A linear expression. More...

#include <Linear_Expression_defs.hh>

Inheritance diagram for Parma_Polyhedra_Library::Linear_Expression:

Collaboration diagram for Parma_Polyhedra_Library::Linear_Expression:

Classes
class	const_iterator

Public Types
typedef const Linear_Expression &	const_reference

typedef Linear_Expression	raw_type

Public Member Functions
	Linear_Expression (Representation r=default_representation)
	Default constructor: returns a copy of Linear_Expression::zero(). More...

	Linear_Expression (const Linear_Expression &e)
	Ordinary copy constructor. More...

	Linear_Expression (const Linear_Expression &e, Representation r)
	Copy constructor that takes also a Representation. More...

template<typename LE_Adapter >
	Linear_Expression (const LE_Adapter &e, typename Enable_If< Is_Same_Or_Derived< Expression_Adapter_Base, LE_Adapter >::value, void * >::type=0)
	Copy constructor from a linear expression adapter. More...

template<typename LE_Adapter >
	Linear_Expression (const LE_Adapter &e, Representation r, typename Enable_If< Is_Same_Or_Derived< Expression_Adapter_Base, LE_Adapter >::value, void * >::type=0)
	Copy constructor from a linear expression adapter that takes a Representation. More...

template<typename LE_Adapter >
	Linear_Expression (const LE_Adapter &e, dimension_type space_dim, typename Enable_If< Is_Same_Or_Derived< Expression_Adapter_Base, LE_Adapter >::value, void * >::type=0)
	Copy constructor from a linear expression adapter that takes a space dimension. More...

template<typename LE_Adapter >
	Linear_Expression (const LE_Adapter &e, dimension_type space_dim, Representation r, typename Enable_If< Is_Same_Or_Derived< Expression_Adapter_Base, LE_Adapter >::value, void * >::type=0)
	Copy constructor from a linear expression adapter that takes a space dimension and a Representation. More...

Linear_Expression &	operator= (const Linear_Expression &e)
	Assignment operator. More...

	~Linear_Expression ()
	Destructor. More...

	Linear_Expression (Coefficient_traits::const_reference n, Representation r=default_representation)
	Builds the linear expression corresponding to the inhomogeneous term `n`. More...

	Linear_Expression (Variable v, Representation r=default_representation)
	Builds the linear expression corresponding to the variable `v`. More...

Representation	representation () const
	Returns the current representation of *this. More...

void	set_representation (Representation r)
	Converts *this to the specified representation. More...

const_iterator	begin () const

const_iterator	end () const

const_iterator	lower_bound (Variable v) const

dimension_type	space_dimension () const
	Returns the dimension of the vector space enclosing `*this`. More...

void	set_space_dimension (dimension_type n)
	Sets the dimension of the vector space enclosing `*this` to `n` . More...

Coefficient_traits::const_reference	coefficient (Variable v) const
	Returns the coefficient of `v` in `*this`. More...

void	set_coefficient (Variable v, Coefficient_traits::const_reference n)
	Sets the coefficient of `v` in `*this` to `n`. More...

Coefficient_traits::const_reference	inhomogeneous_term () const
	Returns the inhomogeneous term of `*this`. More...

void	set_inhomogeneous_term (Coefficient_traits::const_reference n)
	Sets the inhomogeneous term of `*this` to `n`. More...

void	linear_combine (const Linear_Expression &y, Variable v)

void	linear_combine (const Linear_Expression &y, Coefficient_traits::const_reference c1, Coefficient_traits::const_reference c2)

void	linear_combine_lax (const Linear_Expression &y, Coefficient_traits::const_reference c1, Coefficient_traits::const_reference c2)

void	swap_space_dimensions (Variable v1, Variable v2)
	Swaps the coefficients of the variables `v1` and `v2` . More...

void	remove_space_dimensions (const Variables_Set &vars)
	Removes all the specified dimensions from the expression. More...

void	shift_space_dimensions (Variable v, dimension_type n)

void	permute_space_dimensions (const std::vector< Variable > &cycle)
	Permutes the space dimensions of the expression. More...

bool	is_zero () const
	Returns `true` if and only if `*this` is . More...

bool	all_homogeneous_terms_are_zero () const
	Returns `true` if and only if all the homogeneous terms of `*this` are . More...

memory_size_type	total_memory_in_bytes () const
	Returns a lower bound to the total size in bytes of the memory occupied by `*this`. More...

memory_size_type	external_memory_in_bytes () const
	Returns the size in bytes of the memory managed by `*this`. More...

bool	OK () const
	Checks if all the invariants are satisfied. More...

void	ascii_dump () const
	Writes to `std::cerr` an ASCII representation of `*this`. More...

void	ascii_dump (std::ostream &s) const
	Writes to `s` an ASCII representation of `*this`. More...

void	print () const
	Prints `*this` to `std::cerr` using `operator<<`. More...

bool	ascii_load (std::istream &s)
	Loads from `s` an ASCII representation (as produced by ascii_dump(std::ostream&) const) and sets `*this` accordingly. Returns `true` if successful, `false` otherwise. More...

void	m_swap (Linear_Expression &y)
	Swaps `*this` with `y`. More...

	Linear_Expression (const Linear_Expression &e, dimension_type space_dim)
	Copy constructor with a specified space dimension. More...

	Linear_Expression (const Linear_Expression &e, dimension_type space_dim, Representation r)
	Copy constructor with a specified space dimension and representation. More...

bool	is_equal_to (const Linear_Expression &x) const

void	normalize ()

void	sign_normalize ()

bool	all_zeroes (const Variables_Set &vars) const
	Returns `true` if the coefficient of each variable in `vars`[i] is . More...

Static Public Member Functions
static dimension_type	max_space_dimension ()
	Returns the maximum space dimension a Linear_Expression can handle. More...

static void	initialize ()
	Initializes the class. More...

static void	finalize ()
	Finalizes the class. More...

static const Linear_Expression &	zero ()
	Returns the (zero-dimension space) constant 0. More...

Static Public Attributes
static const Representation	default_representation = SPARSE

Private Member Functions
	Linear_Expression (dimension_type space_dim, bool, Representation r=default_representation)
	Implementation sizing constructor. More...

Coefficient_traits::const_reference	get (dimension_type i) const
	Returns the i-th coefficient. More...

void	set (dimension_type i, Coefficient_traits::const_reference n)
	Sets the i-th coefficient to n. More...

Coefficient_traits::const_reference	get (Variable v) const
	Returns the coefficient of v. More...

void	set (Variable v, Coefficient_traits::const_reference n)
	Sets the coefficient of v to n. More...

bool	all_zeroes (dimension_type start, dimension_type end) const
	Returns `true` if (*this)[i] is , for each i in [start, end). More...

dimension_type	num_zeroes (dimension_type start, dimension_type end) const
	Returns the number of zero coefficient in [start, end). More...

