MODULE int_procs

 USE local
 IMPLICIT NONE
 PUBLIC  ::  trap_simple, trap_int, romb_int
 REAL(r8), PUBLIC :: inte, a, b

 INTERFACE
  FUNCTION func(x)
   USE local
   IMPLICIT NONE
   REAL(r8) :: func
   REAL(r8), INTENT(IN) :: x
  END FUNCTION func
 END INTERFACE

 CONTAINS

  SUBROUTINE trap_simple(k)
!
! This routine calculates the kth refinement of the trapezoidal rule.
!
   USE local
   IMPLICIT NONE
   INTEGER(i8) :: i, i_max
   INTEGER(i4), INTENT(IN) :: k
   REAL(r8) :: sum, h_k_1, x

! Calculate new_sum to be averaged with the old

  RETURN
  END SUBROUTINE trap_simple

  SUBROUTINE trap_int(eps)
!
! This routine calculates the composite trapezoidal rule using the
! integrand func and the lower and upper limits of integration
! a and b until convergence set by eps is satisfied.
!
   USE local
   IMPLICIT NONE
   INTEGER(i4) :: i, max_div = 30
   REAL(r8), INTENT(IN) :: eps
   REAL(r8) :: old_int

! Loop over successive approximations and check convergence
 
   old_int = 1.e-30
   DO i=1,max_div
    CALL trap_simple(i)
    IF(abs(inte-old_int).le.eps*abs(old_int).or. &
      (abs(inte).lt.eps.and.i.gt.15)) RETURN
    old_int = inte
   END DO                     
 
  RETURN
  END SUBROUTINE trap_int               

  SUBROUTINE romb_int(eps)
!
! This routine does Romberg integration using the integrand func and 
! the lower and upper limits of integration a and b until convergence 
! set by eps is satisfied.
!
   IMPLICIT NONE
 
   INTEGER(i4), PARAMETER :: max_div = 20       ! maximum divisions of [a,b]
   INTEGER(i4) :: k, m
   REAL(r8), INTENT(IN) :: eps
   REAL(r8), DIMENSION(max_div) :: h, int_arr
   REAL(r8) :: error, zero, r_int
 
! Outer loop yields next composite trapezoidal rule estimate
   DO k = 1,max_div



! Inner loop produces entire row of Romberg tableau
    DO i=1,k-1



     IF(abs(error).le.eps*abs(r_int).or. &
       (abs(r_int).lt.eps.and.k.gt.15)) THEN
       inte = r_int
       RETURN
     ENDIF
    ENDDO

   ENDDO

  RETURN
  END SUBROUTINE romb_int                

END MODULE int_procs