Source code for ffc.quadrature.quadraturetransformerbase
# -*- coding: utf-8 -*-
"""QuadratureTransformerBase, a common class for quadrature
transformers to translate UFL expressions."""
# 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 Martin Sandve Alnæs, 2013
# Modified by Garth N. Wells, 2013
# Modified by Lizao Li, 2015
# Modified by Anders Logg, 2015
# Python modules
import functools
from numpy import shape, array
# UFL Classes
from ufl.classes import FixedIndex, Index
from ufl.utils.stacks import StackDict, Stack
from ufl.permutation import build_component_numbering
from ufl import custom_integral_types
# UFL Algorithms
from ufl.algorithms import Transformer
# FFC modules.
from ffc.log import ffc_assert, error
from ffc.fiatinterface import MixedElement, create_element, map_facet_points
from ffc.quadrature.cpp import format
# FFC utils
from ffc.utils import listcopy
from ffc.representationutils import transform_component
# Utility and optimisation functions for quadraturegenerator.
from ffc.quadrature.quadratureutils import create_psi_tables
from ffc.quadrature.symbolics import BASIS, IP, GEO
[docs]class FFCMultiIndex:
"""A MultiIndex represents a list of indices and holds the following
data:
rank - rank of multiindex
dims - a list of dimensions
indices - a list of all possible multiindex values
"""
def __init__(self, dims):
"Create multiindex from given list of ranges"
def outer_join(a, b):
"""Let a be a list of lists and b a list. We append each element of b
to each list in a and return the resulting list of lists.
"""
outer = []
for i in range(len(a)):
for j in range(len(b)):
outer += [a[i] + [b[j]]]
return outer
def build_indices(dims):
"Create a list of all index combinations."
if not dims:
return [[]]
ranges = listcopy(dims)
return functools.reduce(outer_join, ranges, [[]])
self.rank = len(dims)
self.dims = [len(dim) for dim in dims]
self.indices = build_indices(dims)
return
def __str__(self):
"Return informal string representation (pretty-print)."
return "rank = %d dims = %s indices = %s" % (self.rank, str(self.dims), str(self.indices))
[docs]class QuadratureTransformerBase(Transformer):
"Transform UFL representation to quadrature code."
def __init__(self,
psi_tables,
quad_weights,
gdim,
tdim,
entity_type,
function_replace_map,
optimise_parameters):
Transformer.__init__(self)
# Save optimise_parameters, weights and fiat_elements_map.
self.optimise_parameters = optimise_parameters
# Map from original functions with possibly incomplete
# elements to functions with properly completed elements
self._function_replace_map = function_replace_map
self._function_replace_values = set(function_replace_map.values()) # For assertions
# Create containers and variables.
self.used_psi_tables = set()
self.psi_tables_map = {}
self.used_weights = set()
self.quad_weights = quad_weights
self.used_nzcs = set()
self.ip_consts = {}
self.trans_set = set()
self.function_data = {}
self.tdim = tdim
self.gdim = gdim
self.entity_type = entity_type
self.points = 0
self.facet0 = None
self.facet1 = None
self.vertex = None
self.restriction = None
self.avg = None
self.coordinate = None
self.conditionals = {}
self.additional_includes_set = set()
# Stacks.
self._derivatives = []
self._index2value = StackDict()
self._components = Stack()
self.element_map, self.name_map, self.unique_tables =\
create_psi_tables(psi_tables,
self.optimise_parameters["eliminate zeros"],
self.entity_type)
