mirror of
https://github.com/openmc-dev/openmc.git
synced 2026-07-25 04:25:29 -04:00
548 lines
17 KiB
Python
548 lines
17 KiB
Python
from math import pi
|
|
|
|
import numpy as np
|
|
import pytest
|
|
import openmc
|
|
import openmc.stats
|
|
from scipy.integrate import trapezoid
|
|
|
|
|
|
def assert_sample_mean(samples, expected_mean):
|
|
# Calculate sample standard deviation
|
|
std_dev = samples.std() / np.sqrt(samples.size - 1)
|
|
|
|
# Means should agree within 4 sigma 99.993% of the time. Note that this is
|
|
# expected to fail about 1 out of 16,000 times
|
|
assert np.abs(expected_mean - samples.mean()) < 4*std_dev
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_discrete():
|
|
x = [0.0, 1.0, 10.0]
|
|
p = [0.3, 0.2, 0.5]
|
|
d = openmc.stats.Discrete(x, p)
|
|
elem = d.to_xml_element('distribution')
|
|
|
|
d = openmc.stats.Discrete.from_xml_element(elem)
|
|
np.testing.assert_array_equal(d.x, x)
|
|
np.testing.assert_array_equal(d.p, p)
|
|
assert len(d) == len(x)
|
|
|
|
d = openmc.stats.Univariate.from_xml_element(elem)
|
|
assert isinstance(d, openmc.stats.Discrete)
|
|
|
|
# Single point
|
|
d2 = openmc.stats.Discrete(1e6, 1.0)
|
|
assert d2.x == [1e6]
|
|
assert d2.p == [1.0]
|
|
assert len(d2) == 1
|
|
|
|
vals = np.array([1.0, 2.0, 3.0])
|
|
probs = np.array([0.1, 0.7, 0.2])
|
|
|
|
exp_mean = (vals * probs).sum()
|
|
|
|
d3 = openmc.stats.Discrete(vals, probs)
|
|
|
|
# sample discrete distribution and check that the mean of the samples is
|
|
# within 4 std. dev. of the expected mean
|
|
n_samples = 1_000_000
|
|
samples = d3.sample(n_samples)
|
|
assert_sample_mean(samples, exp_mean)
|
|
|
|
|
|
def test_delta_function():
|
|
d = openmc.stats.delta_function(14.1e6)
|
|
assert isinstance(d, openmc.stats.Discrete)
|
|
np.testing.assert_array_equal(d.x, [14.1e6])
|
|
np.testing.assert_array_equal(d.p, [1.0])
|
|
|
|
|
|
def test_merge_discrete():
|
|
x1 = [0.0, 1.0, 10.0]
|
|
p1 = [0.3, 0.2, 0.5]
|
|
d1 = openmc.stats.Discrete(x1, p1)
|
|
|
|
x2 = [0.5, 1.0, 5.0]
|
|
p2 = [0.4, 0.5, 0.1]
|
|
d2 = openmc.stats.Discrete(x2, p2)
|
|
|
|
# Merged distribution should have x values sorted and probabilities
|
|
# appropriately combined. Duplicate x values should appear once.
|
|
merged = openmc.stats.Discrete.merge([d1, d2], [0.6, 0.4])
|
|
assert merged.x == pytest.approx([0.0, 0.5, 1.0, 5.0, 10.0])
|
|
assert merged.p == pytest.approx(
|
|
[0.6*0.3, 0.4*0.4, 0.6*0.2 + 0.4*0.5, 0.4*0.1, 0.6*0.5])
|
|
assert merged.integral() == pytest.approx(1.0)
|
|
|
|
# Probabilities add up but are not normalized
|
|
d1 = openmc.stats.Discrete([3.0], [1.0])
|
|
triple = openmc.stats.Discrete.merge([d1, d1, d1], [1.0, 2.0, 3.0])
|
|
assert triple.x == pytest.approx([3.0])
|
|
assert triple.p == pytest.approx([6.0])
|
|
assert triple.integral() == pytest.approx(6.0)
|
|
|
|
|
|
def test_clip_discrete():
|
|
# Create discrete distribution with two points that are not important, one
|
|
# because the x value is very small, and one because the p value is very
|
|
# small
|
|
d = openmc.stats.Discrete([1e-8, 1.0, 2.0, 1000.0], [3.0, 2.0, 5.0, 1e-12])
|
|
|
|
# Clipping the distribution should result in two points
|
|
d_clip = d.clip(1e-6)
|
|
assert d_clip.x.size == 2
|
|
assert d_clip.p.size == 2
|
|
|
|
# Make sure inplace returns same object
|
|
d_same = d.clip(1e-6, inplace=True)
|
|
assert d_same is d
|
|
|
|
with pytest.raises(ValueError):
|
|
d.clip(-1.)
