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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2008-2009 - INRIA - Michael Baudin
// Copyright (C) 2010 - DIGITEO - Allan CORNET
// Copyright (C) 2011 - DIGITEO - Michael Baudin
// Copyright (C) 2012 - Scilab Enterprises - Adeline CARNIS
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
function demo_mckinnon2()
mprintf(_("Defining McKinnon function...\n"));
//% MCKINNON computes the McKinnon function.
//
// Discussion:
//
// This function has a global minimizer:
//
// X* = ( 0.0, -0.5 ), F(X*) = -0.25
//
// There are three parameters, TAU, THETA and PHI.
//
// 1 < TAU, then F is strictly convex.
// and F has continuous first derivatives.
// 2 < TAU, then F has continuous second derivatives.
// 3 < TAU, then F has continuous third derivatives.
//
// However, this function can cause the Nelder-Mead optimization
// algorithm to "converge" to a point which is not the minimizer
// of the function F.
//
// Sample parameter values which cause problems for Nelder-Mead
// include:
//
// TAU = 1, THETA = 15, PHI = 10;
// TAU = 2, THETA = 6, PHI = 60;
// TAU = 3, THETA = 6, PHI = 400;
//
// To get the bad behavior, we also assume the initial simplex has the form
//
// X1 = (0,0),
// X2 = (1,1),
// X3 = (A,B),
//
// where
//
// A = (1+sqrt(33))/8 = 0.84307...
// B = (1-sqrt(33))/8 = -0.59307...
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 09 February 2008
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Ken McKinnon,
// Convergence of the Nelder-Mead simplex method to a nonstationary point,
// SIAM Journal on Optimization,
// Volume 9, Number 1, 1998, pages 148-158.
//
// Parameters:
//
// Input, real X(2), the argument of the function.
//
// Output, real F, the value of the function at X.
//
// Copyright (C) 2009 - INRIA - Michael Baudin, Scilab port
function [ f , index ] = mckinnon3 ( x , index )
if ( length ( x ) ~= 2 )
error (_("Error: function expects a two dimensional input\n"));
end
tau = 3.0;
theta = 6.0;
phi = 400.0;
if ( x(1) <= 0.0 )
f = theta * phi * abs ( x(1) ).^tau + x(2) * ( 1.0 + x(2) );
else
f = theta * x(1).^tau + x(2) * ( 1.0 + x(2) );
end
endfunction
function y = mckinnon3C ( x1 , x2 )
y = mckinnon3 ( [x1 , x2] , 2 )
endfunction
lambda1 = (1.0 + sqrt(33.0))/8.0;
lambda2 = (1.0 - sqrt(33.0))/8.0;
coords0 = [
1.0 1.0
0.0 0.0
lambda1 lambda2
];
x0 = [1.0 1.0]';
mprintf(_("x0=%s\n"), strcat(string(x0)," "));
mprintf(_("Creating object...\n"));
nm = nmplot_new ();
nm = nmplot_configure(nm, "-numberofvariables",2);
nm = nmplot_configure(nm, "-function",mckinnon3);
nm = nmplot_configure(nm, "-x0",x0);
nm = nmplot_configure(nm, "-maxiter",200);
nm = nmplot_configure(nm, "-maxfunevals",300);
nm = nmplot_configure(nm, "-tolsimplexizerelative",1.e-6);
nm = nmplot_configure(nm, "-simplex0method","given");
nm = nmplot_configure(nm, "-coords0",coords0);
nm = nmplot_configure(nm, "-kelleystagnationflag",%t);
nm = nmplot_configure(nm, "-restartflag",%t);
nm = nmplot_configure(nm, "-restartdetection","kelley");
//
// Setup output files
//
simplexfn = TMPDIR + filesep() + "history.simplex.txt";
fbarfn = TMPDIR + filesep() + "history.fbar.txt";
foptfn = TMPDIR + filesep() + "history.fopt.txt";
sigmafn = TMPDIR + filesep() + "history.sigma.txt";
nm = nmplot_configure(nm, "-simplexfn",simplexfn);
nm = nmplot_configure(nm, "-fbarfn",fbarfn);
nm = nmplot_configure(nm, "-foptfn",foptfn);
nm = nmplot_configure(nm, "-sigmafn",sigmafn);
//
// Perform optimization
//
mprintf(_("Searching (please wait) ...\n"));
nm = nmplot_search(nm);
disp(nm);
//
// Plot
//
mprintf(_("Plot contour (please wait) ...\n"));
xmin = -0.2;
xmax = 1.2 ;
ymin = -2.0 ;
ymax = 2.0 ;
nx = 50 ;
ny = 50;
xdata=linspace(xmin,xmax,nx);
ydata=linspace(ymin,ymax,ny);
scf();
f = gcf();
f.axes_size = [710, 560];
subplot(2,2,1)
xset("fpf"," ")
drawlater();
contour ( xdata , ydata , mckinnon3C , [-0.2 0.0 1.0 2.0 5.0 10.0 20.0] )
nmplot_simplexhistory ( nm );
drawnow();
subplot(2,2,2)
mytitle = _("Function Value Average");
myxlabel = _("Iterations");
nmplot_historyplot ( nm , fbarfn, mytitle , myxlabel );
subplot(2,2,3)
mytitle = _("Minimum Function Value") ;
myxlabel = _("Iterations");
nmplot_historyplot ( nm , foptfn, mytitle , myxlabel );
subplot(2,2,4)
mytitle = _("Maximum Oriented length") ;
myxlabel = _("Iterations") ;
nmplot_historyplot ( nm , sigmafn, mytitle , myxlabel );
demo_viewCode("nmplot_mckinnon2.sce");
deletefile(simplexfn);
deletefile(fbarfn);
deletefile(foptfn);
deletefile(sigmafn);
nm = nmplot_destroy(nm);
mprintf(_("End of demo.\n"));
endfunction
demo_mckinnon2();
clear demo_mckinnon2
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