Source code for ufl.algorithms.formtransformations
"""Utilities for transforming complete Forms into new related Forms."""
# Copyright (C) 2008-2016 Martin Sandve Alnæs
#
# This file is part of UFL (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
#
# Modified by Anders Logg, 2008-2009.
# Modified by Garth N. Wells, 2010.
# Modified by Marie E. Rognes, 2010.
import warnings
from logging import debug
from ufl.algebra import Conj
# Other algorithms:
from ufl.algorithms.map_integrands import map_integrands
from ufl.algorithms.replace import replace
from ufl.algorithms.transformer import Transformer
from ufl.argument import Argument
from ufl.coefficient import Coefficient
from ufl.constantvalue import Zero
# All classes:
from ufl.core.expr import ufl_err_str
# FIXME: Don't use this below, it makes partextracter more expensive than necessary
def _expr_has_terminal_types(expr, ufl_types):
"""Check if an expression has terminal types."""
input = [expr]
while input:
e = input.pop()
ops = e.ufl_operands
if ops:
input.extend(ops)
elif isinstance(e, ufl_types):
return True
return False
[docs]def zero_expr(e):
"""Create a zero expression."""
return Zero(e.ufl_shape, e.ufl_free_indices, e.ufl_index_dimensions)
[docs]class PartExtracter(Transformer):
"""PartExtracter extracts those parts of a form that contain the given argument(s)."""
def __init__(self, arguments):
"""Initialise."""
Transformer.__init__(self)
self._want = set(arguments)
[docs] def expr(self, x):
"""Apply to expr.
The default is a nonlinear operator not accepting any Arguments among its children.
"""
if _expr_has_terminal_types(x, Argument):
raise ValueError(f"Found Argument in {ufl_err_str(x)}, this is an invalid expression.")
return (x, set())
# Terminals that are not Variables or Arguments behave as default
# expr-s.
terminal = expr
[docs] def variable(self, x):
"""Return relevant parts of this variable."""
# Extract parts/provides from this variable's expression
expression, label = x.ufl_operands
part, provides = self.visit(expression)
# If the extracted part is zero or we provide more than we
# want, return zero
if isinstance(part, Zero) or (provides - self._want):
return (zero_expr(x), set())
# Reuse varible if possible (or reconstruct from part)
x = self.reuse_if_possible(x, part, label)
return (x, provides)
[docs] def argument(self, x):
"""Return itself unless itself provides too much."""
# An argument provides itself
provides = {x}
# If we provide more than we want, return zero
if provides - self._want:
return (zero_expr(x), set())
return (x, provides)
[docs] def sum(self, x):
"""Return the terms that might eventually yield the correct parts(!).
The logic required for sums is a bit elaborate:
A sum may contain terms providing different arguments. We
should return (a sum of) a suitable subset of these
terms. Those should all provide the same arguments.
For each term in a sum, there are 2 simple possibilities:
1a) The relevant part of the term is zero -> skip.
1b) The term provides more arguments than we want -> skip
2) If all terms fall into the above category, we can just
return zero.
Any remaining terms may provide exactly the arguments we want,
or fewer. This is where things start getting interesting.
3) Bottom-line: if there are terms with providing different
arguments -- provide terms that contain the most arguments. If
there are terms providing different sets of same size -> throw
error (e.g. Argument(-1) + Argument(-2)).
"""
parts_that_provide = {}
# 1. Skip terms that provide too much
original_terms = x.ufl_operands
assert len(original_terms) == 2
for term in original_terms:
# Visit this term in the sum
part, term_provides = self.visit(term)
# If this part is zero or it provides more than we want,
# skip it
if isinstance(part, Zero) or (term_provides - self._want):
continue
# Add the contributions from this part to temporary list
term_provides = frozenset(term_provides)
if term_provides in parts_that_provide:
parts_that_provide[term_provides] += [part]
else:
parts_that_provide[term_provides] = [part]
# 2. If there are no remaining terms, return zero
if not parts_that_provide:
return (zero_expr(x), set())
# 3. Return the terms that provide the biggest set
most_provided = frozenset()
for provideds, parts in parts_that_provide.items(): # TODO: Just sort instead?
# Throw error if size of sets are equal (and not zero)
if len(provideds) == len(most_provided) and len(most_provided):
raise ValueError("Don't know what to do with sums with different Arguments.")
if provideds > most_provided:
most_provided = provideds
terms = parts_that_provide[most_provided]
if len(terms) == 2:
x = self.reuse_if_possible(x, *terms)
else:
(x,) = terms
return (x, most_provided)
[docs] def product(self, x, *ops):
"""Apply to product.
