COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/lemon/lp_base.h @ 1377:bfbb5b30c5b8

Last change on this file since 1377:bfbb5b30c5b8 was 1377:bfbb5b30c5b8, checked in by athos, 15 years ago

_clearObj instead of _setObj.

File size: 24.8 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 void _clearObj()=0;
438//     virtual void _setObj(int length,
439//                          int  const * indices,
440//                          Value  const * values ) = 0;
441    virtual SolveExitStatus _solve() = 0;
442    virtual Value _getPrimal(int i) = 0;
443    virtual Value _getPrimalValue() = 0;
444    virtual SolutionStatus _getPrimalStatus() = 0;
445    virtual void _setMax() = 0;
446    virtual void _setMin() = 0;
447   
448    //Own protected stuff
449   
450    //Constant component of the objective function
451    Value obj_const_comp;
452   
453
454
455   
456  public:
457
458    ///\e
459    LpSolverBase() : obj_const_comp(0) {}
460
461    ///\e
462    virtual ~LpSolverBase() {}
463
464    ///Creates a new LP problem
465    LpSolverBase &newLp() {return _newLp();}
466    ///Make a copy of the LP problem
467    LpSolverBase &copyLp() {return _copyLp();}
468   
469    ///\name Build up and modify of the LP
470
471    ///@{
472
473    ///Add a new empty column (i.e a new variable) to the LP
474    Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;}
475
476    ///\brief Adds several new columns
477    ///(i.e a variables) at once
478    ///
479    ///This magic function takes a container as its argument
480    ///and fills its elements
481    ///with new columns (i.e. variables)
482    ///\param t can be
483    ///- a standard STL compatible iterable container with
484    ///\ref Col as its \c values_type
485    ///like
486    ///\code
487    ///std::vector<LpSolverBase::Col>
488    ///std::list<LpSolverBase::Col>
489    ///\endcode
490    ///- a standard STL compatible iterable container with
491    ///\ref Col as its \c mapped_type
492    ///like
493    ///\code
494    ///std::map<AnyType,LpSolverBase::Col>
495    ///\endcode
496    ///- an iterable lemon \ref concept::WriteMap "write map" like
497    ///\code
498    ///ListGraph::NodeMap<LpSolverBase::Col>
499    ///ListGraph::EdgeMap<LpSolverBase::Col>
500    ///\endcode
501    ///\return The number of the created column.
502#ifdef DOXYGEN
503    template<class T>
504    int addColSet(T &t) { return 0;}
505#else
506    template<class T>
507    typename enable_if<typename T::value_type::LpSolverCol,int>::type
508    addColSet(T &t,dummy<0> = 0) {
509      int s=0;
510      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
511      return s;
512    }
513    template<class T>
514    typename enable_if<typename T::value_type::second_type::LpSolverCol,
515                       int>::type
516    addColSet(T &t,dummy<1> = 1) {
517      int s=0;
518      for(typename T::iterator i=t.begin();i!=t.end();++i) {
519        i->second=addCol();
520        s++;
521      }
522      return s;
523    }
524    template<class T>
525    typename enable_if<typename T::ValueSet::value_type::LpSolverCol,
526                       int>::type
527    addColSet(T &t,dummy<2> = 2) {
528      ///\bug <tt>return addColSet(t.valueSet());</tt> should also work.
529      int s=0;
530      for(typename T::ValueSet::iterator i=t.valueSet().begin();
531          i!=t.valueSet().end();
532          ++i)
533        {
534          *i=addCol();
535          s++;
536        }
537      return s;
538    }
539#endif
540
541    ///Add a new empty row (i.e a new constaint) to the LP
542
543    ///This function adds a new empty row (i.e a new constaint) to the LP.
544    ///\return The created row
545    Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;}
546
547    ///Set a row (i.e a constaint) of the LP
548
549    ///\param r is the row to be modified
550    ///\param l is lower bound (-\ref INF means no bound)
551    ///\param e is a linear expression (see \ref Expr)
552    ///\param u is the upper bound (\ref INF means no bound)
553    ///\bug This is a temportary function. The interface will change to
554    ///a better one.
555    ///\todo Option to control whether a constraint with a single variable is
556    ///added or not.
557    void setRow(Row r, Value l,const Expr &e, Value u) {
558      std::vector<int> indices;
559      std::vector<Value> values;
560      indices.push_back(0);
561      values.push_back(0);
562      for(Expr::const_iterator i=e.begin(); i!=e.end(); ++i)
563        if((*i).second!=0) { ///\bug EPSILON would be necessary here!!!
