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).

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).

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.

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)