r9060 - /1.3/maths_fns/rotation_matrix.py -- May 15, 2009 - 11:58

Author: bugman
Date: Fri May 15 11:58:55 2009
New Revision: 9060

URL: http://svn.gna.org/viewcvs/relax?rev=9060&view=rev
Log:
Added the functions random_rot_axis() and random_R() to generate random 
rotations.


Modified:
    1.3/maths_fns/rotation_matrix.py

Modified: 1.3/maths_fns/rotation_matrix.py
URL: 
http://svn.gna.org/viewcvs/relax/1.3/maths_fns/rotation_matrix.py?rev=9060&r1=9059&r2=9060&view=diff
==============================================================================
--- 1.3/maths_fns/rotation_matrix.py (original)
+++ 1.3/maths_fns/rotation_matrix.py Fri May 15 11:58:55 2009
@@ -1,6 +1,6 @@
 
###############################################################################
 #                                                                            
 #
-# Copyright (C) 2004-2005, 2008 Edward d'Auvergne                            
 #
+# Copyright (C) 2004-2005, 2008-2009 Edward d'Auvergne                       
 #
 #                                                                            
 #
 # This file is part of the program relax.                                    
 #
 #                                                                            
 #
@@ -21,9 +21,10 @@
 
###############################################################################
 
 # Python module imports.
+from math import acos, cos, pi, sin
 from numpy import cross, dot
 from numpy.linalg import norm
-from math import acos, cos, sin
+from random import uniform
 
 
 def R_2vect(R, vector_orig, vector_fin):
@@ -201,3 +202,42 @@
     matrix[0,2] = -sin_b * cos_g
     matrix[1,2] =  sin_b * sin_g
     matrix[2,2] =  cos_b
+
+
+def random_rot_axis(axis):
+    """Generate a random rotation axis.
+
+    Uniform point sampling on a unit sphere is used to generate a random 
axis orientation.
+
+    @param axis:    The 3D rotation axis.
+    @type axis:     numpy array, len 3
+    """
+
+    # Random azimuthal angle.
+    u = uniform(0, 1)
+    theta = 2*pi*u
+
+    # Random polar angle.
+    v = uniform(0, 1)
+    phi = acos(2.0*v - 1)
+
+    # Random rotation axis.
+    axis[0] = cos(theta) * sin(phi)
+    axis[1] = sin(theta) * sin(phi)
+    axis[2] = cos(phi)
+
+
+def random_R(matrix, angle=0.0):
+    """Generate a random rotation matrix of fixed angle via the axis-angle 
notation.
+
+    Uniform point sampling on a unit sphere is used to generate a random 
axis orientation.  This,
+    together with the fixed rotation angle, is used to generate the random 
rotation matrix.
+
+    """
+
+    # Random rotation axis.
+    rot_axis = zeros(3, float64)
+    random_rot_axis(rot_axis)
+
+    # Generate the rotation matrix.
+    R_axis_angle(matrix, rot_axis, angle)