def test_metropolis(nconfig=1000, ndim=3, nelec=2, nstep=100, tau=0.5):
# This part of the code will test your implementation.
# You can modify the parameters to see how they affect the results.
from slaterwf import ExponentSlaterWF
from hamiltonian import Hamiltonian
wf = ExponentSlaterWF(alpha=1.0)
ham = Hamiltonian(Z=1)
possample = np.random.randn(nelec, ndim, nconfig)
possample, acc = metropolis_sample(possample, wf, tau=tau, nstep=nstep)
# calculate kinetic energy
ke = -0.5 * np.sum(wf.laplacian(possample), axis=0)
# calculate potential energy
vion = ham.pot_en(possample)
# The local energy.
eloc = ke + vion
# report
print("Cycle finished; acceptance = {acc:3.2f}.".format(acc=acc))
for nm, quant, ref in zip(['kinetic', 'Electron-nucleus', 'total'],
[ke, vion, eloc], [1.0, -2.0, -1.0]):
avg = np.mean(quant)
err = np.std(quant) / np.sqrt(nconfig)
print("{name:20s} = {avg:10.6f} +- {err:8.6f}; reference = {ref:5.2f}".
format(name=nm, avg=avg, err=err, ref=ref))
def check_wfs():
newdf=check_singularity(
wf=ExponentSlaterWF(1.0),
ham=Hamiltonian(Z=2)
)
newdf['wf']='slater unopt.'
resdf=newdf
resdf['electron-nucleus']
newdf=check_singularity(
wf=ExponentSlaterWF(2.0),
ham=Hamiltonian(Z=2)
)
newdf['wf']='slater opt.'
resdf=pd.concat([resdf,newdf])
newdf=check_singularity(
wf=MultiplyWF(ExponentSlaterWF(2.0),JastrowWF(0.5)),
ham=Hamiltonian(Z=2)
)
newdf['wf']='slater-jastrow'
resdf=pd.concat([resdf,newdf])
return resdf
def compare_optimal():
wf = ExponentSlaterWF(1.7)
slater_dist = pair_distribution(wf)
wf = MultiplyWF(ExponentSlaterWF(1.9), JastrowWF(0.3))
slaterjastrow_dist = pair_distribution(wf)
print("Slater", slater_dist)
print("Slater-Jastrow", slaterjastrow_dist)
def compare_samealpha():
wf = ExponentSlaterWF(2.0)
slater_dist = pair_distribution(wf)
wf = MultiplyWF(ExponentSlaterWF(2.0), JastrowWF(0.5))
slaterjastrow_dist = pair_distribution(wf)
print("Slater", slater_dist)
print("Slater-Jastrow", slaterjastrow_dist)
eloc = []
acc = []
virial = []
vele = []
venu = []
ham = Hamiltonian(Z=2) # Helium
# Best Slater determinant.
n = 51
ast = 1.5
aen = 2.5
bst = -0.5
ben = 1.5
alphas = np.linspace(ast, aen, n)
betas = np.linspace(bst, ben, n)
for alpha in alphas:
ewf = ExponentSlaterWF(alpha=alpha)
pos = np.random.randn(nelec, ndim, nconfig)
pos, _ = metropolis_sample(pos=pos, wf=ewf, tau=tau, nstep=nstep)
acc.append(_)
ke.append(np.mean(-0.5 * np.sum(ewf.laplacian(pos), axis=0)))
vele.append(np.mean(ham.pot_ee(pos)))
venu.append(np.mean(ham.pot_en(pos)))
potential.append(np.mean(ham.pot(pos)))
eloc.append(ke[-1] + potential[-1])
virial.append(potential[-1] / ke[-1])
fig = plt.figure(1)
ax = fig.add_subplot(111)
ax.plot(alphas, eloc)
x = alphas
popt, pcov = curve_fit(func, x, eloc)
a, b, c = popt
"acceptance", acc_ratio)
df['step'].append(istep)
df['elocal'].append(np.mean(eloc))
df['weight'].append(np.mean(weight))
df['elocalvar'].append(np.std(eloc))
df['weightvar'].append(np.std(weight))
df['eref'].append(eref)
df['tau'].append(tau)
weight.fill(wavg)
return pd.DataFrame(df)
#####################################
if __name__ == '__main__':
from slaterwf import ExponentSlaterWF
from wavefunction import MultiplyWF, JastrowWF
from hamiltonian import Hamiltonian
nconfig = 50000
dfs = []
for tau in [.01, .005, .0025]:
dfs.append(
simple_dmc(MultiplyWF(ExponentSlaterWF(2.0), JastrowWF(0.5)),
Hamiltonian(),
pos=np.random.randn(2, 3, nconfig),
tau=tau,
nstep=10000))
df = pd.concat(dfs)
df.to_csv("dmc.csv", index=False)
import numpy as np
from slaterwf import ExponentSlaterWF
from wavefunction import MultiplyWF, JastrowWF
from metropolis import metropolis_sample
def pair_distribution(wf):
nelec = 2
ndim = 3
nconfig = 1000
nstep = 100
tau = 0.2
sample, acc = metropolis_sample(np.random.randn(nelec, ndim, nconfig),
wf,
tau=tau,
nstep=nstep)
dist = np.mean((sample[0] - sample[1])**2)**0.5
print(dist)
if __name__ == '__main__':
wf = ExponentSlaterWF(1.0)
pair_distribution(wf)
wf = MultiplyWF(ExponentSlaterWF(1.0), JastrowWF(0.5))
pair_distribution(wf)
nstep = 100
tau = 0.2
# All the quantities we will keep track of
df = {}
quantities = ['kinetic', 'electron-nucleus', 'electron-electron']
for i in quantities:
df[i] = []
for i in ['alpha', 'beta', 'acceptance']:
df[i] = []
ham = Hamiltonian(Z=2) # Helium
# Best Slater determinant.
beta = 0.0 # For book keeping.
for alpha in np.linspace(1.5, 2.5, 11):
wf = ExponentSlaterWF(alpha=alpha)
sample, acc = metropolis_sample(np.random.randn(nelec, ndim, nconfig),
wf,
tau=tau,
nstep=nstep)
ke = -0.5 * np.sum(wf.laplacian(sample), axis=0)
vion = ham.pot_en(sample)
vee = ham.pot_ee(sample)
for i in range(nconfig):
for nm, quant in zip(quantities, [ke, vion, vee]):
df[nm].append(quant[i])
df['alpha'].append(alpha)
df['beta'].append(beta)
df['acceptance'].append(acc)
nstep = 100
tau = 0.2
# All the quantities we will keep track of
df = {}
quantities = ['kinetic', 'electron-nucleus', 'electron-electron']
for i in quantities:
df[i] = []
for i in ['alpha', 'beta', 'acceptance']:
df[i] = []
ham = Hamiltonian(Z=2) # Helium
# Best Slater determinant.
beta = 0.0 # For book keeping.
for alpha in np.linspace(1.5, 2.5, 11):
wf = ExponentSlaterWF(alpha=alpha)
sample, acc = metropolis_sample(np.random.randn(nelec, ndim, nconfig),
wf,
tau=tau,
nstep=nstep)
ke = -0.5 * np.sum(wf.laplacian(sample), axis=0)
vion = ham.pot_en(sample)
vee = ham.pot_ee(sample)
for i in range(nconfig):
for nm, quant in zip(quantities, [ke, vion, vee]):
df[nm].append(quant[i])
df['alpha'].append(alpha)
df['beta'].append(beta)
df['acceptance'].append(acc)