from collections import OrderedDict
import copy
import itertools
from numbers import Integral
import os
import numpy as np
import openmc
import openmc.checkvalue as cv
from openmc.mgxs import MGXS
from .mgxs import _DOMAIN_TO_FILTER
# Supported cross section types
MDGXS_TYPES = (
'delayed-nu-fission',
'chi-delayed',
'beta',
'decay-rate',
'delayed-nu-fission matrix'
)
# Maximum number of delayed groups, from src/constants.F90
MAX_DELAYED_GROUPS = 8
[docs]class MDGXS(MGXS):
"""An abstract multi-delayed-group cross section for some energy and delayed
group structures within some spatial domain.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group and multi-delayed-group cross sections for downstream
neutronics calculations.
NOTE: Users should instantiate the subclasses of this abstract class.
Parameters
----------
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
name : str, optional
Name of the multi-group cross section. Used as a label to identify
tallies in OpenMC 'tallies.xml' file.
delayed_groups : list of int, optional
Delayed groups to filter out the xs
num_polar : Integral, optional
Number of equi-width polar angle bins for angle discretization;
defaults to one bin
num_azimuthal : Integral, optional
Number of equi-width azimuthal angle bins for angle discretization;
defaults to one bin
Attributes
----------
name : str, optional
Name of the multi-group cross section
rxn_type : str
Reaction type (e.g., 'chi-delayed', 'beta', etc.)
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
Domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
Domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
Energy group structure for energy condensation
delayed_groups : list of int, optional
Delayed groups to filter out the xs
num_polar : Integral
Number of equi-width polar angle bins for angle discretization
num_azimuthal : Integral
Number of equi-width azimuthal angle bins for angle discretization
tally_trigger : openmc.Trigger
An (optional) tally precision trigger given to each tally used to
compute the cross section
scores : list of str
The scores in each tally used to compute the multi-group cross section
filters : list of openmc.Filter
The filters in each tally used to compute the multi-group cross section
tally_keys : list of str
The keys into the tallies dictionary for each tally used to compute
the multi-group cross section
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
unless the multi-group cross section has been computed.
xs_tally : openmc.Tally
Derived tally for the multi-group cross section. This attribute
is None unless the multi-group cross section has been computed.
num_subdomains : int
The number of subdomains is unity for 'material', 'cell', and 'universe'
domain types. This is equal to the number of cell instances for
'distribcell' domain types (it is equal to unity prior to loading
tally data from a statepoint file) and the number of mesh cells for
'mesh' domain types.
num_nuclides : int
The number of nuclides for which the multi-group cross section is
being tracked. This is unity if the by_nuclide attribute is False.
nuclides : Iterable of str or 'sum'
The optional user-specified nuclides for which to compute cross
sections (e.g., 'U-238', 'O-16'). If by_nuclide is True but nuclides
are not specified by the user, all nuclides in the spatial domain
are included. This attribute is 'sum' if by_nuclide is false.
sparse : bool
Whether or not the MGXS' tallies use SciPy's LIL sparse matrix format
for compressed data storage
loaded_sp : bool
Whether or not a statepoint file has been loaded with tally data
derived : bool
Whether or not the MGXS is merged from one or more other MGXS
hdf5_key : str
The key used to index multi-group cross sections in an HDF5 data store
"""
def __init__(self, domain=None, domain_type=None, energy_groups=None,
delayed_groups=None, by_nuclide=False, name='',
num_polar=1, num_azimuthal=1):
super().__init__(domain, domain_type, energy_groups, by_nuclide, name,
num_polar, num_azimuthal)
self._delayed_groups = None
if delayed_groups is not None:
self.delayed_groups = delayed_groups
def __deepcopy__(self, memo):
existing = memo.get(id(self))
# If this is the first time we have tried to copy this object, copy it
if existing is None:
clone = type(self).__new__(type(self))
clone._name = self.name
clone._rxn_type = self.rxn_type
clone._by_nuclide = self.by_nuclide
clone._nuclides = copy.deepcopy(self._nuclides)
clone._domain = self.domain
clone._domain_type = self.domain_type
clone._energy_groups = copy.deepcopy(self.energy_groups, memo)
clone._delayed_groups = copy.deepcopy(self.delayed_groups, memo)
clone._num_polar = self.num_polar
clone._num_azimuthal = self.num_azimuthal
clone._tally_trigger = copy.deepcopy(self.tally_trigger, memo)
clone._rxn_rate_tally = copy.deepcopy(self._rxn_rate_tally, memo)
clone._xs_tally = copy.deepcopy(self._xs_tally, memo)
clone._sparse = self.sparse
clone._derived = self.derived
clone._tallies = OrderedDict()
for tally_type, tally in self.tallies.items():
clone.tallies[tally_type] = copy.deepcopy(tally, memo)
memo[id(self)] = clone
return clone
# If this object has been copied before, return the first copy made
else:
return existing
@property
def _dont_squeeze(self):
"""Create a tuple of axes which should not be removed during the get_xs
process
"""
if self.num_polar > 1 or self.num_azimuthal > 1:
return (0, 1, 3, 4)
else:
return (1, 2)
@property
def delayed_groups(self):
return self._delayed_groups
@property
def num_delayed_groups(self):
if self.delayed_groups is None:
return 1
else:
return len(self.delayed_groups)
@delayed_groups.setter
def delayed_groups(self, delayed_groups):
if delayed_groups is not None:
cv.check_type('delayed groups', delayed_groups, list, int)
cv.check_greater_than('num delayed groups', len(delayed_groups), 0)
# Check that the groups are within [1, MAX_DELAYED_GROUPS]
for group in delayed_groups:
cv.check_greater_than('delayed group', group, 0)
cv.check_less_than('delayed group', group, MAX_DELAYED_GROUPS,
equality=True)
self._delayed_groups = delayed_groups
@property
def filters(self):
# Create the non-domain specific Filters for the Tallies
group_edges = self.energy_groups.group_edges
energy_filter = openmc.EnergyFilter(group_edges)
if self.delayed_groups != None:
delayed_filter = openmc.DelayedGroupFilter(self.delayed_groups)
filters = [[energy_filter], [delayed_filter, energy_filter]]
else:
filters = [[energy_filter], [energy_filter]]
return self._add_angle_filters(filters)
[docs] @staticmethod
def get_mgxs(mdgxs_type, domain=None, domain_type=None, energy_groups=None,
delayed_groups=None, by_nuclide=False, name='',
num_polar=1, num_azimuthal=1):
"""Return a MDGXS subclass object for some energy group structure within
some spatial domain for some reaction type.
This is a factory method which can be used to quickly create MDGXS
subclass objects for various reaction types.
Parameters
----------
mdgxs_type : {'delayed-nu-fission', 'chi-delayed', 'beta', 'decay-rate', 'delayed-nu-fission matrix'}
The type of multi-delayed-group cross section object to return
domain : openmc.Material or openmc.Cell or openmc.Universe or
openmc.RegularMesh
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain.
Defaults to False
name : str, optional
Name of the multi-group cross section. Used as a label to identify
tallies in OpenMC 'tallies.xml' file. Defaults to the empty string.
delayed_groups : list of int, optional
Delayed groups to filter out the xs
num_polar : Integral, optional
Number of equi-width polar angle bins for angle discretization;
defaults to one bin
num_azimuthal : Integral, optional
Number of equi-width azimuthal angle bins for angle discretization;
defaults to one bin
Returns
-------
openmc.mgxs.MDGXS
A subclass of the abstract MDGXS class for the multi-delayed-group
cross section type requested by the user
"""
cv.check_value('mdgxs_type', mdgxs_type, MDGXS_TYPES)
if mdgxs_type == 'delayed-nu-fission':
mdgxs = DelayedNuFissionXS(domain, domain_type, energy_groups,
delayed_groups)
elif mdgxs_type == 'chi-delayed':
mdgxs = ChiDelayed(domain, domain_type, energy_groups,
delayed_groups)
elif mdgxs_type == 'beta':
mdgxs = Beta(domain, domain_type, energy_groups, delayed_groups)
elif mdgxs_type == 'decay-rate':
mdgxs = DecayRate(domain, domain_type, energy_groups, delayed_groups)
elif mdgxs_type == 'delayed-nu-fission matrix':
mdgxs = DelayedNuFissionMatrixXS(domain, domain_type, energy_groups,
delayed_groups)
mdgxs.by_nuclide = by_nuclide
mdgxs.name = name
mdgxs.num_polar = num_polar
mdgxs.num_azimuthal = num_azimuthal
return mdgxs
[docs] def get_xs(self, groups='all', subdomains='all', nuclides='all',
xs_type='macro', order_groups='increasing',
value='mean', delayed_groups='all', squeeze=True, **kwargs):
"""Returns an array of multi-delayed-group cross sections.
This method constructs a 4D NumPy array for the requested
multi-delayed-group cross section data for one or more
subdomains (1st dimension), delayed groups (2nd demension),
energy groups (3rd dimension), and nuclides (4th dimension).
Parameters
----------
groups : Iterable of Integral or 'all'
Energy groups of interest. Defaults to 'all'.
subdomains : Iterable of Integral or 'all'
Subdomain IDs of interest. Defaults to 'all'.
nuclides : Iterable of str or 'all' or 'sum'
A list of nuclide name strings (e.g., ['U-235', 'U-238']). The
special string 'all' will return the cross sections for all nuclides
in the spatial domain. The special string 'sum' will return the
cross section summed over all nuclides. Defaults to 'all'.
xs_type: {'macro', 'micro'}
Return the macro or micro cross section in units of cm^-1 or barns.
Defaults to 'macro'.
order_groups: {'increasing', 'decreasing'}
Return the cross section indexed according to increasing or
decreasing energy groups (decreasing or increasing energies).
Defaults to 'increasing'.
value : {'mean', 'std_dev', 'rel_err'}
A string for the type of value to return. Defaults to 'mean'.
delayed_groups : list of int or 'all'
Delayed groups of interest. Defaults to 'all'.
squeeze : bool
A boolean representing whether to eliminate the extra dimensions
of the multi-dimensional array to be returned. Defaults to True.
Returns
-------
numpy.ndarray
A NumPy array of the multi-group cross section indexed in the order
each group, subdomain and nuclide as listed in the parameters.
Raises
------
ValueError
When this method is called before the multi-delayed-group cross
section is computed from tally data.
