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425 lines
13 KiB
Python
425 lines
13 KiB
Python
from math import pi
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import numpy as np
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import pytest
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import openmc
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import openmc.stats
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def assert_sample_mean(samples, expected_mean):
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# Calculate sample standard deviation
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std_dev = samples.std() / np.sqrt(samples.size - 1)
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# Means should agree within 4 sigma 99.993% of the time. Note that this is
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# expected to fail about 1 out of 16,000 times
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assert np.abs(expected_mean - samples.mean()) < 4*std_dev
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def test_discrete():
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x = [0.0, 1.0, 10.0]
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p = [0.3, 0.2, 0.5]
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d = openmc.stats.Discrete(x, p)
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elem = d.to_xml_element('distribution')
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d = openmc.stats.Discrete.from_xml_element(elem)
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np.testing.assert_array_equal(d.x, x)
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np.testing.assert_array_equal(d.p, p)
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assert len(d) == len(x)
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d = openmc.stats.Univariate.from_xml_element(elem)
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assert isinstance(d, openmc.stats.Discrete)
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# Single point
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d2 = openmc.stats.Discrete(1e6, 1.0)
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assert d2.x == [1e6]
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assert d2.p == [1.0]
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assert len(d2) == 1
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vals = np.array([1.0, 2.0, 3.0])
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probs = np.array([0.1, 0.7, 0.2])
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exp_mean = (vals * probs).sum()
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d3 = openmc.stats.Discrete(vals, probs)
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# sample discrete distribution and check that the mean of the samples is
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# within 4 std. dev. of the expected mean
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n_samples = 1_000_000
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samples = d3.sample(n_samples)
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assert_sample_mean(samples, exp_mean)
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def test_merge_discrete():
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x1 = [0.0, 1.0, 10.0]
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p1 = [0.3, 0.2, 0.5]
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d1 = openmc.stats.Discrete(x1, p1)
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x2 = [0.5, 1.0, 5.0]
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p2 = [0.4, 0.5, 0.1]
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d2 = openmc.stats.Discrete(x2, p2)
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# Merged distribution should have x values sorted and probabilities
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# appropriately combined. Duplicate x values should appear once.
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merged = openmc.stats.Discrete.merge([d1, d2], [0.6, 0.4])
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assert merged.x == pytest.approx([0.0, 0.5, 1.0, 5.0, 10.0])
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assert merged.p == pytest.approx(
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[0.6*0.3, 0.4*0.4, 0.6*0.2 + 0.4*0.5, 0.4*0.1, 0.6*0.5])
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assert merged.integral() == pytest.approx(1.0)
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# Probabilities add up but are not normalized
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d1 = openmc.stats.Discrete([3.0], [1.0])
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triple = openmc.stats.Discrete.merge([d1, d1, d1], [1.0, 2.0, 3.0])
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assert triple.x == pytest.approx([3.0])
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assert triple.p == pytest.approx([6.0])
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assert triple.integral() == pytest.approx(6.0)
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def test_uniform():
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a, b = 10.0, 20.0
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d = openmc.stats.Uniform(a, b)
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elem = d.to_xml_element('distribution')
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d = openmc.stats.Uniform.from_xml_element(elem)
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assert d.a == a
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assert d.b == b
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assert len(d) == 2
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t = d.to_tabular()
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np.testing.assert_array_equal(t.x, [a, b])
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np.testing.assert_array_equal(t.p, [1/(b-a), 1/(b-a)])
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assert t.interpolation == 'histogram'
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# Sample distribution and check that the mean of the samples is within 4
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# std. dev. of the expected mean
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exp_mean = 0.5 * (a + b)
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n_samples = 1_000_000
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samples = d.sample(n_samples)
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assert_sample_mean(samples, exp_mean)
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def test_powerlaw():
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a, b, n = 10.0, 100.0, 2.0
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d = openmc.stats.PowerLaw(a, b, n)
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elem = d.to_xml_element('distribution')
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d = openmc.stats.PowerLaw.from_xml_element(elem)
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assert d.a == a
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assert d.b == b
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assert d.n == n
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assert len(d) == 3
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# Determine mean of distribution
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exp_mean = (n+1)*(b**(n+2) - a**(n+2))/((n+2)*(b**(n+1) - a**(n+1)))
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# sample power law distribution and check that the mean of the samples is
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# within 4 std. dev. of the expected mean
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n_samples = 1_000_000
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samples = d.sample(n_samples)
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assert_sample_mean(samples, exp_mean)
