COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/lp_base.h @ 1899:2d4835f5a86a

Last change on this file since 1899:2d4835f5a86a was 1899:2d4835f5a86a, checked in by Alpar Juttner, 14 years ago
  • setCol() -> col()
  • better doc.
File size: 38.9 KB
Line 
1/* -*- C++ -*-
2 * lemon/lp_base.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_LP_BASE_H
18#define LEMON_LP_BASE_H
19
20#include<vector>
21#include<map>
22#include<limits>
23#include<cmath>
24
25#include<lemon/utility.h>
26#include<lemon/error.h>
27#include<lemon/invalid.h>
28
29///\file
30///\brief The interface of the LP solver interface.
31///\ingroup gen_opt_group
32namespace lemon {
33 
34  ///Internal data structure to convert floating id's to fix one's
35   
36  ///\todo This might be implemented to be also usable in other places.
37  class _FixId
38  {
39  protected:
40    std::vector<int> index;
41    std::vector<int> cross;
42    int first_free;
43  public:
44    _FixId() : first_free(-1) {};
45    ///Convert a floating id to a fix one
46
47    ///\param n is a floating id
48    ///\return the corresponding fix id
49    int fixId(int n) const {return cross[n];}
50    ///Convert a fix id to a floating one
51
52    ///\param n is a fix id
53    ///\return the corresponding floating id
54    int floatingId(int n) const { return index[n];}
55    ///Add a new floating id.
56
57    ///\param n is a floating id
58    ///\return the fix id of the new value
59    ///\todo Multiple additions should also be handled.
60    int insert(int n)
61    {
62      if(n>=int(cross.size())) {
63        cross.resize(n+1);
64        if(first_free==-1) {
65          cross[n]=index.size();
66          index.push_back(n);
67        }
68        else {
69          cross[n]=first_free;
70          int next=index[first_free];
71          index[first_free]=n;
72          first_free=next;
73        }
74        return cross[n];
75      }
76      ///\todo Create an own exception type.
77      else throw LogicError(); //floatingId-s must form a continuous range;
78    }
79    ///Remove a fix id.
80
81    ///\param n is a fix id
82    ///
83    void erase(int n)
84    {
85      int fl=index[n];
86      index[n]=first_free;
87      first_free=n;
88      for(int i=fl+1;i<int(cross.size());++i) {
89        cross[i-1]=cross[i];
90        index[cross[i]]--;
91      }
92      cross.pop_back();
93    }
94    ///An upper bound on the largest fix id.
95
96    ///\todo Do we need this?
97    ///
98    std::size_t maxFixId() { return cross.size()-1; }
99 
100  };
101   
102  ///Common base class for LP solvers
103 
104  ///\todo Much more docs
105  ///\ingroup gen_opt_group
106  class LpSolverBase {
107
108  public:
109
110    ///Possible outcomes of an LP solving procedure
111    enum SolveExitStatus {
112      ///This means that the problem has been successfully solved: either
113      ///an optimal solution has been found or infeasibility/unboundedness
114      ///has been proved.
115      SOLVED = 0,
116      ///Any other case (including the case when some user specified limit has been exceeded)
117      UNSOLVED = 1
118    };
119     
120      ///\e
121    enum SolutionStatus {
122      ///Feasible solution has'n been found (but may exist).
123
124      ///\todo NOTFOUND might be a better name.
125      ///
126      UNDEFINED = 0,
127      ///The problem has no feasible solution
128      INFEASIBLE = 1,
129      ///Feasible solution found
130      FEASIBLE = 2,
131      ///Optimal solution exists and found
132      OPTIMAL = 3,
133      ///The cost function is unbounded
134
135      ///\todo Give a feasible solution and an infinite ray (and the
136      ///corresponding bases)
137      INFINITE = 4
138    };
139
140    ///\e The type of the investigated LP problem
141    enum ProblemTypes {
142      ///Primal-dual feasible
143      PRIMAL_DUAL_FEASIBLE = 0,
144      ///Primal feasible dual infeasible
145      PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
146      ///Primal infeasible dual feasible
147      PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
148      ///Primal-dual infeasible
149      PRIMAL_DUAL_INFEASIBLE = 3,
150      ///Could not determine so far
151      UNKNOWN = 4
152    };
153
154    ///The floating point type used by the solver
155    typedef double Value;
156    ///The infinity constant
157    static const Value INF;
158    ///The not a number constant
159    static const Value NaN;
160   
161    ///Refer to a column of the LP.
162
163    ///This type is used to refer to a column of the LP.
164    ///
165    ///Its value remains valid and correct even after the addition or erase of
166    ///other columns.
167    ///
168    ///\todo Document what can one do with a Col (INVALID, comparing,
169    ///it is similar to Node/Edge)
170    class Col {
171    protected:
172      int id;
173      friend class LpSolverBase;
174    public:
175      typedef Value ExprValue;
176      typedef True LpSolverCol;
177      Col() {}
178      Col(const Invalid&) : id(-1) {}
179      bool operator<(Col c) const  {return id<c.id;}
180      bool operator==(Col c) const  {return id==c.id;}
181      bool operator!=(Col c) const  {return id==c.id;}
182    };
183
184    ///Refer to a row of the LP.
185
186    ///This type is used to refer to a row of the LP.
187    ///
188    ///Its value remains valid and correct even after the addition or erase of
189    ///other rows.
