BuildModalTransform Subroutine

  1. SELF_RefinementIndicator_2D_t.f90
  2. SELF_RefinementIndicator_2D_t
  3. BuildModalTransform

public subroutine BuildModalTransform(controlPoints, N, Pmodal)

Build the nodal->modal transform Pmodal for a 1-D degree-N interpolant whose nodes are controlPoints(1:N+1). The transform is the exact inverse of the L2-normalized Legendre Vandermonde V(i,p) = Ltilde_{p-1}(x_i); Pmodal(ii,p) stores V^{-1}(p,ii) so that uhat(p) = sum_ii Pmodal(ii,p) * u(ii). The Vandermonde inverse is formed in double precision for conditioning and cast back to the working precision.

Arguments

TypeIntentOptionalAttributesName
real(kind=prec), intent(in) :: controlPoints(1:N+1)
integer, intent(in) :: N
real(kind=prec), intent(out) :: Pmodal(1:N+1,1:N+1)

Calls

proc~~buildmodaltransform~~CallsGraph proc~buildmodaltransform BuildModalTransform proc~normalizedlegendre NormalizedLegendre proc~buildmodaltransform->proc~normalizedlegendre proc~invertmatrix InvertMatrix proc~buildmodaltransform->proc~invertmatrix

Called by

proc~~buildmodaltransform~~CalledByGraph proc~buildmodaltransform BuildModalTransform proc~init_refinementindicator2d_t Init_RefinementIndicator2D_t proc~init_refinementindicator2d_t->proc~buildmodaltransform proc~init_refinementindicator2d Init_RefinementIndicator2D proc~init_refinementindicator2d->proc~init_refinementindicator2d_t

Contents

Source Code

BuildModalTransform

Source Code

  subroutine BuildModalTransform(controlPoints,N,Pmodal)
    !! Build the nodal->modal transform Pmodal for a 1-D degree-N interpolant whose nodes are
    !! controlPoints(1:N+1). The transform is the exact inverse of the L2-normalized Legendre
    !! Vandermonde V(i,p) = Ltilde_{p-1}(x_i); Pmodal(ii,p) stores V^{-1}(p,ii) so that
    !! uhat(p) = sum_ii Pmodal(ii,p) * u(ii). The Vandermonde inverse is formed in double
    !! precision for conditioning and cast back to the working precision.
    implicit none
    integer,intent(in) :: N
    real(prec),intent(in) :: controlPoints(1:N+1)
    real(prec),intent(out) :: Pmodal(1:N+1,1:N+1)
    ! Local
    integer :: i,p
    real(real64) :: V(1:N+1,1:N+1)
    real(real64) :: Vinv(1:N+1,1:N+1)

    ! Vandermonde in the normalized Legendre basis: column p (degree p-1) evaluated at node i.
    do i = 1,N+1
      do p = 1,N+1
        V(i,p) = NormalizedLegendre(p-1,real(controlPoints(i),real64))
      enddo
    enddo

    call InvertMatrix(V,Vinv,N+1)

    ! Store the transpose of the inverse so the summed (input node) index comes first,
    ! matching the SELF matrix-application convention.
    do p = 1,N+1
      do i = 1,N+1
        Pmodal(i,p) = real(Vinv(p,i),prec)
      enddo
    enddo

  endsubroutine BuildModalTransform