octave: scripts/polynomial/roots.m annotate

annotate scripts/polynomial/roots.m @ 33617:ec2635a02328 bytecode-interpreter tip

maint: Merge default to bytecode-interpreter.

author	Markus Mützel <markus.muetzel@gmx.de>
date	Tue, 21 May 2024 18:29:03 +0200
parents	2e484f9f1f18
children

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 ##
32632 2e484f9f1f18 maint: update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 31706 diff changeset	3 ## Copyright (C) 1994-2024 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: 6850 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 ########################################################################
1025 f558749713f1 [project @ 1995-01-11 20:52:10 by jwe] jwe parents: 944 diff changeset	25
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 2847 diff changeset	26 ## -- texinfo --
30875 5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files. Rik <rik@octave.org> parents: 30564 diff changeset	27 ## @deftypefn {} {@var{r} =} roots (@var{c})
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	28 ##
20165 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	29 ## Compute the roots of the polynomial @var{c}.
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	30 ##
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	31 ## For a vector @var{c} with @math{N} components, return the roots of the
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	32 ## polynomial
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 2847 diff changeset	33 ## @tex
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 2847 diff changeset	34 ## $$
20165 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	35 ## c_1 x^{N-1} + \cdots + c_{N-1} x + c_N.
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 2847 diff changeset	36 ## $$
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 2847 diff changeset	37 ## @end tex
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	38 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	39 ##
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 2847 diff changeset	40 ## @example
20165 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	41 ## c(1) * x^(N-1) + @dots{} + c(N-1) * x + c(N)
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 2847 diff changeset	42 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	43 ##
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	44 ## @end ifnottex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	45 ##
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	46 ## As an example, the following code finds the roots of the quadratic
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	47 ## polynomial
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	48 ## @tex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	49 ## $$ p(x) = x^2 - 5. $$
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	50 ## @end tex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	51 ## @ifnottex
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	52 ##
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	53 ## @example
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	54 ## p(x) = x^2 - 5.
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	55 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	56 ##
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	57 ## @end ifnottex
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	58 ##
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	59 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	60 ## @group
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	61 ## c = [1, 0, -5];
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	62 ## roots (c)
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	63 ## @result{} 2.2361
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	64 ## @result{} -2.2361
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	65 ## @end group
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	66 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	67 ##
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	68 ## Note that the true result is
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	69 ## @tex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	70 ## $\pm \sqrt{5}$
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	71 ## @end tex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	72 ## @ifnottex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	73 ## @math{+/- sqrt(5)}
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	74 ## @end ifnottex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	75 ## which is roughly
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	76 ## @tex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	77 ## $\pm 2.2361$.
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	78 ## @end tex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	79 ## @ifnottex
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	80 ## @math{+/- 2.2361}.
9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6372 diff changeset	81 ## @end ifnottex
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	82 ## @seealso{poly, compan, fzero}
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 2847 diff changeset	83 ## @end deftypefn
2311 2b5788792cad [project @ 1996-07-11 20:18:38 by jwe] jwe parents: 2303 diff changeset	84
22765 01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	85 function r = roots (c)
904 3470f1e25a79 [project @ 1994-11-09 21:22:15 by jwe] jwe parents: 787 diff changeset	86
