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ccc
obtain new SEED for ran2.f
open(21,file=’SEED’)
read(21,*) idum
rewind 21
idum = −abs(idum)
ccc
ccc
Monte Carlo: gives back NCF evaluations of
the propagator for each one of the N time slices
call mc(n,ncor,ncf,a,eps,g)
35
90
ccc
95
update SEED file for the next calculation
write(21,*) abs(idum)
close(21)
end
CCC
END OF MAIN
CCCCCCCCCCCCCCCCCCCCCC
100
105
CCCCCCCCCCCCCCCCCCC
CCC
ROUTINE MC
ccc
generates propagators g through Monte Carlo Method
ccc
INPUT: n,ncor,ncf,a,eps
ccc
OUTPUT: g(1:2000,0:50)
subroutine mc(n,ncor,ncf,a,eps,g)
implicit none
integer n,ncor,ncf,nalpha,nn
real x(0:50),a,eps,avg,g(1:2000,0:50),compute,y
integer j
ccc
initial configuration
do j=0,n−1
x(j)=0.
enddo
ccc
lattice thermalization
do j=1,5*ncor
call update(x)
enddo
ccc
generates NCF configurations
do nalpha=1,ncf
ccc
jump NCOR updates
do j=1,ncor
call update(x)
enddo
ccc
evaluates g
do nn=0,n−1
g(nalpha,nn)=compute(x,nn)
enddo
115
45
ccc
Bootstrap and Binning Error Analysis
do nn=0,n−1 !each nn corresponds to a different time slice
ccc
bin the data
do nalpha=1,ncf
call bin_rout(g,bin,nn,nbin,ncf)
enddo
50
ccc
ccc
55
60
generates nbtcp bootstrap copies for G(t)
from the ncf2 binned samples
do j=1,nbtcp
avg = 0.
call bootstrap(bin,boot,nn,ncf2)
do k=1,ncf2
avg = avg+ boot(k,nn)
enddo
gaux(j,nn) = avg/float(ncf2)
enddo
enddo
120
125
130
135
65
ccc
70
Evaluations of \DeltaE(t)
do j=1,nbtcp
do nn=0,n/2−6 ! safe range for non−negative ratio
ratio = (gaux(j,nn)/gaux(j,nn+1))
del(j,nn) = log(ratio)/a
enddo
85
110
40
Mean values and errors of \DeltaE(t)
savg=0.
savg2=0.
do nn=0,n/2−6
call dvt(del,nn,savg,savg2,sig,nbtcp)
write(25,*) nn*a,savg,sig
!output in file fort.25
enddo
80
20
ccc
75
3
P) 0
\
15
Mean values and errors of G(t)
savg=0.
savg2=0.
do nn=0,n−1
call dvt(gaux,nn,savg,savg2,sig,nbtcp)
write(24,*) nn*a,savg,sig
!output in file fort.24
enddo
140
enddo
return
end
CCC
END OF ROUTINE MC
CCCCCCCCCCCCCCCCCCCCCCC
10
enddo
ccc
5
***********************************************************************
*
*
QUANTUM HARMONIC OSCILlATOR
*
MONTE CARLO SIMULATION CODE
*
by A. Taurines, 09/2003
*
*
based on proposed problem in
*
G. P. Lepage’s ‘‘Lattice QCD for novices’’
*
***********************************************************************
*
This package is free software and you can use this under:
*
"the GNU General Public Lisense" published by the FSF.
***********************************************************************
implicit none
integer n,ncor,ncf,nn,nalpha,idum,nbin,
#
ncf2,nbtcp,j,k
real a,eps,avg,g(1:2000,0:50),boot(1:2000,0:50)
real gaux(1:2000,0:50),bin(1:2000,0:50)
real del(1:2000,0:50),del2(1:2000,0:50)
real ratio,sig,savg,savg2,den
common /data/ n,a
common /data2/ idum,eps
common /data3/ ncf
external compute,uniform,actionj
n = 20
!# of time slices, n<50
ncor = 40
!# of decorrelation steps, \propto 1/a^2
ncf = 2000
!# of configurations, ncf<2000
nbin = 20
!bin spacing, must be a divisor of ncf
nbtcp = 100
!# of bootstrap copies
eps = 1.4
!maximum step for update
a = .5
!lattice spacing
ncf2 = ncf/nbin
sweep the lattice
do j=0,n−1
ccc
evaluates present action
old_x = x(j)
old_sj = actionj(j,x)
ccc
trial value for x(j)
x(j) = x(j) + uniform(−eps,eps)
ccc
evaluates \DeltaS
ds=actionj(j,x)−old_sj
ccc
Metropolis steps
if(ds.gt.0.) then
eaux=exp(−ds)
ale = uniform(0.,1.)
if(eaux.lt.ale)then
x(j)=old_x
i = i+1
endif
endif
enddo
225
230
235
165
240
T !
R !
" N!
