# Source code for FIAT.brezzi_douglas_marini

    # Copyright (C) 2008-2012 Robert C. Kirby (Texas Tech University)
    # Modified by Andrew T. T. McRae (Imperial College London)
    #
    # This file is part of FIAT (https://www.fenicsproject.org)
    #
    # SPDX-License-Identifier:    LGPL-3.0-or-later

    from FIAT import (finite_element, quadrature, functional, dual_set,
                      polynomial_set, nedelec)
    from FIAT.check_format_variant import check_format_variant

    class BDMDualSet(dual_set.DualSet):
        def __init__(self, ref_el, degree, variant, quad_deg):

            # Initialize containers for map: mesh_entity -> dof number and
            # dual basis
            entity_ids = {}
            nodes = []

            sd = ref_el.get_spatial_dimension()
            t = ref_el.get_topology()

            if variant == "integral":
                facet = ref_el.get_facet_element()
                # Facet nodes are \int_F v\cdot n p ds where p \in P_{q-1}
                # degree is q - 1
                Q = quadrature.make_quadrature(facet, quad_deg)
                Pq = polynomial_set.ONPolynomialSet(facet, degree)
                Pq_at_qpts = Pq.tabulate(Q.get_points())[tuple([0]*(sd - 1))]
                for f in range(len(t[sd - 1])):
                    for i in range(Pq_at_qpts.shape[0]):
                        phi = Pq_at_qpts[i, :]
                        nodes.append(functional.IntegralMomentOfScaledNormalEvaluation(ref_el, Q, phi, f))

                # internal nodes
                if degree > 1:
                    Q = quadrature.make_quadrature(ref_el, quad_deg)
                    qpts = Q.get_points()
                    Nedel = nedelec.Nedelec(ref_el, degree - 1, variant)
                    Nedfs = Nedel.get_nodal_basis()
                    zero_index = tuple([0 for i in range(sd)])
                    Ned_at_qpts = Nedfs.tabulate(qpts)[zero_index]

                    for i in range(len(Ned_at_qpts)):
                        phi_cur = Ned_at_qpts[i, :]
                        l_cur = functional.FrobeniusIntegralMoment(ref_el, Q, phi_cur)
                        nodes.append(l_cur)

            elif variant == "point":
                # Define each functional for the dual set
                # codimension 1 facets
                for i in range(len(t[sd - 1])):
                    pts_cur = ref_el.make_points(sd - 1, i, sd + degree)
                    for j in range(len(pts_cur)):
                        pt_cur = pts_cur[j]
                        f = functional.PointScaledNormalEvaluation(ref_el, i, pt_cur)
                        nodes.append(f)

                # internal nodes
                if degree > 1:
                    Q = quadrature.make_quadrature(ref_el, 2 * (degree + 1))
                    qpts = Q.get_points()
                    Nedel = nedelec.Nedelec(ref_el, degree - 1, variant)
                    Nedfs = Nedel.get_nodal_basis()
                    zero_index = tuple([0 for i in range(sd)])
                    Ned_at_qpts = Nedfs.tabulate(qpts)[zero_index]

                    for i in range(len(Ned_at_qpts)):
                        phi_cur = Ned_at_qpts[i, :]
                        l_cur = functional.FrobeniusIntegralMoment(ref_el, Q, phi_cur)
                        nodes.append(l_cur)

            # sets vertices (and in 3d, edges) to have no nodes
            for i in range(sd - 1):
                entity_ids[i] = {}
                for j in range(len(t[i])):
                    entity_ids[i][j] = []

            cur = 0

            # set codimension 1 (edges 2d, faces 3d) dof
            pts_facet_0 = ref_el.make_points(sd - 1, 0, sd + degree)
            pts_per_facet = len(pts_facet_0)

            entity_ids[sd - 1] = {}
            for i in range(len(t[sd - 1])):
                entity_ids[sd - 1][i] = list(range(cur, cur + pts_per_facet))
                cur += pts_per_facet

            # internal nodes, if applicable
            entity_ids[sd] = {0: []}

            if degree > 1:
                num_internal_nodes = len(Ned_at_qpts)
                entity_ids[sd][0] = list(range(cur, cur + num_internal_nodes))

            super(BDMDualSet, self).__init__(nodes, ref_el, entity_ids)

    class BrezziDouglasMarini(finite_element.CiarletElement):
        """
        The BDM element

        :arg ref_el: The reference element.
        :arg k: The degree.
        :arg variant: optional variant specifying the types of nodes.

        variant can be chosen from ["point", "integral", "integral(quadrature_degree)"]
        "point" -> dofs are evaluated by point evaluation. Note that this variant has suboptimal
        convergence order in the H(div)-norm
        "integral" -> dofs are evaluated by quadrature rule. The quadrature degree is chosen to integrate
        polynomials of degree 5*k so that most expressions will be interpolated exactly. This is important
        when you want to have (nearly) divergence-preserving interpolation.
        "integral(quadrature_degree)" -> dofs are evaluated by quadrature rule of degree quadrature_degree
        """

        def __init__(self, ref_el, k, variant=None):

            (variant, quad_deg) = check_format_variant(variant, k, "BDM")

            if k < 1:
                raise Exception("BDM_k elements only valid for k >= 1")

            sd = ref_el.get_spatial_dimension()
            poly_set = polynomial_set.ONPolynomialSet(ref_el, k, (sd, ))
            dual = BDMDualSet(ref_el, k, variant, quad_deg)
            formdegree = sd - 1  # (n-1)-form
            super(BrezziDouglasMarini, self).__init__(poly_set, dual, k, formdegree,
                                                      mapping="contravariant piola")