# Source code for ufl_legacy.algorithms.domain_analysis

    # -*- coding: utf-8 -*-
    """Algorithms for building canonical data structure for integrals over subdomains."""

    # Copyright (C) 2009-2016 Anders Logg and Martin Sandve Alnæs
    #
    # This file is part of UFL (https://www.fenicsproject.org)
    #
    # SPDX-License-Identifier:    LGPL-3.0-or-later

    from collections import defaultdict

    import ufl_legacy as ufl
    from ufl_legacy.log import error
    from ufl_legacy.integral import Integral
    from ufl_legacy.form import Form
    from ufl_legacy.sorting import cmp_expr, sorted_expr
    from ufl_legacy.utils.sorting import canonicalize_metadata, sorted_by_key
    from ufl_legacy.algorithms.coordinate_derivative_helpers import attach_coordinate_derivatives, strip_coordinate_derivatives
    import numbers

    class IntegralData(object):
        """Utility class with the members (domain, integral_type,
            subdomain_id, integrals, metadata)

        where metadata is an empty dictionary that may be used for
        associating metadata with each object.

        """
        __slots__ = ('domain', 'integral_type', 'subdomain_id',
                     'integrals', 'metadata',
                     'integral_coefficients',
                     'enabled_coefficients')

        def __init__(self, domain, integral_type, subdomain_id, integrals,
                     metadata):
            if 1 != len(set(itg.ufl_domain() for itg in integrals)):
                error("Multiple domains mismatch in integral data.")
            if not all(integral_type == itg.integral_type() for itg in integrals):
                error("Integral type mismatch in integral data.")
            if not all(subdomain_id == itg.subdomain_id() for itg in integrals):
                error("Subdomain id mismatch in integral data.")

            self.domain = domain
            self.integral_type = integral_type
            self.subdomain_id = subdomain_id

            self.integrals = integrals

            # This is populated in preprocess using data not available at
            # this stage:
            self.integral_coefficients = None
            self.enabled_coefficients = None

            # TODO: I think we can get rid of this with some refactoring
            # in ffc:
            self.metadata = metadata

        def __lt__(self, other):
            # To preserve behaviour of extract_integral_data:
            return ((self.integral_type, self.subdomain_id,
                     self.integrals, self.metadata) <
                    (other.integral_type, other.subdomain_id, other.integrals,
                     other.metadata))

        def __eq__(self, other):
            # Currently only used for tests:
            return (self.integral_type == other.integral_type and
                    self.subdomain_id == other.subdomain_id and
                    self.integrals == other.integrals and
                    self.metadata == other.metadata)

        def __str__(self):
            s = "IntegralData over domain(%s, %s), with integrals:\n%s\nand metadata:\n%s" % (
                self.integral_type, self.subdomain_id,
                '\n\n'.join(map(str, self.integrals)), self.metadata)
            return s

    def dicts_lt(a, b):
        na = 0 if a is None else len(a)
        nb = 0 if b is None else len(b)
        if na != nb:
            return len(a) < len(b)
        for ia, ib in zip(sorted_by_key(a), sorted_by_key(b)):
            # Assuming keys are sortable (usually str)
            if ia[0] != ib[0]:
                return (ia[0].__class__.__name__, ia[0]) < (ib[0].__class__.__name__, ib[0])  # Hack to preserve type sorting in py3
            # Assuming values are sortable
            if ia[1] != ib[1]:
                return (ia[1].__class__.__name__, ia[1]) < (ib[1].__class__.__name__, ib[1])  # Hack to preserve type sorting in py3

    # Tuple comparison helper

    class ExprTupleKey(object):
        __slots__ = ('x',)

        def __init__(self, x):
            self.x = x

        def __lt__(self, other):
            # Comparing expression first
            c = cmp_expr(self.x[0], other.x[0])
            if c < 0:
                return True
            elif c > 0:
                return False
            else:
                # Comparing form compiler data
                mds = canonicalize_metadata(self.x[1])
                mdo = canonicalize_metadata(other.x[1])
                return mds < mdo

    def group_integrals_by_domain_and_type(integrals, domains):
        """
        Input:
            integrals: list of Integral objects
            domains: list of AbstractDomain objects from the parent Form