# Cache.
self.argument_cache = {}
self.function_cache = {}
[docs] def update_cell(self):
ffc_assert(self.entity_type == "cell",
"Not expecting update_cell on a %s." % self.entity_type)
self.facet0 = None
self.facet1 = None
self.vertex = None
self.coordinate = None
self.conditionals = {}
[docs] def update_facets(self, facet0, facet1):
ffc_assert(self.entity_type == "facet",
"Not expecting update_facet on a %s." % self.entity_type)
self.facet0 = facet0
self.facet1 = facet1
self.vertex = None
self.coordinate = None
self.conditionals = {}
[docs] def update_vertex(self, vertex):
ffc_assert(self.entity_type == "vertex",
"Not expecting update_vertex on a %s." % self.entity_type)
self.facet0 = None
self.facet1 = None
self.vertex = vertex
self.coordinate = None
self.conditionals = {}
[docs] def update_points(self, points):
self.points = points
self.coordinate = None
# Reset functions everytime we move to a new quadrature loop
self.conditionals = {}
self.function_data = {}
# Reset cache
self.argument_cache = {}
self.function_cache = {}
[docs] def disp(self):
print("\n\n **** Displaying QuadratureTransformer ****")
print("\nQuadratureTransformer, element_map:\n", self.element_map)
print("\nQuadratureTransformer, name_map:\n", self.name_map)
print("\nQuadratureTransformer, unique_tables:\n", self.unique_tables)
print("\nQuadratureTransformer, used_psi_tables:\n",
self.used_psi_tables)
print("\nQuadratureTransformer, psi_tables_map:\n", self.psi_tables_map)
print("\nQuadratureTransformer, used_weights:\n", self.used_weights)
[docs] def component(self):
"Return current component tuple."
if len(self._components):
return self._components.peek()
return ()
[docs] def derivatives(self):
"Return all derivatives tuple."
if len(self._derivatives):
return tuple(self._derivatives[:])
return ()
# -------------------------------------------------------------------------
# Start handling UFL classes.
# -------------------------------------------------------------------------
# Nothing in expr.py is handled. Can only handle children of these clases.
error("This expression is not handled: " + repr(o))
# Nothing in terminal.py is handled. Can only handle children of
# these clases.
error("This terminal is not handled: " + repr(o))
# -------------------------------------------------------------------------
# Things which should not be here (after expansion etc.) from:
# algebra.py, differentiation.py, finiteelement.py, form.py,
# geometry.py, indexing.py, integral.py, tensoralgebra.py,
# variable.py.
# -------------------------------------------------------------------------
error("All derivatives apart from Grad should have been expanded!!")
[docs] def compound_tensor_operator(self, o):
print("\n\nVisiting CompoundTensorOperator: ", repr(o))
error("CompoundTensorOperator should have been expanded.")
error("What is a Lable doing in the integrand?")
# -------------------------------------------------------------------------
# Things which are not supported yet, from:
# condition.py, constantvalue.py, function.py, geometry.py, lifting.py,
# mathfunctions.py, restriction.py
# -------------------------------------------------------------------------
error("This type of Condition is not supported (yet).")
error("This type of ConstantValue is not supported (yet).")
error("This type of GeometricQuantity is not supported (yet).")
error("This MathFunction is not supported (yet).")
error("Atan2Function is not implemented (yet).")
error("BesselFunction is not implemented (yet).")
error("This type of Restricted is not supported (only positive and negative are currently supported).")
# -------------------------------------------------------------------------
# Handlers that should be implemented by child classes.
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# AlgebraOperators (algebra.py).
# -------------------------------------------------------------------------
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
# -------------------------------------------------------------------------
# FacetNormal, CellVolume, Circumradius (geometry.py).
# -------------------------------------------------------------------------
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
# -------------------------------------------------------------------------
# Things that can be handled by the base class.
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# Argument (basisfunction.py).
# -------------------------------------------------------------------------
[docs] def argument(self, o):
# print("\nVisiting Argument:" + repr(o))
# Create aux. info.
components = self.component()
derivatives = self.derivatives()
# Check if basis is already in cache
key = (o, components, derivatives, self.restriction, self.avg)
basis = self.argument_cache.get(key, None)
tdim = self.tdim
# FIXME: Why does using a code dict from cache make the
# expression manipulations blow (MemoryError) up later?
if basis is None or self.optimise_parameters["optimisation"]:
# Get auxiliary variables to generate basis
(component, local_elem, local_comp, local_offset, ffc_element,
transformation,
multiindices) = self._get_auxiliary_variables(o, components,
derivatives)
# Create mapping and code for basis function and add to
# dict.
basis = self.create_argument(o, derivatives, component, local_comp,
local_offset, ffc_element,
transformation, multiindices,
tdim, self.gdim, self.avg)
self.argument_cache[key] = basis
return basis
# -------------------------------------------------------------------------
# Constant values (constantvalue.py).
# -------------------------------------------------------------------------
[docs] def identity(self, o):
# Get components
i, j = self.component()
# Only return a value if i==j
if i == j:
return self._format_scalar_value(1.0)
else:
return self._format_scalar_value(None)
return self._format_scalar_value(o.value())
return self._format_scalar_value(None)
# -------------------------------------------------------------------------
# Grad (differentiation.py).
# -------------------------------------------------------------------------
[docs] def grad(self, o):
# Get expression
derivative_expr, = o.ufl_operands
# Get components
components = self.component()
en = len(derivative_expr.ufl_shape)
cn = len(components)
ffc_assert(len(o.ufl_shape) == cn,
"Expecting rank of grad expression to match components length.")
