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 }1 [& n% F+ r2 o5 j3 @9 S' N/ l%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
# \7 E/ z& \+ \! F. y+ I: H! `% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
/ _5 G. g1 g3 X. J6 Q, P% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
! @7 a+ S. M. E3 R( U% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
2 P  G4 I# M! V7 z, B# Yformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
1 K! _- y+ v  \, ?' W' [  Kinetics=[0    0.25    0           0    0       0
- Z; Y0 \4 Y6 B          15    0.2319    0.01257    0.0048    0    2.50E-04
8 [6 h$ V4 r+ u  ~5 [          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
9 r7 H; H' o% }  ?1 z, U          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
, i" l, o: t- z) D1 Q          180    0.04488    0.0682    0.07135    0.0091    0.03623
6 c1 h! Q0 q% `9 j# a, C# x          240    0.03653    0.06488    0.08945    0.01828    0.05452
9 y1 ?% A+ ]2 F9 ]* l0 n# L          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
9 {9 R. u; Y0 K- ^4 P1 ^) kk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
# e6 S: f0 g+ @0 _) W2 D* ylb = [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
# o- w4 t0 r  D' g7 t7 q6 Ux0 = [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
[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')
/ M0 E6 U+ O+ Hfprintf('\tk1 = %.11f\n',k(1))
# n" a' P, ^( f" }/ [4 }" ffprintf('\tk2 = %.11f\n',k(2))
& }7 _5 m' A4 m5 A- |$ O' Qfprintf('\tk3 = %.11f\n',k(3))
; Y# N0 g, U6 c+ e- C. nfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
% b8 d8 ]2 s% ]9 o% Pfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
* s, ]5 ~0 _% r- y+ Lfprintf('\tk9 = %.11f\n',k(9))
2 |! }" X9 f1 Y$ ?, Q& U6 Efprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
' C9 c3 ]+ a' T5 {k_fm= k;
3 H! H  \) K, W8 u5 o  J' _: Z7 m% warning off
: G0 t1 e: {2 e/ |% d% 使用函数lsqnonlin()进行参数估计
  p- k0 N. n1 _! G; g8 `& g, {' C( R' w[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
( C6 q/ S2 l! C2 n" @    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
( y* d. x. t% f. L9 tci = nlparci(k,residual,jacobian);
0 J  R$ D; O' s- d( h$ Efprintf('\n\n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))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
6 T3 w" l$ h2 ofprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
- c* c7 L4 u: n- s+ Qoutput
5 q+ z8 Q9 {% p7 V! o; Iwarning off
1 K2 K* A- S3 H& X9 z4 y  q4 }- S% 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
/ B8 n" O: I# e6 ]/ Q2 ^  wk0 = k_fm;
+ Q) N$ }6 t8 m0 R( J& j[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
" g/ z  h! J. \; ~6 A/ t+ d    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
  |! x2 J0 j6 f8 _) D2 \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')
; x: Q; l: s& t: Y/ a% cfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
& Y; {% B* D3 u5 K" h, J1 ufprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
) L2 k8 _5 t# G, D8 Ofprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
' F& u! I7 N' \6 Afprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
( c5 ]0 B5 Q! r# b& |2 ltspan = [0 15 30 45 60 90 120 180 240 300 360];
6 c1 U6 d7 ~- C/ ^  H[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
* v- ~* c5 S2 W* r7 j. }# e/ ffigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
8 I0 H9 b" G$ I; V7 a/ D) b) ?+ Nhold on
! J$ \% k( |5 pplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
4 I9 ~$ c; O+ G8 \/ m! {) {' _


. N' d$ |$ @5 X8 Yfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
  k# `# O- N+ T& E$ F: I! Af1 = y(:,2) - yexp(:,2);
- n% @6 z6 k' u. p. vf2 = y(:,3) - yexp(:,3);
3 ?( ~5 j) X* D' d$ S2 ff3 = y(:,4) - yexp(:,4);
5 e- Y- g' D; L1 \5 m/ z* Nf4 = y(:,5) - yexp(:,5);
) ?3 f" W0 r% F7 Hf5 = y(:,6) - yexp(:,6);
) H1 V1 b! d& d! @f = [f1; f2; f3; f4; f5];

3 B. _4 c  y* q/ @4 W* w% u- c

& Q2 w8 I+ ]: y$ T2 n9 \+ Hfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
9 b) W- Q4 {, Z4 O& Ay(:,2) = x(:,1);
: p) n  k- \- V# j5 ?: Z. |& H" ey(:,3:6) = x(:,2:5);
% i1 }2 g# l) }( T9 J. Vf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;

0 n; u: N5 D! Q
* m  y2 w- w5 z  @, ~8 t

1 Y) p( w4 N, wfunction 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);
+ Y  a0 \& x& u; V" V0 p" AdFadt = 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);
" j6 S2 t& a2 [1 [4 c# {dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
+ x" ]9 `/ o/ U0 E6 N

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