# Source code for ufl_legacy.measure

    # -*- coding: utf-8 -*-
    """The Measure class."""

    # 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 2008-2016
    # Modified by Massimiliano Leoni, 2016.

    import numbers

    from itertools import chain

    from ufl_legacy.log import error, deprecate
    from ufl_legacy.core.expr import Expr
    from ufl_legacy.checks import is_true_ufl_scalar
    from ufl_legacy.constantvalue import as_ufl
    from ufl_legacy.utils.dicts import EmptyDict
    from ufl_legacy.domain import as_domain, AbstractDomain, extract_domains
    from ufl_legacy.protocols import id_or_none, metadata_equal, metadata_hashdata

    # Export list for ufl_legacy.classes
    __all_classes__ = ["Measure", "MeasureSum", "MeasureProduct"]

    # TODO: Design a class IntegralType(name, shortname, codim, num_cells, ...)?
    # TODO: Improve descriptions below:

    # Enumeration of valid domain types
    _integral_types = [
        # === Integration over full topological dimension:
        ("cell", "dx"),                     # Over cells of a mesh
        # ("macro_cell", "dE"),              # Over a group of adjacent cells (TODO: Arbitrary cell group? Not currently used.)

        # === Integration over topological dimension - 1:
        ("exterior_facet", "ds"),           # Over one-sided exterior facets of a mesh
        ("interior_facet", "dS"),           # Over two-sided facets between pairs of adjacent cells of a mesh

        # === Integration over topological dimension 0
        ("vertex", "dP"),                    # Over vertices of a mesh
        # ("vertex", "dV"),                  # TODO: Use this over vertices?
        # ("point", "dP"),                   # TODO: Use this over arbitrary points inside cells?

        # === Integration over custom domains
        ("custom", "dc"),                 # Over custom user-defined domains (run-time quadrature points)
        ("cutcell", "dC"),                # Over a cell with some part cut away (run-time quadrature points)
        ("interface", "dI"),              # Over a facet fragment overlapping with two or more cells (run-time quadrature points)
        ("overlap", "dO"),                # Over a cell fragment overlapping with two or more cells (run-time quadrature points)

        # === Firedrake specific hacks on the way out:
        # TODO: Remove these, firedrake can use metadata instead
        # and create the measure objects in firedrake:
        ("exterior_facet_bottom", "ds_b"),  # Over bottom facets on extruded mesh
        ("exterior_facet_top", "ds_t"),     # Over top facets on extruded mesh
        ("exterior_facet_vert", "ds_v"),    # Over side facets of an extruded mesh
        ("interior_facet_horiz", "dS_h"),   # Over horizontal facets of an extruded mesh
        ("interior_facet_vert", "dS_v"),  # Over vertical facets of an extruded mesh
    ]

    integral_type_to_measure_name = dict((l, s) for l, s in _integral_types)
    measure_name_to_integral_type = dict((s, l) for l, s in _integral_types)

    custom_integral_types = ("custom", "cutcell", "interface", "overlap")
    point_integral_types = ("vertex",)  # "point")
    facet_integral_types = ("exterior_facet", "interior_facet")

    def register_integral_type(integral_type, measure_name):
        global integral_type_to_measure_name, measure_name_to_integral_type
        if measure_name != integral_type_to_measure_name.get(integral_type, measure_name):
            error("Integral type already added with different measure name!")
        if integral_type != measure_name_to_integral_type.get(measure_name, integral_type):
            error("Measure name already used for another domain type!")
        integral_type_to_measure_name[integral_type] = measure_name
        measure_name_to_integral_type[measure_name] = integral_type

    def as_integral_type(integral_type):
        "Map short name to long name and require a valid one."
        integral_type = integral_type.replace(" ", "_")
        integral_type = measure_name_to_integral_type.get(integral_type,
                                                          integral_type)
        if integral_type not in integral_type_to_measure_name:
            error("Invalid integral_type.")
        return integral_type

    def integral_types():
        "Return a tuple of all domain type strings."
        return tuple(sorted(integral_type_to_measure_name.keys()))

    def measure_names():
        "Return a tuple of all measure name strings."
        return tuple(sorted(measure_name_to_integral_type.keys()))

    class Measure(object):
        __slots__ = ("_integral_type",
                     "_domain",
                     "_subdomain_id",
                     "_metadata",
                     "_subdomain_data")
        """Representation of an integration measure.

