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
( \+ ]' D( `2 G0 R%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
+ y2 r- l6 @' \& |8 P% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
" s- Z+ o1 D. @; ^$ _: }- U% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
0 T2 Y+ a) J! s2 Q% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
5 V" [8 w  H1 V& n( Lclc
format long
' L" J' U  v6 |$ }; T%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
' c; E( u; p! X" c9 {; \          15    0.2319    0.01257    0.0048    0    2.50E-04
0 _& `+ S$ `$ @          30    0.19345    0.027    0.00868    0    7.00E-04
0 W  W3 ?( k5 |3 y3 h2 J          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
4 N2 d2 H) a$ t          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
1 x" N6 S$ O' e" }          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
: j5 `: Q+ {) x7 V8 R. Olb = [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];
/ q; q8 l2 c. _- p3 g" Uyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
* h# {1 F- W: p3 C4 H" d% warning off
0 P. [! Q5 }( u) D2 J% 使用函数 ()进行参数估计
/ S, `4 Y0 f8 Y. m- ~( Z2 C[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')
3 X9 y: S* n, ]7 ^# [fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
" b7 t/ b$ X6 H7 ?" s! r3 Dfprintf('\tk4 = %.11f\n',k(4))
5 A( {& N5 U; y5 ?' [fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
5 Y/ I: z: A5 M: Gfprintf('\tk8 = %.11f\n',k(8))
. B6 v8 W2 _4 W! rfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
9 t1 w5 X( Y8 d- ofprintf('  The sum of the squares is: %.1e\n\n',fval)
1 [: _0 c9 A% u  U' B' w& G1 x9 rk_fm= k;
% warning off
* N) S6 G' i* e( C+ ?% 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);      
ci = nlparci(k,residual,jacobian);
- l# f2 e; R2 b% |fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
3 D  [( I! h% T" W2 C3 z% ifprintf('\tk1 = %.11f\n',k(1))
) F) l# M" s2 x+ e) }fprintf('\tk2 = %.11f\n',k(2))
# `4 u1 O6 p2 y" I- ~: s: B, rfprintf('\tk3 = %.11f\n',k(3))
" C1 p! o5 s( `7 |- j6 i, N9 Rfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
+ b& j* b% s6 X/ W- V/ J9 wfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
8 _) I! l" Z" B$ I5 p. P# bfprintf('\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)
' z# y  L: d# ^- b( X, fk_ls = k;
output
  n$ x# j( S* s) V% R) f8 owarning 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 |* t! X9 m% Ck0 = k_fm;
2 s( V* X  \% M7 J[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
. f+ j( |6 Q6 L# u5 Z, q5 R& G) S    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
/ d3 t; ]( h4 {3 D7 u: i+ Rci = nlparci(k,residual,jacobian);
& u% G* f. M$ e! N8 \! 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')
8 L& y; Q0 O: m5 }7 `' v- X" qfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
6 j- G6 m- l3 B& X( W7 xfprintf('\tk3 = %.11f\n',k(3))
* g; S0 E6 A% q! P$ W; C+ efprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
* C: E# Y5 M. a0 Y) h1 R& {fprintf('\tk7 = %.11f\n',k(7))
, N/ `5 F: l. n4 q' d4 yfprintf('\tk8 = %.11f\n',k(8))
/ e, ^$ U$ @5 y1 ?! Xfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
. Y6 T7 o8 {: ^( ]. `7 D" Tfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
2 c; x/ I9 Q8 k1 M3 S% Q0 Ck_fmls = k;
: ?" Y: P! u' Noutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
; z5 L# J, S7 J0 U; o* n[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
1 Z% F8 W% ?& A2 j, ^figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
4 u2 s8 j. ?. T! G& e$ E. Up=x(:,1:5)
0 e' X+ H; r  k- u* khold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')


" i( ?! U. S; O# y1 j/ {$ L
" W+ S( A8 G+ r2 x! Sfunction f = ObjFunc7LNL(k,x0,yexp)
& I1 [) A# r6 W' b1 D( M6 C+ jtspan = [0 15 30 45 60 90 120 180 240 300 360];
4 J: Y: Y7 q8 z* V) c6 p, Z! i$ q[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
  R- B$ G- q0 Qy(:,2) = x(:,1);
, ^* Z' `2 A: L& j& `1 G& f# }' M* Ay(:,3:6) = x(:,2:5);
# _+ Z/ r' x  h1 b, Jf1 = y(:,2) - yexp(:,2);
9 b6 ]& x# I, |: N# V; y, hf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
0 W1 s- q% b& }  {" _: cf4 = y(:,5) - yexp(:,5);
0 }4 W6 Z8 r1 i) M, n1 L1 ?7 jf5 = y(:,6) - yexp(:,6);
# Q7 k  E; K  [* |! uf = [f1; f2; f3; f4; f5];
6 s2 ~) q# A/ D8 I0 p2 N
' ^- o4 R' v3 j; a
5 B" E; r' \+ S( E$ c" o
function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
/ [) n# i, Q# ]5 z" _$ r1 d  Q; p[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,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) ;




function dxdt = KineticEqs(t,x,k)
8 R' b1 T# {( T4 d1 G: m! d* g. ^dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
% R/ k3 K* q/ Q: _- J$ @$ IdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
$ t9 E3 K7 b! t0 a* Q& Y- 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);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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