Bisection mode

All the solving procedures proceed by considering a box for the variables. Some calculation is performed with the current box (for example trying to reduce the width of the box). Then this box will be bisected. Hence the bisection process is a key element of the algorithms and ALIAS offers various bisection modes that are controlled through the variable `ALIAS/single_bisection:

• 0: all the ranges of the $n$ variables are bisected at their middle point. Hence $2^n$ new boxes are created after the bisection process. This is a mode that has to be avoided
• $>0$: a single variable will be bisected. The choice of the bisected variable will depend on the the value of `ALIAS/single_bisection variable: see the C++ manual for the possible values of this variable
• 20: you have defined your own bisection procedure. This procedure should be written in the file BISSECTION_USER.C which must include the procedure

   
  int Select_Best_Direction_Interval_User(int DimVar,int DimEq,
  INTERVAL_VECTOR (* TheIntervalFunction)(int,int,INTERVAL_VECTOR &),
  INTERVAL_VECTOR &Input)
  

  where DimVar is the size of the unknown vector, DimEq the number of equations, TheIntervalFunction the evaluation function of your problem (by default F)and Input the current box. This procedure shall return the variable number that will be bisected.

• a mix of these 2 modes in which $m$ ranges among the $n$ available will be bisected. `ALIAS/mixed_bisection. gives the number of bisected ranges