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);
$ g  V( U. _; }( J# p# |+ o! {% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
$ C8 D& n& Q) e  g$ C% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
1 B" I- X/ \) x% S! K+ g3 Q6 h% dLadt = k(7)*C(Hmf);
$ ]4 x3 X' C, l! p, q; P%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
9 k  C! |; g9 X9 C0 w7 Sclear all
# h/ a: n, \1 S0 M  G5 d8 Gclc
/ I- l9 t0 W/ E8 I1 tformat long
- t+ n5 O# P1 {+ g%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
" ~. B( b: k# D9 H* Z  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
* w( X* y) j5 W6 C* X$ Q/ ?          30    0.19345    0.027    0.00868    0    7.00E-04
* {$ S- D' Z. ?9 W/ u( Q          45    0.15105    0.06975    0.02473    0    0.0033
. P/ j4 \0 m, m% w# G8 o+ v- s; w          60    0.13763    0.07397    0.02615    0    0.00428
# }6 D' d7 n) B) b8 j5 q! R          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
3 s; [8 O( c: m! U' i; G  R          300    0.02738    0.05448    0.09098    0.0227    0.0597
! R9 e3 z6 @' a3 v          360    0.01855    0.04125    0.09363    0.0239    0.06495];
' e' {! U: F# ?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
ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
7 ?# f" D0 d5 k9 n6 [& Xyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
2 K7 M$ s3 }' V9 l% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
; K9 ?8 `, ], Y4 Ifprintf('\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))
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))
9 p/ J) \# a' t, Xfprintf('\tk9 = %.11f\n',k(9))
9 G# W3 C( \0 ^# m- c1 r4 k1 Ofprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
1 L  y8 C9 Z, B; C, [8 ek_fm= k;
0 W/ Z8 J$ h) K& N. p  j% warning off
% 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);      
- f* a6 T% e0 I7 q3 E+ t( n& ~3 {2 zci = nlparci(k,residual,jacobian);
# R' @9 `$ ?' |8 vfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
' z6 X# t8 U; ~$ M7 w/ U* Jfprintf('\tk1 = %.11f\n',k(1))
- P& b) `' P3 Q( E$ [. E# Ofprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
6 A) t( \* `3 Kfprintf('\tk4 = %.11f\n',k(4))
) i7 j9 T+ H6 ^, Ufprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
5 H: c. p7 ^3 H! M  S: Zfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
. H9 r) M% P) n) lfprintf('\tk10 = %.11f\n',k(10))
$ c3 K4 a- L2 @) rfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
& V7 F5 p) I# q8 |4 [5 ooutput
* X; j+ Q# O+ p5 N! Zwarning off
" `3 Y" \3 i% g6 D5 O! u. \% 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
9 |2 C: L* Y( h0 e1 ~* C- _k0 = k_fm;
) q* }% B" C, {[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
9 j7 p6 g+ L# e& ~0 K4 Xfprintf('\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 R( J  Z/ ^fprintf('\tk1 = %.11f\n',k(1))
6 s6 f# }: y/ i7 T8 v6 Ffprintf('\tk2 = %.11f\n',k(2))
: \- ^5 o' \9 L6 L0 H/ C4 H; U9 Bfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
  v; E# ^- ]- o7 bfprintf('\tk5 = %.11f\n',k(5))
! a# k5 s4 H/ o& Cfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
) u6 l" y4 b: w5 T  h' Efprintf('\tk9 = %.11f\n',k(9))
9 j  b7 m# ~2 {$ _. j. i; ]: X3 Kfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
1 h+ A% A( P) @) q$ @: Kk_fmls = k;
! T2 u8 x% j! J* Doutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
6 B# Z9 {* V" f9 f$ o  S, f: cplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
9 C  X0 D/ \/ _2 n' N  i: z# |" v* Sfigure;plot(t,x(:,2:5));
p=x(:,1:5)
hold on
! [. B2 X9 [/ L+ u2 Dplot(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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6 Y% D* |7 g7 {/ t: a3 x& p! p" b, ufunction f = ObjFunc7LNL(k,x0,yexp)
! K8 I+ G4 `, G' o( z& T  t0 gtspan = [0 15 30 45 60 90 120 180 240 300 360];
6 |# [- }* \. N* X, d1 P$ l[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
$ |9 A2 B! B7 M/ `! C, Kf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
! W1 L! [( M% J, T; K$ {5 r  t6 Uf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

3 c- ?( b/ _! e1 v# {
* h: L( g$ O5 J5 p0 u
function f = ObjFunc7Fmincon(k,x0,yexp)
9 d! F4 m  j0 i. _2 s7 \tspan = [0 15 30 45 60 90 120 180 240 300 360];
$ R8 T9 g7 g/ n5 [0 a. H+ R1 F[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
) `; p" Z7 |2 R% I  p# I! @y(:,3:6) = x(:,2:5);
5 B! o* t' k$ ]4 _# L+ H0 k( s# 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)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
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% U7 x8 D! b8 i" Zfunction 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);
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
) Y. _- F/ i# fdLadt = k(7)*x(5);
5 D. B  g1 o7 S2 YdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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