tide_ell

 TIDE_ELL calculates tidal ellipse parameters from TIDE_FIT output.
 TIDE_ELL(ucoef,periods) computes the tidal ellipse parameters from the 
 TIDE_FIT output "ucoef" for the components specified in "periods",i.e.,

 [ucoef,unew]=tide_fit(jd,uv,periods,goplot)
          ell=tide_ell(ucoef,periods)

 where 
     ell(:,1) = constitutent period(s)in hr.
     ell(:,2) = umaj  = major axis.
     ell(:,3) = umin  = minor axis, where the sign indicates the
                        rotation of the ellipse.  A positive sign
                        of umin indicates counterclockwise rotation.
     ell(:,4) = inc   = counterclockwise inclination from 
                        positive x axis (degrees). The inclination
                        will always be in the upper half plane [0:pi].
     ell(:,5) = phase = phase relative to t=0 (degrees).

0001   function ell=tide_ell(ucoef,periods)
0002 % TIDE_ELL calculates tidal ellipse parameters from TIDE_FIT output.
0003 % TIDE_ELL(ucoef,periods) computes the tidal ellipse parameters from the
0004 % TIDE_FIT output "ucoef" for the components specified in "periods",i.e.,
0005 %
0006 % [ucoef,unew]=tide_fit(jd,uv,periods,goplot)
0007 %          ell=tide_ell(ucoef,periods)
0008 %
0009 % where
0010 %     ell(:,1) = constitutent period(s)in hr.
0011 %     ell(:,2) = umaj  = major axis.
0012 %     ell(:,3) = umin  = minor axis, where the sign indicates the
0013 %                        rotation of the ellipse.  A positive sign
0014 %                        of umin indicates counterclockwise rotation.
0015 %     ell(:,4) = inc   = counterclockwise inclination from
0016 %                        positive x axis (degrees). The inclination
0017 %                        will always be in the upper half plane [0:pi].
0018 %     ell(:,5) = phase = phase relative to t=0 (degrees).
0019 
0020 % Uses notation of M.G.G FOREMAN'S (1978) least squares harmonic
0021 % analysis. Adapted from R. Signell's TIDE_ELL.
0022 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0023 % 5/20/98:
0024 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0025 
0026 % convert input into format for tide_ell
0027 periods=periods(:);
0028 NC=length(periods);
0029 
0030 cx=zeros(NC,1);
0031 sx=cx;cy=cx;sy=cx;
0032 
0033 for nc=1:NC
0034    cx(nc)=ucoef(2*(nc-1)+2,1);
0035    sx(nc)=ucoef(2*(nc-1)+3,1);
0036    cy(nc)=ucoef(2*(nc-1)+2,2);
0037    sy(nc)=ucoef(2*(nc-1)+3,2);
0038 end
0039 
0040 % begin tide_ell
0041 [imax,jmax]=size(cx);
0042 if imax>jmax
0043         cx=cx'; sx=sx'; cy=cy'; sy=sy';
0044 end
0045 
0046 template=ones(size(cx))*NaN;
0047 umaj=template;umin=template;inc=template;phase=template;
0048 ell=zeros(length(cx),4);
0049 
0050 ind=find(~isnan(cx));
0051 cx=cx(ind);sx=sx(ind);cy=cy(ind);sy=sy(ind);
0052 
0053 p=(cx+sy)/2+i*(cy-sx)/2;
0054 m=(cx-sy)/2+i*(cy+sx)/2;
0055 
0056 ap=abs(p);
0057 epsp=angle(p);
0058 
0059 am=abs(m);
0060 epsm=angle(m);
0061 
0062 umaj(ind)=ap+am;
0063 umin(ind)=ap-am;
0064 
0065 ieps=find((epsp+epsm)<0); % choose inc to range from [0:pi]
0066 
0067 if length(ieps)>1
0068          epsp(ieps)=epsp(ieps)+2*pi*ones(size(ieps));
0069 else
0070          epsp(ieps)=epsp(ieps)+2*pi;
0071 end
0072 inc(ind)=.5*(epsp+epsm)*180/pi;
0073 phase(ind)=-.5*(epsp-epsm)*180/pi;
0074 ipha=find(phase<0);
0075 phase(ipha)=phase(ipha)+360;
0076 ell=[umaj(:) umin(:) inc(:) phase(:)];
0077 
0078 ell=[periods ell];