"""
cv.check_value('value', value, ['mean', 'std_dev', 'rel_err'])
cv.check_value('xs_type', xs_type, ['macro', 'micro'])
# FIXME: Unable to get microscopic xs for mesh domain because the mesh
# cells do not know the nuclide densities in each mesh cell.
if self.domain_type == 'mesh' and xs_type == 'micro':
msg = 'Unable to get micro xs for mesh domain since the mesh ' \
'cells do not know the nuclide densities in each mesh cell.'
raise ValueError(msg)
filters = []
filter_bins = []
# Construct a collection of the domain filter bins
if not isinstance(subdomains, str):
cv.check_iterable_type('subdomains', subdomains, Integral,
max_depth=3)
for subdomain in subdomains:
filters.append(_DOMAIN_TO_FILTER[self.domain_type])
filter_bins.append((subdomain,))
# Construct list of energy group bounds tuples for all requested groups
if not isinstance(groups, str):
cv.check_iterable_type('groups', groups, Integral)
for group in groups:
filters.append(openmc.EnergyFilter)
filter_bins.append(
(self.energy_groups.get_group_bounds(group),))
# Construct list of delayed group tuples for all requested groups
if not isinstance(delayed_groups, str):
cv.check_type('delayed groups', delayed_groups, list, int)
for delayed_group in delayed_groups:
filters.append(openmc.DelayedGroupFilter)
filter_bins.append((delayed_group,))
# Construct a collection of the nuclides to retrieve from the xs tally
if self.by_nuclide:
if nuclides == 'all' or nuclides == 'sum' or nuclides == ['sum']:
query_nuclides = self.get_nuclides()
else:
query_nuclides = nuclides
else:
query_nuclides = ['total']
# If user requested the sum for all nuclides, use tally summation
if nuclides == 'sum' or nuclides == ['sum']:
xs_tally = self.xs_tally.summation(nuclides=query_nuclides)
xs = xs_tally.get_values(filters=filters,
filter_bins=filter_bins, value=value)
else:
xs = self.xs_tally.get_values(filters=filters,
filter_bins=filter_bins,
nuclides=query_nuclides, value=value)
# Divide by atom number densities for microscopic cross sections
if xs_type == 'micro' and self._divide_by_density:
if self.by_nuclide:
densities = self.get_nuclide_densities(nuclides)
else:
densities = self.get_nuclide_densities('sum')
if value == 'mean' or value == 'std_dev':
xs /= densities[np.newaxis, :, np.newaxis]
# Eliminate the trivial score dimension
xs = np.squeeze(xs, axis=len(xs.shape) - 1)
xs = np.nan_to_num(xs)
if groups == 'all':
num_groups = self.num_groups
else:
num_groups = len(groups)
if delayed_groups == 'all':
num_delayed_groups = self.num_delayed_groups
else:
num_delayed_groups = len(delayed_groups)
# Reshape tally data array with separate axes for domain,
# energy groups, delayed groups, and nuclides
# Accommodate the polar and azimuthal bins if needed
num_subdomains = \
int(xs.shape[0] / (num_groups * num_delayed_groups *
self.num_polar * self.num_azimuthal))
if self.num_polar > 1 or self.num_azimuthal > 1:
new_shape = (self.num_polar, self.num_azimuthal, num_subdomains,
num_delayed_groups, num_groups)
else:
new_shape = (num_subdomains, num_delayed_groups, num_groups)
new_shape += xs.shape[1:]
xs = np.reshape(xs, new_shape)
# Reverse data if user requested increasing energy groups since
# tally data is stored in order of increasing energies
if order_groups == 'increasing':
xs = xs[..., ::-1, :]
if squeeze:
# We want to squeeze out everything but the polar, azimuthal,
# delayed group, and energy group data.
xs = self._squeeze_xs(xs)
return xs
[docs] def get_slice(self, nuclides=[], groups=[], delayed_groups=[]):
"""Build a sliced MDGXS for the specified nuclides, energy groups,
and delayed groups.
This method constructs a new MDGXS to encapsulate a subset of the data
represented by this MDGXS. The subset of data to include in the tally
slice is determined by the nuclides, energy groups, delayed groups
specified in the input parameters.
Parameters
----------
nuclides : list of str
A list of nuclide name strings
(e.g., ['U-235', 'U-238']; default is [])
groups : list of int
A list of energy group indices starting at 1 for the high energies
(e.g., [1, 2, 3]; default is [])
delayed_groups : list of int
A list of delayed group indices
(e.g., [1, 2, 3]; default is [])
Returns
-------
openmc.mgxs.MDGXS
A new MDGXS object which encapsulates the subset of data requested
for the nuclide(s) and/or energy group(s) and/or delayed group(s)
requested in the parameters.
"""
cv.check_iterable_type('nuclides', nuclides, str)
cv.check_iterable_type('energy_groups', groups, Integral)
cv.check_type('delayed groups', delayed_groups, list, int)
# Build lists of filters and filter bins to slice
filters = []
filter_bins = []
if len(groups) != 0:
energy_bins = []
for group in groups:
group_bounds = self.energy_groups.get_group_bounds(group)
energy_bins.append(group_bounds)
filter_bins.append(tuple(energy_bins))
filters.append(openmc.EnergyFilter)
if len(delayed_groups) != 0:
filter_bins.append(tuple(delayed_groups))
filters.append(openmc.DelayedGroupFilter)
# Clone this MGXS to initialize the sliced version
slice_xs = copy.deepcopy(self)
slice_xs._rxn_rate_tally = None
slice_xs._xs_tally = None
# Slice each of the tallies across nuclides and energy groups
for tally_type, tally in slice_xs.tallies.items():
slice_nuclides = [nuc for nuc in nuclides if nuc in tally.nuclides]
if filters != []:
tally_slice = tally.get_slice(filters=filters,
filter_bins=filter_bins,
nuclides=slice_nuclides)
else:
tally_slice = tally.get_slice(nuclides=slice_nuclides)
slice_xs.tallies[tally_type] = tally_slice
# Assign sliced energy group structure to sliced MDGXS
if groups:
new_group_edges = []
for group in groups:
group_edges = self.energy_groups.get_group_bounds(group)
new_group_edges.extend(group_edges)
new_group_edges = np.unique(new_group_edges)
slice_xs.energy_groups.group_edges = sorted(new_group_edges)
# Assign sliced delayed group structure to sliced MDGXS
if delayed_groups:
slice_xs.delayed_groups = delayed_groups
# Assign sliced nuclides to sliced MGXS
if nuclides:
slice_xs.nuclides = nuclides
slice_xs.sparse = self.sparse
return slice_xs
[docs] def merge(self, other):
"""Merge another MGXS with this one
MGXS are only mergeable if their energy groups and nuclides are either
identical or mutually exclusive. If results have been loaded from a
statepoint, then MGXS are only mergeable along one and only one of
energy groups or nuclides.
Parameters
----------
other : openmc.mgxs.MDGXS
MDGXS to merge with this one
Returns
-------
merged_mdgxs : openmc.mgxs.MDGXS
Merged MDGXS
"""
merged_mdgxs = super().merge(other)
# Merge delayed groups
if self.delayed_groups != other.delayed_groups:
merged_mdgxs.delayed_groups = list(set(self.delayed_groups +
other.delayed_groups))
return merged_mdgxs
[docs] def print_xs(self, subdomains='all', nuclides='all', xs_type='macro'):
"""Print a string representation for the multi-group cross section.
Parameters
----------
subdomains : Iterable of Integral or 'all'
The subdomain IDs of the cross sections to include in the report.
Defaults to 'all'.
nuclides : Iterable of str or 'all' or 'sum'
The nuclides of the cross-sections to include in the report. This
may be a list of nuclide name strings (e.g., ['U-235', 'U-238']).
The special string 'all' will report the cross sections for all
nuclides in the spatial domain. The special string 'sum' will report
the cross sections summed over all nuclides. Defaults to 'all'.
xs_type: {'macro', 'micro'}
Return the macro or micro cross section in units of cm^-1 or barns.
Defaults to 'macro'.
"""
if self.delayed_groups is None:
super().print_xs(subdomains, nuclides, xs_type)
return
# Construct a collection of the subdomains to report
if not isinstance(subdomains, str):
cv.check_iterable_type('subdomains', subdomains, Integral)
elif self.domain_type == 'distribcell':
subdomains = np.arange(self.num_subdomains, dtype=np.int)
elif self.domain_type == 'mesh':
xyz = [range(1, x + 1) for x in self.domain.dimension]
subdomains = list(itertools.product(*xyz))
else:
subdomains = [self.domain.id]
# Construct a collection of the nuclides to report
if self.by_nuclide:
if nuclides == 'all':
nuclides = self.get_nuclides()
elif nuclides == 'sum':
nuclides = ['sum']
else:
cv.check_iterable_type('nuclides', nuclides, str)
else:
nuclides = ['sum']
cv.check_value('xs_type', xs_type, ['macro', 'micro'])
# Build header for string with type and domain info
string = 'Multi-Delayed-Group XS\n'
string += '{0: <16}=\t{1}\n'.format('\tReaction Type', self.rxn_type)
string += '{0: <16}=\t{1}\n'.format('\tDomain Type', self.domain_type)
string += '{0: <16}=\t{1}\n'.format('\tDomain ID', self.domain.id)
# Generate the header for an individual XS
xs_header = '\tCross Sections [{0}]:'.format(self.get_units(xs_type))
# If cross section data has not been computed, only print string header
if self.tallies is None:
print(string)
return
# Set polar/azimuthal bins
if self.num_polar > 1 or self.num_azimuthal > 1:
polar_bins = np.linspace(0., np.pi, num=self.num_polar + 1,
endpoint=True)
azimuthal_bins = np.linspace(-np.pi, np.pi,
num=self.num_azimuthal + 1,
endpoint=True)
# Loop over all subdomains
for subdomain in subdomains:
if self.domain_type == 'distribcell' or self.domain_type == 'mesh':
string += '{0: <16}=\t{1}\n'.format('\tSubdomain', subdomain)
# Loop over all Nuclides
for nuclide in nuclides:
# Build header for nuclide type
if nuclide != 'sum':
string += '{0: <16}=\t{1}\n'.format('\tNuclide', nuclide)
# Add the cross section header
string += '{0: <16}\n'.format(xs_header)
for delayed_group in self.delayed_groups:
template = '{0: <12}Delayed Group {1}:\t'
string += template.format('', delayed_group)
string += '\n'
template = '{0: <12}Group {1} [{2: <10} - {3: <10}eV]:\t'
average_xs = self.get_xs(nuclides=[nuclide],
subdomains=[subdomain],
xs_type=xs_type, value='mean',
delayed_groups=[delayed_group])
rel_err_xs = self.get_xs(nuclides=[nuclide],
subdomains=[subdomain],
xs_type=xs_type, value='rel_err',
delayed_groups=[delayed_group])
rel_err_xs = rel_err_xs * 100.
if self.num_polar > 1 or self.num_azimuthal > 1:
# Loop over polar, azimuthal, and energy group ranges
for pol in range(len(polar_bins) - 1):
pol_low, pol_high = polar_bins[pol: pol + 2]
for azi in range(len(azimuthal_bins) - 1):
azi_low, azi_high = azimuthal_bins[azi: azi + 2]
string += '\t\tPolar Angle: [{0:5f} - {1:5f}]'.format(
pol_low, pol_high) + \
'\tAzimuthal Angle: [{0:5f} - {1:5f}]'.format(
azi_low, azi_high) + '\n'
for group in range(1, self.num_groups + 1):
bounds = \
self.energy_groups.get_group_bounds(group)
string += '\t' + template.format('', group,
bounds[0],
bounds[1])
string += '{0:.2e} +/- {1:.2e}%'.format(
average_xs[pol, azi, group - 1],
rel_err_xs[pol, azi, group - 1])
string += '\n'
string += '\n'
else:
# Loop over energy groups ranges
for group in range(1, self.num_groups+1):
bounds = self.energy_groups.get_group_bounds(group)
string += template.format('', group, bounds[0], bounds[1])
string += '{0:.2e} +/- {1:.2e}%'.format(
average_xs[group - 1], rel_err_xs[group - 1])
string += '\n'
string += '\n'
string += '\n'
print(string)
[docs] def export_xs_data(self, filename='mgxs', directory='mgxs',
format='csv', groups='all', xs_type='macro',
delayed_groups='all'):
"""Export the multi-delayed-group cross section data to a file.
