/usr/lib/python2.7/dist-packages/ffc/quadrature/quadraturerepresentation.py is in python-ffc 1.3.0-2.
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# Copyright (C) 2009-2013 Kristian B. Oelgaard
#
# This file is part of FFC.
#
# FFC is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# FFC is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with FFC. If not, see <http://www.gnu.org/licenses/>.
#
# Modified by Anders Logg, 2009.
# Modified by Martin Alnaes, 2013
#
# First added: 2009-01-07
# Last changed: 2013-02-10
import numpy
# UFL modules
from ufl.classes import Form, Integral, Grad
from ufl.algorithms import extract_unique_elements, extract_type, extract_elements
from ufl.sorting import sorted_expr_sum
# FFC modules
from ffc.log import ffc_assert, info, error
from ffc.fiatinterface import create_element
from ffc.fiatinterface import map_facet_points, reference_cell_vertices
from ffc.fiatinterface import cellname_to_num_entities
from ffc.quadrature.quadraturetransformer import QuadratureTransformer
from ffc.quadrature.optimisedquadraturetransformer import QuadratureTransformerOpt
from ffc.quadrature_schemes import create_quadrature
from ffc.representationutils import initialize_integral_ir
def compute_integral_ir(itg_data,
form_data,
form_id,
parameters):
"Compute intermediate represention of integral."
info("Computing quadrature representation")
# Initialise representation
ir = initialize_integral_ir("quadrature", itg_data, form_data, form_id)
# Sort integrals into a dict with number of integral points as key
sorted_integrals = _sort_integrals(itg_data.integrals, itg_data.metadata, form_data)
# Tabulate quadrature points and basis function values in these points
integrals_dict, psi_tables, quad_weights = \
_tabulate_basis(sorted_integrals, itg_data.domain_type, form_data)
# Save tables for quadrature weights and points
ir["quadrature_weights"] = quad_weights
# Create dimensions of primary indices, needed to reset the argument 'A'
# given to tabulate_tensor() by the assembler.
ir["prim_idims"] = [create_element(ufl_element).space_dimension()
for ufl_element in form_data.argument_elements]
# Create and save the optisation parameters.
ir["optimise_parameters"] = _parse_optimise_parameters(parameters)
# Create transformer.
if ir["optimise_parameters"]["optimisation"]:
QuadratureTransformerClass = QuadratureTransformerOpt
else:
QuadratureTransformerClass = QuadratureTransformer
transformer = QuadratureTransformerClass(psi_tables,
quad_weights,
form_data.geometric_dimension,
form_data.topological_dimension,
ir["entitytype"],
form_data.function_replace_map,
ir["optimise_parameters"])
# Transform integrals.
ir["trans_integrals"] = _transform_integrals_by_type(ir, transformer, integrals_dict,
itg_data.domain_type, form_data.cell)
# Save tables populated by transformer
ir["name_map"] = transformer.name_map
ir["unique_tables"] = transformer.unique_tables # Basis values?
# Save tables map, to extract table names for optimisation option -O.
ir["psi_tables_map"] = transformer.psi_tables_map
ir["additional_includes_set"] = transformer.additional_includes_set
# Insert empty data which will be populated if optimization is turned on
ir["geo_consts"] = {}
return ir
def _parse_optimise_parameters(parameters):
optimise_parameters = {"eliminate zeros": False,
"optimisation": False,
"ignore ones": False,
"remove zero terms": False,
"ignore zero tables": False}
if parameters["optimize"]:
optimise_parameters["ignore ones"] = True
optimise_parameters["remove zero terms"] = True
optimise_parameters["ignore zero tables"] = True
# Do not include this in below if/else clause since we want to be
# able to switch on this optimisation in addition to the other
# optimisations.
if "eliminate_zeros" in parameters:
optimise_parameters["eliminate zeros"] = True
if "simplify_expressions" in parameters:
optimise_parameters["optimisation"] = "simplify_expressions"
elif "precompute_ip_const" in parameters:
optimise_parameters["optimisation"] = "precompute_ip_const"
elif "precompute_basis_const" in parameters:
optimise_parameters["optimisation"] = "precompute_basis_const"
