Example 4: Lowermost mantle anisotropy
======================================

This code demonstrates the use of MSAT to calculate derived properties from
a set of elastic constants. The model used is a model of lowermost mantle
anisotropy from link:http://dx.doi.org/10.1029/2011GC003732[Walker et al (2011)],
specifically 'TX2008.V1.P010.dat'. See
link:http://www1.gly.bris.ac.uk/CoMITAC/software.htm[www1.gly.bris.ac.uk/CoMITAC/software.htm] for details. 

The source code for this 
example are contained in the file
lmm_anisotropy_example.m in the examples/lowermost
directory distributed with MSAT. This
directory also contains the data file needed to run the example.

Much of the example is similar to the calculations 
described in example 2. However, one important 
additional calculation is performed, specifically
the symmetry based analysis of  
link:http://dx.doi.org/10.1111/j.1365-246X.2004.02415.x[Browaeys and Chevrot (2004)].
This analysis is performed in three stages. First `MS_axes` is used to 
find the principal axes of the stress tensor needed to cause an isotropic
strain and the elasticity tensor `Chere` rotated to be aligned with this. 
The second step uses `MS_decomp` to split the matrix into contributions 
from the six symmetry classes. `MS_norms` then calculates the Euclidean
norm of each contributing elasticity matrix before, for this application,
the percentage of the sum of the norms that is contributed from the 
hexagonal matrix is calculated.
[code, python]
----
         ChereR = MS_axes(Chere) ;
         [C_iso,C_hex,C_tet,C_ort,C_mon,C_tri] = MS_decomp(ChereR);
         P = MS_norms(ChereR,C_iso,C_hex,C_tet,C_ort,C_mon,C_tri) ;
         SumA = sum(P(2:end)) ;
         PercH(ila(i),ilo(i)) = P(2)./SumA ;
----
