?? 關(guān)于圓內(nèi)均勻分布模擬的實現(xiàn).txt
字號:
下面這個是我寫的(已修正其中考慮不周之處），請大家測試：
Module Random2d
Implicit None
Type Point
Real(8) x,y
End Type
Contains
Subroutine Random_Circle(Num,R,Pnt)
Integer,Intent(in)::Num
Real(4),Intent(in)::R
Type(Point),Dimension(Num),Intent(Out)::Pnt
Real(4) x,y
Integer i
Do i=1,Num
15 CALL RANDOM(x)
CALL RANDOM(y)
If (x*(1-x)+y*(1-y)<0.25) Goto 15
Pnt(i).x=R*x
Pnt(i).y=R*y
End Do
Return
EndSubroutine
End Module
Program Main
Use Random2d
Implicit None
Integer Num
Parameter(Num=10000)
Real(4) R
Integer i
Type(Point),Dimension(Num)::Pnt
Print*, "Please Input the radius:"
Read(*,*) R
Call Random_Circle(Num,R,Pnt)
Open(1,File='Rd2d_Circle.dat',Status='Unknown')
Do i=1,Num
Write(1,'(2(f12.6,2x))') Pnt(i).x,Pnt(i).y
EndDo
Close(1)
End Program Main
不懂就不要死撐，我沒有說你的方法不能實現(xiàn)，只是一直在強調(diào)，你的方法遠(yuǎn)非最佳！
看看這個吧。
! this module is to the date type Operating System independent
module TypeKind
implicit none
integer(kind = kind(1)), parameter:: IP = kind(1)
integer(kind = IP), parameter:: LP = kind(.true.)
integer(kind = IP), parameter:: SP = kind(1.0)
integer(kind = IP), parameter:: DP = kind(1.d0)
end module TypeKind
! this subroutine generate Circle-Uniform-Distribution
! sample efficient 100%
subroutine CircleUniform(NO, radii, r)
use TypeKind, WP => DP
implicit none
! the number of point you want to simulation
integer(kind = IP), intent(in):: NO
! the radii of the cycle
real(kind = WP), intent(in):: radii
real(kind = WP), intent(out):: r(NO)
integer(kind = IP):: i ! for loop
real(kind = WP):: r1(NO)
call Random_Number( r1 )
call Random_Number( r )
forall( i = 1 : NO : 1 )
r(i) = max( r(i), r1(i) )
end forall
r = radii * r
return
end subroutine
program main
use TypeKind, WP => DP
implicit none
! the number of point you want to simulation
integer(kind = IP), parameter:: NO = 10000
! the radii of the cycle
real(kind = WP):: radii
real(kind = WP):: r(NO)
real(kind = WP):: theta(NO)
integer(kind = IP):: i ! for loop
! parameter
real(kind = WP), parameter:: Pi = 3.14159265358979_WP
call Random_Seed()
radii = 1._WP
call CircleUniform(NO, radii, r)
! 至此，已經(jīng)得到圓均勻分布，但為了畫出圖形，還是把極角也
! 用 Monte-Carlo 撒點吧。
call Random_Number( theta )
theta = 2 * theta * Pi
open(5, file = "Out06.dat")
do i = 1, NO, 1
!write(5, *) r(i), theta(i)
! 若是 不是去畫圖，這些完全沒有必要。
write(5, *) r(i) * cos(theta(i)), r(i) * sin(theta(i))
end do
close(5)
stop
end program main
! this module is to the date type Operating System independent
module TypeKind
implicit none
integer(kind = kind(1)), parameter:: IP = kind(1)
integer(kind = IP), parameter:: LP = kind(.true.)
integer(kind = IP), parameter:: SP = kind(1.0)
integer(kind = IP), parameter:: DP = kind(1.d0)
end module TypeKind
! this subroutine generate Circle-Uniform-Distribution
! sample efficient 100%
subroutine CircleUniform(NO, radii, r)
use TypeKind, WP => DP
implicit none
! the number of point you want to simulation
integer(kind = IP), intent(in):: NO
! the radii of the cycle
real(kind = WP), intent(in):: radii
real(kind = WP), intent(out):: r(NO)
integer(kind = IP):: i ! for loop
real(kind = WP):: r1(NO)
call Random_Number( r1 )
call Random_Number( r )
forall( i = 1 : NO : 1 )
r(i) = max( r(i), r1(i) )
end forall
r = radii * r
return
end subroutine
program main
use TypeKind, WP => DP
implicit none
! the number of point you want to simulation
integer(kind = IP), parameter:: NO = 20000
! the radii of the cycle
real(kind = WP):: radii
real(kind = WP):: r(NO)
real(kind = WP):: theta(NO)
integer(kind = IP):: i ! for loop
! parameter
real(kind = WP), parameter:: Pi = 3.14159265358979_WP
Integer(2) itime(2,4),intet(4),ihr,imin,isec,i100th
call gettim(ihr,imin,isec,i100th)
itime(1,1)=ihr
itime(1,2)=imin
itime(1,3)=isec
itime(1,4)=i100th
call Random_Seed()
radii = 1._WP
Do i=1,No