Coefficient	gcd (dimension_type start, dimension_type end) const
	Returns the gcd of the nonzero coefficients in [start,end). If all the coefficients in this range are 0 returns 0. More...

void	exact_div_assign (Coefficient_traits::const_reference c, dimension_type start, dimension_type end)

void	linear_combine (const Linear_Expression &y, dimension_type i)

void	linear_combine (const Linear_Expression &y, Coefficient_traits::const_reference c1, Coefficient_traits::const_reference c2, dimension_type start, dimension_type end)

void	linear_combine_lax (const Linear_Expression &y, Coefficient_traits::const_reference c1, Coefficient_traits::const_reference c2, dimension_type start, dimension_type end)

void	mul_assign (Coefficient_traits::const_reference n, dimension_type start, dimension_type end)
	Equivalent to `(this)[i] = n`, for each i in [start, end). More...

dimension_type	last_nonzero () const

dimension_type	last_nonzero (dimension_type first, dimension_type last) const

dimension_type	first_nonzero (dimension_type first, dimension_type last) const

bool	all_zeroes_except (const Variables_Set &vars, dimension_type start, dimension_type end) const
	Returns `true` if all coefficients in [start,end), except those corresponding to variables in `vars`, are zero. More...

void	scalar_product_assign (Coefficient &result, const Linear_Expression &y) const
	Sets results to the sum of (this)[i]y[i], for each i. More...

void	scalar_product_assign (Coefficient &result, const Linear_Expression &y, dimension_type start, dimension_type end) const
	Sets results to the sum of (this)[i]y[i], for each i in [start,end). More...

int	scalar_product_sign (const Linear_Expression &y) const
	Computes the sign of the sum of (this)[i]y[i], for each i. More...

int	scalar_product_sign (const Linear_Expression &y, dimension_type start, dimension_type end) const

void	has_a_free_dimension_helper (std::set< dimension_type > &x) const
	Removes from the set x all the indexes of nonzero elements of *this. More...

bool	is_equal_to (const Linear_Expression &x, dimension_type start, dimension_type end) const
	Returns `true` if (*this)[i] is equal to x[i], for each i in [start,end). More...

bool	is_equal_to (const Linear_Expression &x, Coefficient_traits::const_reference c1, Coefficient_traits::const_reference c2, dimension_type start, dimension_type end) const

void	get_row (Dense_Row &r) const
	Sets `r` to a copy of the row that implements `*this`. More...

void	get_row (Sparse_Row &r) const
	Sets `r` to a copy of the row that implements `*this`. More...

bool	have_a_common_variable (const Linear_Expression &x, Variable first, Variable last) const
	Returns `true` if there is a variable from index `first` (included) to index `last` (excluded) whose coefficient is nonzero in both `*this` and `x`. More...

void	negate (dimension_type first, dimension_type last)
	Negates the elements from index `first` (included) to index `last` (excluded). More...

Private Attributes
Linear_Expression_Interface *	impl

Static Private Attributes
static const Linear_Expression *	zero_p = 0
	Holds (between class initialization and finalization) a pointer to the (zero-dimension space) constant 0. More...

Friends
template<typename Row >
class	Linear_Expression_Impl

class	Grid

class	Congruence

class	Polyhedron

class	PIP_Tree_Node

class	Grid_Generator

class	Generator

class	Constraint

class	Constraint_System

class	PIP_Problem

class	BHRZ03_Certificate

class	Scalar_Products

class	MIP_Problem

class	Box_Helpers

class	Congruence_System

class	BD_Shape_Helpers

class	Octagonal_Shape_Helper

class	Termination_Helpers

template<typename T >
class	BD_Shape

template<typename T >
class	Octagonal_Shape

template<typename T >
class	Linear_System

template<typename T >
class	Box

template<typename T >
class	Expression_Adapter

template<typename T >
class	Expression_Hide_Inhomo

template<typename T >
class	Expression_Hide_Last

Linear_Expression	operator+ (const Linear_Expression &e1, const Linear_Expression &e2)

Linear_Expression	operator+ (Coefficient_traits::const_reference n, const Linear_Expression &e)

Linear_Expression	operator+ (const Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression	operator+ (Variable v, const Linear_Expression &e)

Linear_Expression	operator+ (Variable v, Variable w)

Linear_Expression	operator- (const Linear_Expression &e)

Linear_Expression	operator- (const Linear_Expression &e1, const Linear_Expression &e2)

Linear_Expression	operator- (Variable v, Variable w)

Linear_Expression	operator- (Coefficient_traits::const_reference n, const Linear_Expression &e)

Linear_Expression	operator- (const Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression	operator- (Variable v, const Linear_Expression &e)

Linear_Expression	operator- (const Linear_Expression &e, Variable v)

Linear_Expression	operator* (Coefficient_traits::const_reference n, const Linear_Expression &e)

Linear_Expression	operator* (const Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression &	operator+= (Linear_Expression &e1, const Linear_Expression &e2)

Linear_Expression &	operator+= (Linear_Expression &e, Variable v)

Linear_Expression &	operator+= (Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression &	operator-= (Linear_Expression &e1, const Linear_Expression &e2)

Linear_Expression &	operator-= (Linear_Expression &e, Variable v)

Linear_Expression &	operator-= (Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression &	operator*= (Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression &	operator/= (Linear_Expression &e, Coefficient_traits::const_reference n)

void	neg_assign (Linear_Expression &e)

Linear_Expression &	add_mul_assign (Linear_Expression &e, Coefficient_traits::const_reference n, Variable v)

Linear_Expression &	sub_mul_assign (Linear_Expression &e, Coefficient_traits::const_reference n, Variable v)

void	add_mul_assign (Linear_Expression &e1, Coefficient_traits::const_reference factor, const Linear_Expression &e2)

void	sub_mul_assign (Linear_Expression &e1, Coefficient_traits::const_reference factor, const Linear_Expression &e2)

int	compare (const Linear_Expression &x, const Linear_Expression &y)

std::ostream &	Parma_Polyhedra_Library::IO_Operators::operator<< (std::ostream &s, const Linear_Expression &e)

Related Functions
(Note that these are not member functions.)
Linear_Expression	operator+ (const Linear_Expression &e1, const Linear_Expression &e2)
	Returns the linear expression `e1` + `e2`. More...

Linear_Expression	operator+ (Variable v, Variable w)
	Returns the linear expression `v` + `w`. More...

Linear_Expression	operator+ (Variable v, const Linear_Expression &e)
	Returns the linear expression `v` + `e`. More...

Linear_Expression	operator+ (const Linear_Expression &e, Variable v)
	Returns the linear expression `e` + `v`. More...

Linear_Expression	operator+ (Coefficient_traits::const_reference n, const Linear_Expression &e)
	Returns the linear expression `n` + `e`. More...

Linear_Expression	operator+ (const Linear_Expression &e, Coefficient_traits::const_reference n)
	Returns the linear expression `e` + `n`. More...

Linear_Expression	operator+ (const Linear_Expression &e)
	Returns the linear expression `e`. More...

Linear_Expression	operator- (const Linear_Expression &e)
	Returns the linear expression - `e`. More...

Linear_Expression	operator- (const Linear_Expression &e1, const Linear_Expression &e2)
	Returns the linear expression `e1` - `e2`. More...

Linear_Expression	operator- (Variable v, Variable w)
	Returns the linear expression `v` - `w`. More...

Linear_Expression	operator- (Variable v, const Linear_Expression &e)
	Returns the linear expression `v` - `e`. More...

Linear_Expression	operator- (const Linear_Expression &e, Variable v)
	Returns the linear expression `e` - `v`. More...

Linear_Expression	operator- (Coefficient_traits::const_reference n, const Linear_Expression &e)
	Returns the linear expression `n` - `e`. More...

Linear_Expression	operator- (const Linear_Expression &e, Coefficient_traits::const_reference n)
	Returns the linear expression `e` - `n`. More...

Linear_Expression	operator* (Coefficient_traits::const_reference n, const Linear_Expression &e)
	Returns the linear expression `n` * `e`. More...

Linear_Expression	operator* (const Linear_Expression &e, Coefficient_traits::const_reference n)
	Returns the linear expression `e` * `n`. More...

Linear_Expression &	operator+= (Linear_Expression &e1, const Linear_Expression &e2)
	Returns the linear expression `e1` + `e2` and assigns it to `e1`. More...

Linear_Expression &	operator+= (Linear_Expression &e, Variable v)
	Returns the linear expression `e` + `v` and assigns it to `e`. More...

