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1 ## Copyright (C) 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 2, or (at your option) |
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8 ## 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, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} peaks () |
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22 ## @deftypefnx {Function File} {} peaks (@var{n}) |
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23 ## @deftypefnx {Function File} {} peaks (@var{x}, @var{y}) |
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24 ## @deftypefnx {Function File} {@var{z} =} peaks (@dots{}) |
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25 ## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} peaks (@dots{}) |
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26 ## Generate a function with lots of local maxima and minima. The function |
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27 ## has the form |
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28 ## |
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29 ## @iftex |
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30 ## @tex |
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31 ## $f(x,y) = 3 (1 - x) ^ 2 e ^ {\left(-x^2 - (y+1)^2\right)} - 10 \left({x \over 5} - x^3 - y^5)\right) - {1 \over 3} e^{\left(-(x+1)^2 - y^2\right)}$ |
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32 ## @end tex |
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33 ## @end iftex |
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34 ## @ifnottex |
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35 ## @verbatim |
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36 ## f(x,y) = 3*(1-x)^2*exp(-x^2 - (y+1)^2) ... |
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37 ## - 10*(x/5 - x^3 - y^5)*exp(-x^2-y^2) ... |
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38 ## - 1/3*exp(-(x+1)^2 - y^2) |
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39 ## @end verbatim |
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40 ## @end ifnottex |
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41 ## |
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42 ## Called without a return argument, @code{peaks} plots the surface of the |
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43 ## above function using @code{mesh}. If @var{n} is a scalar, the @code{peaks} |
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44 ## returns the values of the above funxtion on a @var{n}-by-@var{n} mesh over |
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45 ## the range @code{[-3,3]}. The default value for @var{n} is 49. |
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46 ## |
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47 ## If @var{n} is a vector, then it represents the @var{x} and @var{y} values |
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48 ## of the grid on which to calculate the above function. The @var{x} and |
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49 ## @var{y} values can be specified separately. |
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50 ## @seealso{mesh} |
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51 ## @end deftypefn |
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52 |
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53 ## Expression for peaks function was taken from the following paper: |
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54 ## http://www.control.hut.fi/Kurssit/AS-74.115/Material/GENALGgoga.pdf |
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55 function [X_out, Y_out, Z_out] = peaks (x, y) |
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56 |
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57 if nargin == 0 |
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58 x = y = linspace(-3,3,49); |
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59 elseif nargin == 1 |
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60 if length(x) > 1 |
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61 y = x; |
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62 else |
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63 x = y = linspace(-3,3,x); |
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64 endif |
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65 endif |
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66 |
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67 if (isvector(x) && isvector(y)) |
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68 [X, Y] = meshgrid (x, y); |
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69 else |
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70 X = x; |
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71 Y = y; |
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72 endif |
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73 |
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74 Z = 3 * (1 - X) .^ 2 .* exp(- X .^ 2 - (Y + 1) .^ 2) \ |
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75 - 10 * (X / 5 - X .^ 3 - Y .^ 5) .* exp(- X .^ 2 - Y .^ 2) \ |
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76 - 1 / 3 * exp(- (X + 1) .^ 2 - Y .^ 2); |
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77 |
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78 if nargout == 0 |
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79 mesh (x, y, Z); |
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80 elseif nargout == 1 |
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81 X_out = Z; |
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82 else |
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83 X_out = X; |
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84 Y_out = Y; |
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85 Z_out = Z; |
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86 endif |
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87 |
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88 endfunction |