This method leverages the functionality in the Pandas library to export
the multi-group cross section data in a variety of output file formats
for storage and/or post-processing.
Parameters
----------
filename : str
Filename for the exported file. Defaults to 'mgxs'.
directory : str
Directory for the exported file. Defaults to 'mgxs'.
format : {'csv', 'excel', 'pickle', 'latex'}
The format for the exported data file. Defaults to 'csv'.
groups : Iterable of Integral or 'all'
Energy groups of interest. Defaults to 'all'.
xs_type: {'macro', 'micro'}
Store the macro or micro cross section in units of cm^-1 or barns.
Defaults to 'macro'.
delayed_groups : list of int or 'all'
Delayed groups of interest. Defaults to 'all'.
"""
cv.check_type('filename', filename, str)
cv.check_type('directory', directory, str)
cv.check_value('format', format, ['csv', 'excel', 'pickle', 'latex'])
cv.check_value('xs_type', xs_type, ['macro', 'micro'])
# Make directory if it does not exist
if not os.path.exists(directory):
os.makedirs(directory)
filename = os.path.join(directory, filename)
filename = filename.replace(' ', '-')
# Get a Pandas DataFrame for the data
df = self.get_pandas_dataframe(groups=groups, xs_type=xs_type,
delayed_groups=delayed_groups)
# Export the data using Pandas IO API
if format == 'csv':
df.to_csv(filename + '.csv', index=False)
elif format == 'excel':
if self.domain_type == 'mesh':
df.to_excel(filename + '.xls')
else:
df.to_excel(filename + '.xls', index=False)
elif format == 'pickle':
df.to_pickle(filename + '.pkl')
elif format == 'latex':
if self.domain_type == 'distribcell':
msg = 'Unable to export distribcell multi-group cross section' \
'data to a LaTeX table'
raise NotImplementedError(msg)
df.to_latex(filename + '.tex', bold_rows=True,
longtable=True, index=False)
# Surround LaTeX table with code needed to run pdflatex
with open(filename + '.tex','r') as original:
data = original.read()
with open(filename + '.tex','w') as modified:
modified.write(
'\\documentclass[preview, 12pt, border=1mm]{standalone}\n')
modified.write('\\usepackage{caption}\n')
modified.write('\\usepackage{longtable}\n')
modified.write('\\usepackage{booktabs}\n')
modified.write('\\begin{document}\n\n')
modified.write(data)
modified.write('\n\\end{document}')
[docs] def get_pandas_dataframe(self, groups='all', nuclides='all',
xs_type='macro', paths=True,
delayed_groups='all'):
"""Build a Pandas DataFrame for the MDGXS data.
This method leverages :meth:`openmc.Tally.get_pandas_dataframe`, but
renames the columns with terminology appropriate for cross section data.
Parameters
----------
groups : Iterable of Integral or 'all'
Energy groups of interest. Defaults to 'all'.
nuclides : Iterable of str or 'all' or 'sum'
The nuclides of the cross-sections to include in the dataframe. This
may be a list of nuclide name strings (e.g., ['U-235', 'U-238']).
The special string 'all' will include the cross sections for all
nuclides in the spatial domain. The special string 'sum' will
include the cross sections summed over all nuclides. Defaults
to 'all'.
xs_type: {'macro', 'micro'}
Return macro or micro cross section in units of cm^-1 or barns.
Defaults to 'macro'.
paths : bool, optional
Construct columns for distribcell tally filters (default is True).
The geometric information in the Summary object is embedded into
a Multi-index column with a geometric "path" to each distribcell
instance.
delayed_groups : list of int or 'all'
Delayed groups of interest. Defaults to 'all'.
Returns
-------
pandas.DataFrame
A Pandas DataFrame for the cross section data.
Raises
------
ValueError
When this method is called before the multi-delayed-group cross
section is computed from tally data.
"""
if not isinstance(groups, str):
cv.check_iterable_type('groups', groups, Integral)
if nuclides != 'all' and nuclides != 'sum':
cv.check_iterable_type('nuclides', nuclides, str)
if not isinstance(delayed_groups, str):
cv.check_type('delayed groups', delayed_groups, list, int)
cv.check_value('xs_type', xs_type, ['macro', 'micro'])
# Get a Pandas DataFrame from the derived xs tally
if self.by_nuclide and nuclides == 'sum':
# Use tally summation to sum across all nuclides
xs_tally = self.xs_tally.summation(nuclides=self.get_nuclides())
df = xs_tally.get_pandas_dataframe(paths=paths)
# Remove nuclide column since it is homogeneous and redundant
if self.domain_type == 'mesh':
df.drop('sum(nuclide)', axis=1, level=0, inplace=True)
else:
df.drop('sum(nuclide)', axis=1, inplace=True)
# If the user requested a specific set of nuclides
elif self.by_nuclide and nuclides != 'all':
xs_tally = self.xs_tally.get_slice(nuclides=nuclides)
df = xs_tally.get_pandas_dataframe(paths=paths)
# If the user requested all nuclides, keep nuclide column in dataframe
else:
df = self.xs_tally.get_pandas_dataframe(paths=paths)
# Remove the score column since it is homogeneous and redundant
if self.domain_type == 'mesh':
df = df.drop('score', axis=1, level=0)
else:
df = df.drop('score', axis=1)
# Convert azimuthal, polar, energy in and energy out bin values in to
# bin indices
columns = self._df_convert_columns_to_bins(df)
# Select out those groups the user requested
if not isinstance(groups, str):
if 'group in' in df:
df = df[df['group in'].isin(groups)]
if 'group out' in df:
df = df[df['group out'].isin(groups)]
# If user requested micro cross sections, divide out the atom densities
if xs_type == 'micro' and self._divide_by_density:
if self.by_nuclide:
densities = self.get_nuclide_densities(nuclides)
else:
densities = self.get_nuclide_densities('sum')
densities = np.repeat(densities, len(self.rxn_rate_tally.scores))
tile_factor = int(df.shape[0] / len(densities))
df['mean'] /= np.tile(densities, tile_factor)
df['std. dev.'] /= np.tile(densities, tile_factor)
# Sort the dataframe by domain type id (e.g., distribcell id) and
# energy groups such that data is from fast to thermal
if self.domain_type == 'mesh':
mesh_str = 'mesh {0}'.format(self.domain.id)
df.sort_values(by=[(mesh_str, 'x'), (mesh_str, 'y'),
(mesh_str, 'z')] + columns, inplace=True)
else:
df.sort_values(by=[self.domain_type] + columns, inplace=True)
return df
[docs]class ChiDelayed(MDGXS):
r"""The delayed fission spectrum.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group and multi-delayed-group cross sections for multi-group
neutronics calculations. At a minimum, one needs to set the
:attr:`ChiDelayed.energy_groups` and :attr:`ChiDelayed.domain` properties.
Tallies for the flux and appropriate reaction rates over the specified
domain are generated automatically via the :attr:`ChiDelayed.tallies`
property, which can then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross
section can then be obtained from the :attr:`ChiDelayed.xs_tally` property.
For a spatial domain :math:`V`, energy group :math:`[E_g,E_{g-1}]`, and
delayed group :math:`d`, the delayed fission spectrum is calculated as:
.. math::
\begin{aligned}
\langle \nu^d \sigma_{f,g' \rightarrow g} \phi \rangle &= \int_{r \in V}
dr \int_{4\pi} d\Omega' \int_0^\infty dE' \int_{E_g}^{E_{g-1}} dE \;
\chi(E) \nu^d \sigma_f (r, E') \psi(r, E', \Omega')\\
\langle \nu^d \sigma_f \phi \rangle &= \int_{r \in V} dr \int_{4\pi}
d\Omega' \int_0^\infty dE' \int_0^\infty dE \; \chi(E) \nu^d \sigma_f (r,
E') \psi(r, E', \Omega') \\
\chi_g^d &= \frac{\langle \nu^d \sigma_{f,g' \rightarrow g} \phi \rangle}
{\langle \nu^d \sigma_f \phi \rangle}
\end{aligned}
Parameters
----------
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
The domain type for spatial homogenization
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
name : str, optional
Name of the multi-group cross section. Used as a label to identify
tallies in OpenMC 'tallies.xml' file.
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral, optional
Number of equi-width polar angle bins for angle discretization;
defaults to one bin
num_azimuthal : Integral, optional
Number of equi-width azimuthal angle bins for angle discretization;
defaults to one bin
Attributes
----------
name : str, optional
Name of the multi-group cross section
rxn_type : str
Reaction type (e.g., 'total', 'nu-fission', etc.)
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
Domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
Domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
Energy group structure for energy condensation
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral
Number of equi-width polar angle bins for angle discretization
num_azimuthal : Integral
Number of equi-width azimuthal angle bins for angle discretization
tally_trigger : openmc.Trigger
An (optional) tally precision trigger given to each tally used to
compute the cross section
scores : list of str
The scores in each tally used to compute the multi-group cross section
filters : list of openmc.Filter
The filters in each tally used to compute the multi-group cross section
tally_keys : list of str
The keys into the tallies dictionary for each tally used to compute
the multi-group cross section
estimator : 'analog'
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`ChiDelayed.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
unless the multi-group cross section has been computed.
xs_tally : openmc.Tally
Derived tally for the multi-group cross section. This attribute
is None unless the multi-group cross section has been computed.
num_subdomains : int
The number of subdomains is unity for 'material', 'cell' and 'universe'
domain types. This is equal to the number of cell instances
for 'distribcell' domain types (it is equal to unity prior to loading
tally data from a statepoint file).
num_nuclides : int
The number of nuclides for which the multi-group cross section is
being tracked. This is unity if the by_nuclide attribute is False.
nuclides : Iterable of str or 'sum'
The optional user-specified nuclides for which to compute cross
sections (e.g., 'U-238', 'O-16'). If by_nuclide is True but nuclides
are not specified by the user, all nuclides in the spatial domain
are included. This attribute is 'sum' if by_nuclide is false.
sparse : bool
Whether or not the MGXS' tallies use SciPy's LIL sparse matrix format
for compressed data storage
loaded_sp : bool
Whether or not a statepoint file has been loaded with tally data
derived : bool
Whether or not the MGXS is merged from one or more other MGXS
hdf5_key : str
The key used to index multi-group cross sections in an HDF5 data store
"""
# Store whether or not the number density should be removed for microscopic
# values of this data; since this chi data is normalized to 1.0, the
# data should not be divided by the number density
_divide_by_density = False
def __init__(self, domain=None, domain_type=None, energy_groups=None,
delayed_groups=None, by_nuclide=False, name='',
num_polar=1, num_azimuthal=1):
super().__init__(domain, domain_type, energy_groups, delayed_groups,
by_nuclide, name, num_polar, num_azimuthal)
self._rxn_type = 'chi-delayed'
self._estimator = 'analog'
@property
def scores(self):
return ['delayed-nu-fission', 'delayed-nu-fission']
@property
def filters(self):
# Create the non-domain specific Filters for the Tallies
group_edges = self.energy_groups.group_edges
energyout = openmc.EnergyoutFilter(group_edges)
energyin = openmc.EnergyFilter([group_edges[0], group_edges[-1]])
if self.delayed_groups is not None:
delayed_filter = openmc.DelayedGroupFilter(self.delayed_groups)
filters = [[delayed_filter, energyin], [delayed_filter, energyout]]
else:
filters = [[energyin], [energyout]]
return self._add_angle_filters(filters)
@property
def tally_keys(self):
return ['delayed-nu-fission-in', 'delayed-nu-fission-out']
@property
def rxn_rate_tally(self):
if self._rxn_rate_tally is None:
self._rxn_rate_tally = self.tallies['delayed-nu-fission-out']
self._rxn_rate_tally.sparse = self.sparse
return self._rxn_rate_tally
@property
def xs_tally(self):
if self._xs_tally is None:
delayed_nu_fission_in = self.tallies['delayed-nu-fission-in']
# Remove coarse energy filter to keep it out of tally arithmetic
energy_filter = delayed_nu_fission_in.find_filter(
openmc.EnergyFilter)
delayed_nu_fission_in.remove_filter(energy_filter)
# Compute chi
self._xs_tally = self.rxn_rate_tally / delayed_nu_fission_in
super()._compute_xs()
# Add the coarse energy filter back to the nu-fission tally
delayed_nu_fission_in.filters.append(energy_filter)
return self._xs_tally
[docs] def get_homogenized_mgxs(self, other_mgxs):
"""Construct a homogenized MGXS with other MGXS objects.
