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))
# 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
x = np.linspace(ast, aen, n * 10)
y = func(x, a, b, c)
minidx = np.argmin(y)
ax.plot(x, y)
ax.axvline(x=x[minidx], color='k')
ax.axhline(y=y[minidx], color='k')
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)
# Best Slater-Jastrow.
alpha = 2.0
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,
