qe.pixelization.map2alm_spin() not consistent for Healpix and CAR

[darbykramer]

• falafel version: 0.1.0
• Python version: 3.9.8
• Operating System: Linux (Niagara)

Description

I am using the qe_source() function in my recent theory paper to reconstruct maps from simulations. After building a healpix qe.pixelization object, passing that object and my input alms into qe_source(), I found that I was getting a negative version of the map I expected. This issue does not exist if I use a CAR pixelization, and the differentiation occurs in px.map2alm_spin(). I demo the issue below.

What I Did

import pixell.curvedsky as cs
import numpy as np
from orphics import maps
from pixell import enmap
import healpy as hp
from falafel import qe, utils

# presets 
nside = 1024
res_arc = 3.2 # close to nside resolution
res_rad = res_arc * 1/60 * np.pi/180

shape, wcs = enmap.fullsky_geometry(res=res_arc*1/60*np.pi/180)

lmax = 3000
ells = np.linspace(0,lmax, lmax+1)

# make a power spectrum
tcl = np.ones(lmax+1)

# make a random alm
Talm = hp.synalm(tcl)

# make a car map of the initial alms
imap_car = cs.alm2map(Talm, enmap.ndmap(np.zeros(shape), wcs))

# make an hp map of the initial alms
imap_hp = hp.alm2map(Talm, nside=nside)

# make two pixelization objects from falafel.qe with similar resolution
# first make a CAR one
px_car = qe.pixelization(shape=shape, wcs=wcs)

# next a healpix one
px_hp = qe.pixelization(nside=nside)

# use their map2alm_spin() methods to take the spin-0 SHTs of imap
# change imap to car for the car px:
imap_car = enmap.enmap(imap_car, px_car.wcs)
car_alm = px_car.map2alm_spin(imap_car,lmax,0,0)

# hp:
hp_alm = px_hp.map2alm_spin(imap_hp,lmax,0,0)

# print alms, showing that they are opposites of each other
print("CAR Pixelization Alm = "+str(car_alm))

print("Healpix Pixelization Alm = "+str(hp_alm))

# compare to original Talm
print("Original Alm = "+str(Talm))
 

Outputs:

CAR Pixelization Alm = [[ 0.22765916+0.j          0.40338906+0.j          0.18244621+0.j
  ...  0.30785274-0.16778591j -0.24141246-0.69590157j
   0.37591568+1.38649857j]
 [ 0.        +0.j          0.        +0.j          0.        +0.j
  ...  0.        +0.j          0.        +0.j
   0.        +0.j        ]]

Healpix Pixelization Alm = [array([-0.22771936-0.j        , -0.40346108-0.j        ,
       -0.18257752-0.j        , ..., -0.30785274+0.16778591j,
        0.24141246+0.69590157j, -0.37591568-1.38649857j]), array([-0.-0.j, -0.-0.j, -0.-0.j, ..., -0.-0.j, -0.-0.j, -0.-0.j])]

Original Alm = [ 0.22765916+0.j          0.40338906+0.j          0.18244621+0.j
 ...  0.30785274-0.16778591j -0.24141246-0.69590157j
  0.37591568+1.38649857j]

Therefore, the CAR version is correct, and the map2alm_spin with spin=0 for the healpix pixelization object yields a negative alm of what it should.