CalculateBarycentricWeights Subroutine

  subroutine CalculateBarycentricWeights(this)
    implicit none
    class(Lagrange_t),intent(inout) :: this
    ! Local
    integer :: i,j
    real(real64) :: bWeights(0:this%N)
    real(real64) :: controlPoints(0:this%N)

    do i = 0,this%N
      bWeights(i) = 1.0_real64
      controlPoints(i) = real(this%controlPoints(i+1),real64)
    enddo

    ! Computes the product w_k = w_k*(s_k - s_j), k /= j
    do j = 1,this%N
      do i = 0,j-1

        bWeights(i) = bWeights(i)*(controlPoints(i)-controlPoints(j))
        bWeights(j) = bWeights(j)*(controlPoints(j)-controlPoints(i))

      enddo
    enddo

    do j = 0,this%N
      bWeights(j) = 1.0_prec/bWeights(j)
      this%bWeights(j+1) = real(bWeights(j),prec)
    enddo

  endsubroutine CalculateBarycentricWeights