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

annotate scripts/polynomial/polyval.m @ 14570:d07d96e53612 stable

seconds after the minute can be 0-60, not 0-61 * system.txi (Timing Utilities): Correct possible values for number of seconds in time structures. From Rafael Arndt <rafaelarndt@gmail.com>.

author	John W. Eaton <jwe@octave.org>
date	Tue, 17 Apr 2012 14:42:49 -0400
parents	72c96de7a403
children	f3d52523cde1

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 14104 diff changeset	1 ## Copyright (C) 1994-2012 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: 6046 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: 6046 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: 6046 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: 6046 diff changeset	17 ## <http://www.gnu.org/licenses/>.
904 3470f1e25a79 [project @ 1994-11-09 21:22:15 by jwe] jwe parents: 561 diff changeset	18
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3202 diff changeset	19 ## -- texinfo --
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10224 diff changeset	20 ## @deftypefn {Function File} {@var{y} =} polyval (@var{p}, @var{x})
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	21 ## @deftypefnx {Function File} {@var{y} =} polyval (@var{p}, @var{x}, [], @var{mu})
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	22 ## Evaluate the polynomial @var{p} at the specified values of @var{x}. When
12982 5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	23 ## @var{mu} is present, evaluate the polynomial for
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10224 diff changeset	24 ## (@var{x}-@var{mu}(1))/@var{mu}(2).
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	25 ## If @var{x} is a vector or matrix, the polynomial is evaluated for each of
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3202 diff changeset	26 ## the elements of @var{x}.
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 13963 diff changeset	27 ##
7501 83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	28 ## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s})
83cce070104f style fixes John W. Eaton <jwe@octave.org> parents: 7500 diff changeset	29 ## @deftypefnx {Function File} {[@var{y}, @var{dy}] =} polyval (@var{p}, @var{x}, @var{s}, @var{mu})
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	30 ## In addition to evaluating the polynomial, the second output
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	31 ## represents the prediction interval, @var{y} +/- @var{dy}, which
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	32 ## contains at least 50% of the future predictions. To calculate the
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	33 ## prediction interval, the structured variable @var{s}, originating
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 13963 diff changeset	34 ## from @code{polyfit}, must be supplied.
614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 13963 diff changeset	35 ## @seealso{polyvalm, polyaffine, polyfit, roots, poly}
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3202 diff changeset	36 ## @end deftypefn
1025 f558749713f1 [project @ 1995-01-11 20:52:10 by jwe] jwe parents: 904 diff changeset	37
3202 44d82b369c78 [project @ 1998-10-29 20:27:57 by jwe] jwe parents: 3085 diff changeset	38 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
2312 204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	39 ## Created: June 1994
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	40 ## Adapted-By: jwe
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	41
12982 5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	42 function [y, dy] = polyval (p, x, s = [], mu)
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	43
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	44 if (nargin < 2 \|\| nargin > 4 \|\| (nargout == 2 && nargin < 3))
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5642 diff changeset	45 print_usage ();
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	46 endif
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	47
12982 5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	48 if (isempty (x))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	49 y = [];
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	50 return;
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	51 elseif (isempty (p))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	52 y = zeros (size (x));
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	53 return;
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	54 elseif (! isvector (p))
3458 d25bc039237b [project @ 2000-01-19 09:36:14 by jwe] jwe parents: 3457 diff changeset	55 error ("polyval: first argument must be a vector");
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	56 endif
e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	57
12482 3244c6e0af4a polynomial/polyval.m: Compute offset/normalization only when needed. Ben Abbott <bpabbott@mac.com> parents: 12481 diff changeset	58 if (nargin > 3)
3244c6e0af4a polynomial/polyval.m: Compute offset/normalization only when needed. Ben Abbott <bpabbott@mac.com> parents: 12481 diff changeset	59 x = (x - mu(1)) / mu(2);
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	60 endif
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	61
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	62 n = length (p) - 1;
12481 97d103fcb6dd polynomial/polyval.m: Minor simplification in polynomial evaluation Ben Abbott <bpabbott@mac.com> parents: 12475 diff changeset	63 y = p(1) * ones (size (x));
11110 0be2d25700a7 polynomial/polyval.m: Use Horner's method. Marco Caliari <marco.caliari@univr.it> parents: 10687 diff changeset	64 for i = 2:n+1
12481 97d103fcb6dd polynomial/polyval.m: Minor simplification in polynomial evaluation Ben Abbott <bpabbott@mac.com> parents: 12475 diff changeset	65 y = y .* x + p(i);
11110 0be2d25700a7 polynomial/polyval.m: Use Horner's method. Marco Caliari <marco.caliari@univr.it> parents: 10687 diff changeset	66 endfor
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	67
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	68 if (nargout == 2)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	69 ## Note: the F-Distribution is generally considered to be single-sided.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	70 ## http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	71 ## t = finv (1-alpha, s.df, s.df);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	72 ## dy = t * sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	73 ## If my inference is correct, then t must equal 1 for polyval.
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	74 ## This is because finv (0.5, n, n) = 1.0 for any n.
