s2let_transform_axisym_synthesis_mw

 s2let_transform_axisym_synthesis_mw
 Compute axisymmetric wavelet transform, output in pixel space.

 Default usage :

   f = s2let_transform_axisym_synthesis_mw(f_wav, f_scal, <options>)

 f_wav contains the input wavelet contributions -- MW sampling,
 f_scal contains the input scaling contributions -- MW sampling,
 f is the output field -- MW sampling,

 Option :
  'Reality'         = { false        [do not assume f real (default)],
                        true         [assume f real (improves performance)] }
  'B'               = { Dilation factor; B > 1 (default=2) }
  'L'               = { Harmonic band-limit; L > 1 (default=guessed from input) }
  'Upsample'      = { false        [multiresolution algorithm (default)],
                      true       [full resolution wavelets] }
  'J_min'           = { Minimum wavelet scale to consider;
                        0 <= J_min < log_B(L) (default=0) }

 S2LET package to perform Wavelets transform on the Sphere.
 Copyright (C) 2012-2015  Boris Leistedt & Jason McEwen
 See LICENSE.txt for license details

0001 function f = s2let_transform_axisym_synthesis_mw(f_wav, f_scal, varargin)
0002 
0003 % s2let_transform_axisym_synthesis_mw
0004 % Compute axisymmetric wavelet transform, output in pixel space.
0005 %
0006 % Default usage :
0007 %
0008 %   f = s2let_transform_axisym_synthesis_mw(f_wav, f_scal, <options>)
0009 %
0010 % f_wav contains the input wavelet contributions -- MW sampling,
0011 % f_scal contains the input scaling contributions -- MW sampling,
0012 % f is the output field -- MW sampling,
0013 %
0014 % Option :
0015 %  'Reality'         = { false        [do not assume f real (default)],
0016 %                        true         [assume f real (improves performance)] }
0017 %  'B'               = { Dilation factor; B > 1 (default=2) }
0018 %  'L'               = { Harmonic band-limit; L > 1 (default=guessed from input) }
0019 %  'Upsample'      = { false        [multiresolution algorithm (default)],
0020 %                      true       [full resolution wavelets] }
0021 %  'J_min'           = { Minimum wavelet scale to consider;
0022 %                        0 <= J_min < log_B(L) (default=0) }
0023 %
0024 % S2LET package to perform Wavelets transform on the Sphere.
0025 % Copyright (C) 2012-2015  Boris Leistedt & Jason McEwen
0026 % See LICENSE.txt for license details
0027 
0028 len = size(f_wav);
0029 temp = f_wav{len};
0030 sz = size(temp);
0031 if sz(1) == 2*sz(2)-1 || sz(2) == 2*sz(1)-1
0032     Lguessed = min([sz(1) sz(2)]);
0033 else
0034     Lguessed = min([sz(1) sz(2)])-1;
0035 end
0036 
0037 p = inputParser;
0038 p.addRequired('f_wav');
0039 p.addRequired('f_scal', @isnumeric);
0040 p.addParamValue('B', 2, @isnumeric);
0041 p.addParamValue('L', Lguessed, @isnumeric);
0042 p.addParamValue('J_min', 0, @isnumeric);
0043 p.addParamValue('Upsample', false, @islogical);
0044 p.addParamValue('Reality', false, @islogical);
0045 p.parse(f_wav, f_scal, varargin{:});
0046 args = p.Results;
0047 
0048 f_scal_vec = s2let_mw_arr2vec(f_scal);
0049 
0050 J = s2let_jmax(args.L, args.B);
0051 f_wav_vec = [];
0052 
0053 offset = 0;
0054 for j = args.J_min:J
0055     if args.Upsample
0056       band_limit = args.L;
0057     else
0058       band_limit = min([ s2let_bandlimit(j,args.J_min,args.B,args.L) args.L ]);
0059     end
0060     temp = f_wav{j+1-args.J_min};
0061     for t = 0:band_limit-1
0062         for p = 0:2*band_limit-2
0063           ind = offset + t * ( 2 * band_limit - 1) + p + 1;
0064           f_wav_vec = [f_wav_vec temp(t+1,p+1)];
0065         end
0066     end
0067     offset = offset + band_limit * (2 * band_limit - 1);
0068 end
0069 
0070 f_vec = s2let_transform_axisym_synthesis_mw_mex(f_wav_vec, f_scal_vec, args.B, args.L, args.J_min, args.Reality, args.Upsample);
0071 
0072 f = s2let_mw_vec2arr(f_vec);
0073 
0074 end