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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 T5 {# C3 m2 e+ Y1 R9 `
% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
; D% N" l3 W( \- _+ P/ A9 E& h9 R% k6->k6 k7->k7' _' q% u7 }5 \0 U9 O
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
, G" v/ d( q* N& t% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);" M1 @) G5 U( a
% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);
0 T+ i- ^, `) w; k6 B/ h5 Q% dLadt = k(7)*C(Hmf);5 `% U& J; [/ E9 u9 G% h0 d9 X, z7 S$ `
%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);
% r: h! e9 w! r7 e6 c1 l6 I; |1 Jclear all
0 h8 i3 }1 k5 e# A) n7 Y& S/ E, ~ m Iclc# @6 ^7 I* U: |9 r8 G
format long0 c7 r. V, d, F' Q1 k# @
% t/min Glc Fru Fa La HMF/ mol/L
* |2 H0 R1 d1 l4 z! Q Kinetics=[0 0.25 0 0 0 05 @# E/ P/ N6 ]& ?4 c) B' r) f& S
15 0.2319 0.01257 0.0048 0 2.50E-046 g0 I/ S) H2 N+ P6 [* m
30 0.19345 0.027 0.00868 0 7.00E-04
% ~" d: ~7 {9 R5 s+ B' K 45 0.15105 0.06975 0.02473 0 0.0033% e& r4 U% I+ x6 u0 @, o2 G3 V" Y
60 0.13763 0.07397 0.02615 0 0.004289 N2 ]" w0 O7 H7 W, |" `9 X
90 0.08115 0.07877 0.07485 0 0.014050 Y0 V: F) M, ~
120 0.0656 0.07397 0.07885 0.00573 0.02143
2 T/ M. s! D+ T# F: F8 ~ 180 0.04488 0.0682 0.07135 0.0091 0.03623' G/ P; q: h) K) b! H) u
240 0.03653 0.06488 0.08945 0.01828 0.05452$ L( F/ }* J! D* M
300 0.02738 0.05448 0.09098 0.0227 0.0597! }, ~5 i8 ~4 C! D1 j# O
360 0.01855 0.04125 0.09363 0.0239 0.06495];0 T- n6 ]' b5 Q: g3 ]# ^
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' ]0 W# ]- C3 M1 ^
lb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限" p" k$ D/ B( b% F% V- i, D
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限9 O% s- J4 [& _ f* y" r+ B- L! j$ Q3 M
x0 = [0.25 0 0 0 0];
' r$ @% [, W+ E# |yexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]
9 z1 W/ L! [5 U% I E% warning off5 _* x% U* L. V; q
% 使用函数 ()进行参数估计
3 b. E+ H2 M4 I2 u: \" y2 [( C[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
: A9 V+ V: H& F2 f; |) s& _& ?( \fprintf('\n使用函数fmincon()估计得到的参数值为:\n')+ \/ s: g1 t$ j1 E# V
fprintf('\tk1 = %.11f\n',k(1))! G- {% C3 L. O7 x/ g
fprintf('\tk2 = %.11f\n',k(2))
+ o8 [/ p1 t) E( r0 ~fprintf('\tk3 = %.11f\n',k(3))
[) u4 b; [5 ]* g" O4 ofprintf('\tk4 = %.11f\n',k(4))
7 s/ ^* K- D5 q" Q6 h2 dfprintf('\tk5 = %.11f\n',k(5))
. D! Z ~ Q+ z, h- M' rfprintf('\tk6 = %.11f\n',k(6)). S. X7 r% Y+ m/ J7 l- K
fprintf('\tk7 = %.11f\n',k(7))
- B/ `, R# j9 m+ mfprintf('\tk8 = %.11f\n',k(8))
$ A! e3 L. l2 i/ ~ }+ z. Qfprintf('\tk9 = %.11f\n',k(9))5 w( d5 R( Y% v5 P
fprintf('\tk10 = %.11f\n',k(10))7 K9 F- W) J+ B" U6 I
fprintf(' The sum of the squares is: %.1e\n\n',fval)' N, f* `* G* s4 V! r
k_fm= k;8 H' @: N' i0 {4 y" Z' f
% warning off9 D/ _4 j% Q$ E
% 使用函数lsqnonlin()进行参数估计
& V3 ]" d4 g3 ?& [7 b; C[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...: y' u1 D) Y7 w' _9 g
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
% _- P) z. q: B8 _% G' Hci = nlparci(k,residual,jacobian);
6 j0 D0 \! H5 N H* [fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
8 r2 t$ I% x1 \8 d7 e/ K# z0 Dfprintf('\tk1 = %.11f\n',k(1))- l) n' [8 X0 G4 K, Y
fprintf('\tk2 = %.11f\n',k(2))
* |3 P7 n* p( |. Ffprintf('\tk3 = %.11f\n',k(3))
S( }- B @4 ?2 ?! jfprintf('\tk4 = %.11f\n',k(4))3 `* f0 e' l9 w* o
fprintf('\tk5 = %.11f\n',k(5))
, H$ M% v0 t) Y5 ]- Gfprintf('\tk6 = %.11f\n',k(6))
4 @, f$ M4 Q2 B3 L! S8 G N( Hfprintf('\tk7 = %.11f\n',k(7))+ h; ~7 Q8 m: H0 `5 O# J- I
fprintf('\tk8 = %.11f\n',k(8))" N. u* z/ z. {/ f/ y5 q+ ^, J
fprintf('\tk9 = %.11f\n',k(9))7 _# r* F$ t3 {' A. [
