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
# J& h) n* g0 h2 g2 a6 f" ^* @% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
" y/ l* E+ t; r8 S3 o7 _3 X% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
' y# D4 B3 I" S% dLadt = k(7)*C(Hmf);
7 i* P4 {; y+ e. ^' q/ U! E7 S%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
* a  B% P; w/ i, z( i# U3 d' aclear all
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format long
; l) }5 c, M: S- ~5 b%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
6 Y" M; A+ l3 V% P. c" H          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
; P. Q( s+ e4 a          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
1 a9 u  o* I$ e1 k9 C( F" uk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
" g' v) i5 q+ n3 U" o) ?4 wlb = [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
% x4 ?" V2 O/ |2 y  L' y4 n) B3 D! ~( X[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')
0 y6 L3 o. @; s0 Z4 cfprintf('\tk1 = %.11f\n',k(1))
  O2 m+ A/ c2 J4 c' G  [fprintf('\tk2 = %.11f\n',k(2))
' v. L) F) _5 O' M- r4 O6 B4 i  Yfprintf('\tk3 = %.11f\n',k(3))
4 N( K5 [$ a! B: [* M/ B% v- j& A7 afprintf('\tk4 = %.11f\n',k(4))
0 M$ A2 G! R* Afprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
6 ?+ B! Z" @( N4 }0 Ifprintf('\tk7 = %.11f\n',k(7))
2 g6 Z$ d, h& N- Rfprintf('\tk8 = %.11f\n',k(8))
5 {. p* [. }2 `1 Ufprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
6 J1 i4 q' s% L" a. L& v6 efprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
- a8 B: i/ K3 U% 使用函数lsqnonlin()进行参数估计
1 I9 p" F0 m3 p' A' \' S[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
( D  H/ a/ P$ }! R    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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
: v8 q- u: p0 K: \8 x/ z1 Rfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
! [* R  D: J% Z7 ^! f& k6 ofprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
' {# s2 O! Z1 I, X9 z! Dwarning off
) c; X" k5 B; V4 d8 z' O6 c7 Q1 M- H6 W% 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] = ...
( Y1 `/ I4 u  E- x9 d* E* n5 d    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
: @. }: N1 A* r+ R6 f- N7 p+ z5 F  `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')
3 E# D$ S+ |3 N# E4 W, k8 \- t# Pfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
5 [  \, o; W) @" u# y6 u9 ofprintf('\tk3 = %.11f\n',k(3))
* K6 p" Z! u4 b/ ]; I3 Dfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
; B$ L9 q  l- H! E& v2 Wfprintf('\tk6 = %.11f\n',k(6))
. X. f4 X5 a' P5 Pfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
9 h. f3 y5 `8 i( p7 F# u) Ufprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
/ X& N/ k9 `" O* ~k_fmls = k;
5 H1 I% a, n6 N' v7 Noutput
' q) T4 \5 z* N' Ptspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
; g6 o# `- F) V$ Xfigure;
+ W, i1 d; `! T, P8 i7 _/ Dplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
. ?" r. o, }" j; `! K0 vfigure;plot(t,x(:,2:5));
p=x(:,1:5)
hold 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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) n6 J3 A- D* }3 g% L; O5 Z9 H6 V; `function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
# o8 a5 R5 S* w9 e' Y. h& n[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
' ]" t8 B. s4 {% w) Y4 {/ jy(:,2) = x(:,1);
$ a. v4 M1 ?5 V7 jy(:,3:6) = x(:,2:5);
- B/ C$ B* q1 G' I' Zf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
0 R+ B) E+ P" m3 b5 G% u. X2 yf4 = y(:,5) - yexp(:,5);
! J, U( C4 [' I+ Q5 a. d: Tf5 = y(:,6) - yexp(:,6);
- I8 p# ~6 f* a5 d: ~' k, Qf = [f1; f2; f3; f4; f5];
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function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
# v6 O- ~+ f1 {9 W5 b. A* w[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
* L- M' R  T/ J9 R% V    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
# d2 f9 r$ J, ?# W1 Z. m, m- w    + sum((y(:,6)-yexp(:,6)).^2) ;


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8 j* |. h% ~0 m/ j4 n8 c7 Dfunction dxdt = KineticEqs(t,x,k)
- L+ \+ H1 u5 \: P5 SdGldt = 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);
dLadt = k(7)*x(5);
4 Y' T& N3 W7 U5 q/ w) {dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


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