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升级   87.37% TA的每日心情 | 无聊 2015-10-10 18:19 |
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签到天数: 24 天 [LV.4]偶尔看看III
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10体力
function parafit
# M9 L" x, Z) |9 x6 x% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
2 p) w7 m G5 M+ N# R% k6->k6 k7->k7
( i0 E( G2 D! C0 A% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
/ e9 S3 `8 _0 \; N% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
! B& e! T4 {- ~3 ?% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);* H8 e, p: y( j5 m
% dLadt = k(7)*C(Hmf);; i& k4 S8 Y( l H i
%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);. Y f# g8 S& _; Y
clear all7 y' \$ R; N/ Q; D# N8 a4 |% _
clc
9 H( S* }' V" D/ Nformat long
7 F' F6 n* N+ E! a' ]1 ^, P% t/min Glc Fru Fa La HMF/ mol/L , Z# ~+ K# Z/ v/ F# B0 |
Kinetics=[0 0.25 0 0 0 02 S' p8 B& s) o0 |2 j8 D( F
15 0.2319 0.01257 0.0048 0 2.50E-04
) i, M4 k* Y. r5 ?5 B7 W; Y5 ]. f9 A 30 0.19345 0.027 0.00868 0 7.00E-046 R% [5 D! n$ t7 `& R
45 0.15105 0.06975 0.02473 0 0.0033
, y: Z' p, z* \! W7 r( Q 60 0.13763 0.07397 0.02615 0 0.00428
8 ?9 B' p5 I' T3 K7 m: v 90 0.08115 0.07877 0.07485 0 0.01405, Y$ T9 X& n( P R* i
120 0.0656 0.07397 0.07885 0.00573 0.02143
x* ~8 C: j$ |) r1 n 180 0.04488 0.0682 0.07135 0.0091 0.03623
8 N3 ]$ ]3 t1 D 240 0.03653 0.06488 0.08945 0.01828 0.05452$ b; Z$ _0 z$ L Y# f
300 0.02738 0.05448 0.09098 0.0227 0.0597
% G: N4 d5 k5 q 360 0.01855 0.04125 0.09363 0.0239 0.06495];$ l& x' a. h; @+ S" p' S
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: x' i9 J) h; Qlb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限" }( l1 f, B/ O0 F1 o, _; t
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限
; ~$ | o& r {/ ]x0 = [0.25 0 0 0 0];
) y5 V# Y' g, }6 L3 Tyexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]- M3 y, z+ \ w. Y
% warning off
. B# V2 X2 |, W# t! G% 使用函数 ()进行参数估计( f+ z% M" B2 x2 u+ k
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);2 P2 s* ?: i7 m5 Z5 T: Y/ d
fprintf('\n使用函数fmincon()估计得到的参数值为:\n')
- B1 y7 \6 k+ G0 M/ R: k3 E" Wfprintf('\tk1 = %.11f\n',k(1))
: V% T) W8 z# o3 a# j. q* k$ }0 G9 Bfprintf('\tk2 = %.11f\n',k(2)), g* q2 P4 H0 s' B. Y0 ?2 I" B* d9 l
fprintf('\tk3 = %.11f\n',k(3))1 a" Y2 V4 B5 B! `6 N
fprintf('\tk4 = %.11f\n',k(4))
$ m I* X8 z1 R: U8 C' F1 M1 vfprintf('\tk5 = %.11f\n',k(5))/ W+ f$ s! G$ u# w
fprintf('\tk6 = %.11f\n',k(6)) x& {/ l* U7 y6 B0 E1 w
fprintf('\tk7 = %.11f\n',k(7))' n- y \# Y0 G9 I/ j
fprintf('\tk8 = %.11f\n',k(8))! `$ |7 e' B6 H' y
fprintf('\tk9 = %.11f\n',k(9)): ^' r; C" Q$ C' R" T8 O* q- p' e
fprintf('\tk10 = %.11f\n',k(10))+ N8 C6 Z' M; K" O
fprintf(' The sum of the squares is: %.1e\n\n',fval)6 U, W9 D% H# F3 n3 J2 d2 u) m W
k_fm= k;9 q( q6 ~0 ~8 M. q/ j0 Q) u& W
% warning off. u; o$ c3 ]( y% Z; R/ F7 h3 F' J9 ^
% 使用函数lsqnonlin()进行参数估计8 D3 d- i* h1 r
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
5 e2 X B& [! _ M1 h! d+ Q3 V lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); + j# [ ?! C: V. M$ `+ O
ci = nlparci(k,residual,jacobian);
, _7 ?4 o/ m" V, Z2 O* ?) U4 Mfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')5 ` `5 }; k: I! x. i/ H
fprintf('\tk1 = %.11f\n',k(1))
9 ]1 h P: X& j. D+ y6 y# K( Vfprintf('\tk2 = %.11f\n',k(2))
* c" c f1 o6 m/ `fprintf('\tk3 = %.11f\n',k(3))0 \. g7 b5 c9 t) A7 X8 H, H
fprintf('\tk4 = %.11f\n',k(4))1 f" F: B2 [7 U, V# V
fprintf('\tk5 = %.11f\n',k(5))
2 T* x% o8 A( |7 jfprintf('\tk6 = %.11f\n',k(6))! m* a- V: X$ }, [! @
fprintf('\tk7 = %.11f\n',k(7))
+ ?6 K0 P# @) i" U/ Q! gfprintf('\tk8 = %.11f\n',k(8))* ^" N- }& D5 ~! d0 M! M
fprintf('\tk9 = %.11f\n',k(9))5 N) p7 T- B" v% N( f r# l8 {
fprintf('\tk10 = %.11f\n',k(10))