Linear_Expression &	operator+= (Linear_Expression &e, Coefficient_traits::const_reference n)
	Returns the linear expression `e` + `n` and assigns it to `e`. More...

Linear_Expression &	operator-= (Linear_Expression &e1, const Linear_Expression &e2)
	Returns the linear expression `e1` - `e2` and assigns it to `e1`. More...

Linear_Expression &	operator-= (Linear_Expression &e, Variable v)
	Returns the linear expression `e` - `v` and assigns it to `e`. More...

Linear_Expression &	operator-= (Linear_Expression &e, Coefficient_traits::const_reference n)
	Returns the linear expression `e` - `n` and assigns it to `e`. More...

Linear_Expression &	operator*= (Linear_Expression &e, Coefficient_traits::const_reference n)
	Returns the linear expression `n` * `e` and assigns it to `e`. More...

Linear_Expression &	operator/= (Linear_Expression &e, Coefficient_traits::const_reference n)
	Returns the linear expression `n` / `e` and assigns it to `e`. More...

void	neg_assign (Linear_Expression &e)
	Assigns to `e` its own negation. More...

Linear_Expression &	add_mul_assign (Linear_Expression &e, Coefficient_traits::const_reference n, Variable v)
	Returns the linear expression `e` + `n` * `v` and assigns it to `e`. More...

void	add_mul_assign (Linear_Expression &e1, Coefficient_traits::const_reference factor, const Linear_Expression &e2)
	Sums `e2` multiplied by `factor` into `e1`. More...

void	sub_mul_assign (Linear_Expression &e1, Coefficient_traits::const_reference factor, const Linear_Expression &e2)
	Subtracts `e2` multiplied by `factor` from `e1`. More...

Linear_Expression &	sub_mul_assign (Linear_Expression &e, Coefficient_traits::const_reference n, Variable v)
	Returns the linear expression `e` - `n` * `v` and assigns it to `e`. More...

int	compare (const Linear_Expression &x, const Linear_Expression &y)
	The basic comparison function. More...

std::ostream &	operator<< (std::ostream &s, const Linear_Expression &e)
	Output operator. More...

void	swap (Linear_Expression &x, Linear_Expression &y)
	Swaps `x` with `y`. More...

Linear_Expression	operator+ (const Linear_Expression &e)

Linear_Expression	operator+ (const Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression	operator+ (const Linear_Expression &e, const Variable v)

Linear_Expression	operator- (const Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression	operator- (const Variable v, const Variable w)

Linear_Expression	operator* (const Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression &	operator+= (Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression &	operator-= (Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression	operator+ (const Linear_Expression &e1, const Linear_Expression &e2)

Linear_Expression	operator+ (const Variable v, const Linear_Expression &e)

Linear_Expression	operator+ (Coefficient_traits::const_reference n, const Linear_Expression &e)

Linear_Expression	operator+ (const Variable v, const Variable w)

Linear_Expression	operator- (const Linear_Expression &e)

Linear_Expression	operator- (const Linear_Expression &e1, const Linear_Expression &e2)

Linear_Expression	operator- (const Variable v, const Linear_Expression &e)

Linear_Expression	operator- (const Linear_Expression &e, const Variable v)

Linear_Expression	operator- (Coefficient_traits::const_reference n, const Linear_Expression &e)

Linear_Expression	operator* (Coefficient_traits::const_reference n, const Linear_Expression &e)

Linear_Expression &	operator+= (Linear_Expression &e1, const Linear_Expression &e2)

Linear_Expression &	operator+= (Linear_Expression &e, const Variable v)

Linear_Expression &	operator-= (Linear_Expression &e1, const Linear_Expression &e2)

Linear_Expression &	operator-= (Linear_Expression &e, const Variable v)

Linear_Expression &	operator*= (Linear_Expression &e, Coefficient_traits::const_reference n)

Linear_Expression &	operator/= (Linear_Expression &e, Coefficient_traits::const_reference n)

void	neg_assign (Linear_Expression &e)

Linear_Expression &	add_mul_assign (Linear_Expression &e, Coefficient_traits::const_reference n, const Variable v)

Linear_Expression &	sub_mul_assign (Linear_Expression &e, Coefficient_traits::const_reference n, const Variable v)

std::ostream &	operator<< (std::ostream &s, const Linear_Expression &e)

void	swap (Linear_Expression &x, Linear_Expression &y)

Detailed Description

A linear expression.

An object of the class Linear_Expression represents the linear expression

$\sum_{i=0}^{n-1} a_i x_i + b$

where $n$ is the dimension of the vector space, each $a_i$ is the integer coefficient of the $i$ -th variable $x_i$ and $b$ is the integer for the inhomogeneous term.

How to build a linear expression.

Linear expressions are the basic blocks for defining both constraints (i.e., linear equalities or inequalities) and generators (i.e., lines, rays, points and closure points). A full set of functions is defined to provide a convenient interface for building complex linear expressions starting from simpler ones and from objects of the classes Variable and Coefficient: available operators include unary negation, binary addition and subtraction, as well as multiplication by a Coefficient. The space dimension of a linear expression is defined as the maximum space dimension of the arguments used to build it: in particular, the space dimension of a Variable x is defined as x.id()+1, whereas all the objects of the class Coefficient have space dimension zero.

Example: The following code builds the linear expression , having space dimension :
Linear_Expression e = 4*x - 2*y - z + 14;

Another way to build the same linear expression is:
Linear_Expression e1 = 4*x;

Linear_Expression e2 = 2*y;

Linear_Expression e3 = z;

Linear_Expression e = Linear_Expression(14);

e += e1 - e2 - e3;

Note that e1, e2 and e3 have space dimension 1, 2 and 3, respectively; also, in the fourth line of code, e is created with space dimension zero and then extended to space dimension 3 in the fifth line.

Definition at line 289 of file Linear_Expression_defs.hh.

Member Typedef Documentation

typedef const Linear_Expression& Parma_Polyhedra_Library::Linear_Expression::const_reference

Definition at line 307 of file Linear_Expression_defs.hh.

typedef Linear_Expression Parma_Polyhedra_Library::Linear_Expression::raw_type

Definition at line 308 of file Linear_Expression_defs.hh.

Constructor & Destructor Documentation

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression ( Representation r = default_representation )

explicit

Default constructor: returns a copy of Linear_Expression::zero().

Definition at line 54 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::DENSE, and Parma_Polyhedra_Library::SPARSE.

                                                         {
   switch (r) {
   case DENSE:
     impl = new Linear_Expression_Impl<Dense_Row>();
     break;
   case SPARSE:
     impl = new Linear_Expression_Impl<Sparse_Row>();
     break;
   default:
     PPL_UNREACHABLE;
   }
 }

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression ( const Linear_Expression & e )

Ordinary copy constructor.

Note: The new expression will have the same representation as e (not necessarily the default_representation).

Definition at line 81 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::DENSE, impl, representation(), and Parma_Polyhedra_Library::SPARSE.

                                                                   {
   switch (e.representation()) {
   case DENSE:
     impl = new Linear_Expression_Impl<Dense_Row>(*e.impl);
     break;
   case SPARSE:
     impl = new Linear_Expression_Impl<Sparse_Row>(*e.impl);
     break;
   default:
     PPL_UNREACHABLE;
   }
 }

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	const Linear_Expression &	e,
		Representation	r
	)

Copy constructor that takes also a Representation.

Definition at line 94 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::DENSE, impl, and Parma_Polyhedra_Library::SPARSE.

