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
%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
4 M: w4 n4 {0 }7 t' @! o5 E# e% 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);
" W, i/ [* G7 X$ X5 _* y8 A%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
) a5 R/ O  F1 ?6 y5 P, Eclear all
+ B8 Y. f' N2 i) h4 Y6 q& \clc
  c( u1 g7 W& y1 Pformat long
" e. \8 @8 b: X7 S( Z( i1 P5 G  L2 _%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
5 V5 g) u1 {+ b3 n3 V, o  Kinetics=[0    0.25    0           0    0       0
0 V$ P: b: {$ h+ h) ~+ Y7 O          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
3 x) M$ u# n4 v" b6 H* O% o8 w          45    0.15105    0.06975    0.02473    0    0.0033
/ D5 l- a9 z/ T1 s8 |          60    0.13763    0.07397    0.02615    0    0.00428
( [* y; P9 A7 J* {# b1 Q4 v          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
3 V' _# a. r7 e, ~3 v7 {          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
* o' N  r! N8 o$ F6 F( u* x' V          360    0.01855    0.04125    0.09363    0.0239    0.06495];
: S0 H+ Q% m# [2 b; c* H. Nk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
- H9 O2 O' |1 xlb = [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]
" c! ^$ D. w! L: T6 R% warning off
% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
; V3 x& \; K+ J5 efprintf('\n使用函数fmincon()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
6 ^( ~& X' |( jfprintf('\tk2 = %.11f\n',k(2))
# e6 ?' u6 I0 {6 }fprintf('\tk3 = %.11f\n',k(3))
; y! h( {; F: _, L: Bfprintf('\tk4 = %.11f\n',k(4))
8 ?& g! w0 d& s1 mfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
' r2 M5 W* K6 `fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
( Y( A5 w1 G6 u9 r# W  W  f9 Pfprintf('\tk10 = %.11f\n',k(10))
9 _/ @1 {4 a& k1 J. {( z2 vfprintf('  The sum of the squares is: %.1e\n\n',fval)
( G( @/ v# u& T  gk_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
% T" t, f7 ?9 ?7 u2 A[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
- `2 y' J5 Z2 o. `) w( B    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
) ~! o" U% {8 f7 B7 dci = nlparci(k,residual,jacobian);
# C! B% m  R1 wfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
: a  Y5 J% x  \2 `2 G! Hfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
/ M  N; ?0 q" ?fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
) P5 q) N1 m' Q' E' d; ], `fprintf('\tk7 = %.11f\n',k(7))
# r2 t/ c9 e) N/ H1 b6 P7 Tfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
) r& b# F0 @4 [5 g& Pfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
+ @3 m: b  K8 p! R! W9 f/ uoutput
warning off
% r3 \; o, a$ c+ t% 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
' s$ H5 V# `: u6 Hk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
$ N$ z" ~, b5 Q3 N$ ~. t    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
) d2 R1 y) |% ifprintf('\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')
# s1 M" n" C3 q1 gfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
2 k5 L" _  N7 `+ y/ T- r# rfprintf('\tk3 = %.11f\n',k(3))
4 F8 }( E: C" A- Z; T# G& a2 ]fprintf('\tk4 = %.11f\n',k(4))
# \) l2 {2 y* C# L) \" d& Cfprintf('\tk5 = %.11f\n',k(5))
$ d  ^: u. }+ {fprintf('\tk6 = %.11f\n',k(6))
' h) F( N1 X$ W7 r, L8 @3 Pfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
8 }* p5 j. _! j% d* X8 Dfprintf('\tk9 = %.11f\n',k(9))
5 Q! X8 ?# B( Z$ a) x2 g1 bfprintf('\tk10 = %.11f\n',k(10))
) i$ E4 W; y" ifprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
6 L( C9 y8 P4 W1 B$ Woutput
0 _. t* I" D4 j, h& w0 w% B5 k, Vtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
/ ]. o; @' v7 B! o6 jfigure;
( K2 c4 _) f0 O3 Q0 s; G0 Aplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
6 T, f5 J5 I7 [) f+ f4 Ufigure;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')
# \  W4 Q. L3 o3 j# I: p& f0 _

3 B9 i9 E) \- e7 _% ]8 {
1 o6 o, X; `. C" Q: l! h7 Gfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
4 R( T- H! I- a[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
! Q' u0 g8 X7 F+ K8 N0 @y(:,2) = x(:,1);
" y8 Y# S8 v( z* F0 Ny(:,3:6) = x(:,2:5);
5 M1 w9 w  D4 y  c) ff1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
$ J1 U4 n5 M' gf3 = y(:,4) - yexp(:,4);
5 v- s: r7 Q& x" L8 mf4 = y(:,5) - yexp(:,5);
8 @# S* q9 s+ b- X1 B. L/ V8 Af5 = y(:,6) - yexp(:,6);
( k2 n$ q, Y- U/ r+ m4 X4 kf = [f1; f2; f3; f4; f5];

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; L6 ]3 \: O, m: G$ ^. q/ Hfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
1 }; P+ r- J- d9 C: A[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
3 k8 n- q) o) v; Ry(:,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) ;
. r8 D( t+ E. I6 m4 D- j( |$ A
+ m3 P+ A6 V9 ^+ U


function dxdt = KineticEqs(t,x,k)
. P8 c" x2 R- i" }dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
; `' c* C/ i! \1 mdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
$ R0 X" \# c' W# v6 Z) N# R# ^% BdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
4 h# a1 i4 w9 J7 RdLadt = 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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蒙的一比 大哥