polyfit (1, 2, 1.5)
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	349 %!test <*57964>
39e6308e4251 polyfit.m: Overhaul function (bug #57964). Rik <rik@octave.org> parents: 27985 diff changeset	350 %! fail ("p = polyfit ([1,2], [3,4], 4)", "warning", "solution is not unique");

Mercurial > octave

annotate scripts/polynomial/polyfit.m @ 29359:7854d5752dd2