This routine transform the scalar (and tensor) a_lm coefficients to emulate the effect of an arbitrary rotation of the underlying map. The rotation is done directly on the a_lm using the Wigner rotation matrices, computed by recursion. To rotate the a_lm for $l\leq l_{\rm max}$ the number of operations scales like $l^3_{\rm max}$ .

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

FORMAT

call rotate_alm*( lmax, alm_TGC, psi, theta, phi )

ARGUMENTS

name & dimensionality	kind	in/out	description

nlmax	I4B	IN	maximum l value for the a_lm.
alm_TGC(1:p,0:nlmax,0:nlmax)	SPC/ DPC	INOUT	complex a_lm values before and after rotation of the coordinate system. The first index here runs from 1:1 for temperature only, and 1:3 for polarisation. In the latter case, 1=T, 2=E, 3=B.
psi	DP	IN	first rotation: angle $\psi$ about the z-axis. All angles are in radians and should lie in [-2 $\pi$ ,2 $\pi$ ], the rotations are active and the referential system is assumed to be right handed, the routine coordsys2euler_zyz can be used to generate the Euler angles $\psi, \theta, \varphi$ for rotation between standard astronomical coordinate systems;
theta	DP	IN	second rotation: angle $\theta$ about the original (unrotated) y-axis;
phi	DP	IN	third rotation: angle $\varphi$ about the original (unrotated) z-axis;

EXAMPLE:

use alm_tools, only: rotate_alm ... call rotate_alm(64, alm_TGC, PI/3., 0.5_dp, 0.0_dp)

Transforms scalar and tensor a_lm for $l_{\rm max}=m_{\rm max} = 64$ to emulate a rotation of the underlying map by ( $\psi=\pi/3, \theta=0.5, \varphi=0$ ).

EXAMPLE:

use coord_v_convert, only: coordsys2euler_zyz use alm_tools, only: rotate_alm ... call coordsys2euler_zyz(2000.0_dp, 2000.0_dp, 'E', 'G', psi, theta, phi) call rotate_alm(64, alm_TGC, psi, theta, phi)

Rotate the a_lm from Ecliptic to Galactic coordinates.

RELATED ROUTINES

This section lists the routines related to rotate_alm*

coordsys2euler_zyz: can be used to generate the Euler angles $\psi, \theta, \varphi$ for rotation between standard astronomical coordinate systems
create_alm: Routine to create a_lm coefficients.
alter_alm: Routine to modify a_lm coefficients to apply or remove the effect of an instrumental beam.
map2alm: Routines to analyze a HEALPix sky map into its a_lm coefficients.
alm2map: Routines to synthetize a HEALPix sky map from its a_lm coefficients.
alms2fits, dump_alms: Routines to save a set of a_lm in a FITS file.
xcc_v_convert: rotates a 3D coordinate vector from one astronomical coordinate system to another.

Eric Hivon 2010-06-18

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This routine transform the scalar (and tensor) alm coefficients to emulate the effect of an arbitrary rotation of the underlying map. The rotation is done directly on the alm using the Wigner rotation matrices, computed by recursion. To rotate the alm for the number of operations scales like .

FORMAT

call rotate_alm*( lmax, alm_TGC, psi, theta, phi )

ARGUMENTS

EXAMPLE:

EXAMPLE:

RELATED ROUTINES

This section lists the routines related to rotate_alm*