mirror of
https://github.com/TREX-CoE/qmc-lttc.git
synced 2024-12-13 07:53:52 +01:00
Fixed bugs
This commit is contained in:
parent
b6d70add67
commit
22f1eaf41b
109
QMC.org
109
QMC.org
@ -743,11 +743,18 @@ print(f"E = {E} +/- {deltaE}")
|
||||
: E = -0.4956255109300764 +/- 0.0007082875482711226
|
||||
|
||||
*Fortran*
|
||||
#+begin_note
|
||||
When running Monte Carlo calculations, the number of steps is
|
||||
usually very large. We expect =nmax= to be possibly larger than 2
|
||||
billion, so we use 8-byte integers (=integer*8=) to represent it, as
|
||||
well as the index of the current step.
|
||||
#+end_note
|
||||
|
||||
#+BEGIN_SRC f90
|
||||
subroutine uniform_montecarlo(a,nmax,energy)
|
||||
implicit none
|
||||
double precision, intent(in) :: a
|
||||
integer , intent(in) :: nmax
|
||||
integer*8 , intent(in) :: nmax
|
||||
double precision, intent(out) :: energy
|
||||
|
||||
integer*8 :: istep
|
||||
@ -772,7 +779,7 @@ end subroutine uniform_montecarlo
|
||||
program qmc
|
||||
implicit none
|
||||
double precision, parameter :: a = 0.9
|
||||
integer , parameter :: nmax = 100000
|
||||
integer*8 , parameter :: nmax = 100000
|
||||
integer , parameter :: nruns = 30
|
||||
|
||||
integer :: irun
|
||||
@ -833,18 +840,18 @@ subroutine random_gauss(z,n)
|
||||
! n is even
|
||||
do i=1,n,2
|
||||
z(i) = dsqrt(-2.d0*dlog(u(i)))
|
||||
z(i+1) = z(i) + dsin( two_pi*u(i+1) )
|
||||
z(i) = z(i) + dcos( two_pi*u(i+1) )
|
||||
z(i+1) = z(i) * dsin( two_pi*u(i+1) )
|
||||
z(i) = z(i) * dcos( two_pi*u(i+1) )
|
||||
end do
|
||||
else
|
||||
! n is odd
|
||||
do i=1,n-1,2
|
||||
z(i) = dsqrt(-2.d0*dlog(u(i)))
|
||||
z(i+1) = z(i) + dsin( two_pi*u(i+1) )
|
||||
z(i) = z(i) + dcos( two_pi*u(i+1) )
|
||||
z(i+1) = z(i) * dsin( two_pi*u(i+1) )
|
||||
z(i) = z(i) * dcos( two_pi*u(i+1) )
|
||||
end do
|
||||
z(n) = dsqrt(-2.d0*dlog(u(n)))
|
||||
z(n) = z(n) + dcos( two_pi*u(n+1) )
|
||||
z(n) = z(n) * dcos( two_pi*u(n+1) )
|
||||
end if
|
||||
end subroutine random_gauss
|
||||
#+END_SRC
|
||||
@ -907,7 +914,7 @@ print(f"E = {E} +/- {deltaE}")
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS:
|
||||
: E = -0.49507506093129827 +/- 0.00014164037765553668
|
||||
: E = -0.49511014287471955 +/- 0.00012402022172236656
|
||||
|
||||
|
||||
*Fortran*
|
||||
@ -916,14 +923,14 @@ double precision function gaussian(r)
|
||||
implicit none
|
||||
double precision, intent(in) :: r(3)
|
||||
double precision, parameter :: norm_gauss = 1.d0/(2.d0*dacos(-1.d0))**(1.5d0)
|
||||
gaussian = norm_gauss * dexp( -0.5d0 * dsqrt(r(1)*r(1) + r(2)*r(2) + r(3)*r(3) ))
|
||||
gaussian = norm_gauss * dexp( -0.5d0 * (r(1)*r(1) + r(2)*r(2) + r(3)*r(3) ))
|
||||
end function gaussian
|
||||
|
||||
|
||||
subroutine gaussian_montecarlo(a,nmax,energy)
|
||||
implicit none
|
||||
double precision, intent(in) :: a
|
||||
integer , intent(in) :: nmax
|
||||
integer*8 , intent(in) :: nmax
|
||||
double precision, intent(out) :: energy
|
||||
|
||||
integer*8 :: istep
|
||||
@ -947,7 +954,7 @@ end subroutine gaussian_montecarlo
|
||||
program qmc
|
||||
implicit none
|
||||
double precision, parameter :: a = 0.9
|
||||
integer , parameter :: nmax = 100000
|
||||
integer*8 , parameter :: nmax = 100000
|
||||
integer , parameter :: nruns = 30
|
||||
|
||||
integer :: irun
|
||||
@ -968,13 +975,9 @@ gfortran hydrogen.f90 qmc_stats.f90 qmc_gaussian.f90 -o qmc_gaussian
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
: E = -0.49606057056767766 +/- 1.3918807547836872E-004
