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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
\sum_{j=0}^{d^2-1}\ A_{ij}\ f_j = b_i
\end{displaymath} (15)

with, d=1 or 2, and
b_i = \sum_{p \in \cal{P}} s_i(p) w(p) m(p),
\end{displaymath} (16)

A_{ij} = \sum_{p \in \cal{P}} s_i(p) w(p) s_j(p),
\end{displaymath} (17)

where $\cal{P}$ is the set of valid, unmasked pixels, m is the input map, w is pixel weighting, while s0(p) = 1 and $s_1(p)=x,\ s_2(p)=y,\ s_3(p)=z$ are respectively the monopole and dipole templates. The output map is then
m'(p) = m(p) - \sum_{i=0}^{d^2-1} f_i s_i(p).
\end{displaymath} (18)

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


call remove_dipole*( nside, map, ordering, degree, multipoles, zbounds [, fmissval, mask, weights] )


name & dimensionality kind in/out description
nside I4B IN value of ${N_{\rm side}}$ resolution parameter for input map
map(0:12*nside*nside-1) 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*degree-1) 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 $z=\sin({\rm latitude}) =
\cos(\theta)$. 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*nside-1) (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*nside-1) (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.


s = sin(15.0_dp * PI / 180.0_dp)
call remove_dipole*(128, map, 1, 2, multipoles, ($\backslash$ s, -s $\backslash$) )

Will compute and remove the best fit monopole and dipole from a map with ${N_{\rm side}}=128$ in RING ordering scheme. The fit is performed on pixels with |b|>15o.


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

module, containing:


This section lists the routines related to remove_dipole*

routine to add a dipole and monopole to a map.

Eric Hivon 2010-06-18
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