graph_blockmodel_partition.hh 18.4 KB
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// graph-tool -- a general graph modification and manipulation thingy
//
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// Copyright (C) 2006-2019 Tiago de Paula Peixoto <tiago@skewed.de>
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//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 3
// of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.

#ifndef GRAPH_BLOCKMODEL_PARTITION_HH
#define GRAPH_BLOCKMODEL_PARTITION_HH

#include "../support/util.hh"
#include "../support/int_part.hh"

namespace graph_tool
{

// ===============
// Partition stats
// ===============

constexpr size_t null_group = std::numeric_limits<size_t>::max();

typedef vprop_map_t<std::vector<std::tuple<size_t, size_t, size_t>>>::type
    degs_map_t;

struct simple_degs_t {};

template <class Graph, class Vprop, class Eprop, class F>
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[[gnu::always_inline]] [[gnu::flatten]] inline
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void degs_op(size_t v, Vprop& vweight, Eprop& eweight, const simple_degs_t&,
             Graph& g, F&& f)
{
    f(in_degreeS()(v, g, eweight), out_degreeS()(v, g, eweight), vweight[v]);
}

template <class Graph, class Vprop, class Eprop, class F>
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[[gnu::always_inline]] [[gnu::flatten]] inline
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void degs_op(size_t v, Vprop& vweight, Eprop& eweight,
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             const typename degs_map_t::unchecked_t& degs, Graph& g, F&& f)
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{
    auto& ks = degs[v];
    if (ks.empty())
    {
        degs_op(v, vweight, eweight, simple_degs_t(), g, std::forward<F>(f));
    }
    else
    {
        for (auto& k : ks)
            f(get<0>(k), get<1>(k), get<2>(k));
    }
}

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template <bool use_rmap>
class partition_stats
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{
public:

    typedef gt_hash_map<pair<size_t,size_t>, int> map_t;

    template <class Graph, class Vprop, class VWprop, class Eprop, class Degs,
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              class Vlist>
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    partition_stats(Graph& g, Vprop& b, Vlist& vlist, size_t E, size_t B,
                    VWprop& vweight, Eprop& eweight, Degs& degs,
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                    std::vector<size_t>& bmap)
        : _bmap(bmap), _N(0), _E(E), _total_B(B)
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    {
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        if constexpr (!use_rmap)
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        {
            _hist.resize(num_vertices(g));
            _total.resize(num_vertices(g));
            _ep.resize(num_vertices(g));
            _em.resize(num_vertices(g));
        }

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        for (auto v : vlist)
        {
            if (vweight[v] == 0)
                continue;

            auto r = get_r(b[v]);

            degs_op(v, vweight, eweight, degs, g,
                    [&](auto kin, auto kout, auto n)
                    {
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                        _hist[r][make_pair(kin, kout)] += n;
                        _em[r] += kin * n;
                        _ep[r] += kout * n;
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                        _total[r] += n;
                        _N += n;
                    });
        }

        _actual_B = 0;
        for (auto n : _total)
        {
            if (n > 0)
                _actual_B++;
        }
    }

    size_t get_r(size_t r)
    {
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        if constexpr (use_rmap)
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        {
            constexpr size_t null =
                std::numeric_limits<size_t>::max();
            if (r >= _bmap.size())
                _bmap.resize(r + 1, null);
            size_t nr = _bmap[r];
            if (nr == null)
                nr = _bmap[r] = _hist.size();
            r = nr;
        }
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        if (r >= _hist.size())
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        {
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            _hist.resize(r + 1);
            _total.resize(r + 1);
            _ep.resize(r + 1);
            _em.resize(r + 1);
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        }
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        return r;
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    }

    double get_partition_dl()
    {
        double S = 0;
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        S += lbinom(_N - 1, _actual_B - 1);
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        S += lgamma_fast(_N + 1);
        for (auto nr : _total)
            S -= lgamma_fast(nr + 1);
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        S += safelog_fast(_N);
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        return S;
    }

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    template <class Rs, class Ks>
    double get_deg_dl_ent(Rs&& rs, Ks&& ks)
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    {
        double S = 0;
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        for (auto r : rs)
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        {
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            r = get_r(r);
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            size_t total = 0;
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            if (ks.empty())
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            {
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                for (auto& k_c : _hist[r])
                {
                    S -= xlogx_fast(k_c.second);
                    total += k_c.second;
                }
            }
            else
            {
                auto& h = _hist[r];
                for (auto& k : ks)
                {
                    auto iter = h.find(k);
                    auto k_c = (iter != h.end()) ? iter->second : 0;
                    S -= xlogx(k_c);
                }
                total = _total[r];
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            }
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            S += xlogx_fast(total);
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        }
        return S;
    }

