【Matlab编程】马氏链随机模拟
本文是利用蒙特卡罗算法对马氏链过程的模拟。假设有10个状态，从每个状态到与之相邻状态的概率是相同的，仿真次数为1000，及进行了1000次状态转移。我们以动画的形式再现了状态转移的过程，并记录了到达每个状态的次数，具体实现如下：
close all;clc;clear;
figure;
s=1;
n=1000;
r=1; % 圆圈的半径
title('等概率情况的计算机模拟')
set(gcf,'doublebuffer','on'); % 设置图形渲染效果
xlabel('Please press "space" key and see the result!',...
'fontsize',14,'color','r'); % 添加标注文字
hold on;axis equal; % 设置坐标轴属性
axis([-16,16,-16,16]); % 设置坐标轴范围
fill(r*sin(0:.1:2*pi)-7,r*cos(0:.1:2*pi)+13,'w'); % 画出固定点P1
hold on
fill(r*sin(0:.1:2*pi)-11,r*cos(0:.1:2*pi)+9,'w');hold on % 画出固定点P2
fill(r*sin(0:.1:2*pi)-3,r*cos(0:.1:2*pi)+9,'w'); hold on% 画出固定点P3
fill(r*sin(0:.1:2*pi)+5,r*cos(0:.1:2*pi)+9,'w');hold on % 画出固定点P4
fill(r*sin(0:.1:2*pi)+9,r*cos(0:.1:2*pi)+5,'w');hold on % 画出固定点P5
fill(r*sin(0:.1:2*pi)-15,r*cos(0:.1:2*pi)-3,'w');hold on % 画出固定点P6
fill(r*sin(0:.1:2*pi)+1,r*cos(0:.1:2*pi)-3,'w'); hold on% 画出固定点P7
fill(r*sin(0:.1:2*pi)+13,r*cos(0:.1:2*pi)-3,'w');hold on % 画出固定点P8
fill(r*sin(0:.1:2*pi)-7,r*cos(0:.1:2*pi)-11,'w');hold on % 画出固定点P9
fill(r*sin(0:.1:2*pi)+5,r*cos(0:.1:2*pi)-15,'w');hold on % 画出固定点P10
text(-15.4,-3,'6','FontSize',18);hold on
text(-11.4,9,'2','FontSize',18);hold on
text(-7.4,13,'1','FontSize',18);hold on
text(-7.4,-11,'9','FontSize',18);hold on
text(-3.4,9,'3','FontSize',18);hold on
text(0.6,-3,'7','FontSize',18);hold on
text(4.6,9,'4','FontSize',18);hold on
text(4.1,-15,'10','FontSize',18);hold on
text(8.6,5,'5','FontSize',18);hold on
text(12.6,-3,'8','FontSize',18);hold on
hold on
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%plot([8.5,6],[6,8.3],'r-')
hold on
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x45=fliplr(8.3:-0.1:5.8);
y45=fliplr(linspace(5.9,8.2,length(x45)));
x54=8.3:-0.1:5.8;
y54=linspace(5.9,8.2,length(x54));
x85=fliplr(9.4:0.05:12.4);
y85=fliplr(linspace(4.1,-2.2,length(x85)));
x58=9.4:0.05:12.4;
y58=linspace(4.1,-2.2,length(x58));
x80=fliplr(5.8:0.1:12.2);
y80=fliplr(linspace(-14.4,-3.8,length(x80)));
x08=5.8:0.1:12.2;
y08=linspace(-14.4,-3.8,length(x08));
x87=fliplr(2:0.1:12);
y87=-3*ones(1,length(x87));
x78=2:0.1:12;
y78=-3*ones(1,length(x78));
x79=fliplr(-6.2:0.1:0.4);
y79=fliplr(linspace(-10.4,-3.8,length(x79)));
x97=-6.2:0.1:0.4;
y97=linspace(-10.4,-3.8,length(x97));
x73=fliplr(-2.6:0.06:0.9);
y73=fliplr(linspace(7.9,-2,length(x73)));
x37=-2.6:0.06:0.9;
y37=linspace(7.9,-2,length(x37));
x13=-6.4:0.1:-3.8;
y13=linspace(12.2,9.6,length(x13));
x31=fliplr(-6.4:0.1:-3.8);
y31=linspace(9.6,12.2,length(x31));
