Provide a target_nside parameter to the smoothing function

[zonca]

• We need to provide guidelines on how to properly use the code, for example if people want maps at N_side 512, they should run the models at N_side 1024 and transform to target N_side. As we are smoothing at the end, we can easily provide a target_nside parameter, so people can smooth a 1024 map and get a 512 output without transforming twice.

Originally posted by @zonca in https://github.com/galsci/pysm/issues/90#issuecomment-947830102

[zonca]

I'm already doing map2alm and alm2map in:

https://github.com/galsci/pysm/blob/main/pysm3/models/template.py#L99-L152

so it is as easy as providing an extra parameter target_nside and use that for alm2map

[zonca]

from @seclark:

Would make sense to me to let people configure this (with guidelines) but default to running at 2048 for output maps with N_side <= 1024, and default to run at 2*N_side for output maps with 1024 <= N_side<= 4096. i.e., default to our recommended choices.

[zonca]

suggestion my Martin Reinecke, what if we used Gauss Legendre (GL) pixelization internally?

https://github.com/galsci/pysm/issues/92#issuecomment-948962496

So:

• input is Alms
• we transform to GL maps cheaply
• do evaluation of the model in GL pixel space
• map2alm
• beam smoothing
• alm2map HEALPix

I anyone used GL pixelization before, please jump in. Otherwise, I'll give it a try myself using ducc

[zonca]

thanks to @mreineck providing an example of using ducc0 and GL pixels, I made a comparison focused on PySM, I posted the notebook here where it is a bit easier to read (click on button to get the notebook and try it yourself):

https://zonca.dev/2021/11/healpix-gauss-legendre-pysm.html

[mreineck]

Good to see that this works well!

Just one word of caution: since the rings of a GL grid are not equidistant in theta, the GL map plots in the notebook can only be a rough approximantion to the real map; doing this accurately requires using the exact coordinates of every ring (obtainable, e.g., via ducc0.misc.GL_thetas()) and telling them to matplotlib.

[zonca]

will try with a more anisotropic map, for example the GNILC dust maps after adding small scales (#97), which is one of our use cases. We want to verify if error in HEALPix goes higher in such maps.

[zonca]

@seclark @brandonshensley I have added a section in the docs about dealing with Nside, see the commit reference above here.