|
|
|
|
with pytest.raises(ValueError):
|
|
d.clip(5)
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_uniform():
|
|
a, b = 10.0, 20.0
|
|
d = openmc.stats.Uniform(a, b)
|
|
elem = d.to_xml_element('distribution')
|
|
|
|
d = openmc.stats.Uniform.from_xml_element(elem)
|
|
assert d.a == a
|
|
assert d.b == b
|
|
assert len(d) == 2
|
|
|
|
t = d.to_tabular()
|
|
np.testing.assert_array_equal(t.x, [a, b])
|
|
np.testing.assert_array_equal(t.p, [1/(b-a), 1/(b-a)])
|
|
assert t.interpolation == 'histogram'
|
|
|
|
# Sample distribution and check that the mean of the samples is within 4
|
|
# std. dev. of the expected mean
|
|
exp_mean = 0.5 * (a + b)
|
|
n_samples = 1_000_000
|
|
samples = d.sample(n_samples)
|
|
assert_sample_mean(samples, exp_mean)
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_powerlaw():
|
|
a, b, n = 10.0, 100.0, 2.0
|
|
d = openmc.stats.PowerLaw(a, b, n)
|
|
elem = d.to_xml_element('distribution')
|
|
|
|
d = openmc.stats.PowerLaw.from_xml_element(elem)
|
|
assert d.a == a
|
|
assert d.b == b
|
|
assert d.n == n
|
|
assert len(d) == 3
|
|
|
|
# Determine mean of distribution
|
|
exp_mean = (n+1)*(b**(n+2) - a**(n+2))/((n+2)*(b**(n+1) - a**(n+1)))
|
|
|
|
# sample power law distribution and check that the mean of the samples is
|
|
# within 4 std. dev. of the expected mean
|
|
n_samples = 1_000_000
|
|
samples = d.sample(n_samples)
|
|
assert_sample_mean(samples, exp_mean)
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_maxwell():
|
|
theta = 1.2895e6
|
|
d = openmc.stats.Maxwell(theta)
|
|
elem = d.to_xml_element('distribution')
|
|
|
|
d = openmc.stats.Maxwell.from_xml_element(elem)
|
|
assert d.theta == theta
|
|
assert len(d) == 1
|
|
|
|
exp_mean = 3/2 * theta
|
|
|
|
# sample maxwell distribution and check that the mean of the samples is
|
|
# within 4 std. dev. of the expected mean
|
|
n_samples = 1_000_000
|
|
samples = d.sample(n_samples)
|
|
assert_sample_mean(samples, exp_mean)
|
|
|
|
# A second sample starting from a different seed
|
|
samples_2 = d.sample(n_samples)
|
|
assert_sample_mean(samples_2, exp_mean)
|
|
assert samples_2.mean() != samples.mean()
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_watt():
|
|
a, b = 0.965e6, 2.29e-6
|
|
d = openmc.stats.Watt(a, b)
|
|
elem = d.to_xml_element('distribution')
|
|
|
|
d = openmc.stats.Watt.from_xml_element(elem)