        The Measure object holds information about integration properties
        to be transferred to a Form on multiplication with a scalar
        expression.

        """

        def __init__(self,
                     integral_type,  # "dx" etc
                     domain=None,
                     subdomain_id="everywhere",
                     metadata=None,
                     subdomain_data=None):
            """
            integral_type:
                str, one of "cell", etc.,
                or short form "dx", etc.

            domain:
                an AbstractDomain object (most often a Mesh)

            subdomain_id:
                either string "everywhere",
                a single subdomain id int,
                or tuple of ints

            metadata:
                dict, with additional compiler-specific parameters
                affecting how code is generated, including parameters
                for optimization or debugging of generated code.

            subdomain_data:
                object representing data to interpret subdomain_id with.
            """
            # Map short name to long name and require a valid one
            self._integral_type = as_integral_type(integral_type)

            # Check that we either have a proper AbstractDomain or none
            self._domain = None if domain is None else as_domain(domain)
            if not (self._domain is None or isinstance(self._domain, AbstractDomain)):
                error("Invalid domain.")

            # Store subdomain data
            self._subdomain_data = subdomain_data
            # FIXME: Cannot require this (yet) because we currently have
            # no way to implement ufl_id for dolfin SubDomain
            # if not (self._subdomain_data is None or hasattr(self._subdomain_data, "ufl_id")):
            #     error("Invalid domain data, missing ufl_id() implementation.")

            # Accept "everywhere", single subdomain, or multiple
            # subdomains
            if isinstance(subdomain_id, tuple):
                for did in subdomain_id:
                    if not isinstance(did, numbers.Integral):
                        error("Invalid subdomain_id %s." % (did,))
            else:
                if not (subdomain_id in ("everywhere",) or isinstance(subdomain_id, numbers.Integral)):
                    error("Invalid subdomain_id %s." % (subdomain_id,))
            self._subdomain_id = subdomain_id

            # Validate compiler options are None or dict
            if metadata is not None and not isinstance(metadata, dict):
                error("Invalid metadata.")
            self._metadata = metadata or EmptyDict

        def integral_type(self):
            """Return the domain type.

            Valid domain types are "cell", "exterior_facet", "interior_facet", etc.
            """
            return self._integral_type

        def ufl_domain(self):
            """Return the domain associated with this measure.

            This may be None or a Domain object.
            """
            return self._domain

        def subdomain_id(self):
            "Return the domain id of this measure (integer)."
            return self._subdomain_id

        def metadata(self):
            """Return the integral metadata. This data is not interpreted by UFL.
            It is passed to the form compiler which can ignore it or use
            it to compile each integral of a form in a different way.

            """
            return self._metadata

        def reconstruct(self,
                        integral_type=None,
                        subdomain_id=None,
                        domain=None,
                        metadata=None,
                        subdomain_data=None):
            """Construct a new Measure object with some properties replaced with
            new values.

            Example:
            -------
                <dm = Measure instance>
                b = dm.reconstruct(subdomain_id=2)
                c = dm.reconstruct(metadata={ "quadrature_degree": 3 })

            Used by the call operator, so this is equivalent:
                b = dm(2)
                c = dm(0, { "quadrature_degree": 3 })

            """
            if subdomain_id is None:
                subdomain_id = self.subdomain_id()
            if domain is None:
                domain = self.ufl_domain()
            if metadata is None:
                metadata = self.metadata()
            if subdomain_data is None:
                subdomain_data = self.subdomain_data()
            return Measure(self.integral_type(),
                           domain=domain, subdomain_id=subdomain_id,
                           metadata=metadata, subdomain_data=subdomain_data)

        def subdomain_data(self):
            """Return the integral subdomain_data. This data is not interpreted by
            UFL.  Its intension is to give a context in which the domain
            id is interpreted.

            """
            return self._subdomain_data

        # Note: Must keep the order of the first two arguments here
        # (subdomain_id, metadata) for backwards compatibility, because
        # some tutorials write e.g. dx(0, {...}) to set metadata.
        def __call__(self, subdomain_id=None, metadata=None, domain=None,
                     subdomain_data=None, degree=None, scheme=None, rule=None):
            """Reconfigure measure with new domain specification or metadata."""

