"""This module defines the Action class."""
# Copyright (C) 2021 India Marsden
#
# This file is part of UFL (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
#
# Modified by Nacime Bouziani, 2021-2022.
from itertools import chain
from ufl.algebra import Sum
from ufl.argument import Argument, Coargument
from ufl.coefficient import BaseCoefficient, Coefficient, Cofunction
from ufl.constantvalue import Zero
from ufl.core.base_form_operator import BaseFormOperator
from ufl.core.ufl_type import ufl_type
from ufl.differentiation import CoefficientDerivative
from ufl.form import BaseForm, Form, FormSum, ZeroBaseForm
from ufl.matrix import Matrix
# --- The Action class represents the action of a numerical object that needs
# to be computed at assembly time ---
[docs]@ufl_type()
class Action(BaseForm):
"""UFL base form type: respresents the action of an object on another.
For example:
res = Ax
A would be the first argument, left and x would be the second argument,
right.
Action objects will result when the action of an assembled object
(e.g. a Matrix) is taken. This delays the evaluation of the action until
assembly occurs.
"""
__slots__ = (
"_left",
"_right",
"ufl_operands",
"_repr",
"_arguments",
"_coefficients",
"_domains",
"_hash",
)
def __new__(cls, *args, **kw):
"""Create a new Action."""
left, right = args
# Check trivial case
if left == 0 or right == 0:
if isinstance(left, Zero):
# There is no point in checking the action arguments
# if `left` is a `ufl.Zero` as those objects don't have arguments.
# We can also not reliably determine the `ZeroBaseForm` arguments.
return ZeroBaseForm(())
# Still need to work out the ZeroBaseForm arguments.
new_arguments, _ = _get_action_form_arguments(left, right)
return ZeroBaseForm(new_arguments)
# Coarguments (resp. Argument) from V* to V* (resp. from V to V) are identity matrices,
# i.e. we have: V* x V -> R (resp. V x V* -> R).
if isinstance(left, (Coargument, Argument)):
return right
if isinstance(right, (Coargument, Argument)):
return left
if isinstance(left, (FormSum, Sum)):
# Action distributes over sums on the LHS
return FormSum(*[(Action(component, right), 1) for component in left.ufl_operands])
if isinstance(right, (FormSum, Sum)):
# Action also distributes over sums on the RHS
return FormSum(*[(Action(left, component), 1) for component in right.ufl_operands])
return super(Action, cls).__new__(cls)
def __init__(self, left, right):
"""Initialise."""
BaseForm.__init__(self)
self._left = left
self._right = right
self.ufl_operands = (self._left, self._right)
self._domains = None
# Check compatibility of function spaces
_check_function_spaces(left, right)
self._repr = "Action(%s, %s)" % (repr(self._left), repr(self._right))
self._hash = None
[docs] def ufl_function_spaces(self):
"""Get the tuple of function spaces of the underlying form."""
if isinstance(self._right, Form):
return self._left.ufl_function_spaces()[:-1] + self._right.ufl_function_spaces()[1:]
elif isinstance(self._right, Coefficient):
return self._left.ufl_function_spaces()[:-1]
[docs] def left(self):
"""Get left."""
return self._left
[docs] def right(self):
"""Get right."""
return self._right
def _analyze_form_arguments(self):
"""Compute the Arguments of this Action.
The highest number Argument of the left operand and the lowest number
Argument of the right operand are consumed by the action.
"""
self._arguments, self._coefficients = _get_action_form_arguments(self._left, self._right)
def _analyze_domains(self):
"""Analyze which domains can be found in Action."""
from ufl.domain import join_domains
# Collect domains
self._domains = join_domains(
chain.from_iterable(e.ufl_domains() for e in self.ufl_operands)
)
[docs] def equals(self, other):
"""Check if two Actions are equal."""
if type(other) is not Action:
return False
if self is other:
return True
# Make sure we are returning a boolean as left and right equalities can be `ufl.Equation`s
# if the underlying objects are `ufl.BaseForm`.
return bool(self._left == other._left) and bool(self._right == other._right)
def __str__(self):
"""Format as a string."""
return f"Action({self._left}, {self._right})"
def __repr__(self):
"""Representation."""
return self._repr
def __hash__(self):
"""Hash."""
if self._hash is None:
self._hash = hash(("Action", hash(self._right), hash(self._left)))
return self._hash
def _check_function_spaces(left, right):
"""Check if the function spaces of left and right match."""
if isinstance(right, CoefficientDerivative):
# Action differentiation pushes differentiation through
# right as a consequence of Leibniz formula.
right, *_ = right.ufl_operands
# `left` can also be a Coefficient in V (= V**), e.g.
# `action(Coefficient(V), Cofunction(V.dual()))`.
left_arg = left.arguments()[-1] if not isinstance(left, Coefficient) else left
if isinstance(right, (Form, Action, Matrix, ZeroBaseForm)):
if left_arg.ufl_function_space().dual() != right.arguments()[0].ufl_function_space():
raise TypeError("Incompatible function spaces in Action")
elif isinstance(right, (Coefficient, Cofunction, Argument, BaseFormOperator)):
if left_arg.ufl_function_space() != right.ufl_function_space():
raise TypeError("Incompatible function spaces in Action")
# `Zero` doesn't contain any information about the function space.
# -> Not a problem since Action will get simplified with a
# `ZeroBaseForm` which won't take into account the arguments on
# the right because of argument contraction.
# This occurs for:
# `derivative(Action(A, B), u)` with B is an `Expr` such that dB/du == 0
# -> `derivative(B, u)` becomes `Zero` when expanding derivatives since B is an Expr.
elif not isinstance(right, Zero):
raise TypeError("Incompatible argument in Action: %s" % type(right))
def _get_action_form_arguments(left, right):
"""Perform argument contraction to work out the arguments of Action."""
coefficients = ()
# `left` can also be a Coefficient in V (= V**), e.g.
# `action(Coefficient(V), Cofunction(V.dual()))`.
left_args = left.arguments()[:-1] if not isinstance(left, Coefficient) else ()
if isinstance(right, BaseForm):
arguments = left_args + right.arguments()[1:]
coefficients += right.coefficients()
elif isinstance(right, CoefficientDerivative):
# Action differentiation pushes differentiation through
# right as a consequence of Leibniz formula.
from ufl.algorithms.analysis import extract_arguments_and_coefficients
right_args, right_coeffs = extract_arguments_and_coefficients(right)
arguments = left_args + tuple(right_args)
coefficients += tuple(right_coeffs)
elif isinstance(right, (BaseCoefficient, Zero)):
arguments = left_args
# When right is ufl.Zero, Action gets simplified so updating
# coefficients here doesn't matter
coefficients += (right,)
elif isinstance(right, Argument):
arguments = left_args + (right,)
else:
raise TypeError
if isinstance(left, BaseForm):
coefficients += left.coefficients()
return arguments, coefficients