                                                             {
   switch (r) {
   case DENSE:
     impl = new Linear_Expression_Impl<Dense_Row>(*e.impl);
     break;
   case SPARSE:
     impl = new Linear_Expression_Impl<Sparse_Row>(*e.impl);
     break;
   default:
     PPL_UNREACHABLE;
   }
 }

template<typename LE_Adapter >

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	const LE_Adapter &	e,
		typename Enable_If< Is_Same_Or_Derived< Expression_Adapter_Base, LE_Adapter >::value, void * >::type	= `0`
	)

inlineexplicit

Copy constructor from a linear expression adapter.

Note: The new expression will have the same representation as e (not necessarily the default_representation).

Definition at line 727 of file Linear_Expression_inlines.hh.

References add_mul_assign, impl, set_space_dimension(), Parma_Polyhedra_Library::swap(), and swap().

   : impl(NULL) {
   Linear_Expression tmp(e.representation());
   tmp.set_space_dimension(e.space_dimension());
   tmp.set_inhomogeneous_term(e.inhomogeneous_term());
   for (typename LE_Adapter::const_iterator i = e.begin(),
          i_end = e.end(); i != i_end; ++i) {
     add_mul_assign(tmp, *i, i.variable());
   }
   using std::swap;
   swap(impl, tmp.impl);
 }

template<typename LE_Adapter >

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	const LE_Adapter &	e,
		Representation	r,
		typename Enable_If< Is_Same_Or_Derived< Expression_Adapter_Base, LE_Adapter >::value, void * >::type	= `0`
	)

inline

Copy constructor from a linear expression adapter that takes a Representation.

Definition at line 746 of file Linear_Expression_inlines.hh.

References add_mul_assign, impl, set_inhomogeneous_term(), set_space_dimension(), Parma_Polyhedra_Library::swap(), and swap().

   : impl(NULL) {
   Linear_Expression tmp(r);
   tmp.set_space_dimension(e.space_dimension());
   tmp.set_inhomogeneous_term(e.inhomogeneous_term());
   for (typename LE_Adapter::const_iterator i = e.begin(),
          i_end = e.end(); i != i_end; ++i) {
     add_mul_assign(tmp, *i, i.variable());
   }
   using std::swap;
   swap(impl, tmp.impl);
 }

template<typename LE_Adapter >

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	const LE_Adapter &	e,
		dimension_type	space_dim,
		typename Enable_If< Is_Same_Or_Derived< Expression_Adapter_Base, LE_Adapter >::value, void * >::type	= `0`
	)

inlineexplicit

Copy constructor from a linear expression adapter that takes a space dimension.

Note: The new expression will have the same representation as e (not necessarily default_representation).

Definition at line 766 of file Linear_Expression_inlines.hh.

References add_mul_assign, impl, set_space_dimension(), Parma_Polyhedra_Library::swap(), and swap().

   : impl(NULL) {
   Linear_Expression tmp(e.representation());
   tmp.set_space_dimension(space_dim);
   tmp.set_inhomogeneous_term(e.inhomogeneous_term());
   typedef typename LE_Adapter::const_iterator itr_t;
   itr_t i_end;
   if (space_dim <= e.space_dimension()) {
     i_end = e.lower_bound(Variable(space_dim));
   }
   else {
     i_end = e.end();
   }
   for (itr_t i = e.begin(); i != i_end; ++i) {
     add_mul_assign(tmp, *i, i.variable());
   }
   using std::swap;
   swap(impl, tmp.impl);
 }

template<typename LE_Adapter >

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	const LE_Adapter &	e,
		dimension_type	space_dim,
		Representation	r,
		typename Enable_If< Is_Same_Or_Derived< Expression_Adapter_Base, LE_Adapter >::value, void * >::type	= `0`
	)

inline

Copy constructor from a linear expression adapter that takes a space dimension and a Representation.

Definition at line 793 of file Linear_Expression_inlines.hh.

References add_mul_assign, impl, set_inhomogeneous_term(), set_space_dimension(), Parma_Polyhedra_Library::swap(), and swap().

   : impl(NULL) {
   Linear_Expression tmp(r);
   tmp.set_space_dimension(space_dim);
   tmp.set_inhomogeneous_term(e.inhomogeneous_term());
   typedef typename LE_Adapter::const_iterator itr_t;
   itr_t i_end;
   if (space_dim <= e.space_dimension()) {
     i_end = e.lower_bound(Variable(space_dim));
   }
   else {
     i_end = e.end();
   }
   for (itr_t i = e.begin(); i != i_end; ++i) {
     add_mul_assign(tmp, *i, i.variable());
   }
   using std::swap;
   swap(impl, tmp.impl);
 }

Parma_Polyhedra_Library::Linear_Expression::~Linear_Expression ( )

inline

Destructor.

Definition at line 39 of file Linear_Expression_inlines.hh.

References impl.

                                       {
   delete impl;
 }

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	Coefficient_traits::const_reference	n,
		Representation	r = `default_representation`
	)

explicit

Builds the linear expression corresponding to the inhomogeneous term n.

Definition at line 137 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::DENSE, and Parma_Polyhedra_Library::SPARSE.

                                                             {
   switch (r) {
   case DENSE:
     impl = new Linear_Expression_Impl<Dense_Row>(n);
     break;
   case SPARSE:
     impl = new Linear_Expression_Impl<Sparse_Row>(n);
     break;
   default:
     PPL_UNREACHABLE;
   }
 }

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	Variable	v,
		Representation	r = `default_representation`
	)

Builds the linear expression corresponding to the variable v.

Exceptions

std::length_error Thrown if the space dimension of v exceeds Linear_Expression::max_space_dimension().

Definition at line 151 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::DENSE, and Parma_Polyhedra_Library::SPARSE.

                                                                           {
   switch (r) {
   case DENSE:
     impl = new Linear_Expression_Impl<Dense_Row>(v);
     break;
   case SPARSE:
     impl = new Linear_Expression_Impl<Sparse_Row>(v);
     break;
   default:
     PPL_UNREACHABLE;
     break;
   }
 }

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	const Linear_Expression &	e,
		dimension_type	space_dim
	)

Copy constructor with a specified space dimension.

Definition at line 108 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::DENSE, impl, representation(), and Parma_Polyhedra_Library::SPARSE.

                                                                     {
   switch (e.representation()) {
   case DENSE:
     impl = new Linear_Expression_Impl<Dense_Row>(*e.impl, space_dim);
     break;
   case SPARSE:
     impl = new Linear_Expression_Impl<Sparse_Row>(*e.impl, space_dim);
     break;
   default:
     PPL_UNREACHABLE;
   }
 }

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	const Linear_Expression &	e,
		dimension_type	space_dim,
		Representation	r
	)

Copy constructor with a specified space dimension and representation.

Definition at line 122 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::DENSE, impl, and Parma_Polyhedra_Library::SPARSE.

                                                             {
   switch (r) {
   case DENSE:
     impl = new Linear_Expression_Impl<Dense_Row>(*e.impl, space_dim);
     break;
   case SPARSE:
     impl = new Linear_Expression_Impl<Sparse_Row>(*e.impl, space_dim);
     break;
   default:
     PPL_UNREACHABLE;
   }
 }

Parma_Polyhedra_Library::Linear_Expression::Linear_Expression	(	dimension_type	space_dim,
		bool	x,
		Representation	r = `default_representation`
	)

private

Implementation sizing constructor.

The bool parameter is just to avoid problems with the constructor Linear_Expression(Coefficient_traits::const_reference n).

Definition at line 67 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::DENSE, and Parma_Polyhedra_Library::SPARSE.

