PO SH negative intensities

mfisch

Hi all

spherical_harmonics_hkl sh
sh_order 8
scale_pks = sh;

sometimes leads to negative intensities. Any idea how this macro could be modified so that
I_hkl at 2Th is not smaller than the BG at that 2Th?

rowlesmr

There are two schools of thought.

1) You're over-fitting and should use a lower order, or some other correction.
2) Just make the intensity non-negative.

Regarding (2): you could try scale_pks = Max(sh,0); or scale_pks = Abs(sh);

Mattehw

mfisch

Hi Matthew - both your appraoches work, that's clear.

With respect to thought 1)... Is there any quantitative measure to check that? There are other software packages that are said to do that, i.e. start with highest order, check, if overfitted, switch to lower order, check, etc...
Same seems to be for aniso peak broadening.

Cheers
Martin

rowlesmr

I don't know of any quantitative measure, but I also haven't looked very hard.

There'd probably be something in Bunge's Texture Analysis (https://www.researchgate.net/publication/277308168_Texture_Analysis_in_Materials_Science_H-J_Bunge)

Just having a quick look at things, eqn 4.237 imposes the constraint that the sums of the squares of the Cij values should be a minimum, but I don't know if this holds generally, as he is talking about extending l past l_max, whatever that may mean. That may help in preventing overfitting, but doesn't really define it.

http://www.ccp14.ac.uk/solution/gsas/spher_harmonics.html says that if the texture index (see eq 4.212) is greater than 3, then you're overfitting. But no quantitative statement.