!   D01ARF Example Program Text
!   Mark 27.3 Release. NAG Copyright 2021.

    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
!     .. Accessibility Statements ..
      Private
      Public                           :: f1, f2
!     .. Parameters ..
      Integer, Parameter, Public       :: maxrul = 0, nout = 6
    Contains
      Function f1(x)

!       .. 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)

!       .. 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 d01arfe_mod, Only: f1, f2, maxrul, nout
      Use nag_library, Only: d01arf, nag_wp
!     .. 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 100
      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 100
      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

100   Continue

99999 Format (1X,A,F9.5)
99998 Format (1X,A,E10.2)
99997 Format (1X,A,I4)
    End Program d01arfe