# The current default optimisation (for -O) is equal to
# '-feliminate_zeros -fsimplify_expressions'.
else:
# If '-O -feliminate_zeros' was given on the command line, do not
# simplify expressions
if not "eliminate_zeros" in parameters:
optimise_parameters["eliminate zeros"] = True
optimise_parameters["optimisation"] = "simplify_expressions"
return optimise_parameters
def _transform_integrals_by_type(ir, transformer, integrals_dict, domain_type, cell):
num_facets = cellname_to_num_entities[cell.cellname()][-2]
num_vertices = cellname_to_num_entities[cell.cellname()][0]
if domain_type == "cell":
# Compute transformed integrals.
info("Transforming cell integral")
transformer.update_cell()
terms = _transform_integrals(transformer, integrals_dict, domain_type)
elif domain_type == "exterior_facet":
# Compute transformed integrals.
terms = [None]*num_facets
for i in range(num_facets):
info("Transforming exterior facet integral %d" % i)
transformer.update_facets(i, None)
terms[i] = _transform_integrals(transformer, integrals_dict, domain_type)
elif domain_type == "interior_facet":
# Compute transformed integrals.
terms = [[None]*num_facets for i in range(num_facets)]
for i in range(num_facets):
for j in range(num_facets):
info("Transforming interior facet integral (%d, %d)" % (i, j))
transformer.update_facets(i, j)
terms[i][j] = _transform_integrals(transformer, integrals_dict, domain_type)
elif domain_type == "point":
# Compute transformed integrals.
terms = [None]*num_vertices
for i in range(num_vertices):
info("Transforming point integral (%d)" % i)
transformer.update_vertex(i)
terms[i] = _transform_integrals(transformer, integrals_dict, domain_type)
else:
error("Unhandled domain type: " + str(domain_type))
return terms
def _create_quadrature_points_and_weights(domain_type, cell, degree, rule):
if domain_type == "cell":
(points, weights) = create_quadrature(cell.cellname(), degree, rule)
elif domain_type == "exterior_facet" or domain_type == "interior_facet":
(points, weights) = create_quadrature(cell.facet_cellname(), degree, rule)
elif domain_type == "point":
(points, weights) = ([()], numpy.array([1.0,])) # TODO: Will be fixed
else:
error("Unknown integral type: " + str(domain_type))
return (points, weights)
def _find_element_derivatives(expr, elements, element_replace_map):
"Find the highest derivatives of given elements in expression."
# TODO: This is most likely not the best way to get the highest
# derivative of an element, but it works!
# Initialise dictionary of elements and the number of derivatives.
# (Note that elements are already mapped through the element_replace_map)
num_derivatives = dict((e, 0) for e in elements)
# Extract the derivatives from the integral.
derivatives = set(extract_type(expr, Grad))
# Loop derivatives and extract multiple derivatives.
for d in list(derivatives):
# After UFL has evaluated derivatives, only one element
# can be found inside any single Grad expression
elem, = extract_elements(d.operands()[0])
elem = element_replace_map[elem]
# Set the number of derivatives to the highest value encountered so far.
num_derivatives[elem] = max(num_derivatives[elem], len(extract_type(d, Grad)))
return num_derivatives
def domain_to_entity_dim(domain_type, cell):
tdim = cell.topological_dimension()
if domain_type == "cell":
entity_dim = tdim
elif (domain_type == "exterior_facet" or domain_type == "interior_facet"):
entity_dim = tdim - 1
elif domain_type == "point":
entity_dim = 0
else:
error("Unknown domain_type: %s" % domain_type)
return entity_dim
def _map_entity_points(cell, points, entity_dim, entity):
# Not sure if this is useful anywhere else than in _tabulate_psi_table!
tdim = cell.topological_dimension()
if entity_dim == tdim:
return points
elif entity_dim == tdim-1:
return map_facet_points(points, entity)
elif entity_dim == 0:
return (reference_cell_vertices(cell.cellname())[entity],)
def _tabulate_psi_table(domain_type, cell, element, deriv_order, points):
"Tabulate psi table for different integral types."
