From e083f90ad09a3bd42beffea1e996f3b4a9b3ff76 Mon Sep 17 00:00:00 2001 From: Rémi Flamary Date: Thu, 27 Oct 2016 12:34:42 +0200 Subject: rename emd module to lp --- ot/lp/network_simplex_simple.h | 1543 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1543 insertions(+) create mode 100644 ot/lp/network_simplex_simple.h (limited to 'ot/lp/network_simplex_simple.h') diff --git a/ot/lp/network_simplex_simple.h b/ot/lp/network_simplex_simple.h new file mode 100644 index 0000000..64856a0 --- /dev/null +++ b/ot/lp/network_simplex_simple.h @@ -0,0 +1,1543 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * + * This file has been adapted by Nicolas Bonneel (2013), + * from network_simplex.h from LEMON, a generic C++ optimization library, + * to implement a lightweight network simplex for mass transport, more + * memory efficient that the original file. A previous version of this file + * is used as part of the Displacement Interpolation project, + * Web: http://www.cs.ubc.ca/labs/imager/tr/2011/DisplacementInterpolation/ + * + * + **** Original file Copyright Notice : + * + * Copyright (C) 2003-2010 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_NETWORK_SIMPLEX_SIMPLE_H +#define LEMON_NETWORK_SIMPLEX_SIMPLE_H +#define DEBUG_LVL 0 +#define EPSILON 10*2.2204460492503131e-016 +#define MAX_DEBUG_ITER 100000 + + +/// \ingroup min_cost_flow_algs +/// +/// \file +/// \brief Network Simplex algorithm for finding a minimum cost flow. + +// if your compiler has troubles with stdext or hashmaps, just comment the following line to use a slower std::map instead +//#define HASHMAP + +#include +#include +#include +#ifdef HASHMAP +#include +#else +#include +#endif +#include +//#include "core.h" +//#include "lmath.h" + +//#include "sparse_array_n.h" +#include "full_bipartitegraph.h" + +#define INVALIDNODE -1 +#define INVALID (-1) + +namespace lemon { + + + template + class ProxyObject; + + template + class SparseValueVector + { + public: + SparseValueVector(int n=0) + { + } + void resize(int n=0){}; + T operator[](const int id) const + { +#ifdef HASHMAP + typename stdext::hash_map::const_iterator it = data.find(id); +#else + typename std::map::const_iterator it = data.find(id); +#endif + if (it==data.end()) + return 0; + else + return it->second; + } + + ProxyObject operator[](const int id) + { + return ProxyObject( this, id ); + } + + //private: +#ifdef HASHMAP + stdext::hash_map data; +#else + std::map data; +#endif + + }; + + template + class ProxyObject { + public: + ProxyObject( SparseValueVector *v, int idx ){_v=v; _idx=idx;}; + ProxyObject & operator=( const T &v ) { + // If we get here, we know that operator[] was called to perform a write access, + // so we can insert an item in the vector if needed + if (v!=0) + _v->data[_idx]=v; + return *this; + } + + operator T() { + // If we get here, we know that operator[] was called to perform a read access, + // so we can simply return the existing object +#ifdef HASHMAP + typename stdext::hash_map::iterator it = _v->data.find(_idx); +#else + typename std::map::iterator it = _v->data.find(_idx); +#endif + if (it==_v->data.end()) + return 0; + else + return it->second; + } + + void operator+=(T val) + { + if (val==0) return; +#ifdef HASHMAP + typename stdext::hash_map::iterator it = _v->data.find(_idx); +#else + typename std::map::iterator it = _v->data.find(_idx); +#endif + if (it==_v->data.end()) + _v->data[_idx] = val; + else + { + T sum = it->second + val; + if (sum==0) + _v->data.erase(it); + else + it->second = sum; + } + } + void operator-=(T val) + { + if (val==0) return; +#ifdef HASHMAP + typename stdext::hash_map::iterator it = _v->data.find(_idx); +#else + typename std::map::iterator it = _v->data.find(_idx); +#endif + if (it==_v->data.end()) + _v->data[_idx] = -val; + else + { + T sum = it->second - val; + if (sum==0) + _v->data.erase(it); + else + it->second = sum; + } + } + + SparseValueVector *_v; + int _idx; + }; + + + + /// \addtogroup min_cost_flow_algs + /// @{ + + /// \brief Implementation of the primal Network Simplex algorithm + /// for finding a \ref min_cost_flow "minimum cost flow". + /// + /// \ref NetworkSimplexSimple implements the primal Network Simplex algorithm + /// for finding a \ref min_cost_flow "minimum cost flow" + /// \ref amo93networkflows, \ref dantzig63linearprog, + /// \ref kellyoneill91netsimplex. + /// This algorithm is a highly efficient specialized version of the + /// linear programming simplex method directly for the minimum cost + /// flow problem. + /// + /// In general, %NetworkSimplexSimple is the fastest implementation available + /// in LEMON for this problem. + /// Moreover, it supports both directions of the supply/demand inequality + /// constraints. For more information, see \ref SupplyType. + /// + /// Most of the parameters of the problem (except for the digraph) + /// can be given using separate functions, and the algorithm can be + /// executed using the \ref run() function. If some parameters are not + /// specified, then default values will be used. + /// + /// \tparam