《第7章 蒙特卡罗方法 (附录)》由会员分享，可在线阅读，更多相关《第7章 蒙特卡罗方法 (附录)（25页珍藏版）》请在金锄头文库上搜索。
1、1第 7 章 附录7.2.1 均匀分布随机数例题 7.2.1 计算程序! rand1.forprogram rand1implicit nonereal rinteger n,c,x,iopen(5,file=rand1.txt)n = 32768c = 889x = 13do i = 1,1000x = c*x-n*int(c*x/n)r = real(x)/(n-1)write(5,(f8.5) rend doend!rand2.for!program rand2implicit noneinteger, parameter : n=1000integer ix,ireal ropen(5
2、,file=rand2.txt)ix=32765do i=1,ncall rand(ix,r)write(5,(f8.6) rend doend program rand2subroutine rand(ix,r)i=ix*259ix=i-i/32768*32768r=float(ix)/32768returnend27.2.3 随机抽样例题7.2.2计算程序% 例题 7_2_2.mfigure(1);set(gca,FontSize,16);t = rand(1000,1);y = -log(t);z = exp(-y);plot(y,z,.);xlabel(图7.2-2 例题7.2.2-指
3、数分布抽样)=例题7.2.5计算程序! 例题 7.2.5program scoresparameter(nmax=10,mmax=13)real(8) x(nmax),y(nmax),l(0:nmax),z(mmax),ys(mmax),rinteger i,j,kdata x/5.0,15.0,25.0,35.0,45.0,55.0,65.0,75.0,85.0,95.0/data y/0,0,0,0,0.08,0.19,0.31,0.27,0.11,0.04/open(2,file=scores_old.txt)open(5,file=scores_new.txt) ! mmax个抽样学生
4、成绩open(7,file=scores_sample.txt)write(2,(2f15.5) (x(i),y(i),i=1,nmax)ix=32765l(0)=0do i=1,nmaxl(i)=l(i-1)+y(i)end dodo j=1,mmaxcall rand(ix,r)do k=1,nmaxif(r.le.l(k) goto 11end do11 z(j)=x(k)end dowrite(5,*) (z(i),i=1,mmax)ys=0do i=1,mmaxk=z(i)/float(nmax) ! 确定抽样学生所在的分数段3ys(k)=ys(k)+1.0 ! 统计每个分数段的学生
5、数end dodo i=1,nmaxys(i)=ys(i)/float(mmax)write(7,*) x(i),ys(i)end doendsubroutine rand(ix,r)integer ireal(8) ri=ix*259ix=i-i/32768*32768r=float(ix)/32768returnend=7.3.1 方程求根的 M-C 方法例题 7.3.1 计算程序! 例题 3.1program roots_MC1implicit nonereal b,bmax,a,h,f,xopen(5,file=x.txt)b=0.0; bmax=4.0; h=0.34 a=bb=b+
6、hif(f(a)*f(b).gt.0.0) goto 4call sr(a,b,x)write(5,(f12.8) xwrite(*,(f12.8) xif(b.lt.bmax) goto 4end subroutine sr(a,b,x)implicit nonereal r,xr,x,a,b,p,finteger ix,n,m,iix=32765; n = 4000; m = 0do i =1,ncall rand(ix,r)4xr=a+(b-a)*rif(f(xr).le.0.0) m = m+1end dop = real(m)/real(n)if(f(a).le.0.0) thenx
7、=a+(b-a)*pelsex=a+(b-a)*(1.0-p)end ifreturnendfunction f(x)implicit nonereal x,f! f=exp(x)*(log(x)-x*x)f=(x-10.0)*x+35.0)*x-50.0)*x+24.0returnendsubroutine rand(ix,r)i=ix*259ix=i-i/32768*32768r=float(ix)/32768returnend=例题 7.3.2 计算程序! roots_MC_2.f90 !program roots_MC_2implicit nonereal(8) x,a,b,r,rp,
