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

annotate scripts/polynomial/polygcd.m @ 20595:c1a6c31ac29a

eliminate more simple uses of error_state * ov-classdef.cc: Eliminate simple uses of error_state.

author	John W. Eaton <jwe@octave.org>
date	Tue, 06 Oct 2015 00:20:02 -0400
parents	f1d0f506ee78
children

rev	line source
19731 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19258 diff changeset	1 ## Copyright (C) 2000-2015 Paul Kienzle
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	2 ##
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 diff changeset	3 ## This file is part of Octave.
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	4 ##
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 diff changeset	6 ## under the terms of the GNU General Public License as published by
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 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: 6850 diff changeset	8 ## your option) any later version.
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 diff changeset	9 ##
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6850 diff changeset	13 ## General Public License for more details.
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	14 ##
5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: 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: 6850 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: 6850 diff changeset	17 ## <http://www.gnu.org/licenses/>.
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	18
5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	19 ## -- texinfo --
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	20 ## @deftypefn {Function File} {@var{q} =} polygcd (@var{b}, @var{a})
693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	21 ## @deftypefnx {Function File} {@var{q} =} polygcd (@var{b}, @var{a}, @var{tol})
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	22 ##
20200 f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19731 diff changeset	23 ## Find the greatest common divisor of two polynomials.
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19731 diff changeset	24 ##
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19731 diff changeset	25 ## This is equivalent to the polynomial found by multiplying together all the
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19731 diff changeset	26 ## common roots. Together with deconv, you can reduce a ratio of two
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19731 diff changeset	27 ## polynomials.
f1d0f506ee78 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19731 diff changeset	28 ##
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	29 ## The tolerance @var{tol} defaults to @code{sqrt (eps)}.
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	30 ##
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	31 ## @strong{Caution:} This is a numerically unstable algorithm and should not
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	32 ## be used on large polynomials.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	33 ##
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 13963 diff changeset	34 ## Example code:
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	35 ##
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	36 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	37 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	38 ## polygcd (poly (1:8), poly (3:12)) - poly (3:8)
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6046 diff changeset	39 ## @result{} [ 0, 0, 0, 0, 0, 0, 0 ]
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	40 ## deconv (poly (1:8), polygcd (poly (1:8), poly (3:12))) - poly (1:2)
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6046 diff changeset	41 ## @result{} [ 0, 0, 0 ]
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	42 ## @end group
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	43 ## @end example
14104 614505385171 doc: Overhaul docstrings for polynomial functions. Rik <octave@nomad.inbox5.com> parents: 13963 diff changeset	44 ## @seealso{poly, roots, conv, deconv, residue}
5642 2618a0750ae6 [project @ 2006-03-06 21:26:48 by jwe] jwe parents: 5382 diff changeset	45 ## @end deftypefn
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	46
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	47 function x = polygcd (b, a, tol)
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	48
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	49 if (nargin == 2 \|\| nargin == 3)
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	50 if (nargin == 2)
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7031 diff changeset	51 if (isa (a, "single") \|\| isa (b, "single"))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	52 tol = sqrt (eps ("single"));
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7031 diff changeset	53 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	54 tol = sqrt (eps);
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7031 diff changeset	55 endif
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	56 endif
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	57 if (length (a) == 1 \|\| length (b) == 1)
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	58 if (a == 0)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	59 x = b;
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	60 elseif (b == 0)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	61 x = a;
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	62 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	63 x = 1;
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	64 endif
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	65 else
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	66 a /= a(1);
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	67 while (1)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	68 [d, r] = deconv (b, a);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	69 nz = find (abs (r) > tol);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	70 if (isempty (nz))
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	71 x = a;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	72 break;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	73 else
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	74 r = r(nz(1):length(r));
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	75 endif
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	76 b = a;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	77 a = r / r(1);
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	78 endwhile
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	79 endif
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	80 else
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5642 diff changeset	81 print_usage ();
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	82 endif
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	83
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	84 endfunction
13045 92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	85
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	86
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	87 %!test
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	88 %! poly1 = [1 6 11 6]; # (x+1)(x+2)(x+3);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	89 %! poly2 = [1 3 2]; # (x+1)(x+2);
13045 92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	90 %! poly3 = polygcd (poly1, poly2);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	91 %! assert (poly3, poly2, sqrt (eps));
13045 92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	92
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	93 %!assert (polygcd (poly (1:8), poly (3:12)), poly (3:8), sqrt (eps))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	94 %!assert (deconv (poly (1:8), polygcd (poly (1:8), poly (3:12))), poly (1:2), sqrt (eps))
13045 92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	95
13141 e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 13045 diff changeset	96 %!test
19258 5d3111977623 Change a polygcd test to one that is more numerically accurate (bug #42742). Daniel J Sebald <daniel.sebald@ieee.org> parents: 17744 diff changeset	97 %! for ii=1:100
5d3111977623 Change a polygcd test to one that is more numerically accurate (bug #42742). Daniel J Sebald <daniel.sebald@ieee.org> parents: 17744 diff changeset	98 %! ## Exhibits numerical problems for multipliers of ~4 and greater.
5d3111977623 Change a polygcd test to one that is more numerically accurate (bug #42742). Daniel J Sebald <daniel.sebald@ieee.org> parents: 17744 diff changeset	99 %! p = (unique (randn (10, 1)) * 3).';
13045 92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	100 %! p1 = p(3:end);
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	101 %! p2 = p(1:end-2);
19258 5d3111977623 Change a polygcd test to one that is more numerically accurate (bug #42742). Daniel J Sebald <daniel.sebald@ieee.org> parents: 17744 diff changeset	102 %! assert (polygcd (poly (-p1), poly (-p2)),
5d3111977623 Change a polygcd test to one that is more numerically accurate (bug #42742). Daniel J Sebald <daniel.sebald@ieee.org> parents: 17744 diff changeset	103 %! poly (- intersect (p1, p2)), sqrt (eps));
13045 92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	104 %! endfor
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	105

Mercurial > octave-nkf

annotate scripts/polynomial/polygcd.m @ 20595:c1a6c31ac29a