function [fvec,J] = sing(n,m,x,opt)% ***************************************% Function [fvec,J]= sing(n,m,x,opt)% Powell singular function  [13]% Dimensions:    n=4    m=4% Function definitions:%       f1(x)=x1 + 10x2      %       f2(x)= 5^.5*(x3 - x4)%       f3(x)= (x2-2x3)^2%       f4(x)= 10^.5*(x1-x4)^2% Starting point: (3,-1,0,1)% Minima of f=0 at the origin%% Coded in Matlab  October 31   PLK% **************************************8if((opt ==1 )|(opt ==3))        fvec =  [  x(1)+10*x(2)          	   sqrt(5)*(x(3)-x(4))          	   (x(2)-2*x(3))^2                   sqrt(10)*((x(1)-x(4))^2)  ] ;end;if((opt==2)|(opt==3))J    =  [  1                           10       0                            0           0                            0       sqrt(5)               -sqrt(5)           0              2*(x(2)-2*x(3))      -4*(x(2)-2*x(3))              0            2*sqrt(10)*(x(1)-x(4))       0       0      -2*sqrt(10)*(x(1)-x(4))];end;if((opt<1)|(opt>3))        disp('Error: Option value for SING.M is either <1 or >3');end;