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
' I1 L' \" I' P" B* h! Z% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
! w0 ^+ s* M' M% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
  y' D4 \* N( M! M) ?: }" O/ [% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
5 f) T" Y  a5 F- u- U) X# ~% O%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
" D5 ~, E5 P* i& b+ \$ lclear all
7 U8 W* w3 _$ t' D' x- K1 O6 D2 w: lclc
/ J) @" w: V% G- ]format long
( {( B/ X- @, ?% j- [%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
, I% _! A/ E( M7 ]2 i8 V# n  Kinetics=[0    0.25    0           0    0       0
+ C! I$ ^* ?* `; M2 A          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
7 u4 R( ], H* \. q4 O7 M          45    0.15105    0.06975    0.02473    0    0.0033
; t% K& a9 y  z! b# `- o0 D          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
: ~$ a9 _. ?/ T; n, b. d8 g          120    0.0656    0.07397    0.07885    0.00573    0.02143
6 m/ ]' [3 o1 H+ L# o; O# h) |- J1 m          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
7 D; h( J/ Y$ a) `( M2 v# ]          300    0.02738    0.05448    0.09098    0.0227    0.0597
& Y8 q: H) p7 Z& r6 y' I  @          360    0.01855    0.04125    0.09363    0.0239    0.06495];
2 r7 M5 B3 K9 ]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
" F* I2 p2 X6 z; a4 X1 o" ^lb = [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
' H9 J- x4 X# v/ b7 l( N5 mx0 = [0.25  0  0  0  0];
$ q8 E: N8 y- |3 \# ]7 x9 ]& l/ E; h9 Xyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
) k* b; n, ]& ~( X) B) W+ H% warning off
% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
6 ~+ E; |, K2 k" p: U$ h7 Dfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
* o0 K, R4 z2 p6 W% V$ X/ @8 A) Nfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
- G* e( e! ]8 M8 [0 M5 wfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
  x: p0 I5 C2 V) m9 C0 q- {: Cfprintf('\tk5 = %.11f\n',k(5))
* H% O' E+ K! d7 e- Dfprintf('\tk6 = %.11f\n',k(6))
2 _" q: V, x  kfprintf('\tk7 = %.11f\n',k(7))
0 I5 _7 z& K" d6 mfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
3 d: R" V  O4 J/ ?fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
( Z2 o# t4 v% A0 jk_fm= k;
% warning off
1 b+ b( _% ?4 C7 @6 j% 使用函数lsqnonlin()进行参数估计
0 }# I1 y3 J, Q' ]& a0 D[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
) o- q0 Q: b/ |, r; @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))
9 s: H) n9 t2 G% mfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
% j6 w# K5 i  k9 b# P+ @. Ofprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
5 x: P0 _2 K1 e# Hfprintf('\tk9 = %.11f\n',k(9))
# D  o4 e) J+ f- t, wfprintf('\tk10 = %.11f\n',k(10))
. O( f; W& \/ r, h- X/ g3 `fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
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
# k& t* x  e$ ]: E( U  j" Mk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
: M3 J5 Y. H1 R6 R. U    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
% |/ _( y  v: |0 D( ]6 dfprintf('\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))
fprintf('\tk3 = %.11f\n',k(3))
, ^! G) |, R5 D3 mfprintf('\tk4 = %.11f\n',k(4))
3 |/ O, R+ R# h3 c. kfprintf('\tk5 = %.11f\n',k(5))
. l4 D# H8 U1 l7 U! ~fprintf('\tk6 = %.11f\n',k(6))
; p' e$ F6 Y; I  L$ B1 ^7 R; Ofprintf('\tk7 = %.11f\n',k(7))
5 \" G5 ]" M, R1 y# Yfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
0 z5 q9 G% I* E# R) {fprintf('\tk10 = %.11f\n',k(10))
( ~  ?: Q8 z6 b$ {! nfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
1 S- I/ X# R# z4 R5 Yk_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
) n' I) E. V" G9 tfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
+ c) x  ?" F& D5 e$ b. jp=x(:,1:5)
hold on
  E) f4 A# f9 ~4 jplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



  C2 L$ }+ ?* F9 ]7 d# Y* y. Rfunction f = ObjFunc7LNL(k,x0,yexp)
' [; u5 \: t- ?1 Wtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
7 T# Y  c) n/ o8 H8 ey(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
6 E9 @. p1 l! }; S; V. bf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
' }( ]. g& m6 x: hf = [f1; f2; f3; f4; f5];
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2 G/ o$ N* N: T0 D: J2 A8 M- efunction f = ObjFunc7Fmincon(k,x0,yexp)
# F; {+ ^) J* t4 ytspan = [0 15 30 45 60 90 120 180 240 300 360];
4 k( x5 B" V, O& i. F, `7 r- D* w[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
& r; w( a- d: p, n0 h) N& S+ yy(:,2) = x(:,1);
1 N* M6 l# I' @y(:,3:6) = x(:,2:5);
- H0 e# E! U. e1 f- }f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
) z' M5 m' U5 B% s    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
/ _$ k- f/ t4 E0 X* l# u* b" d. W8 v. ]# b    + sum((y(:,6)-yexp(:,6)).^2) ;

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4 @0 G/ t5 `, \
6 J7 i& Q3 |8 Z( Cfunction dxdt = KineticEqs(t,x,k)
4 ~5 `+ g' E! TdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
$ K6 P5 J" q  K! wdFrdt = 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);
" P: m: A7 i9 ^0 \dLadt = k(7)*x(5);
6 O" }+ P+ w. v/ X3 A! L) ZdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
2 y$ I8 j# j. ?* T4 _. `dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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