S2LET library : documentation for IDL routines and interfaces

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Last modified: Tue Sep 22 12:42:56 2015.


List of Routines


Routine Descriptions

S2LET_AXISYM_HPX_WAV_ANALYSIS

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_hpx_wav_analysis

 PURPOSE:
   Compute wavelet transform of a Healpix map

 CALLING SEQUENCE:
   f_wav = s2let_axisym_hpx_wav_analysis(f, B, L, J_min)

 INPUTS:
   f     - input healpix nside (number of pixels is 12*nside^2)
   B     - Wavelet parameter
   L     - Band-limit to be used for the spherical harmonic transforms
   J_min - First wavelet scale to be used
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)

 OUTPUTS:
   f_wav - Struc containing the wavelets

 EXAMPLE:

   see s2let_hpx_demo

   read_fits_map, file, f
   f_wav = s2let_axisym_hpx_wav_analysis(f, B, L, J_min)
   f_rec = s2let_axisym_hpx_wav_synthesis(f_wav)
   J_max = s2let_j_max(L, b)
   mollview, f_rec, title='Reconstructed map'
   mollview, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
       mollview, f_wav.(j), title='Wavelet map '
            +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   Nside of the input map is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_hpx_wav_analysis.pro)


S2LET_AXISYM_HPX_WAV_SYNTHESIS

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_hpx_wav_synthesis

 PURPOSE:
   Reconstruct a healpix map from its wavelet transform

 CALLING SEQUENCE:
   f = s2let_axisym_hpx_wav_synthesis(f_wav)

 INPUTS:
   f_wav - Struc containing the wavelets maps

 OUTPUTS:
   f - The reconstructed Healpix map

 EXAMPLE:

   see s2let_hpx_demo

   read_fits_map, file, f
   f_wav = s2let_axisym_hpx_wav_analysis(f, B, L, J_min)
   f_rec = s2let_axisym_hpx_wav_synthesis(f_wav)
   J_max = s2let_j_max(L, b)
   mollview, f_rec, title='Reconstructed map'
   mollview, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
       mollview, f_wav.(j), title='Wavelet map '
            +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   B, L and J_min of the input wavelets are automatically detected 

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_hpx_wav_synthesis.pro)


S2LET_AXISYM_MW_WAV_ANALYSIS

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_mw_wav_analysis

 PURPOSE:
   Compute full resolution exact wavelet transform of a complex MW map

 CALLING SEQUENCE:
   f_wav = s2let_axisym_mw_wav_analysis(f, B, J_min)

 INPUTS:
   f     - input MW map (number of pixels is L*(2*L-1))
   B     - Wavelet parameter
   J_min - First wavelet scale to be used
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)

 OUTPUTS:
   f_wav - Struc containing the wavelets

 EXAMPLE:

   see s2let_demo and s2let_test

   f = s2let_read_mw_real_map(file)
   if multires eq 0 then f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min) 
      else f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)
   if multires eq 0 then f_rec = s2let_axisym_mw_wav_synthesis_real(f_wav) 
      else f_rec = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)
   L = s2let_get_mw_bandlimit(f)
   J_max = s2let_j_max(L, B)
   s2let_plot_mollweide, f_rec, title='Band-limited map'
   s2let_plot_mollweide, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
      s2let_plot_mollweide, f_wav.(j), title='Wavelet map '
      +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   The resolution/bandlimit L of the input map is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_mw_wav_analysis.pro)


S2LET_AXISYM_MW_WAV_ANALYSIS_MULTIRES

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_mw_wav_analysis_multires

 PURPOSE:
   Compute multiresolution exact wavelet transform of a complex MW map

 CALLING SEQUENCE:
   f_wav = s2let_axisym_mw_wav_analysis_multires(f, B, J_min)

 INPUTS:
   f     - input MW map (number of pixels is L*(2*L-1))
   B     - Wavelet parameter
   J_min - First wavelet scale to be used
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)

 OUTPUTS:
   f_wav - Struc containing the wavelets

 EXAMPLE:

   see s2let_demo and s2let_test

   f = s2let_read_mw_real_map(file)
   if multires eq 0 then f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min) 
      else f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)
   if multires eq 0 then f_rec = s2let_axisym_mw_wav_synthesis_real(f_wav) 
      else f_rec = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)
   L = s2let_get_mw_bandlimit(f)
   J_max = s2let_j_max(L, B)
   s2let_plot_mollweide, f_rec, title='Band-limited map'
   s2let_plot_mollweide, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
      s2let_plot_mollweide, f_wav.(j), title='Wavelet map '
      +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   The resolution/bandlimit L of the input map is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_mw_wav_analysis_multires.pro)


