Source Code for Module maths_fns.order_parameters

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 2  #                                                                             # 
 3  # Copyright (C) 2010 Edward d'Auvergne                                        # 
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 5  # This file is part of the program relax.                                     # 
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22   
23  # Module docstring. 
24  """Module for the conversion of order parameters to specific model parameters and vice versa.""" 
25   
26  # Python module imports. 
27  from math import acos, cos, pi, sqrt 
28   
29   
30 -def iso_cone_theta_to_S(theta): 
31      """Convert the isotropic cone angle to the order parameter S. 
32   
33      This uses Woessner's diffusion in a cone order parameter defined as:: 
34   
35          S = 1/2 (1 + cos(theta)) * cos(theta) 
36   
37   
38      @param theta:   The isotropic cone angle. 
39      @type theta:    float 
40      @return:        The order parameter value. 
41      @rtype:         float 
42      """ 
43   
44      # Convert. 
45      S = 0.5 * (1.0 + cos(theta)) * cos(theta) 
46   
47      # Return the order parameter. 
48      return S 
49   
50   
51 -def iso_cone_S_to_theta(S): 
52      """Convert the isotropic cone order parameter S into the cone angle. 
53   
54      This uses Woessner's diffusion in a cone order parameter defined as:: 
55   
56          S = 1/2 (1 + cos(theta)) * cos(theta) 
57   
58      The conversion equation is:: 
59   
60          theta = acos((sqrt(8.0*S + 1) - 1)/2) 
61   
62      Hence the cone angle is only between 0 and 2pi/3, as the order parameter for higher cone angles is ambiguous. 
63   
64   
65      @param S:   The order parameter value (not squared). 
66      @type S:    float 
67      @return:    The value of cos(theta). 
68      @rtype:     float 
69      """ 
70   
71      # Catch bad order parameters. 
72      if S > 1.0: 
73          return 0.0 
74      if S < -0.125: 
75          return 2*pi 
76   
77      # Convert. 
78      theta = acos(0.5*(sqrt(8.0*S + 1) - 1)) 
79   
80      # Return theta. 
81      return theta 
82