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
1 f( Z: W$ N  q%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
( L) e4 O; F" j0 i2 n) V% 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);
- U6 J5 D2 G9 m% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
8 h2 g3 _" n4 Xclc
format long
$ Z% {& U. I- `. E3 ?2 G' ]5 z%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
. m7 I9 _: R; |( f          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
% b' H8 n( w" {) \( b2 z0 J% Z          45    0.15105    0.06975    0.02473    0    0.0033
5 X) D. u/ k7 d$ S, B          60    0.13763    0.07397    0.02615    0    0.00428
6 R- |3 l" a) n5 L& N/ G& C' Q          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
+ S3 C! O) X+ V, W. l          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
6 ]# k8 {$ H5 K8 _+ h9 S          360    0.01855    0.04125    0.09363    0.0239    0.06495];
3 `) A2 Z2 r$ A1 `0 p# D4 N; 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
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
) C6 K# _) ]- J4 P8 |x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
/ K, V5 }+ D' J' U4 ]3 `4 Q% warning off
# I" W) M+ H7 }* N% Q1 Y% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
6 x$ T7 w$ ]) c5 lfprintf('\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))
9 g+ Q# g8 T' ?9 K8 h  d1 n6 a$ [1 Rfprintf('\tk3 = %.11f\n',k(3))
. j1 P" Q' Z' afprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
# Z, Y8 ]8 x7 U2 o+ nfprintf('\tk6 = %.11f\n',k(6))
' Q+ s* _  |/ W" M+ bfprintf('\tk7 = %.11f\n',k(7))
, ~& T& e# A6 ~7 }' ~fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
) y1 X# d4 k% t, ifprintf('\tk10 = %.11f\n',k(10))
5 F+ L' U, C# ]3 A$ C5 Bfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
  {6 m  c' H4 T/ ^( x. Q. j% warning off
# J2 h, O6 W2 g. t# x% 使用函数lsqnonlin()进行参数估计
- c  S2 z! v1 K3 l[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
% I) j' b3 l: G3 j' Rfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
' K1 G3 V- @0 y# ], O  r- Ffprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
& Z8 A" D+ V. E- kfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
' R2 E; e: t: O4 `fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
% {7 k  @) B% v$ n! nfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
1 a# W& F+ `% \6 _fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
! v( s5 A" }! k$ [output
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
k0 = k_fm;
1 ]6 ^' X7 f$ i2 k5 q, D[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
6 K- Z0 U% s7 i9 ]# Y    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
- E4 x: l' [5 @: T: A; h6 `9 h! @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))
: C' l# m9 v+ Pfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
- }1 u# T' U" q4 ^* y; Pfprintf('\tk4 = %.11f\n',k(4))
& O! y2 R( D5 `) N) ~. Q. Pfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
# y4 B: Y3 g  Q* G7 W, A3 I* g" e/ jfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
! }" U6 i7 d4 P4 K$ I; c3 Bfprintf('\tk10 = %.11f\n',k(10))
. U$ m+ t' D4 C# P  cfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
8 \9 i& h2 f; [% @0 y8 {' j. u0 Ntspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
, d+ [) F6 c6 B$ wfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
7 }, X, l. N% i9 ]2 `3 C5 M& `" Z8 ]' fhold 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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; q" ~( v) L; U3 gfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
; b4 ~* c2 G, r) `y(:,3:6) = x(:,2:5);
& z2 f/ R( L6 |1 @+ J& A' ff1 = y(:,2) - yexp(:,2);
5 G5 m4 o1 G: D- Ff2 = y(:,3) - yexp(:,3);
# S4 d, ^8 X7 P& m3 Wf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
. c7 k7 K2 W+ I: E8 Nf = [f1; f2; f3; f4; f5];
# _1 `" z2 r( g+ e( e  ^9 j


function f = ObjFunc7Fmincon(k,x0,yexp)
- q& q) H1 o$ `: s+ L) W6 otspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
/ V( [8 u8 w, t9 U5 Ry(:,2) = x(:,1);
1 R! _% ~7 J% |9 L- qy(:,3:6) = x(:,2:5);
6 f2 |' T% ?- h. i& x, |2 Af =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
' e! s& V& q" v7 r) n, n* l# K    + sum((y(:,6)-yexp(:,6)).^2) ;


% f% y" K) h* e
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( c5 ~9 c# Y: L& b& F! a, Ufunction dxdt = KineticEqs(t,x,k)
* G; R4 |0 o0 [dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
, d0 n) i% {$ m0 qdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
5 N/ S( _# L3 [dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
+ G+ }* P5 ^  ]) b; b# E2 @dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
) ~: K) b1 N- Y  y5 d0 @
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