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
2 |* h9 Z' r) D0 M. o2 L%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% I( C8 I5 x, o( o  Q+ N1 r% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
" A1 {3 Y: j" [+ _/ t% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
0 {' i  N5 F7 E! Y5 U% R% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
2 \* e3 O3 t7 c% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
, A0 J5 {  k; P8 Vclear all
; n$ l4 ]' O! r7 Y6 zclc
1 z2 G5 [# Q6 k0 |9 G( w8 ?format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
" `: V# r9 d9 p7 v$ J0 n  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
' |2 ^) N& M  I$ @* A/ `          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
. B' W7 G5 s& u* a          120    0.0656    0.07397    0.07885    0.00573    0.02143
2 p  p  A$ s7 S* V) n          180    0.04488    0.0682    0.07135    0.0091    0.03623
' P/ D) M" N/ N; l( l  I$ F          240    0.03653    0.06488    0.08945    0.01828    0.05452
6 e4 \: y3 e/ C; Q' K$ a          300    0.02738    0.05448    0.09098    0.0227    0.0597
. h+ X+ ?% T% }" K5 `          360    0.01855    0.04125    0.09363    0.0239    0.06495];
( G, B9 M# D& s3 Q1 _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
+ [( H& x% W  glb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
- w$ x+ P7 K' h. {) F9 ?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]
3 v! M) A! B+ c7 P6 \) r2 s+ L9 Q% warning off
: G, I+ W7 O, s, x% S% 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')
% d# i, c) s; u& r2 s3 z7 @fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
+ z$ h  |! [0 T5 ?; {0 hfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
& l4 s/ p: u+ S6 S$ tfprintf('\tk5 = %.11f\n',k(5))
$ O& c* w% E, W3 Ufprintf('\tk6 = %.11f\n',k(6))
. B2 m# k) u1 ?/ Nfprintf('\tk7 = %.11f\n',k(7))
4 D% }1 W5 o! m  ]) r* Tfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
: D3 l7 A2 R) P- {) T% _+ \* u0 P9 Mfprintf('  The sum of the squares is: %.1e\n\n',fval)
) _" n) v9 F* q) t. |3 M8 Ok_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
" v5 A# y; B4 d1 C/ T, R[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
. o( w% d+ ^  r* s    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
( {4 [/ k( ?* \$ w6 sci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
& W, B4 ^3 G! o" ?6 P: |7 T0 ]8 N: Qfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
/ o+ k: @2 q; K+ Dfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
: R; e8 t2 _/ B+ y3 ~' S% ofprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
( c& ]7 I+ r$ n6 Dfprintf('\tk7 = %.11f\n',k(7))
1 G$ b0 T$ `5 k1 P: ~1 Xfprintf('\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)
k_ls = k;
9 N3 A* Y+ T: g6 poutput
8 q9 m3 H3 v' ^( p4 ]" Wwarning off
6 ?6 w6 Y* C, {8 M% 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;
( J# ~/ W/ W! H" o- B[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
& K  K! R1 _# m+ h& B; y    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = 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')
' ~3 v0 [2 S  I7 ]) l) z0 W- }fprintf('\tk1 = %.11f\n',k(1))
5 |2 |2 n  d, K( i+ c9 q) X7 X  Rfprintf('\tk2 = %.11f\n',k(2))
; I1 }7 o4 a5 C7 \fprintf('\tk3 = %.11f\n',k(3))
0 p" \+ `3 _$ Q( }  h" {fprintf('\tk4 = %.11f\n',k(4))
) y; V& F+ z: Q% D( ^( J* `fprintf('\tk5 = %.11f\n',k(5))
' h- A, q7 m: }2 @, N/ {( Wfprintf('\tk6 = %.11f\n',k(6))
7 d+ w) Z2 I; D9 o* q2 d9 w* r8 L) _fprintf('\tk7 = %.11f\n',k(7))
# b9 @: E* K/ ofprintf('\tk8 = %.11f\n',k(8))
/ N8 w/ Z. T: ~' v# G* ]fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
: q0 R* _1 @) |8 W9 p5 Qk_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
, L2 w$ J5 h$ T  ]& d3 w9 e$ `[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
9 ^3 n# u  w* B3 I9 xplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
! s$ K* M5 X" @7 {/ }figure;plot(t,x(:,2:5));
p=x(:,1:5)
: m+ x2 i4 ?! a4 B& m) ~8 \hold on
: J% k) u( \* \$ B6 J2 S# Mplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
* b$ M; ]- Y9 r3 T" `% i, ?
( F8 I% w0 y' _
4 [( H8 I6 ^1 M  C/ k
* x0 S5 o7 i- v& `) b1 Vfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
& r, M* Y! o' x+ r/ u[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
, F9 E' h$ H  uf1 = y(:,2) - yexp(:,2);
' L; U3 o- }3 f9 Y& {4 K$ ]f2 = y(:,3) - yexp(:,3);
: W9 p- G# v8 S  F/ X* @f3 = y(:,4) - yexp(:,4);
2 h1 O$ V0 \; d# C) y9 `. ?f4 = y(:,5) - yexp(:,5);
7 y; G) P7 w2 tf5 = y(:,6) - yexp(:,6);
# v' f9 K) V: y" E' B" P& sf = [f1; f2; f3; f4; f5];


' k& v0 z. ^; H4 J8 k  L
function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
( x6 S( E* J; |- {% E3 B, Ky(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
/ D/ f6 B& W, c" o4 M1 ^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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2 d! V$ P2 i( M2 }, Q0 D( nfunction dxdt = KineticEqs(t,x,k)
7 K1 L5 J8 S! W" j3 A7 _dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
  |1 {" v2 D5 o% l# cdFrdt = 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);
dLadt = k(7)*x(5);
) T1 e: O+ L3 m3 h$ ~dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
- ~. ^. Y6 c% Rdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
& j& S6 x7 W' M; m
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