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
; M2 \  h' L1 L7 [%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
: L+ t" x! N/ P. n7 [. {% k6->k6 k7->k7
) y% a  B0 P6 c3 }+ d4 a: b8 M% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
  ?  U/ ]& P8 r+ w0 L4 x' e% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
+ }7 @. g6 ]; P% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
6 k# z+ C+ O' ^/ X8 o8 P0 ~%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
5 T* T' {; b/ G+ M' ?clear all
, Q" Y) D6 Z+ {4 Pclc
7 L/ |' E4 M" q1 W, C- A- yformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
' z# Q+ X! \2 I( ?* c. ^% j  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
8 m: m( n$ h' q& _6 F          60    0.13763    0.07397    0.02615    0    0.00428
+ M9 f, v% H0 D) F# P          90    0.08115    0.07877    0.07485    0    0.01405
1 i0 A5 |( E  E: N          120    0.0656    0.07397    0.07885    0.00573    0.02143
' g8 f" S5 G0 g- l          180    0.04488    0.0682    0.07135    0.0091    0.03623
- \! s. x: c- M9 e! y          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
" A1 ], I4 l9 h( V# Y          360    0.01855    0.04125    0.09363    0.0239    0.06495];
' B! {" g0 u( Zk0 = [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
% X  M! B/ A( B4 V% 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')
  \" m+ F' T& q& o9 ~5 }fprintf('\tk1 = %.11f\n',k(1))
/ V1 _% S/ A- T, w: A4 Dfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
* {  a4 E9 ]; N( |( \6 Yfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
, Z- j, y/ G/ ]9 Lfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
2 Q- J2 o# j4 L% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
1 x( c) n6 p9 [: Z6 G    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
$ X% x- E* W0 x: I4 t, T/ L3 wfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
$ l6 f+ N3 c: Y4 O7 D! c0 ofprintf('\tk1 = %.11f\n',k(1))
( l7 g) ^. r" F" J2 G% W. C8 Yfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
! Q- a- g. K8 i; gfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
6 @0 r  Q; f* t6 ]8 `fprintf('\tk7 = %.11f\n',k(7))
- x( E) c. R1 C, Zfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
8 S( p& q- |. h. w1 Rfprintf('\tk10 = %.11f\n',k(10))
  ]1 ^; t( k& u1 q( Ofprintf('  The sum of the squares is: %.1e\n\n',resnorm)
1 N' Y8 i+ y: f- I7 O2 f) }' V- [' Kk_ls = k;
# @0 |8 q! k# z! f2 {" ?output
: d" X+ o- E4 b) k2 ~# ?" ^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
$ N9 I$ F5 F! J7 |% F2 {. Q# Ck0 = k_fm;
7 L/ G6 M1 z% U6 J: @% h[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
$ y* |: d+ C8 z5 [+ wci = nlparci(k,residual,jacobian);
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))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
5 h- G/ s8 D+ Q5 \# k# V  F9 R- `fprintf('\tk6 = %.11f\n',k(6))
) Y& c% d* U: x" @4 ]fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
3 x- y9 s; p/ R# J8 dfprintf('\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
tspan = [0 15 30 45 60 90 120 180 240 300 360];
. f! d! w" T" k; P! h) m+ @) \[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
! k6 |3 K1 g3 f" N1 z; }plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
  p* \6 m) X/ o  o: }" Zp=x(:,1:5)
* b5 E9 g. h, n( yhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



/ A" B! z, E6 tfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
* J" q, X( b3 S$ n) k( d# I; ~[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
* K, O! ], }) k1 qy(:,3:6) = x(:,2:5);
6 [# ?9 I, a- Gf1 = y(:,2) - yexp(:,2);
. z1 `2 P( ^; I( @( k4 k: `& \/ ef2 = y(:,3) - yexp(:,3);
$ A) s5 A8 ?; o6 U9 Rf3 = y(:,4) - yexp(:,4);
( ?' v  Y# L# b# `f4 = y(:,5) - yexp(:,5);
+ F! I9 {3 P0 b2 @f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
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" X) T) R+ ~: J" J" z  p8 A1 }

function f = ObjFunc7Fmincon(k,x0,yexp)
' U- D  I$ p; E6 B2 p4 p$ ztspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
5 j* Z: {9 t- `: n8 h0 `: k# Wy(:,2) = x(:,1);
1 z/ z- s5 A" My(:,3:6) = x(:,2:5);
' w, V* D+ L9 ?' @) b7 Nf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
0 g6 L; k& g. M; c3 P/ ]    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;


1 l' f% i/ D9 I" O% A, ^6 ~

function dxdt = KineticEqs(t,x,k)
' W+ L: P' `5 J: |+ {* CdGldt = 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);
: O6 `4 J$ _3 p) N( G7 v$ mdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
0 J+ {2 E6 ]! adLadt = k(7)*x(5);
" A9 C( ]7 ^5 a: j, s7 ZdHmdt = 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