28891 de5f2f9a64ff maint: Use same coding style when checking for a minimum of 1 input. Rik <rik@octave.org> parents: 28886 diff changeset	87 if (nargin < 1 \|\| (! isvector (c) && ! isempty (c)))
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	88 print_usage ();
22765 01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	89 elseif (any (! isfinite (c)))
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 7558 diff changeset	90 error ("roots: inputs must not contain Inf or NaN");
1598 3739611f0803 [project @ 1995-11-01 01:35:40 by jwe] jwe parents: 1337 diff changeset	91 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	92
22765 01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	93 c = c(:);
01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	94 n = numel (c);
1025 f558749713f1 [project @ 1995-01-11 20:52:10 by jwe] jwe parents: 944 diff changeset	95
22765 01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	96 ## If c = [ 0 ... 0 c(k+1) ... c(k+l) 0 ... 0 ],
16765 80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	97 ## we can remove the leading k zeros,
80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	98 ## and n - k - l roots of the polynomial are zero.
904 3470f1e25a79 [project @ 1994-11-09 21:22:15 by jwe] jwe parents: 787 diff changeset	99
22765 01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	100 c_max = max (abs (c));
01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	101 if (isempty (c) \|\| c_max == 0)
16765 80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	102 r = [];
80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	103 return;
7558 690c91f741b8 Apply a scaling factor to leading zero removal in roots.m Sebastien Loisel parents: 7411 diff changeset	104 endif
16765 80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	105
22765 01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	106 f = find (c ./ c_max);
7558 690c91f741b8 Apply a scaling factor to leading zero removal in roots.m Sebastien Loisel parents: 7411 diff changeset	107 m = numel (f);
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	108
22765 01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	109 c = c(f(1):f(m));
01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	110 l = numel (c);
16765 80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	111 if (l > 1)
80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	112 A = diag (ones (1, l-2), -1);
22765 01aae08a0105 maint: Rename variables to match documentation in m-files. Rik <rik@octave.org> parents: 22755 diff changeset	113 A(1,:) = -c(2:l) ./ c(1);
16765 80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	114 r = eig (A);
80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	115 if (f(m) < n)
80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	116 r = [r; zeros(n - f(m), 1)];
787 c5d35bb139b6 [project @ 1994-10-11 00:34:13 by jwe] jwe parents: diff changeset	117 endif
c5d35bb139b6 [project @ 1994-10-11 00:34:13 by jwe] jwe parents: diff changeset	118 else
16765 80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	119 r = zeros (n - f(m), 1);
787 c5d35bb139b6 [project @ 1994-10-11 00:34:13 by jwe] jwe parents: diff changeset	120 endif
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	121
787 c5d35bb139b6 [project @ 1994-10-11 00:34:13 by jwe] jwe parents: diff changeset	122 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	123
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	124
7558 690c91f741b8 Apply a scaling factor to leading zero removal in roots.m Sebastien Loisel parents: 7411 diff changeset	125 %!test
690c91f741b8 Apply a scaling factor to leading zero removal in roots.m Sebastien Loisel parents: 7411 diff changeset	126 %! p = [poly([3 3 3 3]), 0 0 0 0];
690c91f741b8 Apply a scaling factor to leading zero removal in roots.m Sebastien Loisel parents: 7411 diff changeset	127 %! r = sort (roots (p));
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	128 %! assert (r, [0; 0; 0; 0; 3; 3; 3; 3], 0.001);
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	129
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	130 %!assert (isempty (roots ([])))
16765 80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	131 %!assert (isempty (roots ([0 0])))
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	132 %!assert (isempty (roots (1)))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	133 %!assert (roots ([1, -6, 11, -6]), [3; 2; 1], sqrt (eps))
7558 690c91f741b8 Apply a scaling factor to leading zero removal in roots.m Sebastien Loisel parents: 7411 diff changeset	134
16765 80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	135 %!assert (roots ([1e-200, -1e200, 1]), 1e-200)
80b9a9e1c965 roots.m: Fix bug when input is all zeros (bug #38855) Rik <rik@octave.org> parents: 14868 diff changeset	136 %!assert (roots ([1e-200, -1e200 * 1i, 1]), -1e-200 * 1i)
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	137
28886 d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs. Rik <rik@octave.org> parents: 27985 diff changeset	138 %!error <Invalid call> roots ()
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	139 %!error roots ([1, 2; 3, 4])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	140 %!error <inputs must not contain Inf or NaN> roots ([1 Inf 1])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	141 %!error <inputs must not contain Inf or NaN> roots ([1 NaN 1])

Mercurial > octave

annotate scripts/polynomial/roots.m @ 33617:ec2635a02328 bytecode-interpreter tip