function AA
k0=[0.1 2 2];
x0=[0.01 54.026 0.2435];
t1=0:6:48;
tspan=0:6:48;
yexp=load('sample_file.txt')';
lb=[-10 -10 -10];ub=[10 10 10];
[k,resnorm,resid,exitflag,output,lambda,jacobian]=lsqnonlin(@ObjFunc4LNL8,k0,[0 0 0],[],[],x0,yexp);
ci=nlparci(k,resid,jacobian);
y1=[yexp(:,1)]';
y2=[yexp(:,2)]';
y3=[yexp(:,3)]';
[t4plot x4plot]=ode45(@kineticseqs8,[tspan(1) tspan(end)],x0,[],k);
plot(t1,y1,'bo',t1,y2,'g+',t1,y3,'r*',t4plot,x4plot,'k-'),
legend('Exp-biomass','Exp-glucose','Exp-butanol','Model'),
xlabel('time(h)'),ylabel('biomass dry weight(g/l),glucose(g/l),butanol(g/l)')
fprintf('Estimated Parameter\n'),
fprintf('\tk=%.4f %.4f\n',k(1),ci(1,2)-k(1))
fprintf('\tk=%.4f %.4f\n',k(2),ci(2,2)-k(2))
fprintf('\tk=%.4f %.4f\n',k(3),ci(3,2)-k(3))
[t,x]=ode45(@kineticseqs8,tspan,x0,[],k);
figure,plot(x,resid,'*')
xlabel('biomass dry wight(g/l)¡¢glucose(g/l)¡¢butanol(u/ml)'),
ylabel('Residuals(g/l,u/ml)')

function dxdt=kineticseqs8(t,x,k)
% dxdt=[k(1)*(1-x(2)./12)*x(1)
%    -k(2)*x(1).^2
%     k(3)*k(1)*(1-x(2)./12)*x(1)];
dxdt=[k(1)*x(1)*(1-x(1)/3)
   -k(2)*x(1)*x(2)
    k(3)*x(2)*x(1)];

function f=ObjFunc4LNL8(k,x0,yexp)
x0=[0.01 54.026 0.2435];
tspan=[0:6:48]';
[t1 x]=ode45(@kineticseqs8,tspan,x0,[],k);
y(:,1)=x(:,1);y(:,2)=x(:,2);y(:,3)=x(:,3);
f1=y(:,1)-yexp(:,1);f2=y(:,2)-yexp(:,2);f3=y(:,3)-yexp(:,3);
f=[f1 f2 f3];