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Point.hpp
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/** @file Point.hpp
*
* Describes Point class template with accompanying routines.
*
* @date 2010-07-13
* @author ulysses
*/
#ifndef POINT_HPP_
#define POINT_HPP_
#include <array>
#include <algorithm>
#include <iterator>
#include <initializer_list>
#include <iostream>
#include <memory>
#include <sstream>
#include <string>
#include <cstdio>
#include <functional>
#include <boost/foreach.hpp>
//#include <lpsolve/lp_lib.h>
#include <glpk.h>
#include "Utilities.hpp"
namespace mv_poly {
template<typename PointImpl>
struct GradedAntilexMonomialOrder;
template<
int Dim,
template <typename> class OrderPolicy
= GradedAntilexMonomialOrder
>
class Point;
template<int Dim, template <typename> class OrderPolicy>
bool operator==(
Point<Dim, OrderPolicy> const & lhs,
Point<Dim, OrderPolicy> const & rhs);
/**
* \class Point
* Point in N-dimensional integer lattice.
* @param Dim Dimension of point lattice.
*/
template<
int Dim,
template <typename PointImpl> class OrderPolicy
// = GradedAntilexMonomialOrder
> class Point : OrderPolicy< std::array<long, Dim> > {
typedef OrderPolicy< std::array<long, Dim> > MyOrderPolicy;
typedef typename Point::PointImplType ImplType; // PointImplType inherited
// from OrderPolicy
// to avoid duplication
ImplType data;
public:
/// Creates point (0, 0, ..., 0).
Point() {
data.fill(0);
}
bool operator<(Point<Dim, OrderPolicy> const & other) const {
return MyOrderPolicy::totalLess(data, other.data);
}
typedef typename ImplType::value_type value_type;
typedef typename ImplType::size_type size_type;
typedef typename ImplType::reference reference;
typedef typename ImplType::const_reference const_reference;
Point(std::initializer_list<value_type> data) {
std::copy(data.begin(), data.end(), this->data.begin());
}
reference
operator[](size_type n) {
return data[n];
}
const_reference
operator[](size_type n) const {
return data[n];
}
typedef typename ImplType::iterator iterator;
typedef typename ImplType::const_iterator const_iterator;
iterator
begin()
{ return data.begin(); }
const_iterator
begin() const
{ return data.begin(); }
iterator
end()
{ return data.end(); }
const_iterator
end() const
{ return data.end(); }
typedef typename ImplType::reverse_iterator reverse_iterator;
typedef typename ImplType::const_reverse_iterator const_reverse_iterator;
reverse_iterator
rbegin()
{ return data.rbegin(); }
const_reverse_iterator
rbegin() const
{ return data.rbegin(); }
reverse_iterator
rend()
{ return data.rend(); }
const_reverse_iterator
rend() const
{ return data.rend(); }
Point& operator+=(Point const & other) {
std::transform(this->begin(), this->end(),
other.begin(), this->begin(), std::plus<int>());
return *this;
}
Point& operator-=(Point const & other) {
std::transform(this->begin(), this->end(),
other.begin(), this->begin(), std::minus<int>());
return *this;
}
Point& operator++();
Point operator++(int);
/**
* Compaison for equality: two points are equal iff all corresponding coordinates
* are equal.
* @param lhs Left-hand side argument for testing on equality.
* @param rhs Right-hand side argument for testing on equality.
* @return True if all corresponding coordinates of \c lhs and \c rhs are equal,
* false otherwise.
*/
friend
bool operator==<>(
Point<Dim, OrderPolicy> const & lhs,
Point<Dim, OrderPolicy> const & rhs);
;
}; // class Point
template<int Dim, template <typename> class OrderPolicy>
bool operator==(
Point<Dim, OrderPolicy> const & lhs,
Point<Dim, OrderPolicy> const & rhs) {
return lhs.data == rhs.data;
}
/**
* Summs up elements of a given container \c c.
* @param c Container to summ up elements.
* @return Summa of the elements of \c c.
*/
template<typename Cont>
inline
int weight(Cont const & c) {
return std::accumulate(c.begin(), c.end(), 0);
}
template<typename PointImpl>
struct GradedAntilexMonomialOrder {
typedef PointImpl PointImplType;
/**
* This total oreder predicate implements graded antilexicographic order.
