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
/ U* C2 F: _; ?3 S9 g- a# c% k6->k6 k7->k7
3 G# d& O! [, d) F5 b7 n% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
/ b0 B7 W1 K1 e( o1 n( J) r5 m. C% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
  p3 }0 L; W5 H. c% x: e4 d: M% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
0 i( l4 q- e9 G# Uclear all
' @) _- o% p% ^% Z. b6 u+ ~0 Rclc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
6 r- _" W7 s+ ^+ X/ T  Kinetics=[0    0.25    0           0    0       0
3 u8 z- y9 Q7 V4 q# E. H- b) v5 m2 L          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
2 X4 T% s% ?( L) L7 p' F7 M          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
0 V5 }9 f7 o( Q7 v! H5 H0 x) I          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
          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];
& s8 a, i1 ]. Fk0 = [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
0 w, P1 e8 Q% ~( @" H+ P1 l. o, F# o) Ix0 = [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
; c2 G1 v. Z/ d, X# C% W[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')
fprintf('\tk1 = %.11f\n',k(1))
& s! _1 t1 l) }$ p5 R5 A! Tfprintf('\tk2 = %.11f\n',k(2))
5 a/ \: G8 k3 F$ y; qfprintf('\tk3 = %.11f\n',k(3))
/ f1 e" ?' \, B. pfprintf('\tk4 = %.11f\n',k(4))
- E, b; c- e) ~fprintf('\tk5 = %.11f\n',k(5))
6 j1 X( a0 _+ Efprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
  |9 Y0 F' ]1 n  \fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
7 P; N. _0 s& D# _1 Yfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
) u* I6 \; ^% v& J( D% 使用函数lsqnonlin()进行参数估计
1 K# L( X9 Z5 E" v2 K; ?; A) I[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
* y2 V  T% i8 u" T% A( \0 U% ]6 f    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
1 s6 X! o" f5 I5 Bci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
; X  @; N7 O3 E6 H7 f& Rfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
  j" M6 z$ F+ S9 u( Ifprintf('\tk7 = %.11f\n',k(7))
fprintf('\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)
7 G! V, j; t5 M4 N! \, z/ ?k_ls = k;
! D0 j4 w* h5 S+ foutput
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
k0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
/ n5 X; i: i+ B# @# a8 q" P2 q2 o    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
# c3 |- v9 Z7 s& s4 `; F; a/ Lfprintf('\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))
6 I! I6 n2 q. E7 j4 L4 |) F0 Nfprintf('\tk3 = %.11f\n',k(3))
4 ~$ U" P* ?) X! {" J! I; N/ ]fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
- z$ K! J9 ?& D# nfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
6 L2 w( f' R: F8 q2 tfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
" V. `, L* Q" s4 Jfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
: [6 p# ~8 [. _0 \! Gk_fmls = k;
1 b( }% p& B2 ^; zoutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
) h4 }- ~0 e5 O  t+ V7 T% }  o6 U! ofigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;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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8 j! z& P: e8 ^8 l, P6 ]3 ?function f = ObjFunc7LNL(k,x0,yexp)
$ c% P$ Q8 d9 G- h; {" W# |tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
+ W, q6 H" V' G0 Ly(:,2) = x(:,1);
7 Y2 e* ?4 W( D' p' o. Iy(:,3:6) = x(:,2:5);
4 W0 t9 _$ ?' @. V+ Yf1 = y(:,2) - yexp(:,2);
1 q6 m: L, B% @" E! U* Ff2 = y(:,3) - yexp(:,3);
9 Z1 `3 ^8 _1 w6 ]% y; \f3 = y(:,4) - yexp(:,4);
1 Z& N" I" @" P. {6 `f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
# \8 L/ Y5 }; j# A. J# y% `f = [f1; f2; f3; f4; f5];


' A% M! X5 i! \; G6 @
function f = ObjFunc7Fmincon(k,x0,yexp)
4 x( G, C1 C4 A4 I6 Xtspan = [0 15 30 45 60 90 120 180 240 300 360];
* q1 b3 }3 s6 c+ J" d[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
. r& v! m8 x. gy(:,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)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
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function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
& z) A' U; h! TdFrdt = 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);
* S) S0 w* B- D* r0 ]/ qdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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