GR The digraph type the algorithm runs on. + /// \tparam V The number type used for flow amounts, capacity bounds + /// and supply values in the algorithm. By default, it is \c int. + /// \tparam C The number type used for costs and potentials in the + /// algorithm. By default, it is the same as \c V. + /// + /// \warning Both number types must be signed and all input data must + /// be integer. + /// + /// \note %NetworkSimplexSimple provides five different pivot rule + /// implementations, from which the most efficient one is used + /// by default. For more information, see \ref PivotRule. + template + class NetworkSimplexSimple + { + public: + + /// \brief Constructor. + /// + /// The constructor of the class. + /// + /// \param graph The digraph the algorithm runs on. + /// \param arc_mixing Indicate if the arcs have to be stored in a + /// mixed order in the internal data structure. + /// In special cases, it could lead to better overall performance, + /// but it is usually slower. Therefore it is disabled by default. + NetworkSimplexSimple(const GR& graph, bool arc_mixing, int nbnodes, long long nb_arcs,double maxiters) : + _graph(graph), //_arc_id(graph), + _arc_mixing(arc_mixing), _init_nb_nodes(nbnodes), _init_nb_arcs(nb_arcs), + MAX(std::numeric_limits::max()), + INF(std::numeric_limits::has_infinity ? + std::numeric_limits::infinity() : MAX) + { + // Reset data structures + reset(); + max_iter=maxiters; + } + + /// The type of the flow amounts, capacity bounds and supply values + typedef V Value; + /// The type of the arc costs + typedef C Cost; + + public: + + /// \brief Problem type constants for the \c run() function. + /// + /// Enum type containing the problem type constants that can be + /// returned by the \ref run() function of the algorithm. + enum ProblemType { + /// The problem has no feasible solution (flow). + INFEASIBLE, + /// The problem has optimal solution (i.e. it is feasible and + /// bounded), and the algorithm has found optimal flow and node + /// potentials (primal and dual solutions). + OPTIMAL, + /// The objective function of the problem is unbounded, i.e. + /// there is a directed cycle having negative total cost and + /// infinite upper bound. + UNBOUNDED + }; + + /// \brief Constants for selecting the type of the supply constraints. + /// + /// Enum type containing constants for selecting the supply type, + /// i.e. the direction of the inequalities in the supply/demand + /// constraints of the \ref min_cost_flow "minimum cost flow problem". + /// + /// The default supply type is \c GEQ, the \c LEQ type can be + /// selected using \ref supplyType(). + /// The equality form is a special case of both supply types. + enum SupplyType { + /// This option means that there are "greater or equal" + /// supply/demand constraints in the definition of the problem. + GEQ, + /// This option means that there are "less or equal" + /// supply/demand constraints in the definition of the problem. + LEQ + }; + + + + private: + + double max_iter; + TEMPLATE_DIGRAPH_TYPEDEFS(GR); + + typedef std::vector IntVector; + typedef std::vector UHalfIntVector; + typedef std::vector ValueVector; + typedef std::vector CostVector; + // typedef SparseValueVector CostVector; + typedef std::vector BoolVector; + // Note: vector is used instead of vector for efficiency reasons + + // State constants for arcs + enum ArcState { + STATE_UPPER = -1, + STATE_TREE = 0, + STATE_LOWER = 1 + }; + + typedef std::vector StateVector; + // Note: vector is used instead of vector for + // efficiency reasons + + private: + + // Data related to the underlying digraph + const GR &_graph; + int _node_num; + int _arc_num; + int _all_arc_num; + int _search_arc_num; + + // Parameters of the problem + SupplyType _stype; + Value _sum_supply; + + inline int _node_id(int n) const {return _node_num-n-1;} ; + + //IntArcMap _arc_id; + UHalfIntVector _source; + UHalfIntVector _target; + bool _arc_mixing; + public: + // Node and arc data + CostVector _cost; + ValueVector _supply; + ValueVector _flow; + //SparseValueVector _flow; + CostVector _pi; + + + private: + // Data for storing the spanning tree structure + IntVector _parent; + IntVector _pred; + IntVector _thread; + IntVector _rev_thread; + IntVector _succ_num; + IntVector _last_succ; + IntVector _dirty_revs; + BoolVector _forward; + StateVector _state; + int _root; + + // Temporary data used in the current pivot iteration + int in_arc, join, u_in, v_in, u_out, v_out; + int first, second, right, last; + int stem, par_stem, new_stem; + Value delta; + + const Value MAX; + + int mixingCoeff; + + public: + + /// \brief Constant for infinite upper bounds (capacities). + /// + /// Constant for infinite upper bounds (capacities). + /// It is \c std::numeric_limits::infinity() if available, + /// \c std::numeric_limits::max() otherwise. + const Value INF; + + private: + + // thank you to DVK and MizardX from StackOverflow for this function! + inline int sequence(int k) const { + int smallv = (k > num_total_big_subsequence_numbers) & 