imatrix Id ( imatrix& A ) // Interval identity matrix
{ //-------------------------
int i,j;
int lbi = Lb(A,1), ubi = Ub(A,1);
int lbj = Lb(A,2), ubj = Ub(A,2);
imatrix B(lbi,ubi,lbj,ubj);
for (i = lbi; i <= ubi; i++)
for (j = lbj; j <= ubj; j++)
B[i][j] = _interval( (i==j) ? 1.0 : 0.0 );
return B;
}
//----------------------------------------------------------------------------
// Intersection of an interval 'X' and an extended interval 'Y'. The result
// is given as a pair (vector) of intervals, where one or both of them can
// be empty intervals.
//----------------------------------------------------------------------------
ivector operator& ( const interval& X, const xinterval& Y )
{
interval H;
ivector IS(2);
IS[1] = EmptyIntval();
IS[2] = EmptyIntval();
switch (Y.kind) {
case Finite : // [X.inf,X.sup] & [Y.inf,Y.sup]
//------------------------------
H = _interval(Y.inf,Y.sup);
if ( !Disjoint(X,H) ) IS[1] = X & H;
break;
case PlusInfty : // [X.inf,X.sup] & [Y.inf,+oo]
//----------------------------
if (Sup(X) >= Y.inf) {
if (Inf(X) > Y.inf)
IS[1] = X;
else
IS[1] = _interval(Y.inf,Sup(X));
}
break;
case MinusInfty : // [X.inf,X.sup] & [-oo,Y.sup]
//----------------------------
if (Y.sup >= Inf(X)) {
if (Sup(X)<Y.sup)
IS[1] = X;
else
IS[1] = _interval(Inf(X),Y.sup);
}
break;
case Double : if ( (Inf(X) <= Y.sup) && (Y.inf <= Sup(X)) ) {
IS[1] = _interval(Inf(X),Y.sup); // X & [-oo,Y.sup]
IS[2] = _interval(Y.inf,Sup(X)); // X & [Y.inf,+oo]
}
else if (Y.inf <= Sup(X)) // [X.inf,X.sup] & [Y.inf,+oo]
if (Inf(X) >= Y.inf) //----------------------------
IS[1] = X;
else
IS[1] = _interval(Y.inf,Sup(X));
else if (Inf(X) <= Y.sup){// [X.inf,X.sup] & [-oo,Y.sup]
if (Sup(X) <= Y.sup) //----------------------------
IS[1] = X;
else
IS[1] = _interval(Inf(X),Y.sup);
}
break;
case Empty : break; // [X.inf,X.sup] ** [/]
} // switch //---------------------
return IS;
} // operator&
