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
0 G" T: X0 O4 A7 p7 b%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
+ L/ G' L0 p+ E* O! O' a% 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);
% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
format long
( E2 o/ w' {" v5 |. t" e; L%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
3 x, O" }0 G4 R! g! \          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
5 v7 J) V( e* x3 Q& g          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
; C6 T) S/ q7 L          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
7 h# e9 H- r5 _# M' ~          360    0.01855    0.04125    0.09363    0.0239    0.06495];
; q: J) p8 D5 \6 G0 ~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
+ Z/ |- K5 n% h" B6 F. O: \% klb = [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
! u( S! G  R" K# g* o1 m- C% 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))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
* {# I# ]# k# _% D  w3 F, Q% nfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
7 J/ T0 J5 ?2 W/ i6 H$ |fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
1 a. L+ E' I, r) {fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
. M# S. E/ S2 A+ \0 g& G+ p& K1 wfprintf('\tk10 = %.11f\n',k(10))
! t3 c. V2 E8 ~% Z. C" X" Efprintf('  The sum of the squares is: %.1e\n\n',fval)
7 a# h& U. o! E" Y' ]" J3 ^k_fm= k;
3 i$ M/ Q. `: V0 x% warning off
) m: q0 \8 {4 A  d: d1 P- J% 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);      
. n% w" z+ \* s% yci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
) E* }. t* ]' X( efprintf('\tk1 = %.11f\n',k(1))
; Z, N2 }; v3 rfprintf('\tk2 = %.11f\n',k(2))
2 S8 ]% _9 b6 E, n! ?; n8 @fprintf('\tk3 = %.11f\n',k(3))
  k  h$ i  ^; C5 T8 B" Rfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
) G! _0 I! @' q* w7 f: qfprintf('\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))
$ i0 p; U7 j6 J3 t& yfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
. N. m2 |4 [- U/ g# P( w; koutput
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
% U) f  N. |7 E' q& xk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
3 r8 L0 K( W9 _    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
% R7 |3 \2 m. ~- x8 N4 yci = nlparci(k,residual,jacobian);
4 ?" Z0 x! _$ F- nfprintf('\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))
* H2 Q1 Z8 d/ G7 }. Rfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
$ i: z8 B! E$ ^/ i8 J3 zfprintf('\tk4 = %.11f\n',k(4))
3 K* V. B  A6 [; S8 |9 Efprintf('\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))
fprintf('\tk10 = %.11f\n',k(10))
% b4 V- e4 N5 O  y# H! S, A1 g" pfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
+ o9 P  t3 l- ~9 o! Moutput
% G, ]( s; h: |  Jtspan = [0 15 30 45 60 90 120 180 240 300 360];
0 K; M8 |+ Q/ M[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
/ j3 m6 s/ P; Z4 M% Mhold on
plot(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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% \8 Z2 H4 p. l9 Jfunction f = ObjFunc7LNL(k,x0,yexp)
. J2 i3 l( @, H& htspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
% L$ X/ i% w0 D# K0 o! H- y9 Sf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
* W+ Q( g- P( ^' O# i7 Ef = [f1; f2; f3; f4; f5];


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9 J" h! G( {7 o: D  t2 a, s! xfunction f = ObjFunc7Fmincon(k,x0,yexp)
/ a0 r, V0 P% I. R: y! V8 {tspan = [0 15 30 45 60 90 120 180 240 300 360];
/ Q) q3 x' [# E6 q1 m8 z5 S[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
, Q) o! S5 ?6 G$ e5 ^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) ;

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function dxdt = KineticEqs(t,x,k)
2 N0 Y& L: f- q* }dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
( W" y* x/ s6 b- W) i2 U, d% cdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
' p' X' U  e  e+ t. d3 f" `9 ?: m* NdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
+ ^/ b7 b( E* x% M6 R* [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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