Implementation

A regularity test based on this approach is implemented as:

 
int ALIAS_Check_Regularity_Linear_Matrix(int DimA,
   INTERVAL_VECTOR (* Func)(int l1, int l2,INTERVAL_VECTOR & v_IS),
   int (* A_Cond)(int dimA,
      INTERVAL_VECTOR (* Func1)(int l1, int l2,INTERVAL_VECTOR &v_IS),
      INTERVAL_VECTOR & v_IS,INTERVAL_MATRIX &A),
   int Row_Or_Column,
   int Context,
   INTEGER_MATRIX &Implication_Var,
   int Use_Rohn,
   INTERVAL_VECTOR &Domain)

where

• Row_Or_Column: 1 if the row of the matrix are used, 2 if the columns are used
• Context: is used to determine if this procedure is used according to the following rules (see section 7.4 for the meaning of the flag Simp_in_Cond):
  • always used if 100 or if Context is equal to Simp_in_Cond
  • not used if Context lie in [-2,2]
  • not used if Context=3 and Simp_in_Cond $<0$
  • not used if Context=4 and Simp_in_Cond $<1$
  • not used if Context=5 and Simp_in_Cond is not 0 or 1
  • not used if Context=6 and Simp_in_Cond is not 0 or 2
• Implication_Var: an integer matrix of dimension DimA $\times$ $n$, where $n$ is the number of unknowns. If this matrix has a 1 at row $i$, column $j$, then the unknown $x_j$ appear linearly in some elements of row $i$ (or column $i$) of the matrix $A$
• Use_Rohn: 1 if the Rohn consistency test is used to check that a matrix in $H$ has a constant sign
• Domain: the ranges for the input parameters

This procedure return -1 if all elements of $A$ are regular, 0 otherwise