x67=-14:.11:0;
y67=-3*ones(1,length(x67));
x76=0:-0.11:-14;
y76=-3*ones(1,length(x76));
x21=-10.1:.1:-7.8;
y21=linspace(9.5,12.4,length(x21));
x12=-7.8:-0.1:-10.1;
y12=fliplr(linspace(9.5,12.4,length(x12)));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
t6=text(-15.3,-5,'0','FontSize',12,'Color',[1 0 0]);
t2=text(-11.4,7,'0','FontSize',12,'Color',[1 0 0]);
t1=text(-7.2,11,'0','FontSize',12,'Color',[1 0 0]);
t9=text(-7.3,-13,'0','FontSize',12,'Color',[1 0 0]);
t3=text(-4,7,'0','FontSize',12,'Color',[1 0 0]);
t7=text(0.6,-5,'0','FontSize',12,'Color',[1 0 0]);
t4=text(4.7,7,'0','FontSize',12,'Color',[1 0 0]);
t10=text(4.3,-13,'0','FontSize',12,'Color',[1 0 0]);
t5=text(8.3,3,'0','FontSize',12,'Color',[1 0 0]);
t8=text(12.6,-5,'0','FontSize',12,'Color',[1 0 0]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:length(x45)
plot(x45(i),y45(i),'*')
end
for i=1:length(x54)
plot(x54(i),y54(i),'*')
end
for i=1:length(x85)
plot(x85(i),y85(i),'*')
end
for i=1:length(x58)
plot(x58(i),y58(i),'*')
end
for i=1:length(x80)
plot(x80(i),y80(i),'.')
end
for i=1:length(x08)
plot(x08(i),y08(i),'*')
end
for i=1:length(x87)
plot(x87(i),y87(i),'*')
end
for i=1:length(x78)
plot(x78(i),y78(i),'*')
end
for i=1:length(x79)
plot(x79(i),y79(i),'.')
end
for i=1:length(x97)
plot(x97(i),y97(i),'*')
end
for i=1:length(x73)
plot(x73(i),y73(i),'*')
end
for i=1:length(x37)
plot(x37(i),y37(i),'.')
end
for i=1:length(x31)
plot(x31(i),y31(i),'*')
end
for i=1:length(x13)
plot(x13(i),y13(i),'*')
end
for i=1:length(x67)
plot(x67(i),y67(i),'*')
end
for i=1:length(x76)
plot(x76(i),y76(i),'*')
end
for i=1:length(x21)
plot(x21(i),y21(i),'*')
end
for i=1:length(x12)
plot(x12(i),y12(i),'*')
end
plot(x45,y45,'w.')
plot(x85,y85,'w.')
plot(x80,y80,'w.')
plot(x87,y87,'w.')
plot(x79,y79,'w.')
plot(x73,y73,'w.')
plot(x31,y31,'w.')
plot(x21,y21,'w.')
plot(x67,y67,'w.')
plot(x54,y54,'w.')
plot(x58,y58,'w.')
plot(x08,y08,'w.')
plot(x78,y78,'w.')
plot(x97,y97,'w.')
plot(x37,y37,'w.')
plot(x13,y13,'w.')
plot(x12,y12,'w.')
plot(x76,y76,'w.')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
s=1;
p1=0;%pn为到达n村庄的次数
p2=0;p3=0;p4=0;p5=0;p6=0;p7=0;p8=0;p9=0;p10=0;
%plot([-14,0],[-3,-3],'b','linewidth',3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:n
m=get(gcf,'currentkey'); % 获取键入按键的名称
if strcmp(m,'space'); % 检查按下的按键是否为空格键
break;
end
if s==1
possible=round(rand(1));
if possible==1
s=3;
p3=p3+1;
for i=1:length(x13)
plot(x13(i),y13(i),'.')
