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 almT (and if specified almE and almB) values up to the desired order in l (maximum 3*Nside). 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 Nside 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(0:12*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 alm 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 alm 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. 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 $P_{lm}(\theta)$ 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, ($\backslash$ z, -z $\backslash$) , dw8, plm(0:(lmax+1)*(lmax+2)*nside-1))
Analyses temperature and polarisation maps passed in map. The map has an Nside of 256, and the analysis is performed up to 512 in l and m. The resulting alm 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
Note: Starting with version 2.20, libpsht routines will be called when precomputed Plm 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 alm coefficients computed by map2alm* into a FITS file
map2alm_iterative
similar to map2alm* with iterative scheme.

Version 3.31, 2017-01-06