there is no direct relation between a pixel and and the spherical harmonic coefficients. you can imagine it like this: the map pixels are the data and the spherical harmonic functions you "fit" to the data. The spherical harmonic functions is a system of infinitely many (orthonormal) functions. Now you...

Spherical harmonics discretized using HEALPix (either sampled at pixel centers, or avaraged over pixel areas) form a linearly independent system up to lmax = 3 nsmax -1. (from here: HEALPX anafast)

No way to do it right now with healpy There is an open issue on healpy about this: https://github.com/healpy/healpy/issues/19. An alternative is to plot a map directly using matplotlib: https://github.com/zonca/paperplots/blob/master/python/scripts/PlanckFig_map.py...

Is it possible that you are using and old version of healpy? It looks like there used to be a limit of 2000 pixels that was removed few months ago, see: https://github.com/healpy/healpy/commit/2aaa5ba79db8d16aad036b387ff8771838d7768f...

deg refers only to the angles in rot, not to the Rotator itself. The Rotator needs theta (colatitude) and phi (longitude) in radians, see: import healpy as hp import numpy as np r = hp.Rotator(coord = ['G', 'C']) ri = hp.Rotator(coord = ['C', 'G']) gz, ga = np.pi/2, 0. #...

It is due to symmetry. m=-1 and m=1 have the same transform, so HEALPix considers only m>=0. So for example lmax=2 we have: a00 a10 a11 a20 a21 a22 6 coefficients total. The length of the alm array is expected to be: mmax * (2 * lmax + 1 -...

You need to setup IPython to display matplotlib plots. If you are using IPython console %matplotlib If IPython notebook %matplotlib inline ...