COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/lemon/lp_base.h @ 1364:ee5959aa4410

Last change on this file since 1364:ee5959aa4410 was 1364:ee5959aa4410, checked in by Alpar Juttner, 15 years ago
  • compile failure fixed
  • newLp(), copyLp() added
  • more doc.
File size: 24.7 KB
Line 
1/* -*- C++ -*-
2 * src/lemon/lp_base.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2005 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<math.h>
24
25#include<lemon/utility.h>
26#include<lemon/error.h>
27#include<lemon/invalid.h>
28
29//#include"lin_expr.h"
30
31///\file
32///\brief The interface of the LP solver interface.
33///\ingroup gen_opt_group
34namespace lemon {
35 
36  ///Internal data structure to convert floating id's to fix one's
37   
38  ///\todo This might be implemented to be also usable in other places.
39  class _FixId
40  {
41    std::vector<int> index;
42    std::vector<int> cross;
43    int first_free;
44  public:
45    _FixId() : first_free(-1) {};
46    ///Convert a floating id to a fix one
47
48    ///\param n is a floating id
49    ///\return the corresponding fix id
50    int fixId(int n) {return cross[n];}
51    ///Convert a fix id to a floating one
52
53    ///\param n is a fix id
54    ///\return the corresponding floating id
55    int floatingId(int n) { return index[n];}
56    ///Add a new floating id.
57
58    ///\param n is a floating id
59    ///\return the fix id of the new value
60    ///\todo Multiple additions should also be handled.
61    int insert(int n)
62    {
63      if(n>=int(cross.size())) {
64        cross.resize(n+1);
65        if(first_free==-1) {
66          cross[n]=index.size();
67          index.push_back(n);
68        }
69        else {
70          cross[n]=first_free;
71          int next=index[first_free];
72          index[first_free]=n;
73          first_free=next;
74        }
75        return cross[n];
76      }
77      ///\todo Create an own exception type.
78      else throw LogicError(); //floatingId-s must form a continuous range;
79    }
80    ///Remove a fix id.
81
82    ///\param n is a fix id
83    ///
84    void erase(int n)
85    {
86      int fl=index[n];
87      index[n]=first_free;
88      first_free=n;
89      for(int i=fl+1;i<int(cross.size());++i) {
90        cross[i-1]=cross[i];
91        index[cross[i]]--;
92      }
93      cross.pop_back();
94    }
95    ///An upper bound on the largest fix id.
96
97    ///\todo Do we need this?
98    ///
99    std::size_t maxFixId() { return cross.size()-1; }
100 
101  };
102   
103  ///Common base class for LP solvers
104 
105  ///\todo Much more docs
106  ///\ingroup gen_opt_group
107  class LpSolverBase {
108
109  public:
110
111    ///\e
112    enum SolveExitStatus {
113      ///\e
114      SOLVED = 0,
115      ///\e
116      UNSOLVED = 1
117    };
118     
119    ///\e
120    enum SolutionStatus {
121      ///Feasible solution has'n been found (but may exist).
122
123      ///\todo NOTFOUND might be a better name.
124      ///
125      UNDEFINED = 0,
126      ///The problem has no feasible solution
127      INFEASIBLE = 1,
128      ///Feasible solution found
129      FEASIBLE = 2,
130      ///Optimal solution exists and found
131      OPTIMAL = 3,
132      ///The cost function is unbounded
133
134      ///\todo Give a feasible solution and an infinite ray (and the
135      ///corresponding bases)
136      INFINITE = 4
137    };
138     
139    ///The floating point type used by the solver
140    typedef double Value;
141    ///The infinity constant
142    static const Value INF;
143    ///The not a number constant
144    static const Value NaN;
145   
146    ///Refer to a column of the LP.
147
148    ///This type is used to refer to a column of the LP.
149    ///
150    ///Its value remains valid and correct even after the addition or erase of
151    ///other columns.
