def _test_stats_mean_std(hi, ham, ma, n_chains):
sampler = nk.sampler.MetropolisLocal(ma, n_chains=n_chains)
n_samples = 16000
num_samples_per_chain = n_samples // n_chains
# Discard a few samples
sampler.generate_samples(1000)
samples = sampler.generate_samples(num_samples_per_chain)
assert samples.shape == (num_samples_per_chain, n_chains, hi.size)
eloc = np.empty((num_samples_per_chain, n_chains), dtype=np.complex128)
for i in range(num_samples_per_chain):
eloc[i] = local_values(ham, ma, samples[i])
stats = statistics(eloc.T)
# These tests only work for one MPI process
assert nk.stats.MPI.COMM_WORLD.size == 1
assert stats.mean == pytest.approx(np.mean(eloc))
if n_chains > 1:
# variance == average sample variance over chains
assert stats.variance == pytest.approx(np.var(eloc))
# R estimate
B_over_n = stats.error_of_mean ** 2
W = stats.variance
assert stats.R_hat == pytest.approx(np.sqrt(1.0 + B_over_n / W), abs=1e-3)
def _test_stats_mean_std(hi, ham, ma, n_chains):
sampler = nk.sampler.MetropolisLocal(ma, n_chains=n_chains)
n_samples = 16000
num_samples_per_chain = n_samples // n_chains
# Discard a few samples
sampler.generate_samples(1000)
samples = sampler.generate_samples(num_samples_per_chain)
assert samples.shape == (num_samples_per_chain, n_chains, hi.size)
eloc = local_values(ham, ma, samples)
assert eloc.shape == (num_samples_per_chain, n_chains)
stats = statistics(eloc)
# These tests only work for one MPI process
assert nk.MPI.size() == 1
assert stats.mean == pytest.approx(np.mean(eloc))
if n_chains > 1:
# error of mean == stdev of sample mean between chains / sqrt(#chains)
assert stats.error_of_mean == pytest.approx(
eloc.mean(axis=0).std(ddof=0) / np.sqrt(n_chains)
)
# variance == average sample variance over chains
assert stats.variance == pytest.approx(eloc.var(axis=0).mean())
# R estimate
B_over_n = stats.error_of_mean ** 2
W = stats.variance
assert stats.R == pytest.approx(
np.sqrt((n_samples - 1.0) / n_samples + B_over_n / W), abs=1e-3
)
def compute_locals(n_times):
for k in range(n_times):
for i, sample in enumerate(samples):
local_values(ha, ma, sample, out=loc[i])