1; + + k -= num_total_big_subsequence_numbers * smallv; + int subsequence_length2 = subsequence_length- smallv; + int subsequence_num = (k / subsequence_length2) + num_big_subseqiences * smallv; + int subsequence_offset = (k % subsequence_length2) * mixingCoeff; + + return subsequence_offset + subsequence_num; + } + int subsequence_length; + int num_big_subseqiences; + int num_total_big_subsequence_numbers; + + inline int getArcID(const Arc &arc) const + { + //int n = _arc_num-arc._id-1; + int n = _arc_num-GR::id(arc)-1; + + //int a = mixingCoeff*(n%mixingCoeff) + n/mixingCoeff; + //int b = _arc_id[arc]; + if (_arc_mixing) + return sequence(n); + else + return n; + } + + // finally unused because too slow + inline int getSource(const int arc) const + { + //int a = _source[arc]; + //return a; + + int n = _arc_num-arc-1; + if (_arc_mixing) + n = mixingCoeff*(n%mixingCoeff) + n/mixingCoeff; + + int b; + if (n>=0) + b = _node_id(_graph.source(GR::arcFromId( n ) )); + else + { + n = arc+1-_arc_num; + if ( n<=_node_num) + b = _node_num; + else + if ( n>=_graph._n1) + b = _graph._n1; + else + b = _graph._n1-n; + } + + return b; + } + + + + // Implementation of the Block Search pivot rule + class BlockSearchPivotRule + { + private: + + // References to the NetworkSimplexSimple class + const UHalfIntVector &_source; + const UHalfIntVector &_target; + const CostVector &_cost; + const StateVector &_state; + const CostVector &_pi; + int &_in_arc; + int _search_arc_num; + + // Pivot rule data + int _block_size; + int _next_arc; + NetworkSimplexSimple &_ns; + + public: + + // Constructor + BlockSearchPivotRule(NetworkSimplexSimple &ns) : + _source(ns._source), _target(ns._target), + _cost(ns._cost), _state(ns._state), _pi(ns._pi), + _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), + _next_arc(0),_ns(ns) + { + // The main parameters of the pivot rule + const double BLOCK_SIZE_FACTOR = 1.0; + const int MIN_BLOCK_SIZE = 10; + + _block_size = std::max( int(BLOCK_SIZE_FACTOR * + std::sqrt(double(_search_arc_num))), + MIN_BLOCK_SIZE ); + } + // Find next entering arc + bool findEnteringArc() { + Cost c, min = 0; + int e; + int cnt = _block_size; + double a; + for (e = _next_arc; e != _search_arc_num; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < min) { + min = c; + _in_arc = e; + } + if (--cnt == 0) { + a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); + a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); + if (min < -EPSILON*a) goto search_end; + cnt = _block_size; + } + } + for (e = 0; e != _next_arc; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < min) { + min = c; + _in_arc = e; + } + if (--cnt == 0) { + a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); + a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); + if (min < -EPSILON*a) goto search_end; + cnt = _block_size; + } + } + a=fabs(_pi[_source[_in_arc]])>fabs(_pi[_target[_in_arc]]) ? fabs(_pi[_source[_in_arc]]):fabs(_pi[_target[_in_arc]]); + a=a>fabs(_cost[_in_arc])?a:fabs(_cost[_in_arc]); + if (min >= -EPSILON*a) return false; + + search_end: + _next_arc = e; + return true; + } + + }; //class BlockSearchPivotRule + + + + public: + + + + int _init_nb_nodes; + long long _init_nb_arcs; + + /// \name Parameters + /// The parameters of the algorithm can be specified using these + /// functions. + + /// @{ + + + /// \brief Set the costs of the arcs. + /// + /// This function sets the costs of the arcs. + /// If it is not used before calling \ref run(), the costs + /// will be set to \c 1 on all arcs. + /// + /// \param map An arc map storing the costs. + /// Its \c Value type must be convertible to the \c Cost type + /// of the algorithm. + /// + /// \return (*this) + template + NetworkSimplexSimple& costMap(const CostMap& map) { + Arc a; _graph.first(a); + for (; a != INVALID; _graph.next(a)) { + _cost[getArcID(a)] = map[a]; + } + return *this; + } + + + /// \brief Set the costs of one arc. + /// + /// This function sets the costs of one arcs. + /// Done for memory reasons + /// + /// \param arc An arc. + /// \param arc A cost + /// + /// \return (*this) + template + NetworkSimplexSimple& setCost(const Arc& arc, const Value cost) { + _cost[getArcID(arc)] = cost; + return *this; + } + + + /// \brief Set the supply values of the nodes. + /// + /// This function sets the supply values of the nodes. + /// If neither this function nor \ref stSupply() is used before + /// calling \ref run(), the supply of each node will be set to zero. + /// + /// \param map A node map storing the supply values. + /// Its \c Value type must be convertible to the \c Value type + /// of the algorithm. + /// + /// \return (*this) + template + NetworkSimplexSimple& supplyMap(const SupplyMap& map) { + Node n; _graph.first(n); + for (; n != INVALIDNODE; _graph.next(n)) { + _supply[_node_id(n)] = map[n]; + } + return *this; + } + template + NetworkSimplexSimple& supplyMap(const SupplyMap* map1, int n1, const SupplyMap* map2, int n2) { + Node n; _graph.first(n); + for (; n != INVALIDNODE; _graph.next(n)) { + if (n + NetworkSimplexSimple& supplyMapAll(SupplyMap val1, int n1, SupplyMap val2, int n2) { + Node n; _graph.first(n); + for (; n != INVALIDNODE; _graph.next(n)) { + if (n(*this) + NetworkSimplexSimple& stSupply(const Node& s, const Node& t, Value k) { + for (int i = 0; i != _node_num; ++i) { + _supply[i] = 0; + } + _supply[_node_id(s)] = k; + _supply[_node_id(t)] = -k; + return *this; + } + + /// \brief Set the type of the supply constraints. + /// + /// This function sets the type of the supply/demand constraints. + /// If it is not used before calling \ref run(), the \ref GEQ supply + /// type will be used. + /// + /// For more information, see \ref SupplyType. + /// + /// \return (*this) + NetworkSimplexSimple& supplyType(SupplyType supply_type) { + _stype = supply_type; + return *this; + } + + /// @} + + /// \name Execution Control + /// The algorithm can be executed using \ref run(). + + /// @{ + + /// \brief Run the algorithm. + /// + /// This function runs the algorithm. + /// The paramters can be specified using functions \ref lowerMap(), + /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), + /// \ref supplyType(). + /// For example, + /// \code + /// NetworkSimplexSimple ns(graph); + /// ns.lowerMap(lower).upperMap(upper).costMap(cost) + /// .supplyMap(sup).run(); + /// \endcode + /// + /// This function can be called more than once. All the given parameters + /// are kept for the next call, unless \ref resetParams() or \ref reset() + /// is used, thus only the modified parameters have to be set again. + /// If the underlying digraph was also modified after the construction + /// of the class (or the last \ref reset() call), then the \ref reset() + /// function must be called. + /// + /// \param pivot_rule The pivot rule that will be used during the + /// algorithm. For more information, see \ref PivotRule. + /// + /// \return \c INFEASIBLE if no feasible flow exists, + /// \n \c OPTIMAL if the problem has optimal solution + /// (i.e. it is feasible and bounded), and the algorithm has found + /// optimal flow and node potentials (primal and dual solutions), + /// \n \c UNBOUNDED if the objective function of the problem is + /// unbounded, i.e. there is a directed cycle having negative total + /// cost and infinite upper bound. + /// + /// \see ProblemType, PivotRule + /// \see resetParams(), reset() + ProblemType run() { +#if DEBUG_LVL>0 + mexPrintf("OPTIMAL = %d\nINFEASIBLE = %d\nUNBOUNDED = %d\n",OPTIMAL,INFEASIBLE,UNBOUNDED); + mexEvalString("drawnow;"); +#endif + + if (!init()) return INFEASIBLE; +#if DEBUG_LVL>0 + mexPrintf("Init done, starting iterations\n"); + mexEvalString("drawnow;"); +#endif + return start(); + } + + /// \brief Reset all the parameters that have been given before. + /// + /// This function resets all the paramaters that have been given + /// before using functions \ref lowerMap(), \ref upperMap(), + /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType(). + /// + /// It is useful for multiple \ref run() calls. Basically, all the given + /// parameters are kept for the next \ref run() call, unless + /// \ref resetParams() or \ref reset() is used. + /// If the underlying digraph was also modified after the construction + /// of the class or the last \ref reset() call, then the \ref reset() + /// function must be used, otherwise \ref resetParams() is sufficient. + /// + /// For example, + /// \code + /// NetworkSimplexSimple ns(graph); + /// + /// // First run + /// ns.lowerMap(lower).upperMap(upper).costMap(cost) + /// .supplyMap(sup).run(); + /// + /// // Run again with modified cost map (resetParams() is not called, + /// // so only the cost map have to be set again) + /// cost[e] += 100; + /// ns.costMap(cost).run(); + /// + /// // Run again from scratch using resetParams() + /// // (the lower bounds will be set to zero on all arcs) + /// ns.resetParams(); + /// ns.upperMap(capacity).costMap(cost) + /// .supplyMap(sup).run(); + /// \endcode + /// + /// \return (*this) + /// + /// \see reset(), run() + NetworkSimplexSimple& resetParams() { + for (int i = 0; i != _node_num; ++i) { + _supply[i] = 0; + } + for (int i = 0; i != _arc_num; ++i) { + _cost[i] = 1; + } + _stype = GEQ; + return *this; + } + + + + int divid (int x, int y) + { + return (x-x%y)/y; + } + + /// \brief Reset the internal data structures and all the parameters + /// that have been given before. + /// + /// This function resets the internal data structures and all the + /// paramaters that have been given before using functions \ref lowerMap(), + /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), + /// \ref supplyType(). + /// + /// It is useful for multiple \ref run() calls. Basically, all the given + /// parameters are kept for the next \ref run() call, unless + /// \ref resetParams() or \ref reset() is used. + /// If the underlying digraph was also modified after the construction + /// of the class or the last \ref reset() call, then the \ref reset() + /// function must be used, otherwise \ref resetParams() is sufficient. + /// + /// See \ref resetParams() for examples. + /// + /// \return (*this) + /// + /// \see resetParams(), run() + NetworkSimplexSimple& reset() { + // Resize vectors + _node_num = _init_nb_nodes; + _arc_num = _init_nb_arcs; + int all_node_num = _node_num + 1; + int max_arc_num = _arc_num + 2 * _node_num; + + _source.resize(max_arc_num); + _target.resize(max_arc_num); + + _cost.resize(max_arc_num); + _supply.resize(all_node_num); + _flow.resize(max_arc_num); + _pi.resize(all_node_num); + + _parent.resize(all_node_num); + _pred.resize(all_node_num); + _forward.resize(all_node_num); + _thread.resize(all_node_num); + _rev_thread.resize(all_node_num); + _succ_num.resize(all_node_num); + _last_succ.resize(all_node_num); + _state.resize(max_arc_num); + + + //_arc_mixing=false; + if (_arc_mixing) { + // Store the arcs in a mixed order + int k = std::max(int(std::sqrt(double(_arc_num))), 10); + mixingCoeff = k; + subsequence_length = _arc_num / mixingCoeff + 1; + num_big_subseqiences = _arc_num % mixingCoeff; + num_total_big_subsequence_numbers = subsequence_length * num_big_subseqiences; + + int i = 0, j = 0; + Arc a; _graph.first(a); + for (; a != INVALID; _graph.next(a)) { + _source[i] = _node_id(_graph.source(a)); + _target[i] = _node_id(_graph.target(a)); + //_arc_id[a] = i; + if ((i += k) >= _arc_num) i = ++j; + } + } else { + // Store the arcs in the original order + int i = 0; + Arc a; _graph.first(a); + for (; a != INVALID; _graph.next(a), ++i) { + _source[i] = _node_id(_graph.source(a)); + _target[i] = _node_id(_graph.target(a)); + //_arc_id[a] = i; + } + } + + // Reset parameters + resetParams(); + return *this; + } + + /// @} + + /// \name Query Functions + /// The results of the algorithm can be obtained using these + /// functions.\n + /// The \ref run() function must be called before using them. + + /// @{ + + /// \brief Return the total cost of the found flow. + /// + /// This function returns the total cost of the found flow. + /// Its complexity is O(e). + /// + /// \note The return type of the function can be specified as a + /// template parameter. For example, + /// \code + /// ns.totalCost(); + /// \endcode + /// It is useful if the total cost cannot be stored in the \c Cost + /// type of the algorithm, which is the default return type of the + /// function. + /// + /// \pre \ref run() must be called before using this function. + /*template + Number totalCost() const { + Number c = 0; + for (ArcIt a(_graph); a != INVALID; ++a) { + int i = getArcID(a); + c += Number(_flow[i]) * Number(_cost[i]); + } + return c; + }*/ + + template + Number totalCost() const { + Number c = 0; + + /*#ifdef HASHMAP + typename stdext::hash_map::const_iterator it; + #else + typename std::map::const_iterator it; + #endif + for (it = _flow.data.begin(); it!=_flow.data.end(); ++it) + c += Number(it->second) * Number(_cost[it->first]); + return c;*/ + + for (int i=0; i<_flow.size(); i++) + c += _flow[i] * Number(_cost[i]); + return c; + + } + +#ifndef DOXYGEN + Cost totalCost() const { + return totalCost(); + } +#endif + + /// \brief Return the flow on the given arc. + /// + /// This function returns the flow on the given arc. + /// + /// \pre \ref run() must be called before using this function. + Value flow(const Arc& a) const { + return _flow[getArcID(a)]; + } + + /// \brief Return the flow map (the primal solution). + /// + /// This function copies the flow value on each arc into the given + /// map. The \c Value type of the algorithm must be convertible to + /// the \c Value type of the map. + /// + /// \pre \ref run() must be called before using this function. + template + void flowMap(FlowMap &map) const { + Arc a; _graph.first(a); + for (; a != INVALID; _graph.next(a)) { + map.set(a, _flow[getArcID(a)]); + } + } + + /// \brief Return the potential (dual value) of the given node. + /// + /// This function returns the potential (dual value) of the + /// given node. + /// + /// \pre \ref run() must be called before using this function. + Cost potential(const Node& n) const { + return _pi[_node_id(n)]; + } + + /// \brief Return the potential map (the dual solution). + /// + /// This function copies the potential (dual value) of each node + /// into the given map. + /// The \c Cost type of the algorithm must be convertible to the + /// \c Value type of the map. + /// + /// \pre \ref run() must be called before using this function. + template + void potentialMap(PotentialMap &map) const { + Node n; _graph.first(n); + for (; n != INVALID; _graph.next(n)) { + map.set(n, _pi[_node_id(n)]); + } + } + + /// @} + + private: + + // Initialize internal data structures + bool init() { + if (_node_num == 0) return false; + /* + // Check the sum of supply values + _sum_supply = 0; + for (int i = 0; i != _node_num; ++i) { + _sum_supply += _supply[i]; + } + if ( !