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function fit_nonl12
clear all;clc
format long
data=[ 2561.0000 10.0000
    2560.0000 15.0000
    2560.0000 25.0000
    2558.0000 40.0000
    2557.0000 60.0000
    2556.0000 100.0000
    2555.0000 160.0000
    2554.0000 250.0000
    2552.0000 400.0000
    2551.0000 630.0000
    2550.0000 1000.0000
    ];
xspan=data(:,2);
Texp=data(:,1);

k0=[2.0 30.0 6.0 0.5];
lb=[0.1 0.1 0.1 0.0];
ub=[10.0 100.0 20.0 1.0];
%

OPTIONS=optimset('MaxFunEvals',1000);
[k,resnorm,residual,exitflag,output,lambda,jacobian]=...
    lsqnonlin(@ObjFunc,k0,lb,ub,OPTIONS,xspan,Texp);
  
ci=nlparci(k,residual,jacobian);
%residual;
fprintf('\n\nÄâºÏ½á¹û;\n')
fprintf('\n\t²ÎÊý E1 = %.16f',k(1))
fprintf('\n\t²ÎÊý E2 = %.16f',k(2))
fprintf('\n\t²ÎÊý E3 = %.16f',k(3))
fprintf('\n\t²ÎÊý E4 = %.16f',k(4))

y=kineticsEqs(xspan,k);
R2=1-sum((Texp-y).^2)./sum((Texp-mean(y)).^2);
fprintf('\n\tR^2 = %.16f',R2);
figure
plot(xspan,kineticsEqs(xspan,k),'b',xspan,Texp,'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','Best')
%
function f =ObjFunc(k,xspan,Texp)
f=kineticsEqs(xspan,k)-Texp;

function x1 =kineticsEqs(x,k)
E1=k(1);E2=k(2);E3=k(3);E4=k(4);
x1=E1+(((2.*pi.*E3).^(-E4)+x.^(E4).*cos(pi.*E4./2)).*E2.*(2.*pi.*E3).^(-E4))./(((2.*pi.*E3).^(-E4)+x.^(E4).*cos(pi.*E4./2)).^2+(x.*(E4).*sin(pi.*E4./2)).^2);
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