
remove_dipole*
This routine provides a means to fit and remove the dipole and monopole
from a HEALPix map. The fit is obtained by solving the linear system

(15) 
with, d=1 or 2, and

(16) 

(17) 
where is the set of
valid, unmasked pixels, m is the input map, w is pixel weighting, while
s_{0}(p) = 1 and
are
respectively the monopole and dipole templates. The output map is then

(18) 
Location in HEALPix directory tree:
src/f90/mod/pix_tools.f90
FORMAT call remove_dipole*(
nside, map, ordering, degree, multipoles, zbounds [, fmissval, mask, weights]
)
ARGUMENTS
name & dimensionality 
kind 
in/out 
description 




nside 
I4B 
IN 
value of
resolution parameter for input map 
map(0:12*nside*nside1) 
SP/ DP 
INOUT 
HEALPix map from which the monopole and dipole will be
removed. Those are removed from all unflagged pixels,
even those excluded by the cut zounds or the mask. 
ordering 
I4B 
IN 
HEALPix scheme 1:RING, 2: NESTED 
degree 
I4B 
IN 
multipoles to fit and remove. It is either 0 (nothing done),
1 (monopole only) or 2 (monopole and dipole). 
multipoles(0:degree*degree1) 
DP 
OUT 
values of best fit monopole and
dipole. The monopole is described as a scalar in the same
units as the input map, the dipole as a 3D cartesian vector, in the same units. 
zbounds(1:2) 
DP 
IN 
section of the map on which to perform the
fit, expressed in terms of
. If zbounds(1)<zbounds(2), the fit is
performed on the strip zbounds(1)<z<zbounds(2); if not, the
fit is performed outside of the strip
zbounds(2)<z<zbounds(1). 
fmissval (OPTIONAL) 
SP/ DP 
IN 
value used to flag bad pixel on input
default:1.6375e30. Pixels with that value are ignored
during the fit, and left unchanged on output. 
mask(0:12*nside*nside1) (OPTIONAL) 
SP/ DP 
IN 
mask of valid pixels.
Pixels with mask<10^{10} are not used for fit. Note:
the map is not multiplied by the mask. 
weights(0:12*nside*nside1) (OPTIONAL) 
SP/ DP 
IN 
weight to be
given to each map pixel before doing the fit. By default pixels are given
a uniform weight of 1. Note:
the output map is not multiplied by the weights. 
EXAMPLE:
s = sin(15.0_dp * PI / 180.0_dp)
call remove_dipole*(128, map, 1, 2, multipoles, ( s, s ) )
Will compute and remove the best fit monopole and dipole from a map with
in RING ordering scheme. The fit is performed on pixels with b>15^{o}.
MODULES & ROUTINESThis section lists the modules and routines used by remove_dipole*.

pix_tools
 module, containing:
RELATED ROUTINESThis section lists the routines related to remove_dipole*

add_dipole
 routine to add a dipole and
monopole to a map.
Eric Hivon
20100618

