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