s2let_compute_scal

 s2let_compute_scal - Compute a rotated scaling function

 Compute the scaling function, rotated by rho=(alpha, beta, gamma) in
 harmonic space and reconstruct it on the sphere.

 Default usage :

   phi_j = s2let_compute_scal(J_min, alpha, beta, gamma, L, <options>)

 J_min is the 1st wavelet scale of the tiling (and determines at which el
 the scaling function stops).
 rho=(alpha, beta, gamma) is the rotation in SO(3) by which to rotate
 the wavelet wavelet
 L if harmonic band-limit for the reconstruction on the sphere
 phi_j is the reconstructed wavelet on the sphere, at resolution L

 Options consist of parameter type and value pairs.
 Valid options include:

  'B'               = { Dilation factor; B > 1 (default = 2) }
  'N'               = { Azimuthal band-limit; N > 0 (default = L) }
  'Spin'            = { Spin number; Spin >= 0 (default = 0) }

 S2LET package to perform Wavelet transform on the Sphere.
 Copyright (C) 2012-2015-2014  Boris Leistedt, Martin Büttner & Jason McEwen
 See LICENSE.txt for license details

0001 function phi_j = s2let_compute_scal(J_min, alpha, beta, gamma, L, varargin)
0002 % s2let_compute_scal - Compute a rotated scaling function
0003 %
0004 % Compute the scaling function, rotated by rho=(alpha, beta, gamma) in
0005 % harmonic space and reconstruct it on the sphere.
0006 %
0007 % Default usage :
0008 %
0009 %   phi_j = s2let_compute_scal(J_min, alpha, beta, gamma, L, <options>)
0010 %
0011 % J_min is the 1st wavelet scale of the tiling (and determines at which el
0012 % the scaling function stops).
0013 % rho=(alpha, beta, gamma) is the rotation in SO(3) by which to rotate
0014 % the wavelet wavelet
0015 % L if harmonic band-limit for the reconstruction on the sphere
0016 % phi_j is the reconstructed wavelet on the sphere, at resolution L
0017 %
0018 % Options consist of parameter type and value pairs.
0019 % Valid options include:
0020 %
0021 %  'B'               = { Dilation factor; B > 1 (default = 2) }
0022 %  'N'               = { Azimuthal band-limit; N > 0 (default = L) }
0023 %  'Spin'            = { Spin number; Spin >= 0 (default = 0) }
0024 %
0025 % S2LET package to perform Wavelet transform on the Sphere.
0026 % Copyright (C) 2012-2015-2014  Boris Leistedt, Martin Büttner & Jason McEwen
0027 % See LICENSE.txt for license details
0028 
0029 % Parse arguments.
0030 p = inputParser;
0031 p.addRequired('J_min', @isnumeric);
0032 p.addRequired('alpha', @isnumeric);
0033 p.addRequired('beta', @isnumeric);
0034 p.addRequired('gamma', @isnumeric);
0035 p.addRequired('L', @isnumeric);
0036 p.addParamValue('B', 2, @isnumeric);
0037 p.addParamValue('N', -1, @isnumeric);
0038 p.addParamValue('Spin', 0, @isnumeric);
0039 
0040 p.parse(J_min, alpha, beta, gamma, L, varargin{:});
0041 
0042 args = p.Results;
0043 
0044 if args.N == -1
0045     args.N = L;
0046 end
0047 
0048 B = args.B;
0049 N = args.N;
0050 Spin = args.Spin;
0051 
0052 [psi, phi] = s2let_wavelet_tiling(B, L, N, Spin, J_min);
0053 
0054 % Precompute Wigner small-d functions
0055 d = zeros(L, 2*L-1, 2*L-1);
0056 d(1,:,:) = ssht_dl(squeeze(d(1,:,:)), L, 0, beta);
0057 for el = 1:L-1
0058     d(el+1,:,:) = ssht_dl(squeeze(d(el,:,:)), L, el, beta);
0059 end
0060 
0061 % Rotate spherical harmonic
0062 phi_lm_rot = ssht_rotate_flm(phi, d, alpha, gamma, 'Axisymmetric', true);
0063 
0064 
0065 
0066 phi_j = ssht_inverse(complex(real(phi_lm_rot), imag(phi_lm_rot)), L, 'Spin', Spin);
0067 
0068 end