from __future__ import annotations
import typing
import warnings
from abc import ABC, abstractmethod
from collections.abc import Iterable
from functools import wraps
from math import pi, sqrt, atan2
from numbers import Integral, Real
from pathlib import Path
from typing import Optional, Sequence, Tuple
import h5py
import lxml.etree as ET
import numpy as np
import openmc
import openmc.checkvalue as cv
from openmc.checkvalue import PathLike
from ._xml import get_text
from .mixin import IDManagerMixin
from .surface import _BOUNDARY_TYPES
class MeshBase(IDManagerMixin, ABC):
"""A mesh that partitions geometry for tallying purposes.
Parameters
----------
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
Attributes
----------
id : int
Unique identifier for the mesh
name : str
Name of the mesh
bounding_box : openmc.BoundingBox
Axis-aligned bounding box of the mesh as defined by the upper-right and
lower-left coordinates.
indices : Iterable of tuple
An iterable of mesh indices for each mesh element, e.g. [(1, 1, 1), (2, 1, 1), ...]
"""
next_id = 1
used_ids = set()
def __init__(self, mesh_id: Optional[int] = None, name: str = ''):
# Initialize Mesh class attributes
self.id = mesh_id
self.name = name
@property
def name(self):
return self._name
@name.setter
def name(self, name: str):
if name is not None:
cv.check_type(f'name for mesh ID="{self._id}"', name, str)
self._name = name
else:
self._name = ''
@property
def bounding_box(self) -> openmc.BoundingBox:
return openmc.BoundingBox(self.lower_left, self.upper_right)
@property
@abstractmethod
def indices(self):
pass
def __repr__(self):
string = type(self).__name__ + '\n'
string += '{0: <16}{1}{2}\n'.format('\tID', '=\t', self._id)
string += '{0: <16}{1}{2}\n'.format('\tName', '=\t', self._name)
return string
def _volume_dim_check(self):
if self.n_dimension != 3 or \
any([d == 0 for d in self.dimension]):
raise RuntimeError(f'Mesh {self.id} is not 3D. '
'Volumes cannot be provided.')
@classmethod
def from_hdf5(cls, group: h5py.Group):
"""Create mesh from HDF5 group
Parameters
----------
group : h5py.Group
Group in HDF5 file
Returns
-------
openmc.MeshBase
Instance of a MeshBase subclass
"""
mesh_type = group['type'][()].decode()
if mesh_type == 'regular':
return RegularMesh.from_hdf5(group)
elif mesh_type == 'rectilinear':
return RectilinearMesh.from_hdf5(group)
elif mesh_type == 'cylindrical':
return CylindricalMesh.from_hdf5(group)
elif mesh_type == 'spherical':
return SphericalMesh.from_hdf5(group)
elif mesh_type == 'unstructured':
return UnstructuredMesh.from_hdf5(group)
else:
raise ValueError('Unrecognized mesh type: "' + mesh_type + '"')
@classmethod
def from_xml_element(cls, elem: ET.Element):
"""Generates a mesh from an XML element
Parameters
----------
elem : lxml.etree._Element
XML element
Returns
-------
openmc.MeshBase
an openmc mesh object
"""
mesh_type = get_text(elem, 'type')
if mesh_type == 'regular' or mesh_type is None:
return RegularMesh.from_xml_element(elem)
elif mesh_type == 'rectilinear':
return RectilinearMesh.from_xml_element(elem)
elif mesh_type == 'cylindrical':
return CylindricalMesh.from_xml_element(elem)
elif mesh_type == 'spherical':
return SphericalMesh.from_xml_element(elem)
elif mesh_type == 'unstructured':
return UnstructuredMesh.from_xml_element(elem)
else:
raise ValueError(f'Unrecognized mesh type "{mesh_type}" found.')
class StructuredMesh(MeshBase):
"""A base class for structured mesh functionality
Parameters
----------
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
Attributes
----------
id : int
Unique identifier for the mesh
name : str
Name of the mesh
"""
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
@property
@abstractmethod
def dimension(self):
pass
@property
@abstractmethod
def n_dimension(self):
pass
@property
@abstractmethod
def _grids(self):
pass
@property
def vertices(self):
"""Return coordinates of mesh vertices in Cartesian coordinates. Also
see :meth:`CylindricalMesh.vertices_cylindrical` and
:meth:`SphericalMesh.vertices_spherical` for coordinates in other coordinate
systems.
Returns
-------
vertices : numpy.ndarray
Returns a numpy.ndarray representing the coordinates of the mesh
vertices with a shape equal to (dim1 + 1, ..., dimn + 1, ndim). X, Y, Z values
can be unpacked with xx, yy, zz = np.rollaxis(mesh.vertices, -1).
"""
return self._generate_vertices(*self._grids)
@staticmethod
def _generate_vertices(i_grid, j_grid, k_grid):
"""Returns an array with shape (i_grid.size, j_grid.size, k_grid.size, 3)
containing the corner vertices of mesh elements.
"""
return np.stack(np.meshgrid(i_grid, j_grid, k_grid, indexing='ij'), axis=-1)
@staticmethod
def _generate_edge_midpoints(grids):
"""Generates the midpoints of mesh element edges for each dimension of the mesh.
Parameters
----------
grids : numpy.ndarray
The vertex grids along each dimension of the mesh.
Returns
-------
midpoint_grids : list of numpy.ndarray
The edge midpoints for the i, j, and k midpoints of each element in
i, j, k ordering. The shapes of the resulting grids are
[(ni-1, nj, nk, 3), (ni, nj-1, nk, 3), (ni, nj, nk-1, 3)]
"""
# generate a set of edge midpoints for each dimension
midpoint_grids = []
# generate the element edge midpoints in order s.t.
# the epxected element ordering is preserved with respect to the corner vertices
# each grid is comprised of the mid points for one dimension and the
# corner vertices of the other two
for dims in ((0, 1, 2), (1, 0, 2), (2, 0, 1)):
# compute the midpoints along the last dimension
midpoints = grids[dims[0]][:-1] + 0.5 * np.diff(grids[dims[0]])
coords = (midpoints, grids[dims[1]], grids[dims[2]])
i_grid, j_grid, k_grid = [coords[dims.index(i)] for i in range(3)]
# re-use the generate vertices method to create the full mesh grid
# transpose to get (i, j, k) ordering of the gridpoints
midpoint_grid = StructuredMesh._generate_vertices(i_grid, j_grid, k_grid)
midpoint_grids.append(midpoint_grid)
return midpoint_grids
@property
def midpoint_vertices(self):
"""Create vertices that lie on the midpoint of element edges
"""
# generate edge midpoints needed for curvilinear element definition
midpoint_vertices = self._generate_edge_midpoints(self._grids)
# convert each of the midpoint grids to cartesian coordinates
for vertices in midpoint_vertices:
self._convert_to_cartesian(vertices, self.origin)
return midpoint_vertices
@property
def centroids(self):
"""Return coordinates of mesh element centroids.
Returns
-------
centroids : numpy.ndarray
Returns a numpy.ndarray representing the mesh element centroid
coordinates with a shape equal to (dim1, ..., dimn, ndim). X,
Y, Z values can be unpacked with xx, yy, zz =
np.rollaxis(mesh.centroids, -1).
"""
ndim = self.n_dimension
# this line ensures that the vertices aren't adjusted by the origin or
# converted to the Cartesian system for cylindrical and spherical meshes
vertices = StructuredMesh.vertices.fget(self)
s0 = (slice(0, -1),)*ndim + (slice(None),)
s1 = (slice(1, None),)*ndim + (slice(None),)
return (vertices[s0] + vertices[s1]) / 2
@property
def num_mesh_cells(self):
return np.prod(self.dimension)
def write_data_to_vtk(self,
filename: PathLike,
datasets: Optional[dict] = None,
volume_normalization: bool = True,
curvilinear: bool = False):
"""Creates a VTK object of the mesh
Parameters
----------
filename : str
Name of the VTK file to write.
datasets : dict
Dictionary whose keys are the data labels
and values are the data sets.
volume_normalization : bool, optional
Whether or not to normalize the data by
the volume of the mesh elements.
curvilinear : bool
Whether or not to write curvilinear elements. Only applies to
``SphericalMesh`` and ``CylindricalMesh``.