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def test_maxwell():
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theta = 1.2895e6
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d = openmc.stats.Maxwell(theta)
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elem = d.to_xml_element('distribution')
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d = openmc.stats.Maxwell.from_xml_element(elem)
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assert d.theta == theta
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assert len(d) == 1
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exp_mean = 3/2 * theta
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# sample maxwell distribution and check that the mean of the samples is
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# within 4 std. dev. of the expected mean
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n_samples = 1_000_000
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samples = d.sample(n_samples)
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assert_sample_mean(samples, exp_mean)
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# A second sample starting from a different seed
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samples_2 = d.sample(n_samples)
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assert_sample_mean(samples_2, exp_mean)
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assert samples_2.mean() != samples.mean()
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def test_watt():
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a, b = 0.965e6, 2.29e-6
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d = openmc.stats.Watt(a, b)
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elem = d.to_xml_element('distribution')
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d = openmc.stats.Watt.from_xml_element(elem)
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assert d.a == a
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assert d.b == b
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assert len(d) == 2
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# mean value form adapted from
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# "Prompt-fission-neutron average energy for 238U(n, f ) from
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# threshold to 200 MeV" Ethvignot et. al.
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# https://doi.org/10.1016/j.physletb.2003.09.048
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exp_mean = 3/2 * a + a**2 * b / 4
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# sample Watt distribution and check that the mean of the samples is within
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# 4 std. dev. of the expected mean
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n_samples = 1_000_000
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samples = d.sample(n_samples)
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assert_sample_mean(samples, exp_mean)
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def test_tabular():
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x = np.array([0.0, 5.0, 7.0])
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p = np.array([10.0, 20.0, 5.0])
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d = openmc.stats.Tabular(x, p, 'linear-linear')
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elem = d.to_xml_element('distribution')
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d = openmc.stats.Tabular.from_xml_element(elem)
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assert all(d.x == x)
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assert all(d.p == p)
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assert d.interpolation == 'linear-linear'
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assert len(d) == len(x)
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# test linear-linear sampling
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d = openmc.stats.Tabular(x, p)
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n_samples = 100_000
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samples = d.sample(n_samples)
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assert_sample_mean(samples, d.mean())
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# test linear-linear normalization
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d.normalize()
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assert d.integral() == pytest.approx(1.0)
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# test histogram sampling
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d = openmc.stats.Tabular(x, p, interpolation='histogram')
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samples = d.sample(n_samples)
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assert_sample_mean(samples, d.mean())
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d.normalize()
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assert d.integral() == pytest.approx(1.0)
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def test_legendre():
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# Pu239 elastic scattering at 100 keV
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coeffs = [1.000e+0, 1.536e-1, 1.772e-2, 5.945e-4, 3.497e-5, 1.881e-5]
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d = openmc.stats.Legendre(coeffs)
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assert d.coefficients == pytest.approx(coeffs)
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assert len(d) == len(coeffs)
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# Integrating distribution should yield one
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mu = np.linspace(-1., 1., 1000)
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assert np.trapz(d(mu), mu) == pytest.approx(1.0, rel=1e-4)
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with pytest.raises(NotImplementedError):
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d.to_xml_element('distribution')
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def test_mixture():
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d1 = openmc.stats.Uniform(0, 5)
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d2 = openmc.stats.Uniform(3, 7)
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p = [0.5, 0.5]
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mix = openmc.stats.Mixture(p, [d1, d2])
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assert mix.probability == p
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assert mix.distribution == [d1, d2]
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assert len(mix) == 4
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# Sample and make sure sample mean is close to expected mean
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n_samples = 1_000_000
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samples = mix.sample(n_samples)
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assert_sample_mean(samples, (2.5 + 5.0)/2)
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elem = mix.to_xml_element('distribution')
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d = openmc.stats.Mixture.from_xml_element(elem)
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assert d.probability == p
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assert d.distribution == [d1, d2]
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assert len(d) == 4
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def test_polar_azimuthal():
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# default polar-azimuthal should be uniform in mu and phi
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d = openmc.stats.PolarAzimuthal()
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assert isinstance(d.mu, openmc.stats.Uniform)
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assert d.mu.a == -1.
