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maint: merge stable to default.
author John W. Eaton <jwe@octave.org>
date Wed, 10 Feb 2021 10:10:40 -0500
parents 28de41192f3c 0a5b15007766
children 796f54d4ddbf
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2017-2021 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 {} {@var{y} =} humps (@var{x})
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28 ## @deftypefnx {} {[@var{x}, @var{y}] =} humps (@var{x})
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29 ## Evaluate a function with multiple minima, maxima, and zero crossings.
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30 ##
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31 ## The output @var{y} is the evaluation of the rational function:
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32 ##
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33 ## @tex
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34 ## $$y = -{ {1200x^4 - 2880x^3 + 2036x^2 - 340x - 88} \over {200x^4 - 480x^3 + 406x^2 - 138x - 17} }$$
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35 ## @end tex
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36 ## @ifnottex
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37 ##
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38 ## @example
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39 ## @group
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40 ## 1200*@var{x}^4 - 2880*@var{x}^3 + 2036*@var{x}^2 - 348*@var{x} - 88
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41 ## @var{y} = - ---------------------------------------------
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42 ## 200*@var{x}^4 - 480*@var{x}^3 + 406*@var{x}^2 - 138*@var{x} + 17
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43 ## @end group
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44 ## @end example
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45 ##
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46 ## @end ifnottex
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47 ##
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48 ## @var{x} may be a scalar, vector or array. If @var{x} is omitted, the
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49 ## default range [0:0.05:1] is used.
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50 ##
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51 ## When called with two output arguments, [@var{x}, @var{y}], @var{x} will
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52 ## contain the input values, and @var{y} will contain the output from
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53 ## @code{humps}.
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54 ##
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55 ## Programming Notes: @code{humps} has two local maxima located near @var{x} =
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56 ## 0.300 and 0.893, a local minimum near @var{x} = 0.637, and zeros near
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57 ## @var{x} = -0.132 and 1.300. @code{humps} is a useful function for testing
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58 ## algorithms which find zeros or local minima and maxima.
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59 ##
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60 ## Try @code{demo humps} to see a plot of the @code{humps} function.
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61 ## @seealso{fzero, fminbnd, fminunc, fminsearch}
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62 ## @end deftypefn
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63
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64 function [x, y] = humps (x = [0:0.05:1])
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65
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66 y = - 4*( 300*x.^4 - 720*x.^3 + 509*x.^2 - 87*x - 22) ./ ...
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67 ((10*x.^2 - 6*x + 1).*(20*x.^2 - 36*x + 17));
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68
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69 if (nargout <= 1)
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70 x = y;
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71 endif
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72
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73 endfunction
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74
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75
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76 %!demo
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77 %! clf;
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78 %! fplot (@humps, [0, 2]);
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79 %! title ("humps() function");
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80
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81 ## value checks
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82 %!assert (humps (0), 88/17, 10*eps)
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83 %!assert (humps (1), 16, 10*eps)
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84 %!assert (humps (-1), -6376/1241, 10*eps)
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85 %!assert (humps (), [88/17, 16106/1769, 263/17, 82802/3133, 2432/53, ...
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86 %! 2818/37, 193/2, 10538/137, 1376/29, 36434/1261, 19, 5258/377, ...
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87 %! 152/13, 24562/2173, 421/34, 250/17, 232/13, 1762/85, 803/37, ...
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88 %! 58354/2941, 16], 1000*eps)
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89
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90 ## vector checks
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91 %!assert (humps ([0, 1]), [88/17, 16], 10*eps)
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92 %!assert (humps ([0, 1]'), [88/17, 16]', 10*eps)
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93 %!assert (humps ([0, 1; 1, 0]'), [88/17, 16; 16, 88/17]', 10*eps)
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94
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95 ## array checks
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96 %!assert (humps (repmat (eye (2), 1, 1, 2)),
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97 %! repmat ([16, 88/17; 88/17, 16], 1, 1, 2), 10*eps)
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98
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99 ## other checks
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100 %!assert (humps (NaN), NaN)
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101 %!assert (humps ([]), [])
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102
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103 ## Test input validation
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104 %!error humps (1,3)