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1 ## Copyright (C) 2004, 2006, 2007 Paul Kienzle |
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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 ## Original version by Paul Kienzle distributed as free software in the |
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20 ## public domain. |
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21 |
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22 ## -*- texinfo -*- |
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23 ## @deftypefn {Function File} {} nthroot (@var{x}, @var{n}) |
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24 ## |
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25 ## Compute the nth root of @var{x}, returning real results for real |
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26 ## components of @var{x}. For example |
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27 ## |
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28 ## @example |
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29 ## @group |
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30 ## nthroot (-1, 3) |
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31 ## @result{} -1 |
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32 ## (-1) ^ (1 / 3) |
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33 ## @result{} 0.50000 - 0.86603i |
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34 ## @end group |
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35 ## @end example |
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36 ## |
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37 ## @end deftypefn |
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38 |
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39 function y = nthroot (x, m) |
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40 |
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41 if (nargin != 2) |
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42 print_usage (); |
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43 endif |
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44 |
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45 y = x.^(1./m); |
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46 |
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47 if (isscalar (x)) |
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48 x *= ones (size (m)); |
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49 endif |
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50 |
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51 if (isscalar (m)) |
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52 m *= ones (size (x)); |
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53 endif |
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54 |
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55 idx = (mod (m, 2) == 1 & imag (x) == 0 & x < 0); |
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56 |
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57 if (any (idx(:))) |
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58 y(idx) = -(-x(idx)).^(1./m(idx)); |
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59 endif |
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60 |
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61 ## If result is all real, make sure it looks real |
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62 if (all (imag (y) == 0)) |
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63 y = real (y); |
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64 endif |
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65 |
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66 endfunction |
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67 |
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68 %!assert(nthroot(-1,[3,-3]), [-1,-1],eps); |
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69 %!assert(nthroot([-1,1],[3.1,-3]), [-1,1].^(1./[3.1,-3])); |
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70 %!assert(nthroot([-1+1i,-1-1i],3), [-1+1i,-1-1i].^(1/3)); |
