灰色模型 - 数学建模社区-数学中国

clear
7 `! c- [7 C- [
syms a b;
& v# }* d8 f7 R* B
c=[a b]';
2 P" r. r5 C: I+ d3 ^( J
A=[539.658590944408,544.467335019023,543.118901615168,541.395536784412,539.719603563031,538.320685053971,536.799895148485,539.869612431029,534.915223499512,544.533125668254];
9 i* U1 }) }# y* `( o( ^- }
B=cumsum(A);
4 v$ `- q: K$ I1 M$ B, x/ i
n=length(A);
# J6 g- K P1 ]8 x4 p" Y* U& f
for m=1:(n-1)+ N1 C% o0 ~2 n- g
C(m)=(B(m)+B(m+1))/2;
4 i. w7 ]* U' [8 H
end+ C8 ?6 {+ E1 P7 X
D=A;
, @+ u! ~4 r- r/ r) f
D(1)=[];
9 D0 `" m2 {' w( J4 }
D=D';
0 l$ ]- l( j2 `
E=[-C;ones(1,n-1)];
# O' \# I( A! ^; R/ p) f
c=inv(E*E')*E*D;
$ @# P4 X, T: Y; N- [
c=c';
3 p: y& T4 y( L) Y. b3 W
a=c(1);
C; d0 g9 N: T3 Z o
b=c(2);% @: [8 ?/ s, ]: Y7 u7 g3 g
F=[];# M' n9 W, q" c, ]' G* E
F(1)=A(1);- ^5 J* o. n* f3 d* r% F
for m=2:(n+10)
; ?6 ]% g# d8 h) N# X! `4 S6 H* {
F(m)=(A(1)-b/a)/exp(a*(m-1))+b/a;: }+ K- F5 `- F* f' H5 Y \; n5 L$ ]
end4 n9 Q+ t0 ~' u# I- W
G=[];( F% F2 ]) `) Y/ k" S8 W" y
G(1)=A(1);. C j# A- ], I
for m=2:(n+2)
& Z) G5 z' I* v/ |) u
G(m)=F(m)-F(m-1);
. p f* v. G, g7 n% |" X! \! i
end0 w' p. y# W" I( f1 q; E
t1=1:10;+ M( S4 }0 j6 A$ A. `
t2=1:12;3 h9 e8 G" y8 x3 Q0 k
plot(t1,A,'r',t2,G,'g')
& e( e: }1 g4 L# ~

复制代码