diff --git a/lemon/lp_base.h b/lemon/lp_base.h new file mode 100644 --- /dev/null +++ b/lemon/lp_base.h @@ -0,0 +1,1705 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2008 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_LP_BASE_H +#define LEMON_LP_BASE_H + +#include +#include +#include +#include +#include + +#include +#include + +///\file +///\brief The interface of the LP solver interface. +///\ingroup lp_group +namespace lemon { + + /// Function to decide whether a floating point value is finite or not. + + /// Retruns true if the argument is not infinity, minus infinity or NaN. + /// It does the same as the isfinite() function defined by C99. + template + bool isFinite(T value) + { + typedef std::numeric_limits Lim; + if ((Lim::has_infinity && (value == Lim::infinity() || value == + -Lim::infinity())) || + ((Lim::has_quiet_NaN || Lim::has_signaling_NaN) && value != value)) + { + return false; + } + return true; + } + + ///Common base class for LP solvers + + ///\todo Much more docs + ///\ingroup lp_group + class LpSolverBase { + + protected: + + _lp_bits::LpId rows; + _lp_bits::LpId cols; + + public: + + ///Possible outcomes of an LP solving procedure + enum SolveExitStatus { + ///This means that the problem has been successfully solved: either + ///an optimal solution has been found or infeasibility/unboundedness + ///has been proved. + SOLVED = 0, + ///Any other case (including the case when some user specified + ///limit has been exceeded) + UNSOLVED = 1 + }; + + ///\e + enum SolutionStatus { + ///Feasible solution hasn't been found (but may exist). + + ///\todo NOTFOUND might be a better name. + /// + UNDEFINED = 0, + ///The problem has no feasible solution + INFEASIBLE = 1, + ///Feasible solution found + FEASIBLE = 2, + ///Optimal solution exists and found + OPTIMAL = 3, + ///The cost function is unbounded + + ///\todo Give a feasible solution and an infinite ray (and the + ///corresponding bases) + INFINITE = 4 + }; + + ///\e The type of the investigated LP problem + enum ProblemTypes { + ///Primal-dual feasible + PRIMAL_DUAL_FEASIBLE = 0, + ///Primal feasible dual infeasible + PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1, + ///Primal infeasible dual feasible + PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2, + ///Primal-dual infeasible + PRIMAL_DUAL_INFEASIBLE = 3, + ///Could not determine so far + UNKNOWN = 4 + }; + + ///The floating point type used by the solver + typedef double Value; + ///The infinity constant + static const Value INF; + ///The not a number constant + static const Value NaN; + + static inline bool isNaN(const Value& v) { return v!=v; } + + friend class Col; + friend class ColIt; + friend class Row; + + ///Refer to a column of the LP. + + ///This type is used to refer to a column of the LP. + /// + ///Its value remains valid and correct even after the addition or erase of + ///other columns. + /// + ///\todo Document what can one do with a Col (INVALID, comparing, + ///it is similar to Node/Edge) + class Col { + protected: + int id; + friend class LpSolverBase; + friend class MipSolverBase; + explicit Col(int _id) : id(_id) {} + public: + typedef Value ExprValue; + typedef True LpSolverCol; + Col() {} + Col(const Invalid&) : id(-1) {} + bool operator< (Col c) const {return id< c.id;} + bool operator> (Col c) const {return id> c.id;} + bool operator==(Col c) const {return id==c.id;} + bool operator!=(Col c) const {return id!=c.id;} + }; + + class ColIt : public Col { + const LpSolverBase *_lp; + public: + ColIt() {} + ColIt(const LpSolverBase &lp) : _lp(&lp) + { + _lp->cols.firstFix(id); + } + ColIt(const Invalid&) : Col(INVALID) {} + ColIt &operator++() + { + _lp->cols.nextFix(id); + return *this; + } + }; + + static int id(const Col& col) { return col.id; } + + + ///Refer to a row of the LP. + + ///This type is used to refer to a row of the LP. + /// + ///Its value remains valid and correct even after the addition or erase of + ///other rows. + /// + ///\todo Document what can one do with a Row (INVALID, comparing, + ///it is similar to Node/Edge) + class Row { + protected: + int id; + friend class LpSolverBase; + explicit Row(int _id) : id(_id) {} + public: + typedef Value ExprValue; + typedef True LpSolverRow; + Row() {} + Row(const Invalid&) : id(-1) {} + + bool operator< (Row c) const {return id< c.id;} + bool operator> (Row c) const {return id> c.id;} + bool operator==(Row c) const {return id==c.id;} + bool operator!=(Row c) const {return id!