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
, S7 I% [5 I# o% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
3 c# u! N9 a$ E3 Y' c3 b% 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);
: X5 U# q2 U; J, M6 u+ Pclear all
' g0 z+ w% q. c* Sclc
* D) d& G4 f  `8 E& ^format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
2 x3 Z2 ]3 M! e- |: l  Kinetics=[0    0.25    0           0    0       0
/ [  [5 {  Q9 `/ N          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
* \2 z# m) v4 E          45    0.15105    0.06975    0.02473    0    0.0033
3 T$ R) c9 z/ F4 t) v# r) _& v          60    0.13763    0.07397    0.02615    0    0.00428
& ]. l( o, c& M% R6 J/ R          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
9 r( W" b7 w4 l6 n          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
" }( s; ~* {) B! w+ `& j- z# ?          300    0.02738    0.05448    0.09098    0.0227    0.0597
& T) E" ]  q% H! a8 I; A+ p          360    0.01855    0.04125    0.09363    0.0239    0.06495];
  N0 T* N5 @( H1 d. q+ O& Xk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
2 ]/ [& z. f# p* Wlb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
# {+ y; N- j! I1 q* Q0 `9 r" q# _ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
7 v& W! A, Z3 l4 a( Rx0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
' y# s0 ^: N1 \7 q% 使用函数 ()进行参数估计
- j( Z8 b% n% x! r[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))
fprintf('\tk4 = %.11f\n',k(4))
+ H* j/ }. F; _0 q3 Q! q; k. yfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
9 X& E" ~: e7 p6 E! Mfprintf('\tk7 = %.11f\n',k(7))
" P' h2 `" A, ?8 ]fprintf('\tk8 = %.11f\n',k(8))
* W: Y: V$ Y" C6 @* ufprintf('\tk9 = %.11f\n',k(9))
9 H/ A3 U" [, f( afprintf('\tk10 = %.11f\n',k(10))
! S- B. p- B2 d' x, e) I# ^fprintf('  The sum of the squares is: %.1e\n\n',fval)
% S/ U# e# k" R9 v! Wk_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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
  T# Z1 _  O* ?1 v$ C% _fprintf('\tk3 = %.11f\n',k(3))
6 u8 E& a+ \/ t7 Z, Vfprintf('\tk4 = %.11f\n',k(4))
& _- L+ b* B' `fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
( Q) T9 N8 I, I1 x4 g4 ffprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
6 b. n6 m1 p) C( o! ]% v, x3 rfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
2 G7 |) ]  i2 x1 \9 n4 hfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
$ l& e, D4 Y0 t# X, J" j$ w) d  ioutput
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
; o# H3 J- {- r+ zk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
; D( i+ ?% |/ l7 u* l5 ~& y* \; cfprintf('\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))
' a& G9 U' K- A& X1 k& @fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
( U- h  T* Q0 H/ B- sfprintf('\tk5 = %.11f\n',k(5))
% _8 K! k9 r: m  F4 y" x0 _fprintf('\tk6 = %.11f\n',k(6))
6 J( D5 C* ~0 n# p) o1 a" |fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
1 L9 F2 S9 k% a( ~% ffprintf('\tk9 = %.11f\n',k(9))
+ j; v! Y! h, ^: H4 Gfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
/ E4 W7 U6 ^8 x3 W1 k, }- Otspan = [0 15 30 45 60 90 120 180 240 300 360];
" g% h2 e7 y3 v& g[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
' u% a( G, y" A* ^) gfigure;
! _/ x6 G3 d9 d2 Hplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
3 s" F3 \- x. ^( ^figure;plot(t,x(:,2:5));
p=x(:,1:5)
hold on
4 I! x) r$ M; U8 u: Z  cplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')

6 R8 L, N3 j& m6 k

function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
# p& C1 _' u2 |8 ~- j9 k[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
; Z8 U7 q& z; Gf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
1 h# \! t) M5 Nf5 = y(:,6) - yexp(:,6);
: S; s! C- Z. z# z1 m5 I$ t+ t; s) Gf = [f1; f2; f3; f4; f5];

: {% m) s5 H1 f1 B( s7 d: s7 ]
  w3 @  G2 l8 v& t* H4 K* f7 j3 D/ x
& s0 G6 ^5 h& `2 ffunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
: M' y7 Y5 i2 j6 n/ gy(:,2) = x(:,1);
  u7 g- N+ ]) t. ?y(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
" |. u4 L0 m7 y5 y    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
1 V; A# |# \* ?) ^1 A
& o: f/ [6 T; }. z  C
4 e% g* ]+ b5 z0 D1 r. V: p! o

8 k8 y$ y' ^, g! O* wfunction dxdt = KineticEqs(t,x,k)
, y' ]" Z% x, ?# t  ~8 BdGldt = 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);
' R5 R, i+ M0 _2 q8 q" A: DdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
  a& g; O7 ?, n2 o8 C; qdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


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