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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2008-2009 - INRIA - Michael Baudin
//
// 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-en.txt
//
// assert_close --
// Returns 1 if the two real matrices computed and expected are close,
// i.e. if the relative distance between computed and expected is lesser than epsilon.
// Arguments
// computed, expected : the two matrices to compare
// epsilon : a small number
//
function flag = assert_close ( computed, expected, epsilon )
if expected==0.0 then
shift = norm(computed-expected);
else
shift = norm(computed-expected)/norm(expected);
end
if shift < epsilon then
flag = 1;
else
flag = 0;
end
if flag <> 1 then bugmes();quit;end
endfunction
//
// assert_equal --
// Returns 1 if the two real matrices computed and expected are equal.
// Arguments
// computed, expected : the two matrices to compare
// epsilon : a small number
//
function flag = assert_equal ( computed , expected )
if computed==expected then
flag = 1;
else
flag = 0;
end
if flag <> 1 then bugmes();quit;end
endfunction
//
// gould.nonconvex --
// The Gould test case with additionnal inequality constraints.
// Arguments
// x : the point where to compute the cost
// index : a flag which states what is to compute
// * if index=1, or no index, returns the value of the cost
// function (default case)
// * if index=2, returns the value of the nonlinear inequality
// constraints, as a row array
// * if index=3, returns an array which contains
// at index #1, the value of the cost function
// at index #2 to the end is the list of the values of the nonlinear
// inequality constraints
// Discussion:
// The problem is to minimize a cost function with 4 non linear constraints.
// This is Problem 4.1 in Subrahmanyam, extracted from Gould.
// Non convex.
// The constraint region is a narrow winding (half-moon shaped) valley.
// Solution showed with tolerance 1.e-8.
//
// Reference:
// An extension of the simplex method to constrained
// nonlinear optimization
// M.B. Subrahmanyam
// Journal of optimization theory and applications
// Vol. 62, August 1989
//
// Gould F.J.
// Nonlinear Tolerance Programming
// Numerical methods for Nonlinear optimization
// Edited by F.A. Lootsma, pp 349-366, 1972
//
function result = gouldnonconvex ( x , index )
if (~isdef('index','local')) then
index = 1
end
if ( index==1 | index==3 ) then
f = (x(1) - 10.0 )^3 + ( x(2) - 20.0 ) ^ 3
end
if ( index==2 | index==3 ) then
c1 = x(1) - 13.0
c2 = ( x(1) - 5.0 )^2 + (x(2) - 5.0 )^2 - 100.0
c3 = -( x(1) - 6.0 )^2 - (x(2) - 5.0 )^2 + 82.81
c4 = x(2)
end
select index
case 1 then
result = f
mprintf( "Computed f = %e\n", f);
case 2
result = [c1 c2 c3 c4]
mprintf( "Computed constraints = %e %e %e %e\n", c1 , c2 , c3 , c4);
case 3
result = [f c1 c2 c3 c4]
mprintf( "Computed f = %e and constraints = %e %e %e %e\n", f , c1 , c2 , c3 , c4);
else
errmsg = sprintf("Unknown index %d", index )
error(errmsg)
end
endfunction
//
// The same cost function as before, with an
// additionnal argument, which contains parameters of the
// cost function and constraints.
// In this case, the mydata variable is passed
// explicitely by the optimization class.
// So the actual name "mydata" does not matter
// and whatever variable name can be used.
//
function result = gouldnonconvex2 ( x , index , mydata )
if (~isdef('index','local')) then
index = 1
end
if ( index==1 | index==3 ) then
f = (x(1) - mydata.f1 )^3 + ( x(2) - mydata.f2 ) ^ 3
end
if ( index==2 | index==3 ) then
c1 = x(1) - mydata.a1
c2 = ( x(1) - 5.0 )^2 + (x(2) - 5.0 )^2 - mydata.a2
c3 = -( x(1) - 6.0 )^2 - (x(2) - 5.0 )^2 + mydata.a3
c4 = x(2)
end
select index
case 1 then
result = f
mprintf( "Computed f = %e\n", f);
case 2
result = [c1 c2 c3 c4]
mprintf( "Computed constraints = %e %e %e %e\n", c1 , c2 , c3 , c4);
case 3
result = [f c1 c2 c3 c4]
mprintf( "Computed f = %e and constraints = %e %e %e %e\n", f , c1 , c2 , c3 , c4);
else
errmsg = sprintf("Unknown index %d", index )
error(errmsg)
end
endfunction
//
// Test optimbase_isfeasible method
//
// Test with bounds
opt = optimbase_new ();
opt = optimbase_configure(opt,"-numberofvariables",2);
opt = optimbase_configure(opt,"-verbose",1);
opt = optimbase_configure ( opt , "-boundsmin" , [-5.0 -5.0] );
opt = optimbase_configure ( opt , "-boundsmax" , [5.0 5.0] );
[ opt , isfeasible ] = optimbase_isinbounds ( opt , [0.0 0.0] );
assert_equal ( isfeasible , %t );
[ opt , isfeasible ] = optimbase_isinbounds ( opt , [-6.0 0.0] );
Component #1/2 of x is lower than min bound -5.000000e+00
assert_equal ( isfeasible , %f );
[ opt , isfeasible ] = optimbase_isinbounds ( opt , [0.0 6.0] );
Component #2/2 of x is greater than max bound 5.000000e+00
assert_equal ( isfeasible , %f );
opt = optimbase_destroy(opt);
//
// Test with nonlinear inequality constraints
opt = optimbase_new ();
opt = optimbase_configure(opt,"-numberofvariables",2);
opt = optimbase_configure(opt,"-verbose",1);
opt = optimbase_configure(opt,"-nbineqconst",4);
opt = optimbase_configure ( opt , "-function" , gouldnonconvex );
[ opt , isfeasible ] = optimbase_isinbounds ( opt , [ 14.0950013 , 0.8429636 ] );
assert_equal ( isfeasible , %t );
[ opt , isfeasible ] = optimbase_isinbounds ( opt , [ 14.0950013 , 0.0 ] );
assert_equal ( isfeasible , %t );
opt = optimbase_destroy(opt);
//
// Test with nonlinear inequality constraints and additionnal argument in cost function
mystuff = struct();
mystuff.f1 = 10.0;
mystuff.f2 = 20.0;
mystuff.a1 = 13.0;
mystuff.a2 = 100.0;
mystuff.a3 = 82.81;
opt = optimbase_new ();
opt = optimbase_configure ( opt , "-numberofvariables",2);
opt = optimbase_configure ( opt , "-verbose",1);
opt = optimbase_configure ( opt , "-nbineqconst",4);
opt = optimbase_configure ( opt , "-function" , gouldnonconvex2 );
opt = optimbase_configure ( opt , "-costfargument" , mystuff );
[ opt , isfeasible ] = optimbase_isinbounds ( opt , [ 14.0950013 , 0.8429636 ] );
assert_equal ( isfeasible , %t );
[ opt , isfeasible ] = optimbase_isinbounds ( opt , [ 14.0950013 , 0.0 ] );
assert_equal ( isfeasible , %t );
opt = optimbase_destroy(opt);
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