564          indices.push_back(cols.floatingId((*i).first.id));
565          values.push_back((*i).second);
566        }
567      _setRowCoeffs(rows.floatingId(r.id),indices.size()-1,
568                    &indices[0],&values[0]);
569      _setRowLowerBound(rows.floatingId(r.id),l-e.constComp());
570      _setRowUpperBound(rows.floatingId(r.id),u-e.constComp());
571    }
572
573    ///Set a row (i.e a constaint) of the LP
574
575    ///\param r is the row to be modified
576    ///\param c is a linear expression (see \ref Constr)
577    void setRow(Row r, const Constr &c) {
578      setRow(r,
579             c.lowerBounded()?c.lowerBound():-INF,
580             c.expr(),
581             c.upperBounded()?c.upperBound():INF);
582    }
583
584    ///Add a new row (i.e a new constaint) to the LP
585
586    ///\param l is the lower bound (-\ref INF means no bound)
587    ///\param e is a linear expression (see \ref Expr)
588    ///\param u is the upper bound (\ref INF means no bound)
589    ///\return The created row.
590    ///\bug This is a temportary function. The interface will change to
591    ///a better one.
592    Row addRow(Value l,const Expr &e, Value u) {
593      Row r=addRow();
594      setRow(r,l,e,u);
595      return r;
596    }
597
598    ///Add a new row (i.e a new constaint) to the LP
599
600    ///\param c is a linear expression (see \ref Constr)
601    ///\return The created row.
602    Row addRow(const Constr &c) {
603      Row r=addRow();
604      setRow(r,c);
605      return r;
606    }
607
608    /// Set the lower bound of a column (i.e a variable)
609
610    /// The upper bound of a variable (column) has to be given by an
611    /// extended number of type Value, i.e. a finite number of type
612    /// Value or -\ref INF.
613    void colLowerBound(Col c, Value value) {
614      _setColLowerBound(cols.floatingId(c.id),value);
615    }
616    /// Set the upper bound of a column (i.e a variable)
617
618    /// The upper bound of a variable (column) has to be given by an
619    /// extended number of type Value, i.e. a finite number of type
620    /// Value or \ref INF.
621    void colUpperBound(Col c, Value value) {
622      _setColUpperBound(cols.floatingId(c.id),value);
623    };
624    /// Set the lower and the upper bounds of a column (i.e a variable)
625
626    /// The lower and the upper bounds of
627    /// a variable (column) have to be given by an
628    /// extended number of type Value, i.e. a finite number of type
629    /// Value, -\ref INF or \ref INF.
630    void colBounds(Col c, Value lower, Value upper) {
631      _setColLowerBound(cols.floatingId(c.id),lower);
632      _setColUpperBound(cols.floatingId(c.id),upper);
633    }
634   
635    /// Set the lower bound of a row (i.e a constraint)
636
637    /// The lower bound of a linear expression (row) has to be given by an
638    /// extended number of type Value, i.e. a finite number of type
639    /// Value or -\ref INF.
640    void rowLowerBound(Row r, Value value) {
641      _setRowLowerBound(rows.floatingId(r.id),value);
642    };
643    /// Set the upper bound of a row (i.e a constraint)
644
645    /// The upper bound of a linear expression (row) has to be given by an
646    /// extended number of type Value, i.e. a finite number of type
647    /// Value or \ref INF.
648    void rowUpperBound(Row r, Value value) {
649      _setRowUpperBound(rows.floatingId(r.id),value);
650    };
651    /// Set the lower and the upper bounds of a row (i.e a variable)
652
653    /// The lower and the upper bounds of
654    /// a constraint (row) have to be given by an
655    /// extended number of type Value, i.e. a finite number of type
656    /// Value, -\ref INF or \ref INF.
657    void rowBounds(Row c, Value lower, Value upper) {
658      _setRowLowerBound(rows.floatingId(c.id),lower);
659      _setRowUpperBound(rows.floatingId(c.id),upper);
660    }
661   
662    ///Set an element of the objective function
663    void objCoeff(Col c, Value v) {_setObjCoeff(cols.floatingId(c.id),v); };
664    ///Set the objective function
665   
666    ///\param e is a linear expression of type \ref Expr.
667    ///\bug The previous objective function is not cleared!
668    void setObj(Expr e) {
669      _clearObj();
670      for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
671        objCoeff((*i).first,(*i).second);
672      obj_const_comp=e.constComp();
673    }
674
675    ///Maximize
676    void max() { _setMax(); }
677    ///Minimize
678    void min() { _setMin(); }
679
680   
681    ///@}
682
683
684    ///\name Solve the LP
685
686    ///@{
687
688    ///\e
689    SolveExitStatus solve() { return _solve(); }
690   
691    ///@}
692   
693    ///\name Obtain the solution
694
695    ///@{
696
697    ///\e
698    SolutionStatus primalStatus() {
699      return _getPrimalStatus();
700    }
701
702    ///\e
703    Value primal(Col c) { return _getPrimal(cols.floatingId(c.id)); }
704
705    ///\e
706
707    ///\return
708    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
709    /// of the primal problem, depending on whether we minimize or maximize.
710    ///- \ref NaN if no primal solution is found.
711    ///- The (finite) objective value if an optimal solution is found.
