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annotate scripts/polynomial/compan.m @ 10846:a4f482e66b65
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| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 01 Aug 2010 20:22:17 -0700 |
| parents | 693e22af08ae |
| children | fd0a3ac60b0e |
| rev | line source |
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| 7017 | 1 ## Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2004, |
| 9245 | 2 ## 2005, 2006, 2007, 2008, 2009 John W. Eaton |
| 2313 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 2313 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 904 | 19 |
| 3368 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {} compan (@var{c}) | |
| 22 ## Compute the companion matrix corresponding to polynomial coefficient | |
| 23 ## vector @var{c}. | |
| 3426 | 24 ## |
| 3368 | 25 ## The companion matrix is |
| 26 ## @tex | |
| 27 ## $$ | |
| 28 ## A = \left[\matrix{ | |
| 29 ## -c_2/c_1 & -c_3/c_1 & \cdots & -c_N/c_1 & -c_{N+1}/c_1\cr | |
| 30 ## 1 & 0 & \cdots & 0 & 0 \cr | |
| 31 ## 0 & 1 & \cdots & 0 & 0 \cr | |
| 32 ## \vdots & \vdots & \ddots & \vdots & \vdots \cr | |
| 33 ## 0 & 0 & \cdots & 1 & 0}\right]. | |
| 34 ## $$ | |
| 35 ## @end tex | |
| 6850 | 36 ## @ifnottex |
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37 ## @c Set example in small font to prevent overfull line |
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38 ## |
| 3368 | 39 ## @smallexample |
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40 ## @group |
| 3368 | 41 ## _ _ |
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42 ## | -c(2)/c(1) -c(3)/c(1) @dots{} -c(N)/c(1) -c(N+1)/c(1) | |
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43 ## | 1 0 @dots{} 0 0 | |
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44 ## | 0 1 @dots{} 0 0 | |
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45 ## A = | . . . . . | |
| 3368 | 46 ## | . . . . . | |
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47 ## | . . . . . | |
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48 ## |_ 0 0 @dots{} 1 0 _| |
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49 ## @end group |
| 3368 | 50 ## @end smallexample |
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51 ## |
| 6850 | 52 ## @end ifnottex |
| 2311 | 53 ## The eigenvalues of the companion matrix are equal to the roots of the |
| 54 ## polynomial. | |
| 5642 | 55 ## @seealso{poly, roots, residue, conv, deconv, polyval, polyderiv, |
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56 ## polyint} |
| 3368 | 57 ## @end deftypefn |
| 1025 | 58 |
| 3202 | 59 ## Author: Tony Richardson <arichard@stark.cc.oh.us> |
| 2312 | 60 ## Created: June 1994 |
| 61 ## Adapted-By: jwe | |
| 561 | 62 |
| 2312 | 63 function A = compan (c) |
| 561 | 64 |
| 1025 | 65 if (nargin != 1) |
| 6046 | 66 print_usage (); |
| 561 | 67 endif |
| 68 | |
| 4030 | 69 if (! isvector (c)) |
| 3458 | 70 error ("compan: expecting a vector argument"); |
| 561 | 71 endif |
| 72 | |
| 1025 | 73 n = length (c); |
| 2716 | 74 |
| 75 if (n == 1) | |
| 76 A = []; | |
| 77 else | |
| 78 A = diag (ones (n-2, 1), -1); | |
| 79 A(1,:) = -c(2:n) / c(1); | |
| 80 endif | |
| 561 | 81 |
| 82 endfunction | |
| 7411 | 83 |
| 84 %!assert(all (all (compan ([1, 2, 3]) == [-2, -3; 1, 0]))); | |
| 85 | |
| 86 %!assert(all (all (compan ([1; 2; 3]) == [-2, -3; 1, 0]))); | |
| 87 | |
| 88 %!assert(isempty (compan (4))); | |
| 89 | |
| 90 %!assert(all (all (compan ([3, 2, 1]) == [-2/3, -1/3; 1, 0]))); | |
| 91 | |
| 92 %!error compan ([1,2;3,4]); | |
| 93 | |
| 94 %!error compan ([]); | |
| 95 |