Open adigitoleo opened 1 year ago
Current implementation (0c530f6) of the M-index in diagnostics.misorientation_index
is either incorrect or the diagnostic is not much use to us, because it starts at a value around 0.3 and doesn't seem to reflect clustering in the pole figures for the M*=0 2D shear test. The Chi-squared test suffers the same problem.
Attempts to implement the I diagnostic don't seem to yield values in the range suggested by Mainprice 2014 (5.0 for point maximum), instead giving negative values below -6000.
M-index significantly improved by #139
Are you still thinking of implementing all these diagnostics? If not, perhaps best to mention which ones you are targeting.
Eventually I think it's worth trying to implement as many of these as possible to make comparisons with experiments and other studies easier. This can be a tracking issue to show which ones are currently implemented, but for now the M-index is probably the only one I will worry about.
To diagnose CPO texture we have 1) angles between any kind of mean orientation in SO(3) and a reference direction, 2) texture strength and 3) texture symmetry.
Getting the mean angle (without crystalline symmetry considerations) is fairly simple using Bingham averaging. Getting the basic symmetry diagnostics (Vollmer 1990) uses the same inertia matrix, also pretty simple. Texture strength not so much.
There are a few options in the literature (checkboxes for when they are implemented with tests):
C = ln(λ₁/λ₃) using eigenvalues of the inertia (scatter) matrix as used for the Bingham avg., can't add symmetry considerations so can yield "unexpected results" (Mainprice 2014)Let's not do this, we have enough Vollmer-based diagnosics with the PGR symmetry numbersI = (15n/2) (λ₁² + λ₂² + λ₃² - 1/3) for n = n_grains, equation from Mainprice 2014, apparently from Mardia 1972 and/or Mardia & Jupp 2000 (book) but I can't find it, no idea where the 15 comes from, can have negative values which is a bit weird