Combining periodic metric with other metrics

[caspervedder]

Hi Mike,

At the moment, it seems the periodic metric can only be used in combination with the standard Euclidean metric. I was wondering if there’s currently any way—or if it would be possible in the future— to combine the periodic metric with other metrics, such as Rperp? This would be quite useful for my use case.

Best,
Casper

[rmjarvis]

You'd have to define what you actually mean by that. How do you want to define Rpar and Rperp in a periodic space?

[caspervedder]

Thanks for the reply!

Let's say I have a simulation box with length L and I define z as my line of sight. In this case z is Rpar. Then, Rperp would be sqrt(dx^2 + dy^2) = sqrt(r - r_//), given the definitions for dx/dy/dz in the picture from the docs:

However, I am not sure how this would work exactly in treecorr. In this case it might be necessary to put the box at a very large distance from the observer and maybe some rotation analogous to what you proposed in #147 to get the x-y plane to be perpendicular to the observer.

[rmjarvis]

Sounds to me like you just want the 2d version of periodic. Just don't include z in the Catalog, and the periodic distance is what you defined as rperp.

[caspervedder]

Well sort off, the distance I am interested is indeed simply the 2D distance, but I only want to include pairs close to each other along the LOS (and a way this can be done is using Rperp + max_rpar, similar to this issue #17), so it's max_rpar that I am interested in (for which I need the z coord), should have made that more clear.

[rmjarvis]

I think this would need to be a new metric name, which is fine. It wouldn't be very hard to add that. But there isn't any way to get max_rpar to work the way you want with any of our current metrics.

So to be clear, you want:

• measure distances as the normal periodic Euclidean distance in x,y
• require z values to be given, but ignore them for the purpose of computing distances
• define rpar = z for the purpose of min_rpar, max_rpar.

Any request on what this metric should be called?

[caspervedder]

Indeed! That sums it up nicely, this should give the projected correlation function w(rp) given a certain Pi_{max} in a periodic box. I'd like to add that for statistics involving shapes the convention would be the one for 'Flat Geometries' (https://rmjarvis.github.io/TreeCorr/_build/html/shear.html), as in this case we assume z to be the (constant) line of sight.

Furthermore, it would very helpful for me if this would be available for the 3-point stats as well!

As for the name, PeriodicRperp would make most sense to me as Rperp is basically its counterpart in a spherical geometry, but this is a bit wordy, so there might be a better option.