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Use Octave coding conventions in all m-file %!test blocks
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Use Octave coding conventions in all m-file %!test blocks
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 72c96de7a403 |
children | 5d3a684236b0 |
rev | line source |
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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/>. | |
1025 | 18 |
3368 | 19 ## -*- texinfo -*- |
20 ## @deftypefn {Function File} {} roots (@var{v}) | |
3426 | 21 ## |
3499 | 22 ## For a vector @var{v} with @math{N} components, return |
3368 | 23 ## the roots of the polynomial |
24 ## @tex | |
25 ## $$ | |
26 ## v_1 z^{N-1} + \cdots + v_{N-1} z + v_N. | |
27 ## $$ | |
28 ## @end tex | |
6850 | 29 ## @ifnottex |
3426 | 30 ## |
3368 | 31 ## @example |
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32 ## v(1) * z^(N-1) + @dots{} + v(N-1) * z + v(N) |
3368 | 33 ## @end example |
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34 ## |
6850 | 35 ## @end ifnottex |
36 ## | |
37 ## As an example, the following code finds the roots of the quadratic | |
38 ## polynomial | |
39 ## @tex | |
40 ## $$ p(x) = x^2 - 5. $$ | |
41 ## @end tex | |
42 ## @ifnottex | |
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43 ## |
6850 | 44 ## @example |
45 ## p(x) = x^2 - 5. | |
46 ## @end example | |
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47 ## |
6850 | 48 ## @end ifnottex |
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49 ## |
6850 | 50 ## @example |
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51 ## @group |
6850 | 52 ## c = [1, 0, -5]; |
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53 ## roots (c) |
6850 | 54 ## @result{} 2.2361 |
55 ## @result{} -2.2361 | |
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56 ## @end group |
6850 | 57 ## @end example |
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58 ## |
6850 | 59 ## Note that the true result is |
60 ## @tex | |
61 ## $\pm \sqrt{5}$ | |
62 ## @end tex | |
63 ## @ifnottex | |
64 ## @math{+/- sqrt(5)} | |
65 ## @end ifnottex | |
66 ## which is roughly | |
67 ## @tex | |
68 ## $\pm 2.2361$. | |
69 ## @end tex | |
70 ## @ifnottex | |
71 ## @math{+/- 2.2361}. | |
72 ## @end ifnottex | |
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73 ## @seealso{poly, compan, fzero} |
3368 | 74 ## @end deftypefn |
2311 | 75 |
5428 | 76 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
2312 | 77 ## Created: 24 December 1993 |
78 ## Adapted-By: jwe | |
79 | |
787 | 80 function r = roots (v) |
904 | 81 |
6372 | 82 if (nargin != 1 || min (size (v)) > 1) |
6046 | 83 print_usage (); |
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84 elseif (any (isnan(v) | isinf(v))) |
8664 | 85 error ("roots: inputs must not contain Inf or NaN"); |
1598 | 86 endif |
2325 | 87 |
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88 n = numel (v); |
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89 v = v(:); |
1025 | 90 |
2303 | 91 ## If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the |
2325 | 92 ## leading k zeros and n - k - l roots of the polynomial are zero. |
904 | 93 |
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94 if (isempty (v)) |
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95 f = v; |
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96 else |
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97 f = find (v ./ max (abs (v))); |
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98 endif |
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99 m = numel (f); |
2325 | 100 |
1598 | 101 if (m > 0 && n > 1) |
102 v = v(f(1):f(m)); | |
787 | 103 l = max (size (v)); |
104 if (l > 1) | |
105 A = diag (ones (1, l-2), -1); | |
1598 | 106 A(1,:) = -v(2:l) ./ v(1); |
2325 | 107 r = eig (A); |
1598 | 108 if (f(m) < n) |
109 tmp = zeros (n - f(m), 1); | |
3426 | 110 r = [r; tmp]; |
787 | 111 endif |
112 else | |
113 r = zeros (n - f(m), 1); | |
114 endif | |
115 else | |
1598 | 116 r = []; |
787 | 117 endif |
2325 | 118 |
787 | 119 endfunction |
7411 | 120 |
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121 |
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122 %!test |
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123 %! p = [poly([3 3 3 3]), 0 0 0 0]; |
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124 %! r = sort (roots (p)); |
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125 %! assert (r, [0; 0; 0; 0; 3; 3; 3; 3], 0.001); |
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126 |
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127 %!assert (isempty (roots ([]))) |
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128 %!assert (isempty (roots (1))) |
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129 %!assert (roots ([1, -6, 11, -6]), [3; 2; 1], sqrt (eps)) |
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130 |
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131 %!assert(roots ([1e-200, -1e200, 1]), 1e-200) |
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132 %!assert(roots ([1e-200, -1e200 * 1i, 1]), -1e-200 * 1i) |
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133 |
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134 %!error roots () |
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135 %!error roots (1,2) |
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136 %!error roots ([1, 2; 3, 4]) |
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137 %!error <inputs must not contain Inf or NaN> roots ([1 Inf 1]) |
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138 %!error <inputs must not contain Inf or NaN> roots ([1 NaN 1]) |
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139 |