Mercurial > hg > octave-lyh
annotate scripts/polynomial/compan.m @ 14428:099bd779466c
test: Fix failing %!test in fileread.m
* fileread.m: Fix failing %!test.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Fri, 02 Mar 2012 22:14:27 -0800 |
| parents | f3d52523cde1 |
| children |
| rev | line source |
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maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1994-2012 John W. Eaton |
| 2313 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 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 | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 2313 | 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. | |
| 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/>. | |
| 904 | 18 |
| 3368 | 19 ## -*- texinfo -*- |
| 20 ## @deftypefn {Function File} {} compan (@var{c}) | |
| 21 ## Compute the companion matrix corresponding to polynomial coefficient | |
| 22 ## vector @var{c}. | |
| 3426 | 23 ## |
| 3368 | 24 ## The companion matrix is |
| 25 ## @tex | |
| 26 ## $$ | |
| 27 ## A = \left[\matrix{ | |
| 28 ## -c_2/c_1 & -c_3/c_1 & \cdots & -c_N/c_1 & -c_{N+1}/c_1\cr | |
| 29 ## 1 & 0 & \cdots & 0 & 0 \cr | |
| 30 ## 0 & 1 & \cdots & 0 & 0 \cr | |
| 31 ## \vdots & \vdots & \ddots & \vdots & \vdots \cr | |
| 32 ## 0 & 0 & \cdots & 1 & 0}\right]. | |
| 33 ## $$ | |
| 34 ## @end tex | |
| 6850 | 35 ## @ifnottex |
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Rik <rdrider0-list@yahoo.com>
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36 ## @c Set example in small font to prevent overfull line |
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Rik <octave@nomad.inbox5.com>
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37 ## |
| 3368 | 38 ## @smallexample |
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39 ## @group |
| 3368 | 40 ## _ _ |
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Rik <rdrider0-list@yahoo.com>
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41 ## | -c(2)/c(1) -c(3)/c(1) @dots{} -c(N)/c(1) -c(N+1)/c(1) | |
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42 ## | 1 0 @dots{} 0 0 | |
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Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
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43 ## | 0 1 @dots{} 0 0 | |
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44 ## A = | . . . . . | |
| 3368 | 45 ## | . . . . . | |
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46 ## | . . . . . | |
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Rik <rdrider0-list@yahoo.com>
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47 ## |_ 0 0 @dots{} 1 0 _| |
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48 ## @end group |
| 3368 | 49 ## @end smallexample |
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50 ## |
| 6850 | 51 ## @end ifnottex |
| 2311 | 52 ## The eigenvalues of the companion matrix are equal to the roots of the |
| 53 ## polynomial. | |
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54 ## @seealso{roots, poly, eig} |
| 3368 | 55 ## @end deftypefn |
| 1025 | 56 |
| 3202 | 57 ## Author: Tony Richardson <arichard@stark.cc.oh.us> |
| 2312 | 58 ## Created: June 1994 |
| 59 ## Adapted-By: jwe | |
| 561 | 60 |
| 2312 | 61 function A = compan (c) |
| 561 | 62 |
| 1025 | 63 if (nargin != 1) |
| 6046 | 64 print_usage (); |
| 561 | 65 endif |
| 66 | |
| 4030 | 67 if (! isvector (c)) |
| 3458 | 68 error ("compan: expecting a vector argument"); |
| 561 | 69 endif |
| 70 | |
| 1025 | 71 n = length (c); |
| 2716 | 72 |
| 73 if (n == 1) | |
| 74 A = []; | |
| 75 else | |
| 76 A = diag (ones (n-2, 1), -1); | |
| 77 A(1,:) = -c(2:n) / c(1); | |
| 78 endif | |
| 561 | 79 |
| 80 endfunction | |
| 7411 | 81 |
| 82 | |
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Rik <octave@nomad.inbox5.com>
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83 %!assert (compan ([1, 2, 3]), [-2, -3; 1, 0]) |
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Rik <octave@nomad.inbox5.com>
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84 %!assert (compan ([1; 2; 3]), [-2, -3; 1, 0]) |
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85 %!assert (isempty (compan (4))) |
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Rik <octave@nomad.inbox5.com>
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86 %!assert (compan ([3, 2, 1]), [-2/3, -1/3; 1, 0]) |
| 7411 | 87 |
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88 %!error compan ([1,2;3,4]) |
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89 %!error compan ([]) |
| 7411 | 90 |