function res = mefwa2sym(x,pat,tp)% mefwa2sym - 2D forward mirror-extended wave atom transform (symmetric% version)% -----------------% INPUT% --% x is a real N-by-N matrix. 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': frame based on the orthobasis construction of % 		the standard wave atom% 	'directional': real-valued frame with single oscillation direction% 	'complex': complex-valued frame% -----------------% OUTPUT% --% res is an array which contains the wave atom coefficients. If% tp=='ortho', then res is a real array of size 2N-by-2N. If% tp=='directional', then res is a real array of size 2N-by-N-by-2. If% tp=='complex', then res is a complex array of size 2N-by-2N.% -----------------% Written by Lexing Ying and Laurent Demanet, 2007    if( ismember(tp, {'ortho','directional','complex'})==0 | ismember(pat, {'p','q','u'})==0 )    error('wrong');  end    if(    strcmp(tp, 'ortho')==1)    %----------------------------    call = mefwa2(x,pat,tp);    N = size(x,1)*2;    res = zeros(N,N,size(call,2));        for i=1:size(call,2)      c = call(:,i);      y = zeros(N,N);      for s=1:length(c)        D = 2^s;        nw = length(c{s});        for I=0:nw-1          for J=0:nw-1            if(~isempty(c{s}{I+1,J+1}))              y( I*D+[1:D], J*D+[1:D] ) = c{s}{I+1,J+1};            end          end        end      end      res(:,:,i) = y;    end  elseif(strcmp(tp,'complex')==1)    %----------------------------    call = mefwa2(x,pat,tp);    N = size(x,1)*2;    res = zeros(N,N,size(call,2));        for i=1:size(call,2)      c = call(:,i);      y = zeros(N,N);      for s=1:length(c)        D = 2^s;        nw = length(c{s});        for I=0:nw-1          for J=0:nw-1            if(~isempty(c{s}{I+1,J+1}))              y( I*D+[1:D], J*D+[1:D] ) = c{s}{I+1,J+1};            end          end        end      end      res(:,:,i) = y;    end      elseif(strcmp(tp,'directional')==1)    %----------------------------    call = mefwa2(x,pat,tp);    N = size(x,1)*2;    res = zeros(N,N/2,size(call,2));        for i=1:size(call,2)      c = call(:,i);      y = zeros(N,N/2);      for s=1:length(c)        D = 2^s;        nw = length(c{s});        for I=0:nw-1          for J=0:nw-1            if(~isempty(c{s}{I+1,J+1}))              y( I*D+[1:D], J*D/2+[1:D/2] ) = c{s}{I+1,J+1};            end          end        end      end      res(:,:,i) = y;    end  else    error('wrong');  end