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    template <class Rs, class Ks>
    double get_deg_dl_uniform(Rs&& rs, Ks&&)
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    {
        double S = 0;
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        for (auto r : rs)
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        {
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            r = get_r(r);
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            S += lbinom(_total[r] + _ep[r] - 1, _ep[r]);
            S += lbinom(_total[r] + _em[r] - 1, _em[r]);
        }
        return S;
    }

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    template <class Rs, class Ks>
    double get_deg_dl_dist(Rs&& rs, Ks&& ks)
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    {
        double S = 0;
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        for (auto r : rs)
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        {
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            r = get_r(r);
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            S += log_q(_ep[r], _total[r]);
            S += log_q(_em[r], _total[r]);

            size_t total = 0;
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            if (ks.empty())
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            {
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                for (auto& k_c : _hist[r])
                {
                    S -= lgamma_fast(k_c.second + 1);
                    total += k_c.second;
                }
            }
            else
            {
                auto& h = _hist[r];
                for (auto& k : ks)
                {
                    auto iter = h.find(k);
                    auto k_c = (iter != h.end()) ? iter->second : 0;
                    S -= lgamma_fast(k_c + 1);
                }
                total = _total[r];
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            }
            S += lgamma_fast(total + 1);
        }
        return S;
    }

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    template <class Rs, class Ks>
    double get_deg_dl(int kind, Rs&& rs, Ks&& ks)
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    {
        switch (kind)
        {
        case deg_dl_kind::ENT:
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            return get_deg_dl_ent(rs, ks);
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        case deg_dl_kind::UNIFORM:
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            return get_deg_dl_uniform(rs, ks);
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        case deg_dl_kind::DIST:
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            return get_deg_dl_dist(rs, ks);
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        default:
            return numeric_limits<double>::quiet_NaN();
        }
    }

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    double get_deg_dl(int kind)
    {
        return get_deg_dl(kind, boost::counting_range(size_t(0), _total_B),
                          std::array<std::pair<size_t,size_t>,0>());
    }

    template <class Graph>
    double get_edges_dl(size_t B, Graph& g)
    {
        size_t BB = (graph_tool::is_directed(g)) ? B * B : (B * (B + 1)) / 2;
        return lbinom(BB + _E - 1, _E);
    }

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    template <class VProp>
    double get_delta_partition_dl(size_t v, size_t r, size_t nr, VProp& vweight)
    {
        if (r == nr)
            return 0;

        if (r != null_group)
            r = get_r(r);

        if (nr != null_group)
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            nr = get_r(nr);
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        int n = vweight[v];
        if (n == 0)
        {
            if (r == null_group)
                n = 1;
            else
                return 0;
        }

        double S_b = 0, S_a = 0;

        if (r != null_group)
        {
            S_b += -lgamma_fast(_total[r] + 1);
            S_a += -lgamma_fast(_total[r] - n + 1);
        }

        if (nr != null_group)
        {
            S_b += -lgamma_fast(_total[nr] + 1);
            S_a += -lgamma_fast(_total[nr] + n + 1);
        }

        int dN = 0;
        if (r == null_group)
            dN += n;
        if (nr == null_group)
            dN -= n;

        S_b += lgamma_fast(_N + 1);
        S_a += lgamma_fast(_N + dN + 1);

        int dB = 0;
        if (r != null_group && _total[r] == n)
            dB--;
        if (nr != null_group && _total[nr] == 0)
            dB++;

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        if ((dN != 0 || dB != 0))
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        {
            S_b += lbinom_fast(_N - 1, _actual_B - 1);
            S_a += lbinom_fast(_N - 1 + dN, _actual_B + dB - 1);
        }

        if (dN != 0)
        {
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            S_b += safelog_fast(_N);
            S_a += safelog_fast(_N + dN);
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        }

        return S_a - S_b;
    }

    template <class VProp, class Graph>
    double get_delta_edges_dl(size_t v, size_t r, size_t nr, VProp& vweight,
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                              size_t actual_B, Graph& g)
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    {
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        if (r == nr)
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            return 0;

        if (r != null_group)
            r = get_r(r);
        if (nr != null_group)
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            nr = get_r(nr);
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        double S_b = 0, S_a = 0;

        int n = vweight[v];

        if (n == 0)
        {
            if (r == null_group)
                n = 1;
            else
                return 0;
        }

        int dB = 0;
        if (r != null_group && _total[r] == n)
            dB--;
        if (nr != null_group && _total[nr] == 0)
            dB++;

        if (dB != 0)
        {
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            S_b += get_edges_dl(actual_B, g);
            S_a += get_edges_dl(actual_B + dB, g);
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        }