152    ///
153    ///\todo Document what can one do with a Col (INVALID, comparing,
154    ///it is similar to Node/Edge)
155    class Col {
156    protected:
157      int id;
158      friend class LpSolverBase;
159    public:
160      typedef Value ExprValue;
161      typedef True LpSolverCol;
162      Col() {}
163      Col(const Invalid&) : id(-1) {}
164      bool operator<(Col c) const  {return id<c.id;}
165      bool operator==(Col c) const  {return id==c.id;}
166      bool operator!=(Col c) const  {return id==c.id;}
167    };
168
169    ///Refer to a row of the LP.
170
171    ///This type is used to refer to a row of the LP.
172    ///
173    ///Its value remains valid and correct even after the addition or erase of
174    ///other rows.
175    ///
176    ///\todo Document what can one do with a Row (INVALID, comparing,
177    ///it is similar to Node/Edge)
178    class Row {
179    protected:
180      int id;
181      friend class LpSolverBase;
182    public:
183      typedef Value ExprValue;
184      typedef True LpSolverRow;
185      Row() {}
186      Row(const Invalid&) : id(-1) {}
187      typedef True LpSolverRow;
188      bool operator<(Row c) const  {return id<c.id;}
189      bool operator==(Row c) const  {return id==c.id;}
190      bool operator!=(Row c) const  {return id==c.id;}
191   };
192   
193    ///Linear expression of variables and a constant component
194   
195    ///This data structure strores a linear expression of the variables
196    ///(\ref Col "Col"s) and also has a constant component.
197    ///
198    ///There are several ways to access and modify the contents of this
199    ///container.
200    ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
201    ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
202    ///read and modify the coefficients like
203    ///these.
204    ///\code
205    ///e[v]=5;
206    ///e[v]+=12;
207    ///e.erase(v);
208    ///\endcode
209    ///or you can also iterate through its elements.
210    ///\code
211    ///double s=0;
212    ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
213    ///  s+=i->second;
214    ///\endcode
215    ///(This code computes the sum of all coefficients).
216    ///- Numbers (<tt>double</tt>'s)
217    ///and variables (\ref Col "Col"s) directly convert to an
218    ///\ref Expr and the usual linear operations are defined so 
219    ///\code
220    ///v+w
221    ///2*v-3.12*(v-w/2)+2
222    ///v*2.1+(3*v+(v*12+w+6)*3)/2
223    ///\endcode
224    ///are valid \ref Expr "Expr"essions.
225    ///The usual assignment operations are also defined.
226    ///\code
227    ///e=v+w;
228    ///e+=2*v-3.12*(v-w/2)+2;
229    ///e*=3.4;
230    ///e/=5;
231    ///\endcode
232    ///- The constant member can be set and read by \ref constComp()
233    ///\code
234    ///e.constComp()=12;
235    ///double c=e.constComp();
236    ///\endcode
237    ///
238    ///\note \ref clear() not only sets all coefficients to 0 but also
239    ///clears the constant components.
240    ///
241    ///\sa Constr
242    ///
243    class Expr : public std::map<Col,Value>
244    {
245    public:
246      typedef LpSolverBase::Col Key;
247      typedef LpSolverBase::Value Value;
248     
249    protected:
250      typedef std::map<Col,Value> Base;
251     
252      Value const_comp;
253  public:
254      typedef True IsLinExpression;
255      ///\e
256      Expr() : Base(), const_comp(0) { }
257      ///\e
258      Expr(const Key &v) : const_comp(0) {
259        Base::insert(std::make_pair(v, 1));
260      }
261      ///\e
262      Expr(const Value &v) : const_comp(v) {}
263      ///\e
264      void set(const Key &v,const Value &c) {
265        Base::insert(std::make_pair(v, c));
266      }
267      ///\e
268      Value &constComp() { return const_comp; }
269      ///\e
270      const Value &constComp() const { return const_comp; }
271     
272      ///Removes the components with zero coefficient.
