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
. ^& N- E( t3 B%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
7 @# c( W. V0 j! T$ k+ j1 g& M% K% k6->k6 k7->k7
) V; j' B& f, j3 Q3 ?* O% ~% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
  i& M$ q  C4 `+ U. C0 {0 T% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
: i  ?- m* R5 r4 w2 B3 y%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
& S! c8 s/ W8 V+ \5 i7 cclc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
. v" B$ `5 H& ?& j, C  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
/ l' x& h& I9 \& W) I' b2 C          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
& x' Y  {6 D( v1 [: A' H0 H          90    0.08115    0.07877    0.07485    0    0.01405
& p3 v3 ~5 t) G: d) ~4 N% m/ h          120    0.0656    0.07397    0.07885    0.00573    0.02143
1 [  a+ K- g6 }1 `" h          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];
, t' `; K4 x- z  T( Zk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
& y7 R1 X0 b' v0 ?+ Jlb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
" M) a# z( T* u! Hub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
# g+ s. h# Z( f; f- n) [yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
  v" U" [* A% K8 Z) u# d% warning off
# o  v' t, r: p5 H9 _8 I% 使用函数 ()进行参数估计
- F1 ?9 v* k4 W& d, s[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')
9 C# L4 Z" z3 P4 B7 nfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
% C) `9 w1 |2 J: H2 Y7 O  bfprintf('\tk3 = %.11f\n',k(3))
( }( S& P( K* ]; @: P, efprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
( r! A: O. J2 o, _* Xfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
$ m# X% ~: R5 a9 o- }# \fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
8 s1 r$ w4 u1 i1 M6 mk_fm= k;
% 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);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
# h: {" a# o) P; ]- Lfprintf('\tk1 = %.11f\n',k(1))
, q6 i0 ]2 E. S4 K  pfprintf('\tk2 = %.11f\n',k(2))
" E- I, Y+ o' z6 J8 Nfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
6 _) J! N  _- R# E2 Pfprintf('\tk7 = %.11f\n',k(7))
  Y& E7 s9 q5 D- i6 H7 q% U/ S3 ?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)
% E% B$ x8 {  r; k3 X2 ?) s% }k_ls = k;
output
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
) T3 s) A% p) a) i, K* yk0 = k_fm;
/ R- @" [9 B3 f" o9 L5 \' p2 Z% S[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
/ L1 y  x9 [% R1 z* z8 l1 ~    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
& ?* h' Z2 F* Q1 C: M( @ci = nlparci(k,residual,jacobian);
. r& z/ a; [9 y1 G" Y( ofprintf('\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')
fprintf('\tk1 = %.11f\n',k(1))
, o: }9 ~( _4 Hfprintf('\tk2 = %.11f\n',k(2))
5 X9 r8 j4 V# `fprintf('\tk3 = %.11f\n',k(3))
7 ]& Z1 V; N1 r5 `7 Cfprintf('\tk4 = %.11f\n',k(4))
" a' n2 D7 [, Q4 t/ m; M1 Dfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
! E' w9 u; }3 J/ a5 B- w% tfprintf('\tk7 = %.11f\n',k(7))
/ v' M1 I) q: u2 o+ I! Pfprintf('\tk8 = %.11f\n',k(8))
0 @' N5 F0 E& N$ z0 Mfprintf('\tk9 = %.11f\n',k(9))
0 K) A: y) Y: Xfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
: P2 D- o! N# X* o: k$ mk_fmls = k;
" y0 }* J7 D6 j+ z# H' ]) L5 coutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
4 v  ?" o( K7 P2 k' E% [[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
$ _. h) o; [+ xplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
( B8 }7 s( U4 X2 F9 t( }: Dfigure;plot(t,x(:,2:5));
9 x5 R+ ?( w! e1 y1 T. h* L) @p=x(:,1:5)
hold on
3 L. h- f- N- rplot(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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' t6 D4 i: r6 w+ I6 X9 {+ rfunction f = ObjFunc7LNL(k,x0,yexp)
+ `% K: I, P2 A2 ?9 \tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
9 V- M+ S9 l. P1 w5 h6 }: cy(:,3:6) = x(:,2:5);
2 B: S/ m5 q3 n: J, X# Gf1 = y(:,2) - yexp(:,2);
2 m) o+ g$ G: g! gf2 = y(:,3) - yexp(:,3);
) r# q2 K& m* X$ P8 sf3 = y(:,4) - yexp(:,4);
# e' W+ I& ]/ [1 of4 = y(:,5) - yexp(:,5);
" n6 L. M' C* _) Xf5 = y(:,6) - yexp(:,6);
2 g# ~# V/ z# h( w" ?f = [f1; f2; f3; f4; f5];


5 E; u, h. t# k' w
) `2 f, \5 Q) B  g2 ?6 Hfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
! \/ `# x- M7 C/ j[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
% L9 ~$ R; f3 X) ~9 k8 Ty(:,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)   ...
; ~- k" S8 o7 A* U* v- x    + sum((y(:,6)-yexp(:,6)).^2) ;
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function dxdt = KineticEqs(t,x,k)
. L2 s# O% F7 q, ?$ a& U0 ~dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
+ l" h, i# [- k/ e9 ~7 \4 mdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
, G- u4 C3 P  y8 ydFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
" \8 M# H9 T) Y  |7 G7 GdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
  U: Z) ~/ {9 I" r8 pdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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