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)
def test_dmc(
dmc_method,
trial_wf=JastrowWF(100., Z=2.0),
nconf=10000, # number of walkers
proj_time=5., # projection time in a.u.
tau_list=[0.16, 0.08, 0.04]):
# hard-code He
nelec = 2
ndim = 3
Zcharge = 2
# initialize hamiltonian
he_ham = Hamiltonian(Z=Zcharge)
# use VMC to start sample configurations from trial_wf
pos0 = np.random.randn(nelec, ndim, nconf)
pos_vmc, acc_vmc = metropolis_sample(pos0, trial_wf, tau=0.5, nstep=100)
# run DMC to project the VMC wavefunction to ground state
data = []
pos_last = pos_vmc.copy()
weights_last = np.ones(nconf)
for tau in tau_list:
nstep = int(round(proj_time / tau))
half = int(round(nstep / 2)) # assume equilibration at half time
pos_dmc, weights_dmc, acc_dmc, traces = dmc_method(
pos_last,
trial_wf,
he_ham,
weights=weights_last,
weight_desire=nconf,
tau=tau,
nstep=nstep)
print("tau={tau:6.3f}: {acc:d}% {emean:10.6f} +- {err:10.6f}".format(
tau=tau,
acc=int(round(acc_dmc * 100)),
emean=np.mean(traces[half:, 0]),
err=error(traces[half:, 0])))
data.append(traces)
# restart with current walkers
weights_last = weights_dmc
pos_last = pos_dmc
return np.concatenate(data, axis=0)
vion = []
vele = []
potential = []
eloc = []
acc = []
virial = []
vele = []
venu = []
alph = []
bet = []
# Best Slater-Jastrow.
for alpha in alphas:
for beta in betas:
alph.append(alpha)
bet.append(beta)
wf = MultiplyWF(ExponentSlaterWF(alpha), JastrowWF(beta))
pos = np.random.randn(nelec, ndim, nconfig)
pos, _ = metropolis_sample(pos=pos, wf=wf, tau=tau, nstep=nstep)
acc.append(_)
ke.append(np.mean(-0.5 * np.sum(wf.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])
df = pd.DataFrame.from_dict({
'kinetic': ke,
'electron-electron': vele,
'electron-nucleus': venu,
'potential': potential,
"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)
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)
# Best Slater-Jastrow.
for alpha in np.linspace(1.5, 2.5, 11):
for beta in np.linspace(-0.5, 1.5, 11):
wf = MultiplyWF(ExponentSlaterWF(alpha=alpha),
JastrowWF(a_ee=beta))
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)