|
|
assert d.a == a
|
|
assert d.b == b
|
|
assert len(d) == 2
|
|
|
|
# mean value form adapted from
|
|
# "Prompt-fission-neutron average energy for 238U(n, f ) from
|
|
# threshold to 200 MeV" Ethvignot et. al.
|
|
# https://doi.org/10.1016/j.physletb.2003.09.048
|
|
exp_mean = 3/2 * a + a**2 * b / 4
|
|
|
|
# sample Watt distribution and check that the mean of the samples is within
|
|
# 4 std. dev. of the expected mean
|
|
n_samples = 1_000_000
|
|
samples = d.sample(n_samples)
|
|
assert_sample_mean(samples, exp_mean)
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_tabular():
|
|
# test linear-linear sampling
|
|
x = np.array([0.0, 5.0, 7.0, 10.0])
|
|
p = np.array([10.0, 20.0, 5.0, 6.0])
|
|
d = openmc.stats.Tabular(x, p, 'linear-linear')
|
|
n_samples = 100_000
|
|
samples = d.sample(n_samples)
|
|
assert_sample_mean(samples, d.mean())
|
|
|
|
# test linear-linear normalization
|
|
d.normalize()
|
|
assert d.integral() == pytest.approx(1.0)
|
|
|
|
# test histogram sampling
|
|
d = openmc.stats.Tabular(x, p, interpolation='histogram')
|
|
samples = d.sample(n_samples)
|
|
assert_sample_mean(samples, d.mean())
|
|
|
|
d.normalize()
|
|
assert d.integral() == pytest.approx(1.0)
|
|
|
|
# ensure that passing a set of probabilities shorter than x works
|
|
# for histogram interpolation
|
|
d = openmc.stats.Tabular(x, p[:-1], interpolation='histogram')
|
|
d.cdf()
|
|
d.mean()
|
|
assert_sample_mean(d.sample(n_samples), d.mean())
|
|
|
|
# passing a shorter probability set should raise an error for linear-linear
|
|
with pytest.raises(ValueError):
|
|
d = openmc.stats.Tabular(x, p[:-1], interpolation='linear-linear')
|
|
d.cdf()
|
|
|
|
# Use probabilities of correct length for linear-linear interpolation and
|
|
# call the CDF method
|
|
d = openmc.stats.Tabular(x, p, interpolation='linear-linear')
|
|
d.cdf()
|
|
|
|
|
|
def test_tabular_from_xml():
|
|
x = np.array([0.0, 5.0, 7.0, 10.0])
|
|
p = np.array([10.0, 20.0, 5.0, 6.0])
|
|
d = openmc.stats.Tabular(x, p, 'linear-linear')
|
|
elem = d.to_xml_element('distribution')
|
|
|
|
d = openmc.stats.Tabular.from_xml_element(elem)
|
|
assert all(d.x == x)
|
|
assert all(d.p == p)
|
|
assert d.interpolation == 'linear-linear'
|
|
assert len(d) == len(x)
|
|
|
|
# Make sure XML roundtrip works with len(x) == len(p) + 1
|
|
x = np.array([0.0, 5.0, 7.0, 10.0])
|
|
p = np.array([10.0, 20.0, 5.0])
|
|
d = openmc.stats.Tabular(x, p, 'histogram')
|
|
elem = d.to_xml_element('distribution')
|
|
d = openmc.stats.Tabular.from_xml_element(elem)
|
|
assert all(d.x == x)
|
|
assert all(d.p == p)
|
|
|
|
|
|
def test_legendre():
|
|
# Pu239 elastic scattering at 100 keV
|
|
coeffs = [1.000e+0, 1.536e-1, 1.772e-2, 5.945e-4, 3.497e-5, 1.881e-5]
|
|
d = openmc.stats.Legendre(coeffs)
|
|
assert d.coefficients == pytest.approx(coeffs)
|
|
assert len(d) == len(coeffs)
|
|
|
|
# Integrating distribution should yield one
|
|
mu = np.linspace(-1., 1., 1000)
|
|
assert trapezoid(d(mu), mu) == pytest.approx(1.0, rel=1e-4)
|
|
|
|
with pytest.raises(NotImplementedError):
|
|
d.to_xml_element('distribution')
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_mixture():
|
|
d1 = openmc.stats.Uniform(0, 5)
|
|
d2 = openmc.stats.Uniform(3, 7)
|
|
p = [0.5, 0.5]
|