        Output:
            integrals_by_domain_and_type: dict: (domain, integral_type) -> list(Integral)
        """
        integrals_by_domain_and_type = defaultdict(list)
        for itg in integrals:
            if itg.ufl_domain() is None:
                error("Integral has no domain.")
            key = (itg.ufl_domain(), itg.integral_type())

            # Append integral to list of integrals with shared key
            integrals_by_domain_and_type[key].append(itg)

        return integrals_by_domain_and_type

    def integral_subdomain_ids(integral):
        "Get a tuple of integer subdomains or a valid string subdomain from integral."
        did = integral.subdomain_id()
        if isinstance(did, numbers.Integral):
            return (did,)
        elif isinstance(did, tuple):
            if not all(isinstance(d, numbers.Integral) for d in did):
                error("Expecting only integer subdomains in tuple.")
            return did
        elif did in ("everywhere", "otherwise"):
            # TODO: Define list of valid strings somewhere more central
            return did
        else:
            error("Invalid domain id %s." % did)

    def rearrange_integrals_by_single_subdomains(integrals, do_append_everywhere_integrals):
        """Rearrange integrals over multiple subdomains to single subdomain integrals.

        Input:
            integrals: list(Integral)

        Output:
            integrals: dict: subdomain_id -> list(Integral) (reconstructed with single subdomain_id)
        """
        # Split integrals into lists of everywhere and subdomain integrals
        everywhere_integrals = []
        subdomain_integrals = []
        for itg in integrals:
            dids = integral_subdomain_ids(itg)
            if dids == "otherwise":
                error("'otherwise' integrals should never occur before preprocessing.")
            elif dids == "everywhere":
                everywhere_integrals.append(itg)
            else:
                subdomain_integrals.append((dids, itg))

        # Fill single_subdomain_integrals with lists of integrals from
        # subdomain_integrals, but split and restricted to single
        # subdomain ids
        single_subdomain_integrals = defaultdict(list)
        for dids, itg in subdomain_integrals:
            # Region or single subdomain id
            for did in dids:
                # Restrict integral to this subdomain!
                single_subdomain_integrals[did].append(itg.reconstruct(subdomain_id=did))

        # Add everywhere integrals to each single subdomain id integral
        # list
        otherwise_integrals = []
        for ev_itg in everywhere_integrals:
            # Restrict everywhere integral to 'otherwise'
            otherwise_integrals.append(ev_itg.reconstruct(subdomain_id="otherwise"))

            # Restrict everywhere integral to each subdomain
            # and append to each integral list
            if do_append_everywhere_integrals:
                for subdomain_id in sorted(single_subdomain_integrals.keys()):
                    single_subdomain_integrals[subdomain_id].append(
                        ev_itg.reconstruct(subdomain_id=subdomain_id))

        if otherwise_integrals:
            single_subdomain_integrals["otherwise"] = otherwise_integrals

        return single_subdomain_integrals

    def accumulate_integrands_with_same_metadata(integrals):
        """
        Taking input on the form:
            integrals = [integral0, integral1, ...]

        Return result on the form:
            integrands_by_id = [(integrand0, metadata0),
                                (integrand1, metadata1), ...]

        where integrand0 < integrand1 by the canonical ufl expression ordering criteria.
        """
        # Group integrals by compiler data hash
        by_cdid = {}
        for itg in integrals:
            cd = itg.metadata()
            cdid = hash(canonicalize_metadata(cd))
            if cdid not in by_cdid:
                by_cdid[cdid] = ([], cd)
            by_cdid[cdid][0].append(itg)

        # Accumulate integrands separately for each compiler data object
        # id
        for cdid in by_cdid:
            integrals, cd = by_cdid[cdid]
            # Ensure canonical sorting of more than two integrands
            integrands = sorted_expr((itg.integrand() for itg in integrals))
            integrands_sum = sum(integrands[1:], integrands[0])
            by_cdid[cdid] = (integrands_sum, cd)

        # Sort integrands canonically by integrand first then compiler
        # data
        return sorted(by_cdid.values(), key=ExprTupleKey)

    def build_integral_data(integrals):
        """Build integral data given a list of integrals.

        :arg integrals: An iterable of :class:`~.Integral` objects.
        :returns: A tuple of :class:`IntegralData` objects.

