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
- E- Y3 W6 p. ^! U8 [3 N7 }% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
" }, r. [+ H% h0 w% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% 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);
clear all
4 g' x+ Y8 l6 y6 o; z4 ~clc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
$ D+ n- z4 Z) x2 M, j7 N2 m3 Q          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
" r. R8 M  ~% N          60    0.13763    0.07397    0.02615    0    0.00428
" H6 X' \3 z/ u5 K          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
+ N2 U4 [+ L0 {/ u! U  j          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
' d4 L0 n$ T) f$ k          300    0.02738    0.05448    0.09098    0.0227    0.0597
9 b) s6 S- l7 l# z3 W, i  p          360    0.01855    0.04125    0.09363    0.0239    0.06495];
; u8 I* k* Y9 u$ z" r; 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
  v3 P5 Q! l1 Q0 m/ Q: Clb = [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
, F. l' K2 v/ `7 j% N5 b% }% Ox0 = [0.25  0  0  0  0];
* M* j8 E2 [: M  x" r% ]& Ryexp = 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')
- b: l. u* R- v0 x4 u4 S, @fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
4 d; `8 t: y9 n2 d, N8 P7 gfprintf('\tk4 = %.11f\n',k(4))
2 D4 D- g* D, V; ]1 \' `fprintf('\tk5 = %.11f\n',k(5))
3 z, `7 `, R# e5 h' `3 Tfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
5 H6 g/ g6 s& ?fprintf('\tk8 = %.11f\n',k(8))
9 K  x! O$ D( z6 P" Nfprintf('\tk9 = %.11f\n',k(9))
- {% X, B# ?# Qfprintf('\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
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
$ k" B% M5 S# |ci = nlparci(k,residual,jacobian);
fprintf('\n\n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))
  I* {; k0 ^3 t4 W% \3 x! n) o; T- @fprintf('\tk3 = %.11f\n',k(3))
: \' p  t, {; q, F6 Lfprintf('\tk4 = %.11f\n',k(4))
3 h$ ]& }* m0 x; qfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
: C% k, z) T7 n# mfprintf('\tk7 = %.11f\n',k(7))
# a, n: d0 O  z5 M: j$ z) o  [fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
; Z4 w; i% k2 D& W- v: J8 f% W4 Z1 }fprintf('\tk10 = %.11f\n',k(10))
' G; Y2 q3 D/ Q" gfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
+ W- w/ I! Y3 m* dk_ls = k;
1 A3 g1 p' A2 y+ z! k. y% ^output
$ S6 u9 ~/ S* [5 V+ \' b1 ewarning 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
; a, ?' b, c- O4 v5 R8 \' Bk0 = k_fm;
% T! q% i/ a! A- y. x' @[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
) Q& `9 a$ m* h$ w% W    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))
, A- p/ o0 a. F( M( d* ]( {fprintf('\tk2 = %.11f\n',k(2))
* u+ Y- I4 c2 |9 efprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
2 t6 o! y( L7 _/ x: Afprintf('\tk6 = %.11f\n',k(6))
* u2 D& K% ]6 J* w2 x2 z: xfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
6 W0 Q3 d1 [0 W( Mfprintf('\tk9 = %.11f\n',k(9))
, m$ s8 i' w6 a+ b' [fprintf('\tk10 = %.11f\n',k(10))
5 @$ @: \0 m. X/ b$ Rfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
* ?0 C# a- G# _+ Vk_fmls = k;
* m9 @* x3 l% I; eoutput
* L4 C! v, n7 F* h! ntspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
/ Q0 ]7 `& Z5 B6 r+ _; ifigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
5 A8 A/ u6 a3 D$ |p=x(:,1:5)
, o7 O$ H2 J( T1 mhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



7 c6 _% b1 g, q5 [7 Pfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
: h( k0 N2 O/ o& f% L" G[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
6 P: w6 l' ^/ W; q4 R! H" Qy(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
: c3 L. w# P1 m. R, |* d: gf2 = y(:,3) - yexp(:,3);
% V% }6 W7 @; w3 x% Z) {( O- Tf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

$ E* J8 t" ~( [* U' @( d

6 {8 }' O  c% M) Efunction f = ObjFunc7Fmincon(k,x0,yexp)
$ k8 b4 R, j. h$ v3 Xtspan = [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);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
  _) m- ~3 Q- t1 s6 @. m% [    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
6 q% b( S7 X' p1 C    + sum((y(:,6)-yexp(:,6)).^2) ;



( P) w. k3 j+ r; ^
8 n9 ]# v* y1 C9 _  q" C  C5 \( Dfunction dxdt = KineticEqs(t,x,k)
- r5 w# X( }2 N- V3 |dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
5 d- O& T$ w& J+ ]2 b3 l; AdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
. g7 }8 h  Z7 s6 @* U3 \- N8 O8 A1 @dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
- u  s. u) W) {) L% d4 ~dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
, k$ |# S" L+ l, s. @6 A
4 B1 ?$ ]: c9 ?) M- b9 a2 h6 \; m
2 T1 K4 |* L1 L( k+ i4 M