!   D01ATF Example Program Text
!   Mark 27.3 Release. NAG Copyright 2021.

    Module d01atfe_mod

!     D01ATF 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                           :: f
!     .. Parameters ..
      Integer, Parameter, Public       :: lw = 800, nout = 6
      Integer, Parameter, Public       :: liw = lw/4
!     .. Local Scalars ..
      Real (Kind=nag_wp), Public, Save :: pi
    Contains
      Subroutine f(x,fv,n)

!       .. Scalar Arguments ..
        Integer, Intent (In)           :: n
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: fv(n)
        Real (Kind=nag_wp), Intent (In) :: x(n)
!       .. Intrinsic Procedures ..
        Intrinsic                      :: sin, sqrt
!       .. Executable Statements ..
        fv(1:n) = x(1:n)*sin(30.0E0_nag_wp*x(1:n))/sqrt(1.0E0_nag_wp-x(1:n)**2 &
          /(4.0E0_nag_wp*pi**2))

        Return

      End Subroutine f
    End Module d01atfe_mod
    Program d01atfe

!     D01ATF Example Main Program

!     .. Use Statements ..
      Use d01atfe_mod, Only: f, liw, lw, nout, pi
      Use nag_library, Only: d01atf, nag_wp, x01aaf
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: a, abserr, b, epsabs, epsrel, result
      Integer                          :: ifail
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: w(:)
      Integer, Allocatable             :: iw(:)
!     .. Executable Statements ..
      Write (nout,*) 'D01ATF Example Program Results'

      Allocate (w(lw),iw(liw))

      pi = x01aaf(pi)
      epsabs = 0.0_nag_wp
      epsrel = 1.0E-04_nag_wp
      a = 0.0_nag_wp
      b = 2.0_nag_wp*pi

      ifail = -1
      Call d01atf(f,a,b,epsabs,epsrel,result,abserr,w,lw,iw,liw,ifail)

      If (ifail>=0) Then
        Write (nout,*)
        Write (nout,99999) 'A     ', 'lower limit of integration', a
        Write (nout,99999) 'B     ', 'upper limit of integration', b
        Write (nout,99998) 'EPSABS', 'absolute accuracy requested', epsabs
        Write (nout,99998) 'EPSREL', 'relative accuracy requested', epsrel
      End If
      If (ifail>=0 .And. ifail<=5) Then
        Write (nout,*)
        Write (nout,99997) 'RESULT', 'approximation to the integral', result
        Write (nout,99998) 'ABSERR', 'estimate of the absolute error', abserr
        Write (nout,99996) 'IW(1) ', 'number of subintervals used', iw(1)
      End If

99999 Format (1X,A6,' - ',A30,' = ',F10.4)
99998 Format (1X,A6,' - ',A30,' = ',E9.2)
99997 Format (1X,A6,' - ',A30,' = ',F9.5)
99996 Format (1X,A6,' - ',A30,' = ',I4)
    End Program d01atfe