        The integrals you pass in here must have been rearranged and
        gathered (removing the "everywhere" subdomain_id.  To do this, you
        should call :func:`group_form_integrals`.
        """
        itgs = defaultdict(list)

        for integral in integrals:
            domain = integral.ufl_domain()
            integral_type = integral.integral_type()
            subdomain_id = integral.subdomain_id()
            if subdomain_id == "everywhere":
                raise ValueError("'everywhere' not a valid subdomain id.  Did you forget to call group_form_integrals?")
            # Group for integral data (One integral data object for all
            # integrals with same domain, itype, subdomain_id (but
            # possibly different metadata).
            itgs[(domain, integral_type, subdomain_id)].append(integral)

        # Build list with canonical ordering, iteration over dicts
        # is not deterministic across python versions
        def keyfunc(item):
            (d, itype, sid), integrals = item
            return (d._ufl_sort_key_(), itype, (type(sid).__name__, sid))

        integral_datas = []
        for (d, itype, sid), integrals in sorted(itgs.items(), key=keyfunc):
            integral_datas.append(IntegralData(d, itype, sid, integrals, {}))
        return integral_datas

    def group_form_integrals(form, domains, do_append_everywhere_integrals=True):
        """Group integrals by domain and type, performing canonical simplification.

        :arg form: the :class:`~.Form` to group the integrals of.
        :arg domains: an iterable of :class:`~.Domain`s.
        :returns: A new :class:`~.Form` with gathered integrands.
        """
        # Group integrals by domain and type
        integrals_by_domain_and_type = \
            group_integrals_by_domain_and_type(form.integrals(), domains)

        integrals = []
        for domain in domains:
            for integral_type in ufl.measure.integral_types():
                # Get integrals with this domain and type
                ddt_integrals = integrals_by_domain_and_type.get((domain, integral_type))
                if ddt_integrals is None:
                    continue

                # Group integrals by subdomain id, after splitting e.g.
                #   f*dx((1,2)) + g*dx((2,3)) -> f*dx(1) + (f+g)*dx(2) + g*dx(3)
                # (note: before this call, 'everywhere' is a valid subdomain_id,
                # and after this call, 'otherwise' is a valid subdomain_id)
                single_subdomain_integrals = \
                    rearrange_integrals_by_single_subdomains(ddt_integrals, do_append_everywhere_integrals)

                for subdomain_id, ss_integrals in sorted_by_key(single_subdomain_integrals):

                    # strip the coordinate derivatives from all integrals
                    # this yields a list of the form [(coordinate derivative, integral), ...]
                    stripped_integrals_and_coordderivs = strip_coordinate_derivatives(ss_integrals)

                    # now group the integrals by the coordinate derivative
                    def calc_hash(cd):
                        return sum(sum(tuple_elem._ufl_compute_hash_()
                                       for tuple_elem in tuple_) for tuple_ in cd)
                    coordderiv_integrals_dict = {}
                    for integral, coordderiv in stripped_integrals_and_coordderivs:
                        coordderivhash = calc_hash(coordderiv)
                        if coordderivhash in coordderiv_integrals_dict:
                            coordderiv_integrals_dict[coordderivhash][1].append(integral)
                        else:
                            coordderiv_integrals_dict[coordderivhash] = (coordderiv, [integral])

                    # cd_integrals_dict is now a dict of the form
                    # { hash: (CoordinateDerivative, [integral, integral, ...]), ... }
                    # we can now put the integrals back together and then afterwards
                    # apply the CoordinateDerivative again

                    for cdhash, samecd_integrals in sorted_by_key(coordderiv_integrals_dict):

                        # Accumulate integrands of integrals that share the
                        # same compiler data
                        integrands_and_cds = \
                            accumulate_integrands_with_same_metadata(samecd_integrals[1])

                        for integrand, metadata in integrands_and_cds:
                            integral = Integral(integrand, integral_type, domain,
                                                subdomain_id, metadata, None)
                            integral = attach_coordinate_derivatives(integral, samecd_integrals[0])
                            integrals.append(integral)
        return Form(integrals)

    def reconstruct_form_from_integral_data(integral_data):
        integrals = []
        for ida in integral_data:
            integrals.extend(ida.integrals)
        return Form(integrals)