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assert d.mu.b == 1.
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assert isinstance(d.phi, openmc.stats.Uniform)
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assert d.phi.a == 0.
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assert d.phi.b == 2*pi
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mu = openmc.stats.Discrete(1., 1.)
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phi = openmc.stats.Discrete(0., 1.)
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d = openmc.stats.PolarAzimuthal(mu, phi)
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assert d.mu == mu
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assert d.phi == phi
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elem = d.to_xml_element()
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assert elem.tag == 'angle'
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assert elem.attrib['type'] == 'mu-phi'
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assert elem.find('mu') is not None
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assert elem.find('phi') is not None
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d = openmc.stats.PolarAzimuthal.from_xml_element(elem)
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assert d.mu.x == [1.]
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assert d.mu.p == [1.]
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assert d.phi.x == [0.]
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assert d.phi.p == [1.]
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d = openmc.stats.UnitSphere.from_xml_element(elem)
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assert isinstance(d, openmc.stats.PolarAzimuthal)
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def test_isotropic():
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d = openmc.stats.Isotropic()
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elem = d.to_xml_element()
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assert elem.tag == 'angle'
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assert elem.attrib['type'] == 'isotropic'
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d = openmc.stats.Isotropic.from_xml_element(elem)
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assert isinstance(d, openmc.stats.Isotropic)
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def test_monodirectional():
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d = openmc.stats.Monodirectional((1., 0., 0.))
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elem = d.to_xml_element()
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assert elem.tag == 'angle'
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assert elem.attrib['type'] == 'monodirectional'
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d = openmc.stats.Monodirectional.from_xml_element(elem)
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assert d.reference_uvw == pytest.approx((1., 0., 0.))
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def test_cartesian():
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x = openmc.stats.Uniform(-10., 10.)
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y = openmc.stats.Uniform(-10., 10.)
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z = openmc.stats.Uniform(0., 20.)
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d = openmc.stats.CartesianIndependent(x, y, z)
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elem = d.to_xml_element()
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assert elem.tag == 'space'
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assert elem.attrib['type'] == 'cartesian'
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assert elem.find('x') is not None
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assert elem.find('y') is not None
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d = openmc.stats.CartesianIndependent.from_xml_element(elem)
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assert d.x == x
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assert d.y == y
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assert d.z == z
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d = openmc.stats.Spatial.from_xml_element(elem)
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assert isinstance(d, openmc.stats.CartesianIndependent)
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def test_box():
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lower_left = (-10., -10., -10.)
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upper_right = (10., 10., 10.)
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d = openmc.stats.Box(lower_left, upper_right)
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elem = d.to_xml_element()
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assert elem.tag == 'space'
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assert elem.attrib['type'] == 'box'
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assert elem.find('parameters') is not None
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d = openmc.stats.Box.from_xml_element(elem)
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assert d.lower_left == pytest.approx(lower_left)
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assert d.upper_right == pytest.approx(upper_right)
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assert not d.only_fissionable
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# only fissionable parameter
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d2 = openmc.stats.Box(lower_left, upper_right, True)
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assert d2.only_fissionable
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elem = d2.to_xml_element()
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assert elem.attrib['type'] == 'fission'
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d = openmc.stats.Spatial.from_xml_element(elem)
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assert isinstance(d, openmc.stats.Box)
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def test_point():
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p = (-4., 2., 10.)
