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标题: 帮忙做下统计显著性检验和K值的误差以及灵敏度分析 [打印本页]

作者: 箫剑→残念    时间: 2016-10-25 16:51
标题: 帮忙做下统计显著性检验和K值的误差以及灵敏度分析
function parafit4 V8 K: C6 b$ R1 W# y: W
%  k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
2 u$ m, K9 R3 V) X  F) g* _2 |9 y% k6->k6 k7->k7
6 X  b( v# G# h3 }% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
+ {" ]4 r7 y' P& C% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
3 a$ S- Y: ]2 a  h5 w% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);$ P( G5 U4 N2 Q0 _: r: J
% dLadt = k(7)*C(Hmf);7 c3 j3 p  Q+ k% U, _# y% ^
%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);
4 l+ D: h  V  j9 ~3 ]+ vclear all" {8 v/ I  e4 O* s& }
clc
% E  V. }% a  g! A" D" [: v5 yformat long
* z6 A6 h% K6 S5 L%        t/min   Glc    Fru        Fa   La   HMF/ mol/L * O6 M1 ?* B, Q; N/ S/ K1 ]
  Kinetics=[0    0.25    0           0    0       03 |, h/ U2 T' q* {. Q6 P/ j9 j0 v
          15    0.2319    0.01257    0.0048    0    2.50E-048 w, U- P& M+ G( ?# T$ ?; f
          30    0.19345    0.027    0.00868    0    7.00E-04
" {: j% ~9 \% e          45    0.15105    0.06975    0.02473    0    0.0033% Q9 A9 H) w- V+ @7 Q7 V* |
          60    0.13763    0.07397    0.02615    0    0.004286 G% h% Z0 u; D% J( N
          90    0.08115    0.07877    0.07485    0    0.01405* E) M; @3 h- e# s( n4 l6 \7 _2 R0 |
          120    0.0656    0.07397    0.07885    0.00573    0.02143
% h( L" i: O# N4 |5 A. O3 w3 x          180    0.04488    0.0682    0.07135    0.0091    0.036237 }2 `; J, f2 R3 T5 R
          240    0.03653    0.06488    0.08945    0.01828    0.05452
% s* W" }% n& R9 I6 v          300    0.02738    0.05448    0.09098    0.0227    0.0597
# V4 s' _/ b* H7 `          360    0.01855    0.04125    0.09363    0.0239    0.06495];8 O5 l# Y# c# G( I$ g+ h
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
& `! `( g1 q( S! ?% S7 j8 u0 S. C* Klb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限% R9 K" Z4 h7 ~, C
ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限1 ?, E7 E3 X( }6 S6 H  ^# g4 U
x0 = [0.25  0  0  0  0];
0 R. O2 f, E: {( n; C* s$ @yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
/ j  _9 P6 h$ J, b9 |$ k% M% warning off
2 c% S8 M' E) @6 Q3 G5 m% 使用函数 ()进行参数估计
4 l2 Q% _  C# ][k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
' w/ [3 N8 T* k4 N' V" Zfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
: x/ C8 j2 A6 d8 l% y1 M6 ?6 bfprintf('\tk1 = %.11f\n',k(1))' q) J% F3 k! I1 v& M2 G* ?
fprintf('\tk2 = %.11f\n',k(2))
, R2 k: o2 }# q: N( z$ @0 ?3 C7 wfprintf('\tk3 = %.11f\n',k(3))$ J: x4 G! J. Z* o
fprintf('\tk4 = %.11f\n',k(4))( R0 S; |! J; }1 P' \
fprintf('\tk5 = %.11f\n',k(5))3 t) `6 Y- R: e6 V+ U* i! N, d
fprintf('\tk6 = %.11f\n',k(6))+ h5 o) E8 J3 W+ ^. H; D
fprintf('\tk7 = %.11f\n',k(7))" v5 f; C" s, i% e- W- r0 A
fprintf('\tk8 = %.11f\n',k(8))( [, u) p% a/ j* b7 w( _; O4 h
fprintf('\tk9 = %.11f\n',k(9))% B- y1 i" u+ b& l
fprintf('\tk10 = %.11f\n',k(10))
  q3 G" S' J( J* N1 ]' ]fprintf('  The sum of the squares is: %.1e\n\n',fval)/ ?3 X$ A: ?9 J  X8 e* J
k_fm= k;: \5 H0 ?, `/ k6 t: E
% warning off3 g! g& R4 O+ Y. `
% 使用函数lsqnonlin()进行参数估计1 ^# Y. e0 n& c+ E
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
9 B1 V! R3 G1 v+ t1 s: O4 T    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
& o6 L/ S# e$ kci = nlparci(k,residual,jacobian);/ ]0 @' U5 J1 V: L- B- z$ o3 u- V+ I
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
) i& \4 K$ \' R( y' W/ [# ^9 yfprintf('\tk1 = %.11f\n',k(1))
. S# ]1 _  ~9 }! [4 Tfprintf('\tk2 = %.11f\n',k(2))
$ W6 c9 q% G' m& Bfprintf('\tk3 = %.11f\n',k(3))
# B& B( J* B! v6 R2 e9 bfprintf('\tk4 = %.11f\n',k(4))
: h+ a" o1 I( u1 |2 _' gfprintf('\tk5 = %.11f\n',k(5))
4 G% p5 g6 H  Q! P7 ~4 a# \1 [0 b! a# Kfprintf('\tk6 = %.11f\n',k(6))
! S2 U2 h3 x8 `fprintf('\tk7 = %.11f\n',k(7))4 y4 S8 o" v; [' X0 y: u" U% ^* x( O- I- J
fprintf('\tk8 = %.11f\n',k(8))5 A* ^* z$ l- A. s1 R) A0 r! S
fprintf('\tk9 = %.11f\n',k(9))
: u  g: k: b* e/ l# B. F/ hfprintf('\tk10 = %.11f\n',k(10))
% B, q/ T$ I& s9 Kfprintf('  The sum of the squares is: %.1e\n\n',resnorm)5 l' S2 S: s& t9 q# c4 W
k_ls = k;" `/ h( o( l; {' ?5 u* m
output
) a% q* T/ l. q* I# rwarning off$ ~4 F0 _; H5 ?; e
% 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
6 P; T3 b: j. [6 ?- O7 x. T  S( ^6 }k0 = k_fm;
+ S, s1 |* h/ b# [& a; z) G[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
# `5 n  o: K- v. |# q* f5 H0 w    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
. ^3 X& z8 ]$ W3 G1 dci = nlparci(k,residual,jacobian);
$ V% r" @% h7 M* ufprintf('\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')$ A$ r7 w0 |$ B. E: r" _
fprintf('\tk1 = %.11f\n',k(1))
# z! R5 `4 m3 M* g: ]; L  p5 Rfprintf('\tk2 = %.11f\n',k(2))
7 B0 `. {1 y. e/ C7 f0 p( U8 gfprintf('\tk3 = %.11f\n',k(3))
/ e' X1 v" e* B/ {( f/ M- U' efprintf('\tk4 = %.11f\n',k(4))
+ O' ?0 K% ^5 q8 O5 B5 ^fprintf('\tk5 = %.11f\n',k(5)). y3 D% E" L; f' M, \( |. c
fprintf('\tk6 = %.11f\n',k(6))
  Z1 l; Y  J: G4 w* H% @* lfprintf('\tk7 = %.11f\n',k(7))8 X/ [4 ~8 G7 {1 l
fprintf('\tk8 = %.11f\n',k(8))
( R/ N- m8 D& W4 Mfprintf('\tk9 = %.11f\n',k(9))! E% l1 r3 I  H! F
fprintf('\tk10 = %.11f\n',k(10))4 M& X8 D; W6 q8 F: M' W- S
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
- j8 S7 }- ~! w+ B' {$ g( ?) Mk_fmls = k;+ Q& Q  A0 A0 u; I
output
. s$ O* ]0 f( r9 Q* T, g7 Q3 k& ?tspan = [0 15 30 45 60 90 120 180 240 300 360];  z- i1 q4 ]/ l% D4 [' z
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls); 5 K" R' \( X) K/ _8 A& [
figure;
* F2 U; S: i% W2 ?! _  N3 j3 `/ ^plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
( e" i+ s& ^6 v. \9 Tfigure;plot(t,x(:,2:5));1 C. G* j2 u' W* \% P% ^0 \
p=x(:,1:5)
# u, J/ S; J" \& hhold on" S- x& W% T: U0 }: S! |
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')0 j- Z( n% [, g0 y* t* @6 O: x

