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annotate scripts/specfun/nthroot.m @ 15806:01d4f742d75d

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doc: Re-organize and improve Java Interface documentation. * doc/interpreter/java.txi: Add usejava, isjava functions, debug_java, java_matrix_autoconversion, java_unsigned_autoconversion to docs. Re-organize to put functions in logical order. Add new "Dialog Box Functions" node. * doc/interpreter/system.txi: Remove usejava from list of system functions. * libinterp/octave-value/ov-java.cc(FjavaObject, FjavaMethod, Fjava_unsigned_autoconversion): Improve docstrings. * scripts/java/javaArray.m: Tweak docstring. * scripts/java/listdlg.m: Wrap long lines in docstring. Improve code example in docstring.
author Rik <rik@octave.org>
date Mon, 17 Dec 2012 10:23:43 -0800
parents f3d52523cde1
children
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1 ## Copyright (C) 2004-2012 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{x} must have all real entries. @var{n} must be a scalar.
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39 ## If @var{n} is an even integer and @var{X} has negative entries, an
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40 ## error is produced.
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41 ## @seealso{realsqrt, sqrt, cbrt}
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42 ## @end deftypefn
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43
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44 function y = nthroot (x, n)
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45
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46 if (nargin != 2)
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47 print_usage ();
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48 endif
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49
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50 if (any (iscomplex (x(:))))
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51 error ("nthroot: X must not contain complex values");
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52 endif
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53
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54 if (! isscalar (n) || n == 0)
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55 error ("nthroot: N must be a nonzero scalar");
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56 endif
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57
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58 if (n == 3)
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59 y = cbrt (x);
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60 elseif (n == -3)
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61 y = 1 ./ cbrt (x);
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62 elseif (n < 0)
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63 y = 1 ./ nthroot (x, -n);
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64 else
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65 ## Compute using power.
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66 if (n == fix (n) && mod (n, 2) == 1)
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67 y = abs (x) .^ (1/n) .* sign (x);
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68 elseif (any (x(:) < 0))
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69 error ("nthroot: if X contains negative values, N must be an odd integer");
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70 else
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71 y = x .^ (1/n);
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72 endif
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73
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74 if (finite (n) && n > 0 && n == fix (n))
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75 ## Correction.
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76 y = ((n-1)*y + x ./ (y.^(n-1))) / n;
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77 y = merge (finite (y), y, x);
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78 endif
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79
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80 endif
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81
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82 endfunction
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83
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84
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85 %!assert (nthroot (-32,5), -2);
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86 %!assert (nthroot (81,4), 3);
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87 %!assert (nthroot (Inf,4), Inf);
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88 %!assert (nthroot (-Inf,7), -Inf);
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89 %!assert (nthroot (-Inf,-7), 0);
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90
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91 %% Test input validation
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92 %!error (nthroot ())
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93 %!error (nthroot (1))
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94 %!error (nthroot (1,2,3))
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95 %!error (nthroot (1+j,2))
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96 %!error (nthroot (1,[1 2]))
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97 %!error (nthroot (1,0))
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98 %!error (nthroot (-1,2))
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99