Note: Product is a visit-children-first handler. ops are
the visited factors.
"""
provides = set()
factors = []
for factor, factor_provides in ops:
# If any factor is zero, return
if isinstance(factor, Zero):
return (zero_expr(x), set())
# Add factor to factors and extend provides
factors.append(factor)
provides = provides | factor_provides
# If we provide more than we want, return zero
if provides - self._want:
return (zero_expr(x), provides)
# Reuse product if possible (or reconstruct from factors)
x = self.reuse_if_possible(x, *factors)
return (x, provides)
# inner, outer and dot all behave as product
inner = product
outer = product
dot = product
[docs] def division(self, x):
"""Return parts_of_numerator/denominator."""
# Get numerator and denominator
numerator, denominator = x.ufl_operands
# Check for Arguments in the denominator
if _expr_has_terminal_types(denominator, Argument):
raise ValueError(
f"Found Argument in denominator of {ufl_err_str(x)}, this is an invalid expression."
)
# Visit numerator
numerator_parts, provides = self.visit(numerator)
# If numerator is zero, return zero. (No need to check whether
# it provides too much, already checked by visit.)
if isinstance(numerator_parts, Zero):
return (zero_expr(x), set())
# Reuse x if possible, otherwise reconstruct from (parts of)
# numerator and denominator
x = self.reuse_if_possible(x, numerator_parts, denominator)
return (x, provides)
[docs] def linear_operator(self, x, arg):
"""Apply to linear_operator.
A linear operator with a single operand accepting arity > 0,
providing whatever Argument its operand does.
"""
# linear_operator is a visit-children-first handler. Handled
# arguments are in arg.
part, provides = arg
# Discard if part is zero. (No need to check whether we
# provide too much, already checked by children.)
if isinstance(part, Zero):
return (zero_expr(x), set())
x = self.reuse_if_possible(x, part)
return (x, provides)
# Positive and negative restrictions behave as linear operators
positive_restricted = linear_operator
negative_restricted = linear_operator
# Cell and facet average are linear operators
cell_avg = linear_operator
facet_avg = linear_operator
# Grad is a linear operator
grad = linear_operator
# Conj, Real, Imag are linear operators
conj = linear_operator
real = linear_operator
imag = linear_operator
[docs] def linear_indexed_type(self, x):
"""Return parts of expression belonging to this indexed expression."""
expression, index = x.ufl_operands
part, provides = self.visit(expression)
# Return zero if extracted part is zero. (The expression
# should already have checked if it provides too much.)
if isinstance(part, Zero):
return (zero_expr(x), set())
# Reuse x if possible (or reconstruct by indexing part)
x = self.reuse_if_possible(x, part, index)
return (x, provides)
# All of these indexed thingies behave as a linear_indexed_type
indexed = linear_indexed_type
index_sum = linear_indexed_type
component_tensor = linear_indexed_type
[docs] def list_tensor(self, x, *ops):
"""Apply to list_tensor."""
# list_tensor is a visit-children-first handler. ops contains
# the visited operands with their provides. (It follows that
# none of the visited operands provide more than wanted.)
# Extract the most arguments provided by any of the components
most_provides = ops[0][1]
for component, provides in ops:
if provides - most_provides:
most_provides = provides
# Check that all components either provide the same arguments
# or vanish. (This check is here b/c it is not obvious what to
# return if the components provide different arguments, at
# least with the current transformer design.)
for component, provides in ops:
if provides != most_provides and not isinstance(component, Zero):
raise ValueError(
"PartExtracter does not know how to handle list_tensors with "
"non-zero components providing fewer arguments"
)
# Return components
components = [op[0] for op in ops]
x = self.reuse_if_possible(x, *components)
return (x, most_provides)
[docs]def compute_form_with_arity(form, arity, arguments=None):
"""Compute parts of form of given arity."""
# Extract all arguments in form
if arguments is None:
arguments = form.arguments()
parts = [arg.part() for arg in arguments]
if set(parts) - {None}:
raise ValueError("compute_form_with_arity cannot handle parts.")
if len(arguments) < arity:
warnings.warn(f"Form has no parts with arity {arity}.")
return 0 * form
# Assuming that the form is not a sum of terms
# that depend on different arguments, e.g. (u+v)*dx
# would result in just v*dx. But that doesn't make
# any sense anyway.
sub_arguments = set(arguments[:arity])
pe = PartExtracter(sub_arguments)
def _transform(e):
e, provides = pe.visit(e)
if provides == sub_arguments:
return e
return Zero()
return map_integrands(_transform, form)
[docs]def compute_form_arities(form):
"""Return set of arities of terms present in form."""