                                                             {
   switch (r) {
   case DENSE:
     impl = new Linear_Expression_Impl<Dense_Row>(space_dim, x);
     break;
   case SPARSE:
     impl = new Linear_Expression_Impl<Sparse_Row>(space_dim, x);
     break;
   default:
     PPL_UNREACHABLE;
   }
 }

Member Function Documentation

bool Parma_Polyhedra_Library::Linear_Expression::all_homogeneous_terms_are_zero ( ) const

inline

Returns true if and only if all the homogeneous terms of *this are $0$ .

Definition at line 96 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::all_homogeneous_terms_are_zero(), and impl.

                                                         {
   return impl->all_homogeneous_terms_are_zero();
 }

bool Parma_Polyhedra_Library::Linear_Expression::all_zeroes ( const Variables_Set & vars ) const

inline

Returns true if the coefficient of each variable in vars[i] is $0$ .

Definition at line 476 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::all_zeroes(), and impl.

                                                              {
   return impl->all_zeroes(vars);
 }

bool Parma_Polyhedra_Library::Linear_Expression::all_zeroes	(	dimension_type	start,
		dimension_type	end
	)		const

inlineprivate

Returns true if (*this)[i] is $0$ , for each i in [start, end).

Definition at line 437 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::all_zeroes(), and impl.

                                                                             {
   return impl->all_zeroes(start, end);
 }

bool Parma_Polyhedra_Library::Linear_Expression::all_zeroes_except	(	const Variables_Set &	vars,
		dimension_type	start,
		dimension_type	end
	)		const

inlineprivate

Returns true if all coefficients in [start,end), except those corresponding to variables in vars, are zero.

Definition at line 481 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::all_zeroes_except(), and impl.

                                                                {
   return impl->all_zeroes_except(vars, start, end);
 }

void Parma_Polyhedra_Library::Linear_Expression::ascii_dump ( ) const

Writes to std::cerr an ASCII representation of *this.

Referenced by Parma_Polyhedra_Library::PIP_Tree_Node::Artificial_Parameter::ascii_dump(), and Parma_Polyhedra_Library::Generator::ascii_dump().

void Parma_Polyhedra_Library::Linear_Expression::ascii_dump ( std::ostream & s ) const

inline

Writes to s an ASCII representation of *this.

Definition at line 205 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::ascii_dump(), and impl.

                                                  {
   impl->ascii_dump(s);
 }

bool Parma_Polyhedra_Library::Linear_Expression::ascii_load ( std::istream & s )

inline

Loads from s an ASCII representation (as produced by ascii_dump(std::ostream&) const) and sets *this accordingly. Returns true if successful, false otherwise.

Definition at line 210 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::ascii_load(), and impl.

Referenced by Parma_Polyhedra_Library::PIP_Tree_Node::Artificial_Parameter::ascii_load(), Parma_Polyhedra_Library::PIP_Solution_Node::ascii_load(), and Parma_Polyhedra_Library::Generator::ascii_load().

                                            {
   return impl->ascii_load(s);
 }

Linear_Expression::const_iterator Parma_Polyhedra_Library::Linear_Expression::begin ( ) const

inline

Returns an iterator that points to the first nonzero coefficient in the expression.

Definition at line 708 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::begin(), and impl.

               {
   return const_iterator(impl->begin());
 }

Coefficient_traits::const_reference Parma_Polyhedra_Library::Linear_Expression::coefficient ( Variable v ) const

inline

Returns the coefficient of v in *this.

Definition at line 59 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::coefficient(), and impl.

                                                {
   return impl->coefficient(v);
 }

Linear_Expression::const_iterator Parma_Polyhedra_Library::Linear_Expression::end ( ) const

inline

Returns an iterator that points to the last nonzero coefficient in the expression.

Definition at line 714 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::end(), and impl.

             {
   return const_iterator(impl->end());
 }

void Parma_Polyhedra_Library::Linear_Expression::exact_div_assign	(	Coefficient_traits::const_reference	c,
		dimension_type	start,
		dimension_type	end
	)

inlineprivate

Definition at line 453 of file Linear_Expression_inlines.hh.

Referenced by Parma_Polyhedra_Library::PIP_Tree_Node::Artificial_Parameter::Artificial_Parameter(), Parma_Polyhedra_Library::Grid::conversion(), and Parma_Polyhedra_Library::Polyhedron::drop_some_non_integer_points().

                                                              {
   impl->exact_div_assign(c, start, end);
 }

memory_size_type Parma_Polyhedra_Library::Linear_Expression::external_memory_in_bytes ( ) const

inline

Returns the size in bytes of the memory managed by *this.

Definition at line 107 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::total_memory_in_bytes().

Referenced by Parma_Polyhedra_Library::Congruence::external_memory_in_bytes(), Parma_Polyhedra_Library::PIP_Tree_Node::Artificial_Parameter::external_memory_in_bytes(), Parma_Polyhedra_Library::Constraint::external_memory_in_bytes(), Parma_Polyhedra_Library::MIP_Problem::external_memory_in_bytes(), Parma_Polyhedra_Library::Grid_Generator::external_memory_in_bytes(), Parma_Polyhedra_Library::Generator::external_memory_in_bytes(), and total_memory_in_bytes().

                                                   {
   return impl->total_memory_in_bytes();
 }

void Parma_Polyhedra_Library::Linear_Expression::finalize ( )

static

Finalizes the class.

Definition at line 48 of file Linear_Expression.cc.

Referenced by Parma_Polyhedra_Library::Init::~Init().

                                {
   PPL_ASSERT(zero_p != 0);
   delete zero_p;
   zero_p = 0;
 }

dimension_type Parma_Polyhedra_Library::Linear_Expression::first_nonzero	(	dimension_type	first,
		dimension_type	last
	)		const

inlineprivate

Returns the index of the first nonzero element, or last if there are no nonzero elements, considering only elements in [first,last).

Definition at line 520 of file Linear_Expression_inlines.hh.

Referenced by Parma_Polyhedra_Library::Box< ITV >::generalized_affine_image().

                                                                {
   return impl->first_nonzero(first, last);
 }

Coefficient Parma_Polyhedra_Library::Linear_Expression::gcd	(	dimension_type	start,
		dimension_type	end
	)		const

inlineprivate

Returns the gcd of the nonzero coefficients in [start,end). If all the coefficients in this range are 0 returns 0.

Definition at line 447 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::gcd(), and impl.

Referenced by Parma_Polyhedra_Library::PIP_Tree_Node::Artificial_Parameter::Artificial_Parameter().

                                                                      {
   return impl->gcd(start, end);
 }

Coefficient_traits::const_reference Parma_Polyhedra_Library::Linear_Expression::get ( dimension_type i ) const

inlineprivate

Returns the i-th coefficient.

Definition at line 415 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::get(), and impl.

                                              {
   return impl->get(i);
 }

Coefficient_traits::const_reference Parma_Polyhedra_Library::Linear_Expression::get ( Variable v ) const

inlineprivate

Returns the coefficient of v.

Definition at line 426 of file Linear_Expression_inlines.hh.

References Parma_Polyhedra_Library::Linear_Expression_Interface::get(), impl, and Parma_Polyhedra_Library::Variable::space_dimension().

                                        {
   return impl->get(v.space_dimension());
 }

void Parma_Polyhedra_Library::Linear_Expression::get_row ( Dense_Row & r ) const

inlineprivate

Sets r to a copy of the row that implements *this.

Definition at line 554 of file Linear_Expression_inlines.hh.

                             {
   return impl->get_row(r);
 }

void Parma_Polyhedra_Library::Linear_Expression::get_row ( Sparse_Row & r ) const

inlineprivate

Sets r to a copy of the row that implements *this.

Definition at line 560 of file Linear_Expression_inlines.hh.