* @param[in] lhs Left-hand side argument of “less”.
* @param[in] rhs Right-hand side argument of “less”.
* @return Result of comparison two points by current monomial order. True is
* \c lhs less then \c rhs, false otherwise (rhs is less or equal to lhs).
*/
static bool totalLess(PointImplType const & lhs, PointImplType const & rhs) {
int lw = weight(lhs);
int rw = weight(rhs);
return (lw < rw)
|| (lw == rw
&& std::lexicographical_compare(lhs.rbegin(), lhs.rend(),
rhs.rbegin(), rhs.rend()));
}
void inc(PointImplType & data) {
using namespace std::tr1::placeholders;
using std::tr1::bind;
typename PointImplType::iterator
itInc = std::find_if(data.begin(), data.end(),
std::tr1::bind(std::logical_not<bool>(),
std::tr1::bind(std::equal_to<int>(), 0, _1))),
it(itInc++);
if (it == data.end())
data[0] = 1;
else if (itInc == data.end()) {
int a = *it + 1;
*it = 0;
data[0] = a;
} else {
++(*itInc);
int a = *it - 1;
*it = 0;
data[0] = a;
}
}
};
template <int a, int b>
class LpSolveHolder {
static const int dim = 2;
glp_prob *lp;
glp_iocp parm;
public:
LpSolveHolder() {
glp_term_out(GLP_OFF);
const int ne = 2;
int ia[1 + ne], ja[1 + ne];
double ar[1 + ne];
lp = glp_create_prob();
glp_set_obj_dir(lp, GLP_MIN);
glp_add_rows(lp, 1);
glp_add_cols(lp, 2);
glp_set_col_bnds(lp, 1, GLP_DB, 0.0, b - 1); // x1
glp_set_col_bnds(lp, 2, GLP_LO, 0.0, 0.0); // x2
glp_set_col_kind(lp, 1, GLP_IV);
glp_set_col_kind(lp, 2, GLP_IV);
glp_set_obj_coef(lp, 1, a);
glp_set_obj_coef(lp, 2, b);
ia[1] = 1, ja[1] = 1, ar[1] = a;
ia[2] = 1, ja[2] = 2, ar[2] = b;
glp_load_matrix(lp, 2, ia, ja, ar);
//glp_simplex(lp, NULL);
glp_init_iocp(&parm);
parm.presolve = GLP_ON;
}
template <typename Cont>
void lpInc(Cont & c) {
glp_set_row_bnds(lp, 1, GLP_LO, c[0]*a + c[1]*b + 1, 0.0);
glp_intopt(lp, &parm);
c[0] = glp_mip_col_val(lp, 1);
c[1] = glp_mip_col_val(lp, 2);
}
~LpSolveHolder() {
glp_delete_prob(lp);
}
};
template<int a, int b>
struct WeightedOrder {
template<typename PointImpl>
struct impl {
typedef PointImpl PointImplType;
static bool totalLess(PointImplType const & lhs, PointImplType const & rhs) {
return weight(lhs) < weight(rhs);
}
static void inc(PointImplType & data) {
lp.lpInc(data);
}
private:
static LpSolveHolder<a, b> lp;
static int weight(PointImplType const & data) {
return a*data[0] + b*data[1];
}
};
};
template <int a, int b>
template <typename T>
LpSolveHolder<a, b>
WeightedOrder<a, b>::impl<T>::lp = LpSolveHolder<a, b>();
/**
* Simple Point output.
* @param[out] os Target output stream.
* @param[in] pt Point to be outputed in \c os.
* @return Output stream \c os after point \c p have been
* outputed to \c os (conventionally).
*/
template<int Dim, template <typename PointImpl> class OrderPolicy>
inline
std::ostream& operator<<(std::ostream & os, Point<Dim, OrderPolicy> const & pt) {
os << "(";
//std::copy(pt.begin(), pt.end(), std::ostream_iterator<int>(os, ","));
for(int i = 0; i < Dim - 1; ++i)
os << pt[i] << ", ";
os << pt[Dim - 1] << ")";
return os;
}
/**
* Simple 1-dimensional point output.
* @param[out] os Target output stream.
* @param[in] pt Point to be outputed in \c os.
* @return Output stream \c os after point \c p have been
* outputed to \c os (conventionally).