This method constructs a new MGXS object that is the flux-weighted
combination of two MGXS objects. It is equivalent to what one would
obtain if the tally spatial domain were designed to encompass the
individual domains for both MGXS objects.
Parameters
----------
other_mgxs : openmc.mgxs.MGXS or Iterable of openmc.mgxs.MGXS
The MGXS to homogenize with this one.
Returns
-------
openmc.mgxs.MGXS
A new homogenized MGXS
Raises
------
ValueError
If the other_mgxs is of a different type.
"""
return self._get_homogenized_mgxs(other_mgxs, 'delayed-nu-fission-in')
[docs] def get_slice(self, nuclides=[], groups=[], delayed_groups=[]):
"""Build a sliced ChiDelayed for the specified nuclides and energy
groups.
This method constructs a new MGXS to encapsulate a subset of the data
represented by this MGXS. The subset of data to include in the tally
slice is determined by the nuclides and energy groups specified in
the input parameters.
Parameters
----------
nuclides : list of str
A list of nuclide name strings
(e.g., ['U-235', 'U-238']; default is [])
groups : list of Integral
A list of energy group indices starting at 1 for the high energies
(e.g., [1, 2, 3]; default is [])
delayed_groups : list of int
A list of delayed group indices
(e.g., [1, 2, 3]; default is [])
Returns
-------
openmc.mgxs.MDGXS
A new MDGXS which encapsulates the subset of data requested
for the nuclide(s) and/or energy group(s) and/or delayed group(s)
requested in the parameters.
"""
# Temporarily remove energy filter from delayed-nu-fission-in since its
# group structure will work in super MGXS.get_slice(...) method
delayed_nu_fission_in = self.tallies['delayed-nu-fission-in']
energy_filter = delayed_nu_fission_in.find_filter(openmc.EnergyFilter)
delayed_nu_fission_in.remove_filter(energy_filter)
# Call super class method and null out derived tallies
slice_xs = super().get_slice(nuclides, groups, delayed_groups)
slice_xs._rxn_rate_tally = None
slice_xs._xs_tally = None
# Slice energy groups if needed
filters = []
filter_bins = []
if len(groups) != 0:
energy_bins = []
for group in groups:
group_bounds = self.energy_groups.get_group_bounds(group)
energy_bins.append(group_bounds)
filter_bins.append(tuple(energy_bins))
filters.append(openmc.EnergyoutFilter)
if len(delayed_groups) != 0:
filter_bins.append(tuple(delayed_groups))
filters.append(openmc.DelayedGroupFilter)
if filters != []:
# Slice nu-fission-out tally along energyout filter
delayed_nu_fission_out = slice_xs.tallies['delayed-nu-fission-out']
tally_slice = delayed_nu_fission_out.get_slice \
(filters=filters, filter_bins=filter_bins)
slice_xs._tallies['delayed-nu-fission-out'] = tally_slice
# Add energy filter back to nu-fission-in tallies
self.tallies['delayed-nu-fission-in'].add_filter(energy_filter)
slice_xs._tallies['delayed-nu-fission-in'].add_filter(energy_filter)
slice_xs.sparse = self.sparse
return slice_xs
[docs] def merge(self, other):
"""Merge another ChiDelayed with this one
If results have been loaded from a statepoint, then ChiDelayed are only
mergeable along one and only one of energy groups or nuclides.
Parameters
----------
other : openmc.mdgxs.MGXS
MGXS to merge with this one
Returns
-------
merged_mdgxs : openmc.mgxs.MDGXS
Merged MDGXS
"""
if not self.can_merge(other):
raise ValueError('Unable to merge ChiDelayed')
# Create deep copy of tally to return as merged tally
merged_mdgxs = copy.deepcopy(self)
merged_mdgxs._derived = True
merged_mdgxs._rxn_rate_tally = None
merged_mdgxs._xs_tally = None
# Merge energy groups
if self.energy_groups != other.energy_groups:
merged_groups = self.energy_groups.merge(other.energy_groups)
merged_mdgxs.energy_groups = merged_groups
# Merge delayed groups
if self.delayed_groups != other.delayed_groups:
merged_mdgxs.delayed_groups = list(set(self.delayed_groups +
other.delayed_groups))
# Merge nuclides
if self.nuclides != other.nuclides:
# The nuclides must be mutually exclusive
for nuclide in self.nuclides:
if nuclide in other.nuclides:
msg = 'Unable to merge Chi Delayed with shared nuclides'
raise ValueError(msg)
# Concatenate lists of nuclides for the merged MGXS
merged_mdgxs.nuclides = self.nuclides + other.nuclides
# Merge tallies
for tally_key in self.tallies:
merged_tally = self.tallies[tally_key].merge\
(other.tallies[tally_key])
merged_mdgxs.tallies[tally_key] = merged_tally
return merged_mdgxs
[docs] def get_xs(self, groups='all', subdomains='all', nuclides='all',
xs_type='macro', order_groups='increasing',
value='mean', delayed_groups='all', squeeze=True, **kwargs):
"""Returns an array of the delayed fission spectrum.
This method constructs a 4D NumPy array for the requested
multi-delayed-group cross section data for one or more
subdomains (1st dimension), delayed groups (2nd demension),
energy groups (3rd dimension), and nuclides (4th dimension).
Parameters
----------
groups : Iterable of Integral or 'all'
Energy groups of interest. Defaults to 'all'.
delayed_groups : list of int or 'all'
Delayed groups of interest. Defaults to 'all'.
subdomains : Iterable of Integral or 'all'
Subdomain IDs of interest. Defaults to 'all'.
nuclides : Iterable of str or 'all' or 'sum'
A list of nuclide name strings (e.g., ['U-235', 'U-238']). The
special string 'all' will return the cross sections for all nuclides
in the spatial domain. The special string 'sum' will return the
cross section summed over all nuclides. Defaults to 'all'.
xs_type: {'macro', 'micro'}
This parameter is not relevant for chi but is included here to
mirror the parent MGXS.get_xs(...) class method
order_groups: {'increasing', 'decreasing'}
Return the cross section indexed according to increasing or
decreasing energy groups (decreasing or increasing energies).
Defaults to 'increasing'.
value : {'mean', 'std_dev', 'rel_err'}
A string for the type of value to return. Defaults to 'mean'.
squeeze : bool
A boolean representing whether to eliminate the extra dimensions
of the multi-dimensional array to be returned. Defaults to True.
Returns
-------
numpy.ndarray
A NumPy array of the multi-group and multi-delayed-group cross
section indexed in the order each group, subdomain and nuclide is
listed in the parameters.
Raises
------
ValueError
When this method is called before the multi-group cross section is
computed from tally data.
"""
cv.check_value('value', value, ['mean', 'std_dev', 'rel_err'])
cv.check_value('xs_type', xs_type, ['macro', 'micro'])
# FIXME: Unable to get microscopic xs for mesh domain because the mesh
# cells do not know the nuclide densities in each mesh cell.
if self.domain_type == 'mesh' and xs_type == 'micro':
msg = 'Unable to get micro xs for mesh domain since the mesh ' \
'cells do not know the nuclide densities in each mesh cell.'
raise ValueError(msg)
filters = []
filter_bins = []
# Construct a collection of the domain filter bins
if not isinstance(subdomains, str):
cv.check_iterable_type('subdomains', subdomains, Integral,
max_depth=3)
for subdomain in subdomains:
filters.append(_DOMAIN_TO_FILTER[self.domain_type])
filter_bins.append((subdomain,))
# Construct list of energy group bounds tuples for all requested groups
if not isinstance(groups, str):
cv.check_iterable_type('groups', groups, Integral)
for group in groups:
filters.append(openmc.EnergyoutFilter)
filter_bins.append(
(self.energy_groups.get_group_bounds(group),))
# Construct list of delayed group tuples for all requested groups
if not isinstance(delayed_groups, str):
cv.check_type('delayed groups', delayed_groups, list, int)
for delayed_group in delayed_groups:
filters.append(openmc.DelayedGroupFilter)
filter_bins.append((delayed_group,))
# If chi delayed was computed for each nuclide in the domain
if self.by_nuclide:
# Get the sum as the fission source weighted average chi for all
# nuclides in the domain
if nuclides == 'sum' or nuclides == ['sum']:
# Retrieve the fission production tallies
delayed_nu_fission_in = self.tallies['delayed-nu-fission-in']
delayed_nu_fission_out = self.tallies['delayed-nu-fission-out']
# Sum out all nuclides
nuclides = self.get_nuclides()
delayed_nu_fission_in = delayed_nu_fission_in.summation(
nuclides=nuclides)
delayed_nu_fission_out = delayed_nu_fission_out.summation(
nuclides=nuclides)
# Remove coarse energy filter to keep it out of tally arithmetic
energy_filter = delayed_nu_fission_in.find_filter(
openmc.EnergyFilter)
delayed_nu_fission_in.remove_filter(energy_filter)
# Compute chi and store it as the xs_tally attribute so we can
# use the generic get_xs(...) method
xs_tally = delayed_nu_fission_out / delayed_nu_fission_in
# Add the coarse energy filter back to the nu-fission tally
delayed_nu_fission_in.filters.append(energy_filter)
xs = xs_tally.get_values(filters=filters,
filter_bins=filter_bins, value=value)
# Get chi delayed for all nuclides in the domain
elif nuclides == 'all':
nuclides = self.get_nuclides()
xs = self.xs_tally.get_values(filters=filters,
filter_bins=filter_bins,
nuclides=nuclides, value=value)
# Get chi delayed for user-specified nuclides in the domain
else:
cv.check_iterable_type('nuclides', nuclides, str)
xs = self.xs_tally.get_values(filters=filters,
filter_bins=filter_bins,
nuclides=nuclides, value=value)
# If chi delayed was computed as an average of nuclides in the domain
else:
xs = self.xs_tally.get_values(filters=filters,
filter_bins=filter_bins, value=value)
# Eliminate the trivial score dimension
xs = np.squeeze(xs, axis=len(xs.shape) - 1)
xs = np.nan_to_num(xs)
# Reshape tally data array with separate axes for domain and energy
if groups == 'all':
num_groups = self.num_groups
else:
num_groups = len(groups)
if delayed_groups == 'all':
num_delayed_groups = self.num_delayed_groups
else:
num_delayed_groups = len(delayed_groups)
# Reshape tally data array with separate axes for domain, energy
# groups, and accomodate the polar and azimuthal bins if needed
num_subdomains = int(xs.shape[0] / (num_delayed_groups *
num_groups * self.num_polar *
self.num_azimuthal))
if self.num_polar > 1 or self.num_azimuthal > 1:
new_shape = (self.num_polar, self.num_azimuthal, num_subdomains,
num_delayed_groups, num_groups)
else:
new_shape = (num_subdomains, num_delayed_groups, num_groups)
new_shape += xs.shape[1:]
xs = np.reshape(xs, new_shape)
# Reverse data if user requested increasing energy groups since
# tally data is stored in order of increasing energies
if order_groups == 'increasing':
xs = xs[..., ::-1, :]
if squeeze:
# We want to squeeze out everything but the polar, azimuthal,
# and energy group data.
xs = self._squeeze_xs(xs)
return xs
[docs]class DelayedNuFissionXS(MDGXS):
r"""A fission delayed neutron production multi-group cross section.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group fission neutron production cross sections for multi-group
neutronics calculations. At a minimum, one needs to set the
:attr:`DelayedNuFissionXS.energy_groups` and :attr:`DelayedNuFissionXS.domain`
properties. Tallies for the flux and appropriate reaction rates over the
specified domain are generated automatically via the
:attr:`DelayedNuFissionXS.tallies` property, which can then be appended to a
:class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`DelayedNuFissionXS.xs_tally` property.
