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# Source code for fnss.netconfig.capacities

    """
    Provides functions to assign and manipulate link capacities of a topology.

    Link capacities can be assigned either deterministically or randomly, according
    to various models.
    """
    import networkx as nx

    from fnss.util import random_from_pdf
    from fnss.units import capacity_units

    __all__ = [
        'set_capacities_constant',
        'set_capacities_random',
        'set_capacities_random_uniform',
        'set_capacities_random_power_law',
        'set_capacities_random_zipf',
        'set_capacities_random_zipf_mandelbrot',
        'set_capacities_degree_gravity',
        'set_capacities_betweenness_gravity',
        'set_capacities_eigenvector_gravity',
        'set_capacities_communicability_gravity',
        'set_capacities_pagerank_gravity',
        'set_capacities_edge_betweenness',
        'set_capacities_edge_communicability',
        'get_capacities',
        'clear_capacities'
               ]

    def set_capacities_constant(topology, capacity, capacity_unit='Mbps',
                                links=None):
        """
        Set constant link capacities

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacity : float
            The value of capacity to set
        links : iterable, optional
            Iterable container of links, represented as (u, v) tuples to which
            capacity will be set. If None or not specified, the capacity will be
            applied to all links.
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)

        Examples
        --------
        >>> import fnss
        >>> topology = fnss.erdos_renyi_topology(50, 0.1)
        >>> fnss.set_capacities_constant(topology, 10, 'Mbps')
        """
        if capacity <= 0:
            raise ValueError('Capacity must be positive')
        if not capacity_unit in capacity_units:
            raise ValueError("The capacity_unit argument is not valid")
        conversion_factor = 1
        if 'capacity_unit' in topology.graph and links is not None:
            # If a capacity_unit is set, that means that some links have already
            # been assigned capacities, so set these capacity using the same unit
            # already used
            curr_capacity_unit = topology.graph['capacity_unit']
            if curr_capacity_unit != capacity_unit:
                conversion_factor = float(capacity_units[capacity_unit]) \
                                    / capacity_units[curr_capacity_unit]
        else:
            topology.graph['capacity_unit'] = capacity_unit
        edges = topology.edges_iter() if links is None else links
        for u, v in edges:
            topology.edge[u][v]['capacity'] = capacity * conversion_factor
        return

    def set_capacities_random(topology, capacity_pdf, capacity_unit='Mbps'):
        """
        Set random link capacities according to a given probability density
        function

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacity_pdf : dict
            A dictionary representing the probability that a capacity value is
            assigned to a link
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        links : list, optional
            List of links, represented as (u, v) tuples to which capacity will be
            set. If None or not specified, the capacity will be applied to all
            links.

        Examples
        --------
        >>> import fnss
        >>> topology = fnss.erdos_renyi_topology(50, 0.1)
        >>> pdf = {10: 0.5, 100: 0.2, 1000: 0.3}
        >>> fnss.set_capacities_constant(topology, pdf, 'Mbps')
        """
        if not capacity_unit in capacity_units:
            raise ValueError("The capacity_unit argument is not valid")
        if any((capacity < 0 for capacity in capacity_pdf.keys())):
            raise ValueError('All capacities in capacity_pdf must be positive')
        topology.graph['capacity_unit'] = capacity_unit
        for u, v in topology.edges_iter():
            topology.edge[u][v]['capacity'] = random_from_pdf(capacity_pdf)
        return

    def set_capacities_random_power_law(topology, capacities, capacity_unit='Mbps',
                                        alpha=1.1):
        """
        Set random link capacities according to a power-law probability density
        function.

        The probability that a capacity :math:`c_i` is assigned to a link is:

        .. math::
            p(c_i) = \\frac{{c_i}^{-\\alpha}}{\\sum_{c_k \\in C}{{c_k}^{-\\alpha}}}.

