r9063 - /1.3/maths_fns/rotation_matrix.py -- May 28, 2009 - 15:57

Author: bugman
Date: Thu May 28 15:57:48 2009
New Revision: 9063

URL: http://svn.gna.org/viewcvs/relax?rev=9063&view=rev
Log:
Wrote 2 new functions, R_random_hypersphere() and quaternion_to_R().


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=9063&r1=9062&r2=9063&view=diff
==============================================================================
--- 1.3/maths_fns/rotation_matrix.py (original)
+++ 1.3/maths_fns/rotation_matrix.py Thu May 28 15:57:48 2009
@@ -22,9 +22,45 @@
 
 # Python module imports.
 from math import acos, cos, pi, sin
-from numpy import cross, dot
+from numpy import array, cross, dot, float64
 from numpy.linalg import norm
-from random import uniform
+from random import gauss, uniform
+
+
+def quaternion_to_R(quat, matrix):
+    """Convert a quaternion into rotation matrix form.
+
+    @param quat:    The quaternion.
+    @type quat:     numpy 4D, rank-1 array
+    @param matrix:  A 3D matrix to convert to a rotation matrix.
+    @type matrix:   numpy 3D, rank-2 array
+    """
+
+    # Repetitive calculations.
+    q4_2 = quat[3]**2
+    q12 = quat[0] * quat[1]
+    q13 = quat[0] * quat[2]
+    q14 = quat[0] * quat[3]
+    q23 = quat[1] * quat[2]
+    q24 = quat[1] * quat[3]
+    q34 = quat[2] * quat[3]
+
+    # The diagonal.
+    matrix[0, 0] = (quat[0]**2 + q4_2) - 0.5
+    matrix[1, 1] = (quat[1]**2 + q4_2) - 0.5
+    matrix[2, 2] = (quat[2]**2 + q4_2) - 0.5
+
+    # Off-diagonal.
+    matrix[0, 1] = q12 - q34
+    matrix[0, 2] = q13 + q24
+    matrix[1, 2] = q23 - q14
+
+    matrix[1, 0] = q12 + q34
+    matrix[2, 0] = q13 - q24
+    matrix[2, 1] = q23 + q14
+
+    # Double.
+    matrix = 2.0 * matrix
 
 
 def R_2vect(R, vector_orig, vector_fin):
@@ -209,6 +245,11 @@
 
     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.
+
+    @param matrix:  A 3D matrix to convert to a rotation matrix.
+    @type matrix:   numpy 3D, rank-2 array
+    @keyword angle: The fixed rotation angle.
+    @type angle:    float
     """
 
     # Random rotation axis.
@@ -217,6 +258,24 @@
 
     # Generate the rotation matrix.
     R_axis_angle(matrix, rot_axis, angle)
+
+
+def R_random_hypersphere(matrix):
+    """Generate a random rotation matrix using 4D hypersphere point picking.
+
+    A quaternion is generated by creating a 4D vector with each value 
randomly selected from a
+    Gaussian distribution, and then normalising.
+
+    @param matrix:  A 3D matrix to convert to a rotation matrix.
+    @type matrix:   numpy 3D, rank-2 array
+    """
+
+    # The quaternion.
+    quat = array([gauss(0, 1), gauss(0, 1), gauss(0, 1), gauss(0, 1)], 
float64)
+    quat = quat / norm(quat)
+
+    # Convert the quaternion to a rotation matrix.
+    quaternion_to_R(quat, matrix)
 
 
 def random_rot_axis(axis):