# Get direction of derivative
if cn == en + 1:
der = components[en]
self._components.push(components[:en])
elif cn == en:
# This happens in 1D, sligtly messy result of defining
# grad(f) == f.dx(0)
der = 0
else:
error("Unexpected rank %d and component length %d in grad expression." % (en, cn))
# Add direction to list of derivatives
self._derivatives.append(der)
# Visit children to generate the derivative code.
code = self.visit(derivative_expr)
# Remove the direction from list of derivatives
self._derivatives.pop()
if cn == en + 1:
self._components.pop()
return code
# -------------------------------------------------------------------------
# Coefficient and Constants (function.py).
# -------------------------------------------------------------------------
[docs] def coefficient(self, o):
# print("\nVisiting Coefficient: " + repr(o))
# Map o to object with proper element and count
o = self._function_replace_map[o]
# Create aux. info.
components = self.component()
derivatives = self.derivatives()
# Check if function is already in cache
key = (o, components, derivatives, self.restriction, self.avg)
function_code = self.function_cache.get(key)
# FIXME: Why does using a code dict from cache make the
# expression manipulations blow (MemoryError) up later?
if function_code is None or self.optimise_parameters["optimisation"]:
# Get auxiliary variables to generate function
(component, local_elem, local_comp, local_offset,
ffc_element, transformation,
multiindices) = self._get_auxiliary_variables(o, components,
derivatives)
# Check that we don't take derivatives of
# QuadratureElements.
is_quad_element = local_elem.family() == "Quadrature"
ffc_assert(not (derivatives and is_quad_element),
"Derivatives of Quadrature elements are not supported: " + repr(o))
tdim = self.tdim
# Create code for function and add empty tuple to cache
# dict.
function_code = {(): self.create_function(o, derivatives, component,
local_comp, local_offset,
ffc_element,
is_quad_element,
transformation,
multiindices, tdim,
self.gdim, self.avg)}
self.function_cache[key] = function_code
return function_code
# -------------------------------------------------------------------------
# SpatialCoordinate (geometry.py).
# -------------------------------------------------------------------------
[docs] def spatial_coordinate(self, o):
# Get the component.
components = self.component()
c, = components
if self.vertex is not None:
error("Spatial coordinates (x) not implemented for point measure (dP)") # TODO: Implement this, should be just the point.
elif self.points is None:
gdim, = o.ufl_shape
coordinate = "quadrature_points[ip*%d + %d]" % (gdim, c)
return self._create_symbol(coordinate, IP)
else:
# Generate the appropriate coordinate and update tables.
coordinate = format["ip coordinates"](self.points, c)
self._generate_affine_map()
return self._create_symbol(coordinate, IP)
# -------------------------------------------------------------------------
# Indexed (indexed.py).
# -------------------------------------------------------------------------
[docs] def indexed(self, o):
# Get indexed expression and index, map index to current value
# and update components
indexed_expr, index = o.ufl_operands
self._components.push(self.visit(index))
# Visit expression subtrees and generate code.
code = self.visit(indexed_expr)
# Remove component again
self._components.pop()
return code
# -------------------------------------------------------------------------
# MultiIndex (indexing.py).
# -------------------------------------------------------------------------
[docs] def multi_index(self, o):
# Loop all indices in MultiIndex and get current values
subcomp = []
for i in o:
if isinstance(i, FixedIndex):
subcomp.append(i._value)
elif isinstance(i, Index):
subcomp.append(self._index2value[i])
return tuple(subcomp)