273      void simplify() {
274        for (Base::iterator i=Base::begin(); i!=Base::end();) {
275          Base::iterator j=i;
276          ++j;
277          if ((*i).second==0) Base::erase(i);
278          j=i;
279        }
280      }
281
282      ///Sets all coefficients and the constant component to 0.
283      void clear() {
284        Base::clear();
285        const_comp=0;
286      }
287
288      ///\e
289      Expr &operator+=(const Expr &e) {
290        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
291          (*this)[j->first]+=j->second;
292        ///\todo it might be speeded up using "hints"
293        const_comp+=e.const_comp;
294        return *this;
295      }
296      ///\e
297      Expr &operator-=(const Expr &e) {
298        for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
299          (*this)[j->first]-=j->second;
300        const_comp-=e.const_comp;
301        return *this;
302      }
303      ///\e
304      Expr &operator*=(const Value &c) {
305        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
306          j->second*=c;
307        const_comp*=c;
308        return *this;
309      }
310      ///\e
311      Expr &operator/=(const Value &c) {
312        for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
313          j->second/=c;
314        const_comp/=c;
315        return *this;
316      }
317    };
318   
319    ///Linear constraint
320
321    ///This data stucture represents a linear constraint in the LP.
322    ///Basically it is a linear expression with a lower or an upper bound
323    ///(or both). These parts of the constraint can be obtained by the member
324    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
325    ///respectively.
326    ///There are two ways to construct a constraint.
327    ///- You can set the linear expression and the bounds directly
328    ///  by the functions above.
329    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
330    ///  are defined between expressions, or even between constraints whenever
331    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
332    ///  \c s and \c t are numbers, then the followings are valid expressions
333    ///  and thus they can be used directly e.g. in \ref addRow() whenever
334    ///  it makes sense.
335    ///  \code
336    ///  e<=s
337    ///  e<=f
338    ///  s<=e<=t
339    ///  e>=t
340    ///  \endcode
341    ///\warning The validity of a constraint is checked only at run time, so
342    ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
343    ///\ref LogicError exception.
344    class Constr
345    {
346    public:
347      typedef LpSolverBase::Expr Expr;
348      typedef Expr::Key Key;
349      typedef Expr::Value Value;
350     
351//       static const Value INF;
352//       static const Value NaN;
353
354    protected:
355      Expr _expr;
356      Value _lb,_ub;
357    public:
358      ///\e
359      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
360      ///\e
361      Constr(Value lb,const Expr &e,Value ub) :
362        _expr(e), _lb(lb), _ub(ub) {}
363      ///\e
364      Constr(const Expr &e,Value ub) :
365        _expr(e), _lb(NaN), _ub(ub) {}
366      ///\e
367      Constr(Value lb,const Expr &e) :
368        _expr(e), _lb(lb), _ub(NaN) {}
369      ///\e
370      Constr(const Expr &e) :
371        _expr(e), _lb(NaN), _ub(NaN) {}
372      ///\e
373      void clear()
374      {
375        _expr.clear();
376        _lb=_ub=NaN;
377      }
378
379      ///Reference to the linear expression
380      Expr &expr() { return _expr; }
381      ///Cont reference to the linear expression
382      const Expr &expr() const { return _expr; }
383      ///Reference to the lower bound.
384
385      ///\return
386      ///- -\ref INF: the constraint is lower unbounded.
387      ///- -\ref NaN: lower bound has not been set.
388      ///- finite number: the lower bound
389      Value &lowerBound() { return _lb; }
390      ///The const version of \ref lowerBound()
391      const Value &lowerBound() const { return _lb; }
392      ///Reference to the upper bound.
393
394      ///\return
395      ///- -\ref INF: the constraint is upper unbounded.
396      ///- -\ref NaN: upper bound has not been set.
