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plm_gen

This routine computes the latitude dependent part $\lambda_{lm}$ of the spherical harmonics ( $Y_{lm}(\theta,\phi) = \lambda_{lm}(\theta) e^{i m \phi}$ ) of spin 0 and 2 (see HEALPix primer) used to synthetize or analyze HEALPix maps of temperature and polarisation.

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

FORMAT

call plm_gen( nsmax, nlmax, nmmax, plm )

ARGUMENTS

name & dimensionality	kind	in/out	description

nsmax	I4B	IN	The ${N_{\rm side}}$ value for which to compute the $\lambda_{lm}$ .
nlmax	I4B	IN	The maximum multipole order l of the generated $\lambda_{lm}$ .
nmmax	I4B	IN	The maximum degree m of the generated $\lambda_{lm}$ .
plm(0:n_plm-1, 1:p)	DP	OUT	The $\lambda_{lm}$ values, either for temperature only (p=1) or temperature and polarisation (p=3). The number of $\lambda_{lm}$ is n_plm = nsmax(nmmax+1)(2nlmax-nmmax+2). They are stored in the order of increasing order l, increasing degree m, for all the HEALPix* ring colatitudes $\theta$ from North Pole to Equator, ie $\lambda_{00}(\theta_1)$ , $\lambda_{10}(\theta_1)$ , $\lambda_{20}(\theta_1)$ , ..., $\lambda_{11}(\theta_1)$ , $\lambda_{21}(\theta_1)$ ; ..., $\lambda_{00}(\theta_2)$ ...

EXAMPLE:

use healpix_types use alm_tools, only : plm_gen integer(I4B) :: nside, lmax, mmax, n_plm real(DP), dimension(:,:), allocatable :: plm ... nside=256 ; lmax=512 ; mmax=lmax npix=nside2npix(nside) n_plm=nside*(mmax+1)*(2*lmax-mmax+2) allocate(plm(0:n_plm-1,1:3)) ... call plm_gen(nside, lmax, mmax, plm)

Computes the spherical harmonics for temperature and polarisation for N_side= 256, up to 512 in l and m.

MODULES & ROUTINES

This section lists the modules and routines used by plm_gen.

compute_lam_mm, get_pixel_layout,
gen_lamfac,gen_mfac, gen_normpol,
gen_recfac, init_rescale, l_min_ylm: Ancillary routines used for $\lambda_{lm}$ recursion
misc_utils: module, containing:
assert_alloc: routine to print error message, when an array can not be allocated properly

RELATED ROUTINES

This section lists the routines related to plm_gen

alm2map: routine generating maps of temperature and polarisation from their a_lm that can use precomputed $\lambda_{lm}$ generated by plm_gen
map2alm: routine analysing maps of temperature and polarisation that can use precomputed $\lambda_{lm}$ generated by plm_gen
plmgen: executable using plm_gen to compute the $\lambda_{lm}$ and writting them on disc

Eric Hivon 2010-06-18

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This routine computes the latitude dependent part of the spherical harmonics ( ) of spin 0 and 2 (see HEALPix primer) used to synthetize or analyze HEALPix maps of temperature and polarisation.