Math. 555-01, Fall, 1997 Examples

( Wednesday, September 10 )

Interval arithmetic can be accessed on the Ultra system, by compiling and linking with

the macro "if90" that I have placed in the directory /home/rbk5287/courses/555-556/555-fa.97. For example, the following program can be found in that same directory in the file ex2p2.f90. (It is the example in Figure 2.2, page 79, of the book Rigorous Global Search: Continuous Problems.)

!  This standard Fortran-90 routine evaluates X**4 + X**3 + X over [1,2].
!  This is as in Figure 2.2 of "Rigorous Global Search: Continuous Problems."
PROGRAM EVALUATE_EXAMPLE
   USE INTERVAL_ARITHMETIC
   IMPLICIT NONE
   
      TYPE(INTERVAL) :: X, F
      CALL SIMINI
   
      X = INTERVAL(1,2)
      F = X**4 + X**3 + X
      
      WRITE(6,*) F
      
END PROGRAM EVALUATE_EXAMPLE

Examine the following session, run from that directory:

hilbert% if90 ex2p2
hilbert% ex2p2
 2.9999999999999978,  26.000000000000028
hilbert% 

For you to compile programs containing interval arithmetic, you can either copy "if90" to your directory or link to it. For documentation, look at Section 2.2 of Rigorous Global Search: Continuous Problems.