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
% q7 l# n, f0 z- |9 b2 R%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
; F7 y$ I, B' ~, B! A% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
8 G  y0 ]) h& ]$ g% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
4 u# I- U7 _5 \+ o0 j4 |7 i6 |, z2 hclc
format long
4 g% T! L# S9 ^9 h. R2 _! F%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  X8 F6 y/ _( k* L/ k2 J: {  Kinetics=[0    0.25    0           0    0       0
1 H, @6 I. M" Y+ n' q          15    0.2319    0.01257    0.0048    0    2.50E-04
# O0 W2 @+ ~# u          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
          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
, A& K" e( ^) t/ L  d8 @          180    0.04488    0.0682    0.07135    0.0091    0.03623
: h' @* z! q! `0 [. [          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];
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];
/ M+ j) C( _8 g" q7 Nyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
* B: s8 R7 P6 t! W- I' C( K& V8 ]% warning off
% 使用函数 ()进行参数估计
[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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
  h, K+ L6 G- [5 v& e* ufprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
' c" k& ^; y: v* q; T. u. p$ e& wfprintf('\tk6 = %.11f\n',k(6))
6 E  `! v  {$ C5 i% M& t# Wfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
  b+ Q. P; {% Bfprintf('\tk9 = %.11f\n',k(9))
- T6 ^- H" ^1 d- K1 j' h/ t, v* I  Afprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
, m# ?+ M, f( h7 g# l/ h1 [k_fm= k;
3 ~$ _4 I6 P. L3 n7 W6 }5 H/ l( `0 ]% 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);      
0 u  O/ ^7 [/ \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))
/ M% b- {$ `! X9 s, Nfprintf('\tk2 = %.11f\n',k(2))
; {. ~+ d# O/ c6 B- zfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
$ x! D) b- j* ]1 a% a2 |, ^" y- Dfprintf('\tk5 = %.11f\n',k(5))
5 w9 ?; Y; E1 v3 W7 H5 l7 Zfprintf('\tk6 = %.11f\n',k(6))
  O& t% a+ m* C* ]# ^5 Qfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
+ j" A  `$ n% O1 y$ ?' H- c$ h0 cfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
) R' C  {/ e/ v6 P$ y" U# D1 doutput
( b% f7 F' w; I5 X% ]8 Z3 pwarning off
/ |! e4 q# \6 ~  @7 `2 m- T: Y) b6 B% 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;
- X; K: o& N7 w# ^/ v8 j- n[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
6 R" |; e% _& T! J3 e' v9 m    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
8 d# |7 t6 t7 {/ j6 H- n( K2 {% A( O) gci = nlparci(k,residual,jacobian);
- e' h! [: W- E; Qfprintf('\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))
3 r& P1 j1 p/ G; l2 r! Rfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
4 B2 L' |- R. p+ M9 L- l# kfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
- |) e/ b! Y; i( s( G% nfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
2 E4 a$ w5 l) E: C& |; Efprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
( x* r4 y. l# W9 P4 Q5 }tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
# a9 o$ z$ A3 A5 A, B( K9 gplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
# f3 o, w& B8 E" |0 _) f5 K1 Cp=x(:,1:5)
% T* o& G# l& k  v* Z  Fhold on
* R. G! U& C, Y! Z/ w& tplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
3 }$ D' T+ y, W$ T, F+ a$ `: r! m3 ?


function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
9 J. N5 p; v! Xy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
; u$ o" ^6 H6 ?5 C) Sf2 = y(:,3) - yexp(:,3);
$ Q6 x0 j5 P4 g1 jf3 = y(:,4) - yexp(:,4);
: u  Q6 H' u$ H" R! W/ W! o2 @f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
# l' _: H' e! l" N' L' Lf = [f1; f2; f3; f4; f5];
  @- M5 H- R6 y2 A2 I

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function f = ObjFunc7Fmincon(k,x0,yexp)
* x& r  u# g$ R6 F- `3 ~9 j3 Itspan = [0 15 30 45 60 90 120 180 240 300 360];
( u4 `  O- ^7 U$ Q/ N, B[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
3 u) X4 w) t' Ay(:,3:6) = x(:,2:5);
  O3 Y% u+ X# t% I8 f" C( q/ Ff =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
( x8 Q$ |' x/ c; \1 D4 U8 ^    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
* M) D- H) m1 n8 [
1 h) _, f: U" a
! g5 n( \9 s+ M# R

+ t" }1 n) s3 |function 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);
! V9 x; ^+ h# |2 Z3 p  wdFadt = 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);
; O( Z5 H# _  @! K$ Edxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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