# -------------------------------------------------------------------------
# IndexSum (indexsum.py).
# -------------------------------------------------------------------------
[docs] def index_sum(self, o):
# Get expression and index that we're summing over
summand, multiindex = o.ufl_operands
index, = multiindex
# Loop index range, update index/value dict and generate code
ops = []
for i in range(o.dimension()):
self._index2value.push(index, i)
ops.append(self.visit(summand))
self._index2value.pop()
# Call sum to generate summation
code = self.sum(o, *ops)
return code
# -------------------------------------------------------------------------
# MathFunctions (mathfunctions.py).
# -------------------------------------------------------------------------
return self._math_function(operands, format["sqrt"])
return self._math_function(operands, format["exp"])
return self._math_function(operands, format["ln"])
return self._math_function(operands, format["cos"])
return self._math_function(operands, format["sin"])
return self._math_function(operands, format["tan"])
return self._math_function(operands, format["cosh"])
return self._math_function(operands, format["sinh"])
return self._math_function(operands, format["tanh"])
return self._math_function(operands, format["acos"])
return self._math_function(operands, format["asin"])
return self._math_function(operands, format["atan"])
return self._atan_2_function(operands, format["atan_2"])
return self._math_function(operands, format["erf"])
[docs] def bessel_i(self, o, *operands):
self.additional_includes_set.add("#include <boost/math/special_functions.hpp>")
return self._bessel_function(operands, format["bessel_i"])
[docs] def bessel_j(self, o, *operands):
self.additional_includes_set.add("#include <boost/math/special_functions.hpp>")
return self._bessel_function(operands, format["bessel_j"])
[docs] def bessel_k(self, o, *operands):
self.additional_includes_set.add("#include <boost/math/special_functions.hpp>")
return self._bessel_function(operands, format["bessel_k"])
[docs] def bessel_y(self, o, *operands):
self.additional_includes_set.add("#include <boost/math/special_functions.hpp>")
return self._bessel_function(operands, format["bessel_y"])
# -------------------------------------------------------------------------
# PositiveRestricted and NegativeRestricted (restriction.py).
# -------------------------------------------------------------------------
[docs] def positive_restricted(self, o):
# Just get the first operand, there should only be one.
restricted_expr = o.ufl_operands
ffc_assert(len(restricted_expr) == 1,
"Only expected one operand for restriction: " + repr(restricted_expr))
ffc_assert(self.restriction is None,
"Expression is restricted twice: " + repr(restricted_expr))
# Set restriction, visit operand and reset restriction
self.restriction = "+"
code = self.visit(restricted_expr[0])
self.restriction = None
return code
[docs] def negative_restricted(self, o):
# Just get the first operand, there should only be one.
restricted_expr = o.ufl_operands
ffc_assert(len(restricted_expr) == 1,
"Only expected one operand for restriction: " + repr(restricted_expr))
ffc_assert(self.restriction is None,
"Expression is restricted twice: " + repr(restricted_expr))
# Set restriction, visit operand and reset restriction
self.restriction = "-"
code = self.visit(restricted_expr[0])
self.restriction = None
return code
[docs] def cell_avg(self, o):
ffc_assert(self.avg is None, "Not expecting nested averages.")
# Just get the first operand, there should only be one.
expr, = o.ufl_operands
# Set average marker, visit operand and reset marker
self.avg = "cell"
code = self.visit(expr)
self.avg = None
return code
[docs] def facet_avg(self, o):
ffc_assert(self.avg is None, "Not expecting nested averages.")
ffc_assert(self.entity_type != "cell",
"Cannot take facet_avg in a cell integral.")
# Just get the first operand, there should only be one.
expr, = o.ufl_operands
# Set average marker, visit operand and reset marker
self.avg = "facet"
code = self.visit(expr)
self.avg = None
return code
# -------------------------------------------------------------------------
# ComponentTensor (tensors.py).
# -------------------------------------------------------------------------
[docs] def component_tensor(self, o):
# Get expression and indices
component_expr, indices = o.ufl_operands
# Get current component(s)
components = self.component()
ffc_assert(len(components) == len(indices),
"The number of known components must be equal to the number of components of the ComponentTensor for this to work.")