Raises
------
ValueError
When the size of a dataset doesn't match the number of mesh cells
Returns
-------
vtk.StructuredGrid or vtk.UnstructuredGrid
a VTK grid object representing the mesh
"""
import vtk
from vtk.util import numpy_support as nps
# check that the data sets are appropriately sized
if datasets is not None:
self._check_vtk_datasets(datasets)
# write linear elements using a structured grid
if not curvilinear or isinstance(self, (RegularMesh, RectilinearMesh)):
vtk_grid = self._create_vtk_structured_grid()
writer = vtk.vtkStructuredGridWriter()
# write curvilinear elements using an unstructured grid
else:
vtk_grid = self._create_vtk_unstructured_grid()
writer = vtk.vtkUnstructuredGridWriter()
if datasets is not None:
# maintain a list of the datasets as added
# to the VTK arrays to ensure they persist
# in memory until the file is written
datasets_out = []
for label, dataset in datasets.items():
dataset = np.asarray(dataset).flatten()
datasets_out.append(dataset)
if volume_normalization:
dataset /= self.volumes.T.flatten()
dataset_array = vtk.vtkDoubleArray()
dataset_array.SetName(label)
dataset_array.SetArray(nps.numpy_to_vtk(dataset),
dataset.size,
True)
vtk_grid.GetCellData().AddArray(dataset_array)
writer.SetFileName(str(filename))
writer.SetInputData(vtk_grid)
writer.Write()
return vtk_grid
def _create_vtk_structured_grid(self):
"""Create a structured grid
Returns
-------
vtk.vtkStructuredGrid
a VTK structured grid object representing the mesh
"""
import vtk
from vtk.util import numpy_support as nps
vtkPts = vtk.vtkPoints()
vtkPts.SetData(nps.numpy_to_vtk(np.swapaxes(self.vertices, 0, 2).reshape(-1, 3), deep=True))
vtk_grid = vtk.vtkStructuredGrid()
vtk_grid.SetPoints(vtkPts)
vtk_grid.SetDimensions(*[dim + 1 for dim in self.dimension])
return vtk_grid
def _create_vtk_unstructured_grid(self):
"""Create an unstructured grid of curvilinear elements
representing the mesh
Returns
-------
vtk.vtkUnstructuredGrid
a VTK unstructured grid object representing the mesh
"""
import vtk
from vtk.util import numpy_support as nps
corner_vertices = np.swapaxes(self.vertices, 0, 2).reshape(-1, 3)
vtkPts = vtk.vtkPoints()
vtk_grid = vtk.vtkUnstructuredGrid()
vtk_grid.SetPoints(vtkPts)
# add corner vertices to the point set for the unstructured grid
# only insert unique points, we'll get their IDs in the point set to
# define element connectivity later
vtkPts.SetData(nps.numpy_to_vtk(np.unique(corner_vertices, axis=0), deep=True))
# create a locator to assist with duplicate points
locator = vtk.vtkPointLocator()
locator.SetDataSet(vtk_grid)
locator.AutomaticOn() # autmoatically adds points to locator
locator.InitPointInsertion(vtkPts, vtkPts.GetBounds())
locator.BuildLocator()
# this function is used to add new points to the unstructured
# grid. It will return an existing point ID if the point is alread present
def _insert_point(pnt):
result = locator.IsInsertedPoint(pnt)
if result == -1:
point_id = vtkPts.InsertNextPoint(pnt)
locator.InsertPoint(point_id, pnt)
return point_id
else:
return result
# Add all points to the unstructured grid, maintaining a flat list of IDs as we go ###
# flat array storing point IDs for a given vertex
# in the grid
point_ids = []
# add element corner vertices to array
for pnt in corner_vertices:
point_ids.append(_insert_point(pnt))
# get edge midpoints and add them to the
# list of point IDs
midpoint_vertices = self.midpoint_vertices
for edge_grid in midpoint_vertices:
for pnt in np.swapaxes(edge_grid, 0, 2).reshape(-1, 3):
point_ids.append(_insert_point(pnt))
# determine how many elements in each dimension
# and how many points in each grid
n_elem = np.asarray(self.dimension)
n_pnts = n_elem + 1
# create hexes and set points for corner
# vertices
for i, j, k in self.indices:
# handle indices indexed from one
i -= 1
j -= 1
k -= 1
# create a new vtk hex
hex = vtk.vtkQuadraticHexahedron()
# set connectivity the hex corners
for n, (di, dj, dk) in enumerate(_HEX_VERTEX_CONN):
# compute flat index into the point ID list based on i, j, k
# of the vertex
flat_idx = np.ravel_multi_index((i+di, j+dj, k+dk), n_pnts, order='F')
# set corner vertices
hex.GetPointIds().SetId(n, point_ids[flat_idx])
# set connectivity of the hex midpoints
n_midpoint_vertices = [v.size // 3 for v in midpoint_vertices]
for n, (dim, (di, dj, dk)) in enumerate(_HEX_MIDPOINT_CONN):
# initial offset for corner vertices and midpoint dimension
flat_idx = corner_vertices.shape[0] + sum(n_midpoint_vertices[:dim])
# generate a flat index into the table of point IDs
midpoint_shape = midpoint_vertices[dim].shape[:-1]
flat_idx += np.ravel_multi_index((i+di, j+dj, k+dk),
midpoint_shape,
order='F')
# set hex midpoint connectivity
hex.GetPointIds().SetId(_N_HEX_VERTICES + n, point_ids[flat_idx])
# add the hex to the grid
vtk_grid.InsertNextCell(hex.GetCellType(), hex.GetPointIds())
return vtk_grid
def _check_vtk_datasets(self, datasets: dict):
"""Perform some basic checks that the datasets are valid for this mesh
Parameters
----------
datasets : dict
Dictionary whose keys are the data labels
and values are the data sets.
"""
for label, dataset in datasets.items():
errmsg = (
f"The size of the dataset '{label}' ({dataset.size}) should be"
f" equal to the number of mesh cells ({self.num_mesh_cells})"
)
if isinstance(dataset, np.ndarray):
if not dataset.size == self.num_mesh_cells:
raise ValueError(errmsg)
else:
if len(dataset) == self.num_mesh_cells:
raise ValueError(errmsg)
cv.check_type('data label', label, str)
[docs]class RegularMesh(StructuredMesh):
"""A regular Cartesian mesh in one, two, or three dimensions
Parameters
----------
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
Attributes
----------
id : int
Unique identifier for the mesh
name : str
Name of the mesh
dimension : Iterable of int
The number of mesh cells in each direction (x, y, z).
n_dimension : int
Number of mesh dimensions.
lower_left : Iterable of float
The lower-left corner of the structured mesh. If only two coordinate
are given, it is assumed that the mesh is an x-y mesh.
upper_right : Iterable of float
The upper-right corner of the structured mesh. If only two coordinate
are given, it is assumed that the mesh is an x-y mesh.
bounding_box : openmc.BoundingBox
Axis-aligned bounding box of the mesh as defined by the upper-right and
lower-left coordinates.
width : Iterable of float
The width of mesh cells in each direction.
indices : Iterable of tuple
An iterable of mesh indices for each mesh element, e.g. [(1, 1, 1),
(2, 1, 1), ...]
"""
def __init__(self, mesh_id: Optional[int] = None, name: str = ''):
super().__init__(mesh_id, name)
self._dimension = None
self._lower_left = None
self._upper_right = None
self._width = None
@property
def dimension(self):
return tuple(self._dimension)
@dimension.setter
def dimension(self, dimension: typing.Iterable[int]):
cv.check_type('mesh dimension', dimension, Iterable, Integral)
cv.check_length('mesh dimension', dimension, 1, 3)
self._dimension = dimension
@property
def n_dimension(self):
if self._dimension is not None:
return len(self._dimension)
else:
return None
@property
def lower_left(self):
return self._lower_left
@lower_left.setter
def lower_left(self, lower_left: typing.Iterable[Real]):
cv.check_type('mesh lower_left', lower_left, Iterable, Real)
cv.check_length('mesh lower_left', lower_left, 1, 3)
self._lower_left = lower_left
if self.upper_right is not None and any(np.isclose(self.upper_right, lower_left)):
raise ValueError("Mesh cannot have zero thickness in any dimension")
@property
def upper_right(self):
if self._upper_right is not None:
return self._upper_right
elif self._width is not None:
if self._lower_left is not None and self._dimension is not None:
ls = self._lower_left
ws = self._width
dims = self._dimension
return [l + w * d for l, w, d in zip(ls, ws, dims)]
@upper_right.setter
def upper_right(self, upper_right: typing.Iterable[Real]):
cv.check_type('mesh upper_right', upper_right, Iterable, Real)
cv.check_length('mesh upper_right', upper_right, 1, 3)
self._upper_right = upper_right
if self._width is not None:
self._width = None
warnings.warn("Unsetting width attribute.")
if self.lower_left is not None and any(np.isclose(self.lower_left, upper_right)):
raise ValueError("Mesh cannot have zero thickness in any dimension")
@property
def width(self):
if self._width is not None:
return self._width
elif self._upper_right is not None:
if self._lower_left is not None and self._dimension is not None:
us = self._upper_right
ls = self._lower_left
dims = self._dimension
return [(u - l) / d for u, l, d in zip(us, ls, dims)]
@width.setter
def width(self, width: typing.Iterable[Real]):
cv.check_type('mesh width', width, Iterable, Real)
cv.check_length('mesh width', width, 1, 3)
self._width = width
if self._upper_right is not None:
self._upper_right = None
warnings.warn("Unsetting upper_right attribute.")
