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
: [# a& q2 s/ M" K7 E* A6 y% 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);
( F" V7 c7 a/ Q; n2 n6 G" v1 w. K% dLadt = k(7)*C(Hmf);
7 Y4 ]4 I: n+ t* W# p%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
& i5 U) m, m1 u. c, l# t3 fclear all
* x  B$ P$ L9 Q' f( nclc
format long
2 o1 Y/ T4 ~+ }: L* D& Q! t%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
# D7 B$ P1 j8 _* F; H6 o  t/ H  Kinetics=[0    0.25    0           0    0       0
6 M3 R( |' |6 B* H  P- x% |          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
2 Q. K7 P5 `$ N9 Y7 t9 T5 l' {" v          180    0.04488    0.0682    0.07135    0.0091    0.03623
7 t! f7 S4 p' N( ~. d7 I          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
: t" S+ D3 o; A8 j- Y1 u          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
2 O1 {/ S, ]* F5 r/ s6 ?4 P% C  _- d4 Tlb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
. `$ J* J* f* b, f. p) n1 Xub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
  a8 T4 p! P4 @. ^( ayexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
% 使用函数 ()进行参数估计
) o8 P( ~" N9 t[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')
: O0 p/ w! y2 r% {( h' }' S6 Wfprintf('\tk1 = %.11f\n',k(1))
. v+ t4 e/ S  u1 w" gfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
8 p3 R" M* h  Vfprintf('\tk4 = %.11f\n',k(4))
& N* A/ T* S- t* q! ffprintf('\tk5 = %.11f\n',k(5))
8 L) w, @# M; t# }2 v" Pfprintf('\tk6 = %.11f\n',k(6))
8 g. t# z, M5 @( h# R9 V* ?2 Z5 Zfprintf('\tk7 = %.11f\n',k(7))
1 A; E3 B$ n% v: yfprintf('\tk8 = %.11f\n',k(8))
' w& l! M% a, Z) E* Q2 Dfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
$ _4 p8 _' K# R: ~# Sk_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
9 _* c8 d0 x5 i  f& |[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\n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))
  F9 k. h, n8 A  @fprintf('\tk3 = %.11f\n',k(3))
. L# v* e1 t1 Z) K* Qfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
3 X( ^; S: O. w" `  {0 y( Efprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
# q, Z1 q; t; a% s1 `( \! Afprintf('\tk8 = %.11f\n',k(8))
0 S( H. t: G$ H/ ufprintf('\tk9 = %.11f\n',k(9))
1 V  U* _' S" ^3 v) Efprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
9 d$ B* B# b* C% E# a+ vk_ls = k;
. D8 p  E( R. e, E6 routput
# x5 f# @) u: ~4 J. J3 y) pwarning 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
  {$ q  L# p+ a5 s" ~k0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
" Y1 w* j  |3 m. hfprintf('\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')
  u& T4 h* v" Wfprintf('\tk1 = %.11f\n',k(1))
9 D& V- d8 P; I1 ^6 ^2 afprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
# l, a5 z6 w) Q# @fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
: @3 m( s( f$ L/ {, b7 |6 Cfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
0 B/ f1 C8 e2 a" ~* L( X/ y8 ffprintf('\tk9 = %.11f\n',k(9))
, h, t4 {$ E' O: Z7 Q' ~% T" F: f4 Efprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
( r; @6 ?3 ]: i7 z+ A& f! O- xtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
) A) k" B& _( U  k8 _8 tfigure;
7 Q. y! b$ ~" m- k' }* z) D' N2 ]plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
hold on
/ h1 D7 e* K' G! V: k* D  Q9 [- Aplot(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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function f = ObjFunc7LNL(k,x0,yexp)
) _1 Y" x) u8 x) ltspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
3 O6 K0 F( Y" @* ]* X: T0 F9 P3 Iy(:,2) = x(:,1);
% \3 D& a" Y- X: gy(:,3:6) = x(:,2:5);
0 P$ n7 j/ W) l( g. s$ x+ \4 S  of1 = y(:,2) - yexp(:,2);
. U; f( ?( Z/ R9 q" |3 Gf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
% E5 h" Z2 }1 cf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
" e3 T2 E7 H1 n* T! k. bf = [f1; f2; f3; f4; f5];
2 R3 R- V5 ~7 N7 e- j" B

- o- d1 r- M+ ~
; E: ^9 ?/ W* o5 O' Ifunction f = ObjFunc7Fmincon(k,x0,yexp)
  i2 b0 `6 }) G, y1 l/ |8 otspan = [0 15 30 45 60 90 120 180 240 300 360];
% p* I) e. \+ R7 P& \1 G; \[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
' F. u; b5 f; d3 Y8 Pf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
$ G$ J- @2 g; S. x7 P/ A    + sum((y(:,6)-yexp(:,6)).^2) ;
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function dxdt = KineticEqs(t,x,k)
9 y7 g) H: j8 k4 c' o0 udGldt = 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);
1 y" `' ]+ C- K+ EdLadt = k(7)*x(5);
! ~& J% Y, _1 I3 \& b) NdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


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蒙的一比 大哥