|
mix = openmc.stats.Mixture(p, [d1, d2])
|
|
np.testing.assert_allclose(mix.probability, p)
|
|
assert mix.distribution == [d1, d2]
|
|
assert len(mix) == 4
|
|
|
|
# Sample and make sure sample mean is close to expected mean
|
|
n_samples = 1_000_000
|
|
samples = mix.sample(n_samples)
|
|
assert_sample_mean(samples, (2.5 + 5.0)/2)
|
|
|
|
elem = mix.to_xml_element('distribution')
|
|
|
|
d = openmc.stats.Mixture.from_xml_element(elem)
|
|
np.testing.assert_allclose(d.probability, p)
|
|
assert d.distribution == [d1, d2]
|
|
assert len(d) == 4
|
|
|
|
|
|
def test_mixture_clip():
|
|
# Create mixture distribution containing a discrete distribution with two
|
|
# points that are not important, one because the x value is very small, and
|
|
# one because the p value is very small
|
|
d1 = openmc.stats.Discrete([1e-8, 1.0, 2.0, 1000.0], [3.0, 2.0, 5.0, 1e-12])
|
|
d2 = openmc.stats.Uniform(0, 5)
|
|
mix = openmc.stats.Mixture([0.5, 0.5], [d1, d2])
|
|
|
|
# Clipping should reduce the contained discrete distribution to 2 points
|
|
mix_clip = mix.clip(1e-6)
|
|
assert mix_clip.distribution[0].x.size == 2
|
|
assert mix_clip.distribution[0].p.size == 2
|
|
|
|
# Make sure inplace returns same object
|
|
mix_same = mix.clip(1e-6, inplace=True)
|
|
assert mix_same is mix
|
|
|
|
# Make sure clip removes low probability distributions
|
|
d_small = openmc.stats.Uniform(0., 1.)
|
|
d_large = openmc.stats.Uniform(2., 5.)
|
|
mix = openmc.stats.Mixture([1e-10, 1.0], [d_small, d_large])
|
|
mix_clip = mix.clip(1e-3)
|
|
assert mix_clip.distribution == [d_large]
|
|
|
|
# Make sure warning is raised if tolerance is exceeded
|
|
d1 = openmc.stats.Discrete([1.0, 1.001], [1.0, 0.7e-6])
|
|
d2 = openmc.stats.Tabular([0.0, 1.0], [0.7e-6], interpolation='histogram')
|
|
mix = openmc.stats.Mixture([1.0, 1.0], [d1, d2])
|
|
with pytest.warns(UserWarning):
|
|
mix_clip = mix.clip(1e-6)
|
|
|
|
|
|
def test_polar_azimuthal():
|
|
# default polar-azimuthal should be uniform in mu and phi
|
|
d = openmc.stats.PolarAzimuthal()
|
|
assert isinstance(d.mu, openmc.stats.Uniform)
|
|
assert d.mu.a == -1.
|
|
assert d.mu.b == 1.
|
|
assert isinstance(d.phi, openmc.stats.Uniform)
|
|
assert d.phi.a == 0.
|
|
assert d.phi.b == 2*pi
|
|
|
|
mu = openmc.stats.Discrete(1., 1.)
|
|
phi = openmc.stats.Discrete(0., 1.)
|
|
d = openmc.stats.PolarAzimuthal(mu, phi)
|
|
assert d.mu == mu
|
|
assert d.phi == phi
|
|
|
|
elem = d.to_xml_element()
|
|
assert elem.tag == 'angle'
|
|
assert elem.attrib['type'] == 'mu-phi'
|
|
assert elem.find('mu') is not None
|
|
assert elem.find('phi') is not None
|
|
|
|
d = openmc.stats.PolarAzimuthal.from_xml_element(elem)
|
|
assert d.mu.x == [1.]
|
|
assert d.mu.p == [1.]
|
|
assert d.phi.x == [0.]
|
|
assert d.phi.p == [1.]
|
|
|
|
d = openmc.stats.UnitSphere.from_xml_element(elem)
|
|
assert isinstance(d, openmc.stats.PolarAzimuthal)
|
|
|
|
|
|
def test_isotropic():
|
|
d = openmc.stats.Isotropic()
|
|
elem = d.to_xml_element()
|
|
assert elem.tag == 'angle'
|
|
assert elem.attrib['type'] == 'isotropic'
|
|
|
|
d = openmc.stats.Isotropic.from_xml_element(elem)
|
|
assert isinstance(d, openmc.stats.Isotropic)
|
|
|
|
|
|
def test_monodirectional():
|
|
d = openmc.stats.Monodirectional((1., 0., 0.))