@property
def volumes(self):
"""Return Volumes for every mesh cell
Returns
-------
volumes : numpy.ndarray
Volumes
"""
self._volume_dim_check()
return np.full(self.dimension, np.prod(self.width))
@property
def total_volume(self):
return np.prod(self.dimension) * np.prod(self.width)
@property
def indices(self):
ndim = len(self._dimension)
if ndim == 3:
nx, ny, nz = self.dimension
return ((x, y, z)
for z in range(1, nz + 1)
for y in range(1, ny + 1)
for x in range(1, nx + 1))
elif ndim == 2:
nx, ny = self.dimension
return ((x, y)
for y in range(1, ny + 1)
for x in range(1, nx + 1))
else:
nx, = self.dimension
return ((x,) for x in range(1, nx + 1))
@property
def _grids(self):
ndim = len(self._dimension)
if ndim == 3:
x0, y0, z0 = self.lower_left
x1, y1, z1 = self.upper_right
nx, ny, nz = self.dimension
xarr = np.linspace(x0, x1, nx + 1)
yarr = np.linspace(y0, y1, ny + 1)
zarr = np.linspace(z0, z1, nz + 1)
return (xarr, yarr, zarr)
elif ndim == 2:
x0, y0 = self.lower_left
x1, y1 = self.upper_right
nx, ny = self.dimension
xarr = np.linspace(x0, x1, nx + 1)
yarr = np.linspace(y0, y1, ny + 1)
return (xarr, yarr)
else:
nx, = self.dimension
x0, = self.lower_left
x1, = self.upper_right
return (np.linspace(x0, x1, nx + 1),)
def __repr__(self):
string = super().__repr__()
string += '{0: <16}{1}{2}\n'.format('\tDimensions', '=\t', self.n_dimension)
string += '{0: <16}{1}{2}\n'.format('\tVoxels', '=\t', self._dimension)
string += '{0: <16}{1}{2}\n'.format('\tLower left', '=\t', self._lower_left)
string += '{0: <16}{1}{2}\n'.format('\tUpper Right', '=\t', self._upper_right)
string += '{0: <16}{1}{2}\n'.format('\tWidth', '=\t', self._width)
return string
[docs] @classmethod
def from_hdf5(cls, group: h5py.Group):
mesh_id = int(group.name.split('/')[-1].lstrip('mesh '))
# Read and assign mesh properties
mesh = cls(mesh_id)
mesh.dimension = group['dimension'][()]
mesh.lower_left = group['lower_left'][()]
if 'width' in group:
mesh.width = group['width'][()]
elif 'upper_right' in group:
mesh.upper_right = group['upper_right'][()]
else:
raise IOError('Invalid mesh: must have one of "upper_right" or "width"')
return mesh
[docs] @classmethod
def from_rect_lattice(
cls,
lattice: 'openmc.RectLattice',
division: int = 1,
mesh_id: Optional[int] = None,
name: str = ''
):
"""Create mesh from an existing rectangular lattice
Parameters
----------
lattice : openmc.RectLattice
Rectangular lattice used as a template for this mesh
division : int
Number of mesh cells per lattice cell.
If not specified, there will be 1 mesh cell per lattice cell.
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
Returns
-------
openmc.RegularMesh
RegularMesh instance
"""
cv.check_type('rectangular lattice', lattice, openmc.RectLattice)
shape = np.array(lattice.shape)
width = lattice.pitch*shape
mesh = cls(mesh_id=mesh_id, name=name)
mesh.lower_left = lattice.lower_left
mesh.upper_right = lattice.lower_left + width
mesh.dimension = shape*division
return mesh
[docs] @classmethod
def from_domain(
cls,
domain: typing.Union['openmc.Cell', 'openmc.Region', 'openmc.Universe', 'openmc.Geometry'],
dimension: Sequence[int] = (10, 10, 10),
mesh_id: Optional[int] = None,
name: str = ''
):
"""Create mesh from an existing openmc cell, region, universe or
geometry by making use of the objects bounding box property.
Parameters
----------
domain : {openmc.Cell, openmc.Region, openmc.Universe, openmc.Geometry}
The object passed in will be used as a template for this mesh. The
bounding box of the property of the object passed will be used to
set the lower_left and upper_right and of the mesh instance
dimension : Iterable of int
The number of mesh cells in each direction (x, y, z).
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
Returns
-------
openmc.RegularMesh
RegularMesh instance
"""
cv.check_type(
"domain",
domain,
(openmc.Cell, openmc.Region, openmc.Universe, openmc.Geometry),
)
mesh = cls(mesh_id=mesh_id, name=name)
mesh.lower_left = domain.bounding_box[0]
mesh.upper_right = domain.bounding_box[1]
mesh.dimension = dimension
return mesh
[docs] def to_xml_element(self):
"""Return XML representation of the mesh
Returns
-------
element : lxml.etree._Element
XML element containing mesh data
"""
element = ET.Element("mesh")
element.set("id", str(self._id))
if self._dimension is not None:
subelement = ET.SubElement(element, "dimension")
subelement.text = ' '.join(map(str, self._dimension))
subelement = ET.SubElement(element, "lower_left")
subelement.text = ' '.join(map(str, self._lower_left))
if self._upper_right is not None:
subelement = ET.SubElement(element, "upper_right")
subelement.text = ' '.join(map(str, self._upper_right))
if self._width is not None:
subelement = ET.SubElement(element, "width")
subelement.text = ' '.join(map(str, self._width))
return element
[docs] @classmethod
def from_xml_element(cls, elem: ET.Element):
"""Generate mesh from an XML element
Parameters
----------
elem : lxml.etree._Element
XML element
Returns
-------
openmc.Mesh
Mesh generated from XML element
"""
mesh_id = int(get_text(elem, 'id'))
mesh = cls(mesh_id=mesh_id)
mesh_type = get_text(elem, 'type')
if mesh_type is not None:
mesh.type = mesh_type
dimension = get_text(elem, 'dimension')
if dimension is not None:
mesh.dimension = [int(x) for x in dimension.split()]
lower_left = get_text(elem, 'lower_left')
if lower_left is not None:
mesh.lower_left = [float(x) for x in lower_left.split()]
upper_right = get_text(elem, 'upper_right')
if upper_right is not None:
mesh.upper_right = [float(x) for x in upper_right.split()]
width = get_text(elem, 'width')
if width is not None:
mesh.width = [float(x) for x in width.split()]
return mesh
[docs] def build_cells(self, bc: Optional[str] = None):
"""Generates a lattice of universes with the same dimensionality
as the mesh object. The individual cells/universes produced
will not have material definitions applied and so downstream code
will have to apply that information.
Parameters
----------
bc : iterable of {'reflective', 'periodic', 'transmission', 'vacuum', or 'white'}
Boundary conditions for each of the four faces of a rectangle
(if applying to a 2D mesh) or six faces of a parallelepiped
(if applying to a 3D mesh) provided in the following order:
[x min, x max, y min, y max, z min, z max]. 2-D cells do not
contain the z min and z max entries. Defaults to 'reflective' for
all faces.
Returns
-------
root_cell : openmc.Cell
The cell containing the lattice representing the mesh geometry;
this cell is a single parallelepiped with boundaries matching
the outermost mesh boundary with the boundary conditions from bc
applied.
cells : iterable of openmc.Cell
The list of cells within each lattice position mimicking the mesh
geometry.
