Mercurial > hg > octave-lyh
annotate scripts/polynomial/polygcd.m @ 9051:1bf0ce0930be
Grammar check TexInfo in all .m files
Cleanup documentation sources to follow a few consistent rules.
Spellcheck was NOT done. (but will be in another changeset)
| author | Rik <rdrider0-list@yahoo.com> |
|---|---|
| date | Fri, 27 Mar 2009 22:31:03 -0700 |
| parents | eb63fbe60fab |
| children | 16f53d29049f |
| rev | line source |
|---|---|
| 8920 | 1 ## Copyright (C) 2000, 2005, 2006, 2007, 2008 Paul Kienzle |
| 5216 | 2 ## |
| 7016 | 3 ## This file is part of Octave. |
| 5216 | 4 ## |
| 7016 | 5 ## Octave is free software; you can redistribute it and/or modify it |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 8 ## your option) any later version. | |
| 9 ## | |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 5216 | 14 ## |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 5216 | 18 |
| 19 ## -*- texinfo -*- | |
| 5382 | 20 ## @deftypefn {Function File} {@var{q} =} polygcd (@var{b}, @var{a}, @var{tol}) |
| 5216 | 21 ## |
| 22 ## Find greatest common divisor of two polynomials. This is equivalent | |
| 23 ## to the polynomial found by multiplying together all the common roots. | |
| 24 ## Together with deconv, you can reduce a ratio of two polynomials. | |
| 25 ## Tolerance defaults to | |
| 26 ## @example | |
| 27 ## sqrt(eps). | |
| 28 ## @end example | |
| 29 ## Note that this is an unstable | |
| 30 ## algorithm, so don't try it on large polynomials. | |
| 31 ## | |
| 32 ## Example | |
| 33 ## @example | |
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34 ## @group |
| 5382 | 35 ## polygcd (poly(1:8), poly(3:12)) - poly(3:8) |
| 6850 | 36 ## @result{} [ 0, 0, 0, 0, 0, 0, 0 ] |
| 7031 | 37 ## deconv (poly(1:8), polygcd (poly(1:8), poly(3:12))) ... |
| 38 ## - poly(1:2) | |
| 6850 | 39 ## @result{} [ 0, 0, 0 ] |
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parents:
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40 ## @end group |
| 5216 | 41 ## @end example |
| 42 ## @seealso{poly, polyinteg, polyderiv, polyreduce, roots, conv, deconv, | |
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43 ## residue, filter, polyval, polyvalm} |
| 5642 | 44 ## @end deftypefn |
| 5216 | 45 |
| 5217 | 46 function x = polygcd (b, a, tol) |
| 47 | |
| 48 if (nargin == 2 || nargin == 3) | |
| 49 if (nargin == 2) | |
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50 if (isa (a, "single") || isa (b, "single")) |
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51 tol = sqrt (eps ("single")); |
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52 else |
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53 tol = sqrt (eps); |
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parents:
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54 endif |
| 5216 | 55 endif |
| 5217 | 56 if (length (a) == 1 || length (b) == 1) |
| 57 if (a == 0) | |
| 58 x = b; | |
| 59 elseif (b == 0) | |
| 60 x = a; | |
| 61 else | |
| 62 x = 1; | |
| 63 endif | |
| 64 else | |
| 65 a /= a(1); | |
| 66 while (1) | |
| 67 [d, r] = deconv (b, a); | |
| 68 nz = find (abs (r) > tol); | |
| 69 if (isempty (nz)) | |
| 70 x = a; | |
| 71 break; | |
| 72 else | |
| 73 r = r(nz(1):length(r)); | |
| 74 endif | |
| 75 b = a; | |
| 5382 | 76 a = r / r(1); |
| 5217 | 77 endwhile |
| 78 endif | |
| 79 else | |
| 6046 | 80 print_usage (); |
| 5216 | 81 endif |
| 5217 | 82 |
| 83 endfunction |