SUBROUTINE Critical(rvals, vp, nmax, jval, vasy, re, v0re, v1re, v2re, rc, v0rc, v1rc, v2rc, mu, ichanl)
USE Numeric_Kinds_Module
IMPLICIT NONE
!==============================================================================
!this subroutine finds all critical points of the potential function v for
!the specified jval
!==============================================================================
LOGICAL  :: root
INTEGER  :: i, nmax, jval, ichanl
REAL(dp) :: r, v0, v1, v2
REAL(dp) :: rvals(nmax), vp(nmax)
REAL(dp) :: vasy, re, v0re, v1re, v2re, rc, v0rc, v1rc, v2rc, mu

!==============================================================================
! Zero all variables

    r=0.d0
    v0=0.d0
    v1=0.d0
    v2=0.d0
    re=0.d0
    v0re=0.d0
    v1re=0.d0
    v2re=0.d0
    rc=0.d0
    v0rc=0.d0
    v1rc=0.d0
    v2rc=0.d0

!==============================================================================
! Find points at which the potential is equal to vasy
 grid_loop: DO i=2,nmax
  !============================================================================
  ! Find points at which the potential is a maxiumum or minimum
  ! Findextreme sets root to .true. if it finds a maximum or minumum
       CALL findextreme(i, nmax, rvals, vp, jval, r, v0, v1, v2, root, mu, ichanl)
       IF(re.eq.0.d0.and.root)THEN          
          re=r    !sets re to r value just determined if this is the first maximum/minimum findextreme has found
          v0re=v0 !also stores potential at this point and its derivatives
          v1re=v1
          v2re=v2
       ELSE IF(root)THEN             
          rc=r                           !sets rc to r value just determined if this is the second maximum/minimum findextreme has found
          v0rc=v0                        !also stores potential at this point and its derivatives
          v1rc=v1
          v2rc=v2
       ENDIF

    ENDDO grid_loop

    IF (v0rc.eq.0.d0) THEN
      v0rc=vasy
    ENDIF

    RETURN
    END SUBROUTINE Critical