S2LET_AXISYM_MW_WAV_ANALYSIS_MULTIRES_REAL

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_mw_wav_analysis_multires_real

 PURPOSE:
   Compute multiresolution exact wavelet transform of a real MW map

 CALLING SEQUENCE:
   f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)

 INPUTS:
   f     - input MW map (number of pixels is L*(2*L-1))
   B     - Wavelet parameter
   J_min - First wavelet scale to be used
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)

 OUTPUTS:
   f_wav - Struc containing the wavelets

 EXAMPLE:

   see s2let_demo and s2let_test

   f = s2let_read_mw_real_map(file)
   if multires eq 0 then f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min) 
      else f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)
   if multires eq 0 then f_rec = s2let_axisym_mw_wav_synthesis_real(f_wav) 
      else f_rec = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)
   L = s2let_get_mw_bandlimit(f)
   J_max = s2let_j_max(L, B)
   s2let_plot_mollweide, f_rec, title='Band-limited map'
   s2let_plot_mollweide, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
      s2let_plot_mollweide, f_wav.(j), title='Wavelet map '
      +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   The resolution/bandlimit L of the input map is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_mw_wav_analysis_multires_real.pro)


S2LET_AXISYM_MW_WAV_ANALYSIS_REAL

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_mw_wav_analysis_real

 PURPOSE:
   Compute full resolution exact wavelet transform of a real MW map

 CALLING SEQUENCE:
   f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min)

 INPUTS:
   f     - input MW map (number of pixels is L*(2*L-1))
   B     - Wavelet parameter
   J_min - First wavelet scale to be used
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)

 OUTPUTS:
   f_wav - Struc containing the wavelets

 EXAMPLE:

   see s2let_demo and s2let_test

   f = s2let_read_mw_real_map(file)
   if multires eq 0 then f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min) 
      else f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)
   if multires eq 0 then f_rec = s2let_axisym_mw_wav_synthesis_real(f_wav) 
      else f_rec = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)
   L = s2let_get_mw_bandlimit(f)
   J_max = s2let_j_max(L, B)
   s2let_plot_mollweide, f_rec, title='Band-limited map'
   s2let_plot_mollweide, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
      s2let_plot_mollweide, f_wav.(j), title='Wavelet map '
      +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   The resolution/bandlimit L of the input map is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_mw_wav_analysis_real.pro)


S2LET_AXISYM_MW_WAV_SYNTHESIS

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_mw_wav_synthesis

 PURPOSE:
   Reconstruct a complex MW map from its full resolution exact wavelet transform

 CALLING SEQUENCE:
   f = s2let_axisym_mw_wav_synthesis(f_wav)

 INPUTS:
   f_wav - input exact wavelet transfrom 

 OUTPUTS:
   f     - Reconstructed MW map

 EXAMPLE:

   see s2let_demo and s2let_test

   f = s2let_read_mw_real_map(file)
   if multires eq 0 then f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min) 
      else f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)
   if multires eq 0 then f_rec = s2let_axisym_mw_wav_synthesis_real(f_wav) 
      else f_rec = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)
   L = s2let_get_mw_bandlimit(f)
   J_max = s2let_j_max(L, B)
   s2let_plot_mollweide, f_rec, title='Band-limited map'
   s2let_plot_mollweide, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
      s2let_plot_mollweide, f_wav.(j), title='Wavelet map '
      +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   The wavelet parameters B/J_min are automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_mw_wav_synthesis.pro)


S2LET_AXISYM_MW_WAV_SYNTHESIS_MULTIRES

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_mw_wav_synthesis_multires

 PURPOSE:
   Reconstruct a complex MW map from its multiresolution exact wavelet transform

 CALLING SEQUENCE:
   f = s2let_axisym_mw_wav_synthesis_multires(f_wav)

 INPUTS:
   f_wav - input exact wavelet transfrom 

 OUTPUTS:
   f     - Reconstructed MW map

 EXAMPLE:

   see s2let_demo and s2let_test

   f = s2let_read_mw_real_map(file)
   if multires eq 0 then f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min) 
      else f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)
   if multires eq 0 then f_rec = s2let_axisym_mw_wav_synthesis_real(f_wav) 
      else f_rec = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)
   L = s2let_get_mw_bandlimit(f)
   J_max = s2let_j_max(L, B)
   s2let_plot_mollweide, f_rec, title='Band-limited map'
   s2let_plot_mollweide, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
      s2let_plot_mollweide, f_wav.(j), title='Wavelet map '
      +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   The wavelet parameters B/J_min are automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_mw_wav_synthesis_multires.pro)


