rename emd module to lp

1 files changed, 1543 insertions, 0 deletions

diff --git a/ot/lp/network_simplex_simple.h b/ot/lp/network_simplex_simple.h
new file mode 100644
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+++ b/ot/lp/network_simplex_simple.h
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+/* -*- 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 <vector>
+#include <limits>
+#include <algorithm>
+#ifdef HASHMAP
+#include <hash_map>
+#else
+#include <map>
+#endif
+#include <cmath>
+//#include "core.h"
+//#include "lmath.h"
+
+//#include "sparse_array_n.h"
+#include "full_bipartitegraph.h"
+
+#define INVALIDNODE -1
+#define INVALID (-1)
+
+namespace lemon {
+
+
+    template <typename T>
+	class ProxyObject;
+
+	template<typename T>
+	class SparseValueVector
+	{
+	public:
+		SparseValueVector(int n=0)
+		{
+		}
+		void resize(int n=0){};
+		T operator[](const int id) const
+		{
+#ifdef HASHMAP
+			typename stdext::hash_map<int,T>::const_iterator it = data.find(id);
+#else
+			typename std::map<int,T>::const_iterator it = data.find(id);
+#endif
+			if (it==data.end())
+				return 0;
+			else
+				return it->second;
+		}
+
+		ProxyObject<T> operator[](const int id)
+		{
+			return ProxyObject<T>( this, id );
+		}
+
+        //private:
+#ifdef HASHMAP
+		stdext::hash_map<int,T> data;
+#else
+		std::map<int,T> data;
+#endif
+
+	};
+
+	template <typename T>
+	class ProxyObject {
+	public:
+		ProxyObject( SparseValueVector<T> *v, int idx ){_v=v; _idx=idx;};
+		ProxyObject<T> & 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<int,T>::iterator it = _v->data.find(_idx);
+#else
+			typename std::map<int,T>::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<int,T>::iterator it = _v->data.find(_idx);
+#else
+			typename std::map<int,T>::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<int,T>::iterator it = _v->data.find(_idx);
+#else
+			typename std::map<int,T>::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<T> *_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 <typename GR, typename V = int, typename C = V, typename NodesType = unsigned short int>
+    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<Value>::max()),
+        INF(std::numeric_limits<Value>::has_infinity ?
+            std::numeric_limits<Value>::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 <em>"greater or equal"</em>
+            /// supply/demand constraints in the definition of the problem.
+            GEQ,
+            /// This option means that there are <em>"less or equal"</em>
+            /// supply/demand constraints in the definition of the problem.
+            LEQ
+        };
+
+
+
+    private:
+
+        double max_iter;
+        TEMPLATE_DIGRAPH_TYPEDEFS(GR);
+
+        typedef std::vector<int> IntVector;
+        typedef std::vector<NodesType> UHalfIntVector;
+        typedef std::vector<Value> ValueVector;
+        typedef std::vector<Cost> CostVector;
+        //	typedef SparseValueVector<Cost> CostVector;
+        typedef std::vector<char> BoolVector;
+        // Note: vector<char> is used instead of vector<bool> for efficiency reasons
+
+        // State constants for arcs
+        enum ArcState {
+            STATE_UPPER = -1,
+            STATE_TREE  =  0,
+            STATE_LOWER =  1
+        };
+
+        typedef std::vector<signed char> StateVector;
+        // Note: vector<signed char> is used instead of vector<ArcState> 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<Value> _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<Value>::infinity() if available,
+        /// \c std::numeric_limits<Value>::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 <tt>(*this)</tt>
+        template<typename CostMap>
+        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 <tt>(*this)</tt>
+        template<typename Value>
+        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 <tt>(*this)</tt>
+        template<typename SupplyMap>
+        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<typename SupplyMap>
+        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<n1)
+                    _supply[_node_id(n)] = map1[n];
+                else
+                    _supply[_node_id(n)] = map2[n-n1];
+            }
+            return *this;
+        }
+        template<typename SupplyMap>
+        NetworkSimplexSimple& supplyMapAll(SupplyMap val1, int n1, SupplyMap val2, int n2) {
+            Node n; _graph.first(n);
+            for (; n != INVALIDNODE; _graph.next(n)) {
+                if (n<n1)
+                    _supply[_node_id(n)] = val1;
+                else
+                    _supply[_node_id(n)] = val2;
+            }
+            return *this;
+        }
+
+        /// \brief Set single source and target nodes and a supply value.
+        ///
+        /// This function sets a single source node and a single target node
+        /// and the required flow value.
+        /// If neither this function nor \ref supplyMap() is used before
+        /// calling \ref run(), the supply of each node will be set to zero.
+        ///
+        /// Using this function has the same effect as using \ref supplyMap()
+        /// with such a map in which \c k is assigned to \c s, \c -k is
+        /// assigned to \c t and all other nodes have zero supply value.
+        ///
+        /// \param s The source node.
+        /// \param t The target node.
+        /// \param k The required amount of flow from node \c s to node \c t
+        /// (i.e. the supply of \c s and the demand of \c t).
+        ///
+        /// \return <tt>(*this)</tt>
+        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 <tt>(*this)</tt>
+        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<ListDigraph> 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<ListDigraph> 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 <tt>(*this)</tt>
+        ///
+        /// \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 <tt>(*this)</tt>
+        ///
+        /// \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<double>();
+        /// \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 <typename Number>
+         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 <typename Number>
+        Number totalCost() const {
+            Number c = 0;
+
+            /*#ifdef HASHMAP
+             typename stdext::hash_map<int, Value>::const_iterator it;
+             #else
+             typename std::map<int, Value>::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<Cost>();
+        }
+#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 <typename FlowMap>
+        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 <typename PotentialMap>
+        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<Cost>::is_exact) {
+                ART_COST = std::numeric_limits<Cost>::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<Node> 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<bool> reached(_graph, false);
+                    BoolVector reached(_node_num, false);
+                    Node s = supply_nodes[0], t = demand_nodes[0];
+                    std::vector<Node> 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<Cost>::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<Cost>::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<BlockSearchPivotRule>();
+        }
+
+        template <typename PivotRuleImpl>
+        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<Cost>::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<Cost>::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