montecarlo_multintegral.m

monte carlo方法在各个方面中的小应用

clear all 
n=input('n=?');%计算多重积分
B=[5,5,5,5,2*pi,2*pi,2*pi,2*pi]; 
SNR=11.2415;
D0=sqrt(2*10^(SNR/10));
D1=0.5*D0;
D2=D0;    
D3=0.5*D0;
D4=0;
a=1/(10*(pi)^5); 
b=-2/5;
c=4*D1-3*D2+2*D3-D4;
d=-3*D1+6*D2-4*D3+2*D4;
e=2*D1-4*D2+6*D3-3*D4;
f=-D1+2*D2-3*D3+4*D4;  
g=2*D1^2+3*D2^2+3*D3^2+2*D4^2-3*D1*D2+2*D1*D3-D1*D4-4*D2*D3+2*D2*D4-3*D3*D4;  
sum8=0; 
for i=1:n
    r=B.*rand(1,8);
    sum8=sum8+a*r(1)*r(2)*r(3)*r(4)*exp(b*(2*r(1)^2+3*r(2)^2+3*r(3)^2+2*r(4)^2-3*r(1)*r(2)*cos(r(5)-r(6))+2*r(1)*r(3)*cos(r(5)-r(7))-r(1)*r(4)*cos(r(5)-r(8))-4*r(2)*r(3)*cos(r(6)-r(7))+2*r(2)*r(4)*cos(r(6)-r(8))-3*r(3)*r(4)*cos(r(7)-r(8))-c*r(1)*cos(r(5))-d*r(2)*cos(r(6))-e*r(3)*cos(r(7))-f*r(4)*cos(r(8))+g));
end
Q=(5*2*pi)^4*sum8/n