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alm_map_tools.h

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00001 /*
00002  *  This file is part of Healpix_cxx.
00003  *
00004  *  Healpix_cxx is free software; you can redistribute it and/or modify
00005  *  it under the terms of the GNU General Public License as published by
00006  *  the Free Software Foundation; either version 2 of the License, or
00007  *  (at your option) any later version.
00008  *
00009  *  Healpix_cxx is distributed in the hope that it will be useful,
00010  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
00011  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00012  *  GNU General Public License for more details.
00013  *
00014  *  You should have received a copy of the GNU General Public License
00015  *  along with Healpix_cxx; if not, write to the Free Software
00016  *  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
00017  *
00018  *  For more information about HEALPix, see http://healpix.jpl.nasa.gov
00019  */
00020 
00021 /*
00022  *  Healpix_cxx is being developed at the Max-Planck-Institut fuer Astrophysik
00023  *  and financially supported by the Deutsches Zentrum fuer Luft- und Raumfahrt
00024  *  (DLR).
00025  */
00026 
00027 /*! \file alm_map_tools.h
00028  *  Copyright (C) 2003, 2004, 2005 Max-Planck-Society
00029  *  \author Martin Reinecke
00030  */
00031 
00032 #ifndef HEALPIX_ALM_MAP_TOOLS_H
00033 #define HEALPIX_ALM_MAP_TOOLS_H
00034 
00035 #include "xcomplex.h"
00036 #include "arr.h"
00037 
00038 template<typename T> class Alm;
00039 template<typename T> class Healpix_Map;
00040 
00041 /*! \defgroup alm_map_group Conversions between a_lm and maps */
00042 /*! \{ */
00043 
00044 /*! Converts a Healpix map to a set of a_lms.
00045     \param map the input map, which must have RING ordering
00046     \param alm the output a_lms. l_max and m_max of the conversion are
00047            determined from this object.
00048     \param weight array containing the weights for the individual rings of
00049            the map. It must have at least 2*\a map.Nside() entries.
00050     \param add_alm If this is \a true, then the computed a_lm are added
00051            to the values already residing in \a alm. */
00052 template<typename T> void map2alm (const Healpix_Map<T> &map,
00053   Alm<xcomplex<T> > &alm, const arr<double> &weight,
00054     bool add_alm=false);
00055 
00056 /*! Converts a Healpix map to a set of a_lms, using an iterative scheme
00057     which is more accurate than plain map2alm().
00058     \param map the input map, which must have RING ordering.
00059     \param alm the output a_lms. l_max and m_max of the conversion are
00060            determined from this object.
00061     \param num_iter the number of iterations (0 is identical to map2alm()).
00062     \param weight array containing the weights for the individual rings of
00063            the map. It must have at least 2*\a map.Nside() entries. */
00064 template<typename T> void map2alm_iter (const Healpix_Map<T> &map,
00065   Alm<xcomplex<T> > &alm, int num_iter, const arr<double> &weight);
00066 
00067 template<typename T> void map2alm_iter (const Healpix_Map<T> &map,
00068   Alm<xcomplex<T> > &alm, int num_iter)
00069   {
00070   arr<double> wgt(2*map.Nside());
00071   wgt.fill(1);
00072   map2alm_iter(map,alm,num_iter,wgt);
00073   }
00074 
00075 template<typename T> void map2alm_iter2 (const Healpix_Map<T> &map,
00076   Alm<xcomplex<T> > &alm, double err_abs, double err_rel);
00077 
00078 /*! Converts Healpix maps containing the I, Q and U Stokes parameters
00079     to sets of a_lms.
00080     \param mapT the I-Stokes parameter input map
00081     \param mapQ the Q-Stokes parameter input map
00082     \param mapU the U-Stokes parameter input map
00083     \note All maps must have the same nside, and must be in RING scheme.
00084     \param almT the output temperature a_lms
00085     \param almG the output gradient a_lms
00086     \param almC the output curl a_lms
00087     \note all a_lm sets must have the the same lmax and mmax.
00088     \param weightT ring weights for \a mapT.
00089     \param weightQ ring weights for \a mapQ.
00090     \param weightU ring weights for \a mapU.
00091     \param add_alm If this is \a true, then the computed a_lm are added
00092            to the values already residing in \a alm.