397      ///- finite number: the upper bound
398      Value &upperBound() { return _ub; }
399      ///The const version of \ref upperBound()
400      const Value &upperBound() const { return _ub; }
401      ///Is the constraint lower bounded?
402      bool lowerBounded() const {
403        using namespace std;
404        return isfinite(_lb);
405      }
406      ///Is the constraint upper bounded?
407      bool upperBounded() const {
408        using namespace std;
409        return isfinite(_ub);
410      }
411    };
412   
413
414  protected:
415    _FixId rows;
416    _FixId cols;
417
418    //Abstract virtual functions
419    virtual LpSolverBase &_newLp() = 0;
420    virtual LpSolverBase &_copyLp() = 0;
421
422    virtual int _addCol() = 0;
423    virtual int _addRow() = 0;
424    virtual void _setRowCoeffs(int i,
425                               int length,
426                               int  const * indices,
427                               Value  const * values ) = 0;
428    virtual void _setColCoeffs(int i,
429                               int length,
430                               int  const * indices,
431                               Value  const * values ) = 0;
432    virtual void _setColLowerBound(int i, Value value) = 0;
433    virtual void _setColUpperBound(int i, Value value) = 0;
434    virtual void _setRowLowerBound(int i, Value value) = 0;
435    virtual void _setRowUpperBound(int i, Value value) = 0;
436    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
437    virtual SolveExitStatus _solve() = 0;
438    virtual Value _getPrimal(int i) = 0;
439    virtual Value _getPrimalValue() = 0;
440    virtual SolutionStatus _getPrimalStatus() = 0;
441    virtual void _setMax() = 0;
442    virtual void _setMin() = 0;
443   
444    //Own protected stuff
445   
446    //Constant component of the objective function
447    Value obj_const_comp;
448   
449    ///\e
450   
451    ///\bug Unimplemented
452    void clearObj() {}
453   
454  public:
455
456    ///\e
457    LpSolverBase() : obj_const_comp(0) {}
458
459    ///\e
460    virtual ~LpSolverBase() {}
461
462    ///Creates a new LP problem
463    LpSolverBase &newLp() {return _newLp();}
464    ///Make a copy of the LP problem
465    LpSolverBase &copyLp() {return _copyLp();}
466   
467    ///\name Build up and modify of the LP
468
469    ///@{
470
471    ///Add a new empty column (i.e a new variable) to the LP
472    Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;}
473
474    ///\brief Adds several new columns
475    ///(i.e a variables) at once
476    ///
477    ///This magic function takes a container as its argument
478    ///and fills its elements
479    ///with new columns (i.e. variables)
480    ///\param t can be
481    ///- a standard STL compatible iterable container with
482    ///\ref Col as its \c values_type
483    ///like
484    ///\code
485    ///std::vector<LpSolverBase::Col>
486    ///std::list<LpSolverBase::Col>
487    ///\endcode
488    ///- a standard STL compatible iterable container with
489    ///\ref Col as its \c mapped_type
490    ///like
491    ///\code
492    ///std::map<AnyType,LpSolverBase::Col>
493    ///\endcode
494    ///- an iterable lemon \ref concept::WriteMap "write map" like
495    ///\code
496    ///ListGraph::NodeMap<LpSolverBase::Col>
497    ///ListGraph::EdgeMap<LpSolverBase::Col>
498    ///\endcode
499    ///\return The number of the created column.
500#ifdef DOXYGEN
501    template<class T>
502    int addColSet(T &t) { return 0;}
503#else
504    template<class T>
505    typename enable_if<typename T::value_type::LpSolverCol,int>::type
506    addColSet(T &t,dummy<0> = 0) {
507      int s=0;
508      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
509      return s;
510    }
511    template<class T>
512    typename enable_if<typename T::value_type::second_type::LpSolverCol,
513                       int>::type
514    addColSet(T &t,dummy<1> = 1) {
515      int s=0;
516      for(typename T::iterator i=t.begin();i!=t.end();++i) {
517        i->second=addCol();
518        s++;
519      }
520      return s;
521    }
522    template<class T>
523    typename enable_if<typename T::ValueSet::value_type::LpSolverCol,
524                       int>::type
525    addColSet(T &t,dummy<2> = 2) {
526      ///\bug <tt>return addColSet(t.valueSet());</tt> should also work.
