VMC OK
This commit is contained in:
parent
22f1eaf41b
commit
52ed6eff8d
93
QMC.org
93
QMC.org
@ -1248,27 +1248,36 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc.f90 -o vmc
|
|||||||
the move: set $\mathbf{r}_{n+1} = \mathbf{r}_{n}$, but *don't
|
the move: set $\mathbf{r}_{n+1} = \mathbf{r}_{n}$, but *don't
|
||||||
remove the sample from the average!*
|
remove the sample from the average!*
|
||||||
|
|
||||||
|
The /acceptance rate/ is the ratio of the number of accepted step
|
||||||
|
over the total number of steps. The time step should be adapted so
|
||||||
|
that the acceptance rate is around 0.5 for a good efficiency of
|
||||||
|
the simulation.
|
||||||
|
|
||||||
**** TODO Exercise
|
**** TODO Exercise
|
||||||
|
|
||||||
#+begin_exercise
|
#+begin_exercise
|
||||||
Modify the previous program to introduce the accept/reject step.
|
Modify the previous program to introduce the accept/reject step.
|
||||||
You should recover the unbiased result.
|
You should recover the unbiased result.
|
||||||
|
Adjust the time-step so that the acceptance rate is 0.5.
|
||||||
#+end_exercise
|
#+end_exercise
|
||||||
|
|
||||||
*Python*
|
*Python*
|
||||||
#+BEGIN_SRC python :results output
|
#+BEGIN_SRC python :results output
|
||||||
|
from hydrogen import *
|
||||||
|
from qmc_stats import *
|
||||||
|
|
||||||
def MonteCarlo(a,tau,nmax):
|
def MonteCarlo(a,tau,nmax):
|
||||||
E = 0.
|
E = 0.
|
||||||
N = 0.
|
N = 0.
|
||||||
|
accep_rate = 0.
|
||||||
sq_tau = np.sqrt(tau)
|
sq_tau = np.sqrt(tau)
|
||||||
r_old = np.random.normal(loc=0., scale=1.0, size=(3))
|
r_old = np.random.normal(loc=0., scale=1.0, size=(3))
|
||||||
d_old = drift(a,r_old)
|
d_old = drift(a,r_old)
|
||||||
d2_old = np.dot(d_old,d_old)
|
d2_old = np.dot(d_old,d_old)
|
||||||
psi_old = psi(a,r_old)
|
psi_old = psi(a,r_old)
|
||||||
for istep in range(nmax):
|
for istep in range(nmax):
|
||||||
eta = np.random.normal(loc=0., scale=1.0, size=(3))
|
chi = np.random.normal(loc=0., scale=1.0, size=(3))
|
||||||
r_new = r_old + tau * d_old + sq_tau * eta
|
r_new = r_old + tau * d_old + sq_tau * chi
|
||||||
d_new = drift(a,r_new)
|
d_new = drift(a,r_new)
|
||||||
d2_new = np.dot(d_new,d_new)
|
d2_new = np.dot(d_new,d_new)
|
||||||
psi_new = psi(a,r_new)
|
psi_new = psi(a,r_new)
|
||||||
@ -1278,75 +1287,111 @@ def MonteCarlo(a,tau,nmax):
|
|||||||
q = psi_new / psi_old
|
q = psi_new / psi_old
|
||||||
q = np.exp(-argexpo) * q*q
|
q = np.exp(-argexpo) * q*q
|
||||||
if np.random.uniform() < q:
|
if np.random.uniform() < q:
|
||||||
|
accep_rate += 1.
|
||||||
r_old = r_new
|
r_old = r_new
|
||||||
d_old = d_new
|
d_old = d_new
|
||||||
d2_old = d2_new
|
d2_old = d2_new
|
||||||
psi_old = psi_new
|
psi_old = psi_new
|
||||||
N += 1.
|
N += 1.
|
||||||
E += e_loc(a,r_old)
|
E += e_loc(a,r_old)
|
||||||
return E/N
|
return E/N, accep_rate/N
|
||||||
|
|
||||||
|
|
||||||
|
a = 0.9
|
||||||
nmax = 100000
|
nmax = 100000
|
||||||
tau = 0.1
|
tau = 1.0
|
||||||
X = [MonteCarlo(a,tau,nmax) for i in range(30)]
|
X = [MonteCarlo(a,tau,nmax) for i in range(30)]
|
||||||
E, deltaE = ave_error(X)
|
E, deltaE = ave_error([x[0] for x in X])
|
||||||
print(f"E = {E} +/- {deltaE}")
|
A, deltaA = ave_error([x[1] for x in X])
|
||||||
|
print(f"E = {E} +/- {deltaE} {A} +/- {deltaA}")
|
||||||
#+END_SRC
|
#+END_SRC
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
: E = -0.4951783346213532 +/- 0.00022067316984271938
|
: E = -0.49387078389332206 +/- 0.0033326460286729792 0.4983000000000001 +/- 0.006825097363627021
|
||||||
|
|
||||||
*Fortran*
|
*Fortran*
|
||||||
#+BEGIN_SRC f90
|
#+BEGIN_SRC f90
|
||||||
subroutine variational_montecarlo(a,nmax,energy)
|
subroutine variational_montecarlo(a,tau,nmax,energy,accep_rate)
|
||||||
implicit none
|
implicit none
|
||||||
double precision, intent(in) :: a
|
double precision, intent(in) :: a, tau
|
||||||
integer , intent(in) :: nmax
|