            # Deprecation of 'rule' in favour of 'scheme'
            if rule is not None:
                deprecate("Measure argument 'rule' has been renamed to 'scheme'.")
                assert scheme is None or scheme == rule
                scheme = rule

            # Let syntax dx() mean integral over everywhere
            all_args = (subdomain_id, metadata, domain, subdomain_data,
                        degree, scheme)
            if all(arg is None for arg in all_args):
                return self.reconstruct(subdomain_id="everywhere")

            # Let syntax dx(domain) or dx(domain, metadata) mean integral
            # over entire domain.  To do this we need to hijack the first
            # argument:
            if subdomain_id is not None and (isinstance(subdomain_id,
                                                        AbstractDomain) or
                                             hasattr(subdomain_id, 'ufl_domain')):
                if domain is not None:
                    error("Ambiguous: setting domain both as keyword argument and first argument.")
                subdomain_id, domain = "everywhere", as_domain(subdomain_id)

            # If degree or scheme is set, inject into metadata. This is a
            # quick fix to enable the dx(..., degree=3) notation.
            # TODO: Make degree and scheme properties of integrals instead of adding to metadata.
            if (degree, scheme) != (None, None):
                metadata = {} if metadata is None else metadata.copy()
                if degree is not None:
                    metadata["quadrature_degree"] = degree
                if scheme is not None:
                    metadata["quadrature_rule"] = scheme

            # If we get any keywords, use them to reconstruct Measure.
            # Note that if only one argument is given, it is the
            # subdomain_id, e.g. dx(3) == dx(subdomain_id=3)
            return self.reconstruct(subdomain_id=subdomain_id, domain=domain,
                                    metadata=metadata,
                                    subdomain_data=subdomain_data)

        def __getitem__(self, data):
            """This operator supports legacy syntax in python dolfin programs.

            The old documentation reads: Return a new Measure for same
            integration type with an attached context for interpreting
            domain ids. By default this new Measure integrates over
            everywhere, but it can be restricted with a domain id as
            usual. Example: dx = dx[boundaries]; L = f*v*dx + g*v+dx(1).

            """
            deprecate("Notation dx[meshfunction] is deprecated. Please use dx(subdomain_data=meshfunction) instead.")
            return self(subdomain_data=data)

        def __str__(self):
            global integral_type_to_measure_name
            name = integral_type_to_measure_name[self._integral_type]
            args = []

            if self._subdomain_id is not None:
                args.append("subdomain_id=%s" % (self._subdomain_id,))
            if self._domain is not None:
                args.append("domain=%s" % (self._domain,))
            if self._metadata:  # Stored as EmptyDict if None
                args.append("metadata=%s" % (self._metadata,))
            if self._subdomain_data is not None:
                args.append("subdomain_data=%s" % (self._subdomain_data,))

            return "%s(%s)" % (name, ', '.join(args))

        def __repr__(self):
            "Return a repr string for this Measure."
            global integral_type_to_measure_name

            args = []
            args.append(repr(self._integral_type))

            if self._subdomain_id is not None:
                args.append("subdomain_id=%s" % repr(self._subdomain_id))
            if self._domain is not None:
                args.append("domain=%s" % repr(self._domain))
            if self._metadata:  # Stored as EmptyDict if None
                args.append("metadata=%s" % repr(self._metadata))
            if self._subdomain_data is not None:
                args.append("subdomain_data=%s" % repr(self._subdomain_data))

            r = "%s(%s)" % (type(self).__name__, ', '.join(args))
            return r

        def __hash__(self):
            "Return a hash value for this Measure."
            hashdata = (self._integral_type,
                        self._subdomain_id,
                        hash(self._domain),
                        metadata_hashdata(self._metadata),
                        id_or_none(self._subdomain_data))
            return hash(hashdata)

        def __eq__(self, other):
            "Checks if two Measures are equal."
            return (isinstance(other, Measure) and
                    self._integral_type == other._integral_type and
                    self._subdomain_id == other._subdomain_id and
                    self._domain == other._domain and
                    id_or_none(self._subdomain_data) == id_or_none(other._subdomain_data) and
                    metadata_equal(self._metadata, other._metadata))

        def __add__(self, other):
            """Add two measures (self+other).

            Creates an intermediate object used for the notation

              expr * (dx(1) + dx(2)) := expr * dx(1) + expr * dx(2)
            """
            if isinstance(other, Measure):
                # Let dx(1) + dx(2) equal dx((1,2))
                return MeasureSum(self, other)
            else:
                # Can only add Measures
                return NotImplemented

        def __mul__(self, other):
            """Multiply two measures (self*other).