527      int s=0;
528      for(typename T::ValueSet::iterator i=t.valueSet().begin();
529          i!=t.valueSet().end();
530          ++i)
531        {
532          *i=addCol();
533          s++;
534        }
535      return s;
536    }
537#endif
538
539    ///Add a new empty row (i.e a new constaint) to the LP
540
541    ///This function adds a new empty row (i.e a new constaint) to the LP.
542    ///\return The created row
543    Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;}
544
545    ///Set a row (i.e a constaint) of the LP
546
547    ///\param r is the row to be modified
548    ///\param l is lower bound (-\ref INF means no bound)
549    ///\param e is a linear expression (see \ref Expr)
550    ///\param u is the upper bound (\ref INF means no bound)
551    ///\bug This is a temportary function. The interface will change to
552    ///a better one.
553    ///\todo Option to control whether a constraint with a single variable is
554    ///added or not.
555    void setRow(Row r, Value l,const Expr &e, Value u) {
556      std::vector<int> indices;
557      std::vector<Value> values;
558      indices.push_back(0);
559      values.push_back(0);
560      for(Expr::const_iterator i=e.begin(); i!=e.end(); ++i)
561        if((*i).second!=0) { ///\bug EPSILON would be necessary here!!!
562          indices.push_back(cols.floatingId((*i).first.id));
563          values.push_back((*i).second);
564        }
565      _setRowCoeffs(rows.floatingId(r.id),indices.size()-1,
566                    &indices[0],&values[0]);
567      _setRowLowerBound(rows.floatingId(r.id),l-e.constComp());
568      _setRowUpperBound(rows.floatingId(r.id),u-e.constComp());
569    }
570
571    ///Set a row (i.e a constaint) of the LP
572
573    ///\param r is the row to be modified
574    ///\param c is a linear expression (see \ref Constr)
575    void setRow(Row r, const Constr &c) {
576      setRow(r,
577             c.lowerBounded()?c.lowerBound():-INF,
578             c.expr(),
579             c.upperBounded()?c.upperBound():INF);
580    }
581
582    ///Add a new row (i.e a new constaint) to the LP
583
584    ///\param l is the lower bound (-\ref INF means no bound)
585    ///\param e is a linear expression (see \ref Expr)
586    ///\param u is the upper bound (\ref INF means no bound)
587    ///\return The created row.
588    ///\bug This is a temportary function. The interface will change to
589    ///a better one.
590    Row addRow(Value l,const Expr &e, Value u) {
591      Row r=addRow();
592      setRow(r,l,e,u);
593      return r;
594    }
595
596    ///Add a new row (i.e a new constaint) to the LP
597
598    ///\param c is a linear expression (see \ref Constr)
599    ///\return The created row.
600    Row addRow(const Constr &c) {
601      Row r=addRow();
602      setRow(r,c);
603      return r;
604    }
605
606    /// Set the lower bound of a column (i.e a variable)
607
608    /// The upper bound of a variable (column) has to be given by an
609    /// extended number of type Value, i.e. a finite number of type
610    /// Value or -\ref INF.
611    void colLowerBound(Col c, Value value) {
612      _setColLowerBound(cols.floatingId(c.id),value);
613    }
614    /// Set the upper bound of a column (i.e a variable)
615
616    /// The upper bound of a variable (column) has to be given by an
617    /// extended number of type Value, i.e. a finite number of type
618    /// Value or \ref INF.
