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);
1 i& l1 y$ s( T) m6 }  d! T$ H% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
* h, l) w4 v- c* A$ M0 n* Y' ~( i% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
2 J2 S! L5 q5 [) w* N9 M3 l2 M2 H%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
- G7 n: a% f3 W' C1 ]0 zclear all
' S2 W2 v1 _$ I& Q* M! Jclc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
0 v. K/ E2 ?% c) X2 J          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
, M; t  B( ]9 E* r: ^0 l4 w          60    0.13763    0.07397    0.02615    0    0.00428
4 b( a& `* C( o$ u  @+ L% A          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
6 d* `/ }& x% c( h. b; O          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
/ R; O- T1 J3 f) |" t1 T8 |          360    0.01855    0.04125    0.09363    0.0239    0.06495];
+ [. g( a' W4 P2 U% D/ Pk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
5 n3 o; g! P5 H9 ]/ p& C# c0 rlb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
' m" l" m( K5 t7 A% Oub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
7 e2 x% h6 J$ Y& Q$ `' e7 d( t# @x0 = [0.25  0  0  0  0];
# [% r# z" j( E; d0 Q( J7 Xyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
/ T0 N* E" K% ?$ B8 S7 i% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
( l2 l% o$ i# g/ g: }) ^8 f7 Rfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
5 S; \0 `; W) m3 P& Dfprintf('\tk1 = %.11f\n',k(1))
: n4 n/ {/ w4 h8 Gfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
) |- h- V0 l: a2 \9 Cfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
# i$ R8 Q* ^, [7 [# Ffprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
( Z/ d$ d' P$ s% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
  v9 q; l% A4 O9 c& H' `    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 f5 K/ J, E7 ?( yfprintf('\tk1 = %.11f\n',k(1))
  t! Q# n% l8 Y" G, mfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
! ?7 S# s0 J. S5 R, u& bfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
* x8 I5 [0 C+ ]1 j9 M3 w3 Z+ ~8 J$ Lfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
$ t5 `0 v7 L6 E: F. q4 S- U" m8 H0 jfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
6 _: E6 o/ w2 f+ m9 l" q1 Y% j6 Sk_ls = k;
* d& z, e. V1 q& ?. M$ _) C: O- ioutput
$ k7 Q; t! e/ B* @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;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
, ~1 T8 O* N( p3 t4 Y% a    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
# b6 w4 L( s6 q* Y4 n1 }, V" Qci = nlparci(k,residual,jacobian);
! m; m% F4 e9 o$ S, D3 f6 rfprintf('\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')
+ \: Y" P7 E7 }2 p! Y4 yfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
: T5 L+ e2 u$ |3 Y0 Pfprintf('\tk4 = %.11f\n',k(4))
8 Q* u6 A( [* Sfprintf('\tk5 = %.11f\n',k(5))
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))
' ?" \) I) G8 u9 pfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
" t* l, l5 {, u  g$ {  p# y4 P% D% u[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
1 s$ A' x. Z, tplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
9 ]% ?  p. K) G2 N) ^) Gfigure;plot(t,x(:,2:5));
. p) o$ H3 L7 C$ w( r# p% u9 D& K/ vp=x(:,1:5)
2 l- G, m, U: T% G5 }& b8 _- t3 bhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')


' c4 \) T, _9 N0 C0 b
6 v( I7 ?4 J+ j+ Efunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
# q, [& m! E, ?3 r* p1 U2 `9 D[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
- v# o% s5 O) q, @y(:,2) = x(:,1);
2 Y. ?' T1 v, }2 my(:,3:6) = x(:,2:5);
2 s7 K" R3 v, Jf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
  m5 \5 o' v9 E, l: K) m& }f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];


& r9 O5 t8 b# W) U3 g5 e5 [
$ s  s9 e7 g9 A3 o9 afunction f = ObjFunc7Fmincon(k,x0,yexp)
" F- W- V1 ^) atspan = [0 15 30 45 60 90 120 180 240 300 360];
" P1 ~, e) X& P: T1 k% f: c) X$ d[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
9 Y% m% p/ M" ]8 f  P, hy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
; h# a+ f1 J0 g+ yf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
4 D7 s! |  @8 Q6 C. n7 ]    + sum((y(:,6)-yexp(:,6)).^2) ;

3 o+ Y2 O& {" w( a- O
# Z3 g+ `6 M, v; P& h

: C+ J: N' z% [) L, |# wfunction dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
+ i0 u! ^1 S4 z: edFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
( j: D: d/ y0 d- p% B! G  W6 m5 edFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
7 a( e" L9 f4 E4 T6 v+ L' TdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
" j/ t+ e3 ^& L( S8 n8 Bdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
/ N" K3 ?2 t+ _. C. U( E0 ~1 x! x
; J) b  Y  r, V9 f