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
6 u- q6 @# ]* Z: N' d# `% k6->k6 k7->k7
% 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);
+ s# j# ?! z  n8 K! |8 B% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
( _$ @+ x' E  w; z5 D" \clear all
  D) p( Y; S- s3 ?8 y. p8 gclc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
3 n% U- c0 V# p2 J4 u, U/ R: p; r          45    0.15105    0.06975    0.02473    0    0.0033
, `" `9 G  H# C) k: F& O; E0 C          60    0.13763    0.07397    0.02615    0    0.00428
5 N! ]+ @$ x, q/ e' T# j& |          90    0.08115    0.07877    0.07485    0    0.01405
) S4 Z  k/ e& p          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
% ], t& \& e4 I- d$ f+ w* h( @          240    0.03653    0.06488    0.08945    0.01828    0.05452
" z% P! c/ B" m8 [+ H- c          300    0.02738    0.05448    0.09098    0.0227    0.0597
7 o4 j3 p$ {" d% h1 m          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
; G2 K* L0 P) ]% {2 c, t) M; ?9 N$ rlb = [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
# R/ b. o$ W& M* B8 v# d6 D- y1 {  T[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
9 |# L6 m/ }& N3 tfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
* r6 j% }# d% x$ G; pfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
" @4 O/ ?# s- T$ rfprintf('\tk8 = %.11f\n',k(8))
) e' M) ]  P4 P5 lfprintf('\tk9 = %.11f\n',k(9))
$ S+ k: I. S& l. Xfprintf('\tk10 = %.11f\n',k(10))
4 A5 O) n1 @# jfprintf('  The sum of the squares is: %.1e\n\n',fval)
( o9 o/ M% J9 y" f5 }k_fm= k;
% warning off
) \6 i5 P0 y- }3 f. p# E% 使用函数lsqnonlin()进行参数估计
# t" t6 m5 D& N/ z8 X4 E, z9 N[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
* c, u* e% ^/ {2 Z: i3 R% t    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
8 ^3 a1 V- k1 ~2 cci = nlparci(k,residual,jacobian);
) V8 t! Y% U# ]; e! _* e4 R+ {fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
7 {$ g/ D0 k0 u0 qfprintf('\tk1 = %.11f\n',k(1))
+ u' a: r9 v: x. R' ~fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
# A! {3 I9 y. y$ ?9 ffprintf('\tk4 = %.11f\n',k(4))
/ ~2 \6 z5 ]' z7 ^fprintf('\tk5 = %.11f\n',k(5))
' p4 S7 V8 Y$ z0 E2 _/ k! v# jfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
; y' G5 c7 j% t( n: T( Zfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
- J9 `$ l" `7 {; Gk_ls = k;
7 A9 D% P" D9 Doutput
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
7 d. H! X% h" P- L4 F/ T: V" \k0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = 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')
4 }: q" r2 @$ M4 H4 Sfprintf('\tk1 = %.11f\n',k(1))
' H6 k2 J& R0 V* C+ o  Z) sfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
+ H; f' u2 c# Yfprintf('\tk5 = %.11f\n',k(5))
+ }0 o0 L; H1 g, ~9 Yfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
7 R+ r* |% g5 _+ \, Vfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
6 s2 O. `7 b% z+ A2 efprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
; X) ~) o, s' j  |6 t) |: Htspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
! Z. Y1 {3 k2 i3 up=x(:,1:5)
; g7 n* q0 e, [( `8 s* z: Z, k* zhold on
2 Z' k7 W: y; a/ [0 Nplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
( r6 y# V: L; ]( g/ I

! v" l0 x6 m& R3 r& J1 ~
: G! J1 H! Y  C% ofunction f = ObjFunc7LNL(k,x0,yexp)
# ?7 |* h) G+ v4 a$ ^tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
8 v; @* ?- Z) V& G$ y0 z/ y$ b5 s; Qy(:,3:6) = x(:,2:5);
# g" Y6 m6 {' k2 N. G9 Z, bf1 = y(:,2) - yexp(:,2);
6 Z' |! E) x) G6 Rf2 = y(:,3) - yexp(:,3);
9 d! ^9 q$ w( R& b3 j+ }f3 = y(:,4) - yexp(:,4);
0 F* p7 _7 w' df4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
( k; ]! h; n# i2 n9 v* c0 Xf = [f1; f2; f3; f4; f5];


1 `5 p4 b1 Z! `/ H' D
8 V" V9 y4 E: |. p8 tfunction f = ObjFunc7Fmincon(k,x0,yexp)
3 U1 z6 M9 m. o$ y' B/ Stspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
# X' ?, z2 Z2 t: {6 ~y(:,3:6) = x(:,2:5);
- u$ V: A6 B( R% ]  _  f$ ^/ Y( tf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
# q* J  w. N2 G( A7 v& Q    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
# a: u" V: y' _# T6 ]1 f    + sum((y(:,6)-yexp(:,6)).^2) ;


& P8 H1 A; M8 Y- Y

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);
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
  u4 C4 S7 S) a* i9 {dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
. ]& D% u) W% n* u& A3 V8 {5 _