S2LET_AXISYM_MW_WAV_SYNTHESIS_MULTIRES_REAL

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_mw_wav_synthesis_multires_real

 PURPOSE:
   Reconstruct a complex MW map from its full resolution exact wavelet transform

 CALLING SEQUENCE:
   f = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)

 INPUTS:
   f_wav - input exact wavelet transfrom 

 OUTPUTS:
   f     - Reconstructed MW map

 EXAMPLE:

   see s2let_demo and s2let_test

   f = s2let_read_mw_real_map(file)
   if multires eq 0 then f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min) 
      else f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)
   if multires eq 0 then f_rec = s2let_axisym_mw_wav_synthesis_real(f_wav) 
      else f_rec = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)
   L = s2let_get_mw_bandlimit(f)
   J_max = s2let_j_max(L, B)
   s2let_plot_mollweide, f_rec, title='Band-limited map'
   s2let_plot_mollweide, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
      s2let_plot_mollweide, f_wav.(j), title='Wavelet map '
      +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   The wavelet parameters B/J_min are automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_mw_wav_synthesis_multires_real.pro)


S2LET_AXISYM_MW_WAV_SYNTHESIS_REAL

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_axisym_mw_wav_synthesis_real

 PURPOSE:
   Reconstruct a real MW map from its full resolution exact wavelet transform

 CALLING SEQUENCE:
   f = s2let_axisym_mw_wav_synthesis_real(f_wav)

 INPUTS:
   f_wav - input exact wavelet transfrom 

 OUTPUTS:
   f     - Reconstructed MW map

 EXAMPLE:

   see s2let_demo and s2let_test

   f = s2let_read_mw_real_map(file)
   if multires eq 0 then f_wav = s2let_axisym_mw_wav_analysis_real(f, B, J_min) 
      else f_wav = s2let_axisym_mw_wav_analysis_multires_real(f, B, J_min)
   if multires eq 0 then f_rec = s2let_axisym_mw_wav_synthesis_real(f_wav) 
      else f_rec = s2let_axisym_mw_wav_synthesis_multires_real(f_wav)
   L = s2let_get_mw_bandlimit(f)
   J_max = s2let_j_max(L, B)
   s2let_plot_mollweide, f_rec, title='Band-limited map'
   s2let_plot_mollweide, f_wav.scal, title='Scaling map'
   for j=0, J_max-J_min do begin
      s2let_plot_mollweide, f_wav.(j), title='Wavelet map '
      +strtrim(j+1,2)+' on '+strtrim(J_max-J_min+1,2)
   endfor
   
 COMMENTS:
   The wavelet parameters B/J_min are automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_axisym_mw_wav_synthesis_real.pro)


S2LET_DEMO1

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_demo1

 PURPOSE:
   Demo 1 : test the exactness of all MW spherical harmonics and wavelet
   transforms for a tomography map of the earth and plot the wavelet maps

 OPTIONAL KEYWORDS:
   B - The wavelet parameter for the test
   J_min - The first wavelet scale to be used for the transform
   multires - multiresolution flag (1 if yes, else 0)
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)
   DEFAULT VALUES: B=3, J_min=2, multires=0, wavtype=1

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_demo1.pro)


S2LET_DEMO2

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_demo2

 PURPOSE:
   Demo : read Healpix map, convert it to MW map, then test the
   exactness of all MW spherical harmonics and wavelet
   transforms and plot the wavelet maps

 OPTIONAL KEYWORDS:
   L - The bandlimit for the spherical harmonic transforms
   B - The wavelet parameter for the test
   J_min - The first wavelet scale to be used for the transform
   multires - multiresolution flag (1 if yes, else 0)
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)
   DEFAULT VALUES: L=128, B=3, J_min=2, multires=0, wavtype=1

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_demo2.pro)


S2LET_DYLIB_EXISTS

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_dylib_exists

 PURPOSE:
   Check if the s2let dynamic library exists somewhere in the path

 CALLING SEQUENCE:
   status = s2let_dylib_exists()

 OUTPUT
   1 if found, 0 otherwise

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_dylib_exists.pro)


S2LET_GET_DYLIB

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_get_dylib

 PURPOSE:
   Get the location/name of the s2let dynamic library

 CALLING SEQUENCE:
   location = s2let_get_dylib()

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_get_dylib.pro)


