function hopf=p_tohopf(point)% function hopf_point=p_tohopf(point)% INPUT:%	point with stability information % OUTPUT:%	hopf_point uncorrected starting guess for hopf point% (c) DDE-BIFTOOL v. 1.01, 14/07/2000hopf.kind='hopf';hopf.parameter=point.parameter;if point.kind=='stst' | point.kind=='fold' | point.kind=='hopf'  if ~isfield(point,'stability')    error('P_TOHOPF: point does not contain stability information!');  end;  if isempty(point.stability)    error('P_TOHOPF: point does not contain stability information!');  end;  l1=point.stability.l1;  if isempty(l1)    error('P_TOHOPF: point does not contain enough stability information!');  end;  if point.kind=='hopf';    % remove known imaginary pair    [i1,i2]=min(abs(real(l1))+abs(abs(imag(l1))-abs(point.omega)));    l1(i2)=0;     [i1,i2]=min(abs(real(l1))+abs(abs(imag(l1))-abs(point.omega)));    l1(i2)=0;  end;  % look for non-real complex pair closest to imaginary axis  m=max(abs(real(l1)));  not_found=1;  while not_found>0    [i1,i2]=min(abs(real(l1)));    omega=abs(imag(l1(i2)));    if omega>0      not_found=0;    elseif abs(real(l1(i2)))>m+1      not_found=-1;    else      l1(i2)=-m-2;    end;  end;  x=point.x;  if not_found==-1    error('P_TOHOPF: no good pair of complex roots found.');  end;elseif point.kind=='psol'  x=sum(point.profile,2)/size(point.profile,2);  omega=2*pi/point.period;end;hopf.x=x;[D,dD]=root_cha(x,point.parameter,sqrt(-1)*omega);[E1,E2]=eig(D);[i1,i2]=min(abs(diag(E2)));hopf.v=E1(:,i2);hopf.omega=omega;return;