add getAverageOrientation() to Orientation class as class method.

lib/damask/orientation.py

@@ -1,5 +1,9 @@
 # -*- coding: UTF-8 no BOM -*-
 
+###################################################
+# NOTE: everything here needs to be a numpy array #
+###################################################
+
 import numpy,math,random
 
 # ******************************************************************************************
@@ -849,3 +853,23 @@ class Orientation:
       if inSST: break
 
     return color
+
+  @classmethod
+  def getAverageOrientation(cls, orientationList):
+    """RETURN THE AVERAGE ORIENTATION
+    ref: F. Landis Markley, Yang Cheng, John Lucas Crassidis, and Yaakov Oshman.
+         Averaging Quaternions,
+         Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4 (2007), pp. 1193-1197.
+         doi: 10.2514/1.28949
+    usage:
+         a = Orientation(Eulers=np.radians([10, 10, 0]), symmetry='hexagonal')
+         b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry='hexagonal')
+         avg = Orientation.getAverageOrientation([a,b])"""
+    if not all(isinstance(item, Orientation) for item in orientationList):
+        raise TypeError("Only instances of Orientation can be averaged.")
+    n = len(orientationList)
+    tmp_m = orientationList.pop(0).quaternion.asM()
+    for tmp_o in orientationList:
+      tmp_m += tmp_o.quaternion.asM()
+    eig, vec = numpy.linalg.eig(tmp_m/n)
+    return Orientation( quaternion=Quaternion(quatArray=vec.T[eig.argmax()]) )