EDDYFIT2D is the jOceans module of jLab.

 EDDYFIT2D  Least squares fit of 2D velocity data to an eddy profile.
    least squares fit of 2D velocity measurements to a Guassian eddy.
    The fit involves four parameters, the eddy center location as well as
    the core radius R and peak velocity V.
    The velocity measurements U and V are 3D arrays taken at times NUM,
    latitudes LAT, and longitudes LON, each of which is a 1D array. U and V
    have LENGTH(LAT) rows, LENGTH(LON) columns, and LENGTH(NUM) pages along
    the third dimension.  NUM is in Matlab's DATENUM format.
    A fit is performed to all data points less than D kilometers distant
    from the point with coordinates LATO and LONO, as well as over sets of 
    time slices specified by INDEX.  
    INDEX can be one of the following:
         INDEX = empty, []  -- Fit to velocity averaged over all pages
         INDEX = array   -- Fit to velocity averaged over INDEX pages
         INDEX = cell of N arrays --  N fits, averaged over INDEX{1}, etc.
    The arrays Z0, ZA, and ZB provide the initial guesses, lower bounds,
    and upper bounds for three of the four parameters of the fit, with 
         Z0 = [L0 R0 V0],  ZA = [LA RA VA],   ZB = [LB RB VB].
    Here L is the distance of the eddy center to the origin (LATO,LONO) in 
    kilometers, R is the eddy core radius in kilometers, and V is the
    signed azimuthal velocity at the core radius R in cm/s.
    To have no upper bound or lower bound, use e.g. VB = inf or VB = -inf.
    Only three rather than four parameters are initialized becaues the fit
    is performed in cylindical coordinates, with no bounds being set on the
    value of the azimuth angle. 
    The output FIT is a structure with the following fields:
         FIT.NUM        Date in DATENUM format, as input 
         FIT.LONE       Estimated eddy center longitudes  
         FIT.R          Estimated eddy core radii in kilometers
         FIT.V          Estimated signed peak azimuthal velocity in cm/s
         FIT.ERR        Total root-mean-square velocity error 
         FIT.ERRP       Root-mean-square error from azimuthal velocities 
         FIT.ERRN       Root-mean-square error from normal velocities 
         FIT.FLAG       The exit flag from the optimization
         FIT.COUNT      Total number of good velocity points in the fit
         FIT.OUTPUT     Output fields from the optimization
         FIT.LAT        Latitudes of observations, as input
         FIT.LON        Longitudes of observations, as input 
         FIT.UM         3D array of observed averaged zonal velocities 
         FIT.VM         3D array of observed averaged meridional velocities 
         FIT.UE         3D array of zonal velocities implied by eddy 
         FIT.VE         3D array of meridional velocities implied by eddy 
    All fields except OUTPUT and those following are N x 1 arrays, where N 
    is the total number of fits. N = 1 unless INDEX is a cell array, in 
    which case N = LENGTH(INDEX).  
    COUNT keeps track of the totalnumber of good data points involved in 
    the fit. OUTPUT is an N x 1 cell array of structures containing
    information from the optimatization routine. 
    UM, VM, UE, and VE are of size LENGTH(LAT) x LENGTH(LON) x N, with UM 
    and VM containing the averaged velocites observed over each element of
    INDEX, and UE and VE containing the velocities implied by the eddy fit. 
    The errors are related by ERR.^2=ERRP.^2+ERRN.^2.  The error is related
    to the observed mean (MU,MV) and predicted velocities (UE,VE) by 
    ERR.^2 = MEAN((UM-UE).^2+(VM-VE).^2), where MEAN is over all finite 
    values of velocity in the time slices specified by INDEX. 
    EDDYFIT2D(...,'parallel') parallelizes the computation with a PARFOR
    loop over the elements of INDEX, provides this is a cell array.  This 
    option requires Matlab's Parallel Computing Toolbox be installed.
    Algorithm details
    EDDYFIT2D works by applying FMINSEARCHBND to solve the constrained
    optimization problem.  FMINSEARCHBND, by is an open-source modification 
    of Matlab's standard FMINSEARCH, and is distributed with JLAB. 
    In order to deal with the cyclic nature of the azimuth angle, two fits
    are performed, first with bounds -pi and pi and guess 0, and second
    with bounds 0 and 2pi and guess pi; then the better of these fits is
    chosen.  This avoids the possibility of edge effects impacting the fit. 
    Usage: fit=eddyfit2d(num,lat,lon,u,v,lato,lono,D,index,z0,za,zb);
    This is part of JLAB --- type 'help jlab' for more information
    (C) 2020 J.M. Lilly --- type 'help jlab_license' for details

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