((_stype == GEQ && _sum_supply <= _epsilon ) || + (_stype == LEQ && _sum_supply >= -_epsilon )) ) return false; + */ + + // Initialize artifical cost + Cost ART_COST; + if (std::numeric_limits::is_exact) { + ART_COST = std::numeric_limits::max() / 2 + 1; + } else { + ART_COST = 0; + for (int i = 0; i != _arc_num; ++i) { + if (_cost[i] > ART_COST) ART_COST = _cost[i]; + } + ART_COST = (ART_COST + 1) * _node_num; + } + + // Initialize arc maps + for (int i = 0; i != _arc_num; ++i) { + //_flow[i] = 0; //by default, the sparse matrix is empty + _state[i] = STATE_LOWER; + } + + // Set data for the artificial root node + _root = _node_num; + _parent[_root] = -1; + _pred[_root] = -1; + _thread[_root] = 0; + _rev_thread[0] = _root; + _succ_num[_root] = _node_num + 1; + _last_succ[_root] = _root - 1; + _supply[_root] = -_sum_supply; + _pi[_root] = 0; + + // Add artificial arcs and initialize the spanning tree data structure + if (_sum_supply == 0) { + // EQ supply constraints + _search_arc_num = _arc_num; + _all_arc_num = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _pred[u] = e; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + _state[e] = STATE_TREE; + if (_supply[u] >= 0) { + _forward[u] = true; + _pi[u] = 0; + _source[e] = u; + _target[e] = _root; + _flow[e] = _supply[u]; + _cost[e] = 0; + } else { + _forward[u] = false; + _pi[u] = ART_COST; + _source[e] = _root; + _target[e] = u; + _flow[e] = -_supply[u]; + _cost[e] = ART_COST; + } + } + } + else if (_sum_supply > 0) { + // LEQ supply constraints + _search_arc_num = _arc_num + _node_num; + int f = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + if (_supply[u] >= 0) { + _forward[u] = true; + _pi[u] = 0; + _pred[u] = e; + _source[e] = u; + _target[e] = _root; + _flow[e] = _supply[u]; + _cost[e] = 0; + _state[e] = STATE_TREE; + } else { + _forward[u] = false; + _pi[u] = ART_COST; + _pred[u] = f; + _source[f] = _root; + _target[f] = u; + _flow[f] = -_supply[u]; + _cost[f] = ART_COST; + _state[f] = STATE_TREE; + _source[e] = u; + _target[e] = _root; + //_flow[e] = 0; //by default, the sparse matrix is empty + _cost[e] = 0; + _state[e] = STATE_LOWER; + ++f; + } + } + _all_arc_num = f; + } + else { + // GEQ supply constraints + _search_arc_num = _arc_num + _node_num; + int f = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + if (_supply[u] <= 0) { + _forward[u] = false; + _pi[u] = 0; + _pred[u] = e; + _source[e] = _root; + _target[e] = u; + _flow[e] = -_supply[u]; + _cost[e] = 0; + _state[e] = STATE_TREE; + } else { + _forward[u] = true; + _pi[u] = -ART_COST; + _pred[u] = f; + _source[f] = u; + _target[f] = _root; + _flow[f] = _supply[u]; + _state[f] = STATE_TREE; + _cost[f] = ART_COST; + _source[e] = _root; + _target[e] = u; + //_flow[e] = 0; //by default, the sparse matrix is empty + _cost[e] = 0; + _state[e] = STATE_LOWER; + ++f; + } + } + _all_arc_num = f; + } + + return true; + } + + // Find the join node + void findJoinNode() { + int u = _source[in_arc]; + int v = _target[in_arc]; + while (u != v) { + if (_succ_num[u] < _succ_num[v]) { + u = _parent[u]; + } else { + v = _parent[v]; + } + } + join = u; + } + + // Find the leaving arc of the cycle and returns true if the + // leaving arc is not the same as the entering arc + bool findLeavingArc() { + // Initialize first and second nodes according to the direction + // of the cycle + if (_state[in_arc] == STATE_LOWER) { + first = _source[in_arc]; + second = _target[in_arc]; + } else { + first = _target[in_arc]; + second = _source[in_arc]; + } + delta = INF; + int result = 0; + Value d; + int e; + + // Search the cycle along the path form the first node to the root + for (int u = first; u != join; u = _parent[u]) { + e = _pred[u]; + d = _forward[u] ? _flow[e] : INF ; + if (d < delta) { + delta = d; + u_out = u; + result = 1; + } + } + // Search the cycle along the path form the second node to the root + for (int u = second; u != join; u = _parent[u]) { + e = _pred[u]; + d = _forward[u] ? INF : _flow[e]; + if (d <= delta) { + delta = d; + u_out = u; + result = 2; + } + } + + if (result == 1) { + u_in = first; + v_in = second; + } else { + u_in = second; + v_in = first; + } + return result != 0; + } + + // Change _flow and _state vectors + void changeFlow(bool change) { + // Augment along the cycle + if (delta > 0) { + Value val = _state[in_arc] * delta; + _flow[in_arc] += val; + for (int u = _source[in_arc]; u != join; u = _parent[u]) { + _flow[_pred[u]] += _forward[u] ? -val : val; + } + for (int u = _target[in_arc]; u != join; u = _parent[u]) { + _flow[_pred[u]] += _forward[u] ? val : -val; + } + } + // Update the state of the entering and leaving arcs + if (change) { + _state[in_arc] = STATE_TREE; + _state[_pred[u_out]] = + (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; + } else { + _state[in_arc] = -_state[in_arc]; + } + } + + // Update the tree structure + void updateTreeStructure() { + int u, w; + int old_rev_thread = _rev_thread[u_out]; + int old_succ_num = _succ_num[u_out]; + int old_last_succ = _last_succ[u_out]; + v_out = _parent[u_out]; + + u = _last_succ[u_in]; // the last successor of u_in + right = _thread[u]; // the node after it + + // Handle the case when old_rev_thread equals to v_in + // (it also means that join and v_out coincide) + if (old_rev_thread == v_in) { + last = _thread[_last_succ[u_out]]; + } else { + last = _thread[v_in]; + } + + // Update _thread and _parent along the stem nodes (i.e. the nodes + // between u_in and u_out, whose parent have to be changed) + _thread[v_in] = stem = u_in; + _dirty_revs.clear(); + _dirty_revs.push_back(v_in); + par_stem = v_in; + while (stem != u_out) { + // Insert the next stem node into the thread list + new_stem = _parent[stem]; + _thread[u] = new_stem; + _dirty_revs.push_back(u); + + // Remove the subtree of stem from the thread list + w = _rev_thread[stem]; + _thread[w] = right; + _rev_thread[right] = w; + + // Change the parent node and shift stem nodes + _parent[stem] = par_stem; + par_stem = stem; + stem = new_stem; + + // Update u and right + u = _last_succ[stem] == _last_succ[par_stem] ? + _rev_thread[par_stem] : _last_succ[stem]; + right = _thread[u]; + } + _parent[u_out] = par_stem; + _thread[u] = last; + _rev_thread[last] = u; + _last_succ[u_out] = u; + + // Remove the subtree of u_out from the thread list except for + // the case when old_rev_thread equals to v_in + // (it also means that join and v_out coincide) + if (old_rev_thread != v_in) { + _thread[old_rev_thread] = right; + _rev_thread[right] = old_rev_thread; + } + + // Update _rev_thread using the new _thread values + for (int i = 0; i != int(_dirty_revs.size()); ++i) { + u = _dirty_revs[i]; + _rev_thread[_thread[u]] = u; + } + + // Update _pred, _forward, _last_succ and _succ_num for the + // stem nodes from u_out to u_in + int tmp_sc = 0, tmp_ls = _last_succ[u_out]; + u = u_out; + while (u != u_in) { + w = _parent[u]; + _pred[u] = _pred[w]; + _forward[u] = !_forward[w]; + tmp_sc += _succ_num[u] - _succ_num[w]; + _succ_num[u] = tmp_sc; + _last_succ[w] = tmp_ls; + u = w; + } + _pred[u_in] = in_arc; + _forward[u_in] = (u_in == _source[in_arc]); + _succ_num[u_in] = old_succ_num; + + // Set limits for updating _last_succ form v_in and v_out + // towards the root + int up_limit_in = -1; + int up_limit_out = -1; + if (_last_succ[join] == v_in) { + up_limit_out = join; + } else { + up_limit_in = join; + } + + // Update _last_succ from v_in towards the root + for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; + u = _parent[u]) { + _last_succ[u] = _last_succ[u_out]; + } + // Update _last_succ from v_out towards the root + if (join != old_rev_thread && v_in != old_rev_thread) { + for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; + u = _parent[u]) { + _last_succ[u] = old_rev_thread; + } + } else { + for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; + u = _parent[u]) { + _last_succ[u] = _last_succ[u_out]; + } + } + + // Update _succ_num from v_in to join + for (u = v_in; u != join; u = _parent[u]) { + _succ_num[u] += old_succ_num; + } + // Update _succ_num from v_out to join + for (u = v_out; u != join; u = _parent[u]) { + _succ_num[u] -= old_succ_num; + } + } + + // Update potentials + void updatePotential() { + Cost sigma = _forward[u_in] ? + _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : + _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; + // Update potentials in the subtree, which has been moved + int end = _thread[_last_succ[u_in]]; + for (int u = u_in; u != end; u = _thread[u]) { + _pi[u] += sigma; + } + } + + // Heuristic initial pivots + bool initialPivots() { + Value curr, total = 0; + std::vector supply_nodes, demand_nodes; + Node u; _graph.first(u); + for (; u != INVALIDNODE; _graph.next(u)) { + curr = _supply[_node_id(u)]; + if (curr > 0) { + total += curr; + supply_nodes.push_back(u); + } + else if (curr < 0) { + demand_nodes.push_back(u); + } + } + if (_sum_supply > 0) total -= _sum_supply; + if (total <= 0) return true; + + IntVector arc_vector; + if (_sum_supply >= 0) { + if (supply_nodes.size() == 1 && demand_nodes.size() == 1) { + // Perform a reverse graph search from the sink to the source + //typename GR::template NodeMap reached(_graph, false); + BoolVector reached(_node_num, false); + Node s = supply_nodes[0], t = demand_nodes[0]; + std::vector stack; + reached[t] = true; + stack.push_back(t); + while (!stack.empty()) { + Node u, v = stack.back(); + stack.pop_back(); + if (v == s) break; + Arc a; _graph.firstIn(a, v); + for (; a != INVALID; _graph.nextIn(a)) { + if (reached[u = _graph.source(a)]) continue; + int j = getArcID(a); + if (INF >= total) { + arc_vector.push_back(j); + reached[u] = true; + stack.push_back(u); + } + } + } + } else { + // Find the min. cost incomming arc for each demand node + for (int i = 0; i != int(demand_nodes.size()); ++i) { + Node v = demand_nodes[i]; + Cost c, min_cost = std::numeric_limits::max(); + Arc min_arc = INVALID; + Arc a; _graph.firstIn(a, v); + for (; a != INVALID; _graph.nextIn(a)) { + c = _cost[getArcID(a)]; + if (c < min_cost) { + min_cost = c; + min_arc = a; + } + } + if (min_arc != INVALID) { + arc_vector.push_back(getArcID(min_arc)); + } + } + } + } else { + // Find the min. cost outgoing arc for each supply node + for (int i = 0; i != int(supply_nodes.size()); ++i) { + Node u = supply_nodes[i]; + Cost