190    ///
191    ///\todo Document what can one do with a Row (INVALID, comparing,
192    ///it is similar to Node/Edge)
193    class Row {
194    protected:
195      int id;
196      friend class LpSolverBase;
197    public:
198      typedef Value ExprValue;
199      typedef True LpSolverRow;
200      Row() {}
201      Row(const Invalid&) : id(-1) {}
202
203      bool operator<(Row c) const  {return id<c.id;}
204      bool operator==(Row c) const  {return id==c.id;}
205      bool operator!=(Row c) const  {return id==c.id;}
206   };
207   
208    ///Linear expression of variables and a constant component
209   
210    ///This data structure strores a linear expression of the variables
211    ///(\ref Col "Col"s) and also has a constant component.
212    ///
213    ///There are several ways to access and modify the contents of this
214    ///container.
215    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
216    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
217    ///read and modify the coefficients like
218    ///these.
219    ///\code
220    ///e[v]=5;
221    ///e[v]+=12;
222    ///e.erase(v);
223    ///\endcode
224    ///or you can also iterate through its elements.
225    ///\code
226    ///double s=0;
227    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
228    ///  s+=i->second;
229    ///\endcode
230    ///(This code computes the sum of all coefficients).
231    ///- Numbers (<tt>double</tt>'s)
232    ///and variables (\ref Col "Col"s) directly convert to an
233    ///\ref Expr and the usual linear operations are defined so 
234    ///\code
235    ///v+w
236    ///2*v-3.12*(v-w/2)+2
237    ///v*2.1+(3*v+(v*12+w+6)*3)/2
238    ///\endcode
239    ///are valid \ref Expr "Expr"essions.
240    ///The usual assignment operations are also defined.
241    ///\code
242    ///e=v+w;
243    ///e+=2*v-3.12*(v-w/2)+2;
244    ///e*=3.4;
245    ///e/=5;
246    ///\endcode
247    ///- The constant member can be set and read by \ref constComp()
248    ///\code
249    ///e.constComp()=12;
250    ///double c=e.constComp();
251    ///\endcode
252    ///
253    ///\note \ref clear() not only sets all coefficients to 0 but also
254    ///clears the constant components.
255    ///
256    ///\sa Constr
257    ///
258    class Expr : public std::map<Col,Value>
259    {
260    public:
261      typedef LpSolverBase::Col Key;
262      typedef LpSolverBase::Value Value;
263     
264    protected:
265      typedef std::map<Col,Value> Base;
266     
267      Value const_comp;
268  public:
269      typedef True IsLinExpression;
270      ///\e
271      Expr() : Base(), const_comp(0) { }
272      ///\e
273      Expr(const Key &v) : const_comp(0) {
274        Base::insert(std::make_pair(v, 1));
275      }
276      ///\e
277      Expr(const Value &v) : const_comp(v) {}
278      ///\e
279      void set(const Key &v,const Value &c) {
280        Base::insert(std::make_pair(v, c));
281      }
282      ///\e
283      Value &constComp() { return const_comp; }
284      ///\e
285      const Value &constComp() const { return const_comp; }
286     
287      ///Removes the components with zero coefficient.
288      void simplify() {
289        for (Base::iterator i=Base::begin(); i!=Base::end();) {
290          Base::iterator j=i;
291          ++j;
292          if ((*i).second==0) Base::erase(i);
293          j=i;
294        }
295      }
296
297      ///Removes the coefficients closer to zero than \c tolerance.
298      void simplify(double &tolerance) {
299        for (Base::iterator i=Base::begin(); i!=Base::end();) {
300          Base::iterator j=i;
301          ++j;
302          if (std::fabs((*i).second)<tolerance) Base::erase(i);
303          j=i;
304        }
305      }
306
307      ///Sets all coefficients and the constant component to 0.
308      void clear() {
309        Base::clear();
310        const_comp=0;
311      }
312
313      ///\e
314      Expr &operator+=(const Expr &e) {
315        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
316          (*this)[j->first]+=j->second;
317        const_comp+=e.const_comp;
318        return *this;
319      }
320      ///\e
321      Expr &operator-=(const Expr &e) {
322        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
323          (*this)[j->first]-=j->second;
324        const_comp-=e.const_comp;
325        return *this;
326      }
327      ///\e
328      Expr &operator*=(const Value &c) {
329        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
330          j->second*=c;
331        const_comp*=c;
332        return *this;
333      }
334      ///\e
335      Expr &operator/=(const Value &c) {
336        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
337          j->second/=c;
338        const_comp/=c;
339        return *this;
340      }
341    };
342   
343    ///Linear constraint
344
345    ///This data stucture represents a linear constraint in the LP.
346    ///Basically it is a linear expression with a lower or an upper bound
347    ///(or both). These parts of the constraint can be obtained by the member
348    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
349    ///respectively.
350    ///There are two ways to construct a constraint.
351    ///- You can set the linear expression and the bounds directly
352    ///  by the functions above.
353    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
354    ///  are defined between expressions, or even between constraints whenever
355    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
356    ///  \c s and \c t are numbers, then the followings are valid expressions
357    ///  and thus they can be used directly e.g. in \ref addRow() whenever
358    ///  it makes sense.
359    ///  \code
360    ///  e<=s
361    ///  e<=f
362    ///  s<=e<=t
363    ///  e>=t
364    ///  \endcode
365    ///\warning The validity of a constraint is checked only at run time, so
366    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
367    ///\ref LogicError exception.
