diff --git a/docs/source/pythonapi/data.rst b/docs/source/pythonapi/data.rst index c74769be6..454409f1f 100644 --- a/docs/source/pythonapi/data.rst +++ b/docs/source/pythonapi/data.rst @@ -61,6 +61,7 @@ Core Functions atomic_mass atomic_weight + combine_distributions decay_constant dose_coefficients gnd_name diff --git a/openmc/data/decay.py b/openmc/data/decay.py index 51a594bc8..2c2505bf5 100644 --- a/openmc/data/decay.py +++ b/openmc/data/decay.py @@ -9,7 +9,9 @@ from uncertainties import ufloat, UFloat import openmc.checkvalue as cv from openmc.mixin import EqualityMixin +from openmc.stats import Discrete, Tabular, combine_distributions from .data import ATOMIC_SYMBOL, ATOMIC_NUMBER +from .function import INTERPOLATION_SCHEME from .endf import Evaluation, get_head_record, get_list_record, get_tab1_record @@ -314,6 +316,12 @@ class Decay(EqualityMixin): 'excited_state', 'mass', 'stable', 'spin', and 'parity'. spectra : dict Resulting radiation spectra for each radiation type. + sources : dict + Radioactive decay source distributions represented as a dictionary + mapping particle types (e.g., 'photon') to instances of + :class:`openmc.stats.Univariate`. + + .. versionadded:: 0.13.1 """ def __init__(self, ev_or_filename): @@ -329,6 +337,7 @@ class Decay(EqualityMixin): self.modes = [] self.spectra = {} self.average_energies = {} + self._sources = None # Get head record items = get_head_record(file_obj) @@ -495,3 +504,69 @@ class Decay(EqualityMixin): """ return cls(ev_or_filename) + + @property + def sources(self): + """Radioactive decay source distributions""" + # If property has been computed already, return it + # TODO: Replace with functools.cached_property when support is Python 3.9+ + if self._sources is not None: + return self._sources + + sources = {} + name = self.nuclide['name'] + decay_constant = self.decay_constant.n + for particle, spectra in self.spectra.items(): + # Set particle type based on 'particle' above + particle_type = { + 'gamma': 'photon', + 'beta-': 'electron', + 'ec/beta+': 'positron', + 'alpha': 'alpha', + 'n': 'neutron', + 'sf': 'fragment', + 'p': 'proton', + 'e-': 'electron', + 'xray': 'photon', + 'anti-neutrino': 'anti-neutrino', + 'neutrino': 'neutrino', + }[particle] + + if particle_type not in sources: + sources[particle_type] = [] + + # Create distribution for discrete + if spectra['continuous_flag'] in ('discrete', 'both'): + energies = [] + intensities = [] + for discrete_data in spectra['discrete']: + energies.append(discrete_data['energy'].n) + intensities.append(discrete_data['intensity'].n) + energies = np.array(energies) + intensity = spectra['discrete_normalization'].n + rates = decay_constant * intensity * np.array(intensities) + dist_discrete = Discrete(energies, rates) + sources[particle_type].append(dist_discrete) + + # Create distribution for continuous + if spectra['continuous_flag'] in ('continuous', 'both'): + f = spectra['continuous']['probability'] + if len(f.interpolation) > 1: + raise NotImplementedError("Multiple interpolation regions: {name}, {particle}") + interpolation = INTERPOLATION_SCHEME[f.interpolation[0]] + if interpolation not in ('histogram', 'linear-linear'): + raise NotImplementedError("Continuous spectra with {interpolation} interpolation ({name}, {particle}) not supported") + + intensity = spectra['continuous_normalization'].n + rates = decay_constant * intensity * f.y + dist_continuous = Tabular(f.x, rates, interpolation) + sources[particle_type].append(dist_continuous) + + # Combine discrete distributions + merged_sources = {} + for particle_type, dist_list in sources.items(): + merged_sources[particle_type] = combine_distributions( + dist_list, [1.0]*len(dist_list)) + + self._sources = merged_sources + return self._sources diff --git a/openmc/stats/univariate.py b/openmc/stats/univariate.py index 5528bdb30..58b7c6172 100644 --- a/openmc/stats/univariate.py +++ b/openmc/stats/univariate.py @@ -1,6 +1,7 @@ from abc import ABC, abstractmethod from collections import defaultdict from collections.abc import Iterable +from copy import deepcopy from numbers import Real from xml.etree import ElementTree as ET @@ -95,9 +96,9 @@ class Discrete(Univariate): Attributes ---------- - x : Iterable of float + x : numpy.ndarray Values of the random variable - p : Iterable of float + p : numpy.ndarray Discrete probability for each value """ @@ -122,7 +123,7 @@ class Discrete(Univariate): if isinstance(x, Real): x = [x] cv.check_type('discrete values', x, Iterable, Real) - self._x = x + self._x = np.array(x, dtype=float) @p.setter def p(self, p): @@ -131,14 +132,15 @@ class Discrete(Univariate): cv.check_type('discrete probabilities', p, Iterable, Real) for pk in p: cv.check_greater_than('discrete probability', pk, 0.0, True) - self._p = p + self._p = np.array(p, dtype=float) def cdf(self): return np.insert(np.cumsum(self.p), 0, 0.0) def sample(self, n_samples=1, seed=None): np.random.seed(seed) - return np.random.choice(self.x, n_samples, p=self.p) + p = self.p / self.p.sum() + return np.random.choice(self.x, n_samples, p=p) def normalize(self): """Normalize the probabilities stored on the distribution""" @@ -220,6 +222,18 @@ class Discrete(Univariate): p_arr = np.array([p_merged[x] for x in x_arr]) return cls(x_arr, p_arr) + def integral(self): + """Return integral of distribution + + .. versionadded:: 0.13.1 + + Returns + ------- + float + Integral of discrete distribution + """ + return np.sum(self.p) + class Uniform(Univariate): """Distribution with constant probability over a finite interval [a,b] @@ -825,9 +839,9 @@ class Tabular(Univariate): Attributes ---------- - x : Iterable of float + x : numpy.ndarray Tabulated values of the random variable - p : Iterable of float + p : numpy.ndarray Tabulated probabilities interpolation : {'histogram', 'linear-linear', 'linear-log', 'log-linear', 'log-log'}, optional Indicate whether the density function is constant between tabulated @@ -860,7 +874,7 @@ class Tabular(Univariate): @x.setter def x(self, x): cv.check_type('tabulated values', x, Iterable, Real) - self._x = x + self._x = np.array(x, dtype=float) @p.setter def p(self, p): @@ -868,7 +882,7 @@ class Tabular(Univariate): if not self._ignore_negative: for pk in p: cv.check_greater_than('tabulated probability', pk, 0.0, True) - self._p = p + self._p = np.array(p, dtype=float) @interpolation.setter def interpolation(self, interpolation): @@ -881,8 +895,8 @@ class Tabular(Univariate): 'distributions using histogram or ' 'linear-linear interpolation') c = np.zeros_like(self.x) - x = np.asarray(self.x) - p = np.asarray(self.p) + x = self.x + p = self.p if self.interpolation == 'histogram': c[1:] = p[:-1] * np.diff(x) @@ -922,7 +936,7 @@ class Tabular(Univariate): def normalize(self): """Normalize the probabilities stored on the distribution""" - self.p = np.asarray(self.p) / self.cdf().max() + self.p /= self.cdf().max() def sample(self, n_samples=1, seed=None): if not self.interpolation in ('histogram', 'linear-linear'): @@ -931,10 +945,11 @@ class Tabular(Univariate): 'linear-linear interpolation') np.random.seed(seed) xi = np.random.rand(n_samples) - cdf = self.cdf() - cdf /= cdf.max() + # always use normalized probabilities when sampling + cdf = self.cdf() p = self.p / cdf.max() + cdf /= cdf.max() # get CDF bins that are above the # sampled values @@ -949,7 +964,7 @@ class Tabular(Univariate): # the random number is less than the next cdf # entry x_i = self.x[cdf_idx] - p_i = self.p[cdf_idx] + p_i = p[cdf_idx] if self.interpolation == 'histogram': # mask where probability is greater than zero @@ -967,7 +982,7 @@ class Tabular(Univariate): # get variable and probability values for the # next entry x_i1 = self.x[cdf_idx + 1] - p_i1 = self.p[cdf_idx + 1] + p_i1 = p[cdf_idx + 1] # compute slope between entries m = (p_i1 - p_i) / (x_i1 - x_i) # set values for zero slope @@ -1027,6 +1042,24 @@ class Tabular(Univariate): p = params[len(params)//2:] return cls(x, p, interpolation) + def integral(self): + """Return integral of distribution + + .. versionadded: 0.13.1 + + Returns + ------- + float + Integral of tabular distrbution + """ + if self.interpolation == 'histogram': + return np.sum(np.diff(self.x) * self.p[:-1]) + elif self.interpolation == 'linear-linear': + return np.trapz(self.p, self.x) + else: + raise NotImplementedError( + f'integral() not supported for {self.inteprolation} interpolation') + class Legendre(Univariate): r"""Probability density given by a Legendre polynomial expansion @@ -1135,9 +1168,10 @@ class Mixture(Univariate): def sample(self, n_samples=1, seed=None): np.random.seed(seed) - idx = np.random.choice(self.distribution, n_samples, p=self.probability) + idx = np.random.choice(range(len(self.distribution)), + n_samples, p=self.probability) - out = np.zeros_like(idx) + out = np.empty_like(idx, dtype=float) for i in np.unique(idx): n_dist_samples = np.count_nonzero(idx == i) samples = self.distribution[i].sample(n_dist_samples) @@ -1199,3 +1233,68 @@ class Mixture(Univariate): distribution.append(Univariate.from_xml_element(pair.find("dist"))) return cls(probability, distribution) + + def integral(self): + """Return integral of the distribution + + .. versionadded:: 0.13.1 + + Returns + ------- + float + Integral of the distribution + """ + return sum([ + p*dist.integral() + for p, dist in zip(self.probability, self.distribution) + ]) + + +def combine_distributions(dists, probs): + """Combine distributions with specified probabilities + + This function can be used to combine multiple instances of + :class:`~openmc.stats.Discrete` and `~openmc.stats.Tabular`. Multiple + discrete distributions are merged into a single distribution and the + remainder of the distributions are put into a :class:`~openmc.stats.Mixture` + distribution. + + .. versionadded:: 0.13.1 + + Parameters + ---------- + dists : iterable of openmc.stats.Univariate + Distributions to combine + probs : iterable of float + Probability (or intensity) of each distribution + + """ + # Get copy of distribution list so as not to modify the argument + dist_list = deepcopy(dists) + + # Get list of discrete/continuous distribution indices + discrete_index = [i for i, d in enumerate(dist_list) if isinstance(d, Discrete)] + cont_index = [i for i, d in enumerate(dist_list) if isinstance(d, Tabular)] + + # Apply probabilites to continuous distributions + for i in cont_index: + dist = dist_list[i] + dist.p *= probs[i] + + if discrete_index: + # Create combined discrete distribution + dist_discrete = [dist_list[i] for i in discrete_index] + discrete_probs = [probs[i] for i in discrete_index] + combined_dist = Discrete.merge(dist_discrete, discrete_probs) + + # Replace multiple discrete distributions with merged + for idx in reversed(discrete_index): + dist_list.pop(idx) + dist_list.append(combined_dist) + + # Combine discrete and continuous if present + if len(dist_list) > 1: + probs = [d.integral() for d in dist_list] + dist_list[:] = [Mixture(probs, dist_list.copy())] + + return dist_list[0] diff --git a/tests/unit_tests/test_data_decay.py b/tests/unit_tests/test_data_decay.py index 06b8e6bed..f0bda1bd9 100644 --- a/tests/unit_tests/test_data_decay.py +++ b/tests/unit_tests/test_data_decay.py @@ -23,6 +23,14 @@ def nb90(): return openmc.data.Decay.from_endf(filename) +@pytest.fixture(scope='module') +def ba137m(): + """Ba137_m1 decay data.""" + endf_data = os.environ['OPENMC_ENDF_DATA'] + filename = os.path.join(endf_data, 'decay', 'dec-056_Ba_137m1.endf') + return openmc.data.Decay.from_endf(filename) + + @pytest.fixture(scope='module') def u235_yields(): """U235 fission product yield data.""" @@ -48,6 +56,7 @@ def test_nb90_halflife(nb90): ufloat_close(nb90.decay_constant, log(2.)/nb90.half_life) ufloat_close(nb90.decay_energy, ufloat(2265527.5, 25159.400474401213)) + def test_nb90_nuclide(nb90): assert nb90.nuclide['atomic_number'] == 41 assert nb90.nuclide['mass_number'] == 90 @@ -91,3 +100,29 @@ def test_fpy(u235_yields): assert len(u235_yields.independent) == 3 thermal = u235_yields.independent[0] ufloat_close(thermal['I135'], ufloat(0.0292737, 0.000819663)) + + +def test_sources(ba137m, nb90): + # Running .sources twice should give same objects + sources = ba137m.sources + sources2 = ba137m.sources + for key in sources: + assert sources[key] is sources2[key] + + # Each source should be a univariate distribution + for dist in sources.values(): + assert isinstance(dist, openmc.stats.Univariate) + + # Check for presence of 662 keV gamma ray in decay of Ba137m + gamma_source = ba137m.sources['photon'] + assert isinstance(gamma_source, openmc.stats.Discrete) + b = np.isclose(gamma_source.x, 661657.) + assert np.count_nonzero(b) == 1 + + # Check value of decay/s/atom + idx = np.flatnonzero(b)[0] + assert gamma_source.p[idx] == pytest.approx(0.004069614) + + # Nb90 decays by β+ and should emit positrons, electrons, and photons + sources = nb90.sources + assert len(set(sources.keys()) ^ {'positron', 