pause(0.00000000001)
end
delete(t3);
t3=text(-4,7,num2str(p3),'FontSize',12,'Color',[1 0 0]);
else
s=2;
p2=p2+1;
for i=1:length(x12)
plot(x12(i),y12(i),'.')
pause(0.00000000001)
end
delete(t2)
t2=text(-11.4,7,num2str(p2),'FontSize',12,'Color',[1 0 0]);
end
elseif s==2
s=1;
p1=p1+1;
for i=1:length(x21)
plot(x21(i),y21(i),'.')
pause(0.00000000001)
end
delete(t1)
t1=text(-7.2,11,num2str(p1),'FontSize',12,'Color',[1 0 0]);
elseif s==3
possible=round(rand(1));
if possible==1
s=7;
p7=p7+1;
for i=1:length(x37)
plot(x37(i),y37(i),'.')
pause(0.00000000001)
end
delete(t7)
t7=text(0.6,-5,num2str(p7),'FontSize',12,'Color',[1 0 0]);
else
s=1;
p1=p1+1;
for i=1:length(x31)
plot(x31(i),y31(i),'.')
pause(0.00000000001)
end
delete(t1)
t1=text(-7.2,11,num2str(p1),'FontSize',12,'Color',[1 0 0]);
end
elseif s==4
s=5;
p5=p5+1;
for i=1:length(x45)
plot(x45(i),y45(i),'.')
pause(0.00000000001)
end
delete(t5)
t5=text(8.3,3,num2str(p5),'FontSize',12,'Color',[1 0 0]);
elseif s==5
possible=round(rand(1));
if possible==1
s=8;
p8=p8+1;
for i=1:length(x58)
plot(x58(i),y58(i),'.')
pause(0.00000000001)
end
delete(t8)
t8=text(12.6,-5,num2str(p8),'FontSize',12,'Color',[1 0 0]);
else
s=4;
p4=p4+1;
for i=1:length(x54)
plot(x54(i),y54(i),'.')
pause(0.00000000001)
end
delete(t4)
t4=text(4.7,7,num2str(p4),'FontSize',12,'Color',[1 0 0]);
end
elseif s==6
s=7;
p7=p7+1;
for i=1:length(x67)
plot(x67(i),y67(i),'.')
pause(0.00000000001)
end
delete(t7)
t7=text(0.6,-5,num2str(p7),'FontSize',12,'Color',[1 0 0]);
elseif s==7
possible=floor(rand(1)*4);
if possible==0
s=6;
p6=p6+1;
for i=1:length(x76)
plot(x76(i),y76(i),'.')
pause(0.00000000001)
end
delete(t6)
t6=text(-15.3,-5,num2str(p6),'FontSize',12,'Color',[1 0 0]);
elseif possible==1
s=3;
p3=p3+1;
for i=1:length(x73)
plot(x73(i),y73(i),'.')
pause(0.00000000001)
end
delete(t3)
t3=text(-4,7,num2str(p3),'FontSize',12,'Color',[1 0 0]);
elseif possible==2
s=9;
p9=p9+1;
for i=1:length(x79)
plot(x79(i),y79(i),'.')
pause(0.00000000001)
end
delete(t9)
t9=text(-7.3,-13,num2str(p9),'FontSize',12,'Color',[1 0 0]);
else
s=8;
p8=p8+1;
for i=1:length(x78)
plot(x78(i),y78(i),'.')
pause(0.00000000001)
end
delete(t8)
t8=text(12.6,-5,num2str(p8),'FontSize',12,'Color',[1 0 0]);
end
elseif s==8
possible=floor(rand(1)*3);
if possible==0
s=7;
p7=p7+1;
for i=1:length(x87)
plot(x87(i),y87(i),'.')
pause(0.00000000001)
end
delete(t7)
t7=text(0.6,-5,num2str(p7),'FontSize',12,'Color',[1 0 0]);
elseif possible==1
s=5;
p5=p5+1;
for i=1:length(x85)
plot(x85(i),y85(i),'.')