368    class Constr
369    {
370    public:
371      typedef LpSolverBase::Expr Expr;
372      typedef Expr::Key Key;
373      typedef Expr::Value Value;
374     
375//       static const Value INF;
376//       static const Value NaN;
377
378    protected:
379      Expr _expr;
380      Value _lb,_ub;
381    public:
382      ///\e
383      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
384      ///\e
385      Constr(Value lb,const Expr &e,Value ub) :
386        _expr(e), _lb(lb), _ub(ub) {}
387      ///\e
388      Constr(const Expr &e,Value ub) :
389        _expr(e), _lb(NaN), _ub(ub) {}
390      ///\e
391      Constr(Value lb,const Expr &e) :
392        _expr(e), _lb(lb), _ub(NaN) {}
393      ///\e
394      Constr(const Expr &e) :
395        _expr(e), _lb(NaN), _ub(NaN) {}
396      ///\e
397      void clear()
398      {
399        _expr.clear();
400        _lb=_ub=NaN;
401      }
402
403      ///Reference to the linear expression
404      Expr &expr() { return _expr; }
405      ///Cont reference to the linear expression
406      const Expr &expr() const { return _expr; }
407      ///Reference to the lower bound.
408
409      ///\return
410      ///- \ref INF "INF": the constraint is lower unbounded.
411      ///- \ref NaN "NaN": lower bound has not been set.
412      ///- finite number: the lower bound
413      Value &lowerBound() { return _lb; }
414      ///The const version of \ref lowerBound()
415      const Value &lowerBound() const { return _lb; }
416      ///Reference to the upper bound.
417
418      ///\return
419      ///- \ref INF "INF": the constraint is upper unbounded.
420      ///- \ref NaN "NaN": upper bound has not been set.
421      ///- finite number: the upper bound
422      Value &upperBound() { return _ub; }
423      ///The const version of \ref upperBound()
424      const Value &upperBound() const { return _ub; }
425      ///Is the constraint lower bounded?
426      bool lowerBounded() const {
427        using namespace std;
428        return finite(_lb);
429      }
430      ///Is the constraint upper bounded?
431      bool upperBounded() const {
432        using namespace std;
433        return finite(_ub);
434      }
435    };
436   
437    ///Linear expression of rows
438   
439    ///This data structure represents a column of the matrix,
440    ///thas is it strores a linear expression of the dual variables
441    ///(\ref Row "Row"s).
442    ///
443    ///There are several ways to access and modify the contents of this
444    ///container.
445    ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
446    ///if \c e is an DualExpr and \c v
447    ///and \c w are of type \ref Row, then you can
448    ///read and modify the coefficients like
449    ///these.
450    ///\code
451    ///e[v]=5;
452    ///e[v]+=12;
453    ///e.erase(v);
454    ///\endcode
455    ///or you can also iterate through its elements.
456    ///\code
457    ///double s=0;
458    ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
459    ///  s+=i->second;
460    ///\endcode
461    ///(This code computes the sum of all coefficients).
462    ///- Numbers (<tt>double</tt>'s)
463    ///and variables (\ref Row "Row"s) directly convert to an
464    ///\ref DualExpr and the usual linear operations are defined so 
465    ///\code
466    ///v+w
467    ///2*v-3.12*(v-w/2)
468    ///v*2.1+(3*v+(v*12+w)*3)/2
469    ///\endcode
470    ///are valid \ref DualExpr "DualExpr"essions.
471    ///The usual assignment operations are also defined.
472    ///\code
473    ///e=v+w;
474    ///e+=2*v-3.12*(v-w/2);
475    ///e*=3.4;
476    ///e/=5;
477    ///\endcode
478    ///
479    ///\sa Expr
480    ///
481    class DualExpr : public std::map<Row,Value>
482    {
483    public:
484      typedef LpSolverBase::Row Key;
485      typedef LpSolverBase::Value Value;
486     
487    protected:
488      typedef std::map<Row,Value> Base;
489     
490    public:
491      typedef True IsLinExpression;
492      ///\e
493      DualExpr() : Base() { }
494      ///\e
495      DualExpr(const Key &v) {
496        Base::insert(std::make_pair(v, 1));
497      }
498      ///\e
499      void set(const Key &v,const Value &c) {
500        Base::insert(std::make_pair(v, c));
501      }
502     
503      ///Removes the components with zero coefficient.
504      void simplify() {
505        for (Base::iterator i=Base::begin(); i!=Base::end();) {
506          Base::iterator j=i;
507          ++j;
508          if ((*i).second==0) Base::erase(i);
509          j=i;
510        }
511      }
512
513      ///Removes the coefficients closer to zero than \c tolerance.
514      void simplify(double &tolerance) {
515        for (Base::iterator i=Base::begin(); i!=Base::end();) {
516          Base::iterator j=i;
517          ++j;
518          if (std::fabs((*i).second)<tolerance) Base::erase(i);
519          j=i;
520        }
521      }
522
523
524      ///Sets all coefficients to 0.
525      void clear() {
526        Base::clear();
527      }
528
529      ///\e
530      DualExpr &operator+=(const DualExpr &e) {
531        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
532          (*this)[j->first]+=j->second;
533        return *this;
534      }
535      ///\e
536      DualExpr &operator-=(const DualExpr &e) {
537        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
538          (*this)[j->first]-=j->second;
539        return *this;
540      }
541      ///\e
542      DualExpr &operator*=(const Value &c) {
543        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
544          j->second*=c;
545        return *this;
546      }
547      ///\e
548      DualExpr &operator/=(const Value &c) {
549        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
550          j->second/=c;
551        return *this;
552      }
553    };
554   
555
556  protected:
557    _FixId rows;
558    _FixId cols;
559
560    //Abstract virtual functions
561    virtual LpSolverBase &_newLp() = 0;
562    virtual LpSolverBase &_copyLp(){
563      ///\todo This should be implemented here, too,  when we have problem retrieving routines. It can be overriden.
