Using the generic analyzer in a program

You may use directly the analyzer in a program using the following syntax:

int Equation_Analyzer(int Dimension,int Dimension_Eq,int MaxBox,
         char *formula_file,char *gradient_file,char *hessian_file,
         char *inequalities_file,char *dimension_file,char *coeff_file,
         char *gradient_coeff_file,
                      int method,int nb_inequalities,int equation_processed,
                      INTERVAL_VECTOR &Input,
                      double Acc_Var,double Acc_Eq,double Acc_Kanto,
                      int Depth_Level,
                      INTERVAL_MATRIX &Range,
                      int *Nb_Range);

with:

• Dimension: the number of unknowns in the system
• Dimension_Eq: the number of equations in the system
• MaxBox: the maximum number of ranges that may be produced at any step of the algorithm
• formula_file: if the system has already been processed the name of the file which contain the equations in parser format
• gradient_file: if the system has already been processed the name of the file which contain the gradient equations in parser format
• hessian_file: if the system has already been processed the name of the file which contain the gradient equations in parser format
• inequalities_file: if the system has already been processed the name of the file which contain the inequalities equations in parser format. The number of inequalities must be given in nb_inequalities
• dimension_file: the name of the dimension file, i.e. the file which contain the degree of the equations in the unknowns (see section 12.4.4.1). If this string has 0 length the analyzer will assume that you have filed the integer array Dimen_IA(Dimension_Eq,Dimension with the appropriate number: for example Dimen_IA(1,2) should contain the degree of the first equation in the second variable (the order of the variable is their order of occurrence in the string array that contain their names).
• coeff_file: the base-name for the files containing the coefficients of the equations. For example
  coeff_file1-2 must contain the coefficients of the first equation considered as a univariate polynomial in the second variable
• gradient_coeff_file: the base-name for the files containing the gradient of the coefficients of the equations. For example
  gradient_coeff_file1-2 must contain the gradient of the coefficients of the first equation considered as a univariate polynomial in the second variable
• method: an integer describing the method you are using for evaluating the equation:
  • 0: straightforward interval evaluation
  • 1: evaluation using the gradient of the equation
  • 2: use Kantorovitch and Newton scheme to determine roots of the system and intervals containing unique roots of the system.
• nb_inequalities: the number of inequalities constraints you have
• equation_processed: an integer which may be 0 or 1.
  • 0: you have not processed your system. The analyzer will consider that the argument formula_file is a MAPLE program that contain the description of your equations. It will then create all the necessary intermediate files (see section 12.4.4.1). Note that in that case all the string files of this procedure will be substituted by the names of the corresponding intermediary files. The storage space of these strings must therefore be sufficient.
  • 1: the system has already been processed and the name indicated in the arguments of this procedure are parser files
• Input: the initial set of ranges for the unknowns
• Acc_Var: unused at this time
• Acc_Eq: if method is 2 the threshold under which an equation will be considered to be equal to 0 in the Newton scheme
• Acc_Kanto: if method is 2, the maximal diameter in a set of ranges under which we start applying Kantorovitch. A typical value is 0.5
• Depth_Level: the level of bisection that will be used by the analyzer (from 0 to some positive value)
• Range: the sets of ranges produced by the algorithm
• Nb_Range: the number of sets in Range

Beside these arguments you must fill the string array variable_name_IS with the name of the unknowns. If you have a parametric system you must indicate the name of the parameters in the string array parameter_name_IS, their values in the array of doubles parameter_value_IS and set the integer variable Nb_Parameter_IA to the number of parameters.