帮忙做下统计显著性检验和K值的误差以及灵敏度分析

箫剑→残念

function parafit
: `  u  f8 Y5 {8 r4 a: h0 I%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
4 b0 [& ^0 k3 T/ |4 |, J% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
+ k# q6 q: k1 k; z* l% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
  i% \% l2 a4 D: f# @, K' oformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
/ o( X) j1 c. R5 `          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
$ p6 j+ o3 J) R+ y% _/ m; ^          90    0.08115    0.07877    0.07485    0    0.01405
0 U, @7 V9 H, N; V( ^. S          120    0.0656    0.07397    0.07885    0.00573    0.02143
0 A8 Z' X7 ]5 t5 _2 {          180    0.04488    0.0682    0.07135    0.0091    0.03623
4 f" O+ |) _9 g' O2 t5 ]6 b- J2 ^  S          240    0.03653    0.06488    0.08945    0.01828    0.05452
1 @: ]3 j4 Y3 a          300    0.02738    0.05448    0.09098    0.0227    0.0597
$ c! Q) C# ]- m! r: }          360    0.01855    0.04125    0.09363    0.0239    0.06495];
k0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
lb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
4 e3 o) [' H+ u0 yub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
4 h. t( ]6 i3 Q; t4 B7 b6 Rx0 = [0.25  0  0  0  0];
7 @% y- f  G5 p+ ^yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
- R8 [5 Q7 A* W% warning off
% 使用函数 ()进行参数估计
+ t/ ~8 ~' n+ w: t4 Q7 s[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
fprintf('\n使用函数fmincon()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
( n- Z9 h+ v5 t/ }fprintf('\tk3 = %.11f\n',k(3))
* h% x9 v$ ?& W+ s$ Jfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
! x% B% b3 {+ c  u9 w: N! ifprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
; I# G% A9 ?( b/ n! r# k" D- Ffprintf('\tk8 = %.11f\n',k(8))
- D( ?+ I2 t, Vfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
5 O- K: a3 K( F) K[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
# Q: n* T0 `) [& t  k    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
$ e: c* h& _2 T' r/ wfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
3 n' Y+ U7 O' Lfprintf('\tk4 = %.11f\n',k(4))
* U' K. ^8 B2 V: O5 p! K/ I& Tfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
$ w5 j! s: t# L1 r' s- i, {7 Zfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
9 V3 s* j" a4 P4 cfprintf('\tk9 = %.11f\n',k(9))
* k9 ?- [8 I# k" M: l+ ?: `* afprintf('\tk10 = %.11f\n',k(10))
5 B) Y- `* z! u1 `$ mfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
2 T' H# }6 Q5 ]  e6 S" P" `k_ls = k;
output
warning off
% 以函数fmincon()估计得到的结果为初值，使用函数lsqnonlin()进行参数估计
k0 = k_fm;
' K: o& k6 K( L: u5 ~) C2 A[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
5 [" @% B+ K5 [' L) ~) H    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
4 }% ~: r& D( b  f: tci = nlparci(k,residual,jacobian);
0 h% K. g& J) [' n8 b: V8 A7 N+ Ifprintf('\n\n以fmincon()的结果为初值，使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
* c$ K5 f+ ]. x4 D: ]7 S: Yfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
) f" b0 R6 F6 Y- Yfprintf('\tk10 = %.11f\n',k(10))
' M4 z! _, a- V: X5 p  tfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
( g" w, Y9 n' Ofigure;
6 W& t) I( o  F- }& Oplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
" b1 O* A5 S$ [7 n+ w/ `2 mfigure;plot(t,x(:,2:5));
p=x(:,1:5)
/ D5 {( B. I, p) z; m0 g" Nhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')

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0 }/ B- g: a+ p) g8 ]6 d4 U
function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
4 @2 x9 J$ J$ @6 u; f9 t. By(:,2) = x(:,1);
6 |& u' `8 G& c: T" f; E/ Gy(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
# @: j& f9 [* [2 e. rf4 = y(:,5) - yexp(:,5);
1 D+ \% D/ l& N6 _3 K) Kf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];


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5 C7 I0 x8 H9 f  x* [- ~) cfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
3 v# c: q& n$ [' y1 f[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
# g# k. Z3 m2 Ly(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
  v9 g8 C4 ~! w1 wf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
) F1 ~- c! h4 V1 t9 O    + sum((y(:,6)-yexp(:,6)).^2) ;

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) e. |  C7 s+ F  @! g1 Ofunction dxdt = KineticEqs(t,x,k)
" p  r. l# C, a, u1 K& VdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
: b* Q2 C# n) l' Y0 S& B) UdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
% t5 g7 l5 U3 T6 Z; GdLadt = k(7)*x(5);
  z. \3 H& Y4 a: l# }0 [dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
( r  h. ?/ E0 S* K% X6 c7 O6 qdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];