564
565      //Starting:
566      LpSolverBase & newlp(_newLp());
567      return newlp;
568      //return *(LpSolverBase*)0;
569    };
570
571    virtual int _addCol() = 0;
572    virtual int _addRow() = 0;
573    virtual void _eraseCol(int col) = 0;
574    virtual void _eraseRow(int row) = 0;
575    virtual void _getColName(int col,       std::string & name) = 0;
576    virtual void _setColName(int col, const std::string & name) = 0;
577    virtual void _setRowCoeffs(int i,
578                               int length,
579                               int  const * indices,
580                               Value  const * values ) = 0;
581    virtual void _setColCoeffs(int i,
582                               int length,
583                               int  const * indices,
584                               Value  const * values ) = 0;
585    virtual void _setCoeff(int row, int col, Value value) = 0;
586    virtual void _setColLowerBound(int i, Value value) = 0;
587    virtual void _setColUpperBound(int i, Value value) = 0;
588//     virtual void _setRowLowerBound(int i, Value value) = 0;
589//     virtual void _setRowUpperBound(int i, Value value) = 0;
590    virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
591    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
592    virtual void _clearObj()=0;
593//     virtual void _setObj(int length,
594//                          int  const * indices,
595//                          Value  const * values ) = 0;
596    virtual SolveExitStatus _solve() = 0;
597    virtual Value _getPrimal(int i) = 0;
598    virtual Value _getDual(int i) = 0;
599    virtual Value _getPrimalValue() = 0;
600    virtual bool _isBasicCol(int i) = 0;
601    virtual SolutionStatus _getPrimalStatus() = 0;
602    virtual SolutionStatus _getDualStatus() = 0;
603    ///\todo This could be implemented here, too, using _getPrimalStatus() and
604    ///_getDualStatus()
605    virtual ProblemTypes _getProblemType() = 0;
606
607    virtual void _setMax() = 0;
608    virtual void _setMin() = 0;
609   
610    //Own protected stuff
611   
612    //Constant component of the objective function
613    Value obj_const_comp;
614   
615
616
617   
618  public:
619
620    ///\e
621    LpSolverBase() : obj_const_comp(0) {}
622
623    ///\e
624    virtual ~LpSolverBase() {}
625
626    ///Creates a new LP problem
627    LpSolverBase &newLp() {return _newLp();}
628    ///Makes a copy of the LP problem
629    LpSolverBase &copyLp() {return _copyLp();}
630   
631    ///\name Build up and modify the LP
632
633    ///@{
634
635    ///Add a new empty column (i.e a new variable) to the LP
636    Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;}
637
638    ///\brief Adds several new columns
639    ///(i.e a variables) at once
640    ///
641    ///This magic function takes a container as its argument
642    ///and fills its elements
643    ///with new columns (i.e. variables)
644    ///\param t can be
645    ///- a standard STL compatible iterable container with
646    ///\ref Col as its \c values_type
647    ///like
648    ///\code
649    ///std::vector<LpSolverBase::Col>
650    ///std::list<LpSolverBase::Col>
651    ///\endcode
652    ///- a standard STL compatible iterable container with
653    ///\ref Col as its \c mapped_type
654    ///like
655    ///\code
656    ///std::map<AnyType,LpSolverBase::Col>
657    ///\endcode
658    ///- an iterable lemon \ref concept::WriteMap "write map" like
659    ///\code
660    ///ListGraph::NodeMap<LpSolverBase::Col>
661    ///ListGraph::EdgeMap<LpSolverBase::Col>
662    ///\endcode
663    ///\return The number of the created column.
664#ifdef DOXYGEN
665    template<class T>
666    int addColSet(T &t) { return 0;}
667#else
668    template<class T>
669    typename enable_if<typename T::value_type::LpSolverCol,int>::type
670    addColSet(T &t,dummy<0> = 0) {
671      int s=0;
672      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
673      return s;
674    }
675    template<class T>
676    typename enable_if<typename T::value_type::second_type::LpSolverCol,
677                       int>::type
678    addColSet(T &t,dummy<1> = 1) {
679      int s=0;
680      for(typename T::iterator i=t.begin();i!=t.end();++i) {
681        i->second=addCol();
682        s++;
683      }
684      return s;
685    }
686    template<class T>
687    typename enable_if<typename T::MapIt::Value::LpSolverCol,
688                       int>::type
689    addColSet(T &t,dummy<2> = 2) {
690      int s=0;
691      for(typename T::MapIt i(t); i!=INVALID; ++i)
692        {
693          i.set(addCol());
694          s++;
695        }
696      return s;
697    }
698#endif
699
700    ///Set a column (i.e a dual constraint) of the LP
701
702    ///\param c is the column to be modified
703    ///\param e is a dual linear expression (see \ref DualExpr)
704    ///a better one.
705    void col(Col c,const DualExpr &e) {
706      std::vector<int> indices;
707      std::vector<Value> values;
708      indices.push_back(0);
709      values.push_back(0);
710      for(DualExpr::const_iterator i=e.begin(); i!=e.end(); ++i)
711        if((*i).second!=0) {
712          indices.push_back(rows.floatingId((*i).first.id));
713          values.push_back((*i).second);
714        }
715      _setColCoeffs(cols.floatingId(c.id),indices.size()-1,
716                    &indices[0],&values[0]);
717    }
718
719    ///Add a new column to the LP
720
721    ///\param e is a dual linear expression (see \ref DualExpr)
722    ///\param obj is the corresponding component of the objective
723    ///function. It is 0 by default.
