;  Given a number of points and a spacing, return an
;  array of the wavelet fourier series and the
;  array of frequencies (2 pi/wavelength) for the
;  j, k wavelet as defined by Sato.

function dangle_jk_xL, H, d, xh, j, k, xL

  psihatL=dangle_jk_wL(H, d, xh, j, k, wL)
  n = n_elements(wL)
  dn = d * n
  xL=[findgen(n/2)-n/2,findgen(n/2)] * d + (xh-H)
  psiL=shift(float(fft( shift(psihatL,n/2)/dn, /inverse)),n/2)
  
  return, psiL

end

pro dangle_jk_xL_test

  H = 32.
  d = 1.
  j=3
  k=1
  xh=0.
  psirefrL = refr_jk_xL(H, d, xh, 0, 0, xL)
  psirefrjkL = refr_jk_xL(H, d, xh, j, k, xL)
  psiphaseL = dangle_jk_xL(H, d, xh, 0, 0, xL)
  psiphasejkL = dangle_jk_xL(H, d, xh, j, k, xL)
  window, 0, xs=1000,ys=500
  !p.multi=[0,2,0]
  plot, xL/H, psirefrjkL, xr=xh + [-5,5], /xs,/ys
  oplot, xL/H, psirefrL, li=2

  plot, xL/H, psiphasejkL, xr=xh + [-5,5], /xs,/ys
  oplot, xL/H, psiphaseL, li=2

end

pro dangle_jk_xL_test2, j, k

  H = 32.
  d = 1.
  xh=32000.
;  xh=0
;  j=2
;  k=7
  
  psirefrL = refr_jk_xL(H, d, xh, j,k, xL)
  zL = (xL-xH)/H
  c = 0.5 / max(psirefrL) * 2.^(-j)
  refrL = exp(-zL) * (1 + c * psirefrL)
  
  psiangleL = angle_jk_xL(H, d, xh, j,k, xL)
  angleL = H * exp(-zL) * (1 + c * psiangleL)
  yL = xL - angleL
  
  psidangleL = dangle_jk_xL(H, d, xh, j,k, xL)
  dangleL = exp(-zL) * (1 + c * psidangleL)
  fluxL = 1./abs((1. + dangleL))
  
  window, 0, xs=1000,ys=500
  !p.multi=[0,2,0]
  plot, zL, psirefrL
  plot, (yL-xh)/H, fluxL, xr=[-20,10], ps=3
  
end