|
|
elem = d.to_xml_element()
|
|
assert elem.tag == 'angle'
|
|
assert elem.attrib['type'] == 'monodirectional'
|
|
|
|
d = openmc.stats.Monodirectional.from_xml_element(elem)
|
|
assert d.reference_uvw == pytest.approx((1., 0., 0.))
|
|
|
|
|
|
def test_cartesian():
|
|
x = openmc.stats.Uniform(-10., 10.)
|
|
y = openmc.stats.Uniform(-10., 10.)
|
|
z = openmc.stats.Uniform(0., 20.)
|
|
d = openmc.stats.CartesianIndependent(x, y, z)
|
|
|
|
elem = d.to_xml_element()
|
|
assert elem.tag == 'space'
|
|
assert elem.attrib['type'] == 'cartesian'
|
|
assert elem.find('x') is not None
|
|
assert elem.find('y') is not None
|
|
|
|
d = openmc.stats.CartesianIndependent.from_xml_element(elem)
|
|
assert d.x == x
|
|
assert d.y == y
|
|
assert d.z == z
|
|
|
|
d = openmc.stats.Spatial.from_xml_element(elem)
|
|
assert isinstance(d, openmc.stats.CartesianIndependent)
|
|
|
|
|
|
def test_box():
|
|
lower_left = (-10., -10., -10.)
|
|
upper_right = (10., 10., 10.)
|
|
d = openmc.stats.Box(lower_left, upper_right)
|
|
|
|
elem = d.to_xml_element()
|
|
assert elem.tag == 'space'
|
|
assert elem.attrib['type'] == 'box'
|
|
assert elem.find('parameters') is not None
|
|
|
|
d = openmc.stats.Box.from_xml_element(elem)
|
|
assert d.lower_left == pytest.approx(lower_left)
|
|
assert d.upper_right == pytest.approx(upper_right)
|
|
|
|
|
|
def test_point():
|
|
p = (-4., 2., 10.)
|
|
d = openmc.stats.Point(p)
|
|
|
|
elem = d.to_xml_element()
|
|
assert elem.tag == 'space'
|
|
assert elem.attrib['type'] == 'point'
|
|
assert elem.find('parameters') is not None
|
|
|
|
d = openmc.stats.Point.from_xml_element(elem)
|
|
assert d.xyz == pytest.approx(p)
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_normal():
|
|
mean = 10.0
|
|
std_dev = 2.0
|
|
d = openmc.stats.Normal(mean,std_dev)
|
|
|
|
elem = d.to_xml_element('distribution')
|
|
assert elem.attrib['type'] == 'normal'
|
|
|
|
d = openmc.stats.Normal.from_xml_element(elem)
|
|
assert d.mean_value == pytest.approx(mean)
|
|
assert d.std_dev == pytest.approx(std_dev)
|
|
assert len(d) == 2
|
|
|
|
# sample normal distribution
|
|
n_samples = 100_000
|
|
samples = d.sample(n_samples)
|
|
assert_sample_mean(samples, mean)
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_muir():
|
|
mean = 10.0
|
|
mass = 5.0
|
|
temp = 20000.
|
|
d = openmc.stats.muir(mean, mass, temp)
|
|
assert isinstance(d, openmc.stats.Normal)
|
|
|
|
elem = d.to_xml_element('energy')
|
|
assert elem.attrib['type'] == 'normal'
|
|
|
|
d = openmc.stats.Univariate.from_xml_element(elem)
|
|
assert isinstance(d, openmc.stats.Normal)
|
|
|
|
# sample muir distribution
|
|
n_samples = 100_000
|
|
samples = d.sample(n_samples)
|
|
assert_sample_mean(samples, mean)
|
|
|
|
|
|
@pytest.mark.flaky(reruns=1)
|
|
def test_combine_distributions():
|
|
# Combine two discrete (same data as in test_merge_discrete)
|
|
x1 = [0.0, 1.0, 10.0]
|
|
p1 = [0.3, 0.2, 0.5]
|
|
d1 = openmc.stats.Discrete(x1, p1)
|
|
x2 = [0.5, 1.0, 5.0]
|
|
p2 = [0.4, 0.5, 0.1]
|
|
d2 = openmc.stats.Discrete(x2, p2)