; W8 ^( L) R3 x! w$ l) ?9 x! y: Y" e5 j4 y. y

8 Z# B+ w  M  p1 ^( {6 ~& afunction f = ObjFunc7LNL(k,x0,yexp)5 F7 L7 X8 a) A( z7 @0 x' ~
tspan = [0 15 30 45 60 90 120 180 240 300 360];1 _, B1 _6 Z8 I1 S- C
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   + I6 ]5 q9 c0 R5 d
y(:,2) = x(:,1);
# I& U' B, I3 `' w' o; qy(:,3:6) = x(:,2:5);
5 b2 H. R# d9 v( p% z& P. ]. [7 sf1 = y(:,2) - yexp(:,2);
6 S+ D! ?' ~* X  [$ y# Q! Pf2 = y(:,3) - yexp(:,3);1 w- g* [: O0 X3 G0 G; x
f3 = y(:,4) - yexp(:,4);
* z/ ~* x( o& G: j1 Y+ Y3 Qf4 = y(:,5) - yexp(:,5);! y) t/ Y& C6 K6 g. a* c- N
f5 = y(:,6) - yexp(:,6);8 A- V+ t5 X5 L7 U* L* |
f = [f1; f2; f3; f4; f5];  _  b8 ]) f! y$ G7 g7 m6 m, o
- H, g% ?- z5 ]2 j

' E9 u. P/ ~, j' _: \; `! ]1 f
. Y  @) c) G4 S9 C( |4 L  s% H+ s+ ]function f = ObjFunc7Fmincon(k,x0,yexp)3 L- q2 s% z" ?$ \
tspan = [0 15 30 45 60 90 120 180 240 300 360];
' a$ s" q! n4 v! n2 l; f[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
8 ^) E4 J  S3 K9 ]/ U& g) k, Wy(:,2) = x(:,1);5 H7 B- |* C! j
y(:,3:6) = x(:,2:5);
1 M# V. P. b0 Z7 o* Y+ x' a0 Uf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...5 j& J* F7 k% y# ]3 c
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
& t  k& H2 m3 F  y    + sum((y(:,6)-yexp(:,6)).^2) ;  H5 W8 h$ |6 B
0 d! J* E' b7 S2 d! l

/ r! F. @$ {$ }# E/ e8 c) f( I$ m1 q! D5 e2 t; f' Q, _. F: b2 h

8 u9 s$ M7 _  a7 m( y$ Zfunction dxdt = KineticEqs(t,x,k)* i, |1 r6 s! N" ^+ O
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
1 p6 u7 B" J5 R/ f5 YdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);0 z" i9 F# I6 [8 r+ i
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);* @. X, x9 t1 s- G. }0 h
dLadt = k(7)*x(5);
4 W$ \+ i* E! L' N. U: W, P" Z: zdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);' i3 K7 \: G( [9 K
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];+ x2 d( v0 ]; }2 j1 H* C! }

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