For a spatial domain :math:`V`, energy group :math:`[E_g,E_{g-1}]`, and
delayed group :math:`d`, the fission delayed neutron production cross
section is calculated as:
.. math::
\frac{\int_{r \in V} dr \int_{4\pi} d\Omega \int_{E_g}^{E_{g-1}} dE \;
\nu^d \sigma_f (r, E) \psi (r, E, \Omega)}{\int_{r \in V} dr \int_{4\pi}
d\Omega \int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega)}.
Parameters
----------
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
The domain type for spatial homogenization
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
name : str, optional
Name of the multi-group cross section. Used as a label to identify
tallies in OpenMC 'tallies.xml' file.
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral, optional
Number of equi-width polar angle bins for angle discretization;
defaults to one bin
num_azimuthal : Integral, optional
Number of equi-width azimuthal angle bins for angle discretization;
defaults to one bin
Attributes
----------
name : str, optional
Name of the multi-group cross section
rxn_type : str
Reaction type (e.g., 'total', 'nu-fission', etc.)
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
Domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
Domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
Energy group structure for energy condensation
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral
Number of equi-width polar angle bins for angle discretization
num_azimuthal : Integral
Number of equi-width azimuthal angle bins for angle discretization
tally_trigger : openmc.Trigger
An (optional) tally precision trigger given to each tally used to
compute the cross section
scores : list of str
The scores in each tally used to compute the multi-group cross section
filters : list of openmc.Filter
The filters in each tally used to compute the multi-group cross section
tally_keys : list of str
The keys into the tallies dictionary for each tally used to compute
the multi-group cross section
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`DelayedNuFissionXS.tally_keys` property
and values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
unless the multi-group cross section has been computed.
xs_tally : openmc.Tally
Derived tally for the multi-group cross section. This attribute
is None unless the multi-group cross section has been computed.
num_subdomains : int
The number of subdomains is unity for 'material', 'cell' and 'universe'
domain types. This is equal to the number of cell instances
for 'distribcell' domain types (it is equal to unity prior to loading
tally data from a statepoint file).
num_nuclides : int
The number of nuclides for which the multi-group cross section is
being tracked. This is unity if the by_nuclide attribute is False.
nuclides : Iterable of str or 'sum'
The optional user-specified nuclides for which to compute cross
sections (e.g., 'U-238', 'O-16'). If by_nuclide is True but nuclides
are not specified by the user, all nuclides in the spatial domain
are included. This attribute is 'sum' if by_nuclide is false.
sparse : bool
Whether or not the MGXS' tallies use SciPy's LIL sparse matrix format
for compressed data storage
loaded_sp : bool
Whether or not a statepoint file has been loaded with tally data
derived : bool
Whether or not the MGXS is merged from one or more other MGXS
hdf5_key : str
The key used to index multi-group cross sections in an HDF5 data store
"""
def __init__(self, domain=None, domain_type=None, energy_groups=None,
delayed_groups=None, by_nuclide=False, name='',
num_polar=1, num_azimuthal=1):
super().__init__(domain, domain_type, energy_groups, delayed_groups,
by_nuclide, name, num_polar, num_azimuthal)
self._rxn_type = 'delayed-nu-fission'
[docs]class Beta(MDGXS):
r"""The delayed neutron fraction.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group and multi-delayed group cross sections for multi-group
neutronics calculations. At a minimum, one needs to set the
:attr:`Beta.energy_groups` and :attr:`Beta.domain` properties. Tallies for
the flux and appropriate reaction rates over the specified domain are
generated automatically via the :attr:`Beta.tallies` property, which can
then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`Beta.xs_tally` property.
For a spatial domain :math:`V`, energy group :math:`[E_g,E_{g-1}]`, and
delayed group :math:`d`, the delayed neutron fraction is calculated as:
.. math::
\begin{aligned}
\langle \nu^d \sigma_f \phi \rangle &= \int_{r \in V} dr \int_{4\pi}
d\Omega' \int_0^\infty dE' \int_0^\infty dE \; \chi(E) \nu^d
\sigma_f (r, E') \psi(r, E', \Omega') \\
\langle \nu \sigma_f \phi \rangle &= \int_{r \in V} dr \int_{4\pi}
d\Omega' \int_0^\infty dE' \int_0^\infty dE \; \chi(E) \nu
\sigma_f (r, E') \psi(r, E', \Omega') \\
\beta_{d,g} &= \frac{\langle \nu^d \sigma_f \phi \rangle}
{\langle \nu \sigma_f \phi \rangle}
\end{aligned}
NOTE: The Beta MGXS is the delayed neutron fraction computed directly from
the nuclear data. Often the delayed neutron fraction is
"importance-weighted" by the adjoint flux and called "beta-effective". It
is important to make clear that this Beta is not importance-weighted.
Parameters
----------
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
The domain type for spatial homogenization
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
name : str, optional
Name of the multi-group cross section. Used as a label to identify
tallies in OpenMC 'tallies.xml' file.
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral, optional
Number of equi-width polar angle bins for angle discretization;
defaults to one bin
num_azimuthal : Integral, optional
Number of equi-width azimuthal angle bins for angle discretization;
defaults to one bin
Attributes
----------
name : str, optional
Name of the multi-group cross section
rxn_type : str
Reaction type (e.g., 'total', 'nu-fission', etc.)
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
Domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
Domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
Energy group structure for energy condensation
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral
Number of equi-width polar angle bins for angle discretization
num_azimuthal : Integral
Number of equi-width azimuthal angle bins for angle discretization
tally_trigger : openmc.Trigger
An (optional) tally precision trigger given to each tally used to
compute the cross section
scores : list of str
The scores in each tally used to compute the multi-group cross section
filters : list of openmc.Filter
The filters in each tally used to compute the multi-group cross section
tally_keys : list of str
The keys into the tallies dictionary for each tally used to compute
the multi-group cross section
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`Beta.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
unless the multi-group cross section has been computed.
xs_tally : openmc.Tally
Derived tally for the multi-group cross section. This attribute
is None unless the multi-group cross section has been computed.
num_subdomains : int
The number of subdomains is unity for 'material', 'cell' and 'universe'
domain types. This is equal to the number of cell instances
for 'distribcell' domain types (it is equal to unity prior to loading
tally data from a statepoint file).
num_nuclides : int
The number of nuclides for which the multi-group cross section is
being tracked. This is unity if the by_nuclide attribute is False.
nuclides : Iterable of str or 'sum'
The optional user-specified nuclides for which to compute cross
sections (e.g., 'U-238', 'O-16'). If by_nuclide is True but nuclides
are not specified by the user, all nuclides in the spatial domain
are included. This attribute is 'sum' if by_nuclide is false.
sparse : bool
Whether or not the MGXS' tallies use SciPy's LIL sparse matrix format
for compressed data storage
loaded_sp : bool
Whether or not a statepoint file has been loaded with tally data
derived : bool
Whether or not the MGXS is merged from one or more other MGXS
hdf5_key : str
The key used to index multi-group cross sections in an HDF5 data store
"""
# Store whether or not the number density should be removed for microscopic
# values of this data; since the beta is not a microscopic or macroscopic
# quantity, it should not be divided by the number density
_divide_by_density = False
def __init__(self, domain=None, domain_type=None, energy_groups=None,
delayed_groups=None, by_nuclide=False, name='',
num_polar=1, num_azimuthal=1):
super().__init__(domain, domain_type, energy_groups, delayed_groups,
by_nuclide, name, num_polar, num_azimuthal)
self._rxn_type = 'beta'
@property
def scores(self):
return ['nu-fission', 'delayed-nu-fission']
@property
def tally_keys(self):
return ['nu-fission', 'delayed-nu-fission']
@property
def rxn_rate_tally(self):
if self._rxn_rate_tally is None:
self._rxn_rate_tally = self.tallies['delayed-nu-fission']
self._rxn_rate_tally.sparse = self.sparse
return self._rxn_rate_tally
@property
def xs_tally(self):
if self._xs_tally is None:
nu_fission = self.tallies['nu-fission']
# Compute beta
self._xs_tally = self.rxn_rate_tally / nu_fission
super()._compute_xs()
return self._xs_tally
[docs] def get_homogenized_mgxs(self, other_mgxs):
"""Construct a homogenized MGXS with other MGXS objects.
This method constructs a new MGXS object that is the flux-weighted
combination of two MGXS objects. It is equivalent to what one would
obtain if the tally spatial domain were designed to encompass the
individual domains for both MGXS objects.
Parameters
----------
other_mgxs : openmc.mgxs.MGXS or Iterable of openmc.mgxs.MGXS
The MGXS to homogenize with this one.
Returns
-------
openmc.mgxs.MGXS
A new homogenized MGXS
Raises
------
ValueError
If the other_mgxs is of a different type.
"""
return self._get_homogenized_mgxs(other_mgxs, 'nu-fission')
[docs]class DecayRate(MDGXS):
r"""The decay rate for delayed neutron precursors.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group and multi-delayed group cross sections for multi-group
neutronics calculations. At a minimum, one needs to set the
:attr:`DecayRate.energy_groups` and :attr:`DecayRate.domain` properties.
Tallies for the flux and appropriate reaction rates over the specified
domain are generated automatically via the :attr:`DecayRate.tallies`
property, which can then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`DecayRate.xs_tally` property.
For a spatial domain :math:`V`, energy group :math:`[E_g,E_{g-1}]`, and
delayed group :math:`d`, the decay rate is calculated as:
.. math::
\begin{aligned}
\langle \lambda_d \nu^d \sigma_f \phi \rangle &= \int_{r \in V} dr
\int_{4\pi} d\Omega' \int_0^\infty dE' \int_0^\infty dE \; \lambda_d \nu^d
\sigma_f (r, E') \psi(r, E', \Omega') \\
\langle \nu^d \sigma_f \phi \rangle &= \int_{r \in V} dr \int_{4\pi}
d\Omega' \int_0^\infty dE' \int_0^\infty dE \; \chi(E) \nu^d
\sigma_f (r, E') \psi(r, E', \Omega') \\
\lambda_d &= \frac{\langle \lambda_d \nu^d \sigma_f \phi \rangle}
{\langle \nu^d \sigma_f \phi \rangle}
\end{aligned}
Parameters
----------
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
The domain type for spatial homogenization
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
name : str, optional
Name of the multi-group cross section. Used as a label to identify
tallies in OpenMC 'tallies.xml' file.
