Source Code for Module lib.frame_order.rotor_axis

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2014 Edward d'Auvergne                                        # 
  4  #                                                                             # 
  5  # This file is part of the program relax (http://www.nmr-relax.com).          # 
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 12  # This program is distributed in the hope that it will be useful,             # 
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 15  # GNU General Public License for more details.                                # 
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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 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 create_rotor_axis_alpha(alpha=None, pivot=None, point=None): 
 39      """Create the rotor axis from the axis alpha angle. 
 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 rotor axis as a unit vector. 
 48      @rtype:         numpy rank-1 3D float64 array 
 49      """ 
 50   
 51      # The CoM-pivot unit vector - the norm of the system (the pivot is defined as the point on the axis closest to the point). 
 52      n = point - pivot 
 53      n /= norm(n) 
 54   
 55      # The vector perpendicular to the CoM-pivot vector and in the xy plane. 
 56      mu_xy = cross(Z_AXIS, n) 
 57      mu_xy /= norm(mu_xy) 
 58   
 59      # Rotate the vector about the CoM-pivot axis by the angle alpha. 
 60      axis_angle_to_R(n, alpha, R) 
 61      axis = dot(R, mu_xy) 
 62   
 63      # Return the new axis. 
 64      return axis 
 65   
 66   
 67 -def create_rotor_axis_euler(alpha=None, beta=None, gamma=None): 
 68      """Create the rotor axis from the Euler angles. 
 69   
 70      @keyword alpha: The alpha Euler angle in the zyz notation. 
 71      @type alpha:    float 
 72      @keyword beta:  The beta Euler angle in the zyz notation. 
 73      @type beta:     float 
 74      @keyword gamma: The gamma Euler angle in the zyz notation. 
 75      @type gamma:    float 
 76      @return:        The rotor axis as a unit vector. 
 77      @rtype:         numpy rank-1 3D float64 array 
 78      """ 
 79   
 80      # Initialise the 3D frame. 
 81      frame = zeros((3, 3), float64) 
 82   
 83      # Euler angle to rotation matrix conversion. 
 84      euler_to_R_zyz(alpha, beta, gamma, frame) 
 85   
 86      # Return the z-axis component. 
 87      return frame[:, 2] 
 88   
 89   
 90 -def create_rotor_axis_spherical(theta=None, phi=None): 
 91      """Create the rotor axis from the spherical coordinates. 
 92   
 93      @keyword theta: The polar spherical angle. 
 94      @type theta:    float 
 95      @keyword phi:   The azimuthal spherical angle. 
 96      @type phi:      float 
 97      @return:        The rotor axis as a unit vector. 
 98      @rtype:         numpy rank-1 3D float64 array 
 99      """ 
100   
101      # Initialise the axis. 
102      axis = zeros(3, float64) 
103   
104      # Parameter conversion. 
105      spherical_to_cartesian([1.0, theta, phi], axis) 
106   
107      # Return the new axis. 
108      return axis 
109