724    ///\return The created column.
725    Col addCol(const DualExpr &e, Value obj=0) {
726      Col c=addCol();
727      col(c,e);
728      objCoeff(c,obj);
729      return c;
730    }
731
732    ///Add a new empty row (i.e a new constraint) to the LP
733
734    ///This function adds a new empty row (i.e a new constraint) to the LP.
735    ///\return The created row
736    Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;}
737
738    ///\brief Add several new rows
739    ///(i.e a constraints) at once
740    ///
741    ///This magic function takes a container as its argument
742    ///and fills its elements
743    ///with new row (i.e. variables)
744    ///\param t can be
745    ///- a standard STL compatible iterable container with
746    ///\ref Row as its \c values_type
747    ///like
748    ///\code
749    ///std::vector<LpSolverBase::Row>
750    ///std::list<LpSolverBase::Row>
751    ///\endcode
752    ///- a standard STL compatible iterable container with
753    ///\ref Row as its \c mapped_type
754    ///like
755    ///\code
756    ///std::map<AnyType,LpSolverBase::Row>
757    ///\endcode
758    ///- an iterable lemon \ref concept::WriteMap "write map" like
759    ///\code
760    ///ListGraph::NodeMap<LpSolverBase::Row>
761    ///ListGraph::EdgeMap<LpSolverBase::Row>
762    ///\endcode
763    ///\return The number of rows created.
764#ifdef DOXYGEN
765    template<class T>
766    int addRowSet(T &t) { return 0;}
767#else
768    template<class T>
769    typename enable_if<typename T::value_type::LpSolverRow,int>::type
770    addRowSet(T &t,dummy<0> = 0) {
771      int s=0;
772      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
773      return s;
774    }
775    template<class T>
776    typename enable_if<typename T::value_type::second_type::LpSolverRow,
777                       int>::type
778    addRowSet(T &t,dummy<1> = 1) {
779      int s=0;
780      for(typename T::iterator i=t.begin();i!=t.end();++i) {
781        i->second=addRow();
782        s++;
783      }
784      return s;
785    }
786    template<class T>
787    typename enable_if<typename T::MapIt::Value::LpSolverRow,
788                       int>::type
789    addRowSet(T &t,dummy<2> = 2) {
790      int s=0;
791      for(typename T::MapIt i(t); i!=INVALID; ++i)
792        {
793          i.set(addRow());
794          s++;
795        }
796      return s;
797    }
798#endif
799
800    ///Set a row (i.e a constraint) of the LP
801
802    ///\param r is the row to be modified
803    ///\param l is lower bound (-\ref INF means no bound)
804    ///\param e is a linear expression (see \ref Expr)
805    ///\param u is the upper bound (\ref INF means no bound)
806    ///\bug This is a temportary function. The interface will change to
807    ///a better one.
808    ///\todo Option to control whether a constraint with a single variable is
809    ///added or not.
810    void row(Row r, Value l,const Expr &e, Value u) {
811      std::vector<int> indices;
812      std::vector<Value> values;
813      indices.push_back(0);
814      values.push_back(0);
815      for(Expr::const_iterator i=e.begin(); i!=e.end(); ++i)
816        if((*i).second!=0) { ///\bug EPSILON would be necessary here!!!
817          indices.push_back(cols.floatingId((*i).first.id));
818          values.push_back((*i).second);
819        }
820      _setRowCoeffs(rows.floatingId(r.id),indices.size()-1,
821                    &indices[0],&values[0]);
822//       _setRowLowerBound(rows.floatingId(r.id),l-e.constComp());
823//       _setRowUpperBound(rows.floatingId(r.id),u-e.constComp());
824       _setRowBounds(rows.floatingId(r.id),l-e.constComp(),u-e.constComp());
825    }
826
827    ///Set a row (i.e a constraint) of the LP
828
829    ///\param r is the row to be modified
830    ///\param c is a linear expression (see \ref Constr)
831    void row(Row r, const Constr &c) {
832      row(r,
833             c.lowerBounded()?c.lowerBound():-INF,
834             c.expr(),
835             c.upperBounded()?c.upperBound():INF);
836    }
837
838    ///Add a new row (i.e a new constraint) to the LP
839
840    ///\param l is the lower bound (-\ref INF means no bound)
841    ///\param e is a linear expression (see \ref Expr)
842    ///\param u is the upper bound (\ref INF means no bound)
843    ///\return The created row.
844    ///\bug This is a temportary function. The interface will change to
845    ///a better one.
846    Row addRow(Value l,const Expr &e, Value u) {
847      Row r=addRow();
848      row(r,l,e,u);
849      return r;
850    }
851
852    ///Add a new row (i.e a new constraint) to the LP
853
854    ///\param c is a linear expression (see \ref Constr)
855    ///\return The created row.