619    void colUpperBound(Col c, Value value) {
620      _setColUpperBound(cols.floatingId(c.id),value);
621    };
622    /// Set the lower and the upper bounds of a column (i.e a variable)
623
624    /// The lower and the upper bounds of
625    /// a variable (column) have to be given by an
626    /// extended number of type Value, i.e. a finite number of type
627    /// Value, -\ref INF or \ref INF.
628    void colBounds(Col c, Value lower, Value upper) {
629      _setColLowerBound(cols.floatingId(c.id),lower);
630      _setColUpperBound(cols.floatingId(c.id),upper);
631    }
632   
633    /// Set the lower bound of a row (i.e a constraint)
634
635    /// The lower bound of a linear expression (row) has to be given by an
636    /// extended number of type Value, i.e. a finite number of type
637    /// Value or -\ref INF.
638    void rowLowerBound(Row r, Value value) {
639      _setRowLowerBound(rows.floatingId(r.id),value);
640    };
641    /// Set the upper bound of a row (i.e a constraint)
642
643    /// The upper bound of a linear expression (row) has to be given by an
644    /// extended number of type Value, i.e. a finite number of type
645    /// Value or \ref INF.
646    void rowUpperBound(Row r, Value value) {
647      _setRowUpperBound(rows.floatingId(r.id),value);
648    };
649    /// Set the lower and the upper bounds of a row (i.e a variable)
650
651    /// The lower and the upper bounds of
652    /// a constraint (row) have to be given by an
653    /// extended number of type Value, i.e. a finite number of type
654    /// Value, -\ref INF or \ref INF.
655    void rowBounds(Row c, Value lower, Value upper) {
656      _setRowLowerBound(rows.floatingId(c.id),lower);
657      _setRowUpperBound(rows.floatingId(c.id),upper);
658    }
659   
660    ///Set an element of the objective function
661    void objCoeff(Col c, Value v) {_setObjCoeff(cols.floatingId(c.id),v); };
662    ///Set the objective function
663   
664    ///\param e is a linear expression of type \ref Expr.
665    ///\bug The previous objective function is not cleared!
666    void setObj(Expr e) {
667      clearObj();
668      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
669        objCoeff((*i).first,(*i).second);
670      obj_const_comp=e.constComp();
671    }
672
673    ///Maximize
674    void max() { _setMax(); }
675    ///Minimize
676    void min() { _setMin(); }
677
678   
679    ///@}
680
681
682    ///\name Solve the LP
683
684    ///@{
685
686    ///\e
687    SolveExitStatus solve() { return _solve(); }
688   
689    ///@}
690   
691    ///\name Obtain the solution
692
693    ///@{
694
695    ///\e
696    SolutionStatus primalStatus() {
697      return _getPrimalStatus();
698    }
699
700    ///\e
701    Value primal(Col c) { return _getPrimal(cols.floatingId(c.id)); }
702
703    ///\e
704
705    ///\return
706    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
707    /// of the primal problem, depending on whether we minimize or maximize.
708    ///- \ref NaN if no primal solution is found.
709    ///- The (finite) objective value if an optimal solution is found.
710    Value primalValue() { return _getPrimalValue()+obj_const_comp;}
711    ///@}
712   
713  }; 
714
715  ///\e
716 
717  ///\relates LpSolverBase::Expr
718  ///
719  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
720                                      const LpSolverBase::Expr &b)
721  {
722    LpSolverBase::Expr tmp(a);
723    tmp+=b; ///\todo Doesn't STL have some special 'merge' algorithm?
724    return tmp;
725  }
726  ///\e
727 
728  ///\relates LpSolverBase::Expr
729  ///
730  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
731                                      const LpSolverBase::Expr &b)
732  {
733    LpSolverBase::Expr tmp(a);
734    tmp-=b; ///\todo Doesn't STL have some special 'merge' algorithm?
735    return tmp;
736  }
737  ///\e
738 
739  ///\relates LpSolverBase::Expr
740  ///
741  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
742                                      const LpSolverBase::Value &b)
743  {
744    LpSolverBase::Expr tmp(a);
745    tmp*=b; ///\todo Doesn't STL have some special 'merge' algorithm?