# Update the index dict (map index values of current known
# indices to those of the component tensor)
for i, v in zip(indices._indices, components):
self._index2value.push(i, v)
# Push an empty component tuple
self._components.push(())
# Visit expression subtrees and generate code.
code = self.visit(component_expr)
# Remove the index map from the StackDict
for i in range(len(components)):
self._index2value.pop()
# Remove the empty component tuple
self._components.pop()
return code
[docs] def list_tensor(self, o):
# Get the component
component = self.component()
# Extract first and the rest of the components
c0, c1 = component[0], component[1:]
# Get first operand
op = o.ufl_operands[c0]
# Evaluate subtensor with this subcomponent
self._components.push(c1)
code = self.visit(op)
self._components.pop()
return code
# -------------------------------------------------------------------------
# Variable (variable.py).
# -------------------------------------------------------------------------
return self.visit(o.expression())
# -------------------------------------------------------------------------
# Generate terms for representation.
# -------------------------------------------------------------------------
[docs] def generate_terms(self, integrand, integral_type):
"Generate terms for code generation."
# Set domain type
self.integral_type = integral_type
# Get terms
terms = self.visit(integrand)
# Get formatting
f_nzc = format["nonzero columns"](0).split("0")[0]
# Loop code and add weight and scale factor to value and sort
# after loop ranges.
new_terms = {}
for key, val in sorted(terms.items()):
# If value was zero continue.
if val is None:
continue
# Create data.
value, ops, sets = self._create_entry_data(val, integral_type)
# Extract nzc columns if any and add to sets.
used_nzcs = set([int(k[1].split(f_nzc)[1].split("[")[0]) for k in key if f_nzc in k[1]])
sets.append(used_nzcs)
# Create loop information and entry from key info and
# insert into dict.
loop, entry = self._create_loop_entry(key, f_nzc)
if loop not in new_terms:
sets.append({})
new_terms[loop] = [sets, [(entry, value, ops)]]
else:
for i, s in enumerate(sets):
new_terms[loop][0][i].update(s)
new_terms[loop][1].append((entry, value, ops))
return new_terms
def _create_loop_entry(self, key, f_nzc):
indices = {0: format["first free index"],
1: format["second free index"]}
# Create appropriate entries.
# FIXME: We only support rank 0, 1 and 2.
entry = ""
loop = ()
if len(key) == 0:
entry = "0"
elif len(key) == 1:
key = key[0]
# Checking if the basis was a test function.
# TODO: Make sure test function indices are always
# rearranged to 0.
ffc_assert(key[0] == -2 or key[0] == 0,
"Linear forms must be defined using test functions only: " + repr(key))
index_j, entry, range_j, space_dim_j = key
loop = ((indices[index_j], 0, range_j),)
if range_j == 1 and self.optimise_parameters["ignore ones"] and not (f_nzc in entry):
loop = ()
elif len(key) == 2:
# Extract test and trial loops in correct order and check
# if for is legal.
key0, key1 = (0, 0)
for k in key:
ffc_assert(k[0] in indices,
"Bilinear forms must be defined using test and trial functions (index -2, -1, 0, 1): " + repr(k))
if k[0] == -2 or k[0] == 0:
key0 = k
else:
key1 = k
index_j, entry_j, range_j, space_dim_j = key0
index_k, entry_k, range_k, space_dim_k = key1
loop = []
if not (range_j == 1 and
self.optimise_parameters["ignore ones"]) or f_nzc in entry_j:
loop.append((indices[index_j], 0, range_j))
if not (range_k == 1 and self.optimise_parameters["ignore ones"]) or f_nzc in entry_k:
loop.append((indices[index_k], 0, range_k))
entry = format["add"]([format["mul"]([entry_j, str(space_dim_k)]), entry_k])
loop = tuple(loop)
else:
error("Only rank 0, 1 and 2 tensors are currently supported: " + repr(key))
# Generate the code line for the entry.
# Try to evaluate entry ("3*6 + 2" --> "20").
try:
entry = str(eval(entry))
except Exception:
pass
return loop, entry
# -------------------------------------------------------------------------
# Helper functions for transformation of UFL objects in base class
# -------------------------------------------------------------------------
def _create_symbol(self, symbol, domain):
error("This function should be implemented by the child class.")
def _create_product(self, symbols):
error("This function should be implemented by the child class.")
def _format_scalar_value(self, value):
error("This function should be implemented by the child class.")
def _math_function(self, operands, format_function):
error("This function should be implemented by the child class.")
def _atan_2_function(self, operands, format_function):
error("This function should be implemented by the child class.")
def _get_auxiliary_variables(self, ufl_function, component, derivatives):
"Helper function for both Coefficient and Argument."