|
|
|
|
# Merged distribution should have x values sorted and probabilities
|
|
# appropriately combined. Duplicate x values should appear once.
|
|
merged = openmc.stats.combine_distributions([d1, d2], [0.6, 0.4])
|
|
assert isinstance(merged, openmc.stats.Discrete)
|
|
assert merged.x == pytest.approx([0.0, 0.5, 1.0, 5.0, 10.0])
|
|
assert merged.p == pytest.approx(
|
|
[0.6*0.3, 0.4*0.4, 0.6*0.2 + 0.4*0.5, 0.4*0.1, 0.6*0.5])
|
|
|
|
# Probabilities add up but are not normalized
|
|
d1 = openmc.stats.Discrete([3.0], [1.0])
|
|
triple = openmc.stats.combine_distributions([d1, d1, d1], [1.0, 2.0, 3.0])
|
|
assert triple.x == pytest.approx([3.0])
|
|
assert triple.p == pytest.approx([6.0])
|
|
|
|
# Combine discrete and tabular
|
|
t1 = openmc.stats.Tabular(x2, p2)
|
|
mixed = openmc.stats.combine_distributions([d1, t1], [0.5, 0.5])
|
|
assert isinstance(mixed, openmc.stats.Mixture)
|
|
assert len(mixed.distribution) == 2
|
|
assert len(mixed.probability) == 2
|
|
|
|
# Combine 1 discrete and 2 tabular -- the tabular distributions should
|
|
# combine to produce a uniform distribution with mean 0.5. The combined
|
|
# distribution should have a mean of 0.25.
|
|
t1 = openmc.stats.Tabular([0., 1.], [2.0, 0.0])
|
|
t2 = openmc.stats.Tabular([0., 1.], [0.0, 2.0])
|
|
d1 = openmc.stats.Discrete([0.0], [1.0])
|
|
combined = openmc.stats.combine_distributions([t1, t2, d1], [0.25, 0.25, 0.5])
|
|
assert combined.integral() == pytest.approx(1.0)
|
|
|
|
# Sample the combined distribution and make sure the sample mean is within
|
|
# uncertainty of the expected value
|
|
samples = combined.sample(10_000)
|
|
assert_sample_mean(samples, 0.25)
|
|
|
|
def test_reference_vwu_projection():
|
|
"""When a non-orthogonal vector is provided, the setter should project out
|
|
any component along reference_uvw so the stored vector is orthogonal.
|
|
"""
|
|
pa = openmc.stats.PolarAzimuthal() # default reference_uvw == (0, 0, 1)
|
|
|
|
# Provide a vector that is not orthogonal to (0,0,1)
|
|
pa.reference_vwu = (2.0, 0.5, 0.3)
|
|
|
|
reference_v = np.asarray(pa.reference_vwu)
|
|
reference_u = np.asarray(pa.reference_uvw)
|
|
|
|
# reference_v should be orthogonal to reference_u
|
|
assert abs(np.dot(reference_v, reference_u)) < 1e-6
|
|
|
|
|
|
def test_reference_vwu_normalization():
|
|
"""When a non-normalized vector is provided, the setter should normalize
|
|
the projected vector to unit length.
|
|
"""
|
|
pa = openmc.stats.PolarAzimuthal() # default reference_uvw == (0, 0, 1)
|
|
|
|
# Provide a vector that is neither orthogonal to (0,0,1) nor unit-length
|
|
pa.reference_vwu = (2.0, 0.5, 0.3)
|
|
|
|
reference_v = np.asarray(pa.reference_vwu)
|
|
|
|
# reference_v should be unit length
|
|
assert np.isclose(np.linalg.norm(reference_v), 1.0, atol=1e-12)
|