# MSA: I attempted to generalize this function, could this way of
# handling domain types generically extend to other parts of the code?
entity_dim = domain_to_entity_dim(domain_type, cell)
num_entities = cellname_to_num_entities[cell.cellname()][entity_dim]
psi_table = {}
for entity in range(num_entities):
entity_points = _map_entity_points(cell, points, entity_dim, entity)
# TODO: Use 0 as key for cell and we may be able to generalize other places:
key = None if domain_type == "cell" else entity
psi_table[key] = element.tabulate(deriv_order, entity_points)
return psi_table
def _tabulate_entities(domain_type, cell):
"Tabulate psi table for different integral types."
# MSA: I attempted to generalize this function, could this way of
# handling domain types generically extend to other parts of the code?
entity_dim = domain_to_entity_dim(domain_type, cell)
num_entities = cellname_to_num_entities[cell.cellname()][entity_dim]
entities = set()
for entity in range(num_entities):
# TODO: Use 0 as key for cell and we may be able to generalize other places:
key = None if domain_type == "cell" else entity
entities.add(key)
return entities
def insert_nested_dict(root, keys, value):
for k in keys[:-1]:
d = root.get(k)
if d is None:
d = {}
root[k] = d
root = d
root[keys[-1]] = value
from ufl.classes import CellAvg, FacetAvg
def _tabulate_basis(sorted_integrals, domain_type, form_data):
"Tabulate the basisfunctions and derivatives."
# MER: Note to newbies: this code assumes that each integral in
# the dictionary of sorted_integrals that enters here, has a
# unique number of quadrature points ...
# Initialise return values.
quadrature_weights = {}
psi_tables = {}
integrals = {}
avg_elements = { "cell": [], "facet": [] }
# Loop the quadrature points and tabulate the basis values.
for pr, integral in sorted_integrals.iteritems():
# Extract number of points and the rule.
degree, rule = pr
# Get all unique elements in integral.
ufl_elements = [form_data.element_replace_map[e]
for e in extract_unique_elements(integral)]
# Find all CellAvg and FacetAvg in integrals and extract elements
for avg, AvgType in (("cell", CellAvg), ("facet", FacetAvg)):
expressions = extract_type(integral, AvgType)
avg_elements[avg] = [form_data.element_replace_map[e]
for expr in expressions
for e in extract_unique_elements(expr)]
# Create a list of equivalent FIAT elements (with same
# ordering of elements).
fiat_elements = [create_element(e) for e in ufl_elements]
# Make quadrature rule and get points and weights.
(points, weights) = _create_quadrature_points_and_weights(domain_type, form_data.cell, degree, rule)
# The TOTAL number of weights/points
len_weights = len(weights)
# Assert that this is unique
ffc_assert(len_weights not in quadrature_weights, \
"This number of points is already present in the weight table: " + repr(quadrature_weights))
ffc_assert(len_weights not in psi_tables, \
"This number of points is already present in the psi table: " + repr(psi_tables))
ffc_assert(len_weights not in integrals, \
"This number of points is already present in the integrals: " + repr(integrals))
# Add points and rules to dictionary.
quadrature_weights[len_weights] = (weights, points)
# Add the number of points to the psi tables dictionary.
psi_tables[len_weights] = {}
# Add the integral with the number of points as a key to the return integrals.
integrals[len_weights] = integral
# Find the highest number of derivatives needed for each element
num_derivatives = _find_element_derivatives(integral.integrand(), ufl_elements,
form_data.element_replace_map)
# Loop FIAT elements and tabulate basis as usual.
for i, element in enumerate(fiat_elements):
# Tabulate table of basis functions and derivatives in points
psi_table = _tabulate_psi_table(domain_type, form_data.cell, element,
num_derivatives[ufl_elements[i]], points)
# Insert table into dictionary based on UFL elements. (None=not averaged)
psi_tables[len_weights][ufl_elements[i]] = { None: psi_table }
# Loop over elements found in CellAvg and tabulate basis averages
len_weights = 1
for avg in ("cell", "facet"):
# Doesn't matter if it's exterior or interior
if avg == "cell":
avg_domain_type = "cell"
elif avg == "facet":
avg_domain_type = "exterior_facet"
for element in avg_elements[avg]:
fiat_element = create_element(element)
