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1 ## Copyright (C) 1995, 1996, 1997, 1999, 2000, 2002, 2004, 2005, 2006, |
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2 ## 2007 Kurt Hornik |
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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 ## -*- texinfo -*- |
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21 ## @deftypefn {Mapping Function} {} erfinv (@var{z}) |
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22 ## Computes the inverse of the error function. |
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23 ## @seealso{erf, erfc} |
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24 ## @end deftypefn |
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25 |
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26 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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27 ## Created: 27 September 1994 |
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28 ## Adapted-By: jwe |
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29 |
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30 function [y, iterations] = erfinv (x) |
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31 |
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32 if (nargin != 1) |
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33 print_usage (); |
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34 endif |
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35 |
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36 maxit = 100; |
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37 tol = eps; |
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38 |
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39 iterations = 0; |
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40 |
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41 sz = size (x); |
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42 nel = numel (x); |
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43 |
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44 x = reshape (x, nel, 1); |
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45 y = zeros (nel, 1); |
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46 |
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47 i = find ((x < -1) | (x > 1) | isnan(x)); |
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48 if any (i) |
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49 y(i) = NaN * ones (length (i), 1); |
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50 endif |
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51 |
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52 t = find (x == -1); |
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53 y (t) = (-Inf) * ones (size (t)); |
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54 |
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55 t = find (x == 1); |
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56 y (t) = Inf * ones (size (t)); |
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57 |
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58 i = find ((x > -1) & (x < 1)); |
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59 if any (i) |
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60 s = sqrt (pi) / 2; |
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61 z_old = ones (length (i), 1); |
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62 z_new = sqrt (-log (1 - abs (x(i)))) .* sign (x(i)); |
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63 while (any (abs (erf (z_new) - x(i)) > tol * abs (x(i)))) |
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64 z_old = z_new; |
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65 z_new = z_old - (erf (z_old) - x(i)) .* exp (z_old.^2) * s; |
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66 if (++iterations > maxit) |
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67 warning ("erfinv: iteration limit exceeded"); |
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68 break; |
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69 endif |
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70 endwhile |
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71 y(i) = z_new; |
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72 endif |
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73 |
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74 y = reshape (y, sz); |
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75 |
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76 endfunction |