"""
if bc is None:
bc = ['reflective'] * 6
if len(bc) not in (4, 6):
raise ValueError('Boundary condition must be of length 4 or 6')
for entry in bc:
cv.check_value('bc', entry, _BOUNDARY_TYPES)
n_dim = self.n_dimension
# Build the cell which will contain the lattice
xplanes = [openmc.XPlane(self.lower_left[0], boundary_type=bc[0]),
openmc.XPlane(self.upper_right[0], boundary_type=bc[1])]
if n_dim == 1:
yplanes = [openmc.YPlane(-1e10, boundary_type='reflective'),
openmc.YPlane(1e10, boundary_type='reflective')]
else:
yplanes = [openmc.YPlane(self.lower_left[1], boundary_type=bc[2]),
openmc.YPlane(self.upper_right[1], boundary_type=bc[3])]
if n_dim <= 2:
# Would prefer to have the z ranges be the max supported float, but
# these values are apparently different between python and Fortran.
# Choosing a safe and sane default.
# Values of +/-1e10 are used here as there seems to be an
# inconsistency between what numpy uses as the max float and what
# Fortran expects for a real(8), so this avoids code complication
# and achieves the same goal.
zplanes = [openmc.ZPlane(-1e10, boundary_type='reflective'),
openmc.ZPlane(1e10, boundary_type='reflective')]
else:
zplanes = [openmc.ZPlane(self.lower_left[2], boundary_type=bc[4]),
openmc.ZPlane(self.upper_right[2], boundary_type=bc[5])]
root_cell = openmc.Cell()
root_cell.region = ((+xplanes[0] & -xplanes[1]) &
(+yplanes[0] & -yplanes[1]) &
(+zplanes[0] & -zplanes[1]))
# Build the universes which will be used for each of the (i,j,k)
# locations within the mesh.
# We will concurrently build cells to assign to these universes
cells = []
universes = []
for _ in self.indices:
cells.append(openmc.Cell())
universes.append(openmc.Universe())
universes[-1].add_cell(cells[-1])
lattice = openmc.RectLattice()
lattice.lower_left = self.lower_left
# Assign the universe and rotate to match the indexing expected for
# the lattice
if n_dim == 1:
universe_array = np.array([universes])
elif n_dim == 2:
universe_array = np.empty(self.dimension[::-1],
dtype=openmc.Universe)
i = 0
for y in range(self.dimension[1] - 1, -1, -1):
for x in range(self.dimension[0]):
universe_array[y][x] = universes[i]
i += 1
else:
universe_array = np.empty(self.dimension[::-1],
dtype=openmc.Universe)
i = 0
for z in range(self.dimension[2]):
for y in range(self.dimension[1] - 1, -1, -1):
for x in range(self.dimension[0]):
universe_array[z][y][x] = universes[i]
i += 1
lattice.universes = universe_array
if self.width is not None:
lattice.pitch = self.width
else:
dx = ((self.upper_right[0] - self.lower_left[0]) /
self.dimension[0])
if n_dim == 1:
lattice.pitch = [dx]
elif n_dim == 2:
dy = ((self.upper_right[1] - self.lower_left[1]) /
self.dimension[1])
lattice.pitch = [dx, dy]
else:
dy = ((self.upper_right[1] - self.lower_left[1]) /
self.dimension[1])
dz = ((self.upper_right[2] - self.lower_left[2]) /
self.dimension[2])
lattice.pitch = [dx, dy, dz]
# Fill Cell with the Lattice
root_cell.fill = lattice
return root_cell, cells
def Mesh(*args, **kwargs):
warnings.warn("Mesh has been renamed RegularMesh. Future versions of "
"OpenMC will not accept the name Mesh.")
return RegularMesh(*args, **kwargs)
[docs]class RectilinearMesh(StructuredMesh):
"""A 3D rectilinear Cartesian mesh
Parameters
----------
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
Attributes
----------
id : int
Unique identifier for the mesh
name : str
Name of the mesh
dimension : Iterable of int
The number of mesh cells in each direction (x, y, z).
n_dimension : int
Number of mesh dimensions (always 3 for a RectilinearMesh).
x_grid : numpy.ndarray
1-D array of mesh boundary points along the x-axis.
y_grid : numpy.ndarray
1-D array of mesh boundary points along the y-axis.
z_grid : numpy.ndarray
1-D array of mesh boundary points along the z-axis.
indices : Iterable of tuple
An iterable of mesh indices for each mesh element, e.g. [(1, 1, 1),
(2, 1, 1), ...]
bounding_box : openmc.BoundingBox
Axis-aligned bounding box of the mesh as defined by the upper-right and
lower-left coordinates.
"""
def __init__(self, mesh_id: int = None, name: str = ''):
super().__init__(mesh_id, name)
self._x_grid = None
self._y_grid = None
self._z_grid = None
@property
def dimension(self):
return (len(self.x_grid) - 1,
len(self.y_grid) - 1,
len(self.z_grid) - 1)
@property
def n_dimension(self):
return 3
@property
def x_grid(self):
return self._x_grid
@x_grid.setter
def x_grid(self, grid):
cv.check_type('mesh x_grid', grid, Iterable, Real)
self._x_grid = np.asarray(grid, dtype=float)
@property
def y_grid(self):
return self._y_grid
@y_grid.setter
def y_grid(self, grid):
cv.check_type('mesh y_grid', grid, Iterable, Real)
self._y_grid = np.asarray(grid, dtype=float)
@property
def z_grid(self):
return self._z_grid
@z_grid.setter
def z_grid(self, grid):
cv.check_type('mesh z_grid', grid, Iterable, Real)
self._z_grid = np.asarray(grid, dtype=float)
@property
def _grids(self):
return (self.x_grid, self.y_grid, self.z_grid)
@property
def lower_left(self):
return np.array([self.x_grid[0], self.y_grid[0], self.z_grid[0]])
@property
def upper_right(self):
return np.array([self.x_grid[-1], self.y_grid[-1], self.z_grid[-1]])
@property
def volumes(self):
"""Return Volumes for every mesh cell
Returns
-------
volumes : numpy.ndarray
Volumes
"""
self._volume_dim_check()
V_x = np.diff(self.x_grid)
V_y = np.diff(self.y_grid)
V_z = np.diff(self.z_grid)
return np.multiply.outer(np.outer(V_x, V_y), V_z)
@property
def total_volume(self):
return np.sum(self.volumes)
@property
def indices(self):
nx = len(self.x_grid) - 1
ny = len(self.y_grid) - 1
nz = len(self.z_grid) - 1
return ((x, y, z)
for z in range(1, nz + 1)
for y in range(1, ny + 1)
for x in range(1, nx + 1))
def __repr__(self):
fmt = '{0: <16}{1}{2}\n'
string = super().__repr__()
string += fmt.format('\tDimensions', '=\t', self.n_dimension)
x_grid_str = str(self._x_grid) if self._x_grid is None else len(self._x_grid)
string += fmt.format('\tN X pnts:', '=\t', x_grid_str)
if self._x_grid is not None:
string += fmt.format('\tX Min:', '=\t', self._x_grid[0])
string += fmt.format('\tX Max:', '=\t', self._x_grid[-1])
y_grid_str = str(self._y_grid) if self._y_grid is None else len(self._y_grid)
string += fmt.format('\tN Y pnts:', '=\t', y_grid_str)
if self._y_grid is not None:
string += fmt.format('\tY Min:', '=\t', self._y_grid[0])
string += fmt.format('\tY Max:', '=\t', self._y_grid[-1])
z_grid_str = str(self._z_grid) if self._z_grid is None else len(self._z_grid)
string += fmt.format('\tN Z pnts:', '=\t', z_grid_str)
if self._z_grid is not None:
string += fmt.format('\tZ Min:', '=\t', self._z_grid[0])
string += fmt.format('\tZ Max:', '=\t', self._z_grid[-1])
return string
[docs] @classmethod
def from_hdf5(cls, group: h5py.Group):
mesh_id = int(group.name.split('/')[-1].lstrip('mesh '))
# Read and assign mesh properties
mesh = cls(mesh_id=mesh_id)
mesh.x_grid = group['x_grid'][()]
mesh.y_grid = group['y_grid'][()]
mesh.z_grid = group['z_grid'][()]
return mesh
[docs] @classmethod
def from_xml_element(cls, elem: ET.Element):
"""Generate a rectilinear mesh from an XML element
Parameters
----------
elem : lxml.etree._Element
XML element
Returns
-------
openmc.RectilinearMesh
Rectilinear mesh object
"""
mesh_id = int(get_text(elem, 'id'))
mesh = cls(mesh_id=mesh_id)
mesh.x_grid = [float(x) for x in get_text(elem, 'x_grid').split()]
mesh.y_grid = [float(y) for y in get_text(elem, 'y_grid').split()]
mesh.z_grid = [float(z) for z in get_text(elem, 'z_grid').split()]
return mesh
[docs] def to_xml_element(self):
"""Return XML representation of the mesh
Returns
-------
element : lxml.etree._Element
XML element containing mesh data
"""
element = ET.Element("mesh")
element.set("id", str(self._id))
element.set("type", "rectilinear")
subelement = ET.SubElement(element, "x_grid")
subelement.text = ' '.join(map(str, self.x_grid))
subelement = ET.SubElement(element, "y_grid")
subelement.text = ' '.join(map(str, self.y_grid))
subelement = ET.SubElement(element, "z_grid")
subelement.text = ' '.join(map(str, self.z_grid))
return element
[docs]class CylindricalMesh(StructuredMesh):
"""A 3D cylindrical mesh
Parameters
----------
r_grid : numpy.ndarray
1-D array of mesh boundary points along the r-axis
Requirement is r >= 0.
z_grid : numpy.ndarray
1-D array of mesh boundary points along the z-axis relative to the
origin.
phi_grid : numpy.ndarray
1-D array of mesh boundary points along the phi-axis in radians.
