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GM(1,1)灰色模型的程序实现function GM1=fungry1(x0) %输入原始数据x00 D) q: P- y! `0 h
T=input('T=');%从键盘输入从最后一个历史数据算起的第T时点9 y2 k- X9 V# `
x1=zeros(1,length(x0));B=zeros(length(x0)-1,2);: D2 O# s* m P6 |/ E1 i9 q, D& z
yn=zeros(length(x0)-1,1);Hatx0=zeros(1,length(x0)+T);
- f: }+ k$ @+ j A: L8 P' x5 c* ?Hatx00=zeros(1,length(x0));Hatx1=zeros(1,length(x0)+T);+ N! }' ^- p' a3 F+ {# D& R
epsilon=zeros(length(x0),1);omega=zeros(length(x0),1);) T' v% I' G- E) f9 _- Y
for i=1:length(x0)% \: Y$ q3 P" ~: p9 A
for j=1:i& U% ?) V! y6 @" f# u4 q, E
x1(i)=x1(i)+x0(j);% \+ X9 q" Q+ V N+ e5 n8 X
end0 _" r) M: H! U- U
end
0 y5 b: ~1 U, s Mfor i=1:length(x0)-1- g" I/ K4 J$ ?3 M5 a/ o
B(i,1)=(-1/2)*(x1(i)+x1(i+1));! e0 l7 I" y; ]4 [- W0 w+ g: Q
B(i,2)=1;. P" P8 B/ @0 p' [
yn(i)=x0(i+1);9 W8 R. Y* Y i3 i, N& q" z
end) L, v' X) Q( E9 Y# s3 f
HatA=(inv(B'*B))*B'*yn % GM(1,1)模型参数估计 I; o7 ~, J/ s, W' J9 @
for k=1:length(x0)+T
/ {* h' |6 s- k& n! W9 A9 ]* u! v Hatx1(k)=(x0(1)-HatA(2)/HatA(1))*exp(-HatA(1)*(k-1))+HatA(2)/HatA(1);2 ]% w9 H& O9 J- Z
end; O P) P a' V! S6 L
Hatx0(1)=Hatx1(1);5 f _7 S0 I4 P6 L" L
for k=2:length(x0)+T
: D9 m1 T& s1 [, n2 t Hatx0(k)=Hatx1(k)-Hatx1(k-1);%累计还原得到历史数据的模拟值6 r& Z! J3 T. m; w& [: e4 e' n8 C
end; }% B: Z* l- k8 G4 Y7 g
for i=1:length(x0) %开始模型检验1 H! A2 @8 P/ K' R3 s$ G
epsilon(i)=x0(i)-Hatx0(i);
- N3 @3 h k5 F# G" i- \; G omega(i)=(epsilon(i)/x0(i))*100;% ?4 c- \0 B/ h% _% M8 Y2 F
end
! v: R2 `- b& T' r- F% x0;Hatx0;epsilon;omega; %必要时去掉%得到各种数据: S, _) r. I* \( N$ \7 z
c=std(epsilon)/std(x0);p=0;
+ d" W; _ C5 _7 X- Ofor i=1:length(x0)6 M' l2 Y: k1 m! M" x
if abs(epsilon(i)-mean(epsilon))<0.6745*std(x0)3 G0 C8 A6 b( }( ~" N* _
p=p+1;
. U V H' d4 Y9 C4 } end
1 n( A/ G2 s- {, j# w1 ~& jend
: O3 ^8 w- I& ]8 g+ ap=p/length(x0)
+ i8 R k; x7 e3 Q9 Rif p>0.95 & c<0.35
% G- y" C# r4 N disp('The model is good,and the forecast is:'),7 p0 f7 X& z% L8 T( q/ o A
disp(Hatx0(length(x0)+T))
& P) T5 S9 x9 C+ |6 m3 Nelseif p>0.85 & c<0.53 ]2 w0 E5 ]* d7 o1 ~/ R% R* \6 b
disp('The model is eligibility,and the forecast is:'),
8 _" A: o5 w2 M* M8 ] disp(Hatx0(length(x0)+T))1 t! [* O4 t# O% q" s* T. o5 @- d$ y; \
elseif p>0.7 & c>0.65: ~' h1 Q% w+ W% c( C3 `
disp('The model is not good,and the forecast is:'),
3 ~' J9 n! i# O' q( v+ v: W disp(Hatx0(length(x0)+T))3 ^& m; E% Y4 u' v* _
else p<=0.7 & c>0.65: y( s3 A# ^9 I" m: v( I
disp('The model is bad and try again')
$ ?, F& i0 b3 H3 F/ a w$ Dend
! u( v3 I7 Q( J" w6 ~5 zfor i=1:length(x0)
" U; p$ M5 h* F7 ]! ^ Hatx00(i)=Hatx0(i);
' s- q* ?8 E! ]) z# lend
m; `' N0 R( J, Q, mz=1:length(x0);9 B& b! b0 r! Y1 c: @. \* {
plot(z,x0,'-',z,Hatx00,':') %将原始数据和模拟值画在一个图上帮助观察
( E8 c, T. a# y; |( F1 {text(2,x0(2),'History data: real line')
6 s- ^3 N- m6 k8 Itext(length(x0)/2,Hatx00(length(x0))/2,'Simulation data:broken line')
1 s7 B6 n) R1 x- d0 kendT=input('T=');%从键盘输入从最后一个历史数据算起的第T时点????是指什么啊,请大哥们,大姐们教一下,我急用,请快,谢谢我的初始值x0=[1.620938526
" N7 p+ ~8 {' U1 l9 h h0.07925621
- ]0 l" `3 {4 S- W: P4 C' v0.052318818
* V* n, j& ~5 v8 G( `0.041252502
. x8 p# \' y9 ^5 F1 L0.021800479* b# q5 J9 \/ r! `$ c5 a
0.053132975
0 x2 U7 r' S6 D% |' Y0.089908836
; c9 i6 V5 {& X- S1 p! V0.109153219
) M4 f" ]* P9 m" u' ^6 s ~0.0793318322 e+ [# y: g' S. }9 _8 l/ y
0.342192598: R u$ I& ?" c# A
0.0997181428 l7 a0 V+ m5 _4 |* z* C' Q
0.135194823
- @7 N4 Z# i, J+ W2 L3 e0.109274037% c" z& [; \3 k) k
0.081520132 ~. I- q# f) l1 J& r3 Y
0.0678763551 u# V! [6 c" S5 P/ [
0.064706843
. r N8 o3 h, ^ k7 U7 l- V v0.0555621977 }8 D" g4 I7 G: U, {; d
0.0508485448 A- \5 n% Q' z# y- L/ N6 M7 @+ {
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