function [fvec,J] = helix(n,m,x,opt)% *******************************************% *******************************************% function [ fvec, J]= helix(n,m,x,opt)%% Helical valley function  [7]% Dimensions    n=3,   m=3% Function Definition:%       f1(x) = 10[x3 - 10*(x1,x2)]%       f2(x) = 10[((x1)^2 + (x2)^2)^.5 -1]%       f3(x) = x3% Standard starting point  x= (-1,0,0)% Minima of f=0 at (1,0,0)%% Revised 10/23/94   PLK% *********************************************  if ((opt==1) | (opt ==3))    if x(1) > 0	   fvec(1)  =  10*(x(3)-10*((1/(2*pi))*atan(x(2)/x(1))));                                            elseif x(1) < 0	   fvec(1)  =  10*(x(3)-10*((1/(2*pi))*atan(x(2)/x(1))+.5));                           end    fvec(2)  = 10*((x(1)^2+x(2)^2)^.5-1);    fvec(3)  = x(3);    fvec=fvec';                   end;if ((opt ==2) | (opt == 3))        J(1,1)   =    (50/pi)*(x(2)/x(1)^2)*(1/(1+(x(2)/x(1))^2));        J(1,2)   =    (-50/pi)*(1/x(1))*(1/(1+(x(2)/x(1))^2));        J(1,3)   =    10;        J(2,1)   =    (10*x(1))/sqrt(x(1)^2+x(2)^2);        J(2,2)   =    (10*x(2))/sqrt(x(1)^2+x(2)^2);        J(2,3)   =    0;        J(3,1)   =    0;        J(3,2)   =    0;        J(3,3)   =    1;end; if ((opt <1) | (opt >3))        disp('Error: Option value sent to HELIX.M is either <1 or >3');end;