ring_analysis

This subroutine computes the Fast Fourier Transform of a single ring of pixels and extends the computed coefficients up to the maximum $m$ of the transform.

Location in HEALPix directory tree: src/f90/mod/alm_tools.F90 

FORMAT

call ring_analysis( nsmax, nlmax, nmmax, datain, nph, dataout, kphi0 )

ARGUMENTS

name & dimensionality	kind	in/out	description
nsmax	I4B	IN	$N_{\mathrm{side}}$ of the map.
nlmax	I4B	IN	Maximum $\ell$ of the analysis.
nmmax	I4B	IN	Maximum $m$ of the analysis.
nph	I4B	IN	The number of points on the ring.
datain(0:nph-1)	DP	IN	Function values on the ring.
dataout(0:nmmax)	DPC	OUT	Fourier components, replicated to $Nmmax$.
kphi0	I4B	IN	0 if the first pixel on the ring is at $\phi=0$; 1 otherwise.

EXAMPLE:

call ring_analysis(64,128,128,datain,8,dataout,0)

Returns the periodically extended complex Fourier Transform of datain in dataout. They are returned in the following order: 0 1 2 3 4 5 6 7 6 5 4 3 2 1 $0\dots$. The value $kphi0=0$ specifies that no phase factor needed to be applied, because the ring starts at $\phi=0$.

MODULES & ROUTINES

This section lists the modules and routines used by ring_analysis.

healpix_fft

module.

RELATED ROUTINES

This section lists the routines related to ring_analysis

ring_synthesis

Inverse transform (complex-to-real), used in alm2map, alm2map_der and synfast