c, min_cost = std::numeric_limits::max(); + Arc min_arc = INVALID; + Arc a; _graph.firstOut(a, u); + for (; a != INVALID; _graph.nextOut(a)) { + c = _cost[getArcID(a)]; + if (c < min_cost) { + min_cost = c; + min_arc = a; + } + } + if (min_arc != INVALID) { + arc_vector.push_back(getArcID(min_arc)); + } + } + } + + // Perform heuristic initial pivots + for (int i = 0; i != int(arc_vector.size()); ++i) { + in_arc = arc_vector[i]; + // l'erreur est probablement ici... + if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] - + _pi[_target[in_arc]]) >= 0) continue; + findJoinNode(); + bool change = findLeavingArc(); + if (delta >= MAX) return false; + changeFlow(change); + if (change) { + updateTreeStructure(); + updatePotential(); + } + } + return true; + } + + // Execute the algorithm + ProblemType start() { + return start(); + } + + template + ProblemType start() { + PivotRuleImpl pivot(*this); + double prevCost=-1; + + // Perform heuristic initial pivots + if (!initialPivots()) return UNBOUNDED; + +#if DEBUG_LVL>0 + int niter=0; +#endif + int iter_number=0; + //pivot.setDantzig(true); + // Execute the Network Simplex algorithm + while (pivot.findEnteringArc()) { + if(++iter_number>=max_iter&&max_iter>0){ + char errMess[1000]; + // sprintf( errMess, "RESULT MIGHT BE INACURATE\nMax number of iteration reached, currently \%d. Sometimes iterations go on in cycle even though the solution has been reached, to check if it's the case here have a look at the minimal reduced cost. If it is very close to machine precision, you might actually have the correct solution, if not try setting the maximum number of iterations a bit higher",iter_number ); + // mexWarnMsgTxt(errMess); + break; + } +#if DEBUG_LVL>0 + if(niter>MAX_DEBUG_ITER) + break; + if(++niter%1000==0||niter%1000==1){ + double curCost=totalCost(); + double sumFlow=0; + double a; + a= (fabs(_pi[_source[in_arc]])>=fabs(_pi[_target[in_arc]])) ? fabs(_pi[_source[in_arc]]) : fabs(_pi[_target[in_arc]]); + a=a>=fabs(_cost[in_arc])?a:fabs(_cost[in_arc]); + for (int i=0; i<_flow.size(); i++) { + sumFlow+=_state[i]*_flow[i]; + } + mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\nReduced cost=%.30f\nPrecision =%.30f\n",sumFlow,niter, curCost,_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -_pi[_target[in_arc]]), -EPSILON*(a)); + mexPrintf("Arc in = (%d,%d)\n",_node_id(_source[in_arc]),_node_id(_target[in_arc])); + mexPrintf("Supplies = (%f,%f)\n",_supply[_source[in_arc]],_supply[_target[in_arc]]); + + mexPrintf("%.30f\n%.30f\n%.30f\n%.30f\n%",_cost[in_arc],_pi[_source[in_arc]],_pi[_target[in_arc]],a); + mexEvalString("drawnow;"); + } +#endif + + findJoinNode(); + bool change = findLeavingArc(); + if (delta >= MAX) return UNBOUNDED; + changeFlow(change); + if (change) { + updateTreeStructure(); + updatePotential(); + } +#if DEBUG_LVL>0 + else{ + mexPrintf("No change\n"); + } +#endif +#if DEBUG_LVL>1 + mexPrintf("Arc in = (%d,%d)\n",_source[in_arc],_target[in_arc]); +#endif + + } + + +#if DEBUG_LVL>0 + double curCost=totalCost(); + double sumFlow=0; + double a; + a= (fabs(_pi[_source[in_arc]])>=fabs(_pi[_target[in_arc]])) ? fabs(_pi[_source[in_arc]]) : fabs(_pi[_target[in_arc]]); + a=a>=fabs(_cost[in_arc])?a:fabs(_cost[in_arc]); + for (int i=0; i<_flow.size(); i++) { + sumFlow+=_state[i]*_flow[i]; + } + mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\nReduced cost=%.30f\nPrecision =%.30f",sumFlow,niter, curCost,_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] -_pi[_target[in_arc]]), -EPSILON*(a)); + mexPrintf("Arc in = (%d,%d)\n",_node_id(_source[in_arc]),_node_id(_target[in_arc])); + mexPrintf("Supplies = (%f,%f)\n",_supply[_source[in_arc]],_supply[_target[in_arc]]); + + mexEvalString("drawnow;"); +#endif + +#if DEBUG_LVL>1 + double sumFlow=0; + for (int i=0; i<_flow.size(); i++) { + sumFlow+=_state[i]*_flow[i]; + if (_state[i]==STATE_TREE) { + mexPrintf("Non zero value at (%d,%d)\n",_node_num+1-_source[i],_node_num+1-_target[i]); + } + } + mexPrintf("Sum of the flow %.100f\n%d iterations, current cost=%.20f\n",sumFlow,niter, totalCost()); + mexEvalString("drawnow;"); +#endif + // Check feasibility + for (int e = _search_arc_num; e != _all_arc_num; ++e) { + if (_flow[e] != 0){ + if (abs(_flow[e]) > EPSILON) + return INFEASIBLE; + else + _flow[e]=0; + + } + } + + // Shift potentials to meet the requirements of the GEQ/LEQ type + // optimality conditions + if (_sum_supply == 0) { + if (_stype == GEQ) { + Cost max_pot = -std::numeric_limits::max(); + for (int i = 0; i != _node_num; ++i) { + if (_pi[i] > max_pot) max_pot = _pi[i]; + } + if (max_pot > 0) { + for (int i = 0; i != _node_num; ++i) + _pi[i] -= max_pot; + } + } else { + Cost min_pot = std::numeric_limits::max(); + for (int i = 0; i != _node_num; ++i) { + if (_pi[i] < min_pot) min_pot = _pi[i]; + } + if (min_pot < 0) { + for (int i = 0; i != _node_num; ++i) + _pi[i] -= min_pot; + } + } + } + + return OPTIMAL; + } + + }; //class NetworkSimplexSimple + + ///@} + +} //namespace lemon + +#endif //LEMON_NETWORK_SIMPLEX_H -- cgit v1.2.3