856    Row addRow(const Constr &c) {
857      Row r=addRow();
858      row(r,c);
859      return r;
860    }
861    ///Erase a coloumn (i.e a variable) from the LP
862
863    ///\param c is the coloumn to be deleted
864    ///\todo Please check this
865    void eraseCol(Col c) {
866      _eraseCol(cols.floatingId(c.id));
867      cols.erase(c.id);
868    }
869    ///Erase a  row (i.e a constraint) from the LP
870
871    ///\param r is the row to be deleted
872    ///\todo Please check this
873    void eraseRow(Row r) {
874      _eraseRow(rows.floatingId(r.id));
875      rows.erase(r.id);
876    }
877
878    /// Get the name of a column
879   
880    ///\param c is the coresponding coloumn
881    ///\return The name of the colunm
882    std::string ColName(Col c){
883      std::string name;
884      _getColName(cols.floatingId(c.id), name);
885      return name;
886    }
887   
888    /// Set the name of a column
889   
890    ///\param c is the coresponding coloumn
891    ///\param name The name to be given
892    void ColName(Col c, const std::string & name){
893      _setColName(cols.floatingId(c.id), name);
894    }
895   
896    /// Set an element of the coefficient matrix of the LP
897
898    ///\param r is the row of the element to be modified
899    ///\param c is the coloumn of the element to be modified
900    ///\param val is the new value of the coefficient
901
902    void Coeff(Row r, Col c, Value val){
903      _setCoeff(rows.floatingId(r.id),cols.floatingId(c.id), val);
904    }
905
906    /// Set the lower bound of a column (i.e a variable)
907
908    /// The lower bound of a variable (column) has to be given by an
909    /// extended number of type Value, i.e. a finite number of type
910    /// Value or -\ref INF.
911    void colLowerBound(Col c, Value value) {
912      _setColLowerBound(cols.floatingId(c.id),value);
913    }
914   
915    ///\brief Set the lower bound of  several columns
916    ///(i.e a variables) at once
917    ///
918    ///This magic function takes a container as its argument
919    ///and applies the function on all of its elements.
920    /// The lower bound of a variable (column) has to be given by an
921    /// extended number of type Value, i.e. a finite number of type
922    /// Value or -\ref INF.
923#ifdef DOXYGEN
924    template<class T>
925    void colLowerBound(T &t, Value value) { return 0;}
926#else
927    template<class T>
928    typename enable_if<typename T::value_type::LpSolverCol,void>::type
929    colLowerBound(T &t, Value value,dummy<0> = 0) {
930      for(typename T::iterator i=t.begin();i!=t.end();++i) {
931        colLowerBound(*i, value);
932      }
933    }
934    template<class T>
935    typename enable_if<typename T::value_type::second_type::LpSolverCol,
936                       void>::type
937    colLowerBound(T &t, Value value,dummy<1> = 1) {
938      for(typename T::iterator i=t.begin();i!=t.end();++i) {
939        colLowerBound(i->second, value);
940      }
941    }
942    template<class T>
943    typename enable_if<typename T::MapIt::Value::LpSolverCol,
944                       void>::type
945    colLowerBound(T &t, Value value,dummy<2> = 2) {
946      for(typename T::MapIt i(t); i!=INVALID; ++i){
947        colLowerBound(*i, value);
948      }
949    }
950#endif
951   
952    /// Set the upper bound of a column (i.e a variable)
953
954    /// The upper bound of a variable (column) has to be given by an
955    /// extended number of type Value, i.e. a finite number of type
956    /// Value or \ref INF.
957    void colUpperBound(Col c, Value value) {
958      _setColUpperBound(cols.floatingId(c.id),value);
959    };
960
961    ///\brief Set the lower bound of  several columns
962    ///(i.e a variables) at once
963    ///
964    ///This magic function takes a container as its argument
965    ///and applies the function on all of its elements.
966    /// The upper bound of a variable (column) has to be given by an
967    /// extended number of type Value, i.e. a finite number of type
968    /// Value or \ref INF.
969#ifdef DOXYGEN
970    template<class T>
971    void colUpperBound(T &t, Value value) { return 0;}
972#else
973    template<class T>
974    typename enable_if<typename T::value_type::LpSolverCol,void>::type
975    colUpperBound(T &t, Value value,dummy<0> = 0) {
976      for(typename T::iterator i=t.begin();i!=t.end();++i) {
977        colUpperBound(*i, value);
978      }
979    }
980    template<class T>
981    typename enable_if<typename T::value_type::second_type::LpSolverCol,
982                       void>::type
983    colUpperBound(T &t, Value value,dummy<1> = 1) {
984      for(typename T::iterator i=t.begin();i!=t.end();++i) {
985        colUpperBound(i->second, value);
986      }
987    }
988    template<class T>
989    typename enable_if<typename T::MapIt::Value::LpSolverCol,
990                       void>::type
991    colUpperBound(T &t, Value value,dummy<2> = 2) {
992      for(typename T::MapIt i(t); i!=INVALID; ++i){
993        colUpperBound(*i, value);
994      }
995    }
996#endif
997
998    /// Set the lower and the upper bounds of a column (i.e a variable)
999
1000    /// The lower and the upper bounds of
1001    /// a variable (column) have to be given by an
1002    /// extended number of type Value, i.e. a finite number of type
1003    /// Value, -\ref INF or \ref INF.
1004    void colBounds(Col c, Value lower, Value upper) {
1005      _setColLowerBound(cols.floatingId(c.id),lower);
1006      _setColUpperBound(cols.floatingId(c.id),upper);
1007    }
1008   
1009    ///\brief Set the lower and the upper bound of several columns
1010    ///(i.e a variables) at once
1011    ///
1012    ///This magic function takes a container as its argument
1013    ///and applies the function on all of its elements.
1014    /// The lower and the upper bounds of
1015    /// a variable (column) have to be given by an
1016    /// extended number of type Value, i.e. a finite number of type
1017    /// Value, -\ref INF or \ref INF.
