alm2map*

This routine is a wrapper to 10 other routines: alm2map_sc_X, alm2map_sc_pre_X, alm2map_pol_X, alm2map_pol_pre1_X, alm2map_pol_pre2_X, where X stands for either s or d. These routines synthesize a HEALPix RING ordered temperature map (and if specified, polarisation maps) from input $a_{\ell m}^T$ (and if specified $a_{\ell m}^E$ and $a_{\ell m}^B$) values. The different routines are called dependent on what parameters are passed. Some routines synthesize maps with or without precomputed harmonics (note that since HEALPix v2.20 precomputed harmonics most likely won't speed up computation) and some with or without polarisation. The routines accept both single and double precision arrays for alm_TGC and map_TQU. The precision of these arrays should match.

Location in HEALPix directory tree: src/f90/mod/alm_tools.F90 

FORMAT

call alm2map*( nsmax, nlmax, nmmax, alm_TGC, map_TQU[, plm=$\vert$ zbounds=] )

ARGUMENTS

name & dimensionality	kind	in/out	description
nsmax	I4B	IN	the $N_{\mathrm{side}}$ value of the map to synthesize.
nlmax	I4B	IN	the maximum $\ell$ value used for the $a_{\ell m}$.
nmmax	I4B	IN	the maximum $m$ value used for the $a_{\ell m}$.
alm_TGC(1:p, 0:nlmax, 0:nmmax)	SPC or DPC	IN	The $a_{\ell m}$ values to make the map from. $p$ is 3 or 1 depending on wether polarisation is respectively included or not. In the former case, the first index runs from 1 to 3 corresponding to (T,E,B).

map_TQU(0:12*nsmax**2-1)	SP or DP	OUT	if only a temperature map is to be synthesized, the map-array should be passed with this rank.
map_TQU(0:12*nsmax**2-1, 1:3)	SP or DP	OUT	if both temperature an polarisation maps are to be synthesized, the map array should have this rank, where the second index is (1,2,3) corresponding to (T,Q,U).
plm(0:n_plm-1), OPTIONAL	DP	IN	If this optional matrix is passed with this rank, precomputed $P_{\ell m}(\theta)$ are used instead of recursion. ( n_plm = nsmax*(nmmax+1)*(2*nlmax-nmmax+2).
plm(0:n_plm-1,1:3), OPTIONAL	DP	IN	If this optional matrix is passed with this rank, precomputed $P_{\ell m}(\theta)$ AND precomputed tensor harmonics are used instead of recursion. (n_plm = nsmax*(nmmax+1)*(2*nlmax-nmmax+2).
zbounds(1:2), OPTIONAL	DP	IN	section of the sphere on which to perform the map synthesis, expressed in terms of $z=\sin(\mathrm{latitude}) = \cos(\theta).$ If zbounds(1)$<$zbounds(2), it is performed on the strip zbounds(1)$<z<$zbounds(2); if not, it is performed outside the strip zbounds(2)$\le z \le$zbounds(1). If absent, the whole map is processed. Currently, zbounds and plm can not be used together.

EXAMPLE:

use healpix_types
use pix_tools, only : nside2npix
use alm_tools, only : alm2map
integer(I4B) :: nside, lmax, mmax, npix
real(SP), dimension(:,:), allocatable :: map
complex(SPC), dimension(:,:,:), allocatable :: alm
real(DP), dimension(1:2) :: zrange
...
nside=256 ; lmax=512 ; mmax=lmax
npix=nside2npix(nside)
allocate(alm(1:3,0:lmax,0:mmax))
allocate(map(0:npix-1,1:3))
...
zrange =(/ 0.0_dp, 0.5_dp /)
call alm2map(nside, lmax, mmax, alm, map, zbounds=zrange)

Make temperature and polarisation maps from the scalar and tensor $a_{\ell m}$ passed in alm. The maps have $N_{\mathrm{side}}$ of 256, and are constructed from $a_{\ell m}$ values up to 512 in $\ell$ and $m$. In order to save time, the maps are only generated on the range $0 < z < 0.5$ (leaving the other pixels to 0) even though the input $a_{\ell m}$ are those of a full sky map.

MODULES & ROUTINES

This section lists the modules and routines used by alm2map*.

ring_synthesis

Performs FFT over $m$ for synthesis of the rings.

compute_lam_mm, get_pixel_layout,

gen_lamfac,gen_mfac, gen_normpol,

gen_recfac, init_rescale, l_min_ylm

Ancillary routines used for $Y_{\ell m}$ recursion

misc_utils

module, containing:

assert_alloc

routine to print error message, when an array can not be allocated properly

Note: Starting with version 3.10, libsharp routines will be called when precomputed $P_{\ell m}$ are not provided.

RELATED ROUTINES

This section lists the routines related to alm2map*

alm2map_der

routine generating a map and its derivatives from its $a_{\ell m}$

alm2map_spin

routine generating maps of arbitrary spin from their ${_s}a_{\ell m}$

smoothing

executable using alm2map* to smooth maps

synfast

executable using alm2map* to synthesize maps.

map2alm

routine performing the inverse transform of alm2map*.

create_alm

routine to generate randomly distributed $a_{\ell m}$ coefficients according to a given power spectrum

pixel_window, generate_beam

return the $\ell$-space HEALPix -pixel and beam window function respectively

alter_alm

modifies $a_{\ell m}$ to emulate effect of real space filtering