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
5 H2 g6 v7 U# K9 R; {& g! T% k6->k6 k7->k7
0 A+ Y: ^: |! v% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
& Y0 L& w- Z! `- Y) i, o$ B% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
9 Y/ [  T2 F; M6 r" R4 ?2 |7 l% dLadt = k(7)*C(Hmf);
6 }' ?! e4 P/ d7 o%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
# g( N8 |7 e7 F- A1 }format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
/ y/ p  a! P) u8 b# Q          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
5 o9 G2 A( g7 A8 t2 n7 c8 `          45    0.15105    0.06975    0.02473    0    0.0033
# C$ f. x- L. N* G3 h9 V          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
          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
2 B; H* S8 o; C) B          360    0.01855    0.04125    0.09363    0.0239    0.06495];
% T" P5 t& E0 O6 B2 N' bk0 = [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
; K8 D+ W" Q; i" Y- Y+ ~ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
7 d% m5 o4 F2 i& _. Y' Kx0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
& z; z- t2 A$ R. \0 V& K* c/ Q3 A- m% 使用函数 ()进行参数估计
% z( a8 w* c' ?[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
9 r# A, \/ I! D3 ofprintf('\n使用函数fmincon()估计得到的参数值为:\n')
) p% N6 ]* R' w1 D/ H* nfprintf('\tk1 = %.11f\n',k(1))
4 o  U" Y* n# B" @6 B; v+ wfprintf('\tk2 = %.11f\n',k(2))
/ c* O/ r: t/ q9 ?' b$ Y( X; m1 Kfprintf('\tk3 = %.11f\n',k(3))
- v& k8 l/ l* ~- w# ~fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
# F1 x- Y/ H0 X% ^1 ffprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
* s( U3 @5 A0 M3 Ufprintf('\tk10 = %.11f\n',k(10))
- J% Z( \( C9 I1 s; Ofprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
8 T% F- C# V$ }/ i% 使用函数lsqnonlin()进行参数估计
: u- w+ w! u9 v[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
5 ]+ b1 O& A! [& d3 U/ T) Bci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
$ T# t- B6 V3 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))
; C' W: }6 Q# {! f# [fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\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)
k_ls = k;
* o: L9 H4 K8 G6 X; coutput
warning off
* F3 \1 G6 c# n3 d4 o% 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;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
" S" k" q+ L" y0 h! oci = nlparci(k,residual,jacobian);
$ B+ Y5 |) x, O9 D5 N9 c6 Yfprintf('\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))
fprintf('\tk2 = %.11f\n',k(2))
8 {! j' G: n% n1 P6 m2 t3 efprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
) k) h9 A8 O4 d* F+ o7 [fprintf('\tk5 = %.11f\n',k(5))
! {" k' r9 E1 M- W1 G" Q, Efprintf('\tk6 = %.11f\n',k(6))
' O9 {! B: h8 U3 f; s; Cfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
4 O# [; e" N# Q  ^/ W* t5 Gfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
9 a4 K# }$ ^4 a& S1 ltspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
0 e( `' b$ F+ n. T$ f; D* _9 mplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
% [8 W- T% ~! X6 T) hfigure;plot(t,x(:,2:5));
p=x(:,1:5)
  p/ q0 w- H1 @6 }" D3 z6 ]$ s4 Whold on
! b3 H  o8 T8 B* f; Hplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')


# Z) |; |! O1 ], h0 t* |
6 R8 x% l1 t! F; R4 @+ ]6 V5 wfunction f = ObjFunc7LNL(k,x0,yexp)
* T' i5 R* _" [6 ]2 atspan = [0 15 30 45 60 90 120 180 240 300 360];
' }, y+ W: Z& D5 N' ]3 J8 [[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
) F: C) Q2 ~2 R5 F. N0 L! [y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
5 G) R* n/ _6 _7 h' \f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

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function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
7 \  w  B5 A( |- h9 C6 P& t[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
4 g* g9 x4 v0 p0 @) Py(:,2) = x(:,1);
! ?: a  _) T9 P7 Vy(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
/ T! u' V1 q) B+ y, [7 W1 }    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
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function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
/ ~& _9 G2 s+ n$ ^$ jdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
5 r' b" M5 [, B1 EdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
, Q5 j' B' G  Z* fdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
  f% v$ [' L3 s/ |8 v5 f" n$ Pdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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蒙的一比 大哥
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