=c.id;} + }; + + class RowIt : public Row { + const LpSolverBase *_lp; + public: + RowIt() {} + RowIt(const LpSolverBase &lp) : _lp(&lp) + { + _lp->rows.firstFix(id); + } + RowIt(const Invalid&) : Row(INVALID) {} + RowIt &operator++() + { + _lp->rows.nextFix(id); + return *this; + } + }; + + static int id(const Row& row) { return row.id; } + + protected: + + int _lpId(const Col& c) const { + return cols.floatingId(id(c)); + } + + int _lpId(const Row& r) const { + return rows.floatingId(id(r)); + } + + Col _item(int i, Col) const { + return Col(cols.fixId(i)); + } + + Row _item(int i, Row) const { + return Row(rows.fixId(i)); + } + + + public: + + ///Linear expression of variables and a constant component + + ///This data structure stores a linear expression of the variables + ///(\ref Col "Col"s) and also has a constant component. + /// + ///There are several ways to access and modify the contents of this + ///container. + ///- Its it fully compatible with \c std::map, so for expamle + ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can + ///read and modify the coefficients like + ///these. + ///\code + ///e[v]=5; + ///e[v]+=12; + ///e.erase(v); + ///\endcode + ///or you can also iterate through its elements. + ///\code + ///double s=0; + ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i) + /// s+=i->second; + ///\endcode + ///(This code computes the sum of all coefficients). + ///- Numbers (double's) + ///and variables (\ref Col "Col"s) directly convert to an + ///\ref Expr and the usual linear operations are defined, so + ///\code + ///v+w + ///2*v-3.12*(v-w/2)+2 + ///v*2.1+(3*v+(v*12+w+6)*3)/2 + ///\endcode + ///are valid \ref Expr "Expr"essions. + ///The usual assignment operations are also defined. + ///\code + ///e=v+w; + ///e+=2*v-3.12*(v-w/2)+2; + ///e*=3.4; + ///e/=5; + ///\endcode + ///- The constant member can be set and read by \ref constComp() + ///\code + ///e.constComp()=12; + ///double c=e.constComp(); + ///\endcode + /// + ///\note \ref clear() not only sets all coefficients to 0 but also + ///clears the constant components. + /// + ///\sa Constr + /// + class Expr : public std::map + { + public: + typedef LpSolverBase::Col Key; + typedef LpSolverBase::Value Value; + + protected: + typedef std::map Base; + + Value const_comp; + public: + typedef True IsLinExpression; + ///\e + Expr() : Base(), const_comp(0) { } + ///\e + Expr(const Key &v) : const_comp(0) { + Base::insert(std::make_pair(v, 1)); + } + ///\e + Expr(const Value &v) : const_comp(v) {} + ///\e + void set(const Key &v,const Value &c) { + Base::insert(std::make_pair(v, c)); + } + ///\e + Value &constComp() { return const_comp; } + ///\e + const Value &constComp() const { return const_comp; } + + ///Removes the components with zero coefficient. + void simplify() { + for (Base::iterator i=Base::begin(); i!=Base::end();) { + Base::iterator j=i; + ++j; + if ((*i).second==0) Base::erase(i); + i=j; + } + } + + void simplify() const { + const_cast(this)->simplify(); + } + + ///Removes the coefficients closer to zero than \c tolerance. + void simplify(double &tolerance) { + for (Base::iterator i=Base::begin(); i!=Base::end();) { + Base::iterator j=i; + ++j; + if (std::fabs((*i).second)first]+=j->second; + const_comp+=e.const_comp; + return *this; + } + ///\e + Expr &operator-=(const Expr &e) { + for (Base::const_iterator j=e.begin(); j!=e.end(); ++j) + (*this)[j->first]-=j->second; + const_comp-=e.const_comp; + return *this; + } + ///\e + Expr &operator*=(const Value &c) { + for (Base::iterator j=Base::begin(); j!=Base::end(); ++j) + j->second*=c; + const_comp*=c; + return *this; + } + ///\e + Expr &operator/=(const Value &c) { + for (Base::iterator j=Base::begin(); j!=Base::end(); ++j) + j->second/=c; + const_comp/=c; + return *this; + } + + }; + + ///Linear constraint + + ///This data stucture represents a linear constraint in the LP. + ///Basically it is a linear expression with a lower or an upper bound + ///(or both). These parts of the constraint can be obtained by the member + ///functions \ref expr(), \ref lowerBound() and \ref upperBound(), + ///respectively. + ///There are two ways to construct a constraint. + ///- You can set the linear expression and the bounds directly + /// by the functions above. + ///- The operators \<=, == and \>= + /// are defined between expressions, or even between constraints whenever + /// it makes sense. Therefore if \c e and \c f are linear expressions and + /// \c s and \c t are numbers, then the followings are valid expressions + /// and thus they can be used directly e.g. in \ref addRow() whenever + /// it makes sense. + ///\code + /// e<=s + /// e<=f + /// e==f + /// s<=e<=t + /// e>=t + ///\endcode + ///\warning The validity of a constraint is checked only at run time, so + ///e.g. \ref addRow(x[1]\<=x[2]<=5) will compile, but will throw + ///an assertion. + class Constr + { + public: + typedef LpSolverBase::Expr Expr; + typedef Expr::Key Key; + typedef Expr::Value Value; + + protected: + Expr _expr; + Value _lb,_ub; + public: + ///\e + Constr() : _expr(), _lb(NaN), _ub(NaN) {} + ///\e + Constr(Value lb,const Expr &e,Value ub) : + _expr(e), _lb(lb), _ub(ub) {} + ///\e + Constr(const Expr &e,Value ub) : + _expr(e), _lb(NaN), _ub(ub) {} + ///\e + Constr(Value lb,const Expr &e) : + _expr(e), _lb(lb), _ub(NaN) {} + ///\e + Constr(const Expr &e) : + _expr(e), _lb(NaN), _ub(NaN) {} + ///\e + void clear() + { + _expr.clear(); + _lb=_ub=NaN; + } + + ///Reference to the linear expression + Expr &expr() { return _expr; } + ///Cont reference to the linear expression + const Expr &expr() const { return _expr; } + ///Reference to the lower bound. + + ///\return + ///- \ref INF "INF": the constraint is lower unbounded. + ///- \ref NaN "NaN": lower