160
170
175
180
ccc
185
245
250
n−i = # of updatings
return
end
CCC
END OF ROUTINE UPDATE
CCCCCCCCCCCCCCCCCCCCCCCCCCC
255
260
190
195
200
205
210
CCCCCCCCCCCCCCCCCCCCCC
CCC
FUNCTION ACTIONJ
ccc
evaluates change in action due to change in x(j)
ccc
INPUT: x(*),j
ccc
OUTPUT: actionj
function actionj(j,x)
implicit none
real x(*),actionj,a
integer j,jp,jm,n
common /data/ n,a
jp = mod(j+1,n)
jm = mod(j−1,n)
actionj = a*x(j)**2/2.+x(j)*(x(j)−x(jp)−x(jm))/a
return
end
CCC
END OF FUNCTION ACTIONJ
CCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCC
CCC
FUNCTION COMPUTE
ccc
evaluates propagator for the nn time slice
ccc
INPUT: x(*),nn
ccc
OUTPUT: compute
265
270
275
280
using periodicity properties of propagator
e.g., g(5,3)=g(4,2)=g(3,1)=g(2,0) ...
aux = 0.
do j=0,n−1
k = mod(j+nn,n)
aux = aux + x(j)*x(k)
enddo
compute = aux/float(n)
return
end
CCC
END OF FUNCTION COMPUTE
CCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCC
CCC
ROUTINE BIN_ROUT
ccc
bin the data
ccc
INPUT: g(1:2000,0:50),nn,nbin,ncf
ccc
OUTPUT: bin(1:2000,0:50)
subroutine bin_rout(g,bin,nn,nbin,ncf)
implicit none
integer ncf,nbin,nn,nalpha,j,i
real g(1:2000,0:50),bin(1:2000,0:50)
real aux
i = 0
do nalpha=1,ncf,nbin
i=i+1
aux = 0.
do j=1,nbin
aux = aux + g(nalpha+j,nn)
enddo
bin(i,nn) = aux/float(nbin)
enddo
return
end
CCC
END OF FUNCTION BIN_ROUT
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ccc
ccc
ccc
220
155
function compute(x,nn)
implicit none
real compute,aux,a
integer nn,j,k,n
common /data/ n,a
real x(*)
215
CCCCCCCCCCCCCCCCCCCCCCC
CCC
ROUTINE BOOTSTRAP
ccc
generates bootstrap copies
ccc
INPUT: bin(1:2000,0:50)
ccc
OUTPUT: boot(1:2000,0:50)
subroutine bootstrap(bin,boot,nn,ncf2)
implicit none
integer nalpha,nbeta,nn,ncf2
real bin(1:2000,0:50),boot(1:2000,0:50)
real uniform
do nalpha=1,ncf2
nbeta=int(uniform(1.,float(ncf2)))
boot(nalpha,nn)=bin(nbeta,nn)
enddo
return
end
CCC
END OF ROUTINE BOOTSTRAP
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCC
CCC
ROUTINE DVT
ccc
routine for standard deviation evaluation
ccc
INPUT: del(1:2000,0:50),nn,ncf
ccc
OUTPUT: savg,savg2,sig
150
CCCCCCCCCCCCCCCCCCCCCCC
CCC
ROUTINE UPDATE
ccc
update the n values of x
ccc
INPUT: x(*)
ccc
OUTPUT: x(*)
subroutine update(x)
implicit none
real x(*),old_x,old_sj,actionj,uniform,a,
# eps,ds,eaux,ale
integer n,j,idum,i
common /data/ n,a
common /data2/ idum,eps
external actionj,uniform
i=0 !counter for # of accepted updates
145
310
T !
R " N!
305
315
320
CCCCCCCCCCCCCCCCCCCCCC
CCC
FUNCTION UNIFORM
ccc
returns uniform random value between e_min and e_max
ccc
INPUT: e_min,e_max
ccc
OUTPUT: uniform
function uniform(e_min,e_max)
implicit none
real uniform,ran2,e_min,e_max,eps,ale
integer idum
common /data2/ idum,eps
ale = ran2(idum)
uniform = (e_max−e_min)*ale+e_min
return
end
CCC
END OF UNIFORM
CCCCCCCCCCCCCCCCCCCC
ccc
325
300
295
Standard random number generator (Numerical Recipes)
include ’ran2.f’
290
subroutine dvt(del,nn,savg,savg2,sig,ncf)
implicit none
integer nn,j,ncf
real del(1:2000,0:50),sig,savg,savg2
savg=0.
savg2=0.
do j=1,ncf
savg=savg+del(j,nn)
savg2=savg2+del(j,nn)**2
enddo
savg=savg/float(ncf)
savg2=savg2/float(ncf)
sig = (savg2−savg**2)
sig = sqrt(sig)
return
end
CCC
END OF ROUTINE DVT
CCCCCCCCCCCCCCCCCCCCCCCC
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