S2LET_GET_MW_BANDLIMIT

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_get_mw_bandlimit

 PURPOSE:
   Detect the resolution/bandlimit L of an input MW map

 CALLING SEQUENCE:
   L = s2let_get_mw_bandlimit(f)

 INPUT:
   f - array/map of size L*(2*L-1)

 OUTPUT
   L - the resolution/bandlimit

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_get_mw_bandlimit.pro)


S2LET_GET_WAV_BANDLIMIT

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_get_wav_bandlimit

 PURPOSE:
   Compute the bandlimit of the j-th wavelet constructed with parameter B

 CALLING SEQUENCE:
   bl = s2let_get_wav_bandlimit(B, j)

 OUTPUT
   The bandlimit of the j-th wavelet constructed with parameter B

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_get_wav_bandlimit.pro)


S2LET_HEALPIX2MW

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_healpix2mw

 PURPOSE:
   Convert a real Healpix map to an MW map 
   through the spherical harmonic transform 

 CALLING SEQUENCE:
   mwmap = s2let_healpix2mw(hpxmap, lmax=lmax)

 INPUT:
   hpxmap - The Healpix map (npix = 12*nside*nside)
   lmax - The bandlimit of the SHA transform, thus the
       resolution of the MW map

 OUTPUT
   mwmap - The MW map (npix = lmax*(2*lmax-1))

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_healpix2mw.pro)


S2LET_HPX_ALM2MAP_REAL

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_hpx_alm2map_real

 PURPOSE:
   Reconstruct a real Healpix map from its spherical harmonic
   transform (nb: not an exact transform due to healpix)

 CALLING SEQUENCE:
   f = s2let_hpx_alm2map_real(alm, nside)

 INPUT:
   alm - a complex array containing the spherical harmonic transform
         alm_{el em} can be accessed at alm(ind) with ind = el*el + el + em
   nside - resolution for the output map

 OUTPUT
   f - The Healpix map (npix = 12*nside*nside)

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_hpx_alm2map_real.pro)


S2LET_HPX_DEMO

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_hpx_demo

 PURPOSE:
   Demo : test all HPX spherical harmonics and wavelet transforms
   (not exact due to healpix) for a simulated CMB map and plot the wavelet maps

 OPTIONAL KEYWORDS:
   L - The bandlimit for the spherical harmonic transforms
   B - The wavelet parameter for the test
   J_min - The first wavelet scale to be used for the transform
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)
   DEFAULT VALUES: L=192, B=7, J_min=2, wavtype=1

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_hpx_demo.pro)


S2LET_J_MAX

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_j_max

 PURPOSE:
   Compute the maximum wavelet to be used, given a bandlimit L and a
   wavelet parameter B

 CALLING SEQUENCE:
   J_max = s2let_j_max(L, B)

 OUTPUT
   Compute the maximum wavelet to be used, given a bandlimit L and a
   wavelet parameter B;

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_j_max.pro)


S2LET_MW_ALM2MAP

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_alm2map

 PURPOSE:
   Reconstruct a complex MW map from its exact spherical harmonic transform

 CALLING SEQUENCE:
   f = s2let_mw_alm2map(alm)

 INPUT:
   alm - a complex array containing the spherical harmonic transform
         alm_{el em} can be accessed at alm(ind) with ind = el*el + el + em

 OUTPUT
   f - The MW map (npix = L*(2*L-1), L is detected)

 COMMENT:
   The resolution/bandlimit L is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_alm2map.pro)


S2LET_MW_ALM2MAP_REAL

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_alm2map_real

 PURPOSE:
   Reconstruct a real MW map from its exact spherical harmonic transform

 CALLING SEQUENCE:
   f = s2let_mw_alm2map_real(alm)

 INPUT:
   alm - a complex array containing the spherical harmonic transform
         alm_{el em} can be accessed at alm(ind) with ind = el*el + el + em

 OUTPUT
   f - The MW map (npix = L*(2*L-1), L is detected)

 COMMENT:
   The resolution/bandlimit L is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_alm2map_real.pro)


S2LET_MW_MAP2ALM_REAL[1]

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_map2alm_real

 PURPOSE:
   Compute the spherical harmonic transform of a real Healpix map
   (nb: not an exact transform due to healpix)

 CALLING SEQUENCE:
   alm = s2let_hpx_map2alm_real(f, lmax)

 INPUTS
   f - The input healpix map (npix = 12*nside*nside, nside is detected)

 OUTPUT:
   alm - a complex array containing the spherical harmonic transform
         alm_{el em} can be accessed at alm(ind) with ind = el*el + el + em

 COMMENT:
   The resolution nside is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_hpx_map2alm_real.pro)


