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annotate scripts/specfun/nthroot.m @ 10821:693e22af08ae

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Grammarcheck documentation of m-files Add newlines between @item fields for readability.
author Rik <octave@nomad.inbox5.com>
date Mon, 26 Jul 2010 21:25:36 -0700
parents fbd7843974fa
children 1740012184f9
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1 ## Copyright (C) 2004, 2006, 2007, 2009 Paul Kienzle
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2 ## Copyright (C) 2010 VZLU Prague
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19 ##
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20 ## Original version by Paul Kienzle distributed as free software in the
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21 ## public domain.
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22
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23 ## -*- texinfo -*-
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24 ## @deftypefn {Function File} {} nthroot (@var{x}, @var{n})
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25 ##
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26 ## Compute the n-th root of @var{x}, returning real results for real
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27 ## components of @var{x}. For example:
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28 ##
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29 ## @example
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30 ## @group
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31 ## nthroot (-1, 3)
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32 ## @result{} -1
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33 ## (-1) ^ (1 / 3)
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34 ## @result{} 0.50000 - 0.86603i
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35 ## @end group
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36 ## @end example
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37 ##
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38 ## @var{n} must be a scalar. If @var{n} is not an even integer and @var{X} has
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39 ## negative entries, an error is produced.
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40 ##
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41 ## @end deftypefn
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42
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43 function y = nthroot (x, n)
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44
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45 if (nargin != 2)
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46 print_usage ();
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47 endif
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48
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49 if (! isscalar (n))
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50 error ("nthroot: n must be a nonzero scalar");
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51 endif
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52
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53 if (n == 3)
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54 y = cbrt (x);
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55 elseif (n == -3)
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56 y = 1 ./ cbrt (x);
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57 elseif (n < 0)
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58 y = 1 ./ nthroot (x, -n);
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59 else
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60 ## Compute using power.
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61 if (n == round (n) && mod (n, 2) == 1)
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62 y = abs (x) .^ (1/n) .* sign (x);
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63 elseif (any (x(:) < 0))
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64 error ("nthroot: if x contains negative values, n must be an odd integer");
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65 else
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66 y = x .^ (1/n);
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67 endif
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68
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69 if (finite (n) && n > 0 && n == round (n))
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70 ## Correction.
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71 y = ((n-1)*y + x ./ (y.^(n-1))) / n;
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72 y = merge (finite (y), y, x);
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73 endif
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74
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75 endif
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76
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77 endfunction
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78
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79 %!assert(nthroot(-32,5), -2);
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80 %!assert(nthroot(81,4), 3);
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81 %!assert(nthroot(Inf,4), Inf);
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82 %!assert(nthroot(-Inf,7), -Inf);
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83 %!assert(nthroot(-Inf,-7), 0);