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
%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
* D  E: B% n: U5 ?! k% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
) }$ ]. g4 U( \  i& L* |%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
1 y9 j! l, I/ b" qclear all
5 \; n$ q: u) Z1 d- ^; `clc
: v" M2 t6 W& qformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  n  a8 T6 |* p4 y  Kinetics=[0    0.25    0           0    0       0
2 R* _% ~" u! v, J# N& e. O          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
( ?$ `( e( F7 Q8 `! F, U3 X          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
) z$ j& N1 b- j$ w          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
( Q( a* s- M7 s, o6 q          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
1 Y7 y+ }4 j# W6 l          360    0.01855    0.04125    0.09363    0.0239    0.06495];
( @7 v9 C$ v3 L8 Mk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
9 T2 F+ ~8 M% s  Dlb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
% 使用函数 ()进行参数估计
; V+ x1 M% i1 b. `4 }% r[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
* V" b2 ~7 r  \- w+ Ofprintf('\n使用函数fmincon()估计得到的参数值为:\n')
) n' m  R7 y5 W4 L2 y% ]0 Y( M, mfprintf('\tk1 = %.11f\n',k(1))
' x& S5 ~' M% @- D, G! ufprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
; f* u( N' z( G/ U9 zfprintf('\tk5 = %.11f\n',k(5))
6 H8 v+ h+ Y$ @) d, l4 lfprintf('\tk6 = %.11f\n',k(6))
( D0 W5 {+ [6 M2 kfprintf('\tk7 = %.11f\n',k(7))
1 A; I' y( Q" @' |6 r; W- G8 }fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
. b* Q3 \% b. U0 X! G9 }4 Bfprintf('\tk10 = %.11f\n',k(10))
8 d& u! |6 t( d) r) q9 bfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
2 I. s% x0 y' b" p( b5 O7 l# R# @% warning off
% 使用函数lsqnonlin()进行参数估计
) ?: o' Y( I+ j" Z8 j/ e[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
$ z" Z9 j  n7 A3 B/ K; tci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
1 a' L# Q% U& a' G+ X: S5 {. _0 Zfprintf('\tk2 = %.11f\n',k(2))
: t( n2 e0 C9 {; G: w! Ofprintf('\tk3 = %.11f\n',k(3))
. v, s/ e, ?5 d( d. H9 C( ~7 e- nfprintf('\tk4 = %.11f\n',k(4))
) t; _+ `! Q3 x& Q1 P3 Rfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
' K5 H0 h; D. x* w2 x; [  ~/ Xfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
% O. |, }8 W; M% X0 t5 X  s+ qfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
, r+ W) O$ _4 N8 G4 n- R- \, `. a  Noutput
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
6 Z$ h& i3 D4 l8 @4 hk0 = k_fm;
, k' L/ ?7 K0 ~; ]5 u) y, O$ L8 t% U[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\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')
2 I4 R" L: a3 S. `fprintf('\tk1 = %.11f\n',k(1))
! E& R! f: Q/ yfprintf('\tk2 = %.11f\n',k(2))
1 v0 U# h! `* Sfprintf('\tk3 = %.11f\n',k(3))
* j( Y1 g8 j: y9 L2 C1 A8 u) jfprintf('\tk4 = %.11f\n',k(4))
/ S2 f# h  [/ t0 _$ Ffprintf('\tk5 = %.11f\n',k(5))
; ]/ Q2 k2 H6 f9 _fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
3 D3 z, j& \4 J" N2 P- zfprintf('\tk8 = %.11f\n',k(8))
- o% |9 X; X; d9 k5 _# O0 dfprintf('\tk9 = %.11f\n',k(9))
9 Y0 Y" y+ }; T# {$ [fprintf('\tk10 = %.11f\n',k(10))
. C3 |% |$ M3 T3 p/ k, Yfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
3 C* {# K7 J4 e0 c. B; ^2 Fk_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
( Q8 C7 q5 C- Xfigure;plot(t,x(:,2:5));
% O0 v5 V5 x1 l3 T# ^0 x' A& np=x(:,1:5)
hold on
# C7 V5 f# F7 S# D& |; W7 B5 Wplot(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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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);   
) {' H  P2 E, A# o$ zy(:,2) = x(:,1);
3 k' K! A9 T: d/ C$ v0 py(:,3:6) = x(:,2:5);
8 u, @+ T" s/ `( Of1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
1 _' y" ~7 ~9 h4 if3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
( D8 ]5 M1 g( s9 X9 yf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
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5 `, Y5 d- ?# I5 M0 D  ~% `
) f- {5 ]& e- @' d2 F
! u; L& X- C" r4 a- r8 lfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
6 o+ e# I9 ]. b' ky(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
" `( l/ A. Y1 N! z2 n    + sum((y(:,6)-yexp(:,6)).^2) ;




! i0 W- j1 h4 F! e/ P0 Rfunction dxdt = KineticEqs(t,x,k)
7 w2 U- _6 }. g# w  ^% @dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
dFrdt = 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);
1 {$ F* u& v9 r; L" idLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
/ o$ _1 N  |2 U# U6 j! kdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


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