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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
# C$ A3 L5 P4 k! U% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
# e8 U7 [3 J2 P" C1 [ d" r" Y% k6->k6 k7->k7
( U/ p" d4 b" g B+ C% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);$ w- v) n. ?/ d- Z6 @/ g
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);8 q& @, ~7 m$ |, g0 e/ g
% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);
1 Y8 ]! \5 m/ K9 e+ v& Y3 Z9 u% dLadt = k(7)*C(Hmf);& g3 b N6 {1 s. U0 E
%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);
1 G' C6 o9 N r) h* } kclear all# C' H( [! A$ g# h
clc
4 ` u0 d5 D& ?/ H, } J- wformat long
0 ]( B7 B8 E6 j; P# q% t/min Glc Fru Fa La HMF/ mol/L
8 @% D) [7 v( [2 u' U% J) T Kinetics=[0 0.25 0 0 0 0
( u/ y$ e% v+ y) q/ ^5 } 15 0.2319 0.01257 0.0048 0 2.50E-049 k0 Q" Z" Y$ X5 w! Q6 o
30 0.19345 0.027 0.00868 0 7.00E-04
1 v& R/ `$ [- N 45 0.15105 0.06975 0.02473 0 0.0033- e) W, D, } ?& j$ s
60 0.13763 0.07397 0.02615 0 0.00428
6 l/ O% {3 T1 j% G 90 0.08115 0.07877 0.07485 0 0.01405, L m* W( ]. A. p: a- z1 A
120 0.0656 0.07397 0.07885 0.00573 0.02143/ w# G9 a$ E$ d$ {5 v7 B r
180 0.04488 0.0682 0.07135 0.0091 0.03623
6 F; K$ J2 }5 @1 ^( H; I* L 240 0.03653 0.06488 0.08945 0.01828 0.05452
# i0 a l) m; ? 300 0.02738 0.05448 0.09098 0.0227 0.0597/ f6 K; |5 ]" z$ y9 X; N
360 0.01855 0.04125 0.09363 0.0239 0.06495];
7 s/ }6 P2 k ak0 = [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 Z1 k/ u; D0 D$ k; K. h5 Olb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限. S) ~& e9 F9 Z8 r7 x
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限
. k/ x7 z; J& C' ~x0 = [0.25 0 0 0 0];
/ \. U% N. ?7 c( iyexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]
: Z0 _$ ~. G6 ~$ b ~$ A/ Q% warning off
8 M, z6 l9 ^6 R& I" g& a% 使用函数 ()进行参数估计2 |' o, ]( K1 s* ^% A! W% p4 b
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
) ~: I4 o9 a/ B5 q* ~- i# B3 H6 lfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
" Y: p9 z, d; O3 s4 v1 {fprintf('\tk1 = %.11f\n',k(1))0 A* u( x4 h+ N" |
fprintf('\tk2 = %.11f\n',k(2))& f& F7 ~) E; R: R8 f
fprintf('\tk3 = %.11f\n',k(3))" r% K1 ^- n, c8 f# B
fprintf('\tk4 = %.11f\n',k(4))% I# E3 \6 |6 C& | J, D/ ]- i
fprintf('\tk5 = %.11f\n',k(5))5 V; S3 q1 f) ?
fprintf('\tk6 = %.11f\n',k(6))- [( v6 V/ n! J; M$ g* t
fprintf('\tk7 = %.11f\n',k(7))' e1 m( |0 [ O" Y$ K4 \
fprintf('\tk8 = %.11f\n',k(8))8 f" P( w% x0 Q' \1 v
fprintf('\tk9 = %.11f\n',k(9))
, l" t' p8 Q C% n2 nfprintf('\tk10 = %.11f\n',k(10))
" S9 K" P2 [! a9 r6 ufprintf(' The sum of the squares is: %.1e\n\n',fval)* z/ N) w/ @3 {
k_fm= k;
# h$ o% o7 b* Y' e9 S. [% warning off
* S2 |0 B `/ l2 G# E7 C* ~3 R; \1 X/ @% 使用函数lsqnonlin()进行参数估计
O6 e6 O/ ~" z( ?. e[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...+ `0 {& X# ^, i$ ]! M/ x
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); 5 `+ @2 V& F2 i2 W
ci = nlparci(k,residual,jacobian);* M# C% U8 T* q; \1 @
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')0 I2 F# P- a+ N# [& [
fprintf('\tk1 = %.11f\n',k(1))6 }" i f' P9 |; h/ W. N4 K2 @
fprintf('\tk2 = %.11f\n',k(2))( N; `% s5 T* N" k
fprintf('\tk3 = %.11f\n',k(3))% u1 y" e8 ~5 O. g9 s+ {
fprintf('\tk4 = %.11f\n',k(4))8 j. V7 X0 V3 {9 `3 x7 v" @
fprintf('\tk5 = %.11f\n',k(5))
5 W ?) H# C9 r8 t7 O: R3 N/ m) qfprintf('\tk6 = %.11f\n',k(6))% F- ]0 o9 {/ B- J; J
fprintf('\tk7 = %.11f\n',k(7))& e# T3 C6 F, |
fprintf('\tk8 = %.11f\n',k(8))
7 F! _7 m0 C% n7 y9 n* zfprintf('\tk9 = %.11f\n',k(9))1 d% V( [" V6 f4 v) t
fprintf('\tk10 = %.11f\n',k(10))
2 | M* V) _$ b. H4 kfprintf(' The sum of the squares is: %.1e\n\n',resnorm)
3 r. I7 y% L8 r1 z- Z/ `( a# c! j# pk_ls = k;
