map2alm*

This routine is a wrapper to 5 internal routines:map2alm_sc, map2alm_sc_pre, map2alm_pol, map2alm_pol_pre1, map2alm_pol_pre2. These routines analyse a HEALPix RING ordered map and return $a_{\ell m}^T$ (and if specified $a_{\ell m}^E$ and $a_{\ell m}^B$) values up to the desired order in $\ell$ (maximum 3* $N_{\mathrm{side}}$). The different routines are called depending on what parameters are passed. Some routines analyse with or without precomputed harmonics and some with or without polarisation.

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

FORMAT

call map2alm*( nsmax, nlmax, nmmax, map_TQU, alm_TGC[, zbounds=, w8ring_TQU=, plm=] )

ARGUMENTS

name & dimensionality	kind	in/out	description
nsmax	I4B	IN	the $N_{\mathrm{side}}$ value of the map to analyse.
nlmax	I4B	IN	the maximum $\ell$ value for the analysis.
nmmax	I4B	IN	the maximum $m$ value for the analysis.
map_TQU(0:12*nsmax**2-1)	SP/ DP	IN	if only the temperature map is to be analyse, the map-array should be passed with this rank.
map_TQU(0:12*nsmax**2-1, 1:3)	SP/ DP	IN	if both temperature an polarisation maps are to be analysed, the map array should have this rank, where the second index is (1,2,3) corresponding to (T,Q,U).

alm_TGC(1:p, 0:nlmax, 0:nmmax)	SPC/ DPC	OUT	The $a_{\ell m}$ values output from the analysis. p is 1 or 3 dependent on wether polarisation is included or not. In the former case, the first index is (1,2,3) corresponding to (T,E,B).
zbounds(1:2), OPTIONAL	DP	IN	section of the map on which to perform the $a_{\ell m}$ analysis, 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.
w8ring_TQU(1:2*nsmax, 1:p), OPTIONAL	DP	IN	ring weights for quadrature corrections. If ring weights are not used, this array should be 1 everywhere. p is 1 for a temperature analysis and 3 for (T,Q,U).
plm(0:(nlmax+1)*(nlmax+2)*nsmax-1), OPTIONAL	DP	IN	If this optional matrix is passed with this rank, precomputed $P_{\ell m}(\theta)$ are used instead of recursion. Note that since version 2.20 this feature has become obsolete because of algorithm optimizations.
plm(0:(nlmax+1)*(nlmax+2)*nsmax-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.

EXAMPLE:

use healpix_modules
integer(i4b) :: nside, lmax
real(dp), allocatable, dimension(:,:) :: dw8
real(dp), dimension(2) :: z
real(sp), allocatable, dimension(:,:) :: map
complex(spc), allocatable, dimension(:,:,:) :: alm
nside = 256
lmax = 512
allocate(dw8(1:2*nside, 1:3))
allocate(map(0:nside2npix(nside)-1,1:3))
allocate(alm(1:3, 0:lmax, 0:lmax)
dw8 = 1.0_dp
z = sin(10.0_dp * DEG2RAD)
call map2alm(nside, lmax, lmax, map, alm, (/ z, -z /) , dw8)

Analyses temperature and polarisation maps passed in map. The map has an $N_{\mathrm{side}}$ of 256, and the analysis is performed up to 512 in $\ell$ and $m$. The resulting $a_{\ell m}$ coefficients for temperature and polarisation are returned in alm. A 10°cut on each side of the equator is applied. Uniform weights are used.

MODULES & ROUTINES

This section lists the modules and routines used by map2alm*.

ring_analysis

Performs FFT for the ring analysis.

misc_util

module, containing:

assert_alloc

routine to print error message when an array is not properly allocated

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 map2alm*

anafast

executable using map2alm* to analyse maps.

alm2map

routine performing the inverse transform of map2alm*.

dump_alms

write $a_{\ell m}$ coefficients computed by map2alm* into a FITS file

map2alm_iterative

similar to map2alm* with iterative scheme.