Description of operator *

operator *		Programmers Guide
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Category:intervals,operator

Component type:function

Prototype

template <class Tnum> interval<Tnum> operator * (const interval<Tnum>& x, const interval<Tnum>& y) ;

Description

Multiplies two intervals, returning the product as an outward rounded interval. Uses the algorithm from Moore's book "Methods and Applications of Interval analysis" p12.


 x = [a,b], y = [c,d]

 x*y=

 [ac,bd]                 if a >= 0 and c >= 0

 [bc,bd]                 if a >= 0 and c < 0 *lt; d

 [bc,ad]                 if a >= 0 and d <= 0

 [ad,bc]                 if a < 0 < b and c >= 0

 [bd,ad]                 if a < 0 < b and d<= 0

 [ad,bc]                 if b <= 0 and c >= 0

 [ad,ac]                 if b <= 0 and c < 0 < d 

 [bd,ac]                 if b <= 0 and d <= 0

 [min(bc,ad),max(ac,bd)] if a < 0 < b and c < 0 < d

Returns a proper interval in all cases.

Definition

interval.cct

Preconditions

Complexity

Example

In operator.cc:

  C=A+B;
  cout << "A+B = \n" << C << endl;
  C-=B;
  cout << "A+B-B = \n" << C << endl;
  C/=A;
  cout << "(A+B-B)/A = \n" << C << endl;
  C*=B;
  cout << "((A+B-B)/A)*B = \n" << C << endl;
  C*=Num(5);
  cout << "(((A+B-B)/A)*B)*5.0 = \n" << C << endl;
  C+=Num(2);
  cout << "((((A+B-B)/A)*B)*5.0)+2.0 = \n" << C << endl;
  C-=A;
  cout << "(((((A+B-B)/A)*B)*5.0)+2.0)-A = \n" << C << endl;

Notes

See also