# Source code for ufl.checks

```# -*- coding: utf-8 -*-
"""Utility functions for checking properties of expressions."""

# Copyright (C) 2013-2016 Martin Sandve Alnæs
#
# This file is part of UFL (https://www.fenicsproject.org)
#
#
# Modified by Anders Logg, 2008-2009

from ufl.core.expr import Expr
from ufl.corealg.traversal import traverse_unique_terminals

[docs]def is_python_scalar(expression):
"Return True iff expression is of a Python scalar type."
return isinstance(expression, (int, float, complex))

[docs]def is_ufl_scalar(expression):
"""Return True iff expression is scalar-valued,
but possibly containing free indices."""
return isinstance(expression, Expr) and not expression.ufl_shape

[docs]def is_true_ufl_scalar(expression):
"""Return True iff expression is scalar-valued,
with no free indices."""
return isinstance(expression, Expr) and \
not (expression.ufl_shape or expression.ufl_free_indices)

[docs]def is_cellwise_constant(expr):
"Return whether expression is constant over a single cell."
# TODO: Implement more accurately considering e.g. derivatives?
return all(t.is_cellwise_constant() for t in traverse_unique_terminals(expr))

[docs]def is_globally_constant(expr):
"""Check if an expression is globally constant, which
includes spatially independent constant coefficients that
are not known before assembly time."""
# TODO: This does not consider gradients of coefficients, so false
# negatives are possible.
# from ufl.argument import Argument
# from ufl.coefficient import Coefficient
from ufl.geometry import GeometricQuantity
from ufl.core.terminal import FormArgument
for e in traverse_unique_terminals(expr):
# Return False if any single terminal is not constant
if e._ufl_is_literal_:
# Accept literals first, they are the most common
# terminals
continue
elif isinstance(e, FormArgument):
# Accept only Real valued Arguments and Coefficients
if e.ufl_element().family() == "Real":
continue
else:
return False
elif isinstance(e, GeometricQuantity):
# Reject all geometric quantities, they all vary over
# cells
return False

# All terminals passed constant check
return True

[docs]def is_scalar_constant_expression(expr):
"""Check if an expression is a globally constant scalar expression."""
if is_python_scalar(expr):
return True
if expr.ufl_shape:
return False
return is_globally_constant(expr)
```