如何用FORTRAN语言编程实现生成白噪声数据
如何用FORTRAN语言编程实现生成白噪声数据？ c program to illustrate the colored Gaussian Noise generator CGAUSSc The routine must be initialized with CGAUS0 and calls a flat distribution
c random number generator available with most compilers or you can write your
c own. Here we used the routine RAN1 from Numerical Recipes 2nd Edition, by
c Press, Teukolsky, Vetterling, and Flannery.
! It now uses the F90 intrinsic subroutine RANDOM_NUMBER.
c The White Guassian noise generator GASDEV from Numerical Recipes was
c adapted to produce Colored Gaussian noise. The basic equations for this
c computation are presented in the article by
c Fox et al., Physical Review A vol.38(1988) page 5938.
c This code was compiled and tested with Microsoft Powerstation.
! It was modified by Walt Brainerd to be standard Fortran and
! compiled on NAGWare F90.
real, allocatable :: eps(:,:)
real smean
double precision std,mean,cgauss,dt
c get input parameters (typical values shown)
open(1,file='cnoise.dat')
read(1,*)nreal !number of realizations=1000
read(1,*)nstep !max delay in corr. func=10
read(1,*)dt !time step size=.5
read(1,*)cortim !corr. time in the same units as DT=5
allocate(eps(nreal,-1:nstep*2))
c initialize
call cgaus0(dt,cortim)
c store several series of Gaussian noise values in array EPS.
do i=1,nreal !realizations
do j=0,nstep*2 !time delays
eps(i,j)=cgauss()
enddo
enddo
c calculate the autocorrelation function in variable MEAN.
npts=nstep*nreal
do idly=0,nstep
mean=0.
std=0.
do i=1,nreal
do j=0,nstep
mean=mean+dble(eps(i,j)*eps(i,j+idly))
enddo
enddo
mean=mean/dble(npts)
smean=sngl(mean) !single precision speeds up calculations
c calculate the error in autocorrelation function in variable STD.
do i=1,nreal
do j=0,nstep
std=std+dble((eps(i,j)*eps(i,j+idly)-smean)**2.)
enddo
enddo
std=sqrt(std)/dble(npts-1.)
write(1,*)idly,mean,std !output results
enddo
close(1)
deallocate(eps)
end
c==========================================================================
c initialize the RNG's
c and set the color of gaussian noise
c DT is the time step used in whatever process the colored Gaussian noise
c is used.
c CORTIM is correlation time in the same units as time step DT.
c WHITE=.true. means generate white gaussian noise which happens when
c CORTIM=0. This flag is used in CGAUSS.
c Here we use the flat distribution RAN1 also taken from Numerical Recipe
c but any other good flat distribution random number generator will do.
subroutine cgaus0(dt,cortim)
! double precision ran1,cape,dt,l1me2,cgauss
double precision cape,dt,l1me2,cgauss
real cortim,x
logical white
common /color/l1me2,cape,white
if(cortim.eq.0.)then
white=.true.
l1me2=-2.000 !white noise
cape=0.0
else
white=.false.
cape=dexp(-dt/dble(cortim))
!parameter needed in CGAUSS
l1me2=-(dble(1.)-cape*cape)*dble(2./cortim)
endif
! idum=-1
! x=ran1(idum) !initialize flat rng
x=cgauss() !initialize CGAUSS value
return
END
c==========================================================================
c Program to produce exponentially correlated colored (Gaussian) noise.
c based on Fox et al Physical Review A vol.38(1988)5938 and
c modification of GASDEV from Numerical Recipes for Fortran(2nd ed.pg279)
c CAPE is capital E in the article by Fox et. al.
c PREV is the previous value of CGAUSS used in the next iteration
c L1ME2 is the main parameters causing colored noise in Fox et al
c and represents (lamda*(1-E)^2). Ditto for H in that article.
c routine is illustrated in Double Precision in case it is needed in this
c mode, otherwise all Double Precision variables maybe changed to REAL
c but the corresponding changes must be made to CGAUS0 and the calling
c programs.
double precision FUNCTION cgauss()
! INTEGER idum,iset
INTEGER iset
logical white
! double precisionfac,gset,rsq,v1,v2,ran1,l1me2,h,cape
double precisionfac,gset,rsq,v1,v2,l1me2,h,cape
common /color/l1me2,cape,white
SAVE iset,gset,prev
DATA iset/0/
DATA prev/0.0d0/
if (iset.eq.0) then
!1 v1=2.*ran1(idum)-1.
1 call random_number(v1)
v1=2.*v1-1
! v2=2.*ran1(idum)-1.
call random_number(v2)
v2=2.*v2-1
rsq=v1**2.+v2**2.
if(rsq.ge.1..or.rsq.eq.0.)goto 1
!took out sqrt(2) vs eq(28) Fox etal
fac=dsqrt(l1me2*dlog(rsq)/rsq)
gset=v1*fac
h=v2*fac
iset=1
else
h=gset
iset=0
endif
if(white)then!please note that the time step vs its sqrt
cgauss=h !in integration is previously set in PARAM
else
cgauss=prev*cape+h
prev=cgauss
endif
return
END
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