Source code for openmc.stats.multivariate

from abc import ABC, abstractmethod
from collections.abc import Iterable
from math import pi, cos
from numbers import Real
from xml.etree import ElementTree as ET

import numpy as np

import openmc.checkvalue as cv
from .._xml import get_text
from .univariate import Univariate, Uniform, PowerLaw


[docs]class UnitSphere(ABC): """Distribution of points on the unit sphere. This abstract class is used for angular distributions, since a direction is represented as a unit vector (i.e., vector on the unit sphere). Parameters ---------- reference_uvw : Iterable of float Direction from which polar angle is measured Attributes ---------- reference_uvw : Iterable of float Direction from which polar angle is measured """ def __init__(self, reference_uvw=None): self._reference_uvw = None if reference_uvw is not None: self.reference_uvw = reference_uvw @property def reference_uvw(self): return self._reference_uvw @reference_uvw.setter def reference_uvw(self, uvw): cv.check_type('reference direction', uvw, Iterable, Real) uvw = np.asarray(uvw) self._reference_uvw = uvw/np.linalg.norm(uvw) @abstractmethod def to_xml_element(self): return '' @classmethod @abstractmethod def from_xml_element(cls, elem): distribution = get_text(elem, 'type') if distribution == 'mu-phi': return PolarAzimuthal.from_xml_element(elem) elif distribution == 'isotropic': return Isotropic.from_xml_element(elem) elif distribution == 'monodirectional': return Monodirectional.from_xml_element(elem)
[docs]class PolarAzimuthal(UnitSphere): """Angular distribution represented by polar and azimuthal angles This distribution allows one to specify the distribution of the cosine of the polar angle and the azimuthal angle independently of one another. The polar angle is measured relative to the reference angle. Parameters ---------- mu : openmc.stats.Univariate Distribution of the cosine of the polar angle phi : openmc.stats.Univariate Distribution of the azimuthal angle in radians reference_uvw : Iterable of float Direction from which polar angle is measured. Defaults to the positive z-direction. Attributes ---------- mu : openmc.stats.Univariate Distribution of the cosine of the polar angle phi : openmc.stats.Univariate Distribution of the azimuthal angle in radians """ def __init__(self, mu=None, phi=None, reference_uvw=(0., 0., 1.)): super().__init__(reference_uvw) if mu is not None: self.mu = mu else: self.mu = Uniform(-1., 1.) if phi is not None: self.phi = phi else: self.phi = Uniform(0., 2*pi) @property def mu(self): return self._mu @property def phi(self): return self._phi @mu.setter def mu(self, mu): cv.check_type('cosine of polar angle', mu, Univariate) self._mu = mu @phi.setter def phi(self, phi): cv.check_type('azimuthal angle', phi, Univariate) self._phi = phi
[docs] def to_xml_element(self): """Return XML representation of the angular distribution Returns ------- element : xml.etree.ElementTree.Element XML element containing angular distribution data """ element = ET.Element('angle') element.set("type", "mu-phi") if self.reference_uvw is not None: element.set("reference_uvw", ' '.join(map(str, self.reference_uvw))) element.append(self.mu.to_xml_element('mu')) element.append(self.phi.to_xml_element('phi')) return element
[docs] @classmethod def from_xml_element(cls, elem): """Generate angular distribution from an XML element Parameters ---------- elem : xml.etree.ElementTree.Element XML element Returns ------- openmc.stats.PolarAzimuthal Angular distribution generated from XML element """ mu_phi = cls() params = get_text(elem, 'parameters') if params is not None: mu_phi.reference_uvw = [float(x) for x in params.split()] mu_phi.mu = Univariate.from_xml_element(elem.find('mu')) mu_phi.phi = Univariate.from_xml_element(elem.find('phi')) return mu_phi
[docs]class Isotropic(UnitSphere): """Isotropic angular distribution.""" def __init__(self): super().__init__()
[docs] def to_xml_element(self): """Return XML representation of the isotropic distribution Returns ------- element : xml.etree.ElementTree.Element XML element containing isotropic distribution data """ element = ET.Element('angle') element.set("type", "isotropic") return element
[docs] @classmethod def from_xml_element(cls, elem): """Generate isotropic distribution from an XML element Parameters ---------- elem : xml.etree.ElementTree.Element XML element Returns ------- openmc.stats.Isotropic Isotropic distribution generated from XML element """ return cls()
[docs]class Monodirectional(UnitSphere): """Monodirectional angular distribution. A monodirectional angular distribution is one for which the polar and azimuthal angles are always the same. It is completely specified by the reference direction vector. Parameters ---------- reference_uvw : Iterable of float Direction from which polar angle is measured. Defaults to the positive x-direction. """ def __init__(self, reference_uvw=[1., 0., 0.]): super().__init__(reference_uvw)