1018#ifdef DOXYGEN
1019    template<class T>
1020    void colBounds(T &t, Value lower, Value upper) { return 0;}
1021#else
1022    template<class T>
1023    typename enable_if<typename T::value_type::LpSolverCol,void>::type
1024    colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
1025      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1026        colBounds(*i, lower, upper);
1027      }
1028    }
1029    template<class T>
1030    typename enable_if<typename T::value_type::second_type::LpSolverCol,
1031                       void>::type
1032    colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
1033      for(typename T::iterator i=t.begin();i!=t.end();++i) {
1034        colBounds(i->second, lower, upper);
1035      }
1036    }
1037    template<class T>
1038    typename enable_if<typename T::MapIt::Value::LpSolverCol,
1039                       void>::type
1040    colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
1041      for(typename T::MapIt i(t); i!=INVALID; ++i){
1042        colBounds(*i, lower, upper);
1043      }
1044    }
1045#endif
1046   
1047//     /// Set the lower bound of a row (i.e a constraint)
1048
1049//     /// The lower bound of a linear expression (row) has to be given by an
1050//     /// extended number of type Value, i.e. a finite number of type
1051//     /// Value or -\ref INF.
1052//     void rowLowerBound(Row r, Value value) {
1053//       _setRowLowerBound(rows.floatingId(r.id),value);
1054//     };
1055//     /// Set the upper bound of a row (i.e a constraint)
1056
1057//     /// The upper bound of a linear expression (row) has to be given by an
1058//     /// extended number of type Value, i.e. a finite number of type
1059//     /// Value or \ref INF.
1060//     void rowUpperBound(Row r, Value value) {
1061//       _setRowUpperBound(rows.floatingId(r.id),value);
1062//     };
1063
1064    /// Set the lower and the upper bounds of a row (i.e a constraint)
1065
1066    /// The lower and the upper bounds of
1067    /// a constraint (row) have to be given by an
1068    /// extended number of type Value, i.e. a finite number of type
1069    /// Value, -\ref INF or \ref INF.
1070    void rowBounds(Row c, Value lower, Value upper) {
1071      _setRowBounds(rows.floatingId(c.id),lower, upper);
1072      // _setRowUpperBound(rows.floatingId(c.id),upper);
1073    }
1074   
1075    ///Set an element of the objective function
1076    void objCoeff(Col c, Value v) {_setObjCoeff(cols.floatingId(c.id),v); };
1077    ///Set the objective function
1078   
1079    ///\param e is a linear expression of type \ref Expr.
1080    ///\bug Is should be called obj()
1081    void setObj(Expr e) {
1082      _clearObj();
1083      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
1084        objCoeff((*i).first,(*i).second);
1085      obj_const_comp=e.constComp();
1086    }
1087
1088    ///Maximize
1089    void max() { _setMax(); }
1090    ///Minimize
1091    void min() { _setMin(); }
1092
1093   
1094    ///@}
1095
1096
1097    ///\name Solve the LP
1098
1099    ///@{
1100
1101    ///\e Solve the LP problem at hand
1102    ///
1103    ///\return The result of the optimization procedure. Possible values and their meanings can be found in the documentation of \ref SolveExitStatus.
1104    ///
1105    ///\todo Which method is used to solve the problem
1106    SolveExitStatus solve() { return _solve(); }
1107   
1108    ///@}
1109   
1110    ///\name Obtain the solution
1111
1112    ///@{
1113
1114    /// The status of the primal problem (the original LP problem)
1115    SolutionStatus primalStatus() {
1116      return _getPrimalStatus();
1117    }
1118
1119    /// The status of the dual (of the original LP) problem
1120    SolutionStatus dualStatus() {
1121      return _getDualStatus();
1122    }
1123
1124    ///The type of the original LP problem
1125    ProblemTypes problemType() {
1126      return _getProblemType();
1127    }
1128
1129    ///\e
1130    Value primal(Col c) { return _getPrimal(cols.floatingId(c.id)); }
1131
1132    ///\e
1133    Value dual(Row r) { return _getDual(rows.floatingId(r.id)); }
1134
1135    ///\e
1136    bool isBasicCol(Col c) { return _isBasicCol(cols.floatingId(c.id)); }
1137
1138    ///\e
1139
1140    ///\return
1141    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1142    /// of the primal problem, depending on whether we minimize or maximize.
1143    ///- \ref NaN if no primal solution is found.
1144    ///- The (finite) objective value if an optimal solution is found.
