Misorientation - Return misorientation data for quaternions.

   USAGE:

   angle = Misorientation(q1, q2, sym)
   [angle, mis] = Misorientation(q1, q2, sym)

   INPUT:

   q1 is 4 x n1, 
      is either a single quaternion or a list of n quaternions
   q2 is 4 x n,  
      a list of quaternions
 
   OUTPUT:

   angle is 1 x n, 
         the list of misorientation angles between q2 and q1
   mis   is 4 x n, (optional) 
         is a list of misorientations in the fundamental region 
         (there are many equivalent choices)

   NOTES:

   *  The misorientation is the linear tranformation which
      takes the crystal basis given by q1 to that given by
      q2.  The matrix of this transformation is the same
      in either crystal basis, and that is what is returned
      (as a quaternion).  The result is inverse(q1) * q2.
      In the sample reference frame, the result would be
      q2 * inverse(q1).  With symmetries, the result is put
      in the fundamental region, but not into the Mackenzie cell.

 MisorientationStats - Misorientation correlation statistics.

   USAGE:

   stats = MisorientationStats(misorient, locations)

   INPUT:

   misorient is 4 x n, 
             a list of misorientation quaternions,
             assumed to have been derived from properly clustered 
             orientation data
   locations is d x n, (d <= 3) 
             a list of spatial locations corresponding to the 
             misorientations

   OUTPUT:

   stats is a structure with five components:

         W     is a 3 x 3 matrix (A in Barton paper)
         X     is a d x d matrix (M in Barton paper)
         WX    is a 3 x d matrix (cross-correlation
                    of normalized variables; X in
                    Barton paper)
         wi    is 3 x n, the unnormalized axial vectors
         xi    is d x n, the unnormalized spatial directions
                         from the centroid

   REFERENCE:  

   "A Methodology for Determining Average Lattice Orientation and 
   Its Application to the  Characterization of Grain Substructure",

   Nathan R. Barton and Paul R. Dawson,

   Metallurgical and Materials Transactions A,
   Volume 32A, August 2001, pp. 1967--1975