*/
template<template <typename PointImpl> class OrderPolicy>
inline
std::ostream& operator<<(std::ostream & os, Point<1, OrderPolicy> const & pt) {
os << pt[0];
return os;
}
/**
* Compare two points by coordinates. <tt>byCoordinateLess(lhs, rhs) == true</tt> iff
* lhs[i] <= rhs[i] for all i. It is a partial order on the set of points.
* @param[in] lhs Left-hand side argument of “less”.
* @param[in] rhs Right-hand side argument of “less”.
* @return Result of comparison two points by coordinates: true if
* lhs[i] <= rhs[i] for all i, false otherwise.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy>
inline
bool byCoordinateLess(
Point<Dim, OrderPolicy> const & lhs,
Point<Dim, OrderPolicy> const & rhs) {
return std::inner_product(lhs.begin(), lhs.end(), rhs.begin(), true,
std::logical_and<bool>(), std::less_equal<int>());
}
/**
* Checks if given point \pt is by-coordinate less then any point in
* range given by iterators \c beg and \c end.
* @param[in] pt Point to check for by-coordinate less.
* @param[in] beg Iterator that points to the begining (inclusively) of the
* point sequence to be check against.
* @param[in] end Iterator that points to the end (exclusively) of the
* point sequence to be check against.
* @return True if there exists a point pt' in [*beg, *end) such that
* byCoordinateLess(pt, pt'), false otherwise.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy, typename It>
inline
bool byCoordinateLessThenAny(Point<Dim, OrderPolicy> const & pt, It beg, It end) {
using std::tr1::bind;
using std::tr1::placeholders::_1;
using std::tr1::cref;
return end != std::find_if(beg, end,
std::tr1::bind(&byCoordinateLess<Dim, OrderPolicy>, cref(pt), _1));
}
/**
* Checks if given point \pt is by-coordinate less then any point in
* collection \c c.
* @param[in] pt Point to check for by-coordinate less.
* @param[in] c Container of points to be check against.
* @return True if there exists a point pt' in \c c such that
* byCoordinateLess(pt, pt'), false otherwise.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy, typename PtCont>
inline
bool byCoordinateLessThenAny(Point<Dim, OrderPolicy> const & pt, PtCont const & c) {
return byCoordinateLessThenAny(pt, c.begin(), c.end());
}
/**
* Checks if given point \pt is by-coordinate greater then any point in
* collection \c c.
* @param[in] pt Point to check for by-coordinate greater.
* @param[in] c Container of points to be check against.
* @return True is there exists a point pt' in \c c such that
* byCoordinateLess(pt, pt'), false otherwise.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy, typename PtCont>
inline
bool byCoordinateGreaterThenAny(Point<Dim, OrderPolicy> const & pt,
PtCont const & c) {
using std::tr1::bind;
using std::tr1::placeholders::_1;
using std::tr1::cref;
return c.end() != std::find_if(c.begin(), c.end(),
bind(&byCoordinateLess<Dim, OrderPolicy>, _1, cref(pt)));
}
/**
* Reflexive version of \c operator<.
* @param[in] lhs Left-hand side argument of “less-or-equal”.
* @param[in] rhs Right-hand side argument of “less-or-equal”.
* @return Result of comparison two points by current monomial order. True is
* \c lhs less then or equal to \c rhs, false otherwise.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy>
inline
bool operator<=(Point<Dim, OrderPolicy> const & lhs,
Point<Dim, OrderPolicy> const & rhs) {
return (lhs < rhs) || (lhs == rhs);
}
/**
* Point's pre-increment.
*
* @note Use OrderPolicy.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy>
inline
Point<Dim, OrderPolicy>&
Point<Dim, OrderPolicy>::operator++() {
MyOrderPolicy::inc(data);
return *this;
}
/**
* Point's post-increment.
*
* @note Use OrderPolicy.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy>
inline
Point<Dim, OrderPolicy> Point<Dim, OrderPolicy>::operator++(int) {
Point<Dim, OrderPolicy> old(*this);
++*this;
return old;
}
/**
* Coordinate-wise point summation.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy>
inline
Point<Dim, OrderPolicy>
operator+(Point<Dim, OrderPolicy> lhs, Point<Dim, OrderPolicy> const & rhs) {
// lhs: pass-by-copy optimization
return lhs += rhs;
}
/**
* Coordinate-wise point subtaraction.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy>
inline
Point<Dim, OrderPolicy>
operator-(Point<Dim, OrderPolicy> lhs, Point<Dim, OrderPolicy> const & rhs) {
return lhs -= rhs;
}
/**
* Gets all partial maximums from collection of \c Point (\c points) with
* respect to by-coordinate partial order (cf. \c byCoordinateLess).