pause(0.00000000001)
end
delete(t5)
t5=text(8.3,3,num2str(p5),'FontSize',12,'Color',[1 0 0]);
else
s=10;
p10=p10+1;
for i=1:length(x80)
plot(x80(i),y80(i),'.')
pause(0.00000000001)
end
delete(t10)
t10=text(4.3,-13,num2str(p10),'FontSize',12,'Color',[1 0 0]);
end
elseif s==9
s=7;
p7=p7+1;
for i=1:length(x97)
plot(x97(i),y97(i),'.')
pause(0.00000000001)
end
delete(t7)
t7=text(0.6,-5,num2str(p7),'FontSize',12,'Color',[1 0 0]);
else
s=8;
p8=p8+1;
for i=1:length(x08)
plot(x08(i),y08(i),'.')
pause(0.00000000001)
end
delete(t8)
t8=text(12.6,-5,num2str(p8),'FontSize',12,'Color',[1 0 0]);
end
plot(x45,y45,'w.')
plot(x85,y85,'w.')
plot(x80,y80,'w.')
plot(x87,y87,'w.')
plot(x79,y79,'w.')
plot(x73,y73,'w.')
plot(x31,y31,'w.')
plot(x21,y21,'w.')
plot(x67,y67,'w.')
plot(x54,y54,'w.')
plot(x58,y58,'w.')
plot(x08,y08,'w.')
plot(x78,y78,'w.')
plot(x97,y97,'w.')
plot(x37,y37,'w.')
plot(x13,y13,'w.')
plot(x12,y12,'w.')
plot(x76,y76,'w.')
end
for j=i:n
if s==1
possible=round(rand(1));
if possible==1
s=3;
p3=p3+1;
else
s=2;
p2=p2+1;
end
elseif s==2
s=1;
p1=p1+1;
elseif s==3
possible=round(rand(1));
if possible==1
s=7;
p7=p7+1;
else
s=1;
p1=p1+1;
end
elseif s==4
s=5;
p5=p5+1;
elseif s==5
possible=round(rand(1));
if possible==1
s=8;
p8=p8+1;
else
s=4;
p4=p4+1;
end
elseif s==6
s=7;
p7=p7+1;
elseif s==7
possible=floor(rand(1)*4);
if possible==0
s=6;
p6=p6+1;
elseif possible==1
s=3;
p3=p3+1;
elseif possible==2
s=9;
p9=p9+1;
else
s=8;
p8=p8+1;
end
elseif s==8
possible=floor(rand(1)*3);
if possible==0
s=7;
p7=p7+1;
elseif possible==1
s=5;
p5=p5+1;
else
s=10;
p10=p10+1;
end
elseif s==9
s=7;
p7=p7+1;
else
s=8;
p8=p8+1;
end
end
delete(t1)
delete(t2)
delete(t3)
delete(t4)
delete(t5)
delete(t6)
delete(t7)
delete(t8)
delete(t9)
delete(t10)
t6=text(-15.3,-5,num2str(p6),'FontSize',12,'Color',[1 0 0]);
t2=text(-11.4,7,num2str(p2),'FontSize',12,'Color',[1 0 0]);
t1=text(-7.2,11,num2str(p1),'FontSize',12,'Color',[1 0 0]);
t9=text(-7.3,-13,num2str(p9),'FontSize',12,'Color',[1 0 0]);
t3=text(-4,7,num2str(p3),'FontSize',12,'Color',[1 0 0]);
t7=text(0.6,-5,num2str(p7),'FontSize',12,'Color',[1 0 0]);
t4=text(4.7,7,num2str(p4),'FontSize',12,'Color',[1 0 0]);
t10=text(4.3,-13,num2str(p10),'FontSize',12,'Color',[1 0 0]);
t5=text(8.3,3,num2str(p5),'FontSize',12,'Color',[1 0 0]);
t8=text(12.6,-5,num2str(p8),'FontSize',12,'Color',[1 0 0]);
最终的结果如下：
原文：http://blog.csdn.net/tengweitw/article/details/34063833
作者：nineheadedbird