bound has not been set. + ///- finite number: the lower bound + Value &lowerBound() { return _lb; } + ///The const version of \ref lowerBound() + const Value &lowerBound() const { return _lb; } + ///Reference to the upper bound. + + ///\return + ///- \ref INF "INF": the constraint is upper unbounded. + ///- \ref NaN "NaN": upper bound has not been set. + ///- finite number: the upper bound + Value &upperBound() { return _ub; } + ///The const version of \ref upperBound() + const Value &upperBound() const { return _ub; } + ///Is the constraint lower bounded? + bool lowerBounded() const { + return isFinite(_lb); + } + ///Is the constraint upper bounded? + bool upperBounded() const { + return isFinite(_ub); + } + + }; + + ///Linear expression of rows + + ///This data structure represents a column of the matrix, + ///thas is it strores a linear expression of the dual variables + ///(\ref Row "Row"s). + /// + ///There are several ways to access and modify the contents of this + ///container. + ///- Its it fully compatible with \c std::map, so for expamle + ///if \c e is an DualExpr and \c v + ///and \c w are of type \ref Row, then you can + ///read and modify the coefficients like + ///these. + ///\code + ///e[v]=5; + ///e[v]+=12; + ///e.erase(v); + ///\endcode + ///or you can also iterate through its elements. + ///\code + ///double s=0; + ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i) + /// s+=i->second; + ///\endcode + ///(This code computes the sum of all coefficients). + ///- Numbers (double's) + ///and variables (\ref Row "Row"s) directly convert to an + ///\ref DualExpr and the usual linear operations are defined, so + ///\code + ///v+w + ///2*v-3.12*(v-w/2) + ///v*2.1+(3*v+(v*12+w)*3)/2 + ///\endcode + ///are valid \ref DualExpr "DualExpr"essions. + ///The usual assignment operations are also defined. + ///\code + ///e=v+w; + ///e+=2*v-3.12*(v-w/2); + ///e*=3.4; + ///e/=5; + ///\endcode + /// + ///\sa Expr + /// + class DualExpr : public std::map + { + public: + typedef LpSolverBase::Row Key; + typedef LpSolverBase::Value Value; + + protected: + typedef std::map Base; + + public: + typedef True IsLinExpression; + ///\e + DualExpr() : Base() { } + ///\e + DualExpr(const Key &v) { + Base::insert(std::make_pair(v, 1)); + } + ///\e + void set(const Key &v,const Value &c) { + Base::insert(std::make_pair(v, c)); + } + + ///Removes the components with zero coefficient. + void simplify() { + for (Base::iterator i=Base::begin(); i!=Base::end();) { + Base::iterator j=i; + ++j; + if ((*i).second==0) Base::erase(i); + i=j; + } + } + + void simplify() const { + const_cast(this)->simplify(); + } + + ///Removes the coefficients closer to zero than \c tolerance. + void simplify(double &tolerance) { + for (Base::iterator i=Base::begin(); i!=Base::end();) { + Base::iterator j=i; + ++j; + if (std::fabs((*i).second)first]+=j->second; + return *this; + } + ///\e + DualExpr &operator-=(const DualExpr &e) { + for (Base::const_iterator j=e.begin(); j!=e.end(); ++j) + (*this)[j->first]-=j->second; + return *this; + } + ///\e + DualExpr &operator*=(const Value &c) { + for (Base::iterator j=Base::begin(); j!=Base::end(); ++j) + j->second*=c; + return *this; + } + ///\e + DualExpr &operator/=(const Value &c) { + for (Base::iterator j=Base::begin(); j!=Base::end(); ++j) + j->second/=c; + return *this; + } + }; + + + private: + + template + class MappedOutputIterator { + public: + + typedef std::insert_iterator<_Expr> Base; + + typedef std::output_iterator_tag iterator_category; + typedef void difference_type; + typedef void value_type; + typedef void reference; + typedef void pointer; + + MappedOutputIterator(const Base& _base, const LpSolverBase& _lp) + : base(_base), lp(_lp) {} + + MappedOutputIterator& operator*() { + return *this; + } + + MappedOutputIterator& operator=(const std::pair& value) { + *base = std::make_pair(lp._item(value.first, typename _Expr::Key()), + value.second); + return *this; + } + + MappedOutputIterator& operator++() { + ++base; + return *this; + } + + MappedOutputIterator operator++(int) { + MappedOutputIterator tmp(*this); + ++base; + return tmp; + } + + bool operator==(const MappedOutputIterator& it) const { + return base == it.base; + } + + bool operator!=(const MappedOutputIterator& it) const { + return base != it.base; + } + + private: + Base base; + const LpSolverBase& lp; + }; + + template + class MappedInputIterator { + public: + + typedef typename Expr::const_iterator Base; + + typedef typename Base::iterator_category iterator_category; + typedef typename Base::difference_type difference_type; + typedef const std::pair value_type; + typedef value_type reference; + class pointer { + public: + pointer(value_type& _value) : value(_value) {} + value_type* operator->() { return &value; } + private: + value_type value; + }; + + MappedInputIterator(const Base& _base, const LpSolverBase& _lp) + : base(_base), lp(_lp) {} + + reference operator*() { + return std::make_pair(lp._lpId(base->first), base->second); + } + + pointer operator->() { + return pointer(operator*()); + } + + MappedInputIterator& operator++() { + ++base; + return *this; + } + + MappedInputIterator operator++(int) { + MappedInputIterator tmp(*this); + ++base; + return tmp; + } + + bool operator==(const MappedInputIterator& it) const { + return base == it.base; + } + + bool operator!