AB2KL is the jEllipse module of jLab.

 AB2KL  Converts A and B to ellipse parameters Kappa and Lambda.
 
    [K,L]=AB2KL(A,B)  Convert ellipse semi-major and semi-minor
    axes A and B to ellipse amplitude K and ellipse parameter L.
 
    K and L are related to A and B by
 
           K   = SQRT( (A^2 +B^2) / 2 )
           L   = SIGN(B) * (A^2 - B^2 ) / (A^2 + B^2)
 
    as discussed in Lilly and Gascard (2006).  
  
    A and B are either arrays of the same size, or one may be an array
    and one may be a scalar.
 
    Usage: [kappa,lambda]=ab2kl(a,b)
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    This is part of JLAB --- type 'help jlab' for more information
    (C) 2007--2019 J.M. Lilly --- type 'help jlab_license' for details