                              {
   return impl->get_row(r);
 }

void Parma_Polyhedra_Library::Linear_Expression::has_a_free_dimension_helper ( std::set< dimension_type > & x ) const

inlineprivate

Removes from the set x all the indexes of nonzero elements of *this.

Definition at line 532 of file Linear_Expression_inlines.hh.

                                                              {
   return impl->has_a_free_dimension_helper(x);
 }

bool Parma_Polyhedra_Library::Linear_Expression::have_a_common_variable	(	const Linear_Expression &	x,
		Variable	first,
		Variable	last
	)		const

inlineprivate

Returns true if there is a variable from index first (included) to index last (excluded) whose coefficient is nonzero in both *this and x.

Definition at line 616 of file Linear_Expression_inlines.hh.

References impl.

                                                               {
   return impl->have_a_common_variable(*(x.impl), first, last);
 }

Coefficient_traits::const_reference Parma_Polyhedra_Library::Linear_Expression::inhomogeneous_term ( ) const

inline

Returns the inhomogeneous term of *this.

Definition at line 70 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::inhomogeneous_term().

                                             {
   return impl->inhomogeneous_term();
 }

void Parma_Polyhedra_Library::Linear_Expression::initialize ( )

static

Initializes the class.

Definition at line 42 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::Coefficient_zero().

Referenced by Parma_Polyhedra_Library::Init::Init().

                                  {
   PPL_ASSERT(zero_p == 0);
   zero_p = new Linear_Expression(Coefficient_zero());
 }

bool Parma_Polyhedra_Library::Linear_Expression::is_equal_to ( const Linear_Expression & x ) const

inline

Returns true if *this is equal to x. Note that (*this == x) has a completely different meaning.

Definition at line 592 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::is_equal_to().

Referenced by Parma_Polyhedra_Library::Constraint::is_equivalent_to(), Parma_Polyhedra_Library::Generator::is_equivalent_to(), Parma_Polyhedra_Library::Generator::is_matching_closure_point(), Parma_Polyhedra_Library::Congruence::operator==(), and Parma_Polyhedra_Library::PIP_Tree_Node::Artificial_Parameter::operator==().

                                                                {
   return impl->is_equal_to(*x.impl);
 }

bool Parma_Polyhedra_Library::Linear_Expression::is_equal_to	(	const Linear_Expression &	x,
		dimension_type	start,
		dimension_type	end
	)		const

inlineprivate

Returns true if (*this)[i] is equal to x[i], for each i in [start,end).

Definition at line 538 of file Linear_Expression_inlines.hh.

References impl.

                                                               {
   return impl->is_equal_to(*(x.impl), start, end);
 }

bool Parma_Polyhedra_Library::Linear_Expression::is_equal_to	(	const Linear_Expression &	x,
		Coefficient_traits::const_reference	c1,
		Coefficient_traits::const_reference	c2,
		dimension_type	start,
		dimension_type	end
	)		const

inlineprivate

Returns true if (*this)[i]*c1 is equal to x[i]*c2, for each i in [start,end).

Definition at line 545 of file Linear_Expression_inlines.hh.

References impl.

                                                               {
   return impl->is_equal_to(*(x.impl), c1, c2, start, end);
 }

bool Parma_Polyhedra_Library::Linear_Expression::is_zero ( ) const

inline

Returns true if and only if *this is $0$ .

Definition at line 91 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::is_zero().

                                  {
   return impl->is_zero();
 }

dimension_type Parma_Polyhedra_Library::Linear_Expression::last_nonzero ( ) const

inlineprivate

Returns the index of the last nonzero element, or 0 if there are no nonzero elements.

Definition at line 488 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::last_nonzero().

                                       {
   return impl->last_nonzero();
 }

dimension_type Parma_Polyhedra_Library::Linear_Expression::last_nonzero	(	dimension_type	first,
		dimension_type	last
	)		const

inlineprivate

Returns the index of the last nonzero element in [first,last), or last if there are no nonzero elements.

Definition at line 526 of file Linear_Expression_inlines.hh.

                                                               {
   return impl->last_nonzero(first, last);
 }

void Parma_Polyhedra_Library::Linear_Expression::linear_combine	(	const Linear_Expression &	y,
		Variable	v
	)

Linearly combines *this with y so that the coefficient of v is 0.

Parameters

y	The expression that will be combined with `*this` object;
v	The variable whose coefficient has to become .

Computes a linear combination of *this and y having the coefficient of variable v equal to $0$ . Then it assigns the resulting expression to *this.

*this and y must have the same space dimension.

void Parma_Polyhedra_Library::Linear_Expression::linear_combine	(	const Linear_Expression &	y,
		Coefficient_traits::const_reference	c1,
		Coefficient_traits::const_reference	c2
	)

inline

Equivalent to *this = *this * c1 + y * c2, but assumes that c1 and c2 are not 0.

Definition at line 572 of file Linear_Expression_inlines.hh.

References impl.

                                                        {
   impl->linear_combine(*y.impl, c1, c2);
 }

void Parma_Polyhedra_Library::Linear_Expression::linear_combine	(	const Linear_Expression &	y,
		dimension_type	i
	)

inlineprivate

Linearly combines *this with y so that the coefficient of v is 0.

Parameters

y	The expression that will be combined with `*this` object;
i	The index of the coefficient that has to become .

Computes a linear combination of *this and y having the i-th coefficient equal to $0$ . Then it assigns the resulting expression to *this.

*this and y must have the same space dimension.

Definition at line 566 of file Linear_Expression_inlines.hh.

References impl.

                                                              {
   impl->linear_combine(*y.impl, i);
 }

void Parma_Polyhedra_Library::Linear_Expression::linear_combine	(	const Linear_Expression &	y,
		Coefficient_traits::const_reference	c1,
		Coefficient_traits::const_reference	c2,
		dimension_type	start,
		dimension_type	end
	)

inlineprivate

Equivalent to (*this)[i] = (*this)[i] * c1 + y[i] * c2, for each i in [start, end). It assumes that c1 and c2 are nonzero.

Definition at line 597 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::linear_combine().

                                                       {
   impl->linear_combine(*y.impl, c1, c2, start, end);
 }

void Parma_Polyhedra_Library::Linear_Expression::linear_combine_lax	(	const Linear_Expression &	y,
		Coefficient_traits::const_reference	c1,
		Coefficient_traits::const_reference	c2
	)

inline

Equivalent to *this = *this * c1 + y * c2. c1 and c2 may be 0.

Definition at line 580 of file Linear_Expression_inlines.hh.

References impl.

Referenced by Parma_Polyhedra_Library::Grid::reduce_pc_with_pc().

                                                            {
   impl->linear_combine_lax(*y.impl, c1, c2);
 }

void Parma_Polyhedra_Library::Linear_Expression::linear_combine_lax	(	const Linear_Expression &	y,
		Coefficient_traits::const_reference	c1,
		Coefficient_traits::const_reference	c2,
		dimension_type	start,
		dimension_type	end
	)

inlineprivate

Equivalent to (*this)[i] = (*this)[i] * c1 + y[i] * c2, for each i in [start, end). c1 and c2 may be zero.

Definition at line 606 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::linear_combine_lax().

                                                           {
   impl->linear_combine_lax(*y.impl, c1, c2, start, end);
 }

Linear_Expression::const_iterator Parma_Polyhedra_Library::Linear_Expression::lower_bound ( Variable v ) const

inline

Returns an iterator that points to the first nonzero coefficient of a variable bigger than or equal to v.

Definition at line 720 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::lower_bound().

                               {
   return const_iterator(impl->lower_bound(v));
 }

void Parma_Polyhedra_Library::Linear_Expression::m_swap ( Linear_Expression & y )

inline

Swaps *this with y.

