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
6 c9 X& K. S5 ^8 G9 W$ V" ?%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
9 ~* n& t, D/ x9 G. Y4 j% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
8 ]* x2 l, p  z%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
% j! P+ r, V4 o0 t/ z9 U* {( p4 iclear all
clc
7 T. L: E3 J8 m1 H- |$ Jformat 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
7 r, P- F3 T8 Z5 m          30    0.19345    0.027    0.00868    0    7.00E-04
, q6 O: h7 ?' P. h( L5 c% {          45    0.15105    0.06975    0.02473    0    0.0033
# X5 f, i/ X; c; k6 V4 T% P2 {          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
" i0 ]3 u/ Y7 a7 _* G# d+ A          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
, l" Z$ K/ g: G          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
7 n, R7 {6 D& R  a2 r          360    0.01855    0.04125    0.09363    0.0239    0.06495];
: A! s1 _( H: S( ak0 = [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
5 _$ |, Y/ r0 m: q  S4 @ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
# [9 w2 f  V4 s- _/ G# Mx0 = [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')
: x9 U5 a3 M' \" i  s$ E' D3 yfprintf('\tk1 = %.11f\n',k(1))
( r6 V8 }! Y) t0 l! @/ [3 n% V3 ~/ \4 Pfprintf('\tk2 = %.11f\n',k(2))
+ M1 v% N* n  O2 t. Efprintf('\tk3 = %.11f\n',k(3))
5 Y# v3 v0 w6 j' _5 G6 Ffprintf('\tk4 = %.11f\n',k(4))
* f& f. x9 L  A! P* Efprintf('\tk5 = %.11f\n',k(5))
9 c+ l8 s% o6 @) c, `! |1 Qfprintf('\tk6 = %.11f\n',k(6))
/ w* n( |4 h* Y0 ~( }$ u9 U, ~# dfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
% s; P/ L! @1 ^- v, g& J; Pfprintf('\tk10 = %.11f\n',k(10))
1 H4 r( @3 I+ t0 V; o% e* Kfprintf('  The sum of the squares is: %.1e\n\n',fval)
; C/ N7 X6 _0 A) p5 Nk_fm= k;
% warning off
( W! Z5 N9 k0 T$ ?1 s3 }8 y% 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 a6 e  Y' m9 {  F# Gci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
+ n  K% f6 w, }6 Hfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
* J1 |' N1 p% d/ tfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
/ [6 ]4 i  u9 }  e3 e- X0 yfprintf('\tk7 = %.11f\n',k(7))
- \2 h3 V  O. s* l: {# Qfprintf('\tk8 = %.11f\n',k(8))
% B# c$ t) y% cfprintf('\tk9 = %.11f\n',k(9))
: f1 J- h9 r/ C7 r8 ~! A' j# w, Nfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
& Q2 g+ t, k2 v- J3 {5 ]k_ls = k;
1 N' g/ H# S& ?; Youtput
0 J# p+ _" t% d7 F) L' w2 v% f/ Mwarning 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
: E8 K& R$ u7 j, f0 r3 Yk0 = k_fm;
: S" g, }+ w( S[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
* a) T2 K, x; ^! k4 g; y  Q    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
. x7 ]; s0 x  m6 Nci = nlparci(k,residual,jacobian);
$ o! n; u- s5 w0 N4 q0 ~* M9 Sfprintf('\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$ c. V$ O; M; c: Ufprintf('\tk4 = %.11f\n',k(4))
7 v  l. Y* I9 A' E8 sfprintf('\tk5 = %.11f\n',k(5))
" L# e# A# D; }( B, i" }! ?fprintf('\tk6 = %.11f\n',k(6))
2 `2 T4 _7 |, l6 |fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
, W5 L0 a! x8 D+ e' l6 _fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
( x' F( W' R1 A2 O3 x6 \; ?8 r0 `3 M' ok_fmls = k;
. V' u. ^$ D7 g$ |2 N. toutput
. i% c5 T7 S8 I4 Q* V; ktspan = [0 15 30 45 60 90 120 180 240 300 360];
! k8 g  Q; X/ H& Y: l# F[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
1 R+ @' n! K$ aplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
, d* I+ s5 K' h5 t4 J9 pp=x(:,1:5)
hold on
& z0 C  P8 E+ r8 Gplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



4 ^0 V) ~3 G9 s% X) e$ q! Tfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
, y3 P1 V5 J6 p* K6 Wy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
: V+ z+ f/ H( tf1 = y(:,2) - yexp(:,2);
8 K3 q4 O: B- [, p6 qf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
/ e2 F* d7 D$ b5 s1 qf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
6 v9 q& m* O( |3 n+ S/ Lf = [f1; f2; f3; f4; f5];

8 A; q: c- ^$ a" }  S3 U3 C' {

1 i4 V( l3 j7 D9 s2 P" ifunction f = ObjFunc7Fmincon(k,x0,yexp)
2 x, P7 j, S: vtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
- M- q4 j+ Q: c/ Dy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
) K' B5 X/ v2 r. o3 q3 xf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
9 f0 u* n+ \" ]  Q# j    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
& P. d( T' `7 Z) P  m4 p0 z    + sum((y(:,6)-yexp(:,6)).^2) ;


$ g- U* u# ]$ d7 s2 C# }
# S. P6 U9 l! y1 v8 }- U
; d' e" `( C0 _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);
( L; L( }9 c' wdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
) w5 u6 x& N( \* hdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
4 _# w# U& S! J( i: e! K  o' m0 a