# Get UFL element.
ufl_element = ufl_function.ufl_element()
# Get subelement and the relative (flattened) component (in
# case we have mixed elements).
local_comp, local_elem = ufl_element.extract_component(component)
# For basic tensor elements, local_comp should be flattened
if len(local_comp) and len(local_elem.value_shape()) > 0:
# Map component using component map from UFL. (TODO:
# inefficient use of this function)
comp_map, _ = build_component_numbering(local_elem.value_shape(),
local_elem.symmetry())
local_comp = comp_map[local_comp]
# Set local_comp to 0 if it is ()
if not local_comp:
local_comp = 0
# Check that component != not () since the UFL component map
# will turn it into 0, and () does not mean zeroth component
# in this context.
if len(component):
# Map component using component map from UFL. (TODO:
# inefficient use of this function)
comp_map, comp_num = build_component_numbering(ufl_element.value_shape(), ufl_element.symmetry())
component = comp_map[component]
# Map physical components into reference components
component, dummy = transform_component(component, 0, ufl_element)
# Compute the local offset (needed for non-affine mappings).
local_offset = component - local_comp
else:
# Compute the local offset (needed for non-affine mappings).
local_offset = 0
# Create FFC element.
ffc_element = create_element(ufl_element)
# Assuming that mappings for all basisfunctions are equal
ffc_sub_element = create_element(local_elem)
transformation = ffc_sub_element.mapping()[0]
ffc_assert(all(transformation == mapping for mapping in ffc_sub_element.mapping()),
"Assuming subelement mappings are equal but they differ.")
# Generate FFC multi index for derivatives.
tdim = self.tdim
multiindices = FFCMultiIndex([list(range(tdim))] * len(derivatives)).indices
return (component, local_elem, local_comp, local_offset, ffc_element,
transformation, multiindices)
def _get_current_entity(self):
if self.entity_type == "cell":
# If we add macro cell integration, I guess the 'current
# cell number' would go here?
return 0
elif self.entity_type == "facet":
# Handle restriction through facet.
return {"+": self.facet0, "-": self.facet1,
None: self.facet0}[self.restriction]
elif self.entity_type == "vertex":
return self.vertex
else:
error("Unknown entity type %s." % self.entity_type)
def _create_mapping_basis(self, component, deriv, avg, ufl_argument,
ffc_element):
"Create basis name and mapping from given basis_info."
# Get string for integration points.
f_ip = "0" if (avg or self.points == 1) else format["integration points"]
generate_psi_name = format["psi name"]
# Only support test and trial functions.
indices = {0: format["first free index"],
1: format["second free index"]}
# Check that we have a basis function.
ffc_assert(ufl_argument.number() in indices,
"Currently, Argument number must be either 0 or 1: " + repr(ufl_argument))
ffc_assert(ufl_argument.part() is None,
"Currently, Argument part is not supporte: " + repr(ufl_argument))
# Get element counter and loop index.
element_counter = self.element_map[1 if avg else self.points][ufl_argument.ufl_element()]
loop_index = indices[ufl_argument.number()]
# Offset element space dimension in case of negative
# restriction, need to use the complete element for offset in
# case of mixed element.
space_dim = ffc_element.space_dimension()
offset = {"+": "", "-": str(space_dim), None: ""}[self.restriction]
# If we have a restricted function multiply space_dim by two.
if self.restriction in ("+", "-"):
space_dim *= 2
# Create basis access, we never need to map the entry in the
# basis table since we will either loop the entire space
# dimension or the non-zeros.
if self.restriction in ("+", "-") and self.integral_type in custom_integral_types and offset != "":
# Special case access for custom integrals (all basis
# functions stored in flattened array)
basis_access = format["component"]("", [f_ip, format["add"]([loop_index, offset])])
else:
# Normal basis function access
basis_access = format["component"]("", [f_ip, loop_index])
# Get current cell entity, with current restriction considered
entity = self._get_current_entity()
name = generate_psi_name(element_counter, self.entity_type, entity,
component, deriv, avg)
name, non_zeros, zeros, ones = self.name_map[name]
loop_index_range = shape(self.unique_tables[name])[1]
# If domain type is custom, then special-case set loop index
# range since table is empty
if self.integral_type in custom_integral_types:
loop_index_range = ffc_element.space_dimension() # different from `space_dimension`...