* @param points Collection of points to be looked through for the maximums.
* @return Maximum points with respect to by-coordinate partial order
* (cf. \c byCoordinateLess) from the \c points.
*/
template<
int Dim,
template <typename PointImpl> class OrderPolicy,
template<typename T, typename S = std::allocator<T> > class Cont>
Cont<Point<Dim, OrderPolicy> >
getPartialMaximums(Cont<Point<Dim, OrderPolicy> > const & points) {
using std::tr1::bind;
using std::tr1::placeholders::_1; // usually we use “using” directive:
// using namespace std::tr1::placeholders; — but here it yelds some ambiguity
// while resolving _1 symbol, so we use declaration. Sad but true...
using std::tr1::cref;
using std::find_if;
Cont<Point<Dim, OrderPolicy> > result;
typedef Point<Dim, OrderPolicy> Pt;
BOOST_FOREACH(Pt const & pt, points) {
// if there is a point in result which dominates pt, then throw pt away
if (byCoordinateLessThenAny(pt, result))
continue;
// else we add pt to the result but first delete all points
// in result dominated by pt
result.erase(
remove_if(result.begin(), result.end(),
bind(&byCoordinateLess<Dim, OrderPolicy>, _1, cref(pt))),
result.end());
result.push_back(pt);
}
return result;
}
/**
* Complimentary to \c getPartialMaximums.
* @param points Collection of points to be looked through for the maximums.
* @return Maximum points with respect to by-coordinate partial order
* (cf. \c byCoordinateLess) from the \c points.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy,
template<typename T, typename S = std::allocator<T> > class Cont>
Cont<Point<Dim, OrderPolicy> >
getPartialMinimums(Cont<Point<Dim, OrderPolicy> > const & points) {
// TODO: probably we should refactor out this function together with
// getPartialMaximums to get one generic function
using std::tr1::bind;
using std::tr1::placeholders::_1;
using std::tr1::cref;
using std::find_if;
Cont<Point<Dim, OrderPolicy> > result;
typedef Point<Dim, OrderPolicy> Pt;
BOOST_FOREACH(Pt const & pt, points) {
// if there is a point in result which dominates pt, then throw pt away
if (byCoordinateGreaterThenAny(pt, result))
continue;
// else we add pt to the result but first delete all points
// in result dominated by pt
result.erase(
remove_if(result.begin(), result.end(),
bind(&byCoordinateLess<Dim, OrderPolicy>, _1, cref(pt))),
result.end());
result.push_back(pt);
}
return result;
}
template<int Dim, template <typename PointImpl> class OrderPolicy,
template<typename T, typename S = std::allocator<T> > class Cont>
Cont<Point<Dim, OrderPolicy> >
getConjugatePointCollection(Cont<Point<Dim, OrderPolicy> > const & points) {
// construct some finite approximation set of Sigma-set, which contains conjugate
// point set to be found; then we use exhaustive search in this finite set for
// finding extremums (minimums in this case) as usual (see getPartialMaximums);
// the approximation set defined as follows (and this definition is a
// subject of probable future optimization, specification
// and even correction ;)): it is all points totally
// less (w.r.t. monomial order) then the point which has a weight equal to
// the maximum weight of points in given collection plus 2
// but the (totally) least from all such points
// TODO: proof correctness of the algorithm
using std::tr1::bind;
using std::tr1::function;
using std::tr1::placeholders::_1;
using std::tr1::placeholders::_2;
if (points.empty())
return Cont< Point<Dim, OrderPolicy> >(1);
//function<int (Point<Dim>)> pointWeight = bind(&Point<Dim>::weight, _1);
int max_weight = weight(*std::max_element(points.begin(), points.end(),
std::tr1::bind(std::less<int>(),
std::tr1::bind(&weight< Point<Dim, OrderPolicy> >, _1),
std::tr1::bind(&weight< Point<Dim, OrderPolicy> >, _2))));
Point<Dim, OrderPolicy> upperPoint;
upperPoint[0] = max_weight + 2;
Cont< Point<Dim, OrderPolicy> > approxSigmaSet;
for (Point<Dim, OrderPolicy> i; i < upperPoint; ++i) {
if (! byCoordinateLessThenAny(i, points))
approxSigmaSet.push_back(i);
}
// std::cout << "app set" << std::endl;
// std::copy(approxSigmaSet.begin(), approxSigmaSet.end(),
// std::ostream_iterator< Point<Dim> >(std::cout, "\n"));
return getPartialMinimums(approxSigmaSet);
}
/**
* Point slice. It is kind of Decorator (cf. [GoF]) for point instance which
* shifts the index used in \c Point subscript operator on \c Offset
* positions. It is used when subscript operation goes deeper in the nestedness
* level of or main recursive type \c MVPolyType (which is
* <tt>Polynomial<… Polynomial<T>… ></tt>).