[docs] def to_xml_element(self): """Return XML representation of the monodirectional distribution Returns ------- element : xml.etree.ElementTree.Element XML element containing monodirectional distribution data """ element = ET.Element('angle') element.set("type", "monodirectional") if self.reference_uvw is not None: element.set("reference_uvw", ' '.join(map(str, self.reference_uvw))) return element
[docs] @classmethod def from_xml_element(cls, elem): """Generate monodirectional distribution from an XML element Parameters ---------- elem : xml.etree.ElementTree.Element XML element Returns ------- openmc.stats.Monodirectional Monodirectional distribution generated from XML element """ monodirectional = cls() params = get_text(elem, 'parameters') if params is not None: monodirectional.reference_uvw = [float(x) for x in params.split()] return monodirectional
[docs]class Spatial(ABC): """Distribution of locations in three-dimensional Euclidean space. Classes derived from this abstract class can be used for spatial distributions of source sites. """ @abstractmethod def to_xml_element(self): return '' @classmethod @abstractmethod def from_xml_element(cls, elem): distribution = get_text(elem, 'type') if distribution == 'cartesian': return CartesianIndependent.from_xml_element(elem) elif distribution == 'cylindrical': return CylindricalIndependent.from_xml_element(elem) elif distribution == 'spherical': return SphericalIndependent.from_xml_element(elem) elif distribution == 'box' or distribution == 'fission': return Box.from_xml_element(elem) elif distribution == 'point': return Point.from_xml_element(elem)
[docs]class CartesianIndependent(Spatial): """Spatial distribution with independent x, y, and z distributions. This distribution allows one to specify coordinates whose x-, y-, and z- components are sampled independently from one another. Parameters ---------- x : openmc.stats.Univariate Distribution of x-coordinates y : openmc.stats.Univariate Distribution of y-coordinates z : openmc.stats.Univariate Distribution of z-coordinates Attributes ---------- x : openmc.stats.Univariate Distribution of x-coordinates y : openmc.stats.Univariate Distribution of y-coordinates z : openmc.stats.Univariate Distribution of z-coordinates """ def __init__(self, x, y, z): self.x = x self.y = y self.z = z @property def x(self): return self._x @property def y(self): return self._y @property def z(self): return self._z @x.setter def x(self, x): cv.check_type('x coordinate', x, Univariate) self._x = x @y.setter def y(self, y): cv.check_type('y coordinate', y, Univariate) self._y = y @z.setter def z(self, z): cv.check_type('z coordinate', z, Univariate) self._z = z
[docs] def to_xml_element(self): """Return XML representation of the spatial distribution Returns ------- element : xml.etree.ElementTree.Element XML element containing spatial distribution data """ element = ET.Element('space') element.set('type', 'cartesian') element.append(self.x.to_xml_element('x')) element.append(self.y.to_xml_element('y')) element.append(self.z.to_xml_element('z')) return element
[docs] @classmethod def from_xml_element(cls, elem): """Generate spatial distribution from an XML element Parameters ---------- elem : xml.etree.ElementTree.Element XML element Returns ------- openmc.stats.CartesianIndependent Spatial distribution generated from XML element """ x = Univariate.from_xml_element(elem.find('x')) y = Univariate.from_xml_element(elem.find('y')) z = Univariate.from_xml_element(elem.find('z')) return cls(x, y, z)
[docs]class SphericalIndependent(Spatial): r"""Spatial distribution represented in spherical coordinates. This distribution allows one to specify coordinates whose :math:`r`, :math:`\theta`, and :math:`\phi` components are sampled independently from one another and centered on the coordinates (x0, y0, z0). .. versionadded: 0.12 Parameters ---------- r : openmc.stats.Univariate Distribution of r-coordinates in a reference frame specified by the origin parameter cos_theta : openmc.stats.Univariate Distribution of the cosine of the theta-coordinates (angle relative to the z-axis) in a reference frame specified by the origin parameter phi : openmc.stats.Univariate Distribution of phi-coordinates (azimuthal angle) in a reference frame specified by the origin parameter origin: Iterable of float, optional coordinates (x0, y0, z0) of the center of the spherical reference frame for the source. Defaults to (0.0, 0.0, 0.0) Attributes ---------- r : openmc.stats.Univariate Distribution of r-coordinates in the local reference frame cos_theta : openmc.stats.Univariate Distribution of the cosine of the theta-coordinates (angle relative to the z-axis) in the local reference frame phi : openmc.stats.Univariate Distribution of phi-coordinates (azimuthal angle) in the local reference frame origin: Iterable of float, optional coordinates (x0, y0, z0) of the center of the spherical reference frame. Defaults to (0.0, 0.0, 0.0) """ def __init__(self, r, cos_theta, phi, origin=(0.0, 