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Gaussian sampling
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@ -1,23 +1,23 @@
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import numpy as np
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from hydrogen import e_loc, psi
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interval = np.linspace(-5,5,num=50)
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delta = (interval[1]-interval[0])**3
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interval = np.linspace(-5,5,num=50)
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delta = (interval[1]-interval[0])**3
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r = np.array([0.,0.,0.])
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r = np.array([0.,0.,0.])
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for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
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E = 0.
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norm = 0.
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for x in interval:
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r[0] = x
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for y in interval:
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r[1] = y
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for z in interval:
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r[2] = z
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w = psi(a,r)
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w = w * w * delta
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E += w * e_loc(a,r)
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norm += w
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E = E / norm
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print(f"a = {a} \t E = {E}")
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for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
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E = 0.
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norm = 0.
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for x in interval:
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r[0] = x
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for y in interval:
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r[1] = y
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for z in interval:
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r[2] = z
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w = psi(a,r)
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w = w * w * delta
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E += w * e_loc(a,r)
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norm += w
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E = E / norm
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print(f"a = {a} \t E = {E}")
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@ -13,3 +13,31 @@ subroutine ave_error(x,n,ave,err)
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err = dsqrt(variance/dble(n))
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endif
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end subroutine ave_error
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subroutine random_gauss(z,n)
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implicit none
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integer, intent(in) :: n
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double precision, intent(out) :: z(n)
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double precision :: u(n+1)
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double precision, parameter :: two_pi = 2.d0*dacos(-1.d0)
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integer :: i
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call random_number(u)
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if (iand(n,1) == 0) then
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! n is even
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do i=1,n,2
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z(i) = dsqrt(-2.d0*dlog(u(i)))
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z(i+1) = z(i) + dsin( two_pi*u(i+1) )
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z(i) = z(i) + dcos( two_pi*u(i+1) )
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end do
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else
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! n is odd
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do i=1,n-1,2
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z(i) = dsqrt(-2.d0*dlog(u(i)))
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z(i+1) = z(i) + dsin( two_pi*u(i+1) )
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z(i) = z(i) + dcos( two_pi*u(i+1) )
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end do
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z(n) = dsqrt(-2.d0*dlog(u(n)))
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z(n) = z(n) + dcos( two_pi*u(n+1) )
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end if
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end subroutine random_gauss
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@ -3,9 +3,9 @@ subroutine uniform_montecarlo(a,nmax,energy)
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double precision, intent(in) :: a
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integer , intent(in) :: nmax
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double precision, intent(out) :: energy
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integer*8 :: istep
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double precision :: norm, r(3), w
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double precision, external :: e_loc, psi
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@ -1,19 +1,19 @@
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from hydrogen import *
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from qmc_stats import *
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def MonteCarlo(a, nmax):
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E = 0.
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N = 0.
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for istep in range(nmax):
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r = np.random.uniform(-5., 5., (3))
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w = psi(a,r)
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w = w*w
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N += w
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E += w * e_loc(a,r)
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return E/N
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def MonteCarlo(a, nmax):
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E = 0.
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N = 0.
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for istep in range(nmax):
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r = np.random.uniform(-5., 5., (3))
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w = psi(a,r)
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w = w*w
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N += w
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E += w * e_loc(a,r)
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return E/N
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a = 0.9
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nmax = 100000
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X = [MonteCarlo(a,nmax) for i in range(30)]
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E, deltaE = ave_error(X)
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print(f"E = {E} +/- {deltaE}")
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a = 0.9
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nmax = 100000
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X = [MonteCarlo(a,nmax) for i in range(30)]
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E, deltaE = ave_error(X)
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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.]:
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El = e_loc(a, r)
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E += w * El
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norm += w
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E = E / norm
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s2 = 0.
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E = E / norm
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s2 = 0.
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for x in interval:
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r[0] = x
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for y in interval:
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@ -32,5 +32,5 @@ for a in [0.1, 0.2, 0.5, 0.9, 1., 1.5, 2.]:
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w = w * w * delta
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El = e_loc(a, r)
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s2 += w * (El - E)**2
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s2 = s2 / norm
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print(f"a = {a} \t E = {E:10.8f} \t \sigma^2 = {s2:10.8f}")
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s2 = s2 / norm
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print(f"a = {a} \t E = {E:10.8f} \t \sigma^2 = {s2:10.8f}")
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