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral, optional
Number of equi-width polar angle bins for angle discretization;
defaults to one bin
num_azimuthal : Integral, optional
Number of equi-width azimuthal angle bins for angle discretization;
defaults to one bin
Attributes
----------
name : str, optional
Name of the multi-group cross section
rxn_type : str
Reaction type (e.g., 'total', 'nu-fission', etc.)
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
Domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
Domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
Energy group structure for energy condensation
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral
Number of equi-width polar angle bins for angle discretization
num_azimuthal : Integral
Number of equi-width azimuthal angle bins for angle discretization
tally_trigger : openmc.Trigger
An (optional) tally precision trigger given to each tally used to
compute the cross section
scores : list of str
The scores in each tally used to compute the multi-group cross section
filters : list of openmc.Filter
The filters in each tally used to compute the multi-group cross section
tally_keys : list of str
The keys into the tallies dictionary for each tally used to compute
the multi-group cross section
estimator : {'tracklength', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`DecayRate.tally_keys` property and
values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
unless the multi-group cross section has been computed.
xs_tally : openmc.Tally
Derived tally for the multi-group cross section. This attribute
is None unless the multi-group cross section has been computed.
num_subdomains : int
The number of subdomains is unity for 'material', 'cell' and 'universe'
domain types. This is equal to the number of cell instances
for 'distribcell' domain types (it is equal to unity prior to loading
tally data from a statepoint file).
num_nuclides : int
The number of nuclides for which the multi-group cross section is
being tracked. This is unity if the by_nuclide attribute is False.
nuclides : Iterable of str or 'sum'
The optional user-specified nuclides for which to compute cross
sections (e.g., 'U-238', 'O-16'). If by_nuclide is True but nuclides
are not specified by the user, all nuclides in the spatial domain
are included. This attribute is 'sum' if by_nuclide is false.
sparse : bool
Whether or not the MGXS' tallies use SciPy's LIL sparse matrix format
for compressed data storage
loaded_sp : bool
Whether or not a statepoint file has been loaded with tally data
derived : bool
Whether or not the MGXS is merged from one or more other MGXS
hdf5_key : str
The key used to index multi-group cross sections in an HDF5 data store
"""
# Store whether or not the number density should be removed for microscopic
# values of this data; since the decay rates are not microscopic or
# macroscopic quantities, it should not be divided by the number density.
_divide_by_density = False
def __init__(self, domain=None, domain_type=None, energy_groups=None,
delayed_groups=None, by_nuclide=False, name='',
num_polar=1, num_azimuthal=1):
super().__init__(domain, domain_type, energy_groups, delayed_groups,
by_nuclide, name, num_polar, num_azimuthal)
self._rxn_type = 'decay-rate'
@property
def scores(self):
return ['delayed-nu-fission', 'decay-rate']
@property
def tally_keys(self):
return ['delayed-nu-fission', 'decay-rate']
@property
def filters(self):
# Create the non-domain specific Filters for the Tallies
group_edges = self.energy_groups.group_edges
if self.delayed_groups is not None:
delayed_filter = openmc.DelayedGroupFilter(self.delayed_groups)
filters = [[delayed_filter], [delayed_filter]]
else:
filters = None
return self._add_angle_filters(filters)
@property
def xs_tally(self):
if self._xs_tally is None:
delayed_nu_fission = self.tallies['delayed-nu-fission']
# Compute the decay rate
self._xs_tally = self.rxn_rate_tally / delayed_nu_fission
super()._compute_xs()
return self._xs_tally
[docs] def get_homogenized_mgxs(self, other_mgxs):
"""Construct a homogenized MGXS with other MGXS objects.
This method constructs a new MGXS object that is the flux-weighted
combination of two MGXS objects. It is equivalent to what one would
obtain if the tally spatial domain were designed to encompass the
individual domains for both MGXS objects.
Parameters
----------
other_mgxs : openmc.mgxs.MGXS or Iterable of openmc.mgxs.MGXS
The MGXS to homogenize with this one.
Returns
-------
openmc.mgxs.MGXS
A new homogenized MGXS
Raises
------
ValueError
If the other_mgxs is of a different type.
"""
return self._get_homogenized_mgxs(other_mgxs, 'delayed-nu-fission')
[docs] def get_xs(self, subdomains='all', nuclides='all',
xs_type='macro', order_groups='increasing',
value='mean', delayed_groups='all', squeeze=True, **kwargs):
"""Returns an array of multi-delayed-group cross sections.
This method constructs a 4D NumPy array for the requested
multi-delayed-group cross section data for one or more
subdomains (1st dimension), delayed groups (2nd demension),
energy groups (3rd dimension), and nuclides (4th dimension).
Parameters
----------
subdomains : Iterable of Integral or 'all'
Subdomain IDs of interest. Defaults to 'all'.
nuclides : Iterable of str or 'all' or 'sum'
A list of nuclide name strings (e.g., ['U-235', 'U-238']). The
special string 'all' will return the cross sections for all nuclides
in the spatial domain. The special string 'sum' will return the
cross section summed over all nuclides. Defaults to 'all'.
xs_type: {'macro', 'micro'}
Return the macro or micro cross section in units of cm^-1 or barns.
Defaults to 'macro'.
order_groups: {'increasing', 'decreasing'}
Return the cross section indexed according to increasing or
decreasing energy groups (decreasing or increasing energies).
Defaults to 'increasing'.
value : {'mean', 'std_dev', 'rel_err'}
A string for the type of value to return. Defaults to 'mean'.
delayed_groups : list of int or 'all'
Delayed groups of interest. Defaults to 'all'.
squeeze : bool
A boolean representing whether to eliminate the extra dimensions
of the multi-dimensional array to be returned. Defaults to True.
Returns
-------
numpy.ndarray
A NumPy array of the multi-group cross section indexed in the order
each group, subdomain and nuclide as listed in the parameters.
Raises
------
ValueError
When this method is called before the multi-delayed-group cross
section is computed from tally data.
"""
cv.check_value('value', value, ['mean', 'std_dev', 'rel_err'])
cv.check_value('xs_type', xs_type, ['macro', 'micro'])
# FIXME: Unable to get microscopic xs for mesh domain because the mesh
# cells do not know the nuclide densities in each mesh cell.
if self.domain_type == 'mesh' and xs_type == 'micro':
msg = 'Unable to get micro xs for mesh domain since the mesh ' \
'cells do not know the nuclide densities in each mesh cell.'
raise ValueError(msg)
filters = []
filter_bins = []
# Construct a collection of the domain filter bins
if not isinstance(subdomains, str):
cv.check_iterable_type('subdomains', subdomains, Integral,
max_depth=3)
for subdomain in subdomains:
filters.append(_DOMAIN_TO_FILTER[self.domain_type])
filter_bins.append((subdomain,))
# Construct list of delayed group tuples for all requested groups
if not isinstance(delayed_groups, str):
cv.check_type('delayed groups', delayed_groups, list, int)
for delayed_group in delayed_groups:
filters.append(openmc.DelayedGroupFilter)
filter_bins.append((delayed_group,))
# Construct a collection of the nuclides to retrieve from the xs tally
if self.by_nuclide:
if nuclides == 'all' or nuclides == 'sum' or nuclides == ['sum']:
query_nuclides = self.get_nuclides()
else:
query_nuclides = nuclides
else:
query_nuclides = ['total']
# If user requested the sum for all nuclides, use tally summation
if nuclides == 'sum' or nuclides == ['sum']:
xs_tally = self.xs_tally.summation(nuclides=query_nuclides)
xs = xs_tally.get_values(filters=filters,
filter_bins=filter_bins, value=value)
else:
xs = self.xs_tally.get_values(filters=filters,
filter_bins=filter_bins,
nuclides=query_nuclides, value=value)
# Divide by atom number densities for microscopic cross sections
if xs_type == 'micro' and self._divide_by_density:
if self.by_nuclide:
densities = self.get_nuclide_densities(nuclides)
else:
densities = self.get_nuclide_densities('sum')
if value == 'mean' or value == 'std_dev':
xs /= densities[np.newaxis, :, np.newaxis]
# Eliminate the trivial score dimension
xs = np.squeeze(xs, axis=len(xs.shape) - 1)
xs = np.nan_to_num(xs)
if delayed_groups == 'all':
num_delayed_groups = self.num_delayed_groups
else:
num_delayed_groups = len(delayed_groups)
# Reshape tally data array with separate axes for domain,
# energy groups, delayed groups, and nuclides
# Accommodate the polar and azimuthal bins if needed
num_subdomains = \
int(xs.shape[0] / (num_delayed_groups *
self.num_polar * self.num_azimuthal))
if self.num_polar > 1 or self.num_azimuthal > 1:
new_shape = (self.num_polar, self.num_azimuthal, num_subdomains,
num_delayed_groups)
else:
new_shape = (num_subdomains, num_delayed_groups)
xs = np.reshape(xs, new_shape)
if squeeze:
# We want to squeeze out everything but the polar, azimuthal,
# delayed group, and energy group data.
xs = self._squeeze_xs(xs)
return xs
[docs]class MatrixMDGXS(MDGXS):
"""An abstract multi-delayed-group cross section for some energy group and
delayed group structure within some spatial domain. This class is
specifically intended for cross sections which depend on both the incoming
and outgoing energy groups and are therefore represented by matrices.
An example of this is the delayed-nu-fission matrix.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group and multi-delayed-group cross sections for downstream neutronics
calculations.
NOTE: Users should instantiate the subclasses of this abstract class.
Parameters
----------
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
The domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
name : str, optional
Name of the multi-group cross section. Used as a label to identify
tallies in OpenMC 'tallies.xml' file.
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral, optional
Number of equi-width polar angle bins for angle discretization;
defaults to one bin
num_azimuthal : Integral, optional
Number of equi-width azimuthal angle bins for angle discretization;
defaults to one bin
Attributes
----------
name : str, optional
Name of the multi-group cross section
rxn_type : str
Reaction type (e.g., 'total', 'nu-fission', etc.)