1145    Value primalValue() { return _getPrimalValue()+obj_const_comp;}
1146    ///@}
1147   
1148  }; 
1149
1150  ///\e
1151 
1152  ///\relates LpSolverBase::Expr
1153  ///
1154  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
1155                                      const LpSolverBase::Expr &b)
1156  {
1157    LpSolverBase::Expr tmp(a);
1158    tmp+=b;
1159    return tmp;
1160  }
1161  ///\e
1162 
1163  ///\relates LpSolverBase::Expr
1164  ///
1165  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
1166                                      const LpSolverBase::Expr &b)
1167  {
1168    LpSolverBase::Expr tmp(a);
1169    tmp-=b;
1170    return tmp;
1171  }
1172  ///\e
1173 
1174  ///\relates LpSolverBase::Expr
1175  ///
1176  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
1177                                      const LpSolverBase::Value &b)
1178  {
1179    LpSolverBase::Expr tmp(a);
1180    tmp*=b;
1181    return tmp;
1182  }
1183 
1184  ///\e
1185 
1186  ///\relates LpSolverBase::Expr
1187  ///
1188  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
1189                                      const LpSolverBase::Expr &b)
1190  {
1191    LpSolverBase::Expr tmp(b);
1192    tmp*=a;
1193    return tmp;
1194  }
1195  ///\e
1196 
1197  ///\relates LpSolverBase::Expr
1198  ///
1199  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
1200                                      const LpSolverBase::Value &b)
1201  {
1202    LpSolverBase::Expr tmp(a);
1203    tmp/=b;
1204    return tmp;
1205  }
1206 
1207  ///\e
1208 
1209  ///\relates LpSolverBase::Constr
1210  ///
1211  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1212                                         const LpSolverBase::Expr &f)
1213  {
1214    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
1215  }
1216
1217  ///\e
1218 
1219  ///\relates LpSolverBase::Constr
1220  ///
1221  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
1222                                         const LpSolverBase::Expr &f)
1223  {
1224    return LpSolverBase::Constr(e,f);
1225  }
1226
1227  ///\e
1228 
1229  ///\relates LpSolverBase::Constr
1230  ///
1231  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1232                                         const LpSolverBase::Value &f)
1233  {
1234    return LpSolverBase::Constr(e,f);
1235  }
1236
1237  ///\e
1238 
1239  ///\relates LpSolverBase::Constr
1240  ///
1241  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1242                                         const LpSolverBase::Expr &f)
1243  {
1244    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
1245  }
1246
1247
1248  ///\e
1249 
1250  ///\relates LpSolverBase::Constr
1251  ///
1252  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
1253                                         const LpSolverBase::Expr &f)
1254  {
1255    return LpSolverBase::Constr(f,e);
1256  }
1257
1258
1259  ///\e
1260 
1261  ///\relates LpSolverBase::Constr
1262  ///
1263  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1264                                         const LpSolverBase::Value &f)
1265  {
1266    return LpSolverBase::Constr(f,e);
1267  }
1268
1269  ///\e
1270 
1271  ///\relates LpSolverBase::Constr
1272  ///
1273  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1274                                         const LpSolverBase::Expr &f)
1275  {
1276    return LpSolverBase::Constr(0,e-f,0);
1277  }
1278
1279  ///\e
1280 
1281  ///\relates LpSolverBase::Constr
1282  ///
1283  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
1284                                         const LpSolverBase::Constr&c)
1285  {
1286    LpSolverBase::Constr tmp(c);
1287    ///\todo Create an own exception type.
1288    if(!isnan(tmp.lowerBound())) throw LogicError();
1289    else tmp.lowerBound()=n;
1290    return tmp;
1291  }
1292  ///\e
1293 
1294  ///\relates LpSolverBase::Constr
1295  ///
1296  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
1297                                         const LpSolverBase::Value &n)
1298  {
1299    LpSolverBase::Constr tmp(c);
1300    ///\todo Create an own exception type.
1301    if(!isnan(tmp.upperBound())) throw LogicError();
1302    else tmp.upperBound()=n;
1303    return tmp;
1304  }
1305
1306  ///\e
1307 
1308  ///\relates LpSolverBase::Constr
1309  ///
1310  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
1311                                         const LpSolverBase::Constr&c)
1312  {
1313    LpSolverBase::Constr tmp(c);
1314    ///\todo Create an own exception type.
1315    if(!isnan(tmp.upperBound())) throw LogicError();
1316    else tmp.upperBound()=n;
1317    return tmp;
1318  }
1319  ///\e
1320 
1321  ///\relates LpSolverBase::Constr
1322  ///
1323  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
1324                                         const LpSolverBase::Value &n)
1325  {
1326    LpSolverBase::Constr tmp(c);
1327    ///\todo Create an own exception type.
1328    if(!isnan(tmp.lowerBound())) throw LogicError();
1329    else tmp.lowerBound()=n;
1330    return tmp;
1331  }
1332
1333  ///\e
1334 
1335  ///\relates LpSolverBase::DualExpr
1336  ///
1337  inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
1338                                      const LpSolverBase::DualExpr &b)
1339  {
1340    LpSolverBase::DualExpr tmp(a);
1341    tmp+=b;
1342    return tmp;
1343  }
1344  ///\e
1345 
1346  ///\relates LpSolverBase::DualExpr
1347  ///
1348  inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
1349                                      const LpSolverBase::DualExpr &b)
1350  {
1351    LpSolverBase::DualExpr tmp(a);
1352    tmp-=b;
1353    return tmp;
1354  }
1355  ///\e
1356 
1357  ///\relates LpSolverBase::DualExpr
1358  ///
1359  inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
1360                                      const LpSolverBase::Value &b)
1361  {
1362    LpSolverBase::DualExpr tmp(a);
1363    tmp*=b;
1364    return tmp;
1365  }
1366 
1367  ///\e
1368 
1369  ///\relates LpSolverBase::DualExpr
1370  ///
1371  inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
1372                                      const LpSolverBase::DualExpr &b)
1373  {
1374    LpSolverBase::DualExpr tmp(b);
1375    tmp*=a;
1376    return tmp;
1377  }
1378  ///\e
1379 
1380  ///\relates LpSolverBase::DualExpr
1381  ///
1382  inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
1383                                      const LpSolverBase::Value &b)
1384  {
1385    LpSolverBase::DualExpr tmp(a);
1386    tmp/=b;
1387    return tmp;
1388  }
1389 
1390
1391} //namespace lemon
1392
1393#endif //LEMON_LP_BASE_H
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