=(const MappedInputIterator& it) const { + return base != it.base; + } + + private: + Base base; + const LpSolverBase& lp; + }; + + protected: + + /// STL compatible iterator for lp col + typedef MappedInputIterator ConstRowIterator; + /// STL compatible iterator for lp row + typedef MappedInputIterator ConstColIterator; + + /// STL compatible iterator for lp col + typedef MappedOutputIterator RowIterator; + /// STL compatible iterator for lp row + typedef MappedOutputIterator ColIterator; + + //Abstract virtual functions + virtual LpSolverBase* _newLp() = 0; + virtual LpSolverBase* _copyLp(){ + LpSolverBase* newlp = _newLp(); + + std::map ref; + for (LpSolverBase::ColIt it(*this); it != INVALID; ++it) { + Col ccol = newlp->addCol(); + ref[it] = ccol; + newlp->colName(ccol, colName(it)); + newlp->colLowerBound(ccol, colLowerBound(it)); + newlp->colUpperBound(ccol, colUpperBound(it)); + } + + for (LpSolverBase::RowIt it(*this); it != INVALID; ++it) { + Expr e = row(it), ce; + for (Expr::iterator jt = e.begin(); jt != e.end(); ++jt) { + ce[ref[jt->first]] = jt->second; + } + ce += e.constComp(); + Row r = newlp->addRow(ce); + + double lower, upper; + getRowBounds(it, lower, upper); + newlp->rowBounds(r, lower, upper); + } + + return newlp; + }; + + virtual int _addCol() = 0; + virtual int _addRow() = 0; + + virtual void _eraseCol(int col) = 0; + virtual void _eraseRow(int row) = 0; + + virtual void _getColName(int col, std::string & name) const = 0; + virtual void _setColName(int col, const std::string & name) = 0; + virtual int _colByName(const std::string& name) const = 0; + + virtual void _setRowCoeffs(int i, ConstRowIterator b, + ConstRowIterator e) = 0; + virtual void _getRowCoeffs(int i, RowIterator b) const = 0; + virtual void _setColCoeffs(int i, ConstColIterator b, + ConstColIterator e) = 0; + virtual void _getColCoeffs(int i, ColIterator b) const = 0; + virtual void _setCoeff(int row, int col, Value value) = 0; + virtual Value _getCoeff(int row, int col) const = 0; + virtual void _setColLowerBound(int i, Value value) = 0; + virtual Value _getColLowerBound(int i) const = 0; + virtual void _setColUpperBound(int i, Value value) = 0; + virtual Value _getColUpperBound(int i) const = 0; + virtual void _setRowBounds(int i, Value lower, Value upper) = 0; + virtual void _getRowBounds(int i, Value &lower, Value &upper) const = 0; + + virtual void _setObjCoeff(int i, Value obj_coef) = 0; + virtual Value _getObjCoeff(int i) const = 0; + virtual void _clearObj()=0; + + virtual SolveExitStatus _solve() = 0; + virtual Value _getPrimal(int i) const = 0; + virtual Value _getDual(int i) const = 0; + virtual Value _getPrimalValue() const = 0; + virtual bool _isBasicCol(int i) const = 0; + virtual SolutionStatus _getPrimalStatus() const = 0; + virtual SolutionStatus _getDualStatus() const = 0; + virtual ProblemTypes _getProblemType() const = 0; + + virtual void _setMax() = 0; + virtual void _setMin() = 0; + + + virtual bool _isMax() const = 0; + + //Own protected stuff + + //Constant component of the objective function + Value obj_const_comp; + + public: + + ///\e + LpSolverBase() : obj_const_comp(0) {} + + ///\e + virtual ~LpSolverBase() {} + + ///Creates a new LP problem + LpSolverBase* newLp() {return _newLp();} + ///Makes a copy of the LP problem + LpSolverBase* copyLp() {return _copyLp();} + + ///\name Build up and modify the LP + + ///@{ + + ///Add a new empty column (i.e a new variable) to the LP + Col addCol() { Col c; _addCol(); c.id = cols.addId(); return c;} + + ///\brief Adds several new columns + ///(i.e a variables) at once + /// + ///This magic function takes a container as its argument + ///and fills its elements + ///with new columns (i.e. variables) + ///\param t can be + ///- a standard STL compatible iterable container with + ///\ref Col as its \c values_type + ///like + ///\code + ///std::vector + ///std::list + ///\endcode + ///- a standard STL compatible iterable container with + ///\ref Col as its \c mapped_type + ///like + ///\code + ///std::map + ///\endcode + ///- an iterable lemon \ref concepts::WriteMap "write map" like + ///\code + ///ListGraph::NodeMap + ///ListGraph::EdgeMap + ///\endcode + ///\return The number of the created column. +#ifdef DOXYGEN + template + int addColSet(T &t) { return 0;} +#else + template + typename enable_if::type + addColSet(T &t,dummy<0> = 0) { + int s=0; + for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;} + return s; + } + template + typename enable_if::type + addColSet(T &t,dummy<1> = 1) { + int s=0; + for(typename T::iterator i=t.begin();i!=t.end();++i) { + i->second=addCol(); + s++; + } + return s; + } + template + typename enable_if::type + addColSet(T &t,dummy<2> = 2) { + int s=0; + for(typename T::MapIt i(t); i!