+ ] K6 m7 M! w4 Qfprintf(' The sum of the squares is: %.1e\n\n',resnorm)6 A' B) S, m3 y( |! B0 h
k_ls = k;& ^. ?# L( G- d9 v! e6 U
output$ J k' a9 r9 m$ r
warning off! m. M/ y+ n! F I7 B9 ~+ X; p( s( d
% 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
8 g8 G1 e t( T: \k0 = k_fm;5 n, m: Z5 m0 Z" v8 F5 [
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...9 E$ {5 @3 g5 V1 X
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
% s+ ]5 m4 d) U9 y% zci = nlparci(k,residual,jacobian);) M3 z J; I5 Y: k' @, R% M
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')
* W6 Y* o! ~3 h7 }9 [' nfprintf('\tk1 = %.11f\n',k(1))
. z" j* P9 n9 z1 `8 Y$ P5 Z" cfprintf('\tk2 = %.11f\n',k(2))
, T$ R$ C( S8 n) ]6 u6 a5 `9 `fprintf('\tk3 = %.11f\n',k(3))' N* }) p6 |7 Y% o8 O
fprintf('\tk4 = %.11f\n',k(4))8 Y, ~$ x! k4 v. A; {9 ^& G: {
fprintf('\tk5 = %.11f\n',k(5))9 H# v- k; ?! o& u
fprintf('\tk6 = %.11f\n',k(6)) b/ w* Q j5 `$ A+ X$ g9 P- G% f: T
fprintf('\tk7 = %.11f\n',k(7))9 @: J7 v" |* ^& ^2 v
fprintf('\tk8 = %.11f\n',k(8))
: D g; f' T% v+ D6 o( r: J1 vfprintf('\tk9 = %.11f\n',k(9))
1 e: W/ X/ h/ a; i' \3 A7 n/ e! _fprintf('\tk10 = %.11f\n',k(10))0 }: p, c. W( L5 [
fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
5 H( A: `" K `k_fmls = k;% P+ q5 a6 A3 o4 g7 P
output" `9 R# r9 T6 a' _. \( U1 B
tspan = [0 15 30 45 60 90 120 180 240 300 360];5 B4 |4 u' n, A
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
* Q0 ]% | w- ]. K# Z: G% Xfigure;$ T" |) g+ x k& ]
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')! ~0 Q8 X* y4 j: B A7 g
figure;plot(t,x(:,2:5));; x- U, d( n. o- \6 O
p=x(:,1:5)
2 V# y9 F9 |% I% T. jhold on2 k5 `! f( Z. T6 e, d
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
3 @7 x" H; b& B4 c0 w. x& j; z
6 r' S6 u8 l2 ~7 J# O# m/ Z3 x) {
$ c; Y K9 e# ]% r+ v5 j
% G( {* f2 y0 [) bfunction f = ObjFunc7LNL(k,x0,yexp)" [; ^9 A# f: o8 n, I
tspan = [0 15 30 45 60 90 120 180 240 300 360];- B* h p6 p: V+ D
[t, x] = ode45(@KineticEqs,tspan,x0,[],k); 8 T( L5 _0 H& B& r
y(:,2) = x(:,1);
& `4 E% v3 @3 x# c/ wy(:,3:6) = x(:,2:5); s, g2 g: F$ C, c6 n/ b# A) ?) l$ u$ W
f1 = y(:,2) - yexp(:,2);- y3 n$ @& u9 G7 [% N
f2 = y(:,3) - yexp(:,3);
( h: R5 D2 Z ^f3 = y(:,4) - yexp(:,4);
1 E* E. q# k# N8 H. E7 ~ ?9 `1 p$ _f4 = y(:,5) - yexp(:,5);8 M% z& A. Q. O+ H" h
f5 = y(:,6) - yexp(:,6);
- V1 U, o' P9 q; ~5 D+ ff = [f1; f2; f3; f4; f5];
! t. j# b- ^$ u* {2 l
0 \: W0 F& d# ?2 T* |* S/ G+ s" p* h7 A3 n, }7 c! s+ @: ~! F
/ A4 W9 N; Q6 @4 j
function f = ObjFunc7Fmincon(k,x0,yexp)
6 M0 T$ `$ k+ m+ ]# _% `tspan = [0 15 30 45 60 90 120 180 240 300 360];8 K% e9 j6 @( ^& u0 Z' `; s+ `/ |
[t x] = ode45(@KineticEqs,tspan,x0,[],k);
3 `* U7 i8 y& w' R/ Hy(:,2) = x(:,1);
% m& z+ S. f' gy(:,3:6) = x(:,2:5);
. l5 @0 ?9 f8 u( j7 i* k6 Nf = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...6 m) N8 e( U* S( ^
+ sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...
& a: Z7 m1 V& O + sum((y(:,6)-yexp(:,6)).^2) ;
1 F2 e9 P( H* s( w# B1 ]. K- [% [: e: X: G1 p( s9 M9 f
2 X6 L X) {$ B' D6 F, ?, `8 @6 G5 N
/ w$ f1 k* n2 L, I+ K
function dxdt = KineticEqs(t,x,k)
, q% u$ ?, ~ _dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
5 Y ]8 m) O) S0 Y& ?% b% s$ |7 JdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);) O" _. x3 K' M* c4 _; r
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
( s- `6 Z& J: L; L8 HdLadt = k(7)*x(5);
/ E* e3 q2 x. `- @dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
. U1 [4 A" P' n+ e' f: mdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];# m! b+ w( H& o( g4 m6 N5 h
5 _, N. e2 r2 o6 j& E
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Glc.zip
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