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
( h$ c9 \8 Z$ w9 Q7 F3 C  _%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
4 ]1 s4 B- R& O0 C: P5 ^4 S% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
% `" O' N+ q: Z; b. `2 ?%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
/ F2 y) p" D& `: O$ Gclc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
# g& Y" A) d( @# R) B  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
" |5 }) B5 S4 K' Q+ f          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
$ C0 O8 e2 H0 t( ^# t1 o8 b          60    0.13763    0.07397    0.02615    0    0.00428
3 H% L( d/ ?% n" f! p          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
1 _& Y$ [, X. U" W* c          180    0.04488    0.0682    0.07135    0.0091    0.03623
0 g: P+ J; G; m( _6 X3 C6 u' J          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
% H- E9 A" E, c! c  f+ J          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
: B3 y3 m) X1 |  Slb = [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
6 e7 p8 q& |* yx0 = [0.25  0  0  0  0];
, H6 B5 _# j- p8 a1 lyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
$ F1 g/ I1 u0 S3 F* B+ F/ J% 使用函数 ()进行参数估计
9 O+ o7 m+ R  x4 f* `3 l" |[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')
1 \, s' c5 M. T; [; x5 T7 C' Sfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
: j+ H! ]$ R3 D& N9 h: Efprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
( S3 {: {/ t- ?) ?0 Yfprintf('\tk8 = %.11f\n',k(8))
- c2 V  d1 ~: Z  \1 |0 V# y6 mfprintf('\tk9 = %.11f\n',k(9))
) A( L( g0 @  q% N# ]fprintf('\tk10 = %.11f\n',k(10))
; x, F, k% o( R* u8 n) S& sfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
' Q4 b4 d2 l6 @% 使用函数lsqnonlin()进行参数估计
, f( m% m! z; a) @  f2 S[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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
8 g( N) F( ~' Y( t& rfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
5 p& a( O! y& @fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
. d( G$ ^% i  t: x7 N1 K4 Rfprintf('\tk10 = %.11f\n',k(10))
$ b' o6 e. _0 V9 e( tfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
% q% T! n* _* d5 ]! |, ?output
0 v5 g/ ^/ f7 c* {6 U3 c6 Zwarning 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
7 |+ B0 B! j9 b" U, }6 D1 `; Uk0 = k_fm;
* k) c; J# F! M0 r0 \0 c& c, u[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
7 ~* c  F* L: V0 S- e* R$ f    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
: `  ?. k5 y8 Z( W$ A# l# 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')
fprintf('\tk1 = %.11f\n',k(1))
6 d; _. v- g8 O7 C, T; Vfprintf('\tk2 = %.11f\n',k(2))
$ m4 w7 w, R$ o4 ?+ o) Qfprintf('\tk3 = %.11f\n',k(3))
1 A; D, `- M( l! W1 a) w7 Wfprintf('\tk4 = %.11f\n',k(4))
9 ?3 W5 j4 Q9 j" F, C6 Qfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
2 T3 k  _" V) l$ s5 T7 O  K) sfprintf('\tk7 = %.11f\n',k(7))
; y2 }$ {+ g, p) ffprintf('\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)
( p/ s- r; V+ o0 z$ c- ~% ^k_fmls = k;
" u) p: i4 ^4 [" y3 b+ y/ z  boutput
0 b2 f8 r( m/ I) W6 a. r8 ]tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
' v3 P) O/ Y4 @# vplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
9 O7 J( E6 N% O) e& J# [figure;plot(t,x(:,2:5));
* X0 G" }2 e- g! pp=x(:,1:5)
! U7 r7 v4 X, J& g; {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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  }' E% D- N, A7 a1 i& c# |( n; pfunction f = ObjFunc7LNL(k,x0,yexp)
" {( b0 x$ N0 ^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);
8 A* T5 G! [: O- y1 H( s$ `$ Af1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
, a: a4 c- {8 a- gf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
7 e; b2 `4 ^" ]- T( q, n+ ef5 = y(:,6) - yexp(:,6);
$ |$ _. J2 i* e  ~& Gf = [f1; f2; f3; f4; f5];
8 s; L; t: X  R8 N& T

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0 o/ ]8 W  W* v+ e8 ~function f = ObjFunc7Fmincon(k,x0,yexp)
4 O0 `' ~& u- ]; s1 J5 Y% gtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
- w5 Z. N6 W+ o) r# `* e) Ay(:,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)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
0 s" ]$ f2 ^- V% ^  m

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: Y; `8 `' u2 G6 ~; ~' @, j9 Nfunction dxdt = KineticEqs(t,x,k)
3 a0 I. i% J# z6 ?# W& @. XdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
9 ?/ S% s* M' {# hdFrdt = 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);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
) b: p+ }  h' Xdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

: X" O2 \. Y5 ]2 O6 c! T