=INVALID; ++i) + { + i.set(addCol()); + s++; + } + return s; + } +#endif + + ///Set a column (i.e a dual constraint) of the LP + + ///\param c is the column to be modified + ///\param e is a dual linear expression (see \ref DualExpr) + ///a better one. + void col(Col c,const DualExpr &e) { + e.simplify(); + _setColCoeffs(_lpId(c), ConstColIterator(e.begin(), *this), + ConstColIterator(e.end(), *this)); + } + + ///Get a column (i.e a dual constraint) of the LP + + ///\param r is the column to get + ///\return the dual expression associated to the column + DualExpr col(Col c) const { + DualExpr e; + _getColCoeffs(_lpId(c), ColIterator(std::inserter(e, e.end()), *this)); + return e; + } + + ///Add a new column to the LP + + ///\param e is a dual linear expression (see \ref DualExpr) + ///\param obj is the corresponding component of the objective + ///function. It is 0 by default. + ///\return The created column. + Col addCol(const DualExpr &e, Value o = 0) { + Col c=addCol(); + col(c,e); + objCoeff(c,o); + return c; + } + + ///Add a new empty row (i.e a new constraint) to the LP + + ///This function adds a new empty row (i.e a new constraint) to the LP. + ///\return The created row + Row addRow() { Row r; _addRow(); r.id = rows.addId(); return r;} + + ///\brief Add several new rows + ///(i.e a constraints) at once + /// + ///This magic function takes a container as its argument + ///and fills its elements + ///with new row (i.e. variables) + ///\param t can be + ///- a standard STL compatible iterable container with + ///\ref Row as its \c values_type + ///like + ///\code + ///std::vector + ///std::list + ///\endcode + ///- a standard STL compatible iterable container with + ///\ref Row as its \c mapped_type + ///like + ///\code + ///std::map + ///\endcode + ///- an iterable lemon \ref concepts::WriteMap "write map" like + ///\code + ///ListGraph::NodeMap + ///ListGraph::EdgeMap + ///\endcode + ///\return The number of rows created. +#ifdef DOXYGEN + template + int addRowSet(T &t) { return 0;} +#else + template + typename enable_if::type + addRowSet(T &t,dummy<0> = 0) { + int s=0; + for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;} + return s; + } + template + typename enable_if::type + addRowSet(T &t,dummy<1> = 1) { + int s=0; + for(typename T::iterator i=t.begin();i!=t.end();++i) { + i->second=addRow(); + s++; + } + return s; + } + template + typename enable_if::type + addRowSet(T &t,dummy<2> = 2) { + int s=0; + for(typename T::MapIt i(t); i!=INVALID; ++i) + { + i.set(addRow()); + s++; + } + return s; + } +#endif + + ///Set a row (i.e a constraint) of the LP + + ///\param r is the row to be modified + ///\param l is lower bound (-\ref INF means no bound) + ///\param e is a linear expression (see \ref Expr) + ///\param u is the upper bound (\ref INF means no bound) + ///\bug This is a temporary function. The interface will change to + ///a better one. + ///\todo Option to control whether a constraint with a single variable is + ///added or not. + void row(Row r, Value l, const Expr &e, Value u) { + e.simplify(); + _setRowCoeffs(_lpId(r), ConstRowIterator(e.begin(), *this), + ConstRowIterator(e.end(), *this)); + _setRowBounds(_lpId(r),l-e.constComp(),u-e.constComp()); + } + + ///Set a row (i.e a constraint) of the LP + + ///\param r is the row to be modified + ///\param c is a linear expression (see \ref Constr) + void row(Row r, const Constr &c) { + row(r, c.lowerBounded()?c.lowerBound():-INF, + c.expr(), c.upperBounded()?c.upperBound():INF); + } + + + ///Get a row (i.e a constraint) of the LP + + ///\param r is the row to get + ///\return the expression associated to the row + Expr row(Row r) const { + Expr e; + _getRowCoeffs(_lpId(r), RowIterator(std::inserter(e, e.end()), *this)); + return e; + } + + ///Add a new row (i.e a new constraint) to the LP + + ///\param l is the lower bound (-\ref INF means no bound) + ///\param e is a linear expression (see \ref Expr) + ///\param u is the upper bound (\ref INF means no bound) + ///\return The created row. + ///\bug This is a temporary function. The interface will change to + ///a better one. + Row addRow(Value l,const Expr &e, Value u) { + Row r=addRow(); + row(r,l,e,u); + return r; + } + + ///Add a new row (i.e a new constraint) to the LP + + ///\param c is a linear expression (see \ref Constr) + ///\return The created row. + Row addRow(const Constr &c) { + Row r=addRow(); + row(r,c); + return r; + } + ///Erase a coloumn (i.e a variable) from the LP + + ///\param c is the coloumn to be deleted + ///\todo Please check this + void eraseCol(Col c) { + _eraseCol(_lpId(c)); + cols.eraseId(c.id); + } + ///Erase a row (i.e a constraint) from the LP + + ///\param r is the row to be deleted + ///\todo Please check this + void eraseRow(Row r) { + _eraseRow(_lpId(r)); + rows.eraseId(r.id); + } + + /// Get the name of a column + + ///\param c is the coresponding coloumn + ///\return The name of the colunm + std::string colName(Col c) const { + std::string name; + _getColName(_lpId(c), name); + return name; + } + + /// Set the name of a column + + ///\param c is the coresponding coloumn + ///\param name The name to be given + void colName(Col c, const std::string& name) { + _setColName(_lpId(c), name); + } + + /// Get