def test_decimal_format():
from netket.stats import Stats
assert str(Stats(1.0, 1e-3)) == "1.0000 ± 0.0010 [σ²=nan]"
assert str(Stats(1.0, 1e-6)) == "1.0000000 ± 0.0000010 [σ²=nan]"
assert str(Stats(1.0, 1e-7)) == "1.000e+00 ± 1.000e-07 [σ²=nan]"
assert str(Stats(float("nan"), float("inf"))) == "nan ± inf [σ²=nan]"
assert str(Stats(1.0, float("nan"))) == "1.000e+00 ± nan [σ²=nan]"
assert str(Stats(1.0, float("inf"))) == "1.000e+00 ± inf [σ²=nan]"
assert str(Stats(float("inf"), 0.0)) == "inf ± 0.000e+00 [σ²=nan]"
assert str(Stats(1.0, 0.0)) == "1.000e+00 ± 0.000e+00 [σ²=nan]"
assert str(Stats(1.0, 0.12, 0.5)) == "1.00 ± 0.12 [σ²=0.50]"
assert str(Stats(1.0, 0.12, 0.5, R_hat=1.01)) == "1.00 ± 0.12 [σ²=0.50, R̂=1.0100]"
def expect(vstate: ExactState, Ô: DiscreteOperator) -> Stats: # noqa: F811
_check_hilbert(vstate, Ô)
O = sparsify(Ô)
Ψ = vstate.to_array()
# TODO: This performs the full computation on all MPI ranks.
# It would be great if we could split the computation among ranks.
OΨ = O @ Ψ
expval_O = (Ψ.conj() * OΨ).sum()
variance = jnp.sum(jnp.abs(OΨ - expval_O * Ψ) ** 2)
return Stats(mean=expval_O, error_of_mean=0.0, variance=variance)