        Where :math:`C` is the set of allowed capacity, i.e. the ``capacities``
        argument

        Note that this capacity assignment differs from
        ``set_capacities_random_zipf`` because, while in Zipf assignment the power
        law relationship is between the rank of a capacity and the probability of
        being assigned to a link, in this assignment, the power law is between the
        value of the capacity and the probability of being assigned to a link.

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        """
        if alpha <= 0.0:
            raise ValueError('alpha must be positive')
        capacities = sorted(capacities)
        pdf = [capacities[i]**(-alpha) for i in range(len(capacities))]
        norm_factor = sum(pdf)
        norm_pdf = dict((capacities[i], pdf[i]/norm_factor)
                        for i in range(len(capacities)))
        set_capacities_random(topology, norm_pdf, capacity_unit=capacity_unit)

    def set_capacities_random_zipf_mandelbrot(topology, capacities,
                                              capacity_unit='Mbps', alpha=1.1,
                                              q=0.0, reverse=False):
        """
        Set random link capacities according to a Zipf-Mandelbrot probability
        density function.

        This capacity allocation consists in the following steps:

        1. All capacities are sorted in descending or order (or ascending if
           reverse is True)

        2. The i-th value of the sorted capacities list is then assigned to a link
           with probability

        .. math::
           p(i) = \\frac{1/(i + q)^\\alpha}{\\sum_{i = 1}^{N}{1/(i + q)^\\alpha}}.

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        alpha : float, default 1.1
            The :math`\alpha` parameter of the Zipf-Mandlebrot density function
        q : float, default 0
            The :math`q` parameter of the Zipf-Mandlebrot density function
        reverse : bool, optional
            If False, lower capacity links are the most frequent, if True, higher
            capacity links are more frequent
        """
        if alpha <= 0.0:
            raise ValueError('alpha must be positive')
        if q < 0.0:
            raise ValueError('q must be >= 0')
        capacities = sorted(capacities, reverse=reverse)
        pdf = dict((capacities[i], 1.0 /(i + 1.0 + q)**alpha)
                    for i in range(len(capacities)))
        norm_factor = sum(pdf.values())
        norm_pdf = dict((capacity, pdf[capacity]/norm_factor)
                         for capacity in pdf)
        set_capacities_random(topology, norm_pdf, capacity_unit=capacity_unit)

    def set_capacities_random_zipf(topology, capacities, capacity_unit='Mbps',
                                   alpha=1.1,  reverse=False):
        """
        Set random link capacities according to a Zipf probability density
        function.

        The same objective can be achieved by invoking the function
        ``set_capacities_random_zipf_mandlebrot`` with parameter q set to 0.

        This capacity allocation consists in the following steps:

        1. All capacities are sorted in descending or order (or ascending if
           reverse is True)

        2. The i-th value of the sorted capacities list is then assigned to a link
           with probability

        .. math::
                p(i) = \\frac{1/i^\\alpha}{\\sum_{i = 1}^{N}{1/i^\\alpha}}.

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        alpha : float, default 1.1
            The :math`\alpha` parameter of the Zipf density function
        reverse : bool, optional
            If False, lower capacity links are the most frequent, if True, higher
            capacity links are more frequent
        """
        set_capacities_random_zipf_mandelbrot(topology, capacities, alpha=alpha,
                                              q=0.0, reverse=reverse,
                                              capacity_unit=capacity_unit)

    def set_capacities_random_uniform(topology, capacities, capacity_unit='Mbps'):
        """
        Set random link capacities according to a uniform probability density
        function.

