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

annotate scripts/polynomial/polygcd.m @ 13045:92cb87addf25

codesprint: Add tests to polygcd * polygcd.m : Add tests.

author	Carlo de Falco <kingcrimson@tiscali.it>
date	Sat, 03 Sep 2011 17:44:20 +0200
parents	fd0a3ac60b0e
children	e81ddf9cacd5

rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 10821 diff changeset	1 ## Copyright (C) 2000-2011 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 ##
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	23 ## Find the greatest common divisor of two polynomials. This is equivalent
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	24 ## to the polynomial found by multiplying together all the common roots.
5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	25 ## Together with deconv, you can reduce a ratio of two polynomials.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	26 ## Tolerance defaults to @code{sqrt(eps)}.
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	27 ##
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	28 ## Note that this is a numerically unstable algorithm, and should not be used
693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	29 ## on large polynomials.
693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	30 ##
693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	31 ## Example:
693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	32 ##
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	33 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	34 ## @group
5382 7012c2492c12 [project @ 2005-06-05 13:30:48 by jwe] jwe parents: 5377 diff changeset	35 ## 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	36 ## @result{} [ 0, 0, 0, 0, 0, 0, 0 ]
7031 120f3135952f [project @ 2007-10-15 15:30:03 by jwe] jwe parents: 7017 diff changeset	37 ## deconv (poly(1:8), polygcd (poly(1:8), poly(3:12))) ...
120f3135952f [project @ 2007-10-15 15:30:03 by jwe] jwe parents: 7017 diff changeset	38 ## - poly(1:2)
6850 9398f6a81bdf [project @ 2007-08-31 17:29:22 by jwe] jwe parents: 6046 diff changeset	39 ## @result{} [ 0, 0, 0 ]
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	40 ## @end group
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	41 ## @end example
10224 f6e0404421f4 point to polyint in @seealso, not polyinteg John W. Eaton <jwe@octave.org> parents: 9245 diff changeset	42 ## @seealso{poly, polyint, polyderiv, polyreduce, roots, conv, deconv,
8286 6f2d95255911 fix @seealso references to point to existing anchors Thorsten Meyer <thorsten.meyier@gmx.de> parents: 7795 diff changeset	43 ## residue, filter, polyval, polyvalm}
5642 2618a0750ae6 [project @ 2006-03-06 21:26:48 by jwe] jwe parents: 5382 diff changeset	44 ## @end deftypefn
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	45
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	46 function x = polygcd (b, a, tol)
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	47
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	48 if (nargin == 2 \|\| nargin == 3)
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	49 if (nargin == 2)
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7031 diff changeset	50 if (isa (a, "single") \|\| isa (b, "single"))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	51 tol = sqrt (eps ("single"));
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7031 diff changeset	52 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	53 tol = sqrt (eps);
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7031 diff changeset	54 endif
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	55 endif
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	56 if (length (a) == 1 \|\| length (b) == 1)
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	57 if (a == 0)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	58 x = b;
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	59 elseif (b == 0)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	60 x = a;
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	61 else
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	62 x = 1;
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	63 endif
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	64 else
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	65 a /= a(1);
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	66 while (1)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	67 [d, r] = deconv (b, a);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	68 nz = find (abs (r) > tol);
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	69 if (isempty (nz))
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	70 x = a;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	71 break;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	72 else
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	73 r = r(nz(1):length(r));
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	74 endif
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	75 b = a;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10224 diff changeset	76 a = r / r(1);
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	77 endwhile
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	78 endif
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	79 else
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5642 diff changeset	80 print_usage ();
5216 5ed60b8b1ac4 [project @ 2005-03-16 19:51:39 by jwe] jwe parents: diff changeset	81 endif
5217 e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	82
e88886a6934d [project @ 2005-03-16 20:03:01 by jwe] jwe parents: 5216 diff changeset	83 endfunction
13045 92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	84
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 %!test
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	87 %! poly1 = [1 6 11 6]; % (x+1)(x+2)(x+3)
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	88 %! poly2 = [1 3 2]; % (x+1)(x+2)
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	89 %! poly3 = polygcd (poly1, poly2);
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	90 %! assert (poly3, poly2, sqrt (eps))
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	91
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	92 %!test
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	93 %! assert (polygcd (poly(1:8), poly(3:12)), poly(3:8), sqrt (eps))
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	94
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	95 %!test
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	96 %! assert (deconv (poly(1:8), polygcd (poly(1:8), poly(3:12))), poly(1:2), sqrt (eps))
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	97
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	98 %!test
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	99 %! for ii=1:10
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	100 %! p = (unique (randn (10, 1)) * 10).';
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	101 %! p1 = p(3:end);
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	102 %! p2 = p(1:end-2);
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	103 %! assert (polygcd (poly (-p1), poly (-p2)), poly (- intersect (p1, p2)), sqrt (eps))
92cb87addf25 codesprint: Add tests to polygcd Carlo de Falco <kingcrimson@tiscali.it> parents: 11523 diff changeset	104 %! endfor

Mercurial > hg > octave-lyh

annotate scripts/polynomial/polygcd.m @ 13045:92cb87addf25