Definition at line 194 of file Linear_Expression_inlines.hh.

References impl, Parma_Polyhedra_Library::swap(), and swap().

Referenced by Parma_Polyhedra_Library::PIP_Tree_Node::Artificial_Parameter::m_swap(), and swap().

                                               {
   using std::swap;
   swap(impl, y.impl);
 }

PPL::dimension_type Parma_Polyhedra_Library::Linear_Expression::max_space_dimension ( )

static

Returns the maximum space dimension a Linear_Expression can handle.

Definition at line 35 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::Dense_Row::max_size().

Referenced by Parma_Polyhedra_Library::Congruence::max_space_dimension(), Parma_Polyhedra_Library::Constraint::max_space_dimension(), Parma_Polyhedra_Library::Grid_Generator::max_space_dimension(), Parma_Polyhedra_Library::Generator::max_space_dimension(), operator+(), and operator-().

                                           {
   return Dense_Row::max_size() - 1;
 }

void Parma_Polyhedra_Library::Linear_Expression::mul_assign	(	Coefficient_traits::const_reference	n,
		dimension_type	start,
		dimension_type	end
	)

inlineprivate

Equivalent to (*this)[i] *= n, for each i in [start, end).

Definition at line 460 of file Linear_Expression_inlines.hh.

Referenced by Parma_Polyhedra_Library::Grid::reduce_parameter_with_line().

                                                        {
   impl->mul_assign(c, start, end);
 }

void Parma_Polyhedra_Library::Linear_Expression::negate	(	dimension_type	first,
		dimension_type	last
	)

inlineprivate

Negates the elements from index first (included) to index last (excluded).

Definition at line 471 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::negate().

Referenced by operator-(), and Parma_Polyhedra_Library::Grid::simplify().

                                                                    {
   impl->negate(first, last);
 }

void Parma_Polyhedra_Library::Linear_Expression::normalize ( )

inline

Normalizes the modulo of the coefficients and of the inhomogeneous term so that they are mutually prime.

Computes the Greatest Common Divisor (GCD) among the coefficients and the inhomogeneous term and normalizes them by the GCD itself.

Definition at line 200 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::normalize().

                              {
   impl->normalize();
 }

dimension_type Parma_Polyhedra_Library::Linear_Expression::num_zeroes	(	dimension_type	start,
		dimension_type	end
	)		const

inlineprivate

Returns the number of zero coefficient in [start, end).

Definition at line 442 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::num_zeroes().

                                                                             {
   return impl->num_zeroes(start, end);
 }

bool Parma_Polyhedra_Library::Linear_Expression::OK ( ) const

Checks if all the invariants are satisfied.

Definition at line 177 of file Linear_Expression.cc.

References OK().

Referenced by OK().

                                {
   return impl->OK();
 }

Linear_Expression & Parma_Polyhedra_Library::Linear_Expression::operator= ( const Linear_Expression & e )

inline

Assignment operator.

Definition at line 32 of file Linear_Expression_inlines.hh.

References swap().

                                                        {
   Linear_Expression tmp = e;
   swap(*this, tmp);
   return *this;
 }

void Parma_Polyhedra_Library::Linear_Expression::permute_space_dimensions ( const std::vector< Variable > & cycle )

inline

Permutes the space dimensions of the expression.

Parameters

cycle A vector representing a cycle of the permutation according to which the space dimensions must be rearranged.

The cycle vector represents a cycle of a permutation of space dimensions. For example, the permutation $\{ x_1 \mapsto x_2, x_2 \mapsto x_3, x_3 \mapsto x_1 \}$ can be represented by the vector containing $ x_1, x_2, x_3 $ .

Definition at line 220 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::permute_space_dimensions().

Referenced by Parma_Polyhedra_Library::Congruence::permute_space_dimensions().

                                                                             {
   impl->permute_space_dimensions(cycle);
 }

void Parma_Polyhedra_Library::Linear_Expression::print ( ) const

Prints *this to std::cerr using operator<<.

void Parma_Polyhedra_Library::Linear_Expression::remove_space_dimensions ( const Variables_Set & vars )

inline

Removes all the specified dimensions from the expression.

The space dimension of the variable with the highest space dimension in vars must be at most the space dimension of this.

Definition at line 215 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::remove_space_dimensions().

Referenced by Parma_Polyhedra_Library::Constraint::remove_space_dimensions().

                                                                     {
   impl->remove_space_dimensions(vars);
 }

Representation Parma_Polyhedra_Library::Linear_Expression::representation ( ) const

inline

Returns the current representation of *this.

Definition at line 44 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::representation().

Referenced by Linear_Expression(), Parma_Polyhedra_Library::Congruence::representation(), Parma_Polyhedra_Library::Constraint::representation(), Parma_Polyhedra_Library::Grid_Generator::representation(), and Parma_Polyhedra_Library::Generator::representation().

                                         {
   return impl->representation();
 }

void Parma_Polyhedra_Library::Linear_Expression::scalar_product_assign	(	Coefficient &	result,
		const Linear_Expression &	y
	)		const

inlineprivate

Sets results to the sum of (*this)[i]*y[i], for each i.

Definition at line 494 of file Linear_Expression_inlines.hh.

Referenced by Parma_Polyhedra_Library::Scalar_Products::assign(), Parma_Polyhedra_Library::Scalar_Products::homogeneous_assign(), and Parma_Polyhedra_Library::Scalar_Products::reduced_assign().

                                                                              {
   scalar_product_assign(result, y, 0, space_dimension() + 1);
 }

void Parma_Polyhedra_Library::Linear_Expression::scalar_product_assign	(	Coefficient &	result,
		const Linear_Expression &	y,
		dimension_type	start,
		dimension_type	end
	)		const

inlineprivate

Sets results to the sum of (*this)[i]*y[i], for each i in [start,end).

Definition at line 500 of file Linear_Expression_inlines.hh.

References impl.

                                                                         {
   impl->scalar_product_assign(result, *(y.impl), start, end);
 }

int Parma_Polyhedra_Library::Linear_Expression::scalar_product_sign ( const Linear_Expression & y ) const

inlineprivate

Computes the sign of the sum of (*this)[i]*y[i], for each i.

Definition at line 507 of file Linear_Expression_inlines.hh.

                                                       {
   return scalar_product_sign(y, 0, space_dimension() + 1);
 }

int Parma_Polyhedra_Library::Linear_Expression::scalar_product_sign	(	const Linear_Expression &	y,
		dimension_type	start,
		dimension_type	end
	)		const

inlineprivate

Computes the sign of the sum of (*this)[i]*y[i], for each i in [start,end).

Definition at line 513 of file Linear_Expression_inlines.hh.

References impl.

                                                                       {
   return impl->scalar_product_sign(*(y.impl), start, end);
 }

void Parma_Polyhedra_Library::Linear_Expression::set	(	dimension_type	i,
		Coefficient_traits::const_reference	n
	)

inlineprivate

Sets the i-th coefficient to n.

Definition at line 420 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::set().

Referenced by Parma_Polyhedra_Library::Grid::conversion(), Parma_Polyhedra_Library::Grid::Grid(), and Parma_Polyhedra_Library::Grid_Generator::is_equivalent_to().

                                                             {
   impl->set(i, n);
 }

void Parma_Polyhedra_Library::Linear_Expression::set	(	Variable	v,
		Coefficient_traits::const_reference	n
	)

inlineprivate

Sets the coefficient of v to n.

Definition at line 431 of file Linear_Expression_inlines.hh.

References impl, Parma_Polyhedra_Library::Linear_Expression_Interface::set(), and Parma_Polyhedra_Library::Variable::space_dimension().

                                                             {
   impl->set(v.space_dimension(), n);
 }

void Parma_Polyhedra_Library::Linear_Expression::set_coefficient	(	Variable	v,
		Coefficient_traits::const_reference	n
	)

inline

Sets the coefficient of v in *this to n.

Definition at line 65 of file Linear_Expression_inlines.hh.

                                                                  {
   impl->set_coefficient(v, n);
 }

void Parma_Polyhedra_Library::Linear_Expression::set_inhomogeneous_term ( Coefficient_traits::const_reference n )

inline

Sets the inhomogeneous term of *this to n.

Definition at line 76 of file Linear_Expression_inlines.hh.

                                                             {
   impl->set_inhomogeneous_term(n);
 }

void Parma_Polyhedra_Library::Linear_Expression::set_representation ( Representation r )

Converts *this to the specified representation.

Definition at line 166 of file Linear_Expression.cc.

References Parma_Polyhedra_Library::swap().

Referenced by Parma_Polyhedra_Library::Congruence::set_representation(), Parma_Polyhedra_Library::Constraint::set_representation(), Parma_Polyhedra_Library::Grid_Generator::set_representation(), and Parma_Polyhedra_Library::Generator::set_representation().

                                                          {
   if (representation() == r) {
     return;
   }
   Linear_Expression tmp(*this, r);
   swap(*this, tmp);
 }

void Parma_Polyhedra_Library::Linear_Expression::set_space_dimension ( dimension_type n )

inline

Sets the dimension of the vector space enclosing *this to n .

Definition at line 54 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::set_space_dimension().

                                                        {
   impl->set_space_dimension(n);
 }

void Parma_Polyhedra_Library::Linear_Expression::shift_space_dimensions	(	Variable	v,
		dimension_type	n
	)

inline

Shift by n positions the coefficients of variables, starting from the coefficient of v. This increases the space dimension by n.

Definition at line 86 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::shift_space_dimensions().

Referenced by Parma_Polyhedra_Library::Congruence::shift_space_dimensions(), Parma_Polyhedra_Library::Constraint::shift_space_dimensions(), Parma_Polyhedra_Library::Grid_Generator::shift_space_dimensions(), and Parma_Polyhedra_Library::Generator::shift_space_dimensions().

                                                                       {
   impl->shift_space_dimensions(v, n);
 }

void Parma_Polyhedra_Library::Linear_Expression::sign_normalize ( )

inline

Ensures that the first nonzero homogeneous coefficient is positive, by negating the row if necessary.

Definition at line 466 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::sign_normalize().

                                   {
   impl->sign_normalize();
 }

dimension_type Parma_Polyhedra_Library::Linear_Expression::space_dimension ( ) const

inline

Returns the dimension of the vector space enclosing *this.

Definition at line 49 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::space_dimension().

                                          {
   return impl->space_dimension();
 }

void Parma_Polyhedra_Library::Linear_Expression::swap_space_dimensions	(	Variable	v1,
		Variable	v2
	)

inline

Swaps the coefficients of the variables v1 and v2 .

Definition at line 81 of file Linear_Expression_inlines.hh.

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::swap_space_dimensions().

Referenced by Parma_Polyhedra_Library::Grid_Generator::set_space_dimension(), Parma_Polyhedra_Library::Constraint::set_space_dimension_no_ok(), Parma_Polyhedra_Library::Generator::set_space_dimension_no_ok(), and Parma_Polyhedra_Library::Congruence::swap_space_dimensions().

                                                                  {
   impl->swap_space_dimensions(v1, v2);
 }

memory_size_type Parma_Polyhedra_Library::Linear_Expression::total_memory_in_bytes ( ) const

inline

Returns a lower bound to the total size in bytes of the memory occupied by *this.

Definition at line 112 of file Linear_Expression_inlines.hh.

References external_memory_in_bytes().

                                                {
   return external_memory_in_bytes() + sizeof(*this);
 }

const Linear_Expression & Parma_Polyhedra_Library::Linear_Expression::zero ( )

inlinestatic

Returns the (zero-dimension space) constant 0.

Definition at line 101 of file Linear_Expression_inlines.hh.

References zero_p.

Referenced by Parma_Polyhedra_Library::Generator::closure_point(), Parma_Polyhedra_Library::Grid_Generator::grid_point(), Parma_Polyhedra_Library::Congruence::initialize(), Parma_Polyhedra_Library::Constraint::initialize(), and Parma_Polyhedra_Library::Generator::point().

                         {
   PPL_ASSERT(zero_p != 0);
   return *zero_p;
 }

Friends And Related Function Documentation

Linear_Expression & add_mul_assign	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n,
		Variable	v
	)

void add_mul_assign	(	Linear_Expression &	e1,
		Coefficient_traits::const_reference	factor,
		const Linear_Expression &	e2
	)

Definition at line 401 of file Linear_Expression_inlines.hh.

                                             {
   e1.impl->add_mul_assign(factor, *e2.impl);
 }

Linear_Expression & add_mul_assign	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n,
		const Variable	v
	)

References Parma_Polyhedra_Library::Linear_Expression_Interface::add_mul_assign(), and impl.

                                  {
   e.impl->add_mul_assign(n, v);
   return e;
 }

Linear_Expression& add_mul_assign	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n,
		Variable	v
	)

friend

Referenced by Linear_Expression().

void add_mul_assign	(	Linear_Expression &	e1,
		Coefficient_traits::const_reference	factor,
		const Linear_Expression &	e2
	)

friend

Definition at line 401 of file Linear_Expression_inlines.hh.

                                             {
   e1.impl->add_mul_assign(factor, *e2.impl);
 }

template<typename T >

friend class BD_Shape

friend

Definition at line 840 of file Linear_Expression_defs.hh.

friend class BD_Shape_Helpers

friend

Definition at line 836 of file Linear_Expression_defs.hh.

friend class BHRZ03_Certificate

friend

Definition at line 831 of file Linear_Expression_defs.hh.

template<typename T >

friend class Box

friend

Definition at line 846 of file Linear_Expression_defs.hh.

friend class Box_Helpers

friend

Definition at line 834 of file Linear_Expression_defs.hh.

int compare	(	const Linear_Expression &	x,
		const Linear_Expression &	y
	)

Returns: -1 or -2 if x is less than y, 0 if they are equal and 1 or 2 is y is greater. The absolute value of the result is 1 if the difference is only in the inhomogeneous terms, 2 otherwise

The order is a lexicographic. It starts comparing the variables' coefficient, starting from Variable(0), and at the end it compares the inhomogeneous terms.

Definition at line 587 of file Linear_Expression_inlines.hh.

                                                                 {
   return x.impl->compare(*y.impl);
 }

int compare	(	const Linear_Expression &	x,
		const Linear_Expression &	y
	)

friend

Definition at line 587 of file Linear_Expression_inlines.hh.

                                                                 {
   return x.impl->compare(*y.impl);
 }

friend class Congruence

friend

Definition at line 823 of file Linear_Expression_defs.hh.

friend class Congruence_System

friend

Definition at line 835 of file Linear_Expression_defs.hh.

friend class Constraint

friend

Definition at line 828 of file Linear_Expression_defs.hh.

friend class Constraint_System

friend

Definition at line 829 of file Linear_Expression_defs.hh.

template<typename T >

friend class Expression_Adapter

friend

Definition at line 848 of file Linear_Expression_defs.hh.

template<typename T >

friend class Expression_Hide_Inhomo

friend

Definition at line 850 of file Linear_Expression_defs.hh.

template<typename T >

friend class Expression_Hide_Last

friend

Definition at line 852 of file Linear_Expression_defs