This routine is a wrapper to four other routines that synthesize a HEALPix temperature (and polarisation) map(s), its (their) first derivatives, and optionally its (their) second derivatives. The routines accept both single and double precision arrays for alm, map, der1 and der2. The precision of these arrays should match. All maps produced are RING ordered.
See ''Fortran Facilities'' Appendix for a note on a bug affecting the calculation of polarisation derivatives on past versions of this routine.

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

FORMAT

call alm2map_der*( nsmax, nlmax, nmmax, alm, map, der1 [, der2] )

ARGUMENTS

name & dimensionality	kind	in/out	description

nsmax	I4B	IN	the N_side value of the map to synthesize.
nlmax	I4B	IN	the maximum l value used for the a_lm.
nmmax	I4B	IN	the maximum m value used for the a_lm.
alm(1:p, 0:nlmax, 0:nmmax)	SPC/ DPC	IN	The a_lm values to make the map from. p is either 1 (temperature only) or 3 (temperature+polarisation).
map(0:12nsmax2-1) or (0:12nsmax**2-1,1:3)	SP/ DP	OUT	temperature map T(p) or temperature + polarisation maps T(p), Q(p), U(p) to be synthesized.
der1(0:12nsmax2-1, 1:2p)	SP/ DP	OUT	contains on output the first derivatives of T: $\left({\partial T}/{\partial \theta}, {\partial T}/{\partial \phi}/\sin\theta \right)$ or the interleaved derivatives of T, Q, and U: $\left({\partial T}/{\partial \theta}, {\partial Q}/{\partial \theta}, {\partial U}/{\partial \theta};\right.$ $\left.{\partial T}/{\partial \phi}/\sin\theta, \ldots \right)$
der2(0:12nsmax2-1,1:3p), OPTIONAL	SP/ DP	OUT	If this optional matrix is passed with this rank, it will contain on output the second derivatives $\left({\partial^2 T}/{\partial \theta^2}, {\partial^2 T}/{\partial \theta\partial\phi}/\sin\theta,\right.$ $\left.{\partial^2 T}/{\partial \phi^2}/\sin^2\theta \right)$ or $\left({\partial^2 T}/{\partial \theta^2}, {\partial^2 Q}/{\partial \theta^2}, {\partial^2 Q}/{\partial \theta^2}, \ldots \right)$

EXAMPLE:

use healpix_types use pix_tools, only : nside2npix use alm_tools, only : alm2map_der integer(I4B) :: nside, lmax, mmax, npix, n_plm real(SP), dimension(:), allocatable :: map real(SP), dimension(:,:), allocatable :: der1, der2 complex(SPC), dimension(:,:,:), allocatable :: alm ... nside=256 ; lmax=512 ; mmax=lmax npix=nside2npix(nside) allocate(alm(1:1,0:lmax,0:mmax)) allocate(map(0:npix-1)) allocate(der1(0:npix-1,1:2), der2(0:npix-1,1:3)) ... call alm2map_der(nside, lmax, mmax, alm, map, der1, der2)

Make temperature maps and its derivatives from the a_lm passed in alm. The maps have N_side of 256, and are constructed from a_lm values up to 512 in l and m.

MODULES & ROUTINES

This section lists the modules and routines used by alm2map_der*.

ring_synthesis: Performs FFT over m for synthesis of the rings.
compute_lam_mm, get_pixel_layout,
gen_lamfac_der, gen_mfac,
gen_recfac, init_rescale, l_min_ylm: Ancillary routines used for $\ {_s}Y_{lm}$ 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 alm2map_der*

alm2map: routine generating maps of temperature and polarisation from their a_lm
alm2map_spin: routine generating maps of arbitrary spin from their _sa_lm
synfast: executable using alm2map_der* to synthesize maps.
create_alm: routine to generate randomly distributed a_lm coefficients according to a given power spectrum

Eric Hivon 2010-06-18

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