I'm just starting to work with Healpy and have noticed that if I use a map to get alm's and then use those alm's to generate a new map, I do not get the map I started with. Here's what I'm looking at:
import numpy as np
import healpy as hp
nside = 2 # healpix nside parameter
m = np.arange(hp.nside2npix(nside)) # create a map to test
alm = hp.map2alm(m) # compute alm's
new_map = hp.alm2map(alm, nside) # create new map from computed alm's
# Let's look at two maps
print(m)
[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47] # as expected
print(new_map)
[-23.30522233 -22.54434515 -21.50906755 -20.09203749 -19.48841773
-18.66392484 -16.99593867 -16.789984 -15.14587061 -14.57960049
-13.4403252 -13.35992138 -10.51368725 -10.49793946 -10.1262039
-8.6340571 -7.41789272 -6.87712224 -5.75765487 -3.75121764
-4.35825512 -1.6221964 -1.03902923 -0.41478954 0.52480646
2.34629955 2.1511705 2.40325268 5.39576497 5.38390848
5.78324832 7.24779083 8.4915595 9.0047257 10.15179735
12.1306303 12.62672772 13.4512206 15.11920678 15.32516145
16.96927483 17.53554496 18.67482024 18.75522407 20.42078855
21.18166574 22.21694334 23.6339734 ] # not what I was expecting
As you can see, new_map doesn't match the input map, m. I imagine there's some subtlety to these functions that I'm missing. Any idea?
I get a different result:
print(new_map)
[ 0.15859344, 0.91947062, 1.95474822, 3.37177828,
4.01808325, 4.84257613, 6.51056231, 6.71651698,
8.36063036, 8.92690049, 10.06617577, 10.1465796 ,
12.98620654, 13.00668621, 13.3736899 , 14.87056857,
16.08200108, 16.62750343, 17.74223892, 19.75340803,
19.13441288, 21.8704716 , 22.45363877, 23.07787846,
24.01747446, 25.83896755, 25.6438385 , 25.89592068,
28.89565876, 28.88853415, 29.28314212, 30.7524165 ,
31.9914533 , 32.50935137, 33.65169114, 35.63525597,
36.13322869, 36.95772158, 38.62570775, 38.83166242,
40.47577581, 41.04204594, 42.18132122, 42.26172504,
43.88460433, 44.64548151, 45.68075911, 47.09778917]
Older versions of healpy were automatically removing a constant offset from the map before transformation, better to update healpy to the last version.
The residual difference is related to the fact the pixelization introduces an error, this error is larger at low nside.