|
||||
: E = -0.49517104619091717 +/- 1.0685523607878961E-004
|
||||
|
||||
** Sampling with $\Psi^2$
|
||||
:PROPERTIES:
|
||||
:header-args:python: :tangle vmc.py
|
||||
:header-args:f90: :tangle vmc.f90
|
||||
:END:
|
||||
|
||||
We will now use the square of the wave function to make the sampling:
|
||||
|
||||
@ -991,6 +994,10 @@ gfortran hydrogen.f90 qmc_stats.f90 qmc_gaussian.f90 -o qmc_gaussian
|
||||
|
||||
|
||||
*** Importance sampling
|
||||
:PROPERTIES:
|
||||
:header-args:python: :tangle vmc.py
|
||||
:header-args:f90: :tangle vmc.f90
|
||||
:END:
|
||||
|
||||
To generate the probability density $\Psi^2$, we consider a
|
||||
diffusion process characterized by a time-dependent density
|
||||
@ -1107,20 +1114,22 @@ end subroutine drift
|
||||
#+end_exercise
|
||||
|
||||
*Python*
|
||||
#+BEGIN_SRC python :results output :tangle vmc.py
|
||||
#+BEGIN_SRC python :results output
|
||||
from hydrogen import *
|
||||
from qmc_stats import *
|
||||
|
||||
def MonteCarlo(a,tau,nmax):
|
||||
sq_tau = np.sqrt(tau)
|
||||
|
||||
# Initialization
|
||||
E = 0.
|
||||
N = 0.
|
||||
sq_tau = np.sqrt(tau)
|
||||
r_old = np.random.normal(loc=0., scale=1.0, size=(3))
|
||||
d_old = drift(a,r_old)
|
||||
d2_old = np.dot(d_old,d_old)
|
||||
psi_old = psi(a,r_old)
|
||||
|
||||
for istep in range(nmax):
|
||||
d_old = drift(a,r_old)
|
||||
chi = np.random.normal(loc=0., scale=1.0, size=(3))
|
||||
r_new = r_old + tau * d_old + sq_tau * chi
|
||||
r_new = r_old + tau * d_old + chi*sq_tau
|
||||
N += 1.
|
||||
E += e_loc(a,r_new)
|
||||
r_old = r_new
|
||||
@ -1129,37 +1138,41 @@ def MonteCarlo(a,tau,nmax):
|
||||
|
||||
a = 0.9
|
||||
nmax = 100000
|
||||
tau = 0.001
|
||||
tau = 0.2
|
||||
X = [MonteCarlo(a,tau,nmax) for i in range(30)]
|
||||
E, deltaE = ave_error(X)
|
||||
print(f"E = {E} +/- {deltaE}")
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS:
|
||||
: E = -0.4112049153828464 +/- 0.00027934927432953063
|
||||
|
||||
: E = -0.4858534479298907 +/- 0.00010203236131158794
|
||||
|
||||
*Fortran*
|
||||
#+BEGIN_SRC f90
|
||||
subroutine variational_montecarlo(a,nmax,energy)
|
||||
subroutine variational_montecarlo(a,tau,nmax,energy)
|
||||
implicit none
|
||||
double precision, intent(in) :: a
|
||||
integer , intent(in) :: nmax
|
||||
double precision, intent(in) :: a, tau
|
||||
integer*8 , intent(in) :: nmax
|
||||
double precision, intent(out) :: energy
|
||||
|
||||
integer*8 :: istep
|
||||
double precision :: norm, r_old(3), r_new(3), d_old(3), sq_tau, chi(3)
|
||||
double precision, external :: e_loc
|
||||
|
||||
double precision :: norm, r(3), w
|
||||
|
||||
double precision, external :: e_loc, psi, gaussian
|
||||
|
||||
sq_tau = dsqrt(tau)
|
||||
|
||||
! Initialization
|
||||
energy = 0.d0
|
||||
norm = 0.d0
|
||||
call random_gauss(r_old,3)
|
||||
|
||||
do istep = 1,nmax
|
||||
call random_gauss(r,3)
|
||||
w = psi(a,r)
|
||||
w = w*w / gaussian(r)
|
||||
norm = norm + w
|
||||
energy = energy + w * e_loc(a,r)
|
||||
call drift(a,r_old,d_old)
|
||||
call random_gauss(chi,3)
|
||||
r_new(:) = r_old(:) + tau * d_old(:) + chi(:)*sq_tau
|
||||
norm = norm + 1.d0
|
||||
energy = energy + e_loc(a,r_new)
|
||||
r_old(:) = r_new(:)
|
||||
end do
|
||||
energy = energy / norm
|
||||
end subroutine variational_montecarlo
|
||||
@ -1167,7 +1180,8 @@ end subroutine variational_montecarlo
|
||||
program qmc
|
||||
implicit none
|
||||
double precision, parameter :: a = 0.9
|
||||
integer , parameter :: nmax = 100000
