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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
8 D, n6 F" W+ y4 @* d% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
, B! V* n! b, C7 j0 u% k6->k6 k7->k7: W8 Y( j+ ~* h0 u
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% K6 F: \/ F: {& Q8 C0 @3 [% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
9 E9 a% u9 j' E' Y: P2 r% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);
3 K5 F6 |; l9 L' \, f& G% dLadt = k(7)*C(Hmf);
[- p. Z# E) ^' ?; z%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf); f, N e) F" D5 {
clear all
- U Z2 K* u/ E% tclc
% k6 j) x/ j5 a- ^format long7 b* M, a2 ?7 E5 Z8 ~8 f( O0 E
% t/min Glc Fru Fa La HMF/ mol/L / l8 L" E8 e* d. u5 t( o7 _
Kinetics=[0 0.25 0 0 0 0
7 q) X# D4 a, q& k7 r+ r) a. m 15 0.2319 0.01257 0.0048 0 2.50E-04
6 E9 h4 ] y! O3 h4 F 30 0.19345 0.027 0.00868 0 7.00E-04. i; {! |6 `' w9 w. o) q
45 0.15105 0.06975 0.02473 0 0.0033; U; m+ L' o& H9 d- \
60 0.13763 0.07397 0.02615 0 0.00428
$ R4 j* Y: m3 i+ ?+ p 90 0.08115 0.07877 0.07485 0 0.01405
6 \% g/ B2 ?( C2 m* E9 I 120 0.0656 0.07397 0.07885 0.00573 0.02143, Y' b, U$ E0 j1 P. L n
180 0.04488 0.0682 0.07135 0.0091 0.03623
- J1 Z2 y, J2 @: ]" K0 h 240 0.03653 0.06488 0.08945 0.01828 0.05452
& F, v% O+ N1 M7 ]" A9 R# O! a 300 0.02738 0.05448 0.09098 0.0227 0.05974 h7 T) M* b8 ]8 b0 c
360 0.01855 0.04125 0.09363 0.0239 0.06495];+ t# K' l5 A# d$ V. v* b$ P) }: F0 g
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
" J8 F4 N) R8 n9 Qlb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限- B w$ d2 Q& F
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限( n; |: ^+ G2 H9 z8 b$ B" C
x0 = [0.25 0 0 0 0];. r2 Y, x" v1 w& x0 C# e8 f3 h
yexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]
) i/ D7 D# \; r( S5 {) X1 u* L% warning off
6 z# e' \1 T; y6 }8 h% 使用函数 ()进行参数估计& z7 Q' C! I) W/ j& Y8 u! W3 ?
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
$ [8 E2 z+ S6 b, H7 d, cfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
) `" _, R1 [0 p! \3 s. k0 ^% Wfprintf('\tk1 = %.11f\n',k(1))
) x1 p* W, l$ k1 Ufprintf('\tk2 = %.11f\n',k(2))
; P! d0 `4 D% y2 |8 m6 u0 a# Yfprintf('\tk3 = %.11f\n',k(3))
% s- ^7 v8 ?: ?2 f$ ~- Afprintf('\tk4 = %.11f\n',k(4)), w9 G# m, c! M1 `+ Z. i
fprintf('\tk5 = %.11f\n',k(5))
- N7 s# C. M' W4 t7 u$ Ffprintf('\tk6 = %.11f\n',k(6))
% o5 K7 }* l9 }1 E9 \/ I% X; A/ \fprintf('\tk7 = %.11f\n',k(7)). S: y1 a0 d! m. i+ y( i
fprintf('\tk8 = %.11f\n',k(8))) D7 w0 T$ r( c) k' a6 O
fprintf('\tk9 = %.11f\n',k(9))
: V" L4 G- b* }1 r7 |2 h! Cfprintf('\tk10 = %.11f\n',k(10)) w. A/ p5 \( G7 b4 ~+ m! F5 X
fprintf(' The sum of the squares is: %.1e\n\n',fval)7 F2 _+ o2 B* B9 n+ S" A
k_fm= k;3 ?5 H+ y5 A2 t: u; E$ b
% warning off* b8 k' ~$ c& L. }: Q3 t
% 使用函数lsqnonlin()进行参数估计
- m" o- r' _ \! L6 }[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
( a U# ]. z) @) N; P lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
% _, Y1 }8 u- ~; g5 I" O- ?ci = nlparci(k,residual,jacobian);, }. N+ K% R9 y9 Y: d
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
( h' k, W' S y0 W) d) Z/ ^6 xfprintf('\tk1 = %.11f\n',k(1))
1 F _% d* J+ F+ Q4 yfprintf('\tk2 = %.11f\n',k(2))( F& B( J' h- M: H
fprintf('\tk3 = %.11f\n',k(3)). d' e) r: ~, P& |1 C( }
fprintf('\tk4 = %.11f\n',k(4))
7 L; y$ V6 r. Sfprintf('\tk5 = %.11f\n',k(5))6 ~3 B" J( L+ H& a1 ~9 ?. B! r
fprintf('\tk6 = %.11f\n',k(6))* I, T) T: i6 w& \5 z1 b
fprintf('\tk7 = %.11f\n',k(7))* a# M; y& W; u5 u% }
fprintf('\tk8 = %.11f\n',k(8))
- P9 w% g6 h4 M" Ffprintf('\tk9 = %.11f\n',k(9))/ c" F) d+ G$ j8 c
fprintf('\tk10 = %.11f\n',k(10))
# t4 B s; k6 W W- M. Gfprintf(' The sum of the squares is: %.1e\n\n',resnorm): Y' _& o3 ^# o. M
k_ls = k;
. x' d7 V* Z" W- }1 A0 ]output
% u1 i% @3 j+ `warning off# f, Q0 e% E+ W+ v
% 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( f5 X* y4 ~: {& `6 g+ E( z8 J
k0 = k_fm;6 N1 P8 @: p, y; }- M
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
0 F4 e$ m4 o6 w3 h( T lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); 6 z% O% _+ j4 ?6 t
ci = nlparci(k,residual,jacobian);1 E! X( f$ a3 c+ A* g( ?8 z
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')1 ^) n ^7 d! K" `' k& |4 n3 Q3 ?
