Implementation

The algorithm is implemented as:

 
int Solve_General_Interval(int m,int n,
     INTEGER_VECTOR Type_Eq,
     INTERVAL_VECTOR (* IntervalFunction)(int,int,INTERVAL_VECTOR &), 
     INTERVAL_VECTOR & TheDomain, 
     int Order,int M,int Stop,
     double epsilon,double epsilonf,double Dist,
     INTERVAL_MATRIX & Solution,int Nb,
     int (* Simp_Proc)(INTERVAL_VECTOR &))

the arguments being:

• m: number of unknowns
• n: number of functions, see the note 2.3.4.1
• Type_Eq: type of the functions, see the note 2.3.4.2
• IntervalFunction: a function which return the interval vector evaluation of the functions, see the note 2.3.4.3
• TheDomain: box in which we are looking for solution of the system. A copy of the search domain is available in the global variable ALIAS_Init_Domain
• Order: the type of order which is used to store the intervals created during the bisection process. This order may be either MAX_FUNCTION_ORDER or MAX_MIDDLE_FUNCTION_ORDER. See the note on the order 2.3.4.4.
• M: the maximum number of boxes which may be stored. See the note 2.3.4.5
• Stop: the possible values are 0,1,2
  • 0: the algorithm will look for every solution in TheDomain
  • 1: the algorithm will stop as soon as 1 solution has been found
  • 2: the algorithm will stop as soon as Nb solutions have been found
• epsilon: the maximal width of the solution intervals, see the note 2.3.4.6
• epsilonf: the maximal width of the function intervals for a solution, see the note 2.3.4.6
• Dist: minimal distance between the middle point of two interval solutions, see the note 2.3.4.7
• Solution: an interval matrix of size (Nb,m) which will contained the solution intervals. This list is sorted using the order specified by Order
• Nb: the maximal number of solution which will be returned by the algorithm
• Simp_Proc: a user-supplied procedure that take as input the current box and proceed to some further reduction of the width of the box or even determine that there is no solution for this box, in which case it should return -1. Remember also that you may use the 3B method to improve the efficiency of this algorithm (see section 2.3.2).

Note that the following arguments may be omitted:

• Type_Eq: in that case all the functions will supposed to be equations.
• Simp_Proc: no simplification procedure is provided by the user