The default value is [0, 2Ï€], i.e. the full phi range.
origin : numpy.ndarray
1-D array of length 3 the (x,y,z) origin of the mesh in
cartesian coordinates
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
Attributes
----------
id : int
Unique identifier for the mesh
name : str
Name of the mesh
dimension : Iterable of int
The number of mesh cells in each direction (r_grid, phi_grid, z_grid).
n_dimension : int
Number of mesh dimensions (always 3 for a CylindricalMesh).
r_grid : numpy.ndarray
1-D array of mesh boundary points along the r-axis.
Requirement is r >= 0.
phi_grid : numpy.ndarray
1-D array of mesh boundary points along the phi-axis in radians.
The default value is [0, 2Ï€], i.e. the full phi range.
z_grid : numpy.ndarray
1-D array of mesh boundary points along the z-axis relative to the
origin.
origin : numpy.ndarray
1-D array of length 3 the (x,y,z) origin of the mesh in
cartesian coordinates
indices : Iterable of tuple
An iterable of mesh indices for each mesh element, e.g. [(1, 1, 1),
(2, 1, 1), ...]
lower_left : Iterable of float
The lower-left corner of the structured mesh. If only two coordinate
are given, it is assumed that the mesh is an x-y mesh.
upper_right : Iterable of float
The upper-right corner of the structured mesh. If only two coordinate
are given, it is assumed that the mesh is an x-y mesh.
bounding_box : openmc.BoundingBox
Axis-aligned bounding box of the mesh as defined by the upper-right and
lower-left coordinates.
"""
def __init__(
self,
r_grid: Sequence[float],
z_grid: Sequence[float],
phi_grid: Sequence[float] = (0, 2*pi),
origin: Sequence[float] = (0., 0., 0.),
mesh_id: Optional[int] = None,
name: str = '',
):
super().__init__(mesh_id, name)
self.r_grid = r_grid
self.phi_grid = phi_grid
self.z_grid = z_grid
self.origin = origin
@property
def dimension(self):
return (len(self.r_grid) - 1,
len(self.phi_grid) - 1,
len(self.z_grid) - 1)
@property
def n_dimension(self):
return 3
@property
def origin(self):
return self._origin
@origin.setter
def origin(self, coords):
cv.check_type('mesh origin', coords, Iterable, Real)
cv.check_length("mesh origin", coords, 3)
self._origin = np.asarray(coords)
@property
def r_grid(self):
return self._r_grid
@r_grid.setter
def r_grid(self, grid):
cv.check_type('mesh r_grid', grid, Iterable, Real)
self._r_grid = np.asarray(grid, dtype=float)
@property
def phi_grid(self):
return self._phi_grid
@phi_grid.setter
def phi_grid(self, grid):
cv.check_type('mesh phi_grid', grid, Iterable, Real)
self._phi_grid = np.asarray(grid, dtype=float)
@property
def z_grid(self):
return self._z_grid
@z_grid.setter
def z_grid(self, grid):
cv.check_type('mesh z_grid', grid, Iterable, Real)
self._z_grid = np.asarray(grid, dtype=float)
@property
def _grids(self):
return (self.r_grid, self.phi_grid, self.z_grid)
@property
def indices(self):
nr, np, nz = self.dimension
np = len(self.phi_grid) - 1
nz = len(self.z_grid) - 1
return ((r, p, z)
for z in range(1, nz + 1)
for p in range(1, np + 1)
for r in range(1, nr + 1))
@property
def lower_left(self):
return np.array((
self.origin[0] - self.r_grid[-1],
self.origin[1] - self.r_grid[-1],
self.origin[2] + self.z_grid[0]
))
@property
def upper_right(self):
return np.array((
self.origin[0] + self.r_grid[-1],
self.origin[1] + self.r_grid[-1],
self.origin[2] + self.z_grid[-1]
))
def __repr__(self):
fmt = '{0: <16}{1}{2}\n'
string = super().__repr__()
string += fmt.format('\tDimensions', '=\t', self.n_dimension)
string += fmt.format('\tOrigin', '=\t', self.origin)
r_grid_str = str(self._r_grid) if self._r_grid is None else len(self._r_grid)
string += fmt.format('\tN R pnts:', '=\t', r_grid_str)
if self._r_grid is not None:
string += fmt.format('\tR Min:', '=\t', self._r_grid[0])
string += fmt.format('\tR Max:', '=\t', self._r_grid[-1])
phi_grid_str = str(self._phi_grid) if self._phi_grid is None else len(self._phi_grid)
string += fmt.format('\tN Phi pnts:', '=\t', phi_grid_str)
if self._phi_grid is not None:
string += fmt.format('\tPhi Min:', '=\t', self._phi_grid[0])
string += fmt.format('\tPhi Max:', '=\t', self._phi_grid[-1])
z_grid_str = str(self._z_grid) if self._z_grid is None else len(self._z_grid)
string += fmt.format('\tN Z pnts:', '=\t', z_grid_str)
if self._z_grid is not None:
string += fmt.format('\tZ Min:', '=\t', self._z_grid[0])
string += fmt.format('\tZ Max:', '=\t', self._z_grid[-1])
return string
[docs] def get_indices_at_coords(
self,
coords: Sequence[float]
) -> Tuple[int, int, int]:
"""Finds the index of the mesh voxel at the specified x,y,z coordinates.
Parameters
----------
coords : Sequence[float]
The x, y, z axis coordinates
Returns
-------
Tuple[int, int, int]
The r, phi, z indices
"""
r_value_from_origin = sqrt((coords[0]-self.origin[0])**2 + (coords[1]-self.origin[1])**2)
if r_value_from_origin < self.r_grid[0] or r_value_from_origin > self.r_grid[-1]:
raise ValueError(
f'The specified x, y ({coords[0]}, {coords[1]}) combine to give an r value of '
f'{r_value_from_origin} from the origin of {self.origin}.which '
f'is outside the origin absolute r grid values {self.r_grid}.'
)
r_index = np.searchsorted(self.r_grid, r_value_from_origin) - 1
z_grid_values = np.array(self.z_grid) + self.origin[2]
if coords[2] < z_grid_values[0] or coords[2] > z_grid_values[-1]:
raise ValueError(
f'The specified z value ({coords[2]}) from the z origin of '
f'{self.origin[-1]} is outside of the absolute z grid range {z_grid_values}.'
)
z_index = np.argmax(z_grid_values > coords[2]) - 1
delta_x = coords[0] - self.origin[0]
delta_y = coords[1] - self.origin[1]
# atan2 returns values in -pi to +pi range
phi_value = atan2(delta_y, delta_x)
if delta_x < 0 and delta_y < 0:
# returned phi_value anticlockwise and negative
phi_value += 2 * pi
if delta_x > 0 and delta_y < 0:
# returned phi_value anticlockwise and negative
phi_value += 2 * pi
phi_grid_values = np.array(self.phi_grid)
if phi_value < phi_grid_values[0] or phi_value > phi_grid_values[-1]:
raise ValueError(
f'The phi value ({phi_value}) resulting from the specified x, y '
f'values is outside of the absolute phi grid range {phi_grid_values}.'
)
phi_index = np.argmax(phi_grid_values > phi_value) - 1
return (r_index, phi_index, z_index)
[docs] @classmethod
def from_hdf5(cls, group: h5py.Group):
mesh_id = int(group.name.split('/')[-1].lstrip('mesh '))
# Read and assign mesh properties
mesh = cls(
mesh_id=mesh_id,
r_grid = group['r_grid'][()],
phi_grid = group['phi_grid'][()],
z_grid = group['z_grid'][()],
)
if 'origin' in group:
mesh.origin = group['origin'][()]
return mesh
[docs] @classmethod
def from_domain(
cls,
domain: typing.Union['openmc.Cell', 'openmc.Region', 'openmc.Universe', 'openmc.Geometry'],
dimension: Sequence[int] = (10, 10, 10),
mesh_id: Optional[int] = None,
phi_grid_bounds: Sequence[float] = (0.0, 2*pi),
name: str = ''
):
"""Creates a regular CylindricalMesh from an existing openmc domain.
