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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 #0, the value of the cost function
// at index #1 to the end is the list of the values of the nonlinear
// 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 [ f , c , index ] = gouldnonconvex ( x , index )
f = []
c = []
if ( index==2 | index==6 ) then
f = (x(1) - 10.0 )^3 + ( x(2) - 20.0 ) ^ 3
end
if ( index==5 | index==6 ) 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)
c = [c1 c2 c3 c4]
end
endfunction
//
// Test optimbase_checkx0 method
//
// Test without anything
opt = optimbase_new ();
opt = optimbase_configure ( opt , "-numberofvariables",2);
opt = optimbase_configure ( opt , "-verbose",1);
[ opt , isok ] = optimbase_checkx0 ( opt );
Checking initial guess...
... initial guess is feasible.
assert_equal ( isok , %T );
opt = optimbase_destroy(opt);
//
// Test with satisfied/unsatisfied bounds constraints
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 = optimbase_configure ( opt , "-x0", [1.0 1.0]' );
[ opt , isok ] = optimbase_checkx0 ( opt );
Checking initial guess...
... initial guess is feasible.
assert_equal ( isok , %T );
opt = optimbase_configure ( opt , "-x0",[-6.0 1.0]');
[ opt , isok ] = optimbase_checkx0 ( opt );
Checking initial guess...
Component #1/2 of x is lower than min bound -5.000000e+00
... initial guess is not feasible.
assert_equal ( isok , %F );
opt = optimbase_destroy(opt);
//
// Test with satisfied/unsatisfied 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 = optimbase_configure ( opt , "-x0" , [ 14.0950013 , 0.8429636 ]');
[ opt , isok ] = optimbase_checkx0 ( opt );
Checking initial guess...
Function Evaluation #1 at [14.095001 0.8429636]
... initial guess is feasible.
assert_equal ( isok , %T );
opt = optimbase_configure ( opt , "-x0" , [ 14.0950013 , 0.0 ]');
[ opt , isok ] = optimbase_checkx0 ( opt );
Checking initial guess...
Function Evaluation #2 at [14.095001 0]
Inequality constraint #3/4 is not satisfied for x
... initial guess is not feasible.
assert_equal ( isok , %F );
opt = optimbase_destroy(opt);
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