!   D02BGF Example Program Text
!   Mark 27.3 Release. NAG Copyright 2021.

    Module d02bgfe_mod

!     D02BGF 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                           :: fcn
!     .. Parameters ..
      Integer, Parameter, Public       :: n = 3, nin = 5, nout = 6
!     n: number of differential equations
    Contains
      Subroutine fcn(x,y,f)

!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (In) :: x
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: f(*)
        Real (Kind=nag_wp), Intent (In) :: y(*)
!       .. Intrinsic Procedures ..
        Intrinsic                      :: cos, tan
!       .. Executable Statements ..
        f(1) = tan(y(3))
        f(2) = -0.032E0_nag_wp*tan(y(3))/y(2) - 0.02E0_nag_wp*y(2)/cos(y(3))
        f(3) = -0.032E0_nag_wp/y(2)**2
        Return
      End Subroutine fcn
    End Module d02bgfe_mod

    Program d02bgfe

!     D02BGF Example Main Program

!     .. Use Statements ..
      Use d02bgfe_mod, Only: fcn, n, nin, nout
      Use nag_library, Only: d02bgf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: alpha, hmax, tol, val, x, xend,      &
                                          xinit
      Integer                          :: i, ifail, m
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: w(:,:), y(:), yinit(:)
!     .. Executable Statements ..
      Write (nout,*) 'D02BGF Example Program Results'
!     Skip heading in data file
      Read (nin,*)
!     m: index of mode of solution to attain value alpha
      Read (nin,*) m
      Allocate (w(n,10),y(n),yinit(n))
!     xinit: initial x value,     xend : final x value.
!     alpha: attain y(m) = alpha, yinit: initial solution values.
      Read (nin,*) alpha
      Read (nin,*) xinit
      Read (nin,*) xend
      Read (nin,*) yinit(1:n)
      hmax = 0.0E0_nag_wp
      val = alpha
      Do i = 4, 5
        tol = 10.0E0_nag_wp**(-i)
        x = xinit
        y(1:n) = yinit(1:n)

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
        ifail = 0
        Call d02bgf(x,xend,n,y,tol,hmax,m,val,fcn,w,ifail)

        Write (nout,*)
        Write (nout,99999) 'Calculation with TOL =', tol
        Write (nout,99998) ' Y(M) changes sign at X = ', x
        If (tol<0.0E0_nag_wp) Then
          Write (nout,*) ' Over one-third steps controlled by HMAX'
        End If
      End Do

99999 Format (1X,A,E8.1)
99998 Format (1X,A,F7.4)
    End Program d02bgfe