fprintf('\tk1 = %.11f\n',k(1))4 t8 P2 k! r# n: o! m
fprintf('\tk2 = %.11f\n',k(2))
. y/ C" D- `9 b+ m( Dfprintf('\tk3 = %.11f\n',k(3))+ w0 W5 e" q* l7 s. n) j
fprintf('\tk4 = %.11f\n',k(4))
' q% G/ [! X& x+ ~2 I! kfprintf('\tk5 = %.11f\n',k(5)): `: K# A1 y. D9 w3 p# F5 V
fprintf('\tk6 = %.11f\n',k(6))! m0 w- P \* v! \% u7 w
fprintf('\tk7 = %.11f\n',k(7))
4 ]) h, ]1 m3 }+ l7 dfprintf('\tk8 = %.11f\n',k(8))0 f l7 H( y9 }
fprintf('\tk9 = %.11f\n',k(9))* X; |% G2 T4 A a& g: [# L' d! `
fprintf('\tk10 = %.11f\n',k(10))
* F) _0 D8 @+ {) O% ?4 ~fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
3 @0 p% Q( U- \& W Zk_fmls = k; h1 F# J2 P) a% C
output
9 D6 a) l' B% z6 B3 |7 n# _ P# htspan = [0 15 30 45 60 90 120 180 240 300 360];
; m! G$ g1 ?) o' D6 W+ @2 T" l8 l[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
$ X0 v: Z2 ~" |3 u9 @# Rfigure;
7 i, J5 X/ C0 t3 \/ wplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
/ F/ X. C& E$ J: p. mfigure;plot(t,x(:,2:5));6 L' [+ C2 v A3 {
p=x(:,1:5)& {' i9 g" V, c# I/ N: D
hold on
+ ^/ T. q1 n3 C8 J4 kplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
" l5 y$ S' k8 a5 l2 P6 E* r E" H& I/ ~7 ?1 T; L& G$ c
- M* O0 X* ~' c/ a5 v2 T
7 t2 }3 M) V3 z I7 C: I+ yfunction f = ObjFunc7LNL(k,x0,yexp)
5 o: o# U4 ?* U, h0 Wtspan = [0 15 30 45 60 90 120 180 240 300 360];, ~4 g: `/ a3 z5 _% {& F+ f
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);
- f6 _& }- _* ~7 my(:,2) = x(:,1);. M' l* T5 R# m! p+ ^3 Q: N
y(:,3:6) = x(:,2:5);
- z' A" d# {/ T/ _2 e5 K+ l0 ?( ^f1 = y(:,2) - yexp(:,2);4 v6 } O j% O0 L( X' y4 ~0 _! G L
f2 = y(:,3) - yexp(:,3);
& }+ F; z, ^6 _7 I* Hf3 = y(:,4) - yexp(:,4);8 r0 i/ x! M. x! p8 O7 d* \1 u3 Q
f4 = y(:,5) - yexp(:,5);
/ ?2 U. S+ `" y: `; H8 H$ qf5 = y(:,6) - yexp(:,6);2 H o2 v) Z) {$ I& ~
f = [f1; f2; f3; f4; f5]; `. E* u7 ]' b
5 f3 z6 h+ ]/ e1 I4 S# l, J: ^
! ?7 s- P2 C5 o/ q, y: W6 S$ l
7 q" d, W1 u& wfunction f = ObjFunc7Fmincon(k,x0,yexp)
3 x* n) A' a1 t3 utspan = [0 15 30 45 60 90 120 180 240 300 360];- g' E R# }& s( m- _6 b
[t x] = ode45(@KineticEqs,tspan,x0,[],k); 7 E$ b' Q% `, e T& `; B, B0 U
y(:,2) = x(:,1);+ w7 B2 f- u+ y
y(:,3:6) = x(:,2:5);
; Z( w2 j: s' S+ V) F0 Z6 I: Mf = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
2 E* i, W- ?" d: N2 ?7 q k! _ + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...' d4 E: u/ z8 q8 c6 {0 g
+ sum((y(:,6)-yexp(:,6)).^2) ;0 |- D4 |( `8 V \# G3 f
9 i8 ` b8 n+ S+ A' q8 m- r
: B( Y# q/ a+ q1 [4 ]1 t" A3 t3 V m" ]8 o
4 _' L8 Q8 e: z) W. r
function dxdt = KineticEqs(t,x,k)! |7 v) I% g% }8 q
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1); @3 Z& U5 ?9 R" |. D+ l
dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);' y- C. C G% l6 X7 R
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
9 O/ k! `' K9 o. o6 fdLadt = k(7)*x(5);7 m& D% b% I% u2 G1 {) W
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);* S( k# s( s" Z" T: F" X6 s
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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Glc.zip
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