00093     \note The weight arrays must have at least 2*\a mapT.Nside() entries. */
00094 template<typename T> void map2alm_pol
00095   (const Healpix_Map<T> &mapT,
00096    const Healpix_Map<T> &mapQ,
00097    const Healpix_Map<T> &mapU,
00098    Alm<xcomplex<T> > &almT,
00099    Alm<xcomplex<T> > &almG,
00100    Alm<xcomplex<T> > &almC,
00101    const arr<double> &weightT,
00102    const arr<double> &weightQ,
00103    const arr<double> &weightU,
00104    bool add_alm=false);
00105 /*! Converts Healpix maps containing the I, Q and U Stokes parameters
00106     to sets of a_lms, using an iterative scheme which is more accurate than
00107     plain map2alm_pol().
00108     \param mapT the I-Stokes parameter input map
00109     \param mapQ the Q-Stokes parameter input map
00110     \param mapU the U-Stokes parameter input map
00111     \note All maps must have the same nside, and must be in RING scheme.
00112     \param almT the output temperature a_lms
00113     \param almG the output gradient a_lms
00114     \param almC the output curl a_lms
00115     \note all a_lm sets must have the the same lmax and mmax.
00116     \param num_iter the number of iterations (0 is identical to map2alm_pol()).
00117     \param weightT ring weights for \a mapT.
00118     \param weightQ ring weights for \a mapQ.
00119     \param weightU ring weights for \a mapU.
00120     \note The weight arrays must have at least 2*\a mapT.Nside() entries. */
00121 template<typename T> void map2alm_pol_iter
00122   (const Healpix_Map<T> &mapT,
00123    const Healpix_Map<T> &mapQ,
00124    const Healpix_Map<T> &mapU,
00125    Alm<xcomplex<T> > &almT,
00126    Alm<xcomplex<T> > &almG,
00127    Alm<xcomplex<T> > &almC,
00128    int num_iter,
00129    const arr<double> &weightT,
00130    const arr<double> &weightQ,
00131    const arr<double> &weightU);
00132 
00133 template<typename T> void map2alm_pol_iter
00134   (const Healpix_Map<T> &mapT,
00135    const Healpix_Map<T> &mapQ,
00136    const Healpix_Map<T> &mapU,
00137    Alm<xcomplex<T> > &almT,
00138    Alm<xcomplex<T> > &almG,
00139    Alm<xcomplex<T> > &almC,
00140    int num_iter)
00141   {
00142   arr<double> wgt(2*mapT.Nside());
00143   wgt.fill(1);
00144   map2alm_pol_iter(mapT,mapQ,mapU,almT,almG,almC,num_iter,wgt,wgt,wgt);
00145   }
00146 
00147 template<typename T> void map2alm_pol_iter2
00148   (const Healpix_Map<T> &mapT,
00149    const Healpix_Map<T> &mapQ,
00150    const Healpix_Map<T> &mapU,
00151    Alm<xcomplex<T> > &almT,
00152    Alm<xcomplex<T> > &almG,
00153    Alm<xcomplex<T> > &almC,
00154    double err_abs, double err_rel);
00155 
00156 /*! Converts a a set of a_lm to a HEALPix map.
00157     \param alm the input a_lms. l_max and m_max of the conversion are
00158            determined from this object.
00159     \param map the output map, which must have RING ordering. */
00160 template<typename T> void alm2map (const Alm<xcomplex<T> > &alm,
00161   Healpix_Map<T> &map);
00162 
00163 /*! Converts a a set of polarised a_lm to a HEALPix map.
00164     \param almT the input temperature a_lms
00165     \param almG the input gradient a_lms
00166     \param almC the input curl a_lms
00167     \param mapT the I-Stokes parameter output map
00168     \param mapQ the Q-Stokes parameter output map
00169     \param mapU the U-Stokes parameter output map */
00170 template<typename T> void alm2map_pol
00171   (const Alm<xcomplex<T> > &almT,
00172    const Alm<xcomplex<T> > &almG,
00173    const Alm<xcomplex<T> > &almC,
00174    Healpix_Map<T> &mapT,
00175    Healpix_Map<T> &mapQ,
00176    Healpix_Map<T> &mapU);
00177 
00178 /*! Converts a a set of a_lm to a HEALPix map and its first derivatives.
00179     \param alm the input a_lms. l_max and m_max of the conversion are
00180            determined from this object.
00181     \param map the output map, which must have RING ordering.
00182     \param mapdth an output map containing \f$d (\mbox{map})/d\vartheta\f$,
00183            which must have RING ordering.
00184     \param mapdph an output map containing
00185            \f$(\sin\vartheta)^{-1}d(\mbox{map})/d\varphi\f$,
00186            which must have RING ordering. */
00187 template<typename T> void alm2map_der1
00188   (const Alm<xcomplex<T> > &alm,
00189    Healpix_Map<T> &map,
00190    Healpix_Map<T> &mapdth,
00191    Healpix_Map<T> &mapdph);
00192 
00193 /*! \} */
00194 
00195 #endif

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