12982 5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	75 try
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	76 k = numel (x);
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	77 A = (x(:) * ones (1, n+1)) .^ (ones (k, 1) * (n:-1:0));
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	78 dy = sqrt (1 + sumsq (A/s.R, 2)) * s.normr / sqrt (s.df);
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	79 dy = reshape (dy, size (x));
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	80 catch
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	81 if (isempty (s))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	82 error ("polyval: third input is required.")
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	83 elseif (isstruct (s)
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	84 && all (ismember ({"R", "normr", "df"}, fieldnames (s))))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	85 error (lasterr ())
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	86 elseif (isstruct (s))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	87 error ("polyval: third input is missing the required fields.");
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	88 else
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	89 error ("polyval: third input is not a structure.");
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	90 endif
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	91 end_try_catch
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	92 endif
1025 f558749713f1 [project @ 1995-01-11 20:52:10 by jwe] jwe parents: 904 diff changeset	93
561 e79ff1f4df3c [project @ 1994-07-25 22:32:08 by jwe] jwe parents: diff changeset	94 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	95
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	96 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	97 %! fail("polyval([1,0;0,1],0:10)");
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	98
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	99 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	100 %! r = 0:10:50;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	101 %! p = poly (r);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	102 %! p = p / max(abs(p));
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	103 %! x = linspace(0,50,11);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	104 %! y = polyval(p,x) + 0.25sin(100x);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	105 %! [pf, s] = polyfit (x, y, numel(r));
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	106 %! [y1, delta] = polyval (pf, x, s);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	107 %! expected = [0.37235, 0.35854, 0.32231, 0.32448, 0.31328, ...
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	108 %! 0.32036, 0.31328, 0.32448, 0.32231, 0.35854, 0.37235];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	109 %! assert (delta, expected, 0.00001)
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	110
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	111 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	112 %! x = 10 + (-2:2);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	113 %! y = [0, 0, 1, 0, 2];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	114 %! p = polyfit (x, y, numel (x) - 1);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	115 %! [pn, s, mu] = polyfit (x, y, numel (x) - 1);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	116 %! y1 = polyval (p, x);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	117 %! yn = polyval (pn, x, [], mu);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	118 %! assert (y1, y, sqrt(eps))
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	119 %! assert (yn, y, sqrt(eps))
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	120
7500 2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	121 %!test
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	122 %! p = [0, 1, 0];
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	123 %! x = 1:10;
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	124 %! assert (x, polyval(p,x), eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	125 %! x = x(:);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	126 %! assert (x, polyval(p,x), eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	127 %! x = reshape(x, [2, 5]);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	128 %! assert (x, polyval(p,x), eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	129 %! x = reshape(x, [5, 2]);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	130 %! assert (x, polyval(p,x), eps)
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	131 %! x = reshape(x, [1, 1, 5, 2]);
2df882e69f13 use QR decomposition and normalization for polyfit; normalization for polyval Ben Abbott <bpabbott@mac.com> parents: 7411 diff changeset	132 %! assert (x, polyval(p,x), eps)
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	133
12475 009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	134 %!test
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	135 %! p = [1];
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	136 %! x = 1:10;
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	137 %! y = ones(size(x));
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	138 %! assert (y, polyval(p,x), eps)
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	139 %! x = x(:);
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	140 %! y = ones(size(x));
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	141 %! assert (y, polyval(p,x), eps)
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	142 %! x = reshape(x, [2, 5]);
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	143 %! y = ones(size(x));
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	144 %! assert (y, polyval(p,x), eps)
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	145 %! x = reshape(x, [5, 2]);
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	146 %! y = ones(size(x));
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	147 %! assert (y, polyval(p,x), eps)
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	148 %! x = reshape(x, [1, 1, 5, 2]);
009068efc66d Properly evaluate zeroth order polynomials. Ben Abbott <bpabbott@mac.com> parents: 11587 diff changeset	149
12982 5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	150 %!assert (zeros (1, 10), polyval ([], 1:10))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	151 %!assert ([], polyval (1, []))
5e37369ea13c polyval.m: Return zeros when polynomial is empty (ML Compatibility). Ben Abbott <bpabbott@mac.com> parents: 12482 diff changeset	152 %!assert ([], polyval ([], []))

Mercurial > hg > octave-nkf

annotate scripts/polynomial/polyval.m @ 14570:d07d96e53612 stable