" |1 D7 Z+ }( @% \, [& D* g- l: @' woutput- E5 o& y% ~: ?& Y% V {6 ?9 R
warning off
7 V/ P C, H8 {# x2 n- @% 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5 z: E% u) q- z; P: Q! ^ J
k0 = k_fm;9 G' N. r/ {# f3 H7 K
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...8 D3 k9 T5 q' I/ Z8 N# G
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); 9 [' }, k* [! Y$ n) t; u: u
ci = nlparci(k,residual,jacobian);# ?8 Z0 G( q; \
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')
0 S, C8 {9 `) J& ?5 Gfprintf('\tk1 = %.11f\n',k(1))8 [# ?& U1 ?: \2 o6 I8 F, T$ G
fprintf('\tk2 = %.11f\n',k(2))
0 b2 \8 h6 c/ y( l2 A" X: Q" v) Wfprintf('\tk3 = %.11f\n',k(3))" ^3 V. O5 V$ Z, h
fprintf('\tk4 = %.11f\n',k(4))
# T& q" ]& o7 c+ {fprintf('\tk5 = %.11f\n',k(5))
' q. }1 a, C( yfprintf('\tk6 = %.11f\n',k(6))5 b4 h- D4 i% e! Q& y9 Y
fprintf('\tk7 = %.11f\n',k(7)). E/ T t: }8 h" w; e: y1 {# X, W2 P3 @
fprintf('\tk8 = %.11f\n',k(8))
0 L) x) u1 B. S- O& u7 F) d0 dfprintf('\tk9 = %.11f\n',k(9))
0 w3 V! ^" I9 h' K% gfprintf('\tk10 = %.11f\n',k(10))5 a6 V5 R* r' n/ d) ?- k7 T
fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
3 Z# r F8 M. h9 `k_fmls = k;
+ f# j# H6 g5 uoutput: S/ _8 f" B9 I3 m0 b
tspan = [0 15 30 45 60 90 120 180 240 300 360];6 L0 R* R/ Q/ ~9 [! X
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
2 f0 B" ]1 A: Y$ z, u$ V3 Mfigure;* A5 b8 T2 A6 |# A3 y" e# H- h7 N
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')3 z$ w. N @; i) V+ ?/ L7 Q- R
figure;plot(t,x(:,2:5)); q6 l' [+ Z Z2 }0 Z4 W
p=x(:,1:5)1 W; k: n1 g; O4 A. A1 }
hold on/ S' q# I+ R* q* P2 p
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')& m0 E; ?1 C! ~' Q5 c, Z6 y
% f2 [4 ?5 a5 O
+ f5 a4 f/ K+ @: ]9 x1 r
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function f = ObjFunc7LNL(k,x0,yexp)
) n& q Z6 @$ P4 Wtspan = [0 15 30 45 60 90 120 180 240 300 360];
- }3 L! Q9 c" x6 d& V[t, x] = ode45(@KineticEqs,tspan,x0,[],k); $ n% E7 ~4 n( W7 w: c" a
y(:,2) = x(:,1);
6 B) @4 a9 R4 Y8 _6 t% k. `y(:,3:6) = x(:,2:5);
' p n+ h% c. k2 p0 c* ?8 Hf1 = y(:,2) - yexp(:,2); e* y: q( F1 j( ]- \
f2 = y(:,3) - yexp(:,3);
+ E4 r9 W) ?, K% w1 s8 O$ Yf3 = y(:,4) - yexp(:,4);9 d6 r' W& z! S
f4 = y(:,5) - yexp(:,5);8 }6 d, O( `& K1 D
f5 = y(:,6) - yexp(:,6);9 T: l" Y: v+ e2 g8 T
f = [f1; f2; f3; f4; f5];
0 u# [# ^2 H K$ _" ~3 [# Y2 C% {- b# e* J8 ~0 }+ Y( M
) F% q! w3 p: O# {) A5 @
- x: A- ^; D- J: w* gfunction f = ObjFunc7Fmincon(k,x0,yexp)3 Z; s1 X3 i# _, w+ Z; E4 f( h
tspan = [0 15 30 45 60 90 120 180 240 300 360];
9 p1 U; \; o- _/ \. m3 ]/ l% b[t x] = ode45(@KineticEqs,tspan,x0,[],k); O j$ a8 @! z0 t& l; ? b7 P
y(:,2) = x(:,1);
. j4 u. S' K! l0 f0 Y- \9 F: U: oy(:,3:6) = x(:,2:5);
x2 [0 g/ \$ b6 c. if = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...0 S: X/ ]: r2 y, E* U! x. M' g
+ sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...+ C: Q. T% R7 ^' `& Q5 @
+ sum((y(:,6)-yexp(:,6)).^2) ;
: R) n& L! [+ ~( b: E
% g/ n* h9 D8 D3 P2 X3 p$ N
" [5 u9 ]& D ?2 X2 Q2 x3 C0 U2 E r* u7 B, q) H
. L1 F4 c! m8 @+ j2 h
function dxdt = KineticEqs(t,x,k)
5 _ U' p+ u! w% ^" Q8 {dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
" a4 j* t' n; B) ^8 ?2 Q4 }dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);/ f* M7 e* h* X) }$ R1 ]0 Y) R& P( q
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);$ T, {) \! O. H- S- S: P; W
dLadt = k(7)*x(5);( t& L. O9 Y- J+ E- \. S
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);$ [* V/ F% }8 a
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];' e/ K% w9 Q4 H$ W- @" T
+ \) C" T5 _, P7 r) b7 I; q" ?3 @: T2 W
4 m5 q+ m* O. u4 Z$ M7 p4 X1 B |
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