'electron', 'photon'}) == 0 diff --git a/tests/unit_tests/test_stats.py b/tests/unit_tests/test_stats.py index b57f9578a..1cfcf00c3 100644 --- a/tests/unit_tests/test_stats.py +++ b/tests/unit_tests/test_stats.py @@ -6,6 +6,12 @@ import openmc import openmc.stats +def assert_sample_mean(samples, expected_mean): + std_dev = samples.std() / np.sqrt(samples.size) + assert np.abs(expected_mean - samples.mean()) < 3*std_dev + + + def test_discrete(): x = [0.0, 1.0, 10.0] p = [0.3, 0.2, 0.5] @@ -13,8 +19,8 @@ def test_discrete(): elem = d.to_xml_element('distribution') d = openmc.stats.Discrete.from_xml_element(elem) - assert d.x == x - assert d.p == p + 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) @@ -33,13 +39,11 @@ def test_discrete(): d3 = openmc.stats.Discrete(vals, probs) - # sample discrete distribution + # sample discrete distribution and check that the mean of the samples is + # within 3 std. dev. of the expected mean n_samples = 1_000_000 samples = d3.sample(n_samples, seed=100) - # check that the mean of the samples is within 3 std. dev. - # of the expected mean - std_dev = samples.std() / np.sqrt(n_samples) - assert np.abs(exp_mean - samples.mean()) < 3*std_dev + assert_sample_mean(samples, exp_mean) def test_merge_discrete(): @@ -76,17 +80,16 @@ def test_uniform(): assert len(d) == 2 t = d.to_tabular() - assert t.x == [a, b] - assert t.p == [1/(b-a), 1/(b-a)] + 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 3 + # std. dev. of the expected mean exp_mean = 0.5 * (a + b) n_samples = 1_000_000 samples = d.sample(n_samples, seed=100) - # check that the mean of the samples is within 3 std. dev. - # of the expected mean - std_dev = samples.std() / np.sqrt(n_samples) - assert np.abs(exp_mean - samples.mean()) < 3*std_dev + assert_sample_mean(samples, exp_mean) def test_powerlaw(): @@ -102,13 +105,11 @@ def test_powerlaw(): exp_mean = 100.0 * (n+1) / (n+2) - # sample power law distribution + # sample power law distribution and check that the mean of the samples is + # within 3 std. dev. of the expected mean n_samples = 1_000_000 samples = d.sample(n_samples, seed=100) - # check that the mean of the samples is within 3 std. dev. - # of the expected mean - std_dev = samples.std() / np.sqrt(n_samples) - assert np.abs(exp_mean - samples.mean()) < 3*std_dev + assert_sample_mean(samples, exp_mean) def test_maxwell(): @@ -122,21 +123,15 @@ def test_maxwell(): exp_mean = 3/2 * theta - # sample maxwell distribution + # sample maxwell distribution and check that the mean of the samples is + # within 3 std. dev. of the expected mean n_samples = 1_000_000 samples = d.sample(n_samples, seed=100) - # check that the mean of the samples is within 3 std. dev. - # of the expected mean - std_dev = samples.std() / np.sqrt(n_samples) - assert np.abs(exp_mean - samples.mean()) < 3*std_dev + assert_sample_mean(samples, exp_mean) # A second sample with a different seed samples_2 = d.sample(n_samples, seed=200) - # check that the mean of the samples is within 3 std. dev. - # of the expected mean - std_dev = samples_2.std() / np.sqrt(n_samples) - assert np.abs(exp_mean - samples_2.mean()) < 3*std_dev - + assert_sample_mean(samples_2, exp_mean) assert samples_2.mean() != samples.mean() @@ -156,13 +151,11 @@ def test_watt(): # https://doi.org/10.1016/j.physletb.2003.09.048 exp_mean = 3/2 * a + a**2 * b / 4 - # sample Watt distribution + # sample Watt distribution and check that the mean of the samples is within + # 3 std. dev. of the expected mean n_samples = 1_000_000 samples = d.sample(n_samples, seed=100) - # check that the mean of the samples is within 3 std. dev. - # of the expected mean - std_dev = samples.std() / np.sqrt(n_samples) - assert np.abs(exp_mean - samples.mean()) < 3*std_dev + assert_sample_mean(samples, exp_mean) def test_tabular(): @@ -228,6 +221,11 @@ def test_mixture(): 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) @@ -396,3 +394,47 @@ def test_muir(): assert within_2_sigma / n_samples >= 0.95 within_3_sigma = np.count_nonzero(samples < 3*d.std_dev) assert within_3_sigma / n_samples >= 0.99 + + +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]) + + # Sample the combined distribution and make sure the sample mean is within + # uncertainty of the expected value + samples = combined.sample(10) + assert_sample_mean(samples, 0.25)