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
0 {* @8 |7 c* \  }3 X3 l0 p%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
9 K4 m$ R6 {) @; N3 c7 S/ n% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
' }/ F+ a2 _- B' |% dLadt = k(7)*C(Hmf);
$ K; z  m) ?3 w' c$ x$ q6 ^1 A. e9 G%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
. z% V; g( g6 t$ pclear all
# ~5 ]& h  A) m8 h9 r. zclc
format long
; K! C1 T* G/ q8 H* C8 N6 N+ b: h. i" b%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
* k+ E* Q: l1 ?: L0 {) g  Kinetics=[0    0.25    0           0    0       0
8 i" O+ g/ K8 T: n% i& n          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
          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
" m$ b% [! h) Q  m! n          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
8 k6 D5 j3 p, B2 Y          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
1 T% P) h$ X% W. d# H# c          360    0.01855    0.04125    0.09363    0.0239    0.06495];
# [' U7 c# b) B4 x7 {% Qk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
# r6 M4 j" Z) Y7 F6 Blb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
8 w% _6 j% R; T3 `. iub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
; W& O* w0 F( I$ T! m0 Eyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
  U; c1 o9 \, n; W% 使用函数 ()进行参数估计
0 G8 N& o/ S0 v$ }[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
, K  E0 W, N5 q5 C2 G8 }6 Rfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
* e  |% ~  {6 E& r* W0 ifprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
8 Q& L2 T: J5 Sfprintf('\tk4 = %.11f\n',k(4))
$ a) k. |) {. E  sfprintf('\tk5 = %.11f\n',k(5))
- Y9 [( M% p( b! R6 M3 wfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
0 C4 B+ n: N8 `! V0 j/ nfprintf('  The sum of the squares is: %.1e\n\n',fval)
& K: V& {% q! d2 _) ~k_fm= k;
9 f  Z  v  a, ~' Y' J" r% warning off
2 Y& A- k$ ^8 j' w% k% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
+ |+ e" s3 o) X4 j+ K5 s6 t1 U# ]ci = nlparci(k,residual,jacobian);
$ l' x+ K0 T0 e+ K# vfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
- I" L, F7 j5 q" Qfprintf('\tk1 = %.11f\n',k(1))
/ y* E; \2 }% r3 F: yfprintf('\tk2 = %.11f\n',k(2))
0 \( _$ L6 H) V! m) D/ P8 |fprintf('\tk3 = %.11f\n',k(3))
  ^2 m! l. V- [% A/ W$ xfprintf('\tk4 = %.11f\n',k(4))
1 ^- [) \7 P- @) o9 \fprintf('\tk5 = %.11f\n',k(5))
9 K. x1 t7 H& Y$ U4 m& cfprintf('\tk6 = %.11f\n',k(6))
7 V8 ^! |, r2 k' N8 r1 P2 O; F' r% xfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
) ?; N- f( b  l8 A2 ]fprintf('\tk9 = %.11f\n',k(9))
; p3 d1 _, q+ }7 I* nfprintf('\tk10 = %.11f\n',k(10))
; ?7 p7 {3 v  d2 c! j: Jfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
9 k; I0 l! \. R% B5 aoutput
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,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
/ _0 a! t0 ]; _4 x! Mci = nlparci(k,residual,jacobian);
* p- D2 _9 S0 w# D- @/ Jfprintf('\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')
4 H0 s2 I/ V# wfprintf('\tk1 = %.11f\n',k(1))
8 U7 {2 n1 P* t7 P$ efprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
' Z7 K: A- L* m; E& ~& x# A+ ]fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
9 \, t0 h0 Y8 |fprintf('\tk6 = %.11f\n',k(6))
2 P0 G0 m6 X8 P! o8 Dfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
1 v  @2 m" _) ~! _) W0 n4 ffprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
! M+ t# S* M! R5 @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')
figure;plot(t,x(:,2:5));
; L; q9 L2 P2 A- [p=x(:,1:5)
) G9 z5 ]! `' l4 [6 S4 _, Yhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
) q9 M# O7 {: q

4 F: [$ L9 ]! [: ]9 t2 A; I4 X
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);   
6 \9 u: n5 k' `$ jy(:,2) = x(:,1);
, r3 j7 [& _. a8 G; vy(:,3:6) = x(:,2:5);
& u0 d6 i* O! h1 m# m+ J$ yf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
  N9 u* A* a% O8 O8 X, k6 Yf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
) k0 @6 K) `4 K$ U, e

0 {' \; U0 _& D* l& U: d8 m% M% K
4 e* ?6 }$ K+ Efunction f = ObjFunc7Fmincon(k,x0,yexp)
5 ^& Z  T$ y; g7 ktspan = [0 15 30 45 60 90 120 180 240 300 360];
# U! i9 C, @* l& O" R4 Q[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
- j7 ~! `- ?* D% N1 g' [3 qy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
" R0 b4 H' S( D$ ~( p+ ef =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
% L9 A0 G; f" }    + sum((y(:,6)-yexp(:,6)).^2) ;


: [1 G" V- H% q9 s7 R
! G! w& w$ h0 N
function dxdt = KineticEqs(t,x,k)
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);
4 I4 D1 H: [1 F3 cdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
! L& j3 p' J2 P! ]8 w7 j5 q6 sdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];