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GradJacobiP Function

  1. submodule_DG_implementation.f90
  2. DG_implementation
  3. GradJacobiP

function GradJacobiP(x, alpha, beta, n)

Evaluate the derivative of the Jacobi polynomial of type (α,β)>−1 at points x for order n.

Arguments

Type IntentOptional AttributesName
real(kind=wp), intent(in), dimension(:):: x

The points x∈[−1:1] at which to evaluate the derivative of the Jacobi polynomial.

real(kind=wp), intent(in) :: alpha

The value of α.
real(kind=wp), intent(in) :: beta

The value of β.
integer(kind=ip), intent(in) :: n

The order of the Jacobi polynomials.

Return Value real(kind=wp), dimension(size(x))

The return value is the derivative of the Jacobi polynomial evaluated at xi, dP(α,β)ndx|x=xi


Calls

proc~~gradjacobip~~CallsGraph proc~gradjacobip GradJacobiP proc~jacobip JacobiP proc~gradjacobip->proc~jacobip

Called by

proc~~gradjacobip~~CalledByGraph proc~gradjacobip GradJacobiP proc~gradvandermonde1d GradVandermonde1D proc~gradvandermonde1d->proc~gradjacobip proc~dmatrix1d Dmatrix1D proc~dmatrix1d->proc~gradvandermonde1d proc~init_ref_element init_ref_element proc~init_ref_element->proc~dmatrix1d interface~init_ref_element init_ref_element interface~init_ref_element->proc~init_ref_element interface~ref_element ref_element interface~ref_element->interface~init_ref_element proc~scal_schw_init scal_schw_init proc~scal_schw_init->interface~ref_element program~test test program~test->interface~ref_element interface~scal_schw_init scal_schw_init interface~scal_schw_init->proc~scal_schw_init

Contents

Source Code

GradJacobiP

Source Code

    function GradJacobiP ( x, alpha, beta, n )
    !! Evaluate the derivative of the Jacobi polynomial of type
    !! \((\alpha,\beta)>-1\) at points \(x\) for order \(n\).
      real(wp), dimension(:), intent(in) :: x
      !! The points \(x\in[-1:1]\) at which to evaluate the derivative of the
      !! Jacobi polynomial. 
      real(wp), intent(in) :: alpha
      !! The value of \(\alpha\).
      real(wp), intent(in) :: beta
      !! The value of \(\beta\).
      integer(ip), intent(in) :: n
      !! The order of the Jacobi polynomials.
      real(wp), dimension(size(x)) :: GradJacobiP
      !! The return value is the derivative of the Jacobi polynomial evaluated
      !! at \(x_i\), \(\left .\frac{dP_n^{(\alpha,\beta)}}{dx}
      !! \right |_{x=x_i}\)

      if (n==0) then
        GradJacobiP = 0.0_wp
        return
      end if
      GradJacobiP = sqrt(n*(n+alpha+beta+1))* &
                      JacobiP(x,alpha+1.0_wp,beta+1.0_wp,n-1)
      return
    end function GradJacobiP