basis = ""
# Ignore zeros if applicable
if zeros and (self.optimise_parameters["ignore zero tables"] or self.optimise_parameters["remove zero terms"]):
basis = self._format_scalar_value(None)[()]
# If the loop index range is one we can look up the first
# component in the psi array. If we only have ones we don't
# need the basis.
elif self.optimise_parameters["ignore ones"] and loop_index_range == 1 and ones:
loop_index = "0"
basis = self._format_scalar_value(1.0)[()]
else:
# Add basis name to the psi tables map for later use.
basis = self._create_symbol(name + basis_access, BASIS)[()]
self.psi_tables_map[basis] = name
# Create the correct mapping of the basis function into the
# local element tensor.
basis_map = loop_index
if non_zeros and basis_map == "0":
basis_map = str(non_zeros[1][0])
elif non_zeros:
basis_map = format["component"](format["nonzero columns"](non_zeros[0]), basis_map)
if offset:
basis_map = format["grouping"](format["add"]([basis_map, offset]))
# Try to evaluate basis map ("3 + 2" --> "5").
try:
basis_map = str(eval(basis_map))
except Exception:
pass
# Create mapping (index, map, loop_range, space_dim).
# Example dx and ds: (0, j, 3, 3)
# Example dS: (0, (j + 3), 3, 6), 6=2*space_dim
# Example dS optimised: (0, (nz2[j] + 3), 2, 6), 6=2*space_dim
mapping = ((ufl_argument.number(), basis_map, loop_index_range,
space_dim),)
return (mapping, basis)
def _create_function_name(self, component, deriv, avg, is_quad_element,
ufl_function, ffc_element):
ffc_assert(ufl_function in self._function_replace_values,
"Expecting ufl_function to have been mapped prior to this call.")
# Get string for integration points.
f_ip = "0" if (avg or self.points == 1) else format["integration points"]
# Get the element counter.
element_counter = self.element_map[1 if avg else self.points][ufl_function.ufl_element()]
# Get current cell entity, with current restriction considered
entity = self._get_current_entity()
# Set to hold used nonzero columns
used_nzcs = set()
# Create basis name and map to correct basis and get info.
generate_psi_name = format["psi name"]
psi_name = generate_psi_name(element_counter, self.entity_type, entity,
component, deriv, avg)
psi_name, non_zeros, zeros, ones = self.name_map[psi_name]
# If all basis are zero we just return None.
if zeros and self.optimise_parameters["ignore zero tables"]:
return self._format_scalar_value(None)[()]
# Get the index range of the loop index.
loop_index_range = shape(self.unique_tables[psi_name])[1]
# If domain type is custom, then special-case set loop index
# range since table is empty
if self.integral_type in custom_integral_types:
loop_index_range = ffc_element.space_dimension()
# Create loop index
if loop_index_range > 1:
# Pick first free index of secondary type (could use
# primary indices, but it's better to avoid confusion).
loop_index = format["free indices"][0]
# If we have a quadrature element we can use the ip number to look
# up the value directly. Need to add offset in case of components.
if is_quad_element:
quad_offset = 0
if component:
# FIXME: Should we add a member function elements() to
# FiniteElement?
if isinstance(ffc_element, MixedElement):
for i in range(component):
quad_offset += ffc_element.elements()[i].space_dimension()
elif component != 1:
error("Can't handle components different from 1 if we don't have a MixedElement.")
else:
quad_offset += ffc_element.space_dimension()
if quad_offset:
coefficient_access = format["add"]([f_ip, str(quad_offset)])
else:
if non_zeros and f_ip == "0":