Parameters
----------
domain : openmc.Cell or openmc.Region or openmc.Universe or openmc.Geometry
The object passed in will be used as a template for this mesh. The
bounding box of the property of the object passed will be used to
set the r_grid, z_grid ranges.
dimension : Iterable of int
The number of equally spaced mesh cells in each direction (r_grid,
phi_grid, z_grid)
mesh_id : int
Unique identifier for the mesh
phi_grid_bounds : numpy.ndarray
Mesh bounds points along the phi-axis in radians. The default value
is (0, 2Ï€), i.e., the full phi range.
name : str
Name of the mesh
Returns
-------
openmc.CylindricalMesh
CylindricalMesh instance
"""
cv.check_type(
"domain",
domain,
(openmc.Cell, openmc.Region, openmc.Universe, openmc.Geometry),
)
# loaded once to avoid recalculating bounding box
cached_bb = domain.bounding_box
max_bounding_box_radius = max(
[
cached_bb[0][0],
cached_bb[0][1],
cached_bb[1][0],
cached_bb[1][1],
]
)
r_grid = np.linspace(
0,
max_bounding_box_radius,
num=dimension[0]+1
)
phi_grid = np.linspace(
phi_grid_bounds[0],
phi_grid_bounds[1],
num=dimension[1]+1
)
z_grid = np.linspace(
cached_bb[0][2],
cached_bb[1][2],
num=dimension[2]+1
)
origin = (cached_bb.center[0], cached_bb.center[1], z_grid[0])
# make z-grid relative to the origin
z_grid -= origin[2]
mesh = cls(
r_grid=r_grid,
z_grid=z_grid,
phi_grid=phi_grid,
mesh_id=mesh_id,
name=name,
origin=origin
)
return mesh
[docs] def to_xml_element(self):
"""Return XML representation of the mesh
Returns
-------
element : lxml.etree._Element
XML element containing mesh data
"""
element = ET.Element("mesh")
element.set("id", str(self._id))
element.set("type", "cylindrical")
subelement = ET.SubElement(element, "r_grid")
subelement.text = ' '.join(map(str, self.r_grid))
subelement = ET.SubElement(element, "phi_grid")
subelement.text = ' '.join(map(str, self.phi_grid))
subelement = ET.SubElement(element, "z_grid")
subelement.text = ' '.join(map(str, self.z_grid))
subelement = ET.SubElement(element, "origin")
subelement.text = ' '.join(map(str, self.origin))
return element
[docs] @classmethod
def from_xml_element(cls, elem: ET.Element):
"""Generate a cylindrical mesh from an XML element
Parameters
----------
elem : lxml.etree._Element
XML element
Returns
-------
openmc.CylindricalMesh
Cylindrical mesh object
"""
mesh_id = int(get_text(elem, 'id'))
mesh = cls(
r_grid = [float(x) for x in get_text(elem, "r_grid").split()],
phi_grid = [float(x) for x in get_text(elem, "phi_grid").split()],
z_grid = [float(x) for x in get_text(elem, "z_grid").split()],
origin = [float(x) for x in get_text(elem, "origin", default=[0., 0., 0.]).split()],
mesh_id=mesh_id,
)
return mesh
@property
def volumes(self):
"""Return Volumes for every mesh cell
Returns
-------
volumes : Iterable of float
Volumes
"""
self._volume_dim_check()
V_r = np.diff(np.asarray(self.r_grid)**2 / 2)
V_p = np.diff(self.phi_grid)
V_z = np.diff(self.z_grid)
return np.multiply.outer(np.outer(V_r, V_p), V_z)
@property
def vertices(self):
warnings.warn('Cartesian coordinates are returned from this property as of version 0.14.0')
return self._convert_to_cartesian(self.vertices_cylindrical, self.origin)
@property
def vertices_cylindrical(self):
"""Returns vertices of the mesh in cylindrical coordinates.
"""
return super().vertices
@property
def centroids(self):
warnings.warn('Cartesian coordinates are returned from this property as of version 0.14.0')
return self._convert_to_cartesian(self.centroids_cylindrical, self.origin)
@property
def centroids_cylindrical(self):
"""Returns centroids of the mesh in cylindrical coordinates.
"""
return super().centroids
@staticmethod
def _convert_to_cartesian(arr, origin: Sequence[float]):
"""Converts an array with r, phi, z values in the last dimension (shape (..., 3))
to Cartesian coordinates.
"""
x = arr[..., 0] * np.cos(arr[..., 1]) + origin[0]
y = arr[..., 0] * np.sin(arr[..., 1]) + origin[1]
arr[..., 0] = x
arr[..., 1] = y
arr[..., 2] += origin[2]
return arr
[docs]class SphericalMesh(StructuredMesh):
"""A 3D spherical mesh
Parameters
----------
r_grid : numpy.ndarray
1-D array of mesh boundary points along the r-axis.
Requirement is r >= 0.
phi_grid : numpy.ndarray
1-D array of mesh boundary points along the phi-axis in radians.
The default value is [0, 2Ï€], i.e. the full phi range.
theta_grid : numpy.ndarray
1-D array of mesh boundary points along the theta-axis in radians.
The default value is [0, π], i.e. the full theta range.
origin : numpy.ndarray
1-D array of length 3 the (x,y,z) origin of the mesh in
cartesian coordinates
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
Attributes
----------
id : int
Unique identifier for the mesh
name : str
Name of the mesh
dimension : Iterable of int
The number of mesh cells in each direction (r_grid,
theta_grid, phi_grid).
n_dimension : int
Number of mesh dimensions (always 3 for a SphericalMesh).
r_grid : numpy.ndarray
1-D array of mesh boundary points along the r-axis.
Requirement is r >= 0.
theta_grid : numpy.ndarray
1-D array of mesh boundary points along the theta-axis in radians.
The default value is [0, π], i.e. the full theta range.
phi_grid : numpy.ndarray
1-D array of mesh boundary points along the phi-axis in radians.
The default value is [0, 2Ï€], i.e. the full phi range.
origin : numpy.ndarray
1-D array of length 3 the (x,y,z) origin of the mesh in
cartesian coordinates
indices : Iterable of tuple
An iterable of mesh indices for each mesh element, e.g. [(1, 1, 1),
(2, 1, 1), ...]
lower_left : numpy.ndarray
The lower-left corner of the structured mesh. If only two coordinate
are given, it is assumed that the mesh is an x-y mesh.
upper_right : numpy.ndarray
The upper-right corner of the structured mesh. If only two coordinate
are given, it is assumed that the mesh is an x-y mesh.
bounding_box : openmc.BoundingBox
Axis-aligned bounding box of the mesh as defined by the upper-right and
lower-left coordinates.
