function res = fwa3sym(x,pat,tp)% fwa3sym - 3D forward wave atom transform (symmetric version)% -----------------% INPUT% --% x is a real N-by-N-by-N array. N is a power of 2.% --% pat specifies the type of frequency partition which satsifies% parabolic scaling relationship. pat can either be 'p' or 'q'.% --% tp is the type of tranform.% 	'ortho': orthobasis% 	'directional': real-valued frame with single oscillation direction% 	'complex': complex-valued frame% -----------------% OUTPUT% --% res is an array containing all the wave atom coefficients. If% tp=='ortho', then res is of size N-by-N-by-N. If tp==' If% tp=='directional', then res is of size N-by-N-by-N-by-4. If% tp=='complex', then res is of size N-by-N-by-N-by-8.% -----------------% Written by Lexing Ying and Laurent Demanet, 2007    if( ismember(tp, {'ortho','directional','complex'})==0 | ismember(pat, {'p','q','u'})==0 )    error('wrong');  end    call = fwa3(x,pat,tp);  N = size(x,1);  res = zeros(N,N,N,size(call,2));    for i=1:size(call,2)    c = call(:,i);    y = zeros(N,N,N);    for s=1:length(c)      D = 2^s;      nw = length(c{s});      for I=0:nw-1        for J=0:nw-1          for K=0:nw-1            if(~isempty(c{s}{I+1,J+1,K+1}))              y( I*D+[1:D], J*D+[1:D], K*D+[1:D] ) = c{s}{I+1,J+1,K+1};            end          end        end      end    end    res(:,:,:,i) = y;  end