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
: R5 @% i0 @% W5 ^% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% B2 _0 W& \" i! v/ U( j6 y3 p% 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);
9 U0 L! V3 j1 s- B& T" }clear all
" f( n/ L% B# |5 Lclc
) H! T+ _: W' C6 S7 R1 I8 R! |" G3 [format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
1 v3 H5 F6 Q& a  Kinetics=[0    0.25    0           0    0       0
          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
          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
) l$ y8 X0 ~0 |7 S$ n( e* d          180    0.04488    0.0682    0.07135    0.0091    0.03623
$ E8 N- E" g7 l; U, [- |3 |7 U$ O          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
. L' m0 F4 P/ k3 W3 d4 K2 d6 bk0 = [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
ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
# ]3 k. V7 Q$ [' Zyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
$ K& Q' ?! i4 J. h$ @% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
0 U; @- }- x2 m9 S# S2 ^$ |, G9 Afprintf('\n使用函数fmincon()估计得到的参数值为:\n')
3 v3 F8 c: y7 V+ f# q7 S- Sfprintf('\tk1 = %.11f\n',k(1))
7 i+ @9 L$ _/ Z( K6 i% ofprintf('\tk2 = %.11f\n',k(2))
- `: Y: N6 ~- R( p7 w5 Ffprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
" `# }" K7 i3 xfprintf('\tk5 = %.11f\n',k(5))
, o# H9 U. i+ k+ Ufprintf('\tk6 = %.11f\n',k(6))
8 `$ P. X- O: p1 p3 l  ofprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
; g& x: a7 s5 \2 C  \7 \. g4 |5 x$ efprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
6 X( \& U; I$ e# S% 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);      
+ S) {/ g$ p" A7 d. r$ V/ Zci = nlparci(k,residual,jacobian);
" S' u/ t$ l1 R$ E* W1 {' dfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
/ V4 [, Z- n1 _5 E* Z) D0 zfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
9 L3 k2 C5 a! B1 yfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
3 d4 j) C3 f' M6 `6 u% Kfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
( b* H& i& M' ^' `. d. R+ t8 ofprintf('\tk9 = %.11f\n',k(9))
! h4 c1 X4 S, I  E) Afprintf('\tk10 = %.11f\n',k(10))
6 F/ _3 G2 Q9 M* gfprintf('  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
; W- |; P& Q' U4 y# v) `( x! H: ek0 = k_fm;
2 q) E/ t4 I: q. H& {: L1 t4 B+ u[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
8 \7 Y, t2 z: Tci = nlparci(k,residual,jacobian);
- q; M0 u9 N3 U9 v# j+ ~; Ufprintf('\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')
4 b$ f, F7 z2 A: Q( K. mfprintf('\tk1 = %.11f\n',k(1))
* |+ Y5 j' X: d* `( Yfprintf('\tk2 = %.11f\n',k(2))
1 V0 ?; Y6 w2 k5 i9 l( S: Tfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
% |9 @! R9 |2 Ufprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
# f% \$ ?9 G2 `  T  }& [( K7 |- ofprintf('\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)
k_fmls = k;
output
8 W! j" n+ q8 r; O4 U+ }6 ?; U* Etspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
2 C1 ]5 O, |! y" hfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
. {4 C! Q- ?' i, B6 Q% G5 dhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')

% P, D2 B! z3 k) c" j5 ^  K

function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
9 _9 I' i+ S# M$ [[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
2 M2 \" y+ W& O% J$ rf1 = y(:,2) - yexp(:,2);
; x$ M% ?: r4 I# a8 F$ [+ |f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
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function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
: \: F$ ]. J1 l2 d3 ~5 p  d. y2 C- Ay(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
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)   ...
# X- r  V! D; w9 N, r2 X    + sum((y(:,6)-yexp(:,6)).^2) ;



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! \+ S1 e, p3 D; }" xfunction dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
/ A6 L+ a1 L) H, N, CdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
0 W8 e4 K" l: r1 M1 c5 y0 r1 FdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
6 b; _" E6 l3 F  f& Z( Z) TdLadt = k(7)*x(5);
1 O9 m+ F( G: p* P/ ?# [dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
/ S; _5 p5 L4 G% T# x
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