cs2vec.m

function [outC,outS,nm] = cs2vec(in,ordflag)

% CS2VEC rearranges a field of spherical harmonic coefficients in cs-
% or sc-format to a vector shape. The order will be:
% CASE I: degree-wise (default)
%        nm   = [0    1    1    2    2    2    3    3    3    3  ...
%                0    0    1    0    1    2    0    1    2    3  ...]
% CASE II: order-wise 
%        nm   = [0    1    2    3    1    2    3    2    3    3  ...
%                0    0    0    0    1    1    1    2    2    3  ...]
%
% CALL:   [outC,outS,nm] = cs2vec(in,ordflag)
%
% PARAMETER:  
%   in      [n,m]   input in cs- or sc-format
%   ordflag [bool]  false = degree-wise ordering (default)
%                   true  = order-wise ordering 
% 
% OUTPUT:
%   outC    [k,1]   coefficients in vector shape: cosine part
%   outS    [k,1]   coefficients in vector shape: sine part
%   nm      [2,k]   ordering vector
%
% See also: vec2cs
%
% Uses functions: 
% - cs2sc
% - sc2cs
% 
% Written by Matthias Weigelt 2007-05-02
%--------------------------------------------------------------------------
% revision history
%  12.03.2012, MW: added ordering flag and completed help text
% -------------------------------------------------------------------------

%% INPUT CHECK
% check if there is any NaN
narginchk(1,2);
if nargin < 2 || isempty(ordflag), ordflag = false;                       end
if any(isnan(in)), error('Input may not contain NaNs. Use Inf instead!'); end

% Size determination for field
[row, col]=size(in);
if (row~=col) && (col~=2*row-1)
   error('Input not in cs or sc format');
elseif col~=2*row-1
    % if data is in cs-format we transfer it to sc-format
   in = cs2sc(in,NaN);
   row = size(in,1);
else
   in = sc2cs(in);
   in = cs2sc(in,NaN);
end
lmax = row-1;

%% Processing
if ordflag
    % Order-wise ordering
    % -------------------------------------------
    % split sine and cosine part
    Cnm = in(:,lmax+1:end);
    Snm = [zeros(lmax+1,1) fliplr(in(:,1:lmax))];
    % -------------------------------------------
    % rearrange to a vector ordered by the degree
    outC = Cnm;
    outC = outC(:);
    outC(isnan(outC)) = [];
    outS = Snm;
    outS = outS(:);
    outS(isnan(outS)) = [];
    % -------------------------------------------
    % perpare the degree and order vector
    nelem = sum(0:lmax+1);
    nm    = zeros(2,nelem);
    sidx  = 1;
    for m = 0:lmax
        eidx            = sidx + lmax-m;
        nm(1,sidx:eidx) = m:lmax;
        nm(2,sidx:eidx) = m;
        sidx            = eidx + 1;
    end
    
else
    % Degree-wise ordering
    % -------------------------------------------
    % split sine and cosine part
    Cnm = in(:,lmax+1:end);
    Snm = [zeros(lmax+1,1) fliplr(in(:,1:lmax))];
    % -------------------------------------------
    % rearrange to a vector ordered by the degree
    outC = Cnm';
    outC = outC(:);
    outC(isnan(outC)) = [];
    outS = Snm';
    outS = outS(:);
    outS(isnan(outS)) = [];
    % -------------------------------------------
    % perpare the degree and order vector
    nc   = sum(1:lmax+1);  % number of elements
    i = 1;
    nm = zeros(2,nc);
    for l = 1:lmax+1
        for m = 1:l
            nm(1,i) = l-1;
            nm(2,i) = m-1;
            i = i+1;
        end
    end
    
end
outC = outC';
outS = outS';