|
||||
double precision, parameter :: tau = 0.2
|
||||
integer*8 , parameter :: nmax = 100000
|
||||
integer , parameter :: nruns = 30
|
||||
|
||||
integer :: irun
|
||||
@ -1175,7 +1189,7 @@ program qmc
|
||||
double precision :: ave, err
|
||||
|
||||
do irun=1,nruns
|
||||
call gaussian_montecarlo(a,nmax,X(irun))
|
||||
call variational_montecarlo(a,tau,nmax,X(irun))
|
||||
enddo
|
||||
call ave_error(X,nruns,ave,err)
|
||||
print *, 'E = ', ave, '+/-', err
|
||||
@ -1186,8 +1200,15 @@ end program qmc
|
||||
gfortran hydrogen.f90 qmc_stats.f90 vmc.f90 -o vmc
|
||||
./vmc
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
: E = -0.48584030499187431 +/- 1.0411743995438257E-004
|
||||
|
||||
*** Metropolis algorithm
|
||||
:PROPERTIES:
|
||||
:header-args:python: :tangle vmc_metropolis.py
|
||||
:header-args:f90: :tangle vmc_metropolis.f90
|
||||
:END:
|
||||
|
||||
Discretizing the differential equation to generate the desired
|
||||
probability density will suffer from a discretization error
|
||||
@ -1236,7 +1257,7 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc.f90 -o vmc
|
||||
#+end_exercise
|
||||
|
||||
*Python*
|
||||
#+BEGIN_SRC python
|
||||
#+BEGIN_SRC python :results output
|
||||
def MonteCarlo(a,tau,nmax):
|
||||
E = 0.
|
||||
N = 0.
|
||||
@ -1277,7 +1298,7 @@ print(f"E = {E} +/- {deltaE}")
|
||||
: E = -0.4951783346213532 +/- 0.00022067316984271938
|
||||
|
||||
*Fortran*
|
||||
#+BEGIN_SRC f90
|
||||
#+BEGIN_SRC f90
|
||||
subroutine variational_montecarlo(a,nmax,energy)
|
||||
implicit none
|
||||
double precision, intent(in) :: a
|
||||
@ -1324,9 +1345,15 @@ end program qmc
|
||||
gfortran hydrogen.f90 qmc_stats.f90 vmc.f90 -o vmc
|
||||
./vmc
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
|
||||
|
||||
* TODO Diffusion Monte Carlo
|
||||
:PROPERTIES:
|
||||
:header-args:python: :tangle dmc.py
|
||||
:header-args:f90: :tangle dmc.f90
|
||||
:END:
|
||||
|
||||
We will now consider the H_2 molecule in a minimal basis composed of the
|
||||
$1s$ orbitals of the hydrogen atoms:
|
||||
|
@ -27,17 +27,17 @@ subroutine random_gauss(z,n)
|
||||
! n is even
|
||||
do i=1,n,2
|
||||
z(i) = dsqrt(-2.d0*dlog(u(i)))
|
||||
z(i+1) = z(i) + dsin( two_pi*u(i+1) )
|
||||
z(i) = z(i) + dcos( two_pi*u(i+1) )
|
||||
z(i+1) = z(i) * dsin( two_pi*u(i+1) )
|
||||
z(i) = z(i) * dcos( two_pi*u(i+1) )
|
||||
end do
|
||||
else
|
||||
! n is odd
|
||||
do i=1,n-1,2
|
||||
z(i) = dsqrt(-2.d0*dlog(u(i)))
|
||||
z(i+1) = z(i) + dsin( two_pi*u(i+1) )
|
||||
z(i) = z(i) + dcos( two_pi*u(i+1) )
|
||||
z(i+1) = z(i) * dsin( two_pi*u(i+1) )
|
||||
z(i) = z(i) * dcos( two_pi*u(i+1) )
|
||||
end do
|
||||
z(n) = dsqrt(-2.d0*dlog(u(n)))
|
||||
z(n) = z(n) + dcos( two_pi*u(n+1) )
|
||||
z(n) = z(n) * dcos( two_pi*u(n+1) )
|
||||
end if
|
||||
end subroutine random_gauss
|
||||
|
@ -1,7 +1,7 @@
|
||||
subroutine uniform_montecarlo(a,nmax,energy)
|
||||
implicit none
|
||||
double precision, intent(in) :: a
|
||||
integer , intent(in) :: nmax
|
||||
integer*8 , intent(in) :: nmax
|
||||
double precision, intent(out) :: energy
|
||||
|
||||
integer*8 :: istep
|
||||
@ -26,7 +26,7 @@ end subroutine uniform_montecarlo
|
||||
program qmc
|
||||
implicit none
|
||||
double precision, parameter :: a = 0.9
|
||||
integer , parameter :: nmax = 100000
|
||||
integer*8 , parameter :: nmax = 100000
|
||||
integer , parameter :: nruns = 30
|
||||
|
||||
integer :: irun
|
||||
|
Loading…
Reference in New Issue
Block a user