# If we have non zero column mapping but only one
# value just pick it.
# MSA: This should be an exact refactoring of the
# previous logic, but I'm not sure if these
# lines were originally intended here in the
# quad_element section, or what this even
# does:
coefficient_access = str(non_zeros[1][0])
else:
coefficient_access = f_ip
elif non_zeros:
if loop_index_range == 1:
# If we have non zero column mapping but only one
# value just pick it.
coefficient_access = str(non_zeros[1][0])
else:
used_nzcs.add(non_zeros[0])
coefficient_access = format["component"](format["nonzero columns"](non_zeros[0]), loop_index)
elif loop_index_range == 1:
# If the loop index range is one we can look up the first
# component in the coefficient array.
coefficient_access = "0"
else:
# Or just set default coefficient access.
coefficient_access = loop_index
# Offset by element space dimension in case of negative
# restriction.
offset = {"+": "", "-": str(ffc_element.space_dimension()), None: ""}[self.restriction]
if offset:
coefficient_access = format["add"]([coefficient_access, offset])
# Try to evaluate coefficient access ("3 + 2" --> "5").
try:
coefficient_access = str(eval(coefficient_access))
C_ACCESS = GEO
except Exception:
C_ACCESS = IP
# Format coefficient access
coefficient = format["coefficient"](str(ufl_function.count()),
coefficient_access)
# Build and cache some function data only if we need the basis
# MSA: I don't understand the mix of loop index range check
# and ones check here, but that's how it was.
if is_quad_element or (loop_index_range == 1 and ones and self.optimise_parameters["ignore ones"]):
# If we only have ones or if we have a quadrature element
# we don't need the basis.
function_symbol_name = coefficient
F_ACCESS = C_ACCESS
else:
# Add basis name to set of used tables and add matrix
# access.
# TODO: We should first add this table if the function is
# used later in the expressions. If some term is
# multiplied by zero and it falls away there is no need to
# compute the function value
self.used_psi_tables.add(psi_name)
# Create basis access, we never need to map the entry in
# the basis table since we will either loop the entire
# space dimension or the non-zeros.
basis_index = "0" if loop_index_range == 1 else loop_index
basis_access = format["component"]("", [f_ip, basis_index])
basis_name = psi_name + basis_access
# Try to set access to the outermost possible loop
if f_ip == "0" and basis_access == "0":
B_ACCESS = GEO
F_ACCESS = C_ACCESS
else:
B_ACCESS = IP
F_ACCESS = IP
# Format expression for function
function_expr = self._create_product([self._create_symbol(basis_name, B_ACCESS)[()],
self._create_symbol(coefficient, C_ACCESS)[()]])
# Check if the expression to compute the function value is
# already in the dictionary of used function. If not,
# generate a new name and add.
data = self.function_data.get(function_expr)
if data is None:
function_count = len(self.function_data)
data = (function_count, loop_index_range,
self._count_operations(function_expr),
psi_name, used_nzcs, ufl_function.ufl_element())
self.function_data[function_expr] = data
function_symbol_name = format["function value"](data[0])
# TODO: This access stuff was changed subtly during my
# refactoring, the
# X_ACCESS vars is an attempt at making it right, make sure it
# is correct now!
return self._create_symbol(function_symbol_name, F_ACCESS)[()]
def _generate_affine_map(self):
"""Generate psi table for affine map, used by spatial coordinate to
map integration point to physical element.
"""
# TODO: KBO: Perhaps it is better to create a fiat element and
# tabulate the values at the integration points?
f_FEA = format["affine map table"]
f_ip = format["integration points"]
affine_map = {1: lambda x: [1.0 - x[0], x[0]],
2: lambda x: [1.0 - x[0] - x[1], x[0], x[1]],
3: lambda x: [1.0 - x[0] - x[1] - x[2], x[0], x[1], x[2]]}
num_ip = self.points
w, points = self.quad_weights[num_ip]
if self.facet0 is not None:
# Extract the geometric dimension of the points we want to map
dim = len(points[0]) + 1
dim2cellname = ["interval", "triangle", "tetrahedron"]
cellname = dim2cellname[dim-1]
points = map_facet_points(points, self.facet0, cellname)
name = f_FEA(num_ip, self.facet0)
elif self.vertex is not None:
error("Spatial coordinates (x) not implemented for point measure (dP)") # TODO: Implement this, should be just the point.
else:
name = f_FEA(num_ip, 0)
if name not in self.unique_tables:
self.unique_tables[name] = array([affine_map[len(p)](p) for p in points])
if self.coordinate is None:
ip = f_ip if num_ip > 1 else 0
r = None if self.facet1 is None else "+"
self.coordinate = [name, self.gdim, ip, r]
# -------------------------------------------------------------------------
# Helper functions for code_generation()
# -------------------------------------------------------------------------
def _count_operations(self, expression):
error("This function should be implemented by the child class.")
def _create_entry_data(self, val):
error("This function should be implemented by the child class.")