*
* We probaly should use some polymorphism (either static or dynamic)
* to allow \c pt field contain either Point or ConstSlice itself, but we decided to
* “optimise away” such possibility always keeping a Point instance — this is
* managed by \c make_slice utility which we consider a part of ConstSlice implementation
* so this abstraction is not that leaky. As a proof of this we recall generic
* utility \c apply_subscript which polymorphically calls operator[] for
* either Point or ConstSlice instance.
*
* @param Dim Initial dimension of the point beeing sliced.
* @param Offset Starting index in initial point to subscript from in
* the current slice.
*/
template<typename Body, int Dim, int Offset>
class ConstSlice {
Body const & pt;
public:
ConstSlice(Body const & pt_) : pt(pt_) {}
Body const & getImpl() const {return pt;}
operator Body const &() {return pt;}
typedef typename Body::const_reference const_reference;
typedef typename Body::size_type size_type;
const_reference
operator[](size_type n) const {
return pt[n + Offset];
}
};
/// ConstSlice of the point is “1-slice”, for 1-slice sl[i] ~ pt[i + 1].
template<int Dim, typename Body>
ConstSlice<Body, Dim, 1>
make_slice(Body const & pt) {
return ConstSlice<Body, Dim, 1>(pt);
}
/** ConstSlice of the ConstSlice<Dim, Offset> is ConstSlice<Dim, Offset + 1>.
* It is convinient for us to slice by 1 position each time.
*/
template<typename Body, int Dim, int Offset>
ConstSlice<Body, Dim, Offset + 1>
make_slice(ConstSlice<Body, Dim, Offset> const & sl) {
return ConstSlice<Body, Dim, Offset + 1>(sl.getImpl());
}
/**
* Mutable version of ConstSlice.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy, int Offset>
class Slice {
Point<Dim, OrderPolicy> & pt;
public:
Slice(Point<Dim, OrderPolicy> & pt_) : pt(pt_) {}
Point<Dim, OrderPolicy> & getImpl() const {return pt;}
operator Point<Dim, OrderPolicy> &() {return pt;}
typedef typename Point<Dim, OrderPolicy>::const_reference const_reference;
typedef typename Point<Dim, OrderPolicy>::reference reference;
typedef typename Point<Dim, OrderPolicy>::size_type size_type;
const_reference
operator[](size_type n) const {
return pt[n + Offset];
}
reference
operator[](size_type n) {
return pt[n + Offset];
}
};
/// ConstSlice of the point is “1-slice”, for 1-slice sl[i] ~ pt[i + 1].
template<int Dim, template <typename PointImpl> class OrderPolicy>
Slice<Dim, OrderPolicy, 1>
make_slice(Point<Dim, OrderPolicy> & pt) {
return Slice<Dim, OrderPolicy, 1>(pt);
}
/** ConstSlice of the ConstSlice<Dim, Offset> is ConstSlice<Dim, Offset + 1>.
* It is convinient for us to slice by 1 position each time.
*/
template<int Dim, template <typename PointImpl> class OrderPolicy, int Offset>
Slice<Dim, OrderPolicy, Offset + 1>
make_slice(Slice<Dim, OrderPolicy, Offset> const & sl) {
return Slice<Dim, OrderPolicy, Offset + 1>(sl.getImpl());
}
} // namespace mv_poly
#endif /* POINT_HPP_ */