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
7 N/ v/ s6 S# n3 s8 {0 U5 ~( `; w%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
2 a- H! {5 ?' x5 e2 y% k6->k6 k7->k7
1 f9 m0 `3 d+ u+ E$ D% H% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
9 g, p( G8 s7 H9 j2 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);
8 ^6 [, K0 @4 T( wclear all
2 i6 Z3 j+ i8 P0 Y- qclc
$ F& \$ b. X- c. K8 @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
          45    0.15105    0.06975    0.02473    0    0.0033
& p  D& k  `5 T8 _          60    0.13763    0.07397    0.02615    0    0.00428
  F+ k" _5 l; A, f5 C# Q          90    0.08115    0.07877    0.07485    0    0.01405
# k5 x$ N9 R  A, `0 M$ e          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
( R0 K: n0 L, X9 y6 u5 ~          240    0.03653    0.06488    0.08945    0.01828    0.05452
2 g  f, o8 \8 `- \          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
, z9 C; L0 n; h+ F' D' t. T- dk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
4 |  ^( j( t" J) X. `5 d6 C% \  ?lb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
6 W) `6 ^. o! @6 d( Hub = [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
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
/ W  ^& M/ z# K( Jfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
  D8 S: i( \; K" v4 ~: _; y  Dfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
( N  H6 f, t7 ?fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
1 {; Y( {9 n# Q1 Y: s# d: Efprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
: U8 M: l& V  R2 S, Vfprintf('\tk9 = %.11f\n',k(9))
# N$ u8 a8 L6 f$ @fprintf('\tk10 = %.11f\n',k(10))
2 a$ n+ M, P5 A1 P8 D! ?fprintf('  The sum of the squares is: %.1e\n\n',fval)
2 P! \. O! K: K2 xk_fm= k;
+ ?. [& G* I, D* p7 M3 N% warning off
6 X+ a+ T/ L* E/ j% 使用函数lsqnonlin()进行参数估计
5 ]5 t  _/ ~$ w/ l5 l. l2 T[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')
5 N6 f& H' h; V$ F# n2 [fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
3 C4 N% `* ~" M2 ~2 Wfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
4 K5 ]  X( `3 d2 d# d; K# Cfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
" m; v. X% E8 T* C5 `fprintf('\tk9 = %.11f\n',k(9))
& w% `- ?: N0 v% X! r' t$ A: }3 ffprintf('\tk10 = %.11f\n',k(10))
7 x' K" V+ f/ Y0 _- z8 _6 T, dfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
1 S) e7 r& x5 B; y2 d" l4 foutput
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
0 Q2 z8 @3 [8 vk0 = k_fm;
( r! H5 `. `3 z( J, g6 W4 }/ n[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
) U$ b7 I! `6 q5 C/ d0 _ci = nlparci(k,residual,jacobian);
; @: p- N* {( B+ z( v8 W$ Zfprintf('\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))
7 Y! ]3 n$ ~3 m- zfprintf('\tk3 = %.11f\n',k(3))
$ o$ J0 ^- c9 y+ i" Rfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
7 D( v% Y5 z* G8 M4 Z) ~6 zfprintf('\tk6 = %.11f\n',k(6))
9 E8 g( T4 t- U$ Ufprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
- F4 \# T  M2 }8 A. _& m) Vfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
$ F7 z4 j6 A6 s, B7 Y6 Q3 Routput
, U5 {. q  a+ }4 Xtspan = [0 15 30 45 60 90 120 180 240 300 360];
" F8 K5 }( @( x* L6 V1 {[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));
1 _0 b4 H7 C( T3 a, H6 L8 o; X0 dp=x(:,1:5)
, }6 v& i' J; m; s+ d  C( Fhold on
3 w' g( E) H: x( E( @; l0 Bplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
# [8 O! z5 c, `7 c
% G9 F' g+ u3 c5 f
; a9 B# H( z& j* j
( u( T2 F6 C9 }( efunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
- {1 g, Q0 ?! |  u+ s3 X; ?1 R[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
' P+ f' _" m, W6 _y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
/ s6 a0 N7 m5 of3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
, _+ F; @5 s0 Q$ f


# m+ r; E4 s/ B; V) l  m2 {function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
4 x% y& T  @7 B- [6 n' fy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
7 I& S' z: j  O9 x9 ]8 f. ^+ h( ^f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
5 t/ Y* b. o' @7 G    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
2 j1 D- R2 H+ Y) j    + sum((y(:,6)-yexp(:,6)).^2) ;
% A3 \- D' b+ Z( N7 d


# H% S% ]( J1 z. b  h& @
$ f" n' w1 C5 u" q$ P6 C6 Xfunction 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);
6 }% d5 d9 |5 e/ YdLadt = k(7)*x(5);
8 q( }2 a0 {8 p0 \dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
& R: ^. r; k' Z9 j8 {& B" z+ y

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