C++ (Cpp) IntervalVector::ub Examples

Example #1

File: ibex_utils.cpp Project: ibex-team/ibex-lib

Interval centeredFormEval(const Function& function, const IntervalVector& arg) {
	/*Interval natural_extension = function.eval(arg);
	Interval centered_form = function.eval(arg.mid()) + function.gradient(arg) * (arg - arg.mid());*/
	IntervalVector new_arg_ub(arg);
	IntervalVector new_arg_lb(arg);
	IntervalVector grad = function.gradient(arg);
	for(int i = 0; i < arg.size(); ++i) {
		if(grad[i].lb() > 0) {
			new_arg_ub[i] = arg[i].ub();
			new_arg_lb[i] = arg[i].lb();
		} else if(grad[i].ub() < 0) {
			new_arg_ub[i] = arg[i].lb();
			new_arg_lb[i] = arg[i].ub();
		}
	}
	Interval natural_extension = function.eval(arg);
	Interval centered_form = function.eval(arg.mid()) + grad * (arg - arg.mid());
	Interval ub_form = function.eval(arg.ub()) + grad * (arg - arg.ub());
	Interval lb_form = function.eval(arg.lb()) + grad * (arg - arg.lb());
	Interval res = natural_extension & centered_form & ub_form & lb_form;
	res &= Interval(function.eval(new_arg_lb).lb(), function.eval(new_arg_ub).ub());
	return res;
}

Example #2

File: ibex_Linear.cpp Project: ClementAubry/ibex-lib

void hansen_bliek(const IntervalMatrix& A, const IntervalVector& B, IntervalVector& x) {
	int n=A.nb_rows();
	assert(n == A.nb_cols()); // throw NotSquareMatrixException();
	assert(n == x.size() && n == B.size());

	Matrix Id(n,n);
	for (int i=0; i<n; i++)
		for (int j=0; j<n; j++) {
			Id[i][j]   = i==j;
		}

	IntervalMatrix radA(A-Id);
	Matrix InfA(Id-abs(radA.lb()));
	Matrix M(n,n);

	real_inverse(InfA, M);  // may throw SingularMatrixException...

	for (int i=0; i<n; i++)
		for (int j=0; j<n; j++)
			if (! (M[i][j]>=0.0)) throw NotInversePositiveMatrixException();

	Vector b(B.mid());
	Vector delta = (B.ub())-b;

	Vector xstar = M * (abs(b)+delta);

	double xtildek, xutildek, nuk, max, min;

	for (int k=0; k<n; k++) {
		xtildek = (b[k]>=0) ? xstar[k] : xstar[k] + 2*M[k][k]*b[k];
		xutildek = (b[k]<=0) ? -xstar[k] : -xstar[k] + 2*M[k][k]*b[k];

		nuk = 1/(2*M[k][k]-1);
		max = nuk*xutildek;
		if (max < 0) max = 0;

		min = nuk*xtildek;
		if (min > 0) min = 0;

		/* compute bounds of x(k) */
		if (xtildek >= max) {
			if (xutildek <= min) x[k] = Interval(xutildek,xtildek);
			else x[k] = Interval(max,xtildek);
		} else {
			if (xutildek <= min) x[k] = Interval(xutildek,min);
			else { x.set_empty(); return; }
		}
	}
}