psi 0 0.2 x 1 2.5If f denotes a formula file and r a range file then you may run:
Interval_Solver -F f -R rIn that case the program will call the procedure Solve_General_Interval12.1 of the ALIAS library.
Instead of using the Solve_General_Interval procedure of ALIAS you may use the
Solve_General_Gradient_Interval procedure which requires the gradient of the equations. The gradient equations are defined in a formula file (e.g. g) and you may then run:
Interval_Solver -F f -G g -R rNote that the equations in the gradient formula file should be ordered with respect to the unknowns using the same ordering than the one used in the range file. Thus for the range file:
x 1 2.5 y 0 0.2and the formula file f:
eq=y+3*x eq=x^2+x*ydenoted eq1, eq2, the first line of the gradient formula file should be deq1/dx, the second line deq1/dy and so on, which will lead to the following gradient file:
eq=3 eq=1 eq=2*x+y eq=x
Similarly, instead of using the Solve_General_Gradient_Interval procedure of ALIAS you may use the Solve_General_JH_Interval procedure which requires the gradient and hessian of the equations. The hessian equations are defined in a formula file (e.g. h) and you may then run:
Interval_Solver -F f -G g -H h -R rNote that the hessian formula file should respect the same ordering than for the gradient formula file. For our previous example the hessian file will be:
eq=0 eq=0 eq=0 eq=0 eq=2 eq=1 eq=1 eq=0Note also that the various formula files may be easily obtained by using the MAPLE procedures described in the next section (12.3).
The result of the computation will be written in a result file. Each line of the result file gives the range for one of the unknowns, using the same ordering than for the range file (in our example the range of x, followed by the range for y). A range is indicated by two reals separated by a blanc character. If instead of range the result file contain the keyword FAILED it means that the solver has been unable to solve the equations. This keyword is followed by an integer which indicate the reason of the failure:
Whatever the used solving procedure, some parameters are to be set. The solver will prompt you to give the values of these parameters. If you want to avoid this interactive behavior you may define the parameters in a configuration file and the solver will proceed directly to the solution. A configuration file consists in a list of keywords followed by a value. Most of these keywords refers to parameters in the solving procedure of ALIAS, please refer to the corresponding section for their meaning: