!   D01ARF Example Program Text
!   Mark 23 Release. NAG Copyright 2011.

    MODULE d01arfe_mod

!      D01ARF Example Program Module:
!             Parameters and User-defined Routines

!      .. Use Statements ..
       USE nag_library, ONLY : nag_wp
!      .. Implicit None Statement ..
       IMPLICIT NONE
!      .. Parameters ..
       INTEGER, PARAMETER                  :: maxrul = 0, nout = 6
    CONTAINS
       FUNCTION f1(x)

!         .. Implicit None Statement ..
          IMPLICIT NONE
!         .. Function Return Value ..
          REAL (KIND=nag_wp)                  :: f1
!         .. Scalar Arguments ..
          REAL (KIND=nag_wp), INTENT (IN)     :: x
!         .. Executable Statements ..
          f1 = 4.0E0_nag_wp/(1.0E0_nag_wp+x*x)

          RETURN

       END FUNCTION f1
       FUNCTION f2(x)

!         .. Implicit None Statement ..
          IMPLICIT NONE
!         .. Function Return Value ..
          REAL (KIND=nag_wp)                  :: f2
!         .. Scalar Arguments ..
          REAL (KIND=nag_wp), INTENT (IN)     :: x
!         .. Executable Statements ..
          f2 = x**0.125E0_nag_wp

          RETURN

       END FUNCTION f2
    END MODULE d01arfe_mod
    PROGRAM d01arfe

!      D01ARF Example Main Program

!      .. Use Statements ..
       USE nag_library, ONLY : d01arf, nag_wp
       USE d01arfe_mod, ONLY : f1, f2, maxrul, nout
!      .. Implicit None Statement ..
       IMPLICIT NONE
!      .. Local Scalars ..
       REAL (KIND=nag_wp)                  :: a, absacc, acc, ans, b, relacc
       INTEGER                             :: ifail, iparm, n
!      .. Local Arrays ..
       REAL (KIND=nag_wp)                  :: alpha(390)
!      .. Executable Statements ..
       WRITE (nout,*) 'D01ARF Example Program Results'

       relacc = 0.0E0_nag_wp
       absacc = 1.0E-5_nag_wp

!      Definite integral of F1(x) - no expansion

       iparm = 0
       a = 0.0E0_nag_wp
       b = 1.0E0_nag_wp

       WRITE (nout,*)
       WRITE (nout,*) 'Definite integral of 4/(1+x*x) over (0,1)'

       ifail = -1
       CALL d01arf(a,b,f1,relacc,absacc,maxrul,iparm,acc,ans,n,alpha,ifail)

       SELECT CASE (ifail)
       CASE (:-1)
          GO TO 20
       CASE (0,1)
          WRITE (nout,99999) 'Estimated value of the integral =', ans
          WRITE (nout,99998) 'Estimated absolute error =', acc
          WRITE (nout,99997) 'Number of points used =', n
       END SELECT

!      Definite integral of F2(x) - with expansion

       iparm = 1
       a = 1.0E0_nag_wp
       b = 2.0E0_nag_wp

       WRITE (nout,*)
       WRITE (nout,*) 'Definite integral of x**(1/8) over (1,2)'

       ifail = -1
       CALL d01arf(a,b,f2,relacc,absacc,maxrul,iparm,acc,ans,n,alpha,ifail)

       SELECT CASE (ifail)
       CASE (:-1)
          GO TO 20
       CASE (0,1)
          WRITE (nout,99999) 'Estimated value of the integral =', ans
          WRITE (nout,99998) 'Estimated absolute error =', acc
          WRITE (nout,99997) 'Number of points used =', n
       END SELECT

!      Indefinite integral of F2(x)

       iparm = 2
       a = 1.2E0_nag_wp
       b = 1.8E0_nag_wp

       WRITE (nout,*)
       WRITE (nout,*) 'Indefinite integral of x**(1/8) over (1.2,1.8)'

       ifail = 0
       CALL d01arf(a,b,f2,relacc,absacc,maxrul,iparm,acc,ans,n,alpha,ifail)

       WRITE (nout,99999) 'Estimated value of the integral =', ans

20     CONTINUE

99999  FORMAT (1X,A,F9.5)
99998  FORMAT (1X,A,E10.2)
99997  FORMAT (1X,A,I4)
    END PROGRAM d01arfe