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
% P/ k* i& y- M) t: ?, b%  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);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
9 D- x, C: p0 v  v% dLadt = k(7)*C(Hmf);
, G# w4 L0 Z: S) e%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
8 s9 W  f' ?0 f* Tclear all
% i2 r& g+ S: i0 e3 O5 ]+ O+ N8 tclc
format long
0 p$ @3 N6 L' `; Q$ d. X%        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
          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
. I, Z- i8 ]0 C0 g8 ]          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
1 @" x0 r* j/ ?          180    0.04488    0.0682    0.07135    0.0091    0.03623
# J3 Q3 k" J$ N7 a          240    0.03653    0.06488    0.08945    0.01828    0.05452
2 a: f0 Q; T, z- B" f          300    0.02738    0.05448    0.09098    0.0227    0.0597
( d$ j; C. m! |! E          360    0.01855    0.04125    0.09363    0.0239    0.06495];
5 D5 h4 B0 S; _4 ok0 = [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];
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')
- O! I# t5 e+ \fprintf('\tk1 = %.11f\n',k(1))
" f. k! F7 w: `, i; f% K4 Yfprintf('\tk2 = %.11f\n',k(2))
) O1 r& g1 U8 M$ V, Afprintf('\tk3 = %.11f\n',k(3))
4 g0 e; {+ k' `  Y4 ofprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
! W4 u* k+ E% z* @9 _1 v% Cfprintf('\tk7 = %.11f\n',k(7))
% [: ]; x7 k, k# Z$ Pfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
+ d( o3 y7 E+ }# ~7 \fprintf('  The sum of the squares is: %.1e\n\n',fval)
  h# n. ?5 Q1 b% M) Z7 v9 Vk_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
) @& L% K- Q1 j. h    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
" ?4 C( _6 b) f7 G. x$ R: j7 W5 Jci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
1 P) a& C- K. s4 G# Rfprintf('\tk1 = %.11f\n',k(1))
" f, J3 D8 R0 @( V0 B2 ~# Wfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
7 Z4 _& `4 B$ J- m8 }! y4 k2 ufprintf('\tk4 = %.11f\n',k(4))
- `6 Z% {( v1 Z, |8 U! J- B0 vfprintf('\tk5 = %.11f\n',k(5))
0 i* g. N- |" y' P) J+ qfprintf('\tk6 = %.11f\n',k(6))
3 G1 U: f/ w! Nfprintf('\tk7 = %.11f\n',k(7))
! |/ H6 C0 y- C1 g2 i' f+ lfprintf('\tk8 = %.11f\n',k(8))
) U/ F" J. X6 T% W7 ^1 Q& E- lfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
8 M( X0 [3 l. L1 X5 g* uoutput
3 P) e2 J" s+ Rwarning 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
4 N" P' f# t1 Q5 L# o! Qk0 = k_fm;
7 L" B0 l: S4 p* w[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
2 g/ C1 s, J4 v7 M0 N$ m    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
0 O. Y  E* F8 X; c9 }& Vci = nlparci(k,residual,jacobian);
0 H/ Y" U* Y/ v" R& {fprintf('\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))
/ W" s' M! J* l5 L9 \! L: e8 Qfprintf('\tk4 = %.11f\n',k(4))
  k! H7 R* f  {' t4 O% `fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
" v. S" I: ]5 h% ?fprintf('\tk9 = %.11f\n',k(9))
6 c4 f" l7 c( P% Efprintf('\tk10 = %.11f\n',k(10))
" `( b# A5 ]9 \' O/ mfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
( R9 L: K" G- R' ?output
& Q6 v8 o% ?+ y  N2 Y8 W* A1 {tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
3 _( [3 y0 v; h; b& u" c5 Xfigure;
1 Z$ }( `, }0 k& {" @- bplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
* d( {0 d; Q" i% |0 w6 L3 g4 }3 Kfigure;plot(t,x(:,2:5));
' u* Y5 f0 l! A+ Hp=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')
; W' _; I- Z$ z, B


function f = ObjFunc7LNL(k,x0,yexp)
' f" _0 Z. f5 a2 K" @7 i* S, L  itspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
6 I6 y! N7 _) q9 r$ X9 Hy(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
) l7 s+ J* {& a) U& ?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];

: }( T& B* W+ n6 Q+ G4 W: g

3 d/ j, Y5 i! l8 r: _" i( K6 U3 efunction f = ObjFunc7Fmincon(k,x0,yexp)
$ y5 |3 s( R9 X9 [: M* ^4 y: Htspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
/ J+ ^: V) P' iy(:,2) = x(:,1);
' G  l- v# |2 Fy(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
$ @7 P, n' H) Q1 e    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
% z8 [& z  w( V. I5 g- x! P    + sum((y(:,6)-yexp(:,6)).^2) ;

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$ ?% ?- y) a3 I8 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);
' e. G% @3 O$ wdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
9 W5 H% w: v" X' m( z" idxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
. h* b% y. t! x& b
) R: ?4 b0 _3 T+ t2 G: A1 D