8、rm,f,pinteger ix,n,ia=0.0; b=3.1415926/2.0! a=0.0;b=1.0ix=32765n=2000rp=0.0; rm=1.0 !注意：首先将最大赋值最小， 将最小赋值最大if(f(a)=0.0) thencall amax(r,rp)elsecall amin(r,rm)end ifend doend ifp=(rp+rm)/2.0x=a+(b-a)*pwrite(*,*) x=,xend program roots_MC_2subroutine amax(x,xmax)implicit nonereal(8) x,xmaxif(xmax.ge.x)
9、thenreturnelse xmax=xend ifreturnendsubroutine amin(x,xmin)implicit nonereal(8) x,xminif(xmin.le.x) thenreturnelse xmin=xend ifreturnendfunction f(x)real(8) x6f=exp(-x*x*x)-tan(x)+800.0! f=x-exp(-x)returnendsubroutine rand(ix,r)real(8) rinteger ixi=ix*259ix=i-i/32768*32768r=float(ix)/32768returnend=
10、7.3.2 计算定积分的 M-C 方法例题 7.3.3 计算程序! 例题7.3.3program int_MC1real(8) f,s,a,ba = 2.5 ! 积分下限b = 8.4 ! 积分上限call int_mc(a,b,s)print *,s = , send function f(x)real(8) xf=x*x+sin(x)endsubroutine int_mc(a,b,s)real(8) a,b,f,s,r,xinteger m,ir = 1.0m = 10000s = 0.0do i = 1,mx = a+(b-a)*rand(r)s = s+f(x)end dos=s*(
11、b-a)/real(m)7returnendfunction rand(r)real(8) s,u,v,rinteger ms=65536.0u=2053.0v=13849.0m=r/sr=r-m*sr=u*r+vm=r/sr=r-m*srand=r/sreturnend=例题 7.3.4 计算程序! 例题 3.4program pi_MC1integer m,n,s,ntotalreal(8) r,x,y,rand,iseedopen(5,file=pi.txt)iseed = 1.0n = 100000m = 10000s = 0do ntotal=1,nx=rand(iseed)y=ra
12、nd(iseed)r=sqrt(x*x+y*y)if(r#define f(x,y) x*y*ystatic double xn=1;double rand() double lambda=16807, p=2147483647;xn=fmod(lambda*xn,p);return xn/p; void srand(double seed) xn=seed; main() int i,n=15000; double x, y, s=0;srand(4);for(i=0; istatic double xn=1;double rand() double lambda=16807, p=2147
13、483647;xn=fmod(lambda*xn,p);return xn/p; void srand(double seed) xn=seed; main() int i,n=10000,m=0; double x, y, z, v=0;srand(256);for(i=0; i=0.3)m = m+1;v = 1.*(double)m/n;printf(N=%8d V=% 10.6fn, n, v);=7.3.3 MC 方法求解 Laplace 方程例题 7.3.8 计算程序! program Walk_MC1.for! 蒙特卡罗方法求解2d_Laplacian difference eq
14、uationparameter(imax=50,jmax=50,pi=3.1415926,kmax=10000)dimension T(imax,jmax),a(imax,jmax),& qx(imax,jmax),qy(imax,jmax),q(imax,jmax),an(imax,jmax)real lamda,Tu,Td,Tl,Tr,kpx,kpy,dx,dy,ropen(2,file=walk2.dat)open(3,file=q2.dat)lamda=1.5;Tu=100.;Tl=75.;Tr=50.;Td=0.;dx=0.1;dy=0.1;ix=32765kpx=-0.49/2./
15、dx;kpy=-0.49/2./dyT(:,:)=0.0T(1,1)=0.5*(Td+Tl) ;T(1,jmax)=0.5*(Tl+Tu)T(imax,jmax)=0.5*(Tu+Tr);T(imax,1)=0.5*(Tr+Td)T(1,2:jmax-1)=Tl; T(imax,2:jmax-1)=TrT(2:imax-1,1)=Td; T(2:imax-1,jmax)=Tudo i=2,imax-1print *,i=,iii=i12do j=2,jmax-1jj=jdo 20 k=1,kmaxa(i,j)=T(i,j)6 call rand(ix,r)if(r.le.0.25) then ii
