# Source code for ufl_legacy.algorithms.apply_restrictions

    # -*- coding: utf-8 -*-
    """This module contains the apply_restrictions algorithm which propagates restrictions in a form towards the terminals."""

    # 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

    from ufl_legacy.log import error
    from ufl_legacy.classes import Restricted
    from ufl_legacy.corealg.multifunction import MultiFunction
    from ufl_legacy.corealg.map_dag import map_expr_dag
    from ufl_legacy.algorithms.map_integrands import map_integrand_dags
    from ufl_legacy.measure import integral_type_to_measure_name

    class RestrictionPropagator(MultiFunction):
        def __init__(self, side=None):
            MultiFunction.__init__(self)
            self.current_restriction = side
            self.default_restriction = "+"
            # Caches for propagating the restriction with map_expr_dag
            self.vcaches = {"+": {}, "-": {}}
            self.rcaches = {"+": {}, "-": {}}
            if self.current_restriction is None:
                self._rp = {"+": RestrictionPropagator("+"),
                            "-": RestrictionPropagator("-")}

        def restricted(self, o):
            "When hitting a restricted quantity, visit child with a separate restriction algorithm."
            # Assure that we have only two levels here, inside or outside
            # the Restricted node
            if self.current_restriction is not None:
                error("Cannot restrict an expression twice.")
            # Configure a propagator for this side and apply to subtree
            side = o.side()
            return map_expr_dag(self._rp[side], o.ufl_operands[0],
                                vcache=self.vcaches[side],
                                rcache=self.rcaches[side])

        # --- Reusable rules

        def _ignore_restriction(self, o):
            "Ignore current restriction, quantity is independent of side also from a computational point of view."
            return o

        def _require_restriction(self, o):
            "Restrict a discontinuous quantity to current side, require a side to be set."
            if self.current_restriction is None:
                error("Discontinuous type %s must be restricted." % o._ufl_class_.__name__)
            return o(self.current_restriction)

        def _default_restricted(self, o):
            "Restrict a continuous quantity to default side if no current restriction is set."
            r = self.current_restriction
            if r is None:
                r = self.default_restriction
            return o(r)

        def _opposite(self, o):
            "Restrict a quantity to default side, if the current restriction is different swap the sign, require a side to be set."
            if self.current_restriction is None:
                error("Discontinuous type %s must be restricted." % o._ufl_class_.__name__)
            elif self.current_restriction == self.default_restriction:
                return o(self.default_restriction)
            else:
                return -o(self.default_restriction)

        def _missing_rule(self, o):
            error("Missing rule for %s" % o._ufl_class_.__name__)

        # --- Rules for operators

        # Default: Operators should reconstruct only if subtrees are not touched
        operator = MultiFunction.reuse_if_untouched

        # Assuming apply_derivatives has been called,
        # propagating Grad inside the Restricted nodes.
        # Considering all grads to be discontinuous, may
        # want something else for facet functions in future.
        grad = _require_restriction

        def variable(self, o, op, label):
            "Strip variable."
            return op

        def reference_value(self, o):
            "Reference value of something follows same restriction rule as the underlying object."
            f, = o.ufl_operands
            assert f._ufl_is_terminal_
            g = self(f)
            if isinstance(g, Restricted):
                side = g.side()
                return o(side)
            else:
                return o

        # --- Rules for terminals

        # Require handlers to be specified for all terminals
        terminal = _missing_rule

        multi_index = _ignore_restriction
        label = _ignore_restriction

        # Default: Literals should ignore restriction
        constant_value = _ignore_restriction
        constant = _ignore_restriction

        # Even arguments with continuous elements such as Lagrange must be
        # restricted to associate with the right part of the element
        # matrix
        argument = _require_restriction

        # Defaults for geometric quantities
        geometric_cell_quantity = _require_restriction
        geometric_facet_quantity = _require_restriction