746    return tmp;
747  }
748 
749  ///\e
750 
751  ///\relates LpSolverBase::Expr
752  ///
753  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
754                                      const LpSolverBase::Expr &b)
755  {
756    LpSolverBase::Expr tmp(b);
757    tmp*=a; ///\todo Doesn't STL have some special 'merge' algorithm?
758    return tmp;
759  }
760  ///\e
761 
762  ///\relates LpSolverBase::Expr
763  ///
764  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
765                                      const LpSolverBase::Value &b)
766  {
767    LpSolverBase::Expr tmp(a);
768    tmp/=b; ///\todo Doesn't STL have some special 'merge' algorithm?
769    return tmp;
770  }
771 
772  ///\e
773 
774  ///\relates LpSolverBase::Constr
775  ///
776  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
777                                         const LpSolverBase::Expr &f)
778  {
779    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
780  }
781
782  ///\e
783 
784  ///\relates LpSolverBase::Constr
785  ///
786  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
787                                         const LpSolverBase::Expr &f)
788  {
789    return LpSolverBase::Constr(e,f);
790  }
791
792  ///\e
793 
794  ///\relates LpSolverBase::Constr
795  ///
796  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
797                                         const LpSolverBase::Value &f)
798  {
799    return LpSolverBase::Constr(e,f);
800  }
801
802  ///\e
803 
804  ///\relates LpSolverBase::Constr
805  ///
806  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
807                                         const LpSolverBase::Expr &f)
808  {
809    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
810  }
811
812
813  ///\e
814 
815  ///\relates LpSolverBase::Constr
816  ///
817  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
818                                         const LpSolverBase::Expr &f)
819  {
820    return LpSolverBase::Constr(f,e);
821  }
822
823
824  ///\e
825 
826  ///\relates LpSolverBase::Constr
827  ///
828  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
829                                         const LpSolverBase::Value &f)
830  {
831    return LpSolverBase::Constr(f,e);
832  }
833
834  ///\e
835 
836  ///\relates LpSolverBase::Constr
837  ///
838  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
839                                         const LpSolverBase::Expr &f)
840  {
841    return LpSolverBase::Constr(0,e-f,0);
842  }
843
844  ///\e
845 
846  ///\relates LpSolverBase::Constr
847  ///
848  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
849                                         const LpSolverBase::Constr&c)
850  {
851    LpSolverBase::Constr tmp(c);
852    ///\todo Create an own exception type.
853    if(!isnan(tmp.lowerBound())) throw LogicError();
854    else tmp.lowerBound()=n;
855    return tmp;
856  }
857  ///\e
858 
859  ///\relates LpSolverBase::Constr
860  ///
861  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
862                                         const LpSolverBase::Value &n)
863  {
864    LpSolverBase::Constr tmp(c);
865    ///\todo Create an own exception type.
866    if(!isnan(tmp.upperBound())) throw LogicError();
867    else tmp.upperBound()=n;
868    return tmp;
869  }
870
871  ///\e
872 
873  ///\relates LpSolverBase::Constr
874  ///
875  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
876                                         const LpSolverBase::Constr&c)
877  {
878    LpSolverBase::Constr tmp(c);
879    ///\todo Create an own exception type.
880    if(!isnan(tmp.upperBound())) throw LogicError();
881    else tmp.upperBound()=n;
882    return tmp;
883  }
884  ///\e
885 
886  ///\relates LpSolverBase::Constr
887  ///
888  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
889                                         const LpSolverBase::Value &n)
890  {
891    LpSolverBase::Constr tmp(c);
892    ///\todo Create an own exception type.
893    if(!isnan(tmp.lowerBound())) throw LogicError();
894    else tmp.lowerBound()=n;
895    return tmp;
896  }
897
898
899} //namespace lemon
900
901#endif //LEMON_LP_BASE_H
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