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function odes_fit
format long
clear all
clc
k0=[0 0 0 0 0 0 0 0];%²ÎÊý³õÖµ
lb=[0 0 0 0 0 0 0 0];ub=[+inf +inf +inf +inf +inf +inf +inf +inf];%lb¡¢ub:²ÎÊýÏÂÏÞºÍÉÏÏÞ
x0=[0 0 0 0 0];
data=...
[0.5 1 1.5 2 3 4 5 6
18.7 6.5 2.7 2.1 1.7 1.5 1.2 0.2;
48.9 31.3 15.3 6.9 2.2 1.8 1.7 0.5;
19.3 34.7 41.2 40.9 37.2 31.7 26.1 19.4;
9.7 19.6 28.7 34.5 38.4 38.2 36.3 33.4;
0.2 2.6 5.7 9.3 17.1 24.8 30.5 36.7;
];
x0=data(1,2:end);
tspan = [data(:,1)'];
yexp = [data(2:end,2) data(2:end,3) data(2:end,4) data(2:end,5) data(2:end,6) data(2:end,7) data(2:end,8)];
%ʹÓú¯Êýfmincon()½øÐвÎÊý¹À¼Æ
[k,fval,flag]=fmincon(@ObjFunc4Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\tk1 = %.9f \n',k(1))
fprintf('\tk2 = %.9f \n',k(2))
fprintf('\tk3 = %.9f \n',k(3))
fprintf('\tk4 = %.9f \n',k(4))
fprintf('\tk5 = %.9f \n',k(5))
fprintf('\tk6 = %.9f \n',k(6))
fprintf('The sum of the squares is:%.le\n\n',fval)
k_fmincon=k;
%ʹÓú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ
[k,resnorm,residual,exitflag,output,lambda,jacobian]=...
lsqnonlin(@ObjFunc4LNL,k0,lb,ub,[],x0,yexp);
ci=nlparci(k,residual,jacobian);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýÖµ:\n'),output
%ÒÔº¯Êýfmincon()¹À¼ÆµÃµ½µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ
k0=k_fmincon;
[k,resnorm,residual,exitflag,output,lambda,jacobian]=lsqnonlin(@ObjFunc4LNL,k0,lb,ub,[],x0,yexp);
ci=nlparci(k,residual,jacobian);
fprintf('\n\nÒÔfmincon()µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýÖµ:\n')
output
figure(1)
ts=0(max(tspan)-min(tspan))/100):max(tspan);
[ts, ys] = ode45(@KineticsEqs,ts,x0,[],k);
yy = [data(:,2) data(:,3) data(:,4) data(:,5) data(:,6)];
figure(1)
plot(ts,ys(:,1),'b',tspan,yy(:,1),'bo');
figure(2)
plot(ts,ys(:,2),'r',tspan,yy(:,2),'ro');
figure(3)
plot(ts,ys(:,3),'k',tspan,yy(:,3),'ko');
figure(4)
plot(ts,ys(:,4),'g',tspan,yy(:,4),'ko');
figure(5)
plot(ts,ys(:,4),'g',tspan,yy(:,4),'ko');
figure(6)
plot(ts,ys(:,6),'m',tspan,yy(:,6),'mo');
%legend('C1µÄ¼ÆËãÖµ','C1µÄʵÑéÖµ','C2µÄ¼ÆËãÖµ','C2µÄʵÑéÖµ','C3µÄ¼ÆËãÖµ','C3µÄʵÑéÖµ','C4µÄ¼ÆËãÖµ','C4µÄʵÑéÖµ','C5µÄ¼ÆËãÖµ','C5µÄʵÑéÖµ','C6µÄ¼ÆËãÖµ','Location','best');
function f = ObjFunc(k,tspan,x0,yexp) % Ä¿±êº¯Êý
[t, Xsim] = ode45(@KineticsEqs,tspan,x0,[],k);
Xsim1=Xsim(:,1);
Xsim2=Xsim(:,2);
Xsim3=Xsim(:,3);
Xsim4=Xsim(:,4);
Xsim5=Xsim(:,5);
Xsim6=Xsim(:,6);
ysim(:,1) = Xsim1(2:end);
ysim(:,2) = Xsim2(2:end);
ysim(:,3) = Xsim3(2:end);
ysim(:,4) = Xsim4(2:end);
ysim(:,5) = Xsim5(2:end);
ysim(:,6) = Xsim6(2:end);
f = [(ysim(:,1)-yexp(:,1)) (ysim(:,2)-yexp(:,2)) (ysim(:,3)-yexp(:,3)) (ysim(:,5)-yexp(:,5)) ...
(ysim(:,6)-yexp(:,6))];
function dCdt = KineticsEqs(t,C,k) % ODEÄ£ÐÍ·½³Ì
C1=C(1);C2=C(2);C3=C(3);C4=C(4);C5=C(5);C6=C(6);
k1=k(1);k2=k(2);k3=k(3);k4=k(4);k5=k(5);k6=k(6);k7=k(7);
dC1dt = -k1*C1-k7*C1;
dC2dt = k1*C1-k2*C2-k5*C2;
dC3dt = k2*C2-k3*C3-k6*C3;
dC4dt = k3*C3-k4*C5;
dC5dt = k4*C5;
dC6dt = k5*C2+k6*C3+k7*C1;
dCdt = [dC1dt;dC2dt;dC3dt;dC4dt;dC5dt;dC6dt]; @beefly |