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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2010 - DIGITEO - 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
//
// neldermeadBounds.sce --
// Show a simple neldermead session with bounds.
//
function demo_boxbounds()
filename = "neldermead_boxbounds.sce";
dname = get_absolute_file_path(filename);
mprintf(_("Illustrates Box'' algorithm on a simply bounds-constrained optimization problem.\n"));
// A simple quadratic function
function [ f , index ] = myquad ( x , index )
f = x(1)^2 + x(2)^2
endfunction
function y = myquadC ( x1 , x2 )
y = myquad ( [x1 , x2] , 2 )
endfunction
//
// Initialize the random number generator, so that the results are always the
// same.
//
rand("seed" , 0)
x0 = [1.2 1.9].';
// Compute f(x0) : should be close to -2351244.0
[ fx0 , index ] = myquad ( x0 , 2 );
mprintf("Computed fx0 = %e (expected = %e)\n",fx0 , 5.05 );
xopt = [1 1].';
// Compute f(xopt) : should be 2
[ fopt , index ] = myquad ( xopt , 2 );
mprintf("Computed fopt = %e (expected = %e)\n", fopt , 2 );
nm = nmplot_new ();
nm = nmplot_configure(nm,"-numberofvariables",2);
nm = nmplot_configure(nm,"-function",myquad);
nm = nmplot_configure(nm,"-x0",x0);
nm = nmplot_configure(nm,"-method","box");
nm = nmplot_configure(nm,"-boundsmin",[1 1]);
nm = nmplot_configure(nm,"-boundsmax",[2 2]);
//
// Check that the cost function is correctly connected.
//
[ nm , f ] = nmplot_function ( nm , x0 );
simplexfn = fullfile(TMPDIR , "history.simplex.txt")
nm = nmplot_configure(nm,"-simplexfn",simplexfn);
//
// Perform optimization
//
mprintf(_("Searching (please wait) ...\n"));
nm = nmplot_search(nm);
mprintf(_("...Done\n"));
//
// Print a summary
//
exec(fullfile(dname,"nmplot_summary.sci"),-1);
nmplot_summary(nm)
mprintf("==========================\n");
xcomp = nmplot_get(nm,"-xopt");
mprintf("x expected = %s\n",strcat(string(xopt), " "));
shift = norm(xcomp-xopt)/norm(xopt);
mprintf("Shift = %f\n",shift);
fcomp = nmplot_get(nm,"-fopt");
mprintf("f expected = %f\n",fopt);
shift = abs(fcomp-fopt)/abs(fopt);
mprintf("Shift =%f\n",shift);
//
// Plot
//
mprintf(_("Plot contour (please wait)...\n"));
xmin = 0.5 ;
xmax = 2.1 ;
ymin = 0.5 ;
ymax = 2.1 ;
nx = 50 ;
ny = 50;
xdata=linspace(xmin,xmax,nx);
ydata=linspace(ymin,ymax,ny);
scf();
xset("fpf"," ")
drawlater();
contour ( xdata , ydata , myquadC , 10 )
nmplot_simplexhistory ( nm );
drawnow();
demo_viewCode(filename);
//
// Cleanup
deletefile(simplexfn)
nm = nmplot_destroy(nm);
mprintf(_("End of demo.\n"));
endfunction
demo_boxbounds();
clear demo_boxbounds;
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