0.0, 0.0)): self.r = r self.cos_theta = cos_theta self.phi = phi self.origin = origin @property def r(self): return self._r @property def cos_theta(self): return self._cos_theta @property def phi(self): return self._phi @property def origin(self): return self._origin @r.setter def r(self, r): cv.check_type('r coordinate', r, Univariate) self._r = r @cos_theta.setter def cos_theta(self, cos_theta): cv.check_type('cos_theta coordinate', cos_theta, Univariate) self._cos_theta = cos_theta @phi.setter def phi(self, phi): cv.check_type('phi coordinate', phi, Univariate) self._phi = phi @origin.setter def origin(self, origin): cv.check_type('origin coordinates', origin, Iterable, Real) origin = np.asarray(origin) self._origin = origin
[docs] def to_xml_element(self): """Return XML representation of the spatial distribution Returns ------- element : xml.etree.ElementTree.Element XML element containing spatial distribution data """ element = ET.Element('space') element.set('type', 'spherical') element.append(self.r.to_xml_element('r')) element.append(self.cos_theta.to_xml_element('cos_theta')) element.append(self.phi.to_xml_element('phi')) element.set("origin", ' '.join(map(str, self.origin))) return element
[docs] @classmethod def from_xml_element(cls, elem): """Generate spatial distribution from an XML element Parameters ---------- elem : xml.etree.ElementTree.Element XML element Returns ------- openmc.stats.SphericalIndependent Spatial distribution generated from XML element """ r = Univariate.from_xml_element(elem.find('r')) cos_theta = Univariate.from_xml_element(elem.find('cos_theta')) phi = Univariate.from_xml_element(elem.find('phi')) origin = [float(x) for x in elem.get('origin').split()] return cls(r, cos_theta, phi, origin=origin)
[docs]class CylindricalIndependent(Spatial): r"""Spatial distribution represented in cylindrical coordinates. This distribution allows one to specify coordinates whose :math:`r`, :math:`\phi`, and :math:`z` components are sampled independently from one another and in a reference frame whose origin is specified by the coordinates (x0, y0, z0). .. versionadded:: 0.12 Parameters ---------- r : openmc.stats.Univariate Distribution of r-coordinates in a reference frame specified by the origin parameter phi : openmc.stats.Univariate Distribution of phi-coordinates (azimuthal angle) in a reference frame specified by the origin parameter z : openmc.stats.Univariate Distribution of z-coordinates in a reference frame specified by the origin parameter origin: Iterable of float, optional coordinates (x0, y0, z0) of the center of the cylindrical reference frame. Defaults to (0.0, 0.0, 0.0) Attributes ---------- r : openmc.stats.Univariate Distribution of r-coordinates in the local reference frame phi : openmc.stats.Univariate Distribution of phi-coordinates (azimuthal angle) in the local reference frame z : openmc.stats.Univariate Distribution of z-coordinates in the local reference frame origin: Iterable of float, optional coordinates (x0, y0, z0) of the center of the cylindrical reference frame. Defaults to (0.0, 0.0, 0.0) """ def __init__(self, r, phi, z, origin=(0.0, 0.0, 0.0)): self.r = r self.phi = phi self.z = z self.origin = origin @property def r(self): return self._r @property def phi(self): return self._phi @property def z(self): return self._z @property def origin(self): return self._origin @r.setter def r(self, r): cv.check_type('r coordinate', r, Univariate) self._r = r @phi.setter def phi(self, phi): cv.check_type('phi coordinate', phi, Univariate) self._phi = phi @z.setter def z(self, z): cv.check_type('z coordinate', z, Univariate) self._z = z @origin.setter def origin(self, origin): cv.check_type('origin coordinates', origin, Iterable, Real) origin = np.asarray(origin) self._origin = origin
[docs] def to_xml_element(self): """Return XML representation of the spatial distribution Returns ------- element : xml.etree.ElementTree.Element XML element containing spatial distribution data """ element = ET.Element('space') element.set('type', 'cylindrical') element.append(self.r.to_xml_element('r')) element.append(self.phi.to_xml_element('phi')) element.append(self.z.to_xml_element('z')) element.set("origin", ' '.join(map(str, self.origin))) return element
[docs] @classmethod def from_xml_element(cls, elem): """Generate spatial distribution from an XML element Parameters ---------- elem : xml.etree.ElementTree.Element XML element Returns ------- openmc.stats.CylindricalIndependent Spatial distribution generated from XML element """ r = Univariate.from_xml_element(elem.find('r')) phi = Univariate.from_xml_element(elem.find('phi')) z = Univariate.from_xml_element(elem.find('z')) origin = [float(x) for x in elem.get('origin').split()] return cls(r, phi, z, origin=origin)
