legendre_transform Subroutine

  subroutine legendre_transform (g, tote, totl, tott)  
    use mp, only: nproc
    use theta_grid, only: ntgrid, bmag, bmax
    use species, only: nspec
    use kt_grids, only: naky, ntheta0
    use gs2_layouts, only: g_lo, idx, idx_local
    use mp, only: sum_reduce
    implicit none
    complex, dimension (-ntgrid:,:,g_lo%llim_proc:), intent (in) :: g
    complex, dimension (0:,-ntgrid:,:,:,:), intent (out) :: tote, totl
    complex, dimension (0:,-ntgrid:,:,:,:), intent (out), optional :: tott

    complex :: totfac
    real :: ulim
    integer :: is, il, ie, ik, it, iglo, ig, im, ntrap
    integer, save :: lpesize

    real, dimension (:), allocatable :: nodes
    real, dimension (:,:), allocatable :: lpltmp, lpttmp
!    real, dimension (:,:), allocatable, save :: lpe, lpl
!    real, dimension (:,:,:,:), allocatable, save :: lpt

    if (.not. allocated(lpl)) then
       allocate(lpltmp(ng2,0:ng2-1))
       allocate(lpl(nlambda,0:ng2-1))

       lpesize = nesub
       allocate(lpe(negrid,0:lpesize-1,nspec)) ; lpe = 0.0
       
       ! get value of first nesub legendre polynomials
       ! at each of the grid points on (0,vcut)
       do is = 1,nspec
          call legendre_polynomials (0.0,vcut,speed(:lpesize,is),lpe(:lpesize,:,is))
       end do
       ! TEMP FOR TESTING -- MAB
       !          lpe = 2.*lpe/vcut
       
       ! get value of first ng2 legendre polynomials
       ! at each of the grid points on (0,1)
       call legendre_polynomials (0.0,1.0,xx,lpltmp)

       lpl = 0.0
       lpl(1:ng2,:) = lpltmp

       if (present(tott)) then
          allocate (lpt(nlambda,0:2*(nlambda-ng2-1),-ntgrid:ntgrid,2))
          lpt = 0.0
          do ig = -ntgrid, ntgrid
             ntrap = 1
             if (jend(ig) > ng2+1) then
                ntrap = jend(ig)-ng2
                allocate (nodes(2*ntrap-1))
                allocate (lpttmp(2*ntrap-1,0:2*(ntrap-1)))
                do il = 1, ntrap
                   nodes(il) = -sqrt(max(0.0,1.0-al(ng2+il)*bmag(ig)))
                end do
                nodes(ntrap+1:) = -nodes(ntrap-1:1:-1)
!Can we remove this?
! TEMP FOR TESTING -- MAB
!                nodes = nodes + sqrt(1.0-bmag(ig)/bmax)
!                ulim = 2.*sqrt(1.0-bmag(ig)/bmax)
                ulim = sqrt(1.0-bmag(ig)/bmax)
                call legendre_polynomials (-ulim,ulim,nodes,lpttmp)
                lpt(ng2+1:jend(ig),0:2*(ntrap-1),ig,2) = lpttmp(1:ntrap,:)
                lpt(ng2+1:jend(ig)-1,0:2*(ntrap-1),ig,1) = lpttmp(2*ntrap-1:ntrap+1:-1,:)
!Can we remove this?
!                lpt(ng2+1:jend(ig),0:2*(ntrap-1),ig,1) = lpttmp(2*ntrap-1:ntrap+1:-1,:)
!                do ie = 0, 2*(ntrap-1)
!                   do il = 1, 2*ntrap-1
!                      if (proc0) write (*,*) 'lptrap', ig, ntrap, ulim, ie, il, nodes(il), lpttmp(il,ie)
!                   end do
!                end do
!                do ie = 0, 2*(ntrap-1)
!                   do il = ng2+1,jend(ig)
!                      write (*,*) 'lpt', ig, ie, il, lpt(il,ie,ig,1), lpt(il,ie,ig,2)
!                   end do
!                end do
                deallocate (nodes, lpttmp)
             end if
          end do
       end if

       deallocate (lpltmp)
    end if

    ! carry out legendre transform to get coefficients of
    ! legendre polynomial expansion of g
    totfac = 0. ; tote = 0. ; totl = 0.
    if (present(tott)) tott = 0.

    !Loop over all indices, note this loop is optimal only for layout 'xyles' (at least in terms of
    !g memory access)
    do is = 1, nspec
       do ie = 1, negrid
          do il = 1, nlambda
             do ik = 1, naky       !Swapped ik and it loop order.
                do it = 1, ntheta0
                   iglo = idx (g_lo, ik, it, il, ie, is)
                   if (idx_local (g_lo, iglo)) then
                      do ig=-ntgrid,ntgrid
                         totfac = w(ie,is)*wl(ig,il)*(g(ig,1,iglo)+g(ig,2,iglo))
                         do im=0,lpesize-1
                            tote(im, ig, it, ik, is) = tote(im, ig, it, ik, is) + totfac*lpe(ie,im,is)*(2*im+1)
                         end do
                         do im=0,ng2-1
                            totl(im, ig, it, ik, is) = totl(im, ig, it, ik, is) + totfac*lpl(il,im)*(2*im+1)
                         end do
                         if (present(tott)) then
                            do im=0,2*(jend(ig)-ng2-1)
                               tott(im, ig, it, ik, is) = tott(im, ig, it, ik, is) + &
                                    w(ie,is)*wl(ig,il)*(lpt(il,im,ig,1)*g(ig,1,iglo)+lpt(il,im,ig,2)*g(ig,2,iglo))*(2*im+1)
                            end do
                         end if
                      end do
                   end if
                end do
             end do
          end do
       end do
    end do

    !Do we really need this if?
    if (nproc > 1) then
       !Now complete velocity integral, bringing back results to proc0
       call sum_reduce (tote, 0)
       call sum_reduce (totl, 0)
       if (present(tott)) call sum_reduce (tott, 0)
    end if

  end subroutine legendre_transform