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60<H1><A ID="SECTION6500"></A>
61<A ID="idl:remove_dipole"></A>
62<BR>
63
64</H1>
65
66<P>
67<b><font size=+6><FONT COLOR="#CC0000">remove_dipole</FONT></font></b><hr>
68<H3>This IDL facility provides a means to fit and remove the dipole and monopole
69from a <b>HEALPix</b> map.
70</H3>
71Location in HEALPix directory tree: <a href="https://sourceforge.net/p/healpix/code/1005/tree/trunk/src/idl/misc/remove_dipole.pro"><b>src/idl/misc/remove_dipole.pro</b></a>&nbsp;
72
73<P>
74<hr><h1>FORMAT </h1><h3>IDL>
75REMOVE_DIPOLE,
76<A HREF="#idl:remove_dipole:map"> Map</A> [,
77<A HREF="#idl:remove_dipole:weight"> Weight</A>,
78<A HREF="#idl:remove_dipole:bad_data">BAD_DATA=</A>,
79<A HREF="#idl:remove_dipole:gal_cut">GAL_CUT=</A>,
80<A HREF="#idl:remove_dipole:coord_in">COORD_IN=</A>,
81<A HREF="#idl:remove_dipole:coord_out">COORD_OUT=</A>,
82<A HREF="#idl:remove_dipole:covariance_matrix">Covariance_Matrix=</A>,
83<A HREF="#idl:remove_dipole:dipole">Dipole=</A>,
84<A HREF="#idl:remove_dipole:monopole">Monopole=</A>,
85<A HREF="#idl:remove_dipole:noremove">/NOREMOVE</A>,
86<A HREF="#idl:remove_dipole:nside">NSIDE=</A>,
87<A HREF="#idl:remove_dipole:onlymonopole">/ONLYMONOPOLE</A>,
88<A HREF="#idl:remove_dipole:ordering">ORDERING=</A>,
89<A HREF="#idl:remove_dipole:pixel">PIXEL=</A>,
90<A HREF="#idl:remove_dipole:silent">/SILENT</A>,
91<A HREF="#idl:remove_dipole:units">UNITS=</A>,
92<A HREF="#idl:remove_dipole:help">/HELP</A>]
93</h3>
94
95<P>
96<hr>
97<H1>QUALIFIERS</H1>
98
99  <DL COMPACT><DT>
100<B>Map</B>
101<DD><A ID="idl:remove_dipole:map"></A> input and output, vector
102<BR>
103map from which monopole and dipole are to be removed
104      (also used for output).
105      Assumed to be a full sky data set, unless PIXEL is set and has the same
106      size as map
107    <DT>
108<B>Weight</B>
109<DD><A ID="idl:remove_dipole:weight"></A> input, vector, optional
110<BR>
111same size as map,
112     describe weighting scheme to apply to each pixel for the fit
113<BR>	<b>default:</b>uniform weight
114    <DT>
115<B>BAD_DATA =</B>
116<DD><A ID="idl:remove_dipole:bad_data"></A>
117    scalar float, value given on input to bad pixels
118<BR>          <b>default:</b><TT>!healpix.bad_value</TT> <!-- MATH
119 $\equiv -1.6375\ 10^{30}$
120 -->
121<SPAN CLASS="MATH"><IMG STYLE="height: 1.92ex; vertical-align: -0.29ex; " SRC="idl_img105.png"
122 ALT="$\equiv -1.6375\ 10^{30}$"></SPAN>.
123    <DT>
124<B>GAL_CUT=</B>
125<DD><A ID="idl:remove_dipole:gal_cut"></A>
126    if set to a value larger than 0, the pixels with galactic
127    latitude <SPAN CLASS="MATH">|b|&lt;</SPAN>gal_cut degrees are not considered in the
128      fit.
129<BR><B>NB:</B>
130      the cut is <EM>really</EM> done in Galactic coordinates. If the input
131      coordinates are different (see Coord_In), the map is rotated into galactic
132      before applying the cut.