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d = openmc.stats.Point(p)
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elem = d.to_xml_element()
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assert elem.tag == 'space'
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assert elem.attrib['type'] == 'point'
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assert elem.find('parameters') is not None
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d = openmc.stats.Point.from_xml_element(elem)
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assert d.xyz == pytest.approx(p)
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def test_normal():
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mean = 10.0
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std_dev = 2.0
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d = openmc.stats.Normal(mean,std_dev)
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elem = d.to_xml_element('distribution')
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assert elem.attrib['type'] == 'normal'
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d = openmc.stats.Normal.from_xml_element(elem)
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assert d.mean_value == pytest.approx(mean)
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assert d.std_dev == pytest.approx(std_dev)
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assert len(d) == 2
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# sample normal distribution
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n_samples = 100_000
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samples = d.sample(n_samples)
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assert_sample_mean(samples, mean)
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def test_muir():
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mean = 10.0
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mass = 5.0
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temp = 20000.
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d = openmc.stats.muir(mean, mass, temp)
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assert isinstance(d, openmc.stats.Normal)
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elem = d.to_xml_element('energy')
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assert elem.attrib['type'] == 'normal'
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d = openmc.stats.Univariate.from_xml_element(elem)
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assert isinstance(d, openmc.stats.Normal)
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# sample muir distribution
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n_samples = 100_000
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samples = d.sample(n_samples)
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assert_sample_mean(samples, mean)
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def test_combine_distributions():
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# Combine two discrete (same data as in test_merge_discrete)
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x1 = [0.0, 1.0, 10.0]
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p1 = [0.3, 0.2, 0.5]
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d1 = openmc.stats.Discrete(x1, p1)
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x2 = [0.5, 1.0, 5.0]
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p2 = [0.4, 0.5, 0.1]
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d2 = openmc.stats.Discrete(x2, p2)
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# Merged distribution should have x values sorted and probabilities
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# appropriately combined. Duplicate x values should appear once.
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merged = openmc.stats.combine_distributions([d1, d2], [0.6, 0.4])
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assert isinstance(merged, openmc.stats.Discrete)
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assert merged.x == pytest.approx([0.0, 0.5, 1.0, 5.0, 10.0])
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assert merged.p == pytest.approx(
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[0.6*0.3, 0.4*0.4, 0.6*0.2 + 0.4*0.5, 0.4*0.1, 0.6*0.5])
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# Probabilities add up but are not normalized
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d1 = openmc.stats.Discrete([3.0], [1.0])
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triple = openmc.stats.combine_distributions([d1, d1, d1], [1.0, 2.0, 3.0])
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assert triple.x == pytest.approx([3.0])
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assert triple.p == pytest.approx([6.0])
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# Combine discrete and tabular
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t1 = openmc.stats.Tabular(x2, p2)
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mixed = openmc.stats.combine_distributions([d1, t1], [0.5, 0.5])
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assert isinstance(mixed, openmc.stats.Mixture)
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assert len(mixed.distribution) == 2
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assert len(mixed.probability) == 2
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# Combine 1 discrete and 2 tabular -- the tabular distributions should
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# combine to produce a uniform distribution with mean 0.5. The combined
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# distribution should have a mean of 0.25.
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t1 = openmc.stats.Tabular([0., 1.], [2.0, 0.0])
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t2 = openmc.stats.Tabular([0., 1.], [0.0, 2.0])
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d1 = openmc.stats.Discrete([0.0], [1.0])
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combined = openmc.stats.combine_distributions([t1, t2, d1], [0.25, 0.25, 0.5])
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assert combined.integral() == pytest.approx(1.0)
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# Sample the combined distribution and make sure the sample mean is within
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# uncertainty of the expected value
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samples = combined.sample(10_000)
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assert_sample_mean(samples, 0.25)
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