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Gaussian sampling

This commit is contained in:
Anthony Scemama 2021-01-07 11:07:18 +01:00
parent 8594cdfa39
commit 45bdaf2d41
6 changed files with 516 additions and 392 deletions

802
QMC.org

File diff suppressed because it is too large Load Diff

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@ -1,23 +1,23 @@
import numpy as np
from hydrogen import e_loc, psi
interval = np.linspace(-5,5,num=50)
delta = (interval[1]-interval[0])**3
interval = np.linspace(-5,5,num=50)
delta = (interval[1]-interval[0])**3
r = np.array([0.,0.,0.])
r = np.array([0.,0.,0.])
for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
E = 0.
norm = 0.
for x in interval:
r[0] = x
for y in interval:
r[1] = y
for z in interval:
r[2] = z
w = psi(a,r)
w = w * w * delta
E += w * e_loc(a,r)
norm += w
E = E / norm
print(f"a = {a} \t E = {E}")
for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
E = 0.
norm = 0.
for x in interval:
r[0] = x
for y in interval:
r[1] = y
for z in interval:
r[2] = z
w = psi(a,r)
w = w * w * delta
E += w * e_loc(a,r)
norm += w
E = E / norm
print(f"a = {a} \t E = {E}")

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@ -13,3 +13,31 @@ subroutine ave_error(x,n,ave,err)
err = dsqrt(variance/dble(n))
endif
end subroutine ave_error
subroutine random_gauss(z,n)
implicit none
integer, intent(in) :: n
double precision, intent(out) :: z(n)
double precision :: u(n+1)
double precision, parameter :: two_pi = 2.d0*dacos(-1.d0)
integer :: i
call random_number(u)
if (iand(n,1) == 0) then
! 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) )
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) )
end do
z(n) = dsqrt(-2.d0*dlog(u(n)))
z(n) = z(n) + dcos( two_pi*u(n+1) )
end if
end subroutine random_gauss

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@ -3,9 +3,9 @@ subroutine uniform_montecarlo(a,nmax,energy)
double precision, intent(in) :: a
integer , intent(in) :: nmax
double precision, intent(out) :: energy
integer*8 :: istep
double precision :: norm, r(3), w
double precision, external :: e_loc, psi

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@ -1,19 +1,19 @@
from hydrogen import *
from qmc_stats import *
def MonteCarlo(a, nmax):
E = 0.
N = 0.
for istep in range(nmax):
r = np.random.uniform(-5., 5., (3))
w = psi(a,r)
w = w*w
N += w
E += w * e_loc(a,r)
return E/N
def MonteCarlo(a, nmax):
E = 0.
N = 0.
for istep in range(nmax):
r = np.random.uniform(-5., 5., (3))
w = psi(a,r)
w = w*w
N += w
E += w * e_loc(a,r)
return E/N
a = 0.9
nmax = 100000
X = [MonteCarlo(a,nmax) for i in range(30)]
E, deltaE = ave_error(X)
print(f"E = {E} +/- {deltaE}")
a = 0.9
nmax = 100000
X = [MonteCarlo(a,nmax) for i in range(30)]
E, deltaE = ave_error(X)
print(f"E = {E} +/- {deltaE}")

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@ -20,8 +20,8 @@ for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
El = e_loc(a, r)
E += w * El
norm += w
E = E / norm
s2 = 0.
E = E / norm
s2 = 0.
for x in interval:
r[0] = x
for y in interval:
@ -32,5 +32,5 @@ for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
w = w * w * delta
El = e_loc(a, r)
s2 += w * (El - E)**2
s2 = s2 / norm
print(f"a = {a} \t E = {E:10.8f} \t \sigma^2 = {s2:10.8f}")
s2 = s2 / norm
print(f"a = {a} \t E = {E:10.8f} \t \sigma^2 = {s2:10.8f}")