        return S_a - S_b;
    }

    template <class Graph, class VProp, class EProp, class Degs>
    double get_delta_deg_dl(size_t v, size_t r, size_t nr, VProp& vweight,
                            EProp& eweight, Degs& degs, Graph& g, int kind)
    {
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        if (r == nr || vweight[v] == 0)
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            return 0;
        if (r != null_group)
            r = get_r(r);
        if (nr != null_group)
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            nr = get_r(nr);
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        auto dop =
            [&](auto&& f)
            {
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                degs_op(v, vweight, eweight, degs, g,
                        [&](auto... k) { f(k...); });
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            };

        double dS = 0;
        switch (kind)
        {
        case deg_dl_kind::ENT:
            if (r != null_group)
                dS += get_delta_deg_dl_ent_change(r,  dop, -1);
            if (nr != null_group)
                dS += get_delta_deg_dl_ent_change(nr, dop, +1);
            break;
        case deg_dl_kind::UNIFORM:
            if (r != null_group)
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                dS += get_delta_deg_dl_uniform_change(r,  dop, -1);
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            if (nr != null_group)
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                dS += get_delta_deg_dl_uniform_change(nr, dop, +1);
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            break;
        case deg_dl_kind::DIST:
            if (r != null_group)
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                dS += get_delta_deg_dl_dist_change(r,  dop, -1);
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            if (nr != null_group)
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                dS += get_delta_deg_dl_dist_change(nr, dop, +1);
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            break;
        default:
            dS = numeric_limits<double>::quiet_NaN();
        }
        return dS;
    }

    template <class DegOP>
    double get_delta_deg_dl_ent_change(size_t r, DegOP&& dop, int diff)
    {
        int nr = _total[r];
        auto get_Sk = [&](size_t s, pair<size_t, size_t>& deg, int delta)
            {
                int nd = 0;
                auto iter = _hist[s].find(deg);
                if (iter != _hist[s].end())
                    nd = iter->second;
                assert(nd + delta >= 0);
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                return -xlogx_fast(nd + delta);
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            };

        double S_b = 0, S_a = 0;
        int dn = 0;

        dop([&](size_t kin, size_t kout, int nk)
            {
                dn += diff * nk;
                auto deg = make_pair(kin, kout);
                S_b += get_Sk(r, deg,         0);
                S_a += get_Sk(r, deg, diff * nk);
            });

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        S_b += xlogx_fast(nr);
        S_a += xlogx_fast(nr + dn);
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        return S_a - S_b;
    }

    template <class DegOP>
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    double get_delta_deg_dl_uniform_change(size_t r, DegOP&& dop, int diff)
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    {
        auto get_Se = [&](int dn, int dkin, int dkout)
            {
                double S = 0;
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                S += lbinom_fast(_total[r] + dn + _ep[r] - 1 + dkout, _ep[r] + dkout);
                S += lbinom_fast(_total[r] + dn + _em[r] - 1 + dkin,  _em[r] + dkin);
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                return S;
            };

        double S_b = 0, S_a = 0;
        int tkin = 0, tkout = 0, n = 0;
        dop([&](auto kin, auto kout, int nk)
            {
                tkin += kin * nk;
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                tkout += kout * nk;
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                n += nk;
            });

        S_b += get_Se(       0,           0,            0);
        S_a += get_Se(diff * n, diff * tkin, diff * tkout);
        return S_a - S_b;
    }

    template <class DegOP>
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    double get_delta_deg_dl_dist_change(size_t r, DegOP&& dop, int diff)
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    {
        auto get_Se = [&](int delta, int kin, int kout)
            {
                double S = 0;
                assert(_total[r] + delta >= 0);
                assert(_em[r] + kin >= 0);
                assert(_ep[r] + kout >= 0);
                S += log_q(_em[r] + kin, _total[r] + delta);
                S += log_q(_ep[r] + kout, _total[r] + delta);
                return S;
            };

        auto get_Sr = [&](int delta)
            {
                assert(_total[r] + delta + 1 >= 0);
                return lgamma_fast(_total[r] + delta + 1);
            };

        auto get_Sk = [&](pair<size_t, size_t>& deg, int delta)
            {
                int nd = 0;
                auto iter = _hist[r].find(deg);
                if (iter != _hist[r].end())
                    nd = iter->second;
                assert(nd + delta >= 0);
                return -lgamma_fast(nd + delta + 1);
            };

        double S_b = 0, S_a = 0;
        int tkin = 0, tkout = 0, n = 0;
        dop([&](size_t kin, size_t kout, int nk)
            {
                tkin += kin * nk;
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                tkout += kout * nk;
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                n += nk;

                auto deg = make_pair(kin, kout);
                S_b += get_Sk(deg,         0);
                S_a += get_Sk(deg, diff * nk);
            });

