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.   
 
    ELLPARAMS also works if X and Y are cell arrays with each cell holding
    a different analytic signal. The output will then also be cell arrays. 
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    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.
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    '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);
    __________________________________________________________________
    This is part of JLAB --- type 'help jlab' for more information
    (C) 2009--2018 J.M. Lilly --- type 'help jlab_license' for details

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