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
Domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
Domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
Energy group structure for energy condensation
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral
Number of equi-width polar angle bins for angle discretization
num_azimuthal : Integral
Number of equi-width azimuthal angle bins for angle discretization
tally_trigger : openmc.Trigger
An (optional) tally precision trigger given to each tally used to
compute the cross section
scores : list of str
The scores in each tally used to compute the multi-group cross section
filters : list of openmc.Filter
The filters in each tally used to compute the multi-group cross section
tally_keys : list of str
The keys into the tallies dictionary for each tally used to compute
the multi-group cross section
estimator : {'tracklength', 'collision', 'analog'}
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
unless the multi-group cross section has been computed.
xs_tally : openmc.Tally
Derived tally for the multi-group cross section. This attribute
is None unless the multi-group cross section has been computed.
num_subdomains : int
The number of subdomains is unity for 'material', 'cell' and 'universe'
domain types. This is equal to the number of cell instances
for 'distribcell' domain types (it is equal to unity prior to loading
tally data from a statepoint file) and the number of mesh cells for
'mesh' domain types.
num_nuclides : int
The number of nuclides for which the multi-group cross section is
being tracked. This is unity if the by_nuclide attribute is False.
nuclides : Iterable of str or 'sum'
The optional user-specified nuclides for which to compute cross
sections (e.g., 'U238', 'O16'). If by_nuclide is True but nuclides
are not specified by the user, all nuclides in the spatial domain
are included. This attribute is 'sum' if by_nuclide is false.
sparse : bool
Whether or not the MGXS' tallies use SciPy's LIL sparse matrix format
for compressed data storage
loaded_sp : bool
Whether or not a statepoint file has been loaded with tally data
derived : bool
Whether or not the MGXS is merged from one or more other MGXS
hdf5_key : str
The key used to index multi-group cross sections in an HDF5 data store
"""
@property
def _dont_squeeze(self):
"""Create a tuple of axes which should not be removed during the get_xs
process
"""
if self.num_polar > 1 or self.num_azimuthal > 1:
return (0, 1, 3, 4, 5)
else:
return (1, 2, 3)
@property
def filters(self):
# Create the non-domain specific Filters for the Tallies
group_edges = self.energy_groups.group_edges
energy = openmc.EnergyFilter(group_edges)
energyout = openmc.EnergyoutFilter(group_edges)
if self.delayed_groups is not None:
delayed = openmc.DelayedGroupFilter(self.delayed_groups)
filters = [[energy], [delayed, energy, energyout]]
else:
filters = [[energy], [energy, energyout]]
return self._add_angle_filters(filters)
[docs] def get_xs(self, in_groups='all', out_groups='all',
subdomains='all', nuclides='all',
xs_type='macro', order_groups='increasing',
row_column='inout', value='mean', delayed_groups='all',
squeeze=True, **kwargs):
"""Returns an array of multi-group cross sections.
This method constructs a 4D NumPy array for the requested
multi-group cross section data for one or more subdomains
(1st dimension), delayed groups (2nd dimension), energy groups in
(3rd dimension), energy groups out (4th dimension), and nuclides
(5th dimension).
Parameters
----------
in_groups : Iterable of Integral or 'all'
Incoming energy groups of interest. Defaults to 'all'.
out_groups : Iterable of Integral or 'all'
Outgoing energy groups of interest. Defaults to 'all'.
subdomains : Iterable of Integral or 'all'
Subdomain IDs of interest. Defaults to 'all'.
nuclides : Iterable of str or 'all' or 'sum'
A list of nuclide name strings (e.g., ['U235', 'U238']). The
special string 'all' will return the cross sections for all
nuclides in the spatial domain. The special string 'sum' will
return the cross section summed over all nuclides. Defaults to
'all'.
xs_type: {'macro', 'micro'}
Return the macro or micro cross section in units of cm^-1 or barns.
Defaults to 'macro'.
order_groups: {'increasing', 'decreasing'}
Return the cross section indexed according to increasing or
decreasing energy groups (decreasing or increasing energies).
Defaults to 'increasing'.
row_column: {'inout', 'outin'}
Return the cross section indexed first by incoming group and
second by outgoing group ('inout'), or vice versa ('outin').
Defaults to 'inout'.
value : {'mean', 'std_dev', 'rel_err'}
A string for the type of value to return. Defaults to 'mean'.
delayed_groups : list of int or 'all'
Delayed groups of interest. Defaults to 'all'.
squeeze : bool
A boolean representing whether to eliminate the extra dimensions
of the multi-dimensional array to be returned. Defaults to True.
Returns
-------
numpy.ndarray
A NumPy array of the multi-group cross section indexed in the order
each group and subdomain is listed in the parameters.
Raises
------
ValueError
When this method is called before the multi-group cross section is
computed from tally data.
"""
cv.check_value('value', value, ['mean', 'std_dev', 'rel_err'])
cv.check_value('xs_type', xs_type, ['macro', 'micro'])
# FIXME: Unable to get microscopic xs for mesh domain because the mesh
# cells do not know the nuclide densities in each mesh cell.
if self.domain_type == 'mesh' and xs_type == 'micro':
msg = 'Unable to get micro xs for mesh domain since the mesh ' \
'cells do not know the nuclide densities in each mesh cell.'
raise ValueError(msg)
filters = []
filter_bins = []
# Construct a collection of the domain filter bins
if not isinstance(subdomains, str):
cv.check_iterable_type('subdomains', subdomains, Integral,
max_depth=3)
for subdomain in subdomains:
filters.append(_DOMAIN_TO_FILTER[self.domain_type])
filter_bins.append((subdomain,))
# Construct list of energy group bounds tuples for all requested groups
if not isinstance(in_groups, str):
cv.check_iterable_type('groups', in_groups, Integral)
for group in in_groups:
filters.append(openmc.EnergyFilter)
filter_bins.append((
self.energy_groups.get_group_bounds(group),))
# Construct list of energy group bounds tuples for all requested groups
if not isinstance(out_groups, str):
cv.check_iterable_type('groups', out_groups, Integral)
for group in out_groups:
filters.append(openmc.EnergyoutFilter)
filter_bins.append((
self.energy_groups.get_group_bounds(group),))
# Construct list of delayed group tuples for all requested groups
if not isinstance(delayed_groups, str):
cv.check_type('delayed groups', delayed_groups, list, int)
for delayed_group in delayed_groups:
filters.append(openmc.DelayedGroupFilter)
filter_bins.append((delayed_group,))
# Construct a collection of the nuclides to retrieve from the xs tally
if self.by_nuclide:
if nuclides == 'all' or nuclides == 'sum' or nuclides == ['sum']:
query_nuclides = self.get_nuclides()
else:
query_nuclides = nuclides
else:
query_nuclides = ['total']
# Use tally summation if user requested the sum for all nuclides
if nuclides == 'sum' or nuclides == ['sum']:
xs_tally = self.xs_tally.summation(nuclides=query_nuclides)
xs = xs_tally.get_values(filters=filters, filter_bins=filter_bins,
value=value)
else:
xs = self.xs_tally.get_values(filters=filters,
filter_bins=filter_bins,
nuclides=query_nuclides, value=value)
# Divide by atom number densities for microscopic cross sections
if xs_type == 'micro' and self._divide_by_density:
if self.by_nuclide:
densities = self.get_nuclide_densities(nuclides)
else:
densities = self.get_nuclide_densities('sum')
if value == 'mean' or value == 'std_dev':
xs /= densities[np.newaxis, :, np.newaxis]
# Eliminate the trivial score dimension
xs = np.squeeze(xs, axis=len(xs.shape) - 1)
# Eliminate NaNs which may have been produced by dividing by density
xs = np.nan_to_num(xs)
if in_groups == 'all':
num_in_groups = self.num_groups
else:
num_in_groups = len(in_groups)
if out_groups == 'all':
num_out_groups = self.num_groups
else:
num_out_groups = len(out_groups)
if delayed_groups == 'all':
num_delayed_groups = self.num_delayed_groups
else:
num_delayed_groups = len(delayed_groups)
# Reshape tally data array with separate axes for domain and energy
# Accomodate the polar and azimuthal bins if needed
num_subdomains = int(xs.shape[0] / (num_delayed_groups *
num_in_groups * num_out_groups *
self.num_polar *
self.num_azimuthal))
if self.num_polar > 1 or self.num_azimuthal > 1:
new_shape = (self.num_polar, self.num_azimuthal, num_subdomains,
num_delayed_groups, num_in_groups, num_out_groups)
new_shape += xs.shape[1:]
xs = np.reshape(xs, new_shape)
# Transpose the matrix if requested by user
if row_column == 'outin':
xs = np.swapaxes(xs, 4, 5)
else:
new_shape = (num_subdomains, num_delayed_groups, num_in_groups,
num_out_groups)
new_shape += xs.shape[1:]
xs = np.reshape(xs, new_shape)
# Transpose the matrix if requested by user
if row_column == 'outin':
xs = np.swapaxes(xs, 2, 3)
# Reverse data if user requested increasing energy groups since
# tally data is stored in order of increasing energies
if order_groups == 'increasing':
xs = xs[..., ::-1, ::-1, :]
if squeeze:
# We want to squeeze out everything but the polar, azimuthal,
# and in/out energy group data.
xs = self._squeeze_xs(xs)
return xs
[docs] def get_slice(self, nuclides=[], in_groups=[], out_groups=[],
delayed_groups=[]):
"""Build a sliced MatrixMDGXS object for the specified nuclides and
energy groups.
This method constructs a new MdGXS to encapsulate a subset of the data
represented by this MdGXS. The subset of data to include in the tally
slice is determined by the nuclides, energy groups, and delayed groups
specified in the input parameters.
Parameters
----------
nuclides : list of str
A list of nuclide name strings
(e.g., ['U235', 'U238']; default is [])
in_groups : list of int
A list of incoming energy group indices starting at 1 for the high
energies (e.g., [1, 2, 3]; default is [])
out_groups : list of int
A list of outgoing energy group indices starting at 1 for the high
energies (e.g., [1, 2, 3]; default is [])
delayed_groups : list of int
A list of delayed group indices
(e.g., [1, 2, 3]; default is [])
Returns
-------
openmc.mgxs.MatrixMDGXS
A new MatrixMDGXS object which encapsulates the subset of data
requested for the nuclide(s) and/or energy group(s) requested in
the parameters.
"""
# Call super class method and null out derived tallies
slice_xs = super().get_slice(nuclides, in_groups, delayed_groups)
slice_xs._rxn_rate_tally = None
slice_xs._xs_tally = None
# Slice outgoing energy groups if needed
if len(out_groups) != 0:
filter_bins = []
for group in out_groups:
group_bounds = self.energy_groups.get_group_bounds(group)
filter_bins.append(group_bounds)
filter_bins = [tuple(filter_bins)]
# Slice each of the tallies across energyout groups
for tally_type, tally in slice_xs.tallies.items():
if tally.contains_filter(openmc.EnergyoutFilter):
tally_slice = tally.get_slice(
filters=[openmc.EnergyoutFilter],
filter_bins=filter_bins)
slice_xs.tallies[tally_type] = tally_slice
slice_xs.sparse = self.sparse
return slice_xs
[docs] def print_xs(self, subdomains='all', nuclides='all', xs_type='macro'):
"""Prints a string representation for the multi-group cross section.
Parameters
----------
subdomains : Iterable of Integral or 'all'
The subdomain IDs of the cross sections to include in the report.
Defaults to 'all'.
nuclides : Iterable of str or 'all' or 'sum'
The nuclides of the cross-sections to include in the report. This
may be a list of nuclide name strings (e.g., ['U235', 'U238']).
The special string 'all' will report the cross sections for all
nuclides in the spatial domain. The special string 'sum' will
report the cross sections summed over all nuclides. Defaults to
'all'.
xs_type: {'macro', 'micro'}
Return the macro or micro cross section in units of cm^-1 or barns.
Defaults to 'macro'.
