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
6 i6 U" Q, @( v: r- R" Q+ G%  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);
8 [: t8 t9 N: O& i# D4 u% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
. S" B/ z# @, c5 F%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
0 C+ L" b, E/ v0 a+ ]clear all
2 \2 Y2 {6 U: f! rclc
/ w! a$ l$ O( Q9 T& e* g/ Qformat long
7 Z% g3 H4 T# L) n%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
7 x/ X6 \7 R) d( _1 j' Q' k2 I+ m  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
! ^" Y) }' g: T7 A9 |: W7 q) |          45    0.15105    0.06975    0.02473    0    0.0033
7 c( h& h+ K" ]& ]) s& `  p          60    0.13763    0.07397    0.02615    0    0.00428
- j& f- f/ x" t          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
8 T# ]" y" M' D5 u- g9 }0 }          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
+ ~& b. x4 C5 h5 h' i          360    0.01855    0.04125    0.09363    0.0239    0.06495];
! b/ n, h, ^$ c  ?& R: g0 Kk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
7 h& L  T$ m* j9 rlb = [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')
fprintf('\tk1 = %.11f\n',k(1))
' C1 P" s/ f1 J8 u( Rfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
: z9 u  w6 O8 d3 h+ [9 Rfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
+ k( {: r: ^, s; t' H2 U5 Z* f- \fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
- z" b1 x4 D! |% [" Ffprintf('\tk9 = %.11f\n',k(9))
0 i% Q- V1 W8 y$ V$ n* y0 cfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
1 u+ C: g" q6 J/ p! M( `k_fm= k;
8 u$ {/ H/ {9 [# G, d3 A9 y( N/ k4 J% warning off
9 A  [/ Z: m: }1 g; V% 使用函数lsqnonlin()进行参数估计
/ ]) _" h. {5 g( d! c) a* Z[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))
  q1 A. n" Z" ~2 afprintf('\tk3 = %.11f\n',k(3))
& N" ?) @0 b! |# Cfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
+ z! B/ f- R1 {+ zfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
3 k3 k  {0 ^9 r6 Ofprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
* }% x! x" s8 Q2 G& Kwarning 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
1 X: ^0 P1 Z  I8 F! K* Y6 jk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
+ `9 V+ i! {3 K7 \+ {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))
- @) h& l, D5 ?) F0 i. e5 N. x% v' ^fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
  y9 @! `: ?2 E2 {; T& e! X" j9 `fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
/ e" O$ I+ B; q1 _0 h6 X; ^fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
; i. |/ r, i  ^fprintf('\tk9 = %.11f\n',k(9))
  a& v. c  z2 ]- yfprintf('\tk10 = %.11f\n',k(10))
9 H4 e( L* l: F0 a$ b" Wfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
1 q+ C" Y$ B! b$ goutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
% m" b5 ~+ D% e[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
/ z9 _; s/ I$ L) u0 f( L. ffigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
3 z( z8 j1 ]4 n( G3 ]hold on
& x. c! [. F- E% J: kplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
1 V4 x3 Z4 C, k! y
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" T! U& `7 t& ]& N7 G% Ufunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
- w) c! o) C* Z: ?- x[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
2 \" b6 ^( v9 ^7 o% c( \$ df1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
- W3 J; b1 L9 g2 B$ F" Hf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
1 b0 e, _9 O2 p

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& P6 y4 r5 }: j/ ]6 L' _function f = ObjFunc7Fmincon(k,x0,yexp)
8 o( [3 ~: W3 ?8 V0 ]tspan = [0 15 30 45 60 90 120 180 240 300 360];
2 a+ @" K8 S4 T" d[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
3 @3 R( T) L1 N% K2 @! }' |% }2 Ay(:,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)   ...
  b9 e& K) A* f    + sum((y(:,6)-yexp(:,6)).^2) ;

5 ^1 ?8 C& u+ Q8 k9 ?

8 f: y9 F, ?2 j+ l4 K
function dxdt = KineticEqs(t,x,k)
- Z( F+ m6 V# tdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
; u9 h6 m# C4 H6 T5 n( a/ qdFrdt = 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);
, |2 g: w! v  XdLadt = 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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