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
# C$ A3 L5 P4 k! U%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
# e8 U7 [3 J2 P" C1 [  d" r" Y% k6->k6 k7->k7
( U/ p" d4 b" g  B+ C% 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);
1 Y8 ]! \5 m/ K9 e+ v& Y3 Z9 u% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
1 G' C6 o9 N  r) h* }  kclear all
clc
4 `  u0 d5 D& ?/ H, }  J- wformat long
0 ]( B7 B8 E6 j; P# q%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
8 @% D) [7 v( [2 u' U% J) T  Kinetics=[0    0.25    0           0    0       0
( u/ y$ e% v+ y) q/ ^5 }          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
1 v& R/ `$ [- N          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
6 l/ O% {3 T1 j% G          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
6 F; K$ J2 }5 @1 ^( H; I* L          240    0.03653    0.06488    0.08945    0.01828    0.05452
# i0 a  l) m; ?          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
7 s/ }6 P2 k  ak0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
0 Z1 k/ u; D0 D$ k; K. h5 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
. k/ x7 z; J& C' ~x0 = [0.25  0  0  0  0];
/ \. U% N. ?7 c( iyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
: Z0 _$ ~. G6 ~$ b  ~$ A/ Q% warning off
8 M, z6 l9 ^6 R& I" g& a% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
) ~: I4 o9 a/ B5 q* ~- i# B3 H6 lfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
" Y: p9 z, d; O3 s4 v1 {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))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
, l" t' p8 Q  C% n2 nfprintf('\tk10 = %.11f\n',k(10))
" S9 K" P2 [! a9 r6 ufprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
# h$ o% o7 b* Y' e9 S. [% warning off
* S2 |0 B  `/ l2 G# E7 C* ~3 R; \1 X/ @% 使用函数lsqnonlin()进行参数估计
  O6 e6 O/ ~" z( ?. e[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))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
5 W  ?) H# C9 r8 t7 O: R3 N/ m) qfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
7 F! _7 m0 C% n7 y9 n* zfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
2 |  M* V) _$ b. H4 kfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
3 r. I7 y% L8 r1 z- Z/ `( a# c! j# pk_ls = k;
" |1 D7 Z+ }( @% \, [& D* g- l: @' woutput
warning off
7 V/ P  C, H8 {# x2 n- @% 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;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    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')
0 S, C8 {9 `) J& ?5 Gfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
0 b2 \8 h6 c/ y( l2 A" X: Q" v) Wfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
# T& q" ]& o7 c+ {fprintf('\tk5 = %.11f\n',k(5))
' q. }1 a, C( yfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
0 L) x) u1 B. S- O& u7 F) d0 dfprintf('\tk9 = %.11f\n',k(9))
0 w3 V! ^" I9 h' K% gfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
3 Z# r  F8 M. h9 `k_fmls = k;
+ f# j# H6 g5 uoutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
2 f0 B" ]1 A: Y$ z, u$ V3 Mfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
hold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



function f = ObjFunc7LNL(k,x0,yexp)
) n& q  Z6 @$ P4 Wtspan = [0 15 30 45 60 90 120 180 240 300 360];
- }3 L! Q9 c" x6 d& V[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
6 B) @4 a9 R4 Y8 _6 t% k. `y(:,3:6) = x(:,2:5);
' p  n+ h% c. k2 p0 c* ?8 Hf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
+ E4 r9 W) ?, K% w1 s8 O$ Yf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
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- x: A- ^; D- J: w* gfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
9 p1 U; \; o- _/ \. m3 ]/ l% b[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
. j4 u. S' K! l0 f0 Y- \9 F: U: oy(:,3:6) = x(:,2:5);
  x2 [0 g/ \$ b6 c. if =  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)
5 _  U' p+ u! w% ^" Q8 {dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
" a4 j* t' n; B) ^8 ?2 Q4 }dFrdt = 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);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


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