"""
# Construct a collection of the subdomains to report
if not isinstance(subdomains, str):
cv.check_iterable_type('subdomains', subdomains, Integral)
elif self.domain_type == 'distribcell':
subdomains = np.arange(self.num_subdomains, dtype=np.int)
elif self.domain_type == 'mesh':
xyz = [range(1, x + 1) for x in self.domain.dimension]
subdomains = list(itertools.product(*xyz))
else:
subdomains = [self.domain.id]
# Construct a collection of the nuclides to report
if self.by_nuclide:
if nuclides == 'all':
nuclides = self.get_nuclides()
if nuclides == 'sum':
nuclides = ['sum']
else:
cv.check_iterable_type('nuclides', nuclides, str)
else:
nuclides = ['sum']
cv.check_value('xs_type', xs_type, ['macro', 'micro'])
# Build header for string with type and domain info
string = 'Multi-Delayed-Group XS\n'
string += '{0: <16}=\t{1}\n'.format('\tReaction Type', self.rxn_type)
string += '{0: <16}=\t{1}\n'.format('\tDomain Type', self.domain_type)
string += '{0: <16}=\t{1}\n'.format('\tDomain ID', self.domain.id)
# Generate the header for an individual XS
xs_header = '\tCross Sections [{0}]:'.format(self.get_units(xs_type))
# If cross section data has not been computed, only print string header
if self.tallies is None:
print(string)
return
string += '{0: <16}\n'.format('\tEnergy Groups:')
template = '{0: <12}Group {1} [{2: <10} - {3: <10}eV]\n'
# Loop over energy groups ranges
for group in range(1, self.num_groups + 1):
bounds = self.energy_groups.get_group_bounds(group)
string += template.format('', group, bounds[0], bounds[1])
# Set polar and azimuthal bins if necessary
if self.num_polar > 1 or self.num_azimuthal > 1:
pol_bins = np.linspace(0., np.pi, num=self.num_polar + 1,
endpoint=True)
azi_bins = np.linspace(-np.pi, np.pi, num=self.num_azimuthal + 1,
endpoint=True)
# Loop over all subdomains
for subdomain in subdomains:
if self.domain_type == 'distribcell':
string += '{: <16}=\t{}\n'.format('\tSubdomain', subdomain)
# Loop over all Nuclides
for nuclide in nuclides:
# Build header for nuclide type
if xs_type != 'sum':
string += '{: <16}=\t{}\n'.format('\tNuclide', nuclide)
# Build header for cross section type
string += '{: <16}\n'.format(xs_header)
if self.delayed_groups is not None:
for delayed_group in self.delayed_groups:
template = '{0: <12}Delayed Group {1}:\t'
string += template.format('', delayed_group)
string += '\n'
template = '{0: <12}Group {1} -> Group {2}:\t\t'
average_xs = self.get_xs(nuclides=[nuclide],
subdomains=[subdomain],
xs_type=xs_type, value='mean',
delayed_groups=[delayed_group])
rel_err_xs = self.get_xs(nuclides=[nuclide],
subdomains=[subdomain],
xs_type=xs_type,
value='rel_err',
delayed_groups=[delayed_group])
rel_err_xs = rel_err_xs * 100.
if self.num_polar > 1 or self.num_azimuthal > 1:
# Loop over polar, azi, and in/out group ranges
for pol in range(len(pol_bins) - 1):
pol_low, pol_high = pol_bins[pol: pol + 2]
for azi in range(len(azi_bins) - 1):
azi_low, azi_high = azi_bins[azi: azi + 2]
string += '\t\tPolar Angle: [{0:5f} - {1:5f}]'.format(
pol_low, pol_high) + \
'\tAzimuthal Angle: [{0:5f} - {1:5f}]'.format(
azi_low, azi_high) + '\n'
for in_group in range(1, self.num_groups + 1):
for out_group in range(1, self.num_groups + 1):
string += '\t' + template.format(
'', in_group, out_group)
string += '{0:.2e} +/- {1:.2e}%'.format(
average_xs[pol, azi, in_group - 1,
out_group - 1],
rel_err_xs[pol, azi, in_group - 1,
out_group - 1])
string += '\n'
string += '\n'
string += '\n'
else:
# Loop over incoming/outgoing energy groups ranges
for in_group in range(1, self.num_groups + 1):
for out_group in range(1, self.num_groups + 1):
string += template.format(
'', in_group, out_group)
string += '{:.2e} +/- {:.2e}%'.format(
average_xs[in_group-1, out_group-1],
rel_err_xs[in_group-1, out_group-1])
string += '\n'
string += '\n'
string += '\n'
else:
template = '{0: <12}Group {1} -> Group {2}:\t\t'
average_xs = self.get_xs(nuclides=[nuclide],
subdomains=[subdomain],
xs_type=xs_type, value='mean')
rel_err_xs = self.get_xs(nuclides=[nuclide],
subdomains=[subdomain],
xs_type=xs_type, value='rel_err')
rel_err_xs = rel_err_xs * 100.
if self.num_polar > 1 or self.num_azimuthal > 1:
# Loop over polar, azi, and in/out energy group ranges
for pol in range(len(pol_bins) - 1):
pol_low, pol_high = pol_bins[pol: pol + 2]
for azi in range(len(azi_bins) - 1):
azi_low, azi_high = azi_bins[azi: azi + 2]
string += '\t\tPolar Angle: [{0:5f} - {1:5f}]'.format(
pol_low, pol_high) + \
'\tAzimuthal Angle: [{0:5f} - {1:5f}]'.format(
azi_low, azi_high) + '\n'
for in_group in range(1, self.num_groups + 1):
for out_group in range(1, self.num_groups + 1):
string += '\t' + template.format(
'', in_group, out_group)
string += '{0:.2e} +/- {1:.2e}%'.format(
average_xs[pol, azi, in_group - 1,
out_group - 1],
rel_err_xs[pol, azi, in_group - 1,
out_group - 1])
string += '\n'
string += '\n'
string += '\n'
else:
# Loop over incoming/outgoing energy groups ranges
for in_group in range(1, self.num_groups + 1):
for out_group in range(1, self.num_groups + 1):
string += template.format('', in_group,
out_group)
string += '{0:.2e} +/- {1:.2e}%'.format(
average_xs[in_group - 1, out_group - 1],
rel_err_xs[in_group - 1, out_group - 1])
string += '\n'
string += '\n'
string += '\n'
string += '\n'
string += '\n'
print(string)
[docs]class DelayedNuFissionMatrixXS(MatrixMDGXS):
r"""A fission delayed neutron production matrix multi-group cross section.
This class can be used for both OpenMC input generation and tally data
post-processing to compute spatially-homogenized and energy-integrated
multi-group fission neutron production cross sections for multi-group
neutronics calculations. At a minimum, one needs to set the
:attr:`DelayedNuFissionMatrixXS.energy_groups` and
:attr:`DelayedNuFissionMatrixXS.domain` properties. Tallies for the flux and
appropriate reaction rates over the specified domain are generated
automatically via the :attr:`DelayedNuFissionMatrixXS.tallies` property,
which can then be appended to a :class:`openmc.Tallies` instance.
For post-processing, the :meth:`MGXS.load_from_statepoint` will pull in the
necessary data to compute multi-group cross sections from a
:class:`openmc.StatePoint` instance. The derived multi-group cross section
can then be obtained from the :attr:`DelayedNuFissionMatrixXS.xs_tally`
property.
For a spatial domain :math:`V`, energy group :math:`[E_g,E_{g-1}]`, and
delayed group :math:`d`, the fission delayed neutron production cross
section is calculated as:
.. math::
\begin{aligned}
\langle \nu\sigma_{f,g'\rightarrow g} \phi \rangle &= \int_{r \in V} dr
\int_{4\pi} d\Omega' \int_{E_{g'}}^{E_{g'-1}} dE' \int_{E_g}^{E_{g-1}} dE
\; \chi(E) \nu\sigma_f^d (r, E') \psi(r, E', \Omega')\\
\langle \phi \rangle &= \int_{r \in V} dr \int_{4\pi} d\Omega
\int_{E_g}^{E_{g-1}} dE \; \psi (r, E, \Omega) \\
\nu\sigma_{f,g'\rightarrow g} &= \frac{\langle \nu\sigma_{f,g'\rightarrow
g}^d \phi \rangle}{\langle \phi \rangle}
\end{aligned}
Parameters
----------
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
The domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
The domain type for spatial homogenization
groups : openmc.mgxs.EnergyGroups
The energy group structure for energy condensation
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
name : str, optional
Name of the multi-group cross section. Used as a label to identify
tallies in OpenMC 'tallies.xml' file.
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral, optional
Number of equi-width polar angle bins for angle discretization;
defaults to one bin
num_azimuthal : Integral, optional
Number of equi-width azimuthal angle bins for angle discretization;
defaults to one bin
Attributes
----------
name : str, optional
Name of the multi-group cross section
rxn_type : str
Reaction type (e.g., 'total', 'nu-fission', etc.)
by_nuclide : bool
If true, computes cross sections for each nuclide in domain
domain : openmc.Material or openmc.Cell or openmc.Universe or openmc.RegularMesh
Domain for spatial homogenization
domain_type : {'material', 'cell', 'distribcell', 'universe', 'mesh'}
Domain type for spatial homogenization
energy_groups : openmc.mgxs.EnergyGroups
Energy group structure for energy condensation
delayed_groups : list of int
Delayed groups to filter out the xs
num_polar : Integral
Number of equi-width polar angle bins for angle discretization
num_azimuthal : Integral
Number of equi-width azimuthal angle bins for angle discretization
tally_trigger : openmc.Trigger
An (optional) tally precision trigger given to each tally used to
compute the cross section
scores : list of str
The scores in each tally used to compute the multi-group cross section
filters : list of openmc.Filter
The filters in each tally used to compute the multi-group cross section
tally_keys : list of str
The keys into the tallies dictionary for each tally used to compute
the multi-group cross section
estimator : 'analog'
The tally estimator used to compute the multi-group cross section
tallies : collections.OrderedDict
OpenMC tallies needed to compute the multi-group cross section. The keys
are strings listed in the :attr:`DelayedNuFissionXS.tally_keys` property
and values are instances of :class:`openmc.Tally`.
rxn_rate_tally : openmc.Tally
Derived tally for the reaction rate tally used in the numerator to
compute the multi-group cross section. This attribute is None
unless the multi-group cross section has been computed.
xs_tally : openmc.Tally
Derived tally for the multi-group cross section. This attribute
is None unless the multi-group cross section has been computed.
num_subdomains : int
The number of subdomains is unity for 'material', 'cell' and 'universe'
domain types. This is equal to the number of cell instances
for 'distribcell' domain types (it is equal to unity prior to loading
tally data from a statepoint file).
num_nuclides : int
The number of nuclides for which the multi-group cross section is
being tracked. This is unity if the by_nuclide attribute is False.
nuclides : Iterable of str or 'sum'
The optional user-specified nuclides for which to compute cross
sections (e.g., 'U-238', 'O-16'). If by_nuclide is True but nuclides
are not specified by the user, all nuclides in the spatial domain
are included. This attribute is 'sum' if by_nuclide is false.
sparse : bool
Whether or not the MGXS' tallies use SciPy's LIL sparse matrix format
for compressed data storage
loaded_sp : bool
Whether or not a statepoint file has been loaded with tally data
derived : bool
Whether or not the MGXS is merged from one or more other MGXS
hdf5_key : str
The key used to index multi-group cross sections in an HDF5 data store
"""
def __init__(self, domain=None, domain_type=None, energy_groups=None,
delayed_groups=None, by_nuclide=False, name='',
num_polar=1, num_azimuthal=1):
super().__init__(domain, domain_type, energy_groups, delayed_groups,
by_nuclide, name, num_polar, num_azimuthal)
self._rxn_type = 'delayed-nu-fission'
self._hdf5_key = 'delayed-nu-fission matrix'
self._estimator = 'analog'
self._valid_estimators = ['analog']