plm_gen

This routine computes the latitude dependent part $\lambda_{\ell m}$ of the spherical harmonics ( $Y_{\ell m}(\theta,\phi) = \lambda_{\ell m}(\theta) e^{i m \phi}$) of spin 0 and 2 (see HEALPix primer) used to synthetize or analyze HEALPix maps of temperature and polarisation. Since version 2.20, which introduced optimized algorithms for spherical harmonic transforms, it has become obsolete and should no longer be used.

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 $N_{\mathrm{side}}$ value for which to compute the $\lambda_{\ell m}$.
nlmax	I4B	IN	The maximum multipole order $\ell$ of the generated $\lambda_{\ell m}$.
nmmax	I4B	IN	The maximum degree $m$ of the generated $\lambda_{\ell m}$.
plm(0:n_plm-1, 1:p)	DP	OUT	The $\lambda_{\ell m}$ values, either for temperature only ($p=1$) or temperature and polarisation ($p=3$). The number of $\lambda_{\ell m}$ is n_plm = nsmax*(nmmax+1)*(2*nlmax-nmmax+2). They are stored in the order of increasing order $\ell$, 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 $N_{\mathrm{side}}=256$, up to 512 in $\ell$ 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 $\lambda_{\ell m}$ 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 $a_{\ell m}$ that can use precomputed $\lambda_{\ell m}$ generated by plm_gen

map2alm

routine analysing maps of temperature and polarisation that can use precomputed $\lambda_{\ell m}$ generated by plm_gen

plmgen

executable using plm_gen to compute the $\lambda_{\ell m}$ and writting them on disc