        # Only a few geometric quantities are independent on the restriction:
        facet_coordinate = _ignore_restriction
        quadrature_weight = _ignore_restriction

        # Assuming homogeoneous mesh
        reference_cell_volume = _ignore_restriction
        reference_facet_volume = _ignore_restriction

        def coefficient(self, o):
            "Allow coefficients to be unrestricted (apply default if so) if the values are fully continuous across the facet."
            e = o.ufl_element()
            d = e.degree()
            f = e.family()
            # TODO: Move this choice to the element class?
            continuous_families = ["Lagrange", "Q", "S"]
            if (f in continuous_families and d > 0) or f == "Real":
                # If the coefficient _value_ is _fully_ continuous
                return self._default_restricted(o)  # Must still be computed from one of the sides, we just don't care which
            else:
                return self._require_restriction(o)

        def facet_normal(self, o):
            D = o.ufl_domain()
            e = D.ufl_coordinate_element()
            f = e.family()
            d = e.degree()
            gd = D.geometric_dimension()
            td = D.topological_dimension()

            if f == "Lagrange" and d == 1 and gd == td:
                # For meshes with a continuous linear non-manifold
                # coordinate field, the facet normal from side - points in
                # the opposite direction of the one from side +.  We must
                # still require a side to be chosen by the user but
                # rewrite n- -> n+.  This is an optimization, possibly
                # premature, however it's more difficult to do at a later
                # stage.
                return self._opposite(o)
            else:
                # For other meshes, we require a side to be
                # chosen by the user and respect that
                return self._require_restriction(o)

    def apply_restrictions(expression):
        "Propagate restriction nodes to wrap differential terminals directly."
        integral_types = [k for k in integral_type_to_measure_name.keys()
                          if k.startswith("interior_facet")]
        rules = RestrictionPropagator()
        return map_integrand_dags(rules, expression,
                                  only_integral_type=integral_types)

    class DefaultRestrictionApplier(MultiFunction):
        def __init__(self, side=None):
            MultiFunction.__init__(self)
            self.current_restriction = side
            self.default_restriction = "+"
            if self.current_restriction is None:
                self._rp = {"+": DefaultRestrictionApplier("+"),
                            "-": DefaultRestrictionApplier("-")}

        def terminal(self, o):
            # Most terminals are unchanged
            return o

        # Default: Operators should reconstruct only if subtrees are not touched
        operator = MultiFunction.reuse_if_untouched

        def restricted(self, o):
            # Don't restrict twice
            return o

        def derivative(self, o):
            # I don't think it's safe to just apply default restriction
            # to the argument of any derivative, i.e. grad(cg1_function)
            # is not continuous across cells even if cg1_function is.
            return o

        def _default_restricted(self, o):
            "Restrict a continuous quantity to default side if no current restriction is set."
            r = self.current_restriction
            if r is None:
                r = self.default_restriction
            return o(r)

        # These are the same from either side but to compute them
        # cell (or facet) data from one side must be selected:
        spatial_coordinate = _default_restricted
        # Depends on cell only to get to the facet:
        facet_jacobian = _default_restricted
        facet_jacobian_determinant = _default_restricted
        facet_jacobian_inverse = _default_restricted
        # facet_tangents = _default_restricted
        # facet_midpoint = _default_restricted
        facet_area = _default_restricted
        # facet_diameter = _default_restricted
        min_facet_edge_length = _default_restricted
        max_facet_edge_length = _default_restricted
        facet_origin = _default_restricted  # FIXME: Is this valid for quads?

    def apply_default_restrictions(expression):
        """Some terminals can be restricted from either side.

        This applies a default restriction to such terminals if unrestricted."""
        integral_types = [k for k in integral_type_to_measure_name.keys()
                          if k.startswith("interior_facet")]
        rules = DefaultRestrictionApplier()
        return map_integrand_dags(rules, expression,
                                  only_integral_type=integral_types)