the column by its name + + ///\param name The name of the column + ///\return the proper column or \c INVALID + Col colByName(const std::string& name) const { + int k = _colByName(name); + return k != -1 ? Col(cols.fixId(k)) : Col(INVALID); + } + + /// Set an element of the coefficient matrix of the LP + + ///\param r is the row of the element to be modified + ///\param c is the coloumn of the element to be modified + ///\param val is the new value of the coefficient + + void coeff(Row r, Col c, Value val) { + _setCoeff(_lpId(r),_lpId(c), val); + } + + /// Get an element of the coefficient matrix of the LP + + ///\param r is the row of the element in question + ///\param c is the coloumn of the element in question + ///\return the corresponding coefficient + + Value coeff(Row r, Col c) const { + return _getCoeff(_lpId(r),_lpId(c)); + } + + /// Set the lower bound of a column (i.e a variable) + + /// The lower bound of a variable (column) has to be given by an + /// extended number of type Value, i.e. a finite number of type + /// Value or -\ref INF. + void colLowerBound(Col c, Value value) { + _setColLowerBound(_lpId(c),value); + } + + /// Get the lower bound of a column (i.e a variable) + + /// This function returns the lower bound for column (variable) \t c + /// (this might be -\ref INF as well). + ///\return The lower bound for coloumn \t c + Value colLowerBound(Col c) const { + return _getColLowerBound(_lpId(c)); + } + + ///\brief Set the lower bound of several columns + ///(i.e a variables) at once + /// + ///This magic function takes a container as its argument + ///and applies the function on all of its elements. + /// The lower bound of a variable (column) has to be given by an + /// extended number of type Value, i.e. a finite number of type + /// Value or -\ref INF. +#ifdef DOXYGEN + template + void colLowerBound(T &t, Value value) { return 0;} +#else + template + typename enable_if::type + colLowerBound(T &t, Value value,dummy<0> = 0) { + for(typename T::iterator i=t.begin();i!=t.end();++i) { + colLowerBound(*i, value); + } + } + template + typename enable_if::type + colLowerBound(T &t, Value value,dummy<1> = 1) { + for(typename T::iterator i=t.begin();i!=t.end();++i) { + colLowerBound(i->second, value); + } + } + template + typename enable_if::type + colLowerBound(T &t, Value value,dummy<2> = 2) { + for(typename T::MapIt i(t); i!=INVALID; ++i){ + colLowerBound(*i, value); + } + } +#endif + + /// Set the upper bound of a column (i.e a variable) + + /// The upper bound of a variable (column) has to be given by an + /// extended number of type Value, i.e. a finite number of type + /// Value or \ref INF. + void colUpperBound(Col c, Value value) { + _setColUpperBound(_lpId(c),value); + }; + + /// Get the upper bound of a column (i.e a variable) + + /// This function returns the upper bound for column (variable) \t c + /// (this might be \ref INF as well). + ///\return The upper bound for coloumn \t c + Value colUpperBound(Col c) const { + return _getColUpperBound(_lpId(c)); + } + + ///\brief Set the upper bound of several columns + ///(i.e a variables) at once + /// + ///This magic function takes a container as its argument + ///and applies the function on all of its elements. + /// The upper bound of a variable (column) has to be given by an + /// extended number of type Value, i.e. a finite number of type + /// Value or \ref INF. +#ifdef DOXYGEN + template + void colUpperBound(T &t, Value value) { return 0;} +#else + template + typename enable_if::type + colUpperBound(T &t, Value value,dummy<0> = 0) { + for(typename T::iterator i=t.begin();i!=t.end();++i) { + colUpperBound(*i, value); + } + } + template + typename enable_if::type + colUpperBound(T &t, Value value,dummy<1> = 1) { + for(typename T::iterator i=t.begin();i!=t.end();++i) { + colUpperBound(i->second, value); + } + } + template + typename enable_if::type + colUpperBound(T &t, Value value,dummy<2> = 2) { + for(typename T::MapIt i(t); i!=INVALID; ++i){ + colUpperBound(*i, value); + } + } +#endif + + /// Set the lower and the upper bounds of a column (i.e a variable) + + /// The lower and the upper bounds of + /// a variable (column) have to be given by an + /// extended number of type Value, i.e. a finite number of type + /// Value, -\ref INF or \ref INF. + void colBounds(Col c, Value lower, Value upper) { + _setColLowerBound(_lpId(c),lower); + _setColUpperBound(_lpId(c),upper); + } + + ///\brief Set the lower and the upper bound of several columns + ///(i.e a variables) at once + /// + ///This magic function takes a container as its argument + ///and applies the function on all of its elements. + /// The lower and the upper bounds of + /// a variable (column) have to be given by an + /// extended number of type Value, i.e. a finite number of type + /// Value, -\ref INF or \ref INF. +#ifdef DOXYGEN + template + void colBounds(T &t, Value lower, Value upper) { return 0;} +#else + template + typename enable_if::type + colBounds(T &t, Value lower, Value upper,dummy<0> = 0) { + for(typename T::iterator i=t.begin();i!