function [z, a, b, alpha, phi, step] = ...         pare (X, z, a, b, alpha, meth, show);%PARE   Geometric ellipse fit loop%% [z, a, b, alpha, phi, step] = ...%      pare (X, z, a, b, alpha, meth, show{0});% computes the best fit ellipse in parameterform% x = z(1) + a  cos(phi-alpha), y = z(2) + b sin(phi-alpha)%% X: given points <X(i,1), X(i,2)>% z, a, b, alpha: starting values for ellipse% meth:%   0 --> gauss-newton with marquardt for a near b%   1 --> newton with marquardt for a near b%   2 --> marquardt%   3 --> gauss-newton% show: if (show == 1), test output%% z, a, b, alpha: ellipse found% phi: values for the nearest points (in parametric form)% step: nof iterations    if (nargin < 7), show = 0; end;  if (nargin < 6), meth = 1; end;  epsr  = 1e-5;  m = size (X, 1);  x = zeros (m+5, 1);  x = pare_set (x, phi, alpha, a, b, z);  x = pare_initphi (X, x);  step   = 0;  normr  = 1;  norma  = 1;  lambda = [1;1;1];  while (normr > epsr*norma),    if     (meth == 0), [x, lambda] = pare_gauss_step (X, x, lambda);    elseif (meth == 1), [x, lambda] = pare_newton_step (X, x, lambda);    elseif (meth == 2), [x, lambda] = pare_marq_step (X, x, lambda);    elseif (meth == 3), [x, lambda] = pare_gauss_step (X, x, [0;0;0]);    else                error ('unknown meth');    end    if (step > 0),      normr = norm (x - prevx);      norma = norm (x);    end    prevx = x;    step  = step+1;    if (show == 1),      [phi, alpha, a, b, z] = pare_get (x);      drawellipse(z, a, b, alpha)    end        if (step > 100),      disp ('warning: number of steps exceeded limit');      break;    end  end % while  [phi, alpha, a, b, z] = pare_get (x);end % pare