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# Source code for networkx.algorithms.bipartite.matrix

    """
    ====================
    Biadjacency matrices
    ====================
    """

    import itertools

    import networkx as nx
    from networkx.convert_matrix import _generate_weighted_edges

    __all__ = ["biadjacency_matrix", "from_biadjacency_matrix"]

    @nx._dispatchable(edge_attrs="weight")
    def biadjacency_matrix(
        G, row_order, column_order=None, dtype=None, weight="weight", format="csr"
    ):
        r"""Returns the biadjacency matrix of the bipartite graph G.

        Let `G = (U, V, E)` be a bipartite graph with node sets
        `U = u_{1},...,u_{r}` and `V = v_{1},...,v_{s}`. The biadjacency
        matrix [1]_ is the `r` x `s` matrix `B` in which `b_{i,j} = 1`
        if, and only if, `(u_i, v_j) \in E`. If the parameter `weight` is
        not `None` and matches the name of an edge attribute, its value is
        used instead of 1.

        Parameters
        ----------
        G : graph
           A NetworkX graph

        row_order : list of nodes
           The rows of the matrix are ordered according to the list of nodes.

        column_order : list, optional
           The columns of the matrix are ordered according to the list of nodes.
           If column_order is None, then the ordering of columns is arbitrary.

        dtype : NumPy data-type, optional
            A valid NumPy dtype used to initialize the array. If None, then the
            NumPy default is used.

        weight : string or None, optional (default='weight')
           The edge data key used to provide each value in the matrix.
           If None, then each edge has weight 1.

        format : str in {'bsr', 'csr', 'csc', 'coo', 'lil', 'dia', 'dok'}
            The type of the matrix to be returned (default 'csr').  For
            some algorithms different implementations of sparse matrices
            can perform better.  See [2]_ for details.

        Returns
        -------
        M : SciPy sparse array
            Biadjacency matrix representation of the bipartite graph G.

        Notes
        -----
        No attempt is made to check that the input graph is bipartite.

        For directed bipartite graphs only successors are considered as neighbors.
        To obtain an adjacency matrix with ones (or weight values) for both
        predecessors and successors you have to generate two biadjacency matrices
        where the rows of one of them are the columns of the other, and then add
        one to the transpose of the other.

        See Also
        --------
        adjacency_matrix
        from_biadjacency_matrix

        References
        ----------
        .. [1] https://en.wikipedia.org/wiki/Adjacency_matrix#Adjacency_matrix_of_a_bipartite_graph
        .. [2] Scipy Dev. References, "Sparse Matrices",
           https://docs.scipy.org/doc/scipy/reference/sparse.html
        """
        import scipy as sp

        nlen = len(row_order)
        if nlen == 0:
            raise nx.NetworkXError("row_order is empty list")
        if len(row_order) != len(set(row_order)):
            msg = "Ambiguous ordering: `row_order` contained duplicates."
            raise nx.NetworkXError(msg)
        if column_order is None:
            column_order = list(set(G) - set(row_order))
        mlen = len(column_order)
        if len(column_order) != len(set(column_order)):
            msg = "Ambiguous ordering: `column_order` contained duplicates."
            raise nx.NetworkXError(msg)

        row_index = dict(zip(row_order, itertools.count()))
        col_index = dict(zip(column_order, itertools.count()))

        if G.number_of_edges() == 0:
            row, col, data = [], [], []
        else:
            row, col, data = zip(
                *(
                    (row_index[u], col_index[v], d.get(weight, 1))
                    for u, v, d in G.edges(row_order, data=True)
                    if u in row_index and v in col_index
                )
            )
        A = sp.sparse.coo_array((data, (row, col)), shape=(nlen, mlen), dtype=dtype)
        try:
            return A.asformat(format)
        except ValueError as err:
            raise nx.NetworkXError(f"Unknown sparse array format: {format}") from err

    @nx._dispatchable(graphs=None, returns_graph=True)
    def from_biadjacency_matrix(A, create_using=None, edge_attribute="weight"):
        r"""Creates a new bipartite graph from a biadjacency matrix given as a
        SciPy sparse array.

        Parameters
        ----------
        A: scipy sparse array
          A biadjacency matrix representation of a graph

        create_using: NetworkX graph
           Use specified graph for result.  The default is Graph()

        edge_attribute: string
           Name of edge attribute to store matrix numeric value. The data will
           have the same type as the matrix entry (int, float, (real,imag)).

        Notes
        -----
        The nodes are labeled with the attribute `bipartite` set to an integer
        0 or 1 representing membership in part 0 or part 1 of the bipartite graph.

        If `create_using` is an instance of :class:`networkx.MultiGraph` or
        :class:`networkx.MultiDiGraph` and the entries of `A` are of
        type :class:`int`, then this function returns a multigraph (of the same
        type as `create_using`) with parallel edges. In this case, `edge_attribute`
        will be ignored.

        See Also
        --------
        biadjacency_matrix
        from_numpy_array

        References
        ----------
        [1] https://en.wikipedia.org/wiki/Adjacency_matrix#Adjacency_matrix_of_a_bipartite_graph
        """
        G = nx.empty_graph(0, create_using)
        n, m = A.shape
        # Make sure we get even the isolated nodes of the graph.
        G.add_nodes_from(range(n), bipartite=0)
        G.add_nodes_from(range(n, n + m), bipartite=1)
        # Create an iterable over (u, v, w) triples and for each triple, add an
        # edge from u to v with weight w.
        triples = ((u, n + v, d) for (u, v, d) in _generate_weighted_edges(A))
        # If the entries in the adjacency matrix are integers and the graph is a
        # multigraph, then create parallel edges, each with weight 1, for each
        # entry in the adjacency matrix. Otherwise, create one edge for each
        # positive entry in the adjacency matrix and set the weight of that edge to
        # be the entry in the matrix.
        if A.dtype.kind in ("i", "u") and G.is_multigraph():
            chain = itertools.chain.from_iterable
            triples = chain(((u, v, 1) for d in range(w)) for (u, v, w) in triples)
        G.add_weighted_edges_from(triples, weight=edge_attribute)
        return G