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* lex.ll: Make debug text match change in pattern.
author John W. Eaton <jwe@octave.org>
date Sat, 11 Jan 2014 17:20:38 -0500
parents d63878346099
children 4197fc428c7d
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d63878346099 maint: Update copyright notices for release.
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1 ## Copyright (C) 1994-2013 John W. Eaton
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} roots (@var{v})
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21 ##
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22 ## For a vector @var{v} with @math{N} components, return
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23 ## the roots of the polynomial
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24 ## @tex
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25 ## $$
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26 ## v_1 z^{N-1} + \cdots + v_{N-1} z + v_N.
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27 ## $$
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28 ## @end tex
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29 ## @ifnottex
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30 ##
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31 ## @example
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32 ## v(1) * z^(N-1) + @dots{} + v(N-1) * z + v(N)
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33 ## @end example
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34 ##
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35 ## @end ifnottex
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36 ##
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37 ## As an example, the following code finds the roots of the quadratic
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38 ## polynomial
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39 ## @tex
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40 ## $$ p(x) = x^2 - 5. $$
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41 ## @end tex
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42 ## @ifnottex
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43 ##
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44 ## @example
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45 ## p(x) = x^2 - 5.
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46 ## @end example
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47 ##
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48 ## @end ifnottex
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49 ##
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50 ## @example
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51 ## @group
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52 ## c = [1, 0, -5];
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53 ## roots (c)
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54 ## @result{} 2.2361
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55 ## @result{} -2.2361
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56 ## @end group
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57 ## @end example
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58 ##
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59 ## Note that the true result is
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60 ## @tex
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61 ## $\pm \sqrt{5}$
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62 ## @end tex
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63 ## @ifnottex
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64 ## @math{+/- sqrt(5)}
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65 ## @end ifnottex
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66 ## which is roughly
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67 ## @tex
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68 ## $\pm 2.2361$.
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69 ## @end tex
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70 ## @ifnottex
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71 ## @math{+/- 2.2361}.
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72 ## @end ifnottex
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73 ## @seealso{poly, compan, fzero}
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74 ## @end deftypefn
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75
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76 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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77 ## Created: 24 December 1993
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78 ## Adapted-By: jwe
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79
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80 function r = roots (v)
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81
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82 if (nargin != 1 || (! isvector (v) && ! isempty (v)))
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83 print_usage ();
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84 elseif (any (! isfinite (v)))
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85 error ("roots: inputs must not contain Inf or NaN");
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86 endif
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87
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88 v = v(:);
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89 n = numel (v);
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90
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91 ## If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ],
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92 ## we can remove the leading k zeros,
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93 ## and n - k - l roots of the polynomial are zero.
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94
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95 v_max = max (abs (v));
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96 if (isempty (v) || v_max == 0)
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97 r = [];
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98 return;
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99 endif
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100
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101 f = find (v ./ v_max);
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102 m = numel (f);
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103
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104 v = v(f(1):f(m));
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105 l = numel (v);
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106 if (l > 1)
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107 A = diag (ones (1, l-2), -1);
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108 A(1,:) = -v(2:l) ./ v(1);
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109 r = eig (A);
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110 if (f(m) < n)
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111 r = [r; zeros(n - f(m), 1)];
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112 endif
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113 else
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114 r = zeros (n - f(m), 1);
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115 endif
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116
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117 endfunction
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118
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119
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120 %!test
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121 %! p = [poly([3 3 3 3]), 0 0 0 0];
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122 %! r = sort (roots (p));
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123 %! assert (r, [0; 0; 0; 0; 3; 3; 3; 3], 0.001);
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124
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125 %!assert (isempty (roots ([])))
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126 %!assert (isempty (roots ([0 0])))
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127 %!assert (isempty (roots (1)))
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128 %!assert (roots ([1, -6, 11, -6]), [3; 2; 1], sqrt (eps))
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129
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130 %!assert (roots ([1e-200, -1e200, 1]), 1e-200)
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131 %!assert (roots ([1e-200, -1e200 * 1i, 1]), -1e-200 * 1i)
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132
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133 %!error roots ()
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134 %!error roots (1,2)
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135 %!error roots ([1, 2; 3, 4])
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136 %!error <inputs must not contain Inf or NaN> roots ([1 Inf 1])
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137 %!error <inputs must not contain Inf or NaN> roots ([1 NaN 1])
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