"""
def __init__(
self,
r_grid: Sequence[float],
phi_grid: Sequence[float] = (0, 2*pi),
theta_grid: Sequence[float] = (0, pi),
origin: Sequence[float] = (0., 0., 0.),
mesh_id: Optional[int] = None,
name: str = '',
):
super().__init__(mesh_id, name)
self.r_grid = r_grid
self.theta_grid = theta_grid
self.phi_grid = phi_grid
self.origin = origin
@property
def dimension(self):
return (len(self.r_grid) - 1,
len(self.theta_grid) - 1,
len(self.phi_grid) - 1)
@property
def n_dimension(self):
return 3
@property
def origin(self):
return self._origin
@origin.setter
def origin(self, coords):
cv.check_type('mesh origin', coords, Iterable, Real)
cv.check_length("mesh origin", coords, 3)
self._origin = np.asarray(coords, dtype=float)
@property
def r_grid(self):
return self._r_grid
@r_grid.setter
def r_grid(self, grid):
cv.check_type('mesh r_grid', grid, Iterable, Real)
self._r_grid = np.asarray(grid, dtype=float)
@property
def theta_grid(self):
return self._theta_grid
@theta_grid.setter
def theta_grid(self, grid):
cv.check_type('mesh theta_grid', grid, Iterable, Real)
self._theta_grid = np.asarray(grid, dtype=float)
@property
def phi_grid(self):
return self._phi_grid
@phi_grid.setter
def phi_grid(self, grid):
cv.check_type('mesh phi_grid', grid, Iterable, Real)
self._phi_grid = np.asarray(grid, dtype=float)
@property
def _grids(self):
return (self.r_grid, self.theta_grid, self.phi_grid)
@property
def indices(self):
nr, nt, np = self.dimension
nt = len(self.theta_grid) - 1
np = len(self.phi_grid) - 1
return ((r, t, p)
for p in range(1, np + 1)
for t in range(1, nt + 1)
for r in range(1, nr + 1))
@property
def lower_left(self):
r = self.r_grid[-1]
return np.array((self.origin[0] - r, self.origin[1] - r, self.origin[2] - r))
@property
def upper_right(self):
r = self.r_grid[-1]
return np.array((self.origin[0] + r, self.origin[1] + r, self.origin[2] + r))
def __repr__(self):
fmt = '{0: <16}{1}{2}\n'
string = super().__repr__()
string += fmt.format('\tDimensions', '=\t', self.n_dimension)
string += fmt.format('\tOrigin', '=\t', self.origin)
r_grid_str = str(self._r_grid) if self._r_grid is None else len(self._r_grid)
string += fmt.format('\tN R pnts:', '=\t', r_grid_str)
if self._r_grid is not None:
string += fmt.format('\tR Min:', '=\t', self._r_grid[0])
string += fmt.format('\tR Max:', '=\t', self._r_grid[-1])
theta_grid_str = str(self._theta_grid) if self._theta_grid is None else len(self._theta_grid)
string += fmt.format('\tN Theta pnts:', '=\t', theta_grid_str)
if self._theta_grid is not None:
string += fmt.format('\tTheta Min:', '=\t', self._theta_grid[0])
string += fmt.format('\tTheta Max:', '=\t', self._theta_grid[-1])
phi_grid_str = str(self._phi_grid) if self._phi_grid is None else len(self._phi_grid)
string += fmt.format('\tN Phi pnts:', '=\t', phi_grid_str)
if self._phi_grid is not None:
string += fmt.format('\tPhi Min:', '=\t', self._phi_grid[0])
string += fmt.format('\tPhi Max:', '=\t', self._phi_grid[-1])
return string
[docs] @classmethod
def from_hdf5(cls, group: h5py.Group):
mesh_id = int(group.name.split('/')[-1].lstrip('mesh '))
# Read and assign mesh properties
mesh = cls(
r_grid = group['r_grid'][()],
theta_grid = group['theta_grid'][()],
phi_grid = group['phi_grid'][()],
mesh_id=mesh_id,
)
if 'origin' in group:
mesh.origin = group['origin'][()]
return mesh
[docs] def to_xml_element(self):
"""Return XML representation of the mesh
Returns
-------
element : lxml.etree._Element
XML element containing mesh data
"""
element = ET.Element("mesh")
element.set("id", str(self._id))
element.set("type", "spherical")
subelement = ET.SubElement(element, "r_grid")
subelement.text = ' '.join(map(str, self.r_grid))
subelement = ET.SubElement(element, "theta_grid")
subelement.text = ' '.join(map(str, self.theta_grid))
subelement = ET.SubElement(element, "phi_grid")
subelement.text = ' '.join(map(str, self.phi_grid))
subelement = ET.SubElement(element, "origin")
subelement.text = ' '.join(map(str, self.origin))
return element
[docs] @classmethod
def from_xml_element(cls, elem: ET.Element):
"""Generate a spherical mesh from an XML element
Parameters
----------
elem : lxml.etree._Element
XML element
Returns
-------
openmc.SphericalMesh
Spherical mesh object
"""
mesh_id = int(get_text(elem, 'id'))
mesh = cls(
mesh_id=mesh_id,
r_grid = [float(x) for x in get_text(elem, "r_grid").split()],
theta_grid = [float(x) for x in get_text(elem, "theta_grid").split()],
phi_grid = [float(x) for x in get_text(elem, "phi_grid").split()],
origin = [float(x) for x in get_text(elem, "origin", default=[0., 0., 0.]).split()],
)
return mesh
@property
def volumes(self):
"""Return Volumes for every mesh cell
Returns
-------
volumes : Iterable of float
Volumes
"""
self._volume_dim_check()
V_r = np.diff(np.asarray(self.r_grid)**3 / 3)
V_t = np.diff(-np.cos(self.theta_grid))
V_p = np.diff(self.phi_grid)
return np.multiply.outer(np.outer(V_r, V_t), V_p)
@property
def vertices(self):
warnings.warn('Cartesian coordinates are returned from this property as of version 0.14.0')
return self._convert_to_cartesian(self.vertices_spherical, self.origin)
@property
def vertices_spherical(self):
"""Returns vertices of the mesh in cylindrical coordinates.
"""
return super().vertices
@property
def centroids(self):
warnings.warn('Cartesian coordinates are returned from this property as of version 0.14.0')
return self._convert_to_cartesian(self.centroids_spherical, self.origin)
@property
def centroids_spherical(self):
"""Returns centroids of the mesh in cylindrical coordinates.
"""
return super().centroids
@staticmethod
def _convert_to_cartesian(arr, origin: Sequence[float]):
"""Converts an array with r, theta, phi values in the last dimension (shape (..., 3))
to Cartesian coordinates.
"""
r_xy = arr[..., 0] * np.sin(arr[..., 1])
x = r_xy * np.cos(arr[..., 2])
y = r_xy * np.sin(arr[..., 2])
z = arr[..., 0] * np.cos(arr[..., 1])
arr[..., 0] = x + origin[0]
arr[..., 1] = y + origin[1]
arr[..., 2] = z + origin[2]
return arr
def require_statepoint_data(func):
@wraps(func)
def wrapper(self: UnstructuredMesh, *args, **kwargs):
if not self._has_statepoint_data:
raise AttributeError(f'The "{func.__name__}" property requires '
'information about this mesh to be loaded '
'from a statepoint file.')
return func(self, *args, **kwargs)
return wrapper
[docs]class UnstructuredMesh(MeshBase):
"""A 3D unstructured mesh
.. versionadded:: 0.12
.. versionchanged:: 0.12.2
Support for libMesh unstructured meshes was added.
Parameters
----------
filename : str or pathlib.Path
Location of the unstructured mesh file
library : {'moab', 'libmesh'}
Mesh library used for the unstructured mesh tally
mesh_id : int
Unique identifier for the mesh
name : str
Name of the mesh
length_multiplier: float
Constant multiplier to apply to mesh coordinates
Attributes
----------
id : int
Unique identifier for the mesh
name : str
Name of the mesh
filename : str
Name of the file containing the unstructured mesh
length_multiplier: float
Multiplicative factor to apply to mesh coordinates
library : {'moab', 'libmesh'}
Mesh library used for the unstructured mesh tally
output : bool
Indicates whether or not automatic tally output should be generated for
this mesh
volumes : Iterable of float
Volumes of the unstructured mesh elements
centroids : numpy.ndarray
Centroids of the mesh elements with array shape (n_elements, 3)
vertices : numpy.ndarray
Coordinates of the mesh vertices with array shape (n_elements, 3)
.. versionadded:: 0.13.1
connectivity : numpy.ndarray
Connectivity of the elements with array shape (n_elements, 8)
.. versionadded:: 0.13.1
element_types : Iterable of integers
Mesh element types
.. versionadded:: 0.13.1
total_volume : float
Volume of the unstructured mesh in total
bounding_box : openmc.BoundingBox
Axis-aligned bounding box of the mesh as defined by the upper-right and
lower-left coordinates.
"""
_UNSUPPORTED_ELEM = -1
_LINEAR_TET = 0
_LINEAR_HEX = 1
def __init__(self, filename: PathLike, library: str, mesh_id: Optional[int] = None,
name: str = '', length_multiplier: float = 1.0):
super().__init__(mesh_id, name)
self.filename = filename
self._volumes = None
self._n_elements = None
self._conectivity = None
self._vertices = None
self.library = library
self._output = False
self.length_multiplier = length_multiplier
self._has_statepoint_data = False
@property
def filename(self):
return self._filename
@filename.setter
def filename(self, filename):
cv.check_type('Unstructured Mesh filename', filename, (str, Path))
self._filename = filename
@property
def library(self):
return self._library
@library.setter
def library(self, lib: str):
cv.check_value('Unstructured mesh library', lib, ('moab', 'libmesh'))
self._library = lib
@property
@require_statepoint_data
def size(self):
return self._size
@size.setter
def size(self, size: int):
cv.check_type("Unstructured mesh size", size, Integral)
self._size = size
@property
def output(self):
return self._output
@output.setter
def output(self, val: bool):
cv.check_type("Unstructured mesh output value", val, bool)
self._output = val
@property
@require_statepoint_data
def volumes(self):
"""Return Volumes for every mesh cell if
populated by a StatePoint file
Returns
-------
volumes : numpy.ndarray
Volumes
"""
return self._volumes
@volumes.setter
def volumes(self, volumes: typing.Iterable[Real]):
cv.check_type("Unstructured mesh volumes", volumes, Iterable, Real)
self._volumes = volumes
@property
@require_statepoint_data
def total_volume(self):
return np.sum(self.volumes)
@property
@require_statepoint_data
def vertices(self):
return self._vertices
@property
@require_statepoint_data
def connectivity(self):
return self._connectivity
@property
@require_statepoint_data
def element_types(self):
return self._element_types
@property
@require_statepoint_data
def centroids(self):
return np.array([self.centroid(i) for i in range(self.n_elements)])
@property
@require_statepoint_data
def n_elements(self):
if self._n_elements is None:
raise RuntimeError("No information about this mesh has "
"been loaded from a statepoint file.")
