vvla Subroutine

public subroutine vvla(Va, x, Pv)

Compute parabolic cylinder function Vv(x) for large argument

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: Va

Order
real(kind=wp), intent(in) :: x

Argument
real(kind=wp), intent(out) :: Pv

Vv(x)

Calls

proc~~vvla~~CallsGraph proc~vvla specfun_module::vvla proc~dvla specfun_module::dvla proc~vvla->proc~dvla proc~gamma2 specfun_module::gamma2 proc~vvla->proc~gamma2 proc~dvla->proc~vvla proc~dvla->proc~gamma2

Called by

proc~~vvla~~CalledByGraph proc~vvla specfun_module::vvla proc~dvla specfun_module::dvla proc~vvla->proc~dvla proc~dvla->proc~vvla proc~pbvv specfun_module::pbvv proc~pbvv->proc~vvla proc~pbdv specfun_module::pbdv proc~pbdv->proc~dvla

Source Code

   subroutine vvla(Va,x,Pv)

      real(wp),intent(in) :: x !! Argument
      real(wp),intent(in) :: Va !! Order
      real(wp),intent(out) :: Pv !! `Vv(x)`

      real(wp) :: a0 , dsl , gl , pdl , qe , r , x1
      integer :: k

      real(wp),parameter :: eps = 1.0e-12_wp

      qe = exp(0.25_wp*x*x)
      a0 = abs(x)**(-Va-1.0_wp)*sqrt(2.0_wp/pi)*qe
      r = 1.0_wp
      Pv = 1.0_wp
      do k = 1 , 18
         r = 0.5_wp*r*(2.0_wp*k+Va-1.0_wp)*(2.0_wp*k+Va)/(k*x*x)
         Pv = Pv + r
         if ( abs(r/Pv)<eps ) exit
      enddo
      Pv = a0*Pv
      if ( x<0.0_wp ) then
         x1 = -x
         call dvla(Va,x1,pdl)
         call gamma2(-Va,gl)
         dsl = sin(pi*Va)*sin(pi*Va)
         Pv = dsl*gl/pi*pdl - cos(pi*Va)*Pv
      endif

   end subroutine vvla