[docs]class Box(Spatial): """Uniform distribution of coordinates in a rectangular cuboid. Parameters ---------- lower_left : Iterable of float Lower-left coordinates of cuboid upper_right : Iterable of float Upper-right coordinates of cuboid only_fissionable : bool, optional Whether spatial sites should only be accepted if they occur in fissionable materials Attributes ---------- lower_left : Iterable of float Lower-left coordinates of cuboid upper_right : Iterable of float Upper-right coordinates of cuboid only_fissionable : bool, optional Whether spatial sites should only be accepted if they occur in fissionable materials """ def __init__(self, lower_left, upper_right, only_fissionable=False): self.lower_left = lower_left self.upper_right = upper_right self.only_fissionable = only_fissionable @property def lower_left(self): return self._lower_left @property def upper_right(self): return self._upper_right @property def only_fissionable(self): return self._only_fissionable @lower_left.setter def lower_left(self, lower_left): cv.check_type('lower left coordinate', lower_left, Iterable, Real) cv.check_length('lower left coordinate', lower_left, 3) self._lower_left = lower_left @upper_right.setter def upper_right(self, upper_right): cv.check_type('upper right coordinate', upper_right, Iterable, Real) cv.check_length('upper right coordinate', upper_right, 3) self._upper_right = upper_right @only_fissionable.setter def only_fissionable(self, only_fissionable): cv.check_type('only fissionable', only_fissionable, bool) self._only_fissionable = only_fissionable
[docs] def to_xml_element(self): """Return XML representation of the box distribution Returns ------- element : xml.etree.ElementTree.Element XML element containing box distribution data """ element = ET.Element('space') if self.only_fissionable: element.set("type", "fission") else: element.set("type", "box") params = ET.SubElement(element, "parameters") params.text = ' '.join(map(str, self.lower_left)) + ' ' + \ ' '.join(map(str, self.upper_right)) return element
[docs] @classmethod def from_xml_element(cls, elem): """Generate box distribution from an XML element Parameters ---------- elem : xml.etree.ElementTree.Element XML element Returns ------- openmc.stats.Box Box distribution generated from XML element """ only_fissionable = get_text(elem, 'type') == 'fission' params = [float(x) for x in get_text(elem, 'parameters').split()] lower_left = params[:len(params)//2] upper_right = params[len(params)//2:] return cls(lower_left, upper_right, only_fissionable)
[docs]class Point(Spatial): """Delta function in three dimensions. This spatial distribution can be used for a point source where sites are emitted at a specific location given by its Cartesian coordinates. Parameters ---------- xyz : Iterable of float, optional Cartesian coordinates of location. Defaults to (0., 0., 0.). Attributes ---------- xyz : Iterable of float Cartesian coordinates of location """ def __init__(self, xyz=(0., 0., 0.)): self.xyz = xyz @property def xyz(self): return self._xyz @xyz.setter def xyz(self, xyz): cv.check_type('coordinate', xyz, Iterable, Real) cv.check_length('coordinate', xyz, 3) self._xyz = xyz
[docs] def to_xml_element(self): """Return XML representation of the point distribution Returns ------- element : xml.etree.ElementTree.Element XML element containing point distribution location """ element = ET.Element('space') element.set("type", "point") params = ET.SubElement(element, "parameters") params.text = ' '.join(map(str, self.xyz)) return element
[docs] @classmethod def from_xml_element(cls, elem): """Generate point distribution from an XML element Parameters ---------- elem : xml.etree.ElementTree.Element XML element Returns ------- openmc.stats.Point Point distribution generated from XML element """ xyz = [float(x) for x in get_text(elem, 'parameters').split()] return cls(xyz)
def spherical_uniform(r_outer, r_inner=0.0, thetas=(0., pi), phis=(0., 2*pi), origin=(0., 0., 0.)): """Return a uniform spatial distribution over a spherical shell. This function provides a uniform spatial distribution over a spherical shell between `r_inner` and `r_outer`. Optionally, the range of angles can be restricted by the `thetas` and `phis` arguments. .. versionadded: 0.13.1 Parameters ---------- r_outer : float Outer radius of the spherical shell in [cm] r_inner : float, optional Inner radius of the spherical shell in [cm] thetas : iterable of float, optional Starting and ending theta coordinates (angle relative to the z-axis) in radius in a reference frame centered at `origin` phis : iterable of float, optional Starting and ending phi coordinates (azimuthal angle) in radians in a reference frame centered at `origin` origin: iterable of float, optional Coordinates (x0, y0, z0) of the center of the spherical reference frame for the distribution. Returns ------- openmc.stats.SphericalIndependent Uniform distribution over the spherical shell """ r_dist = PowerLaw(r_inner, r_outer, 2) cos_thetas_dist = Uniform(cos(thetas[1]), cos(thetas[0])) phis_dist = Uniform(phis[0], phis[1]) return SphericalIndependent(r_dist, cos_thetas_dist, phis_dist, origin)