return self._n_elements
@n_elements.setter
def n_elements(self, val: int):
cv.check_type('Number of elements', val, Integral)
self._n_elements = val
@property
def length_multiplier(self):
return self._length_multiplier
@length_multiplier.setter
def length_multiplier(self, length_multiplier):
cv.check_type("Unstructured mesh length multiplier",
length_multiplier,
Real)
self._length_multiplier = length_multiplier
@property
def dimension(self):
return (self.n_elements,)
@property
def n_dimension(self):
return 3
@property
@require_statepoint_data
def indices(self):
return [(i,) for i in range(self.n_elements)]
@property
def has_statepoint_data(self) -> bool:
return self._has_statepoint_data
def __repr__(self):
string = super().__repr__()
string += '{: <16}=\t{}\n'.format('\tFilename', self.filename)
string += '{: <16}=\t{}\n'.format('\tMesh Library', self.library)
if self.length_multiplier != 1.0:
string += '{: <16}=\t{}\n'.format('\tLength multiplier',
self.length_multiplier)
return string
@property
@require_statepoint_data
def lower_left(self):
return self.vertices.min(axis=0)
@property
@require_statepoint_data
def upper_right(self):
return self.vertices.max(axis=0)
[docs] @require_statepoint_data
def centroid(self, bin: int):
"""Return the vertex averaged centroid of an element
Parameters
----------
bin : int
Bin ID for the returned centroid
Returns
-------
numpy.ndarray
x, y, z values of the element centroid
"""
conn = self.connectivity[bin]
# remove invalid connectivity values
conn = conn[conn >= 0]
coords = self.vertices[conn]
return coords.mean(axis=0)
[docs] def write_vtk_mesh(self, **kwargs):
"""Map data to unstructured VTK mesh elements.
.. deprecated:: 0.13
Use :func:`UnstructuredMesh.write_data_to_vtk` instead.
Parameters
----------
filename : str or pathlib.Path
Name of the VTK file to write.
datasets : dict
Dictionary whose keys are the data labels
and values are the data sets.
volume_normalization : bool
Whether or not to normalize the data by the
volume of the mesh elements
"""
warnings.warn(
"The 'UnstructuredMesh.write_vtk_mesh' method has been renamed "
"to 'write_data_to_vtk' and will be removed in a future version "
" of OpenMC.", FutureWarning
)
self.write_data_to_vtk(**kwargs)
[docs] def write_data_to_vtk(
self,
filename: Optional[PathLike] = None,
datasets: Optional[dict] = None,
volume_normalization: bool = True
):
"""Map data to unstructured VTK mesh elements.
Parameters
----------
filename : str or pathlib.Path
Name of the VTK file to write
datasets : dict
Dictionary whose keys are the data labels
and values are numpy appropriately sized arrays
of the data
volume_normalization : bool
Whether or not to normalize the data by the
volume of the mesh elements
"""
import vtk
from vtk.util import numpy_support as nps
if self.connectivity is None or self.vertices is None:
raise RuntimeError('This mesh has not been '
'loaded from a statepoint file.')
if filename is None:
filename = f'mesh_{self.id}.vtk'
writer = vtk.vtkUnstructuredGridWriter()
writer.SetFileName(str(filename))
grid = vtk.vtkUnstructuredGrid()
vtk_pnts = vtk.vtkPoints()
vtk_pnts.SetData(nps.numpy_to_vtk(self.vertices))
grid.SetPoints(vtk_pnts)
n_skipped = 0
for elem_type, conn in zip(self.element_types, self.connectivity):
if elem_type == self._LINEAR_TET:
elem = vtk.vtkTetra()
elif elem_type == self._LINEAR_HEX:
elem = vtk.vtkHexahedron()
elif elem_type == self._UNSUPPORTED_ELEM:
n_skipped += 1
else:
raise RuntimeError(f'Invalid element type {elem_type} found')
for i, c in enumerate(conn):
if c == -1:
break
elem.GetPointIds().SetId(i, c)
grid.InsertNextCell(elem.GetCellType(), elem.GetPointIds())
if n_skipped > 0:
warnings.warn(f'{n_skipped} elements were not written because '
'they are not of type linear tet/hex')
# check that datasets are the correct size
datasets_out = []
if datasets is not None:
for name, data in datasets.items():
if data.shape != self.dimension:
raise ValueError(f'Cannot apply dataset "{name}" with '
f'shape {data.shape} to mesh {self.id} '
f'with dimensions {self.dimension}')
if volume_normalization:
for name, data in datasets.items():
if np.issubdtype(data.dtype, np.integer):
warnings.warn(f'Integer data set "{name}" will '
'not be volume-normalized.')
continue
data /= self.volumes
# add data to the mesh
for name, data in datasets.items():
datasets_out.append(data)
arr = vtk.vtkDoubleArray()
arr.SetName(name)
arr.SetNumberOfTuples(data.size)
for i in range(data.size):
arr.SetTuple1(i, data.flat[i])
grid.GetCellData().AddArray(arr)
writer.SetInputData(grid)
writer.Write()
[docs] @classmethod
def from_hdf5(cls, group: h5py.Group):
mesh_id = int(group.name.split('/')[-1].lstrip('mesh '))
filename = group['filename'][()].decode()
library = group['library'][()].decode()
mesh = cls(filename=filename, library=library, mesh_id=mesh_id)
mesh._has_statepoint_data = True
vol_data = group['volumes'][()]
mesh.volumes = np.reshape(vol_data, (vol_data.shape[0],))
mesh.n_elements = mesh.volumes.size
vertices = group['vertices'][()]
mesh._vertices = vertices.reshape((-1, 3))
connectivity = group['connectivity'][()]
mesh._connectivity = connectivity.reshape((-1, 8))
mesh._element_types = group['element_types'][()]
if 'length_multiplier' in group:
mesh.length_multiplier = group['length_multiplier'][()]
return mesh
[docs] def to_xml_element(self):
"""Return XML representation of the mesh
Returns
-------
element : lxml.etree._Element
XML element containing mesh data
"""
element = ET.Element("mesh")
element.set("id", str(self._id))
element.set("type", "unstructured")
element.set("library", self._library)
subelement = ET.SubElement(element, "filename")
subelement.text = str(self.filename)
if self._length_multiplier != 1.0:
element.set("length_multiplier", str(self.length_multiplier))
return element
[docs] @classmethod
def from_xml_element(cls, elem: ET.Element):
"""Generate unstructured mesh object from XML element
Parameters
----------
elem : lxml.etree._Element
XML element
Returns
-------
openmc.UnstructuredMesh
UnstructuredMesh generated from an XML element
"""
mesh_id = int(get_text(elem, 'id'))
filename = get_text(elem, 'filename')
library = get_text(elem, 'library')
length_multiplier = float(get_text(elem, 'length_multiplier', 1.0))
return cls(filename, library, mesh_id, '', length_multiplier)
def _read_meshes(elem):
"""Generate dictionary of meshes from a given XML node
Parameters
----------
elem : lxml.etree._Element
XML element
Returns
-------
dict
A dictionary with mesh IDs as keys and openmc.MeshBase
instanaces as values
"""
out = {}
for mesh_elem in elem.findall('mesh'):
mesh = MeshBase.from_xml_element(mesh_elem)
out[mesh.id] = mesh
return out
# hexahedron element connectivity
# lower-k connectivity offsets
_HEX_VERTEX_CONN = ((0, 0, 0),
(1, 0, 0),
(1, 1, 0),
(0, 1, 0))
# upper-k connectivity offsets
_HEX_VERTEX_CONN += ((0, 0, 1),
(1, 0, 1),
(1, 1, 1),
(0, 1, 1))
_N_HEX_VERTICES = 8
# lower-k connectivity offsets
_HEX_MIDPOINT_CONN = ((0, (0, 0, 0)),
(1, (1, 0, 0)),
(0, (0, 1, 0)),
(1, (0, 0, 0)))
# upper-k connectivity offsets
_HEX_MIDPOINT_CONN += ((0, (0, 0, 1)),
(1, (1, 0, 1)),
(0, (0, 1, 1)),
(1, (0, 0, 1)))
# mid-plane k connectivity
_HEX_MIDPOINT_CONN += ((2, (0, 0, 0)),
(2, (1, 0, 0)),
(2, (1, 1, 0)),
(2, (0, 1, 0)))