integer*8 , intent(in) :: nmax
|
||||||
double precision, intent(out) :: energy
|
double precision, intent(out) :: energy, accep_rate
|
||||||
|
|
||||||
integer*8 :: istep
|
integer*8 :: istep
|
||||||
|
double precision :: norm, sq_tau, chi(3), d2_old, prod, u
|
||||||
|
double precision :: psi_old, psi_new, d2_new, argexpo, q
|
||||||
|
double precision :: r_old(3), r_new(3)
|
||||||
|
double precision :: d_old(3), d_new(3)
|
||||||
|
double precision, external :: e_loc, psi
|
||||||
|
|
||||||
double precision :: norm, r(3), w
|
sq_tau = dsqrt(tau)
|
||||||
|
|
||||||
double precision, external :: e_loc, psi, gaussian
|
|
||||||
|
|
||||||
|
! Initialization
|
||||||
energy = 0.d0
|
energy = 0.d0
|
||||||
norm = 0.d0
|
norm = 0.d0
|
||||||
|
accep_rate = 0.d0
|
||||||
|
call random_gauss(r_old,3)
|
||||||
|
call drift(a,r_old,d_old)
|
||||||
|
d2_old = d_old(1)*d_old(1) + d_old(2)*d_old(2) + d_old(3)*d_old(3)
|
||||||
|
psi_old = psi(a,r_old)
|
||||||
|
|
||||||
do istep = 1,nmax
|
do istep = 1,nmax
|
||||||
call random_gauss(r,3)
|
call random_gauss(chi,3)
|
||||||
w = psi(a,r)
|
r_new(:) = r_old(:) + tau * d_old(:) + chi(:)*sq_tau
|
||||||
w = w*w / gaussian(r)
|
call drift(a,r_new,d_new)
|
||||||
norm = norm + w
|
d2_new = d_new(1)*d_new(1) + d_new(2)*d_new(2) + d_new(3)*d_new(3)
|
||||||
energy = energy + w * e_loc(a,r)
|
psi_new = psi(a,r_new)
|
||||||
|
! Metropolis
|
||||||
|
prod = (d_new(1) + d_old(1))*(r_new(1) - r_old(1)) + &
|
||||||
|
(d_new(2) + d_old(2))*(r_new(2) - r_old(2)) + &
|
||||||
|
(d_new(3) + d_old(3))*(r_new(3) - r_old(3))
|
||||||
|
argexpo = 0.5d0 * (d2_new - d2_old)*tau + prod
|
||||||
|
q = psi_new / psi_old
|
||||||
|
q = dexp(-argexpo) * q*q
|
||||||
|
call random_number(u)
|
||||||
|
if (u<q) then
|
||||||
|
accep_rate = accep_rate + 1.d0
|
||||||
|
r_old(:) = r_new(:)
|
||||||
|
d_old(:) = d_new(:)
|
||||||
|
d2_old = d2_new
|
||||||
|
psi_old = psi_new
|
||||||
|
end if
|
||||||
|
norm = norm + 1.d0
|
||||||
|
energy = energy + e_loc(a,r_old)
|
||||||
end do
|
end do
|
||||||
energy = energy / norm
|
energy = energy / norm
|
||||||
|
accep_rate = accep_rate / norm
|
||||||
end subroutine variational_montecarlo
|
end subroutine variational_montecarlo
|
||||||
|
|
||||||
program qmc
|
program qmc
|
||||||
implicit none
|
implicit none
|
||||||
double precision, parameter :: a = 0.9
|
double precision, parameter :: a = 0.9
|
||||||
integer , parameter :: nmax = 100000
|
double precision, parameter :: tau = 1.0
|
||||||
|
integer*8 , parameter :: nmax = 100000
|
||||||
integer , parameter :: nruns = 30
|
integer , parameter :: nruns = 30
|
||||||
|
|
||||||
integer :: irun
|
integer :: irun
|
||||||
double precision :: X(nruns)
|
double precision :: X(nruns), accep(nruns)
|
||||||
double precision :: ave, err
|
double precision :: ave, err
|
||||||
|
|
||||||
do irun=1,nruns
|
do irun=1,nruns
|
||||||
call gaussian_montecarlo(a,nmax,X(irun))
|
call variational_montecarlo(a,tau,nmax,X(irun),accep(irun))
|
||||||
enddo
|
enddo
|
||||||
call ave_error(X,nruns,ave,err)
|
call ave_error(X,nruns,ave,err)
|
||||||
print *, 'E = ', ave, '+/-', err
|
print *, 'E = ', ave, '+/-', err
|
||||||
|
call ave_error(accep,nruns,ave,err)
|
||||||
|
print *, 'A = ', ave, '+/-', err
|
||||||
end program qmc
|
end program qmc
|
||||||
#+END_SRC
|
#+END_SRC
|
||||||
|
|
||||||
#+begin_src sh :results output :exports both
|
#+begin_src sh :results output :exports both
|
||||||
gfortran hydrogen.f90 qmc_stats.f90 vmc.f90 -o vmc
|
gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
|
||||||
./vmc
|
./vmc_metropolis
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
|
: E = -0.49499990423528023 +/- 1.5958250761863871E-004
|
||||||
|
: A = 0.78861366666666655 +/- 3.5096729498002445E-004
|
||||||
|
|
||||||
|
|
||||||
* TODO Diffusion Monte Carlo
|
* TODO Diffusion Monte Carlo
|
||||||
|
Loading…
Reference in New Issue
Block a user