# Extract all arguments present in form
arguments = form.arguments()
parts = [arg.part() for arg in arguments]
if set(parts) - {None}:
raise ValueError("compute_form_arities cannot handle parts.")
arities = set()
for arity in range(len(arguments) + 1):
# Compute parts with arity "arity"
parts = compute_form_with_arity(form, arity, arguments)
# Register arity if "parts" does not vanish
if parts and parts.integrals():
arities.add(arity)
return arities
[docs]def compute_form_lhs(form):
"""Compute the left hand side of a form.
Example:
a = u*v*dx + f*v*dx
a = lhs(a) -> u*v*dx
"""
return compute_form_with_arity(form, 2)
[docs]def compute_form_rhs(form):
"""Compute the right hand side of a form.
Example:
a = u*v*dx + f*v*dx
L = rhs(a) -> -f*v*dx
"""
return -compute_form_with_arity(form, 1)
[docs]def compute_form_functional(form):
"""Compute the functional part of a form, that is the terms independent of Arguments.
(Used for testing, not sure if it's useful for anything?)
"""
return compute_form_with_arity(form, 0)
[docs]def compute_form_action(form, coefficient):
"""Compute the action of a form on a Coefficient.
This works simply by replacing the last Argument
with a Coefficient on the same function space (element).
The form returned will thus have one Argument less
and one additional Coefficient at the end if no
Coefficient has been provided.
"""
# TODO: Check whatever makes sense for coefficient
# Extract all arguments
arguments = form.arguments()
parts = [arg.part() for arg in arguments]
if set(parts) - {None}:
raise ValueError("compute_form_action cannot handle parts.")
# Pick last argument (will be replaced)
u = arguments[-1]
fs = u.ufl_function_space()
if coefficient is None:
coefficient = Coefficient(fs)
elif coefficient.ufl_function_space() != fs:
debug("Computing action of form on a coefficient in a different function space.")
return replace(form, {u: coefficient})
[docs]def compute_energy_norm(form, coefficient):
"""Compute the a-norm of a Coefficient given a form a.
This works simply by replacing the two Arguments
with a Coefficient on the same function space (element).
The Form returned will thus be a functional with no
Arguments, and one additional Coefficient at the
end if no coefficient has been provided.
"""
from ufl.formoperators import action # Delayed import to avoid circularity
arguments = form.arguments()
parts = [arg.part() for arg in arguments]
if set(parts) - {None}:
raise ValueError("compute_energy_norm cannot handle parts.")
if len(arguments) != 2:
raise ValueError("Expecting bilinear form.")
v, u = arguments
U = u.ufl_function_space()
V = v.ufl_function_space()
if U != V:
raise ValueError(
f"Expecting equal finite elements for test and trial functions, got '{U}' and '{V}'."
)
if coefficient is None:
coefficient = Coefficient(V)
else:
if coefficient.ufl_function_space() != U:
raise ValueError(
"Trying to compute action of form on a "
"coefficient in an incompatible element space."
)
return action(action(form, coefficient), coefficient)
[docs]def compute_form_adjoint(form, reordered_arguments=None):
"""Compute the adjoint of a bilinear form.
This works simply by swapping the number and part of the two arguments,
but keeping their elements and places in the integrand expressions.
"""
arguments = form.arguments()
parts = [arg.part() for arg in arguments]
if set(parts) - {None}:
raise ValueError("compute_form_adjoint cannot handle parts.")
if len(arguments) != 2:
raise ValueError("Expecting bilinear form.")
v, u = arguments
if v.number() >= u.number():
raise ValueError("Mistaken assumption in code!")
if reordered_arguments is None:
reordered_u = Argument(u.ufl_function_space(), number=v.number(), part=v.part())
reordered_v = Argument(v.ufl_function_space(), number=u.number(), part=u.part())
else:
reordered_u, reordered_v = reordered_arguments
if reordered_u.number() >= reordered_v.number():
raise ValueError("Ordering of new arguments is the same as the old arguments!")
if reordered_u.part() != v.part():
raise ValueError("Ordering of new arguments is the same as the old arguments!")
if reordered_v.part() != u.part():
raise ValueError("Ordering of new arguments is the same as the old arguments!")
if reordered_u.ufl_function_space() != u.ufl_function_space():
raise ValueError("Element mismatch between new and old arguments (trial functions).")
if reordered_v.ufl_function_space() != v.ufl_function_space():
raise ValueError("Element mismatch between new and old arguments (test functions).")
return map_integrands(Conj, replace(form, {v: reordered_v, u: reordered_u}))