MS_axes

MS_AXES - Reorient elasticity matrix for optimal decomposition.
Calculate the principle axes of elasticity tensor C, after:
   Browaeys and Chevrot (GJI, v159, 667-678, 2004)
[ CR, ... ] = MS_axes(C)
[CR] = MS_axes(C)
    Return a rotated elasticity matrix minimising the number of
    distinct elements. This is the orientation which, on further
    decomposition using MS_NORMS, will maximise the high symmetry
    components of the matrix.
[CR, RR] = MS_axes(C)
    In addition, return the rotation matrix, RR, used to perform
    the rotation to generate C from CR.
[ ... ] = MS_axes( C, 'nowarn' )
   Suppress all warnings.
[ ... ] = MS_axes( C, 'X3_stiff' )
   For hexagonal or tetragonal tensors, make X3 the stiffest direction,
   not the distinct direction. For triclinic or monoclinic tensors,
   align the axes with the axes of the dilational stiffness tensor.
[ ... ] = MS_axes( C, 'debug' )
   Enable debugging plots and messages. These are quite messy.
Notes:
    If the input matrix has isotropic, hexagonal or tetragonal
    symmetry there are multiple orentations of the principle axes.
    In the isotropic case CR is not rotated with respect to C (and RR
    is the identity matrix). In the hexagonal and tetragonal cases,
    X3 is defined by the distinct eigenvalue (see Browaeys and Chevrot)
    or, if 'X3_stiff', by the stiffest direction. For the monoclinic or
    triclinic cases we have to make a 'best-guess' and following
    Browraeys and Chevrot we use the bisectrix of each of the
    eigenvectors of d and its closest match in v. Furthermore, in order
    to always give the same output orientation for the lowest symmetry
    cases, a final rotation is performed to place the maximum P-wave
    velocity in the positive quadrent of the output axis system.
References:
    Browaeys, J. T. and S. Chevrot (2004) Decomposition of the elastic
        tensor and geophysical applications. Geophysical Journal
        international v159, 667-678.
    Cowin, S. C. and M. M. Mehrabadi (1987) On the identification of
        material symmetry for anisotropic elastic materials. Quartely
        Journal of Mechanics and Applied Mathematics v40, 451-476.
See also: MS_NORMS, MS_INTERPOLATE, MS_DECOMP