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
% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
; |& v6 @: t$ o) T% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
' u  l: g, B; N$ b% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
% W  G! L$ l7 r1 D- P' g%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
1 S. u0 a+ r: _" z1 n! i/ }format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
) x' t8 F! Q, |* o0 B( H0 \3 l/ d  Kinetics=[0    0.25    0           0    0       0
/ H$ j* K4 _' Q' L5 n# U* w          15    0.2319    0.01257    0.0048    0    2.50E-04
' \5 g* z4 E7 a8 v, }3 \: ?# S6 H          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
$ P5 r+ }/ j; a- p9 f7 I5 G& k4 C          90    0.08115    0.07877    0.07485    0    0.01405
4 i7 x, E, p: q          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
# U  U" o. y; q$ ~3 M4 A' w          240    0.03653    0.06488    0.08945    0.01828    0.05452
: n& \: u6 b1 c, K6 W; t          300    0.02738    0.05448    0.09098    0.0227    0.0597
+ O: `* ~" X* }& w8 r" {          360    0.01855    0.04125    0.09363    0.0239    0.06495];
* G2 R" Z8 ]* O1 Uk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
# ~  W0 P3 U, @% Z. Elb = [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
  D4 p: T% g+ U: }7 l1 m+ _x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
# P  N) S; \  D* v- K. X% w% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
7 m* C" O8 B. e" \6 H& ^* lfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
- W) X& `  V0 n% W( xfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
, H! I! T7 M4 R3 F9 I" Hfprintf('\tk3 = %.11f\n',k(3))
6 O; e- N2 ]6 n2 d: ?" C7 m, mfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
: d2 M% c' b1 G, i8 c9 J6 C: Tfprintf('\tk6 = %.11f\n',k(6))
/ Q1 l: ?. [& f0 l/ A0 hfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
, V% I; h; ]  \/ ]' ifprintf('  The sum of the squares is: %.1e\n\n',fval)
4 `' I+ v* |; k" j2 N& Xk_fm= k;
% warning off
6 T4 d* k  d' a3 T, E8 {: L- K8 s% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
6 B6 N! @3 m2 _! S) i2 `    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
0 y* [( Q* ]. M$ V( M2 F7 \fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
) X7 G& S, P3 Q* s. K1 Q3 zfprintf('\tk1 = %.11f\n',k(1))
0 Q9 }" m& i: C' r5 W2 Ffprintf('\tk2 = %.11f\n',k(2))
7 g8 g9 h- x) m4 ]fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
) p7 o* |' \6 w! |& s, b' Ifprintf('\tk5 = %.11f\n',k(5))
5 P; r  y. A  Ufprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
# n7 p- j7 _+ E( C( V; u5 hfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
/ L5 P3 o, w% K4 l2 w7 Sfprintf('\tk10 = %.11f\n',k(10))
7 }) E. T$ W: l! I6 Gfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
) Q9 o2 o. A. V+ v/ A/ M( V8 @k_ls = k;
' @5 l: X& J, r! y% V3 zoutput
, D* v9 k' _4 b+ Q9 Gwarning off
- O3 m, V* l* I* ^4 n% 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
' r1 w! D0 ]3 p* S2 B9 K& \0 ek0 = 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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
2 l8 g  P0 ]9 d( ~* wfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
; N8 t8 A( H2 K9 Ifprintf('\tk7 = %.11f\n',k(7))
( U, n6 l) V/ `! B8 t* G1 Zfprintf('\tk8 = %.11f\n',k(8))
( N4 I+ I! q& d% E6 [fprintf('\tk9 = %.11f\n',k(9))
3 e" J5 W: R0 l& Yfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
' h0 E8 Z9 P" g4 Tk_fmls = k;
1 R8 O% U* x4 Houtput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
3 i0 h2 \9 D9 f) I[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
: ]+ _0 C' g8 a7 p1 Mfigure;
$ I1 a6 Y5 h# N: uplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
8 E7 ^3 G4 Q, F- D& Zp=x(:,1:5)
  @1 D5 I1 P0 Nhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
3 y. j" D5 y$ A" L- c7 I3 o
: a6 a# p7 O/ Z9 d" L! k$ W; b

function f = ObjFunc7LNL(k,x0,yexp)
' H/ U9 r: I# D# l: E( stspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
' d  h$ ?$ t# {+ j# v* N5 B& iy(:,3:6) = x(:,2:5);
5 m) I* ]( u$ Z0 ^5 B9 if1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
8 b3 w8 S" L9 x; @& \f3 = y(:,4) - yexp(:,4);
3 X7 r% B1 Y7 S7 w( H# \( ]f4 = y(:,5) - yexp(:,5);
) h0 s8 E* E1 G+ L" H4 h! D$ Rf5 = y(:,6) - yexp(:,6);
9 w( G9 _% P% d+ l5 uf = [f1; f2; f3; f4; f5];

. o/ n) @- @+ \4 E% @8 S

& V1 U% ~3 B1 H/ z9 Y" Xfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
: u# S- f! {$ y6 y1 Xy(:,2) = x(:,1);
4 p3 r0 ?$ D! @. Yy(:,3:6) = x(:,2:5);
' i0 o. ]9 M# x2 yf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
$ E( s: @: W; C# f0 p6 C, ~    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
$ w; [5 ~( ]# D, k* x    + sum((y(:,6)-yexp(:,6)).^2) ;
2 Q5 g3 `+ K% f; h: ^
$ o  s% ^6 V- Z  `+ C


) k) p4 F& w1 _8 o2 a6 Wfunction dxdt = KineticEqs(t,x,k)
! Q9 D) |1 r, M( HdGldt = 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);
9 f& L+ p* j0 m  s4 RdLadt = k(7)*x(5);
, {* u$ \/ J" I/ U+ `' w) @& zdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
1 c0 C. m0 Z6 _  o3 ddxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

- p# v$ T. R  c% g7 P8 D$ h