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_lm^T (and if specified a_lm^E and a_lm^B) values up to the desired order in l (maximum 3*N_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_side value of the map to analyse.
nlmax	I4B	IN	the maximum l value for the analysis.
nmmax	I4B	IN	the maximum m value for the analysis.
map_TQU(0:12nsmax*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(0:12nsmax*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_lm 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)	DP	IN	section of the map on which to perform the a_lm analysis, expressed in terms of $z=\sin({\rm latitude}) = \cos(\theta).$ If zbounds(1)<zbounds(2), the analysis is performed on the strip zbounds(1)<z<zbounds(2); if not, it is performed outside of the strip zbounds(2)<z<zbounds(1).
w8ring_TQU(1:2*nsmax, 1:p)	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 $P_{lm}(\theta)$ are used instead of recursion.
plm(0:(nlmax+1)(nlmax+2)nsmax-1,1:3), OPTIONAL	DP	IN	If this optional matrix is passed with this rank, precomputed $P_{lm}(\theta)$ AND precomputed tensor harmonics are used instead of recursion.

EXAMPLE:

use healpix_types use alm_tools use pix_tools 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, plm(0:(lmax+1)*(lmax+2)*nside-1))

Analyses temperature and polarisation maps passed in map. The map has an N_side of 256, and the analysis is performed up to 512 in l and m. The resulting a_lm coefficients for temperature and polarisation are returned in alm. A $10^\circ$ cut on each side of the equator is applied. Uniform weights are used. Since the optional plm array is provided with rank one, precomputed scalar $P_{lm}(\theta)$ are used while tensor harmonics are computed with a recursion.

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

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*.
map2alm_iterative: similar to map2alm* with iterative scheme.

Eric Hivon 2010-06-18

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