712    Value primalValue() { return _getPrimalValue()+obj_const_comp;}
713    ///@}
714   
715  }; 
716
717  ///\e
718 
719  ///\relates LpSolverBase::Expr
720  ///
721  inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
722                                      const LpSolverBase::Expr &b)
723  {
724    LpSolverBase::Expr tmp(a);
725    tmp+=b; ///\todo Doesn't STL have some special 'merge' algorithm?
726    return tmp;
727  }
728  ///\e
729 
730  ///\relates LpSolverBase::Expr
731  ///
732  inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
733                                      const LpSolverBase::Expr &b)
734  {
735    LpSolverBase::Expr tmp(a);
736    tmp-=b; ///\todo Doesn't STL have some special 'merge' algorithm?
737    return tmp;
738  }
739  ///\e
740 
741  ///\relates LpSolverBase::Expr
742  ///
743  inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
744                                      const LpSolverBase::Value &b)
745  {
746    LpSolverBase::Expr tmp(a);
747    tmp*=b; ///\todo Doesn't STL have some special 'merge' algorithm?
748    return tmp;
749  }
750 
751  ///\e
752 
753  ///\relates LpSolverBase::Expr
754  ///
755  inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
756                                      const LpSolverBase::Expr &b)
757  {
758    LpSolverBase::Expr tmp(b);
759    tmp*=a; ///\todo Doesn't STL have some special 'merge' algorithm?
760    return tmp;
761  }
762  ///\e
763 
764  ///\relates LpSolverBase::Expr
765  ///
766  inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
767                                      const LpSolverBase::Value &b)
768  {
769    LpSolverBase::Expr tmp(a);
770    tmp/=b; ///\todo Doesn't STL have some special 'merge' algorithm?
771    return tmp;
772  }
773 
774  ///\e
775 
776  ///\relates LpSolverBase::Constr
777  ///
778  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
779                                         const LpSolverBase::Expr &f)
780  {
781    return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
782  }
783
784  ///\e
785 
786  ///\relates LpSolverBase::Constr
787  ///
788  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
789                                         const LpSolverBase::Expr &f)
790  {
791    return LpSolverBase::Constr(e,f);
792  }
793
794  ///\e
795 
796  ///\relates LpSolverBase::Constr
797  ///
798  inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
799                                         const LpSolverBase::Value &f)
800  {
801    return LpSolverBase::Constr(e,f);
802  }
803
804  ///\e
805 
806  ///\relates LpSolverBase::Constr
807  ///
808  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
809                                         const LpSolverBase::Expr &f)
810  {
811    return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
812  }
813
814
815  ///\e
816 
817  ///\relates LpSolverBase::Constr
818  ///
819  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
820                                         const LpSolverBase::Expr &f)
821  {
822    return LpSolverBase::Constr(f,e);
823  }
824
825
826  ///\e
827 
828  ///\relates LpSolverBase::Constr
829  ///
830  inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
831                                         const LpSolverBase::Value &f)
832  {
833    return LpSolverBase::Constr(f,e);
834  }
835
836  ///\e
837 
838  ///\relates LpSolverBase::Constr
839  ///
840  inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
841                                         const LpSolverBase::Expr &f)
842  {
843    return LpSolverBase::Constr(0,e-f,0);
844  }
845
846  ///\e
847 
848  ///\relates LpSolverBase::Constr
849  ///
850  inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
851                                         const LpSolverBase::Constr&c)
852  {
853    LpSolverBase::Constr tmp(c);
854    ///\todo Create an own exception type.
855    if(!isnan(tmp.lowerBound())) throw LogicError();
856    else tmp.lowerBound()=n;
857    return tmp;
858  }
859  ///\e
860 
861  ///\relates LpSolverBase::Constr
862  ///
863  inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
864                                         const LpSolverBase::Value &n)
865  {
866    LpSolverBase::Constr tmp(c);
867    ///\todo Create an own exception type.
868    if(!isnan(tmp.upperBound())) throw LogicError();
869    else tmp.upperBound()=n;
870    return tmp;
871  }
872
873  ///\e
874 
875  ///\relates LpSolverBase::Constr
876  ///
877  inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
878                                         const LpSolverBase::Constr&c)
879  {
880    LpSolverBase::Constr tmp(c);
881    ///\todo Create an own exception type.
882    if(!isnan(tmp.upperBound())) throw LogicError();
883    else tmp.upperBound()=n;
884    return tmp;
885  }
886  ///\e
887 
888  ///\relates LpSolverBase::Constr
889  ///
890  inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
891                                         const LpSolverBase::Value &n)
892  {
893    LpSolverBase::Constr tmp(c);
894    ///\todo Create an own exception type.
895    if(!isnan(tmp.lowerBound())) throw LogicError();
896    else tmp.lowerBound()=n;
897    return tmp;
898  }
899
900
901} //namespace lemon
902
903#endif //LEMON_LP_BASE_H
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