ELLPARAMS is the jEllipse module of jLab.

 ELLPARAMS  Ellipse parameters of a modulated bivariate or trivariate oscillation.
 
    [KAPPA,LAMBDA,THETA,PHI]=ELLPARAMS(X,Y) where X and Y are analytic 
    signals, returns the parameters of the complex-valued signal 
    Z=REAL(X)+i REAL(Y), expressed as a modulated ellipse.
 
    Here KAPPA is the RMS ellipse amplitude, LAMBDA is the linearity, 
    THETA is the orientation, and PHI is the instantaneous orbital phase.
 
    ELLPARAMS(M), where M is matrix with two columns, also works.
 
    See Lilly and Gascard (2006) and Lilly and Olhede (2010a) for details.
 
    ELLPARAMS is inverted by ELLSIG, which returns the X and Y signals 
    given the ellipse parameters.
 
    ELLPARAMS(...,DIM) performs the analysis with time running along
    dimension DIM, as opposed to the default behavior of DIM=1.    
    _______________________________________________________________________
 
    Trivariate signals
 
    ELLPARAMS also works for trivariate signals, which can be expressed as
    a modulated ellipse in three dimensions.
 
    [KAPPA,LAMBDA,THETA,PHI,ALPHA,BETA]=ELLPARAMS(X,Y,Z), where X, Y, and Z
    are all analytic signals, also returns the zenith angle ALPHA and the 
    azimuth angle BETA in addition to the other ellipse parameters.
 
    ELLPARAMS(M), where M is matrix with three columns, also works.
 
    See Lilly (2010) for details on the trivariate case.
    _______________________________________________________________________
 
    Cell array input / output
 
    [KAPPA,LAMBDA,THETA,PHI]=ELLPARAMS(C) also works if C is a cell array
    containing, say K different X and Y signals, each as a 2-column matrix,
 
          C{1}(:,1)=X1, C{1}(:,2)=Y1
          C{2}(:,1)=X2, C{2}(:,2)=Y2, ...  
          C{K}(:,1)=XK, C{2}(:,2)=YK.  
 
    In this case, the output variables will also be length K cell arrays.
 
    The trivariate form described above also works, with each cell now
    being a matrix with three columns.
 
    This format works with the cell array output format of RIDGEWALK.
    __________________________________________________________________
 
    'ellparams --t' runs a test.
 
    See also ELLSIG, ELLBAND, ELLDIFF, ELLVEL, ELLRAD, KL2AB, AB2KL. 
 
    Usage: [kappa,lambda,theta,phi]=ellparams(x,y);
           [kappa,lambda,theta,phi]=ellparams(x,y,dim);
           [kappa,lambda,theta,phi,alpha,beta]=ellparams(x,y,z);
           [kappa,lambda,theta,phi,alpha,beta]=ellparams([x,y,z]);
           [kappa,lambda,theta,phi]=ellparams(C);
    __________________________________________________________________
    This is part of JLAB --- type 'help jlab' for more information
    (C) 2009--2016 J.M. Lilly --- type 'help jlab_license' for details

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