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maint: update Octave Project Developers copyright for the new year
author John W. Eaton <jwe@octave.org>
date Fri, 22 Dec 2023 12:08:17 -0500
parents 597f3ee61a48
children
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2007-2024 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {} peaks ()
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28 ## @deftypefnx {} {} peaks (@var{n})
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29 ## @deftypefnx {} {} peaks (@var{x}, @var{y})
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30 ## @deftypefnx {} {@var{z} =} peaks (@dots{})
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31 ## @deftypefnx {} {[@var{x}, @var{y}, @var{z}] =} peaks (@dots{})
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32 ## Plot a function with lots of local maxima and minima.
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33 ##
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34 ## The function has the form
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35 ##
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36 ## @tex
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37 ## $$f(x,y) = 3 (1 - x) ^ 2 e ^ {\left(-x^2 - (y+1)^2\right)} - 10 \left({x \over 5} - x^3 - y^5\right) - {1 \over 3} e^{\left(-(x+1)^2 - y^2\right)}$$
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38 ## @end tex
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39 ## @ifnottex
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40 ## @verbatim
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41 ## f(x,y) = 3*(1-x)^2*exp(-x^2 - (y+1)^2) ...
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42 ## - 10*(x/5 - x^3 - y^5)*exp(-x^2-y^2) ...
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43 ## - 1/3*exp(-(x+1)^2 - y^2)
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44 ## @end verbatim
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45 ## @end ifnottex
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46 ##
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47 ## Called without a return argument, @code{peaks} plots the surface of the
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48 ## above function using @code{surf}.
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49 ##
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50 ## If @var{n} is a scalar, @code{peaks} plots the value of the above
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51 ## function on an @var{n}-by-@var{n} mesh over the range [-3,3]. The
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52 ## default value for @var{n} is 49.
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53 ##
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54 ## If @var{n} is a vector, then it represents the grid values over which
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55 ## to calculate the function. If @var{x} and @var{y} are specified then
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56 ## the function value is calculated over the specified grid of vertices.
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57 ##
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58 ## When called with output arguments, return the data for the function
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59 ## evaluated over the meshgrid. This can subsequently be plotted with
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60 ## @code{surf (@var{x}, @var{y}, @var{z})}.
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61 ##
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62 ## @seealso{sombrero, meshgrid, mesh, surf}
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63 ## @end deftypefn
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64
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65 ## Reference: Expression for peaks function was taken from the following paper:
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66 ## http://www.control.hut.fi/Kurssit/AS-74.115/Material/GENALGgoga.pdf
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67
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68 function [X_out, Y_out, Z_out] = peaks (x, y)
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69
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70 if (nargin == 0)
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71 x = y = linspace (-3, 3, 49);
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72 elseif (nargin == 1)
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73 if (length (x) > 1)
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74 y = x;
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75 else
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76 x = y = linspace (-3, 3, x);
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77 endif
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78 endif
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79
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80 if (isvector (x) && isvector (y))
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81 [X, Y] = meshgrid (x, y);
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82 else
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83 X = x;
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84 Y = y;
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85 endif
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86
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87 Z = 3 * (1 - X) .^ 2 .* exp (- X .^ 2 - (Y + 1) .^ 2) ...
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88 - 10 * (X / 5 - X .^ 3 - Y .^ 5) .* exp (- X .^ 2 - Y .^ 2) ...
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89 - 1 / 3 * exp (- (X + 1) .^ 2 - Y .^ 2);
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90
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91 if (nargout == 0)
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92 surf (x, y, Z);
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93 Z_max = max (Z(:));
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94 Z_min = min (Z(:));
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95 axis ([-3, 3, -3, 3, Z_min, Z_max]);
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96 elseif (nargout == 1)
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97 X_out = Z;
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98 else
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99 X_out = X;
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100 Y_out = Y;
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101 Z_out = Z;
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102 endif
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103
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104 endfunction