        S_b += get_Se(       0,           0,            0);
        S_a += get_Se(diff * n, diff * tkin, diff * tkout);

        S_b += get_Sr(       0);
        S_a += get_Sr(diff * n);

        return S_a - S_b;
    }

    template <class Graph, class VWeight, class EWeight, class Degs>
    void change_vertex(size_t v, size_t r, bool deg_corr, Graph& g,
                       VWeight& vweight, EWeight& eweight, Degs& degs,
                       int diff)
    {
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        int vw = vweight[v];
        int dv = vw * diff;

        if (_total[r] == 0 && dv > 0)
            _actual_B++;

        if (_total[r] == vw && dv < 0)
            _actual_B--;

        _total[r] += dv;
        _N += dv;

        assert(_total[r] >= 0);

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        if (deg_corr)
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        {
            degs_op(v, vweight, eweight, degs, g,
                    [&](auto kin, auto kout, auto n)
                    {
                        int dk = diff * n;
                        auto& h = _hist[r];
                        auto deg = make_pair(kin, kout);
                        auto iter = h.insert({deg, 0}).first;
                        iter->second += dk;
                        if (iter->second == 0)
                            h.erase(iter);
                        _em[r] += dk * deg.first;
                        _ep[r] += dk * deg.second;
                    });
        }
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    }

    template <class Graph, class VWeight, class EWeight, class Degs>
    void remove_vertex(size_t v, size_t r, bool deg_corr, Graph& g,
                       VWeight& vweight, EWeight& eweight, Degs& degs)
    {
        if (r == null_group || vweight[v] == 0)
            return;
        r = get_r(r);
        change_vertex(v, r, deg_corr, g, vweight, eweight, degs, -1);
    }

    template <class Graph, class VWeight, class EWeight, class Degs>
    void add_vertex(size_t v, size_t nr, bool deg_corr, Graph& g,
                    VWeight& vweight, EWeight& eweight, Degs& degs)
    {
        if (nr == null_group || vweight[v] == 0)
            return;
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        nr = get_r(nr);
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        change_vertex(v, nr, deg_corr, g, vweight, eweight, degs, 1);
    }

    void change_k(size_t v, size_t r, bool deg_corr, int vweight,
                  int kin, int kout, int diff)
    {
        if (_total[r] == 0 && diff * vweight > 0)
            _actual_B++;

        if (_total[r] == vweight && diff * vweight < 0)
            _actual_B--;

        _total[r] += diff * vweight;
        _N += diff * vweight;

        assert(_total[r] >= 0);

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        if (deg_corr)
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        {
            auto deg = make_pair(kin, kout);
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            auto iter = _hist[r].insert({deg, 0}).first;
            iter->second += diff * vweight;
            if (iter->second == 0)
                _hist[r].erase(iter);
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            _em[r] += diff * deg.first * vweight;
            _ep[r] += diff * deg.second * vweight;
        }
    }

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    void change_E(int dE)
    {
        _E += dE;
    }

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    size_t get_N()
    {
        return _N;
    }

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    size_t get_E()
    {
        return _E;
    }

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    size_t get_actual_B()
    {
        return _actual_B;
    }

    void add_block()
    {
        _total_B++;
    }

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    template <class Graph, class VProp, class VWeight, class EWeight, class Degs>
    bool check_degs(Graph& g, VProp& b, VWeight& vweight, EWeight& eweight, Degs& degs)
    {
        vector<map_t> dhist;
        for (auto v : vertices_range(g))
        {
            degs_op(v, vweight, eweight, degs, g,
                    [&](auto kin, auto kout, auto n)
                    {
                        auto r = get_r(b[v]);
                        if (r >= dhist.size())
                            dhist.resize(r + 1);
                        dhist[r][{kin, kout}] += n;
                    });
        }

        for (size_t r = 0; r < dhist.size(); ++r)
        {
            for (auto& kn : dhist[r])
            {
                auto count = (r >= _hist.size()) ? 0 : _hist[r][kn.first];
                if (kn.second != count)
                {
                    assert(false);
                    return false;
                }
            }
        }

        for (size_t r = 0; r < _hist.size(); ++r)
        {
            for (auto& kn : _hist[r])
            {
                auto count = (r >= dhist.size()) ? 0 : dhist[r][kn.first];
                if (kn.second != count)
                {
                    assert(false);
                    return false;
                }
            }
        }

        return true;
    }
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private:
    vector<size_t>& _bmap;
    size_t _N;
    size_t _E;
    size_t _actual_B;
    size_t _total_B;
    vector<map_t> _hist;
    vector<int> _total;
    vector<int> _ep;
    vector<int> _em;
};

} //namespace graph_tool
#endif // GRAPH_BLOCKMODEL_PARTITION_HH