=t.end();++i) { + colBounds(*i, lower, upper); + } + } + template + typename enable_if::type + colBounds(T &t, Value lower, Value upper,dummy<1> = 1) { + for(typename T::iterator i=t.begin();i!=t.end();++i) { + colBounds(i->second, lower, upper); + } + } + template + typename enable_if::type + colBounds(T &t, Value lower, Value upper,dummy<2> = 2) { + for(typename T::MapIt i(t); i!=INVALID; ++i){ + colBounds(*i, lower, upper); + } + } +#endif + + + /// Set the lower and the upper bounds of a row (i.e a constraint) + + /// The lower and the upper bound of a constraint (row) have to be + /// given by an extended number of type Value, i.e. a finite + /// number of type Value, -\ref INF or \ref INF. There is no + /// separate function for the lower and the upper bound because + /// that would have been hard to implement for CPLEX. + void rowBounds(Row c, Value lower, Value upper) { + _setRowBounds(_lpId(c),lower, upper); + } + + /// Get the lower and the upper bounds of a row (i.e a constraint) + + /// The lower and the upper bound of + /// a constraint (row) are + /// extended numbers of type Value, i.e. finite numbers of type + /// Value, -\ref INF or \ref INF. + /// \todo There is no separate function for the + /// lower and the upper bound because we had problems with the + /// implementation of the setting functions for CPLEX: + /// check out whether this can be done for these functions. + void getRowBounds(Row c, Value &lower, Value &upper) const { + _getRowBounds(_lpId(c),lower, upper); + } + + ///Set an element of the objective function + void objCoeff(Col c, Value v) {_setObjCoeff(_lpId(c),v); }; + + ///Get an element of the objective function + Value objCoeff(Col c) const { return _getObjCoeff(_lpId(c)); }; + + ///Set the objective function + + ///\param e is a linear expression of type \ref Expr. + void obj(Expr e) { + _clearObj(); + for (Expr::iterator i=e.begin(); i!=e.end(); ++i) + objCoeff((*i).first,(*i).second); + obj_const_comp=e.constComp(); + } + + ///Get the objective function + + ///\return the objective function as a linear expression of type \ref Expr. + Expr obj() const { + Expr e; + for (ColIt it(*this); it != INVALID; ++it) { + double c = objCoeff(it); + if (c != 0.0) { + e.insert(std::make_pair(it, c)); + } + } + return e; + } + + + ///Maximize + void max() { _setMax(); } + ///Minimize + void min() { _setMin(); } + + ///Query function: is this a maximization problem? + bool isMax() const {return _isMax(); } + + ///Query function: is this a minimization problem? + bool isMin() const {return !isMax(); } + + ///@} + + + ///\name Solve the LP + + ///@{ + + ///\e Solve the LP problem at hand + /// + ///\return The result of the optimization procedure. Possible + ///values and their meanings can be found in the documentation of + ///\ref SolveExitStatus. + /// + ///\todo Which method is used to solve the problem + SolveExitStatus solve() { return _solve(); } + + ///@} + + ///\name Obtain the solution + + ///@{ + + /// The status of the primal problem (the original LP problem) + SolutionStatus primalStatus() const { + return _getPrimalStatus(); + } + + /// The status of the dual (of the original LP) problem + SolutionStatus dualStatus() const { + return _getDualStatus(); + } + + ///The type of the original LP problem + ProblemTypes problemType() const { + return _getProblemType(); + } + + ///\e + Value primal(Col c) const { return _getPrimal(_lpId(c)); } + ///\e + Value primal(const Expr& e) const { + double res = e.constComp(); + for (std::map::const_iterator it = e.begin(); + it != e.end(); ++it) { + res += _getPrimal(_lpId(it->first)) * it->second; + } + return res; + } + + ///\e + Value dual(Row r) const { return _getDual(_lpId(r)); } + ///\e + Value dual(const DualExpr& e) const { + double res = 0.0; + for (std::map::const_iterator it = e.begin(); + it != e.end(); ++it) { + res += _getPrimal(_lpId(it->first)) * it->second; + } + return res; + } + + ///\e + bool isBasicCol(Col c) const { return _isBasicCol(_lpId(c)); } + + ///\e + + ///\return + ///- \ref INF or -\ref INF means either infeasibility or unboundedness + /// of the primal problem, depending on whether we minimize or maximize. + ///- \ref NaN if no primal solution is found. + ///- The (finite) objective value if an optimal solution is found. + Value primalValue() const { return _getPrimalValue()+obj_const_comp;} + ///@} + + }; + + + /// \ingroup lp_group + /// + /// \brief Common base class for MIP solvers + /// \todo Much more docs + class MipSolverBase : virtual public LpSolverBase{ + public: + + ///Possible variable (coloumn) types (e.g. real, integer, binary etc.) + enum ColTypes { + ///Continuous variable + REAL = 0, + ///Integer variable + + ///Unfortunately, cplex 7.5 somewhere writes something like + ///#define INTEGER 'I' + INT = 1 + ///\todo No support for other types yet. + }; + + ///Sets the type of the given coloumn to the given type + /// + ///Sets the type of the given coloumn to the given type. + void colType(Col c, ColTypes col_type) { + _colType(_lpId(c),col_type); + } + + ///Gives back the type of the column. + /// + ///Gives back the type of the column. + ColTypes colType(Col