            Creates an intermediate object used for the notation

              expr * (dm1 * dm2) := expr * dm1 * dm2

            This is work in progress and not functional.
            """
            if isinstance(other, Measure):
                # Tensor product measure support
                return MeasureProduct(self, other)
            else:
                # Can't multiply Measure from the right with non-Measure type
                return NotImplemented

        def __rmul__(self, integrand):
            """Multiply a scalar expression with measure to construct a form with
            a single integral.

            This is to implement the notation

                form = integrand * self

            Integration properties are taken from this Measure object.

            """
            # Avoid circular imports
            from ufl_legacy.integral import Integral
            from ufl_legacy.form import Form

            # Allow python literals: 1*dx and 1.0*dx
            if isinstance(integrand, (int, float)):
                integrand = as_ufl(integrand)

            # Let other types implement multiplication with Measure if
            # they want to (to support the dolfin-adjoint TimeMeasure)
            if not isinstance(integrand, Expr):
                return NotImplemented

            # Allow only scalar integrands
            if not is_true_ufl_scalar(integrand):
                error("Can only integrate scalar expressions. The integrand is a "
                      "tensor expression with value shape %s and free indices with labels %s." %
                      (integrand.ufl_shape, integrand.ufl_free_indices))

            # If we have a tuple of domain ids build the integrals one by
            # one and construct as a Form in one go.
            subdomain_id = self.subdomain_id()
            if isinstance(subdomain_id, tuple):
                return Form(list(chain(*((integrand * self.reconstruct(subdomain_id=d)).integrals()
                                         for d in subdomain_id))))

            # Check that we have an integer subdomain or a string
            # ("everywhere" or "otherwise", any more?)
            if not isinstance(subdomain_id, (str, numbers.Integral,)):
                error("Expecting integer or string domain id.")

            # If we don't have an integration domain, try to find one in
            # integrand
            domain = self.ufl_domain()
            if domain is None:
                domains = extract_domains(integrand)
                if len(domains) == 1:
                    domain, = domains
                elif len(domains) == 0:
                    error("This integral is missing an integration domain.")
                else:
                    error("Multiple domains found, making the choice of integration domain ambiguous.")

            # Otherwise create and return a one-integral form
            integral = Integral(integrand=integrand,
                                integral_type=self.integral_type(),
                                domain=domain,
                                subdomain_id=subdomain_id,
                                metadata=self.metadata(),
                                subdomain_data=self.subdomain_data())
            return Form([integral])

    class MeasureSum(object):
        """Represents a sum of measures.

        This is a notational intermediate object to translate the notation

            f*(ds(1)+ds(3))

        into

            f*ds(1) + f*ds(3)
        """
        __slots__ = ("_measures",)

        def __init__(self, *measures):
            self._measures = measures

        def __rmul__(self, other):
            integrals = [other * m for m in self._measures]
            return sum(integrals)

        def __add__(self, other):
            if isinstance(other, Measure):
                return MeasureSum(*(self._measures + (other,)))
            elif isinstance(other, MeasureSum):
                return MeasureSum(*(self._measures + other._measures))
            return NotImplemented

        def __str__(self):
            return "{\n    " + "\n  + ".join(map(str, self._measures)) + "\n}"

    class MeasureProduct(object):
        """Represents a product of measures.

        This is a notational intermediate object to handle the notation

            f*(dm1*dm2)

        This is work in progress and not functional. It needs support
        in other parts of ufl and the rest of the code generation chain.

        """
        __slots__ = ("_measures",)

        def __init__(self, *measures):
            "Create MeasureProduct from given list of measures."
            self._measures = measures
            if len(self._measures) < 2:
                error("Expecting at least two measures.")

        def __mul__(self, other):
            """Flatten multiplication of product measures.

            This is to ensure that (dm1*dm2)*dm3 is stored as a simple
            list (dm1,dm2,dm3) in a single MeasureProduct.

            """
            if isinstance(other, Measure):
                measures = self.sub_measures() + [other]
                return MeasureProduct(*measures)
            else:
                return NotImplemented

        def __rmul__(self, integrand):
            error("TODO: Implement MeasureProduct.__rmul__ to construct integral and form somehow.")

        def sub_measures(self):
            "Return submeasures."
            return self._measures