s_bsplines_uniform__eval_deriv Subroutine

  SLL_PURE subroutine s_bsplines_uniform__eval_deriv( self, x, derivs, jmin )
    class(sll_t_bsplines_uniform), intent(in   ) :: self
    real(wp)                     , intent(in   ) :: x
    real(wp)                     , intent(  out) :: derivs(0:)
    integer                      , intent(  out) :: jmin

    integer  :: icell
    real(wp) :: x_offset

    integer  :: j, r
    real(wp) :: j_real
    real(wp) :: xx
    real(wp) :: temp
    real(wp) :: saved

    real(wp) :: bj, bjm1

    ! Check on inputs
    SLL_ASSERT( size(derivs) == 1+self%degree )

    ! 1. Compute cell index 'icell' and x_offset
    call s_bsplines_uniform__get_icell_and_offset( self, x, icell, x_offset )

    ! 2. Compute index range of B-splines with support over cell 'icell'
    jmin = icell - self%offset

    ! 3. Compute derivatives of aforementioned B-splines
    !    Derivatives are normalized, hence they should be divided by dx
    associate( bspl => derivs, spline_degree => self%degree, start => self%inv_dx )

      ! only need splines of lower degree to compute derivatives
      bspl(0) = start
      do j = 1, spline_degree - 1
         j_real = real(j,wp)
         xx     = -x_offset
         saved  = 0.0_wp
         do r = 0, j-1
            xx      = xx + 1.0_wp
            temp    = bspl(r) * inv(j)
            bspl(r) = saved + xx * temp
            saved   = (j_real - xx) * temp
         end do
         bspl(j) = saved
      end do

      ! compute derivatives
      bjm1 = bspl(0)
      bj = bjm1
      bspl(0) = -bjm1
      do j=1, spline_degree - 1
         bj = bspl(j)
         bspl(j) = bjm1 - bj
         bjm1 = bj
      end do
      bspl(spline_degree) = bj

    end associate  ! bspl, spline_degree

  end subroutine s_bsplines_uniform__eval_deriv