c) const { + return _colType(_lpId(c)); + } + + ///Sets the type of the given Col to integer or remove that property. + /// + ///Sets the type of the given Col to integer or remove that property. + void integer(Col c, bool enable) { + if (enable) + colType(c,INT); + else + colType(c,REAL); + } + + ///Gives back whether the type of the column is integer or not. + /// + ///Gives back the type of the column. + ///\return true if the column has integer type and false if not. + bool integer(Col c) const { + return (colType(c)==INT); + } + + /// The status of the MIP problem + SolutionStatus mipStatus() const { + return _getMipStatus(); + } + + protected: + + virtual ColTypes _colType(int col) const = 0; + virtual void _colType(int col, ColTypes col_type) = 0; + virtual SolutionStatus _getMipStatus() const = 0; + + }; + + ///\relates LpSolverBase::Expr + /// + inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a, + const LpSolverBase::Expr &b) + { + LpSolverBase::Expr tmp(a); + tmp+=b; + return tmp; + } + ///\e + + ///\relates LpSolverBase::Expr + /// + inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a, + const LpSolverBase::Expr &b) + { + LpSolverBase::Expr tmp(a); + tmp-=b; + return tmp; + } + ///\e + + ///\relates LpSolverBase::Expr + /// + inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a, + const LpSolverBase::Value &b) + { + LpSolverBase::Expr tmp(a); + tmp*=b; + return tmp; + } + + ///\e + + ///\relates LpSolverBase::Expr + /// + inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a, + const LpSolverBase::Expr &b) + { + LpSolverBase::Expr tmp(b); + tmp*=a; + return tmp; + } + ///\e + + ///\relates LpSolverBase::Expr + /// + inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a, + const LpSolverBase::Value &b) + { + LpSolverBase::Expr tmp(a); + tmp/=b; + return tmp; + } + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e, + const LpSolverBase::Expr &f) + { + return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0); + } + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e, + const LpSolverBase::Expr &f) + { + return LpSolverBase::Constr(e,f); + } + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e, + const LpSolverBase::Value &f) + { + return LpSolverBase::Constr(-LpSolverBase::INF,e,f); + } + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e, + const LpSolverBase::Expr &f) + { + return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0); + } + + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e, + const LpSolverBase::Expr &f) + { + return LpSolverBase::Constr(f,e); + } + + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e, + const LpSolverBase::Value &f) + { + return LpSolverBase::Constr(f,e,LpSolverBase::INF); + } + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e, + const LpSolverBase::Value &f) + { + return LpSolverBase::Constr(f,e,f); + } + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e, + const LpSolverBase::Expr &f) + { + return LpSolverBase::Constr(0,e-f,0); + } + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n, + const LpSolverBase::Constr&c) + { + LpSolverBase::Constr tmp(c); + LEMON_ASSERT(LpSolverBase::isNaN(tmp.lowerBound()), "Wrong LP constraint"); + tmp.lowerBound()=n; + return tmp; + } + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c, + const LpSolverBase::Value &n) + { + LpSolverBase::Constr tmp(c); + LEMON_ASSERT(LpSolverBase::isNaN(tmp.upperBound()), "Wrong LP constraint"); + tmp.upperBound()=n; + return tmp; + } + + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n, + const LpSolverBase::Constr&c) + { + LpSolverBase::Constr tmp(c); + LEMON_ASSERT(LpSolverBase::isNaN(tmp.upperBound()), "Wrong LP constraint"); + tmp.upperBound()=n; + return tmp; + } + ///\e + + ///\relates LpSolverBase::Constr + /// + inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c, + const LpSolverBase::Value &n) + { + LpSolverBase::Constr tmp(c); + LEMON_ASSERT(LpSolverBase::isNaN(tmp.lowerBound()), "Wrong LP constraint"); + tmp.lowerBound()=n; + return tmp; + } + + ///\e + + ///\relates LpSolverBase::DualExpr + /// + inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a, + const LpSolverBase::DualExpr &b) + { + LpSolverBase::DualExpr tmp(a); + tmp+=b; + return tmp; + } + ///\e + + ///\relates LpSolverBase::DualExpr + /// + inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a, + const LpSolverBase::DualExpr &b) + { + LpSolverBase::DualExpr tmp(a); + tmp-=b; + return tmp; + } + ///\e + + ///\relates LpSolverBase::DualExpr + /// + inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a, + const LpSolverBase::Value &b) + { + LpSolverBase::DualExpr tmp(a); + tmp*=b; + return tmp; + } + + ///\e + + ///\relates LpSolverBase::DualExpr + /// + inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a, + const LpSolverBase::DualExpr &b) + { + LpSolverBase::DualExpr tmp(b); + tmp*=a; + return tmp; + } + ///\e + + ///\relates LpSolverBase::DualExpr + /// + inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a, + const LpSolverBase::Value &b) + { + LpSolverBase::DualExpr tmp(a); + tmp/=b; + return tmp; + } + + +} //namespace lemon + +#endif //LEMON_LP_BASE_H