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        """
        capacity_pdf = dict((capacity, 1.0/len(capacities))
                             for capacity in capacities)
        set_capacities_random(topology, capacity_pdf, capacity_unit=capacity_unit)

    def set_capacities_degree_gravity(topology, capacities, capacity_unit='Mbps'):
        """
        Set link capacities proportionally to the product of the degrees of the
        two end-points of the link

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        """
        if topology.is_directed():
            in_degree = nx.in_degree_centrality(topology)
            out_degree = nx.out_degree_centrality(topology)
            gravity = dict(((u, v), out_degree[u] * in_degree[v])
                           for (u, v) in topology.edges_iter())
        else:
            degree = nx.degree_centrality(topology)
            gravity = dict(((u, v), degree[u] * degree[v])
                            for (u, v) in topology.edges_iter())
        _set_capacities_proportionally(topology, capacities, gravity,
                                       capacity_unit=capacity_unit)

    def set_capacities_betweenness_gravity(topology, capacities,
                                           capacity_unit='Mbps', weighted=True):
        """
        Set link capacities proportionally to the product of the betweenness
        centralities of the two end-points of the link

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        weighted : bool, optional
            Indicate whether link weights need to be used to compute shortest
            paths. If links do not have link weights or this parameter is False,
            shortest paths are calculated based on hop count.
        """
        weight = 'weight' if weighted else None
        centrality = nx.betweenness_centrality(topology, normalized=False,
                                               weight=weight)
        _set_capacities_gravity(topology, capacities, centrality, capacity_unit)

    def set_capacities_eigenvector_gravity(topology, capacities,
                                           capacity_unit='Mbps', max_iter=1000):
        """
        Set link capacities proportionally to the product of the eigenvector
        centralities of the two end-points of the link

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        max_iter : int, optional
            The max number of iteration of the algorithm allowed. If a solution is
            not found within this period

        Raises
        ------
        RuntimeError : if the algorithm does not converge in max_iter iterations
        """
        try:
            centrality = nx.eigenvector_centrality(topology, max_iter=max_iter)
        except nx.NetworkXError:
            raise RuntimeError('Algorithm did not converge in %d iterations'
                               % max_iter)
        _set_capacities_gravity(topology, capacities, centrality, capacity_unit)

    def set_capacities_pagerank_gravity(topology, capacities, capacity_unit='Mbps',
                                        alpha=0.85, weight=None):
        """
        Set link capacities proportionally to the product of the Pagerank
        centralities of the two end-points of the link

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        alpha : float, optional
            The apha parameter of the PageRank algorithm
        weight : str, optional
            The name of the link attribute to use for the PageRank algorithm. Valid
            attributes include *capacity* *delay* and *weight*. If ``None``, all
            links are assigned the same weight.
        """
        centrality = nx.pagerank_numpy(topology, alpha=alpha, personalization=None,
                                 weight=weight)
        _set_capacities_gravity(topology, capacities, centrality, capacity_unit)

    def set_capacities_communicability_gravity(topology, capacities,
                                               capacity_unit='Mbps'):
        """
        Set link capacities proportionally to the product of the communicability
        centralities of the two end-points of the link

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        """
        centrality = nx.communicability_centrality(topology)
        _set_capacities_gravity(topology, capacities, centrality, capacity_unit)

    def set_capacities_edge_betweenness(topology, capacities, capacity_unit='Mbps',
                                        weighted=True):
        """
        Set link capacities proportionally to edge betweenness centrality of the
        link.

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        weighted : bool, optional
            Indicate whether link weights need to be used to compute shortest
            paths. If links do not have link weights or this parameter is False,
            shortest paths are calculated based on hop count.
        """
        weight = 'weight' if weighted else None
        centrality = nx.edge_betweenness_centrality(topology, normalized=False,
                                                    weight=weight)
        _set_capacities_proportionally(topology, capacities, centrality,
                                       capacity_unit=capacity_unit)

    def set_capacities_edge_communicability(topology, capacities,
                                            capacity_unit='Mbps'):
        """
        Set link capacities proportionally to edge communicability centrality of
        the link.