fprintf('\tk10 = %.11f\n',k(10))( v) _: t& e8 S+ `% k3 M
fprintf(' The sum of the squares is: %.1e\n\n',resnorm)2 R& ?- P$ ^; Y
k_ls = k;
2 l7 `# X. j$ Q6 |; [output
: {( U/ d4 ^, _; jwarning off
# e2 g- Y. e5 m4 m0 `% 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% R/ J0 P' ~2 ?. W; y4 j
k0 = k_fm;
$ w3 M( l T7 m8 ~; K[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...0 f/ U0 J4 c+ D3 z3 f; O
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); & V: d& t+ L+ ~8 ]' H- f
ci = nlparci(k,residual,jacobian);
1 [# g1 H% b: cfprintf('\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')
% w' ?; K2 N, m7 i/ u. b5 X$ v. }fprintf('\tk1 = %.11f\n',k(1)) Q/ i% |6 o8 J! q8 N% Q
fprintf('\tk2 = %.11f\n',k(2))# j8 l6 [( X* t6 E& W$ b
fprintf('\tk3 = %.11f\n',k(3)), }1 k. i, c3 S8 x* l# u
fprintf('\tk4 = %.11f\n',k(4))# i6 v; N; s0 _1 |3 t
fprintf('\tk5 = %.11f\n',k(5))
% P3 i: S2 \4 U s6 O- v+ ^1 Jfprintf('\tk6 = %.11f\n',k(6))* _$ P5 d, [" Y8 y& k
fprintf('\tk7 = %.11f\n',k(7))
: n. Q$ M! k; i qfprintf('\tk8 = %.11f\n',k(8))5 e$ X" X4 G- T- [8 a" R/ Q
fprintf('\tk9 = %.11f\n',k(9))0 |9 H) n) }/ T
fprintf('\tk10 = %.11f\n',k(10))
' \6 g/ K/ H, Ufprintf(' The sum of the squares is: %.1e\n\n',resnorm)9 j$ E& T/ u1 |
k_fmls = k;
" b6 G0 P3 ~2 Aoutput
' C% [9 j) J/ e* N9 K y& Gtspan = [0 15 30 45 60 90 120 180 240 300 360];$ X5 N9 P# r- N1 D, k; P: e
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls); - W+ ^) i" g8 T
figure;
; I+ f- u3 I' }* `plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')9 k9 C' G% }5 _4 I9 G% P
figure;plot(t,x(:,2:5));1 {" M1 n: G, o! u
p=x(:,1:5)
6 q. o* Q* I; e* ]; z: ]' Dhold on
. K, I# l$ G. `0 H; |plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')( R$ y1 M$ g; q% a
: J7 W; X3 c C! ?; G
6 G, r d0 ~# z u" }
# ?9 }- [3 g( u* ~, X" f# d! X9 yfunction f = ObjFunc7LNL(k,x0,yexp)4 d% I* {5 m" }/ w) l Q1 L
tspan = [0 15 30 45 60 90 120 180 240 300 360];
. N! L+ ~% J# u, R2 r4 ^& Z[t, x] = ode45(@KineticEqs,tspan,x0,[],k);
h; k7 h/ n4 f" U0 O, Hy(:,2) = x(:,1);; ^ s) c: U- L7 w( U% [
y(:,3:6) = x(:,2:5);0 t$ y$ y5 |) z- i2 F7 Y/ e& G
f1 = y(:,2) - yexp(:,2);
4 \, o1 t0 R1 if2 = y(:,3) - yexp(:,3);/ v& [! W! f+ E2 d: s" q
f3 = y(:,4) - yexp(:,4);
/ c, Z3 v% S- j% [ m2 ^f4 = y(:,5) - yexp(:,5);% Y+ u6 D7 P" f2 u8 w
f5 = y(:,6) - yexp(:,6);
7 G* c/ |- [# w; U5 H- z7 Tf = [f1; f2; f3; f4; f5];
4 `. F/ Y( O# x' @6 H7 B" i* a4 u, g4 @0 A
5 X1 {8 n2 Z# P7 f
$ D6 E9 p6 T: ^function f = ObjFunc7Fmincon(k,x0,yexp)" K+ i& U; D7 c O1 \# ?# Q" D/ h2 n
tspan = [0 15 30 45 60 90 120 180 240 300 360];9 u* m5 a ^2 I' _ S
[t x] = ode45(@KineticEqs,tspan,x0,[],k); 1 g( X I6 [4 ~3 o. S9 f: L( Y
y(:,2) = x(:,1);
" a% X8 D( |4 T, H/ e" v! p# by(:,3:6) = x(:,2:5);( @) F2 j9 a9 E' k" e1 n
f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...8 B; {! ^4 k1 q' O8 u
+ sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ... g; S9 K' |& x
+ sum((y(:,6)-yexp(:,6)).^2) ;
& }8 F6 D" d( H1 X* W! B. T
+ J% n {+ T( U0 U: I: E5 |+ n8 ~ D- O
6 l" U) w; p9 @: }! P2 l/ u
' \/ F3 H! s+ r7 bfunction dxdt = KineticEqs(t,x,k) S r3 \; I3 X/ j
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);3 ]5 f5 ~' W; a# n; H& Y
dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);# f1 u! z7 j, @6 Q% _- h
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
# P# G/ R' k: ~; x) J( NdLadt = k(7)*x(5);
" }+ z/ [1 A* {3 J4 GdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
0 a0 b2 O+ S# z/ cdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];/ S' x1 t/ E. E3 v4 y% M& l
% r& l& d* r+ R9 ]. N
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