Source Code for Module lib.frame_order.conversions

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2014 Edward d'Auvergne                                        # 
  4  #                                                                             # 
  5  # This file is part of the program relax (http://www.nmr-relax.com).          # 
  6  #                                                                             # 
  7  # This program is free software: you can redistribute it and/or modify        # 
  8  # it under the terms of the GNU General Public License as published by        # 
  9  # the Free Software Foundation, either version 3 of the License, or           # 
 10  # (at your option) any later version.                                         # 
 11  #                                                                             # 
 12  # This program is distributed in the hope that it will be useful,             # 
 13  # but WITHOUT ANY WARRANTY; without even the implied warranty of              # 
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 15  # GNU General Public License for more details.                                # 
 16  #                                                                             # 
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 18  # along with this program.  If not, see <http://www.gnu.org/licenses/>.       # 
 19  #                                                                             # 
 20  ############################################################################### 
 21   
 22  # Module docstring. 
 23  """Functions for creating or calculating the rotor axis for the frame order models.""" 
 24   
 25  # Python module imports. 
 26  from numpy import array, cross, dot, float64, zeros 
 27  from numpy.linalg import norm 
 28   
 29  # relax module imports. 
 30  from lib.geometry.coord_transform import cartesian_to_spherical, spherical_to_cartesian 
 31  from lib.geometry.rotations import axis_angle_to_R, euler_to_R_zyz 
 32   
 33  # Module variables. 
 34  R = zeros((3, 3), float64)    # A rotation matrix. 
 35  Z_AXIS = array([0, 0, 1], float64) 
 36   
 37   
 38 -def convert_axis_alpha_to_spherical(alpha=None, pivot=None, point=None): 
 39      """Convert the axis alpha angle to spherical angles theta and phi. 
 40   
 41      @keyword alpha: The axis alpha angle, defined as the angle between a vector perpendicular to the pivot-CoM vector in the xy-plane and the rotor axis. 
 42      @type alpha:    float 
 43      @keyword pivot: The pivot point on the rotation axis. 
 44      @type pivot:    numpy rank-1 3D array 
 45      @keyword point: The reference point in space. 
 46      @type point:    numpy rank-1 3D array 
 47      @return:        The theta and phi spherical angles. 
 48      @rtype:         float, float 
 49      """ 
 50   
 51      # Create the axis. 
 52      axis = create_rotor_axis_alpha(alpha=alpha, pivot=pivot, point=point) 
 53   
 54      # Coordinate system transform. 
 55      r, theta, phi = cartesian_to_spherical(axis) 
 56   
 57      # Return the angles. 
 58      return theta, phi 
 59   
 60   
 61 -def create_rotor_axis_alpha(alpha=None, pivot=None, point=None): 
 62      """Create the rotor axis from the axis alpha angle. 
 63   
 64      @keyword alpha: The axis alpha angle, defined as the angle between a vector perpendicular to the pivot-CoM vector in the xy-plane and the rotor axis. 
 65      @type alpha:    float 
 66      @keyword pivot: The pivot point on the rotation axis. 
 67      @type pivot:    numpy rank-1 3D array 
 68      @keyword point: The reference point in space. 
 69      @type point:    numpy rank-1 3D array 
 70      @return:        The rotor axis as a unit vector. 
 71      @rtype:         numpy rank-1 3D float64 array 
 72      """ 
 73   
 74      # The CoM-pivot unit vector - the norm of the system (the pivot is defined as the point on the axis closest to the point). 
 75      n = point - pivot 
 76      n /= norm(n) 
 77   
 78      # The vector perpendicular to the CoM-pivot vector and in the xy plane. 
 79      mu_xy = cross(Z_AXIS, n) 
 80      mu_xy /= norm(mu_xy) 
 81   
 82      # Rotate the vector about the CoM-pivot axis by the angle alpha. 
 83      axis_angle_to_R(n, alpha, R) 
 84      axis = dot(R, mu_xy) 
 85   
 86      # Return the new axis. 
 87      return axis 
 88   
 89   
 90 -def create_rotor_axis_euler(alpha=None, beta=None, gamma=None): 
 91      """Create the rotor axis from the Euler angles. 
 92   
 93      @keyword alpha: The alpha Euler angle in the zyz notation. 
 94      @type alpha:    float 
 95      @keyword beta:  The beta Euler angle in the zyz notation. 
 96      @type beta:     float 
 97      @keyword gamma: The gamma Euler angle in the zyz notation. 
 98      @type gamma:    float 
 99      @return:        The rotor axis as a unit vector. 
100      @rtype:         numpy rank-1 3D float64 array 
101      """ 
102   
103      # Initialise the 3D frame. 
104      frame = zeros((3, 3), float64) 
105   
106      # Euler angle to rotation matrix conversion. 
107      euler_to_R_zyz(alpha, beta, gamma, frame) 
108   
109      # Return the z-axis component. 
110      return frame[:, 2] 
111   
112   
113 -def create_rotor_axis_spherical(theta=None, phi=None): 
114      """Create the rotor axis from the spherical coordinates. 
115   
116      @keyword theta: The polar spherical angle. 
117      @type theta:    float 
118      @keyword phi:   The azimuthal spherical angle. 
119      @type phi:      float 
120      @return:        The rotor axis as a unit vector. 
121      @rtype:         numpy rank-1 3D float64 array 
122      """ 
123   
124      # Initialise the axis. 
125      axis = zeros(3, float64) 
126   
127      # Parameter conversion. 
128      spherical_to_cartesian([1.0, theta, phi], axis) 
129   
130      # Return the new axis. 
131      return axis 
132