function [z, a, b, alpha, step] = ...        alge_odr (X, z, a, b, alpha, show);%ALGE_ODR       %       %       [z, a, b, alpha, step] = ...%       alge_odr (X, z, a, b, alpha, show);%       %       computes the best fit ellipse in parameterform%       x = z(1) + a  cos(phi-alpha), y = z(2) + b sin(phi-alpha)%       using the odr algorithm.  %%       X: given points <X(i,1), X(i,2)>%       z, a, b, alpha: starting values%       show: if (show), test output%%       z, a, b, alpha: ellipse found%       step: nof iterations%%       See also ODR, ALGE_ODR_HOOK%       This implicit problem is solved by successive%       solution of weighted explicit problems.%       For further discussion see%       Gill/Murray/Wright%       "Practical Optimization"%       Academic Press, New York, 1981.  OPTI_ONEW = 9;  OPTI_ONED = 10;  wate = sqrt(eps);  awate = sqrt(sqrt(wate))+1e-3;  c = cos(alpha); s = sin(alpha);  Q = [c -s; s c];  A = Q*[1/(a^2) 0; 0 1/(b^2)]*Q';  beta = [z(1); z(2); A(1,1); A(1,2); A(2,2)];  delta = zeros(size(X));  step = 0;  while (awate >= wate),    OPTIONS = [[OPTI_ONED, awate]];    [beta, delta, err, astep] = odr ('alge_odr_hook', ...      X, zeros(size(X,1),1), beta, OPTIONS, [], [], delta);    awate = awate^2;    step = step + astep;  end  [zno, a, b, alpha, err] = ellipse_params (...    [beta(3); 2*beta(4); beta(5); 0; 0; -1]);  z = [beta(1); beta(2)];end % alge_odr