function x = iwa2sym(res,pat,tp)% iwa3sym - 3D inverse wave atom transform (symmetric version)% -----------------% INPUT% --% 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.% --% 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% --% x is a real N-by-N-by-N array. N is a power of 2.% -----------------% Written by Lexing Ying and Laurent Demanet, 2007    if( ismember(tp, {'ortho','directional','complex'})==0 | ismember(pat, {'p','q','u'})==0 )    error('wrong');  end    N = size(res,1);  H = N/2;  lst = freq_pat(H,pat);  red = size(res,4);    call = cell(length(lst),red);  for i=1:red    y = res(:,:,:,i);    c = cell(length(lst),1);    for s=1:length(lst)      B = 2^(s-1);    D = 2*B;      nw = length(lst{s});      c{s} = cell(nw,nw,nw);      for I=0:nw-1        for J=0:nw-1          for K=0:nw-1            if(lst{s}(I+1)==0 & lst{s}(J+1)==0 & lst{s}(K+1)==0)              c{s}{I+1,J+1,K+1} = [];            else              c{s}{I+1,J+1,K+1} = y( I*D+[1:D], J*D+[1:D], K*D+[1:D] );            end          end        end      end    end    call(:,i) = c;  end  x = iwa3(call,pat,tp);