Chi square calculation

[Martin-Rey]

Following our discussion, I have been looking at the chi square calculation.

The method historically used for chi^2 calculation looked like this: https://github.com/ucl-cosmoparticles/genetIC/blob/a04d1188450880974ef48a63e02532240bd94b61/genetIC/src/simulation/field/multilevelfield.hpp#L323-L341

I refactored it into the ability to transform a vector to convector ( by dividing by the covariance matrix in fourier space) to look like this: https://github.com/ucl-cosmoparticles/genetIC/blob/3b337c37075ca50b91d76519e1d4ba9f5b017162/genetIC/src/simulation/field/multilevelfield.hpp#L325-L334

The two method differ for the following reasons:

• The norm factor in the old method. Why is the chi^2 divided by the size of the field ? (this is the reason for the huge difference in order of magnitude)
• Handling of the zero-th mode. How many elements of spectrum[] would you expect to be zero ? I find that the first two are always zero.

Even though the recent method is neater in mathematical term, it creates an unneeded copy of the field so it might be worth going back to the old version.

[Martin-Rey]

Quick question, could the 1/n factor in the old implementation be a FFT norm factor ? The calculation was always assumed to be performed in Fourier space.

[apontzen]

Could be. In principle it should be possible to figure this out by looking at the git history, but I'd suggest instead just going for the approach of getting an implementation that passes the chi^2~DOF test for the initial random field.