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        """
        communicability = nx.communicability(topology)
        centrality = dict(((u, v), communicability[u][v])
                          for (u, v) in topology.edges_iter())
        _set_capacities_proportionally(topology, capacities, centrality,
                                       capacity_unit=capacity_unit)

    def _set_capacities_gravity(topology, capacities, node_metric,
                                capacity_unit='Mbps'):
        """
        Set link capacities proportionally to the product of the values of a given
        node metric of the two end-points of the link

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        node_metric : dict
            A dictionary with all values of the given node metric, keyed by node
            name
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        """
        gravity = dict(((u, v), node_metric[u] * node_metric[v])
                       for (u, v) in topology.edges_iter())
        _set_capacities_proportionally(topology, capacities, gravity,
                                       capacity_unit=capacity_unit)

    def _set_capacities_proportionally(topology, capacities, metric,
                                       capacity_unit='Mbps'):
        """
        Set link capacities proportionally to the value of a given edge metric.

        Parameters
        ----------
        topology : Topology
            The topology to which link capacities will be set
        capacities : list
            A list of all possible capacity values
        metric : dict
            A dictionary with all values of the given edge metric, keyed by edge
            name
        capacity_unit : str, optional
            The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
        """
        if not capacity_unit in capacity_units:
            raise ValueError("The capacity_unit argument is not valid")
        if any((capacity < 0 for capacity in capacities)):
            raise ValueError('All capacities must be positive')
        if len(capacities) == 0:
            raise ValueError('The list of capacities cannot be empty')

        topology.graph['capacity_unit'] = capacity_unit

        # If there is only one capacity the capacities list then all links are
        # assigned the same capacity
        if len(capacities) == 1:
            set_capacities_constant(topology, capacities[0], capacity_unit)
            return

        # get min and max of selected edge metric
        min_metric = min(metric.values())
        max_metric = max(metric.values())

        capacities = sorted(capacities)

        min_capacity = capacities[0] - 0.5 * (capacities[1] - capacities[0])
        max_capacity = capacities[-1] + 0.5 * (capacities[-1] - capacities[-2])
        capacity_boundaries = [0.5*(capacities[i] + capacities[i + 1])
                               for i in range(len(capacities) - 1)]
        capacity_boundaries.append(max_capacity)

        metric_boundaries = [(capacity_boundary - min_capacity) *
                             ((max_metric - min_metric)/
                              (max_capacity - min_capacity)) + min_metric
                             for capacity_boundary in capacity_boundaries]
        # to prevent float rounding errors
        metric_boundaries[-1] = max_metric + 0.1

        for (u, v), metric_value in metric.items():
            for i in range(len(metric_boundaries)):
                if metric_value <= metric_boundaries[i]:
                    capacity = capacities[i]
                    topology.edge[u][v]['capacity'] = capacity
                    break
            # if the loop is not stopped yet, it means that because of float
            # rounding error, max_capacity <  metric_boundaries[-1], so we set the
            # greatest capacity value.
            # Anyway, the code should never reach this point, because before the
            # for loop we are already adjusting the value of metric_boundaries[-1]
            # to make it > max_capacity
            else: topology.edge[u][v]['capacity'] = capacities[-1]

    def get_capacities(topology):
        """
        Returns a dictionary with all link capacities.

        Parameters
        ----------
        topology : Topology
            The topology whose link delays are requested

        Returns
        -------
        capacities : dict
            Dictionary of link capacities keyed by link.

        Examples
        --------
        >>> import fnss
        >>> topology = fnss.Topology()
        >>> topology.add_path([1,2,3])
        >>> fnss.set_capacities_constant(topology, 10, 'Mbps')
        >>> capacity = get_capacities(topology)
        >>> capacity[(1,2)]
        10
        """
        return nx.get_edge_attributes(topology, 'capacity')

    def clear_capacities(topology):
        """
        Remove all capacities from the topology.

        Parameters
        ----------
        topology : Topology
        """
        if 'capacity_unit' in topology.graph:
            del topology.graph['capacity_unit']
        for u, v in topology.edges_iter():
            if 'capacity' in topology.edge[u][v]:
                del topology.edge[u][v]['capacity']

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