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
) K3 a5 ?7 h" V. Q* z7 ?/ _% k6->k6 k7->k7
6 w% @3 P. z7 D  @3 h# T; w% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
6 Y0 R; H# d! A+ ]. B2 r/ [% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
/ |5 G' C- q' C7 ^' b, F4 T3 R% 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);
0 _, |& b* k+ G  _8 X7 `5 Vclear all
+ B0 f4 E- Q8 I& Y( Aclc
  S9 B1 V1 b1 }' Pformat long
/ u% I' O- Q& T9 n%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
1 i6 s% g& Z: ~. {2 B! x6 [; l. }  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
. w, c- P1 U5 q9 H6 V& y          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
          90    0.08115    0.07877    0.07485    0    0.01405
) v- I) o+ Z6 h          120    0.0656    0.07397    0.07885    0.00573    0.02143
. ^7 s- M! i6 M0 {6 ?          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
4 F4 ^, g/ @/ C* S9 ^' o          300    0.02738    0.05448    0.09098    0.0227    0.0597
( j; b  w7 g1 K! Q& P          360    0.01855    0.04125    0.09363    0.0239    0.06495];
k0 = [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
- W4 P2 M) u7 sub = [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);
fprintf('\n使用函数fmincon()估计得到的参数值为:\n')
2 `9 Y2 f' g" V/ d7 J4 ofprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
0 H3 ~' }% M7 H- P9 yfprintf('\tk3 = %.11f\n',k(3))
# s- B: _) }5 q2 \fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
( w; ?' @9 @4 i9 Q) |fprintf('\tk8 = %.11f\n',k(8))
% A( `- n) Y9 K" G: I0 vfprintf('\tk9 = %.11f\n',k(9))
. V( I8 ]. A. e' J- Q) ]7 N2 W4 P* yfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
4 b: p- t8 G  s5 h7 _. K# _6 i[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
: v5 ^! k* @; g( G6 Zci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
  G# ]3 Q& Y  c$ {fprintf('\tk1 = %.11f\n',k(1))
* P" W9 F( ?6 Lfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
0 M4 c( x3 r& ^fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
5 G) Y& Y: Y/ B; Gfprintf('\tk6 = %.11f\n',k(6))
- S9 ^- ]1 o+ y- j) ]3 `$ P5 m9 }* pfprintf('\tk7 = %.11f\n',k(7))
( J1 \8 W5 ~) d! i  L) _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)
- O9 Q/ y4 Y) d0 V: ik_ls = k;
output
8 I  @9 u9 e& X4 L, c: Fwarning 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 i4 ^* [' |6 a0 v[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
! Y  O; T+ m0 J  }9 fci = nlparci(k,residual,jacobian);
3 T; d$ ]! m5 f4 lfprintf('\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))
) k+ }  `9 i6 I# H- T$ lfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
. V) [9 ?6 u; q1 K8 m3 X1 rfprintf('\tk6 = %.11f\n',k(6))
& T- x) d& l9 Y: mfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
: R8 z- @$ Z# b; U" g( _4 u, bfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
4 A  i" ?! ~4 s% N7 Xfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
* f% g) ^; Z! |k_fmls = k;
output
( y' ]) B. Z8 X1 h$ g  Qtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
0 d) y/ L  y+ ^$ W4 |plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
& q# j: [% Q1 _2 w9 D" Dp=x(:,1:5)
hold 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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" r& q/ h1 h4 wfunction f = ObjFunc7LNL(k,x0,yexp)
% J2 n2 _* _( o* }% d& \tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
3 ?8 b% r% N2 z$ f5 ~f1 = y(:,2) - yexp(:,2);
) k; f! i5 I) mf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
5 q; [' s# \; N6 r* K! s1 Nf4 = y(:,5) - yexp(:,5);
. a* [: e8 E9 c5 P; X" n! V$ m8 w! zf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
/ j* ~! o' J. K6 @/ I# r% [
! L. ]% n. [/ n: B, Z4 M3 k

3 j9 V) C& {; F! Ofunction f = ObjFunc7Fmincon(k,x0,yexp)
7 R" T' X; i, C3 z1 w2 p3 r& [tspan = [0 15 30 45 60 90 120 180 240 300 360];
, F$ J. \: u8 A+ N+ l1 ~' S[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
& K. Q: l0 E2 P6 v6 @% `y(:,2) = x(:,1);
, U9 \; A: X; E' f. Y  ?8 vy(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
' J6 q" k1 I. i7 r+ E    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
; F5 p# o: N5 i1 f0 r8 e, I
$ Y6 Q7 ~/ h2 o0 O7 s. [8 o1 s

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function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
% d3 x) }7 L% @dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
! e6 q& U& q8 B# C; {2 HdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
' d7 t$ F  W  C; Y! ^( _3 T  bdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
. O, C* \8 J5 W) F1 wdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
) v+ b3 P1 Q, P; M! M

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