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"""Functions to check properties of forms and integrals."""

# Copyright (C) 2008-2014 Martin Sandve Alnes and Anders Logg
#
# This file is part of UFL.
#
# UFL 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.
#
# UFL 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 UFL. If not, see <http://www.gnu.org/licenses/>.
#
# First added:  2008-03-14
# Last changed: 2012-04-12

from ufl.log import warning, debug
from ufl.algorithms.traversal import iter_expressions
from ufl.algorithms.argument_dependencies import extract_argument_dependencies, NotMultiLinearException

#--- Utilities for checking properties of forms ---

def is_multilinear(form):
    "Check if form is multilinear in arguments."
    # An attempt at implementing is_multilinear using extract_argument_dependencies.
    # TODO: This has some false negatives for "multiple configurations". (Does it still? Needs testing!)
    # TODO: FFC probably needs a variant of this which checks for some sorts of linearity
    #       in Coefficients as well, this should be a fairly simple extension of the current algorithm.
    try:
        for e in iter_expressions(form):
            deps = extract_argument_dependencies(e)
            nargs = [len(d) for d in deps]
            if len(nargs) == 0:
                debug("This form is a functional.")
            if len(nargs) == 1:
                debug("This form is linear in %d arguments." % nargs[0])
            if len(nargs) > 1:
                warning("This form has more than one argument "\
                    "'configuration', it has terms that are linear in %s "\
                    "arguments respectively." % str(nargs))

    except NotMultiLinearException, msg:
        warning("Form is not multilinear, the offending term is: %s" % msg)
        return False

    return True


# TODO: Remove this code if nobody needs it for anything:
#===============================================================================
# def is_multilinear(form):
#    "Check if form is multilinear."
#
#    # Check that we get a form
#    ufl_assert(isinstance(form, Form), "Not a form: %s" % str(form))
#
#    # Check that all operators applied to arguments are linear
#    for e in iter_expressions(form):
#        stack = []
#        for o in pre_traversal(e, stack):
#            if isinstance(o, Argument):
#                for operator in stack:
#                    if not operator.is_linear():
#                        warning("Nonlinear operator applied to argument:" + str(operator))
#                        return False
#
#    # Extract monomials
#    monomials = []
#    for e in iter_expressions(form):
#        monomials += _extract_monomials(e)
#
#    # Extract arguments
#    arguments = set()
#    for monomial in monomials:
#        for v in monomial:
#            arguments.add(v)
#
#    # Check that each argument appears exactly once in each monomial term
#    for monomial in monomials:
#        for v in arguments:
#            if not len([w for w in monomial if w == v]) == 1:
#                warning("Argument %s does not appear exactly once in each term." % str(v))
#                return False
#
#    return True
#===============================================================================