灰色模型 - 数学建模社区-数学中国

clear8 [# [9 K+ Y" }8 ?+ R! u
syms a b;; \ l5 e$ B2 D1 w' D
c=[a b]';1 H% D9 F, z: P. {
A=[539.658590944408,544.467335019023,543.118901615168,541.395536784412,539.719603563031,538.320685053971,536.799895148485,539.869612431029,534.915223499512,544.533125668254];
# n1 [+ |6 q& _' M% P
B=cumsum(A);
; B& X, X) ^$ i; a
n=length(A);
4 f" o/ d7 @% l
for m=1:(n-1)
1 k, S( v- w" V x0 q7 k1 d
C(m)=(B(m)+B(m+1))/2;
4 R2 Q% W: A# `0 v a
end
5 U+ T4 @. {9 c) Z& p. t
D=A;3 y7 `# x- T7 D( ~6 E9 L) ]5 q, U
D(1)=[];
" C5 S4 D! G) H
D=D';- o/ _: U- Y3 ^. C, {6 Y3 I
E=[-C;ones(1,n-1)];
, Z1 ]: N; V$ Z" J3 O
c=inv(E*E')*E*D;* c( @; s% i* M
c=c';
$ ?( Y/ [. j/ w: P
a=c(1);
- p" ?, U% X( h# ?4 a( D% G7 \
b=c(2);
2 |0 G6 h! A3 C; K1 _7 }1 l
F=[];& v+ R7 `, z, Z) M" X* h8 H4 @
F(1)=A(1);
2 y# A7 S4 H$ @
for m=2:(n+10)4 I2 D% {5 e9 F, N2 C0 u
F(m)=(A(1)-b/a)/exp(a*(m-1))+b/a;" w6 q; H, O9 O; u2 k
end
( I0 H0 C- F7 _0 X
G=[];
$ `! N! ?0 n2 m) ^
G(1)=A(1);+ W3 _1 b6 [$ v! F: L$ F
for m=2:(n+2)+ |2 ~! n% q) l9 a7 t* j/ d6 `
G(m)=F(m)-F(m-1);0 a+ l+ k: L& E3 d0 b
end: n& K9 ^: R! H! J3 T
t1=1:10;. L+ g( n# c0 y. q1 [
t2=1:12;7 z$ F d: v% a2 ~8 e D% c5 y. B
plot(t1,A,'r',t2,G,'g')# O7 T( A2 ]! [

复制代码