# Make quadrature rule and get points and weights.
(points, weights) = _create_quadrature_points_and_weights(avg_domain_type, form_data.cell, element.degree(), "default")
wsum = sum(weights)
# Tabulate table of basis functions and derivatives in points
entity_psi_tables = _tabulate_psi_table(avg_domain_type, form_data.cell, fiat_element, 0, points)
rank = len(element.value_shape())
# Hack, duplicating table with per-cell values for each facet in the case of cell_avg(f) in a facet integral
actual_entities = _tabulate_entities(domain_type, form_data.cell)
if len(actual_entities) > len(entity_psi_tables):
assert len(entity_psi_tables) == 1
assert avg_domain_type == "cell"
assert "facet" in domain_type
v, = entity_psi_tables.values()
entity_psi_tables = dict((e, v) for e in actual_entities)
for entity, deriv_table in entity_psi_tables.items():
deriv, = list(deriv_table.keys()) # Not expecting derivatives of averages
psi_table = deriv_table[deriv]
if rank:
# Compute numeric integral
num_dofs, num_components, num_points = psi_table.shape
ffc_assert(num_points == len(weights), "Weights and table shape does not match.")
avg_psi_table = numpy.asarray([[[numpy.dot(psi_table[j,k,:], weights) / wsum]
for k in range(num_components)]
for j in range(num_dofs)])
else:
# Compute numeric integral
num_dofs, num_points = psi_table.shape
ffc_assert(num_points == len(weights), "Weights and table shape does not match.")
avg_psi_table = numpy.asarray([[numpy.dot(psi_table[j,:], weights) / wsum] for j in range(num_dofs)])
# Insert table into dictionary based on UFL elements.
insert_nested_dict(psi_tables, (len_weights, element, avg, entity, deriv), avg_psi_table)
return (integrals, psi_tables, quadrature_weights)
def _sort_integrals(integrals, metadata, form_data):
"""Sort integrals according to the number of quadrature points needed per axis.
Only consider those integrals defined on the given domain."""
# Get domain type and id
if integrals:
domain_type = integrals[0].domain_type()
domain_id = integrals[0].domain_id()
ffc_assert(all(domain_type == itg.domain_type() for itg in integrals),
"Expecting only integrals on the same subdomain.")
ffc_assert(all(domain_id == itg.domain_id() for itg in integrals),
"Expecting only integrals on the same subdomain.")
sorted_integrands = {}
# TODO: We might want to take into account that a form like
# a = f*g*h*v*u*dx(0, quadrature_order=4) + f*v*u*dx(0, quadrature_order=2),
# although it involves two integrals of different order, will most
# likely be integrated faster if one does
# a = (f*g*h + f)*v*u*dx(0, quadrature_order=4)
# It will of course only work for integrals defined on the same
# subdomain and representation.
for integral in integrals:
# Get default degree and rule.
degree = metadata["quadrature_degree"]
rule = metadata["quadrature_rule"]
# Override if specified in integral metadata
integral_compiler_data = integral.compiler_data()
if not integral_compiler_data is None:
if "quadrature_degree" in integral_compiler_data:
degree = integral_compiler_data["quadrature_degree"]
if "quadrature_rule" in integral_compiler_data:
rule = integral_compiler_data["quadrature_rule"]
# Add integrand to dictionary according to degree and rule.
if not (degree, rule) in sorted_integrands:
sorted_integrands[(degree, rule)] = [integral.integrand()]
else:
sorted_integrands[(degree, rule)] += [integral.integrand()]
# Create integrals from accumulated integrands.
sorted_integrals = {}
for key, integrands in sorted_integrands.items():
# Summing integrands in a canonical ordering defined by UFL
integrand = sorted_expr_sum(integrands)
sorted_integrals[key] = Integral(integrand, domain_type, domain_id, {}, None)
return sorted_integrals
def _transform_integrals(transformer, integrals, domain_type):
"Transform integrals from UFL expression to quadrature representation."
transformed_integrals = []
for point, integral in integrals.items():
transformer.update_points(point)
terms = transformer.generate_terms(integral.integrand(), domain_type)
transformed_integrals.append((point, terms, transformer.function_data,
{}, transformer.coordinate, transformer.conditionals))
return transformed_integrals
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