new_contents: # -*- coding: utf-8 -*-
  """
  Created on Wed Jul 16 10:29:40 2014
  
  @author: Jens von der Linden
  
  Tests based on relations in Goedbloed (2010) Principles of MHD.
  All equation references are from the book unless ofterwise noted.
  """
  
  import eigenvalue_goedbloed as eigen
  from nose.tools import assert_almost_equal, assert_greater_equal
  
  delta = 10E-5
  test_equil()
  
  
  def test_equil():
      """
      Create equilibrium for testing.
  
      Can start with simple constant density, axial current and field.
      """
  
  def test_freq_ordering():
      """
      Tests the frequency ordering given in equation (9.38).
      """
      radii = []
      for radius in radii:
          test_omega_alfven = eigen.omega_alfven()
          test_omega_sound = eigen.omega_sound()
          test_omega_s0 = eigen.omega_s0()
          test_omega_f0 = eigen.omega_f0()
  
          assert_greater_equal(test_omega_s0, test_omega_sound)
          assert_greater_equal(test_omega_alfven, test_omega_s0)
          assert_greater_equal(test_omega_f0, test_omega_alfven)
  
  
  def test_n():
      """
      Tests different formulations for n equations (9.32) & (9.36).
      """
      test_n_freq = eigen.n_freq()
      test_n_fb = eigen.n_fb()
  
      assert_almost_equal(test_n_freq, test_n_fb, delta=delta)
  
  
  def test_d():
      """
      Tests different formulations for d equations (9.30) & (9.36).
      """
      test_d_freq = eigen.d_freq()
      test_d_fb = eigen.d_fb()
  
      assert_almost_equal(test_d_freq, test_d_fb, delta=delta)
  
  
  def test_freq_limits():
      """
      Tests frequency limis given below equation (9.38).
  
      Notes
      -----
      May not be possible to implement numerically as these limits are for r->0,
      where the functions blow up.
      """
      pass
  
  
  def test_newcomb_limit():
      """
      Tests limit of omega_sq=0 where the eigenvalue equations should become
      newcomb's equations.
  
      Notes
      -----
      Have to think about if it will be possible to implement this limit
      numerically.
      """
      pass
subject: Add template for testing goedbloed eigenvalue problem