update packages

[CreaPhase.git] / octave_packages / m / plot / peaks.m

diff --git a/octave_packages/m/plot/peaks.m b/octave_packages/m/plot/peaks.m
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+## Copyright (C) 2007-2012 Paul Kienzle
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} peaks ()
+## @deftypefnx {Function File} {} peaks (@var{n})
+## @deftypefnx {Function File} {} peaks (@var{x}, @var{y})
+## @deftypefnx {Function File} {@var{z} =} peaks (@dots{})
+## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} peaks (@dots{})
+## Generate 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{mesh}.  If @var{n} is a scalar, the @code{peaks}
+## returns the values of the above function on a @var{n}-by-@var{n} mesh over
+## the range @code{[-3,3]}.  The default value for @var{n} is 49.
+##
+## If @var{n} is a vector, then it represents the @var{x} and @var{y} values
+## of the grid on which to calculate the above function.  The @var{x} and
+## @var{y} values can be specified separately.
+## @seealso{surf, mesh, meshgrid}
+## @end deftypefn
+
+## Expression for the 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);
+  elseif (nargout == 1)
+    X_out = Z;
+  else
+    X_out = X;
+    Y_out = Y;
+    Z_out = Z;
+  endif
+
+endfunction