133    <DT>
134<B>COORD_IN =</B>
135<DD><A ID="idl:remove_dipole:coord_in"></A>
136     string, map coordinate system (either 'Q' or 'C': equatorial,
137    'G': galactic or 'E': ecliptic; upper/lower case accepted)
138<BR>         <b>default:</b>'G' (galactic)
139    <DT>
140<B>COORD_OUT =</B>
141<DD><A ID="idl:remove_dipole:coord_out"></A>
142    string, coordinate system (see above) in which
143    to output dipole vector in variable Dipole
144<BR>         <b>default:</b>same as coord_in
145    <DT>
146<B>Covariance_Matrix =</B>
147<DD><A ID="idl:remove_dipole:covariance_matrix"></A>
148    OUTPUT, scalar (or symmetric 4x4 matrix),
149<BR>
150covariance
151     of the statistical errors made on monopole (and dipole) determination
152    <DT>
153<B>Dipole=</B>
154<DD><A ID="idl:remove_dipole:dipole"></A>
155	OUTPUT, 3d vector,
156<BR>
157coordinates of best fit dipole (done simultaneously with monopole), same
158        units as input map
159    <DT>
160<B>Monopole=</B>
161<DD><A ID="idl:remove_dipole:monopole"></A>
162        OUTPUT, scalar float,
163<BR>
164value found for the best fit monopole (done simultaneously with dipole),
165        same units as input map
166    <DT>
167<B>NSIDE=</B>
168<DD><A ID="idl:remove_dipole:nside"></A>
169    scalar integer, healpix resolution parameter
170    <DT>
171<B>ORDERING=</B>
172<DD><A ID="idl:remove_dipole:ordering"></A>
173    string, ordering scheme (either 'RING' or 'NESTED')
174    <DT>
175<B>PIXEL=</B>
176<DD><A ID="idl:remove_dipole:pixel"></A>
177    input, vector, gives the Healpix index of the pixels
178        whose temperature is actually given in map (for cut sky
179    maps). If present, must match Map in size. If absent, it is
180    assumed that the map covers the whole sky.
181    <DT>
182<B>UNITS=</B>
183<DD><A ID="idl:remove_dipole:units"></A>
184   string, units of the input map
185  </DL>
186
187<P>
188<hr><H1>KEYWORDS</H1>
189
190  <DL COMPACT><DT>
191<B>/NOREMOVE</B>
192<DD><A ID="idl:remove_dipole:noremove"></A>
193   if set, the best fit dipole and monopole are computed but not
194    removed (ie, Map is unchanged)
195    <DT>
196<B>/ONLYMONOPOLE</B>
197<DD><A ID="idl:remove_dipole:onlymonopole"></A>
198   if set, fit (and remove) only the monopole
199    <DT>
200<B>/HELP</B>
201<DD><A ID="idl:remove_dipole:help"></A>
202    if set, only display documentation header
203    <DT>
204<B>/SILENT</B>
205<DD><A ID="idl:remove_dipole:silent"></A>
206    if set, the routine works silently
207  </DL>
208
209<P>
210<hr>
211<H1>DESCRIPTION</H1>
212<blockquote>
213remove_dipolemakes a simultaneous least square fit of the monopole and dipole on all the valid
214pixels of Map (those with a value different from BAD_DATA) with a galactic
215latitude larger in magnitude than GAL_CUT (in degrees). The position of the pixels
216on the sky is reconstructed from NSIDE and ORDERING.
217If Map does not cover the full sky, the actual indices of the concerned pixels should be given in PIXEL
218</blockquote>
219
220<P>
221<hr><H1>RELATED ROUTINES</H1><h3>This section lists the routines related to <b><FONT COLOR="#CC0000">remove_dipole</FONT></b></h3>
222
223  <DL COMPACT><DT>
224<B>idl</B>
225<DD>version 6.4 or more is necessary to run remove_dipole.
226  </DL>
227
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