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
+ ^. j' x6 g3 ?% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
/ x- q- G* p& f1 ~" @% 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);
( O$ Q8 k# n' c% Q2 \, `+ B%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
8 E4 D9 {' S3 x0 f: ]          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
* g& B% @3 l; f% J8 I3 X          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
2 m4 z/ m" n& q4 `: C8 X          180    0.04488    0.0682    0.07135    0.0091    0.03623
+ _; ^0 a+ y* ^" `          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
: I, B4 c9 K- }+ i; B( U" A          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
( a% H% x) Q2 d1 ]! z; \: `; H! tub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
5 Z- C# X$ Q- d: T; t, C4 B  byexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
* L" j6 M; D# u8 I- w- a% warning off
% 使用函数 ()进行参数估计
5 }9 B/ l6 g' X[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
% R  G9 G) A& a2 xfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
6 s% ]" D' H3 |7 I6 Yfprintf('\tk2 = %.11f\n',k(2))
1 R' `( r2 u8 z6 |- `6 cfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
/ L7 a( |, }3 G& A$ S, W: N( @fprintf('\tk5 = %.11f\n',k(5))
6 u0 U, E: K, ufprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
% o! \4 a) j* i  t; z" ]5 }3 Sfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
3 _3 E4 C8 r, v1 Y6 A; e! W0 Ufprintf('\tk10 = %.11f\n',k(10))
) M% k) N2 Y% y( q/ hfprintf('  The sum of the squares is: %.1e\n\n',fval)
' z: q7 d  }% b8 pk_fm= k;
! D: _0 h# d# ~$ O+ a% 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);      
3 [9 n$ E0 r" x; E5 Bci = nlparci(k,residual,jacobian);
+ V, w- Q/ U( D2 j6 Mfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
; t1 T4 N. b8 |3 P  ]3 Wfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
2 R' e: D9 ~0 ~. ~& s+ Q3 y9 Tfprintf('\tk4 = %.11f\n',k(4))
# z/ \2 U3 ?9 b* \4 A8 Ofprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
/ Q4 n4 `5 z4 b* L" ]- V+ bfprintf('\tk7 = %.11f\n',k(7))
7 T& r" s- e- ~$ J' K! u4 h$ Dfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
* M7 p+ S( P# y, n2 [1 i5 g( Q5 Dfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
' C- I4 o# L, P; N4 U$ A0 o9 gk_ls = k;
( ~$ v1 U" u# P6 Q) U5 j  Joutput
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+ o) n' u- M" A( Ck0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
9 Y0 Y: b* }0 y1 _8 [: e2 z) xci = nlparci(k,residual,jacobian);
' K( H) U( A. Afprintf('\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')
& a% M$ a7 h/ |- I" `0 I2 E9 Pfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
6 ^. r3 Q2 n1 y8 W7 Nfprintf('\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))
1 g! u! d! m+ h5 R: U+ tfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
. c# k+ G' w7 H7 Z; W- u; Jfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
$ Y+ y5 j7 J$ v: Wk_fmls = k;
output
) G0 j/ w, A* `) z" x! c. u# C+ ]- otspan = [0 15 30 45 60 90 120 180 240 300 360];
. a4 `8 N5 ~5 K7 ~[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
& x4 n! n  y2 m' ]1 xfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
! T+ G* f* h$ B  k, R4 Lfigure;plot(t,x(:,2:5));
p=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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- a# Y+ v3 x+ |$ ^6 e- P
/ H: L2 j* }& }9 T/ Hfunction f = ObjFunc7LNL(k,x0,yexp)
9 r1 z7 ^$ \. l$ Etspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
% ^# @/ A' `* Z1 j" p4 py(:,3:6) = x(:,2:5);
# X' w, q' q6 K6 E$ |& h( t3 if1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
# u+ R. @) C6 C; k! r$ U* L, X4 \f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
% ]8 B% O, j1 gf = [f1; f2; f3; f4; f5];
$ R- o4 X/ w# {& @7 q% }3 a

& M" u+ j0 w* ]$ O, L* ?$ D1 a; Y) i
9 n! X" v; m6 l7 M% N4 sfunction f = ObjFunc7Fmincon(k,x0,yexp)
- f7 n* m* f9 R' h1 b+ @! vtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
/ N! V1 ^* o0 |* ~  W; x; Qy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
, X) B* M- w! y5 t3 u+ {f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
, i0 Y" u# g8 U9 G) i/ E6 K% \" S4 \    + sum((y(:,6)-yexp(:,6)).^2) ;

6 I/ m4 x$ A( E9 R- I. I5 P
1 h: b! z; q5 I

function dxdt = KineticEqs(t,x,k)
dGldt = 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);
dLadt = k(7)*x(5);
1 |6 M2 N$ w* U- K; L7 PdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
) I9 `5 n7 n* N3 I( jdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

  f. h2 k8 w2 d, V4 {