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1 ## Copyright (C) 1995, 1996 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## usage: erfinv (x) |
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18 ## |
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19 ## Computes the inverse of the error function erf. |
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20 |
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21 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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22 ## Created: 27 September 1994 |
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23 ## Adapted-By: jwe |
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24 |
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25 function [y, iterations] = erfinv (x) |
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26 |
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27 if (nargin != 1) |
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28 usage ("erfinv (x)"); |
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29 endif |
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30 |
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31 maxit = 100; |
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32 tol = eps; |
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33 |
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34 iterations = 0; |
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35 |
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36 [m, n] = size (x); |
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37 x = reshape (x, m * n, 1); |
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38 y = zeros (m * n, 1); |
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39 |
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40 i = find ((x < -1) | (x > 1)); |
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41 if any (i) |
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42 y(i) = NaN * ones (length (i), 1); |
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43 endif |
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44 |
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45 t = find (x == -1); |
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46 y (t) = (-Inf) * ones (size (t)); |
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47 |
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48 t = find (x == 1); |
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49 y (t) = Inf * ones (size (t)); |
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50 |
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51 i = find ((x > -1) & (x < 1)); |
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52 if any (i) |
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53 s = sqrt (pi) / 2; |
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54 z_old = ones (length (i), 1); |
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55 z_new = sqrt (-log (1 - abs (x(i)))) .* sign (x(i)); |
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56 while (any (abs (erf (z_old) - x(i)) > tol * abs (x(i)))) |
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57 z_old = z_new; |
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58 z_new = z_old - (erf (z_old) - x(i)) .* exp (z_old.^2) * s; |
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59 if (++iterations > maxit) |
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60 warning ("erfinv: iteration limit exceeded"); |
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61 break; |
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62 endif |
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63 endwhile |
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64 y(i) = z_new; |
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65 endif |
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66 |
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67 y = reshape (y, m, n); |
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68 |
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69 endfunction |