S2LET_MW_MAP2ALM_REAL[2]

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_map2alm_real

 PURPOSE:
   Compute exact spherical harmonic transform of a complex MW map

 CALLING SEQUENCE:
   alm = s2let_mw_map2alm(f)

 INPUTS
   f - The input MW map (npix = L*(2*L-1), L is detected)

 OUTPUT:
   alm - a complex array containing the spherical harmonic transform
         alm_{el em} can be accessed at alm(ind) with ind = el*el + el + em

 COMMENT:
   The resolution/bandlimit L is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_map2alm.pro)


S2LET_MW_MAP2ALM_REAL[3]

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_map2alm_real

 PURPOSE:
   Compute exact spherical harmonic transform of a real MW map

 CALLING SEQUENCE:
   alm = s2let_mw_map2alm_real(f)

 INPUTS
   f - The input MW map (npix = L*(2*L-1), L is detected)

 OUTPUT:
   alm - a complex array containing the spherical harmonic transform
         alm_{el em} can be accessed at alm(ind) with ind = el*el + el + em

 COMMENT:
   The resolution/bandlimit L is automatically detected

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_map2alm_real.pro)


S2LET_MW_PIXEL_EDGES

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_pixel_edges

 PURPOSE:
   Get (theta, phi) coordinates for the corners of the i-th pixel in
   the MW sampling

 CALLING SEQUENCE:
   arr = s2let_mw_pixel_edges(L, i)

 INPUTS
   L - resolution/bandlimit of the MW map
   i - pixel index

 OUTPUT:
   arr - an array containing four numbers: theta1, theta2, phi1 and phi2
       which are the locations of the corners of the pixel

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_pixel_edges.pro)


S2LET_MW_PLOT_MOLLWEIDE

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_plot_mollweide

 PURPOSE:
   Plot a real MW map (from data of FITS file) under Mollweide projection

 CALLING SEQUENCE:
   s2let_mw_plot_mollweide, mapfile, title='My map'

 INPUTS
   maporfile - filename for the FITS or map read with s2let_read_mw_real_map

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_plot_mollweide.pro)


S2LET_MW_SAMPLING

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_sampling

 PURPOSE:
   Compute the coordinates of the nodes of the MW sampling for a
   given bandlimit/resolution

 CALLING SEQUENCE:
   s2let_mw_sampling, L, thetas, phis

 INPUT:
   L - resolution/bandlimit

 OUTPUT
   thetas - The theta coordinates of the nodes
   phis - The phi coordinates of the nodes

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_sampling.pro)


S2LET_MW_WRITE_REAL_MAP

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_mw_write_real_map

 PURPOSE:
   Write a real MW map to a FITS file

 CALLING SEQUENCE:
   s2let_mw_write_real_map, map, file

 INPUTS:
   map - input MW map (npix=L*(2*L-1), L is detected)
   file - filename for the FITS

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_write_real_map.pro)


S2LET_READ_MW_REAL_MAP

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_read_mw_real_map

 PURPOSE:
   Read a real MW map from a FITS file

 CALLING SEQUENCE:
   f = s2let_mw_read_real_map(file)

 INPUTS
   file - filename for the FITS

 OUTPUT:
   map - MW map (npix=L*(2*L-1), L is detected)

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_mw_read_real_map.pro)


S2LET_TEST

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_test

 PURPOSE:
   Test the exactness of all MW spherical harmonics and wavelet
   transform for real and complex signals on the sphere

 OPTIONAL KEYWORDS:
   L - The bandlimit/resolution for the test
   B - The wavelet parameter for the test
   J_min - The first wavelet scale to be used for the transform
   multires - multiresolution flag (1 if yes, else 0)
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)
   DEFAULT VALUES: L=64, B=3, J_min=2, multires=0, wavtype=1

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_test.pro)


S2LET_VALID_WAV_PARAMETERS

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 S2LET package - Copyright (C) 2012 
 Boris Leistedt & Jason McEwen

 NAME:
   s2let_valid_wav_parameters

 PURPOSE:
   Check and test a set of wavelet parameters

 CALLING SEQUENCE:
   status = s2let_valid_wav_parameters(B, L, J_min)

 INPUTS:
   B     - Wavelet parameter
   L     - Band-limit to be used for the spherical harmonic transforms
   J_min - First wavelet scale to be used
   wavtype - Wavelet type (1: scale-discretised, 2:needlets, 3: cubic splines)

(See /Users/bl/Dropbox/Wavelets/s2let/src/main/idl/s2let_valid_wav_parameters.pro)