call CircleUniform(NO, radii, r)
! 至此，已經(jīng)得到圓均勻分布，但為了畫出圖形，還是把極角也
! 用 Monte-Carlo 撒點吧。
call Random_Number( theta )
theta = 2 * theta * Pi
EndDo
! open(5, file = "Out06.dat")
! do i = 1, NO, 1
! !write(5, *) r(i), theta(i)
! ! 若是 不是去畫圖，這些完全沒有必要。
! write(5, *) r(i) * cos(theta(i)), r(i) * sin(theta(i))
! end do
! close(5)
call gettim(ihr,imin,isec,i100th)
itime(2,1)=ihr
itime(2,2)=imin
itime(2,3)=isec
itime(2,4)=i100th
do 50 i=1,4
if(itime(2,i).ge.itime(1,i))then
intet(i)=itime(2,i)-itime(1,i)
else
intet(i-1)=intet(i-1)-1
if(i.ne.4)then
intet(i)=itime(2,i)+60-itime(1,i)
else
intet(i)=itime(2,i)+100-itime(1,i)
endif
endif
50 continue
write(*,200) intet(1),':',intet(2),':',intet(3),':',intet(4)
200 format(2x,3(i2,a1),i2)
stop
end program main
以上是Asym的程序
以下是我的程序
Module Random2d
Implicit None
Type Point
Real(8) x,y
End Type
Contains
Subroutine Random_Circle(Num,R,Pnt)
Integer,Intent(in)::Num
Real(4),Intent(in)::R
Type(Point),Dimension(Num),Intent(Out)::Pnt
Real(4) x,y
Integer i
y=0
Do i=1,Num
x=5
Do While(x-x*x+y-y*y<0.25)
CALL RANDOM(x)
CALL RANDOM(y)
EndDo
Pnt(i).x=R*x
Pnt(i).y=R*y
Enddo
Return
EndSubroutine
End Module
Program Main
Use Random2d
Implicit None
Integer Num
Parameter(Num=20000)
Real(4) R
Integer i
Type(Point),Dimension(Num)::Pnt
Integer(2) itime(2,4),intet(4),ihr,imin,isec,i100th
call gettim(ihr,imin,isec,i100th)
itime(1,1)=ihr
itime(1,2)=imin
itime(1,3)=isec
itime(1,4)=i100th
! Print*, "Please Input the radius:"
! Read(*,*) R
R=100
Do i=1,Num
Call Random_Circle(Num,R,Pnt)
Enddo
! Open(1,File='Rd2d_Circle.dat',Status='Unknown')
! Do i=1,Num
! Write(1,'(2(f12.6,2x))') Pnt(i).x,Pnt(i).y
! EndDo
! Close(1)
call gettim(ihr,imin,isec,i100th)
itime(2,1)=ihr
itime(2,2)=imin
itime(2,3)=isec
itime(2,4)=i100th
do 50 i=1,4
if(itime(2,i).ge.itime(1,i))then
intet(i)=itime(2,i)-itime(1,i)
else
intet(i-1)=intet(i-1)-1
if(i.ne.4)then
intet(i)=itime(2,i)+60-itime(1,i)
else
intet(i)=itime(2,i)+100-itime(1,i)
endif
endif
50 continue
write(*,200) intet(1),':',intet(2),':',intet(3),':',intet(4)
200 format(2x,3(i2,a1),i2)
End Program Main
測試結(jié)果是
我的43.71秒,
Asym的44.69秒。
比如我說，產(chǎn)生 100000 事例，看看在 r ＝ 0.5 圓內(nèi)的幾率有多少。
我的程序如下：
! this module is to the date type Operating System independent
module TypeKind
implicit none
integer(kind = kind(1)), parameter:: IP = kind(1)
integer(kind = IP), parameter:: LP = kind(.true.)
integer(kind = IP), parameter:: SP = kind(1.0)
integer(kind = IP), parameter:: DP = kind(1.d0)
end module TypeKind
Module CUMC
use TypeKind, WP => DP
implicit none
contains
! this subroutine generate Circle-Uniform-Distribution
! sample efficient 100%
subroutine CircleUniform(NO, radii, r)
implicit none
! the number of point you want to simulation
integer(kind = IP), intent(in):: NO
! the radii of the cycle
real(kind = WP), intent(in):: radii
real(kind = WP), intent(out):: r(NO)
integer(kind = IP):: i ! for loop
real(kind = WP):: r1(NO)
call Random_Number( r1 )
call Random_Number( r )
forall( i = 1 : NO : 1 )
r(i) = max( r(i), r1(i) )
end forall
r = radii * r
return
end subroutine
subroutine Probability(a, P)
implicit none
real(kind = WP), intent(in):: a
real(kind = WP), intent(out):: P
! the number of point you want to simulation
integer(kind = IP), parameter:: NO = 100000
! the radii of the cycle
real(kind = WP):: radii
real(kind = WP):: r(NO)
real(kind = WP):: theta(NO)
integer(kind = IP):: i ! for loop
integer(kind = IP):: COUNT
radii = 1._WP
call CircleUniform(NO, radii, r)
COUNT = 0
do i = 1, NO, 1
if ( r(i) < a ) then
COUNT = COUNT + 1
end if
end do
P = 1._WP * COUNT / NO
return
end subroutine
end module
program main
use CUMC
implicit none
real(kind = WP):: a
real(kind = WP):: P
a = 0.5_WP
call Probability(a, P)
write(*, *) "P = ", P
stop
end program main
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