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
/ A. _5 J$ W5 H, t' C%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
! t1 w& n* g+ D# V- C4 N! U# f3 |% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
4 E( P. ?3 W8 }3 [& i% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
1 I. Y0 _" E! B/ Q8 Y%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
& Y8 M; i- f4 R$ g2 X2 }0 I& Aclear all
! E4 f  j9 q5 V! c% @clc
5 e% _$ A. E9 m. H2 ]0 |format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
; `1 M0 |- X/ Q6 z# d  Kinetics=[0    0.25    0           0    0       0
. T/ I0 c0 R! t8 V: \, b( \          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
: l5 u7 S- k+ @3 D8 f          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
3 n4 I9 N) N& w          120    0.0656    0.07397    0.07885    0.00573    0.02143
% c* S0 N# l. j& b: Z          180    0.04488    0.0682    0.07135    0.0091    0.03623
6 h, l$ N5 U4 I5 e          240    0.03653    0.06488    0.08945    0.01828    0.05452
/ g+ e' `9 {  s/ u          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
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
) U1 J  t& F8 C* G4 j8 E: Plb = [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
* E9 C0 R& |& F+ x' V% _[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
& Z# ?0 a3 ]8 v) Q+ e6 Ffprintf('\n使用函数fmincon()估计得到的参数值为:\n')
& @" b5 D! y1 {: P# [: mfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
1 g% V' P9 M/ i5 Y) Lfprintf('\tk4 = %.11f\n',k(4))
) f9 d' b- I5 ?0 Y5 zfprintf('\tk5 = %.11f\n',k(5))
7 y, P  S& ]" f- B( Y! y' o6 Rfprintf('\tk6 = %.11f\n',k(6))
1 j$ K# U. C8 U. t  u0 ?' Z/ l; rfprintf('\tk7 = %.11f\n',k(7))
0 o! a4 X. l1 @0 N+ Wfprintf('\tk8 = %.11f\n',k(8))
( b; Q% K9 X' n5 vfprintf('\tk9 = %.11f\n',k(9))
9 z6 t/ K' Y  O! z. g! {' afprintf('\tk10 = %.11f\n',k(10))
2 I+ n; f9 H, R2 mfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
6 U0 h, k. v6 z9 ?% 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);
; r9 ?4 x' b$ V# ~) H1 k7 ^& G. i$ Xfprintf('\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))
; @  j, g" v2 s& y2 [fprintf('\tk3 = %.11f\n',k(3))
# w7 L. S: _2 G- pfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
0 \9 p  @6 m% H1 z+ zfprintf('\tk6 = %.11f\n',k(6))
; }9 A) `- ]% _/ q% s4 ufprintf('\tk7 = %.11f\n',k(7))
9 h" x2 N! s1 x! m4 s* X" Gfprintf('\tk8 = %.11f\n',k(8))
. f1 v1 Q& K! C( B# F( ^: u$ c% K' vfprintf('\tk9 = %.11f\n',k(9))
+ C7 ^% m" B! `9 p. ]fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
, _3 b8 l/ o. c4 Mk_ls = k;
output
. p4 i7 q9 [8 ]5 Hwarning off
4 ~, A6 K$ u- b3 W- \5 k% 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;
9 \5 l9 S# N* M1 w[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
, m" |1 b) A' I6 Z/ w    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
3 C" u: K, s7 s4 b5 @( J9 Yci = nlparci(k,residual,jacobian);
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')
% h8 E) M2 V+ L, o- Ofprintf('\tk1 = %.11f\n',k(1))
; h0 ~; c4 V  ~9 o$ ]fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
( [0 Q8 _( }% L6 y9 H1 Efprintf('\tk4 = %.11f\n',k(4))
4 f& h! f7 `, p3 r, F0 o/ Tfprintf('\tk5 = %.11f\n',k(5))
% K* e! p- @) k4 v9 @fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
0 `: z& z/ d  U" }# b$ a9 Q/ |fprintf('\tk8 = %.11f\n',k(8))
2 Z! q# o( c0 A5 Wfprintf('\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;
; |$ S1 h( b/ e1 R* x1 S. k4 @output
4 ?9 y) V! {" y1 b& K8 ]7 Jtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
& A, i+ V2 h. d( |/ pfigure;
6 B1 x8 g! k  e! ~; h5 xplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
  L, ?9 A2 m$ ]; Lfigure;plot(t,x(:,2:5));
p=x(:,1:5)
hold on
+ {% g+ E1 I* Cplot(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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: `8 M7 C$ _. b8 Pfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
8 @: ?- I1 N9 g* b  y+ L  G! u* B[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
. c) n8 r+ c6 Z& G- U. q2 Ey(:,2) = x(:,1);
, ?1 _$ e' @& e# b; B  Vy(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
- b7 L  u! G4 k( Kf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
/ |$ {" V* R4 _f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
! S7 Q: D6 B& G1 Hf = [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];
9 u" m( e* e! H0 m. Q: c+ Q1 B[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
6 \# _9 I3 x% ay(:,2) = x(:,1);
: a2 f2 j3 M& j; }7 V2 gy(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
. }! \, U4 V% n6 [, n2 O    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
0 |) s& z5 n' C* E) H    + sum((y(:,6)-yexp(:,6)).^2) ;

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) W4 J, o; O7 n/ ifunction dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
* @5 \+ t# g" Z: Q0 m3 z: xdFrdt = 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);
8 I' D- C4 o: e6 F" k0 S. M$ XdLadt = k(7)*x(5);
$ L! X5 i6 a6 j/ _$ f% NdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
. f' q+ u3 Y, ^, s/ T( v( ddxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];