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Update variance

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This commit is contained in:
Anthony Scemama 2021-01-20 21:18:22 +01:00
parent 3877c981a3
commit c9696b0944
4 changed files with 27 additions and 49 deletions
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39
QMC.org
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@ -478,7 +478,7 @@ gfortran hydrogen.f90 energy_hydrogen.f90 -o energy_hydrogen
*** Exercise (optional) *** Exercise (optional)
#+begin_exercise #+begin_exercise
Prove that : Prove that :
$$ \sigma^2(E_L) = \langle E^2 \rangle - \langle E \rangle^2 $$ $$\langle E - \langle E \rangle \rangle^2 = \langle E^2 \rangle - \langle E \rangle^2 $$
#+end_exercise #+end_exercise
*** Exercise *** Exercise
@ -537,6 +537,7 @@ program variance_hydrogen
implicit none implicit none
double precision, external :: e_loc, psi double precision, external :: e_loc, psi
double precision :: x(50), w, delta, energy, dx, r(3), a(6), norm, s2 double precision :: x(50), w, delta, energy, dx, r(3), a(6), norm, s2
double precision :: e, energy2
integer :: i, k, l, j integer :: i, k, l, j
a = (/ 0.1d0, 0.2d0, 0.5d0, 1.d0, 1.5d0, 2.d0 /) a = (/ 0.1d0, 0.2d0, 0.5d0, 1.d0, 1.5d0, 2.d0 /)
@ -552,6 +553,7 @@ program variance_hydrogen
do j=1,size(a) do j=1,size(a)
energy = 0.d0 energy = 0.d0
energy2 = 0.d0
norm = 0.d0 norm = 0.d0
do i=1,size(x) do i=1,size(x)
r(1) = x(i) r(1) = x(i)
@ -561,29 +563,16 @@ program variance_hydrogen
r(3) = x(l) r(3) = x(l)
w = psi(a(j),r) w = psi(a(j),r)
w = w * w * delta w = w * w * delta
energy = energy + w * e_loc(a(j), r) e = e_loc(a(j), r)
energy = energy + w * e
energy2 = energy2 + w * e * e
norm = norm + w norm = norm + w
end do end do
end do end do
end do end do
energy = energy / norm energy = energy / norm
energy2 = energy2 / norm
s2 = 0.d0 s2 = energy2 - energy*energy
norm = 0.d0
do i=1,size(x)
r(1) = x(i)
do k=1,size(x)
r(2) = x(k)
do l=1,size(x)
r(3) = x(l)
w = psi(a(j),r)
w = w * w * delta
s2 = s2 + w * ( e_loc(a(j), r) - energy )**2
norm = norm + w
end do
end do
end do
s2 = s2 / norm
print *, 'a = ', a(j), ' E = ', energy, ' s2 = ', s2 print *, 'a = ', a(j), ' E = ', energy, ' s2 = ', s2
end do end do
@ -598,12 +587,12 @@ gfortran hydrogen.f90 variance_hydrogen.f90 -o variance_hydrogen
#+end_src #+end_src
#+RESULTS: #+RESULTS:
: a = 0.10000000000000001 E = -0.24518438948809140 s2 = 2.6965218719733813E-002 : a = 0.10000000000000001 E = -0.24518438948809140 s2 = 2.6965218719722767E-002
: a = 0.20000000000000001 E = -0.26966057967803236 s2 = 3.7197072370217653E-002 : a = 0.20000000000000001 E = -0.26966057967803236 s2 = 3.7197072370201284E-002
: a = 0.50000000000000000 E = -0.38563576125173815 s2 = 5.3185967578488862E-002 : a = 0.50000000000000000 E = -0.38563576125173815 s2 = 5.3185967578480653E-002
: a = 1.0000000000000000 E = -0.50000000000000000 s2 = 0.0000000000000000 : a = 1.0000000000000000 E = -0.50000000000000000 s2 = 0.0000000000000000
: a = 1.5000000000000000 E = -0.39242967082602065 s2 = 0.31449670909180444 : a = 1.5000000000000000 E = -0.39242967082602065 s2 = 0.31449670909172917
: a = 2.0000000000000000 E = -8.0869806678448772E-002 s2 = 1.8068814270851303 : a = 2.0000000000000000 E = -8.0869806678448772E-002 s2 = 1.8068814270846534
* Variational Monte Carlo * Variational Monte Carlo

27
variance_hydrogen.f90
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@ -2,6 +2,7 @@ program variance_hydrogen
implicit none implicit none
double precision, external :: e_loc, psi double precision, external :: e_loc, psi
double precision :: x(50), w, delta, energy, dx, r(3), a(6), norm, s2 double precision :: x(50), w, delta, energy, dx, r(3), a(6), norm, s2
double precision :: e, energy2
integer :: i, k, l, j integer :: i, k, l, j
a = (/ 0.1d0, 0.2d0, 0.5d0, 1.d0, 1.5d0, 2.d0 /) a = (/ 0.1d0, 0.2d0, 0.5d0, 1.d0, 1.5d0, 2.d0 /)
@ -17,6 +18,7 @@ program variance_hydrogen
do j=1,size(a) do j=1,size(a)
energy = 0.d0 energy = 0.d0
energy2 = 0.d0
norm = 0.d0 norm = 0.d0
do i=1,size(x) do i=1,size(x)
r(1) = x(i) r(1) = x(i)
@ -26,29 +28,16 @@ program variance_hydrogen
r(3) = x(l) r(3) = x(l)
w = psi(a(j),r) w = psi(a(j),r)
w = w * w * delta w = w * w * delta
energy = energy + w * e_loc(a(j), r) e = e_loc(a(j), r)
energy = energy + w * e
energy2 = energy2 + w * e * e
norm = norm + w norm = norm + w
end do end do
end do end do
end do end do
energy = energy / norm energy = energy / norm
energy2 = energy2 / norm
s2 = 0.d0 s2 = energy2 - energy*energy
norm = 0.d0
do i=1,size(x)
r(1) = x(i)
do k=1,size(x)
r(2) = x(k)
do l=1,size(x)
r(3) = x(l)
w = psi(a(j),r)
w = w * w * delta
s2 = s2 + w * ( e_loc(a(j), r) - energy )**2
norm = norm + w
end do
end do
end do
s2 = s2 / norm
print *, 'a = ', a(j), ' E = ', energy, ' s2 = ', s2 print *, 'a = ', a(j), ' E = ', energy, ' s2 = ', s2
end do end do

6
vmc_metropolis.f90
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@ -12,7 +12,7 @@ subroutine variational_montecarlo(a,tau,nmax,energy,accep_rate)
double precision, external :: e_loc, psi double precision, external :: e_loc, psi
sq_tau = dsqrt(tau) sq_tau = dsqrt(tau)
! Initialization ! Initialization
energy = 0.d0 energy = 0.d0
norm = 0.d0 norm = 0.d0
@ -30,8 +30,8 @@ subroutine variational_montecarlo(a,tau,nmax,energy,accep_rate)
psi_new = psi(a,r_new) psi_new = psi(a,r_new)
! Metropolis ! Metropolis
prod = (d_new(1) + d_old(1))*(r_new(1) - r_old(1)) + & 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(2) + d_old(2))*(r_new(2) - r_old(2)) + &
(d_new(3) + d_old(3))*(r_new(3) - r_old(3)) (d_new(3) + d_old(3))*(r_new(3) - r_old(3))
argexpo = 0.5d0 * (d2_new - d2_old)*tau + prod argexpo = 0.5d0 * (d2_new - d2_old)*tau + prod
q = psi_new / psi_old q = psi_new / psi_old
q = dexp(-argexpo) * q*q q = dexp(-argexpo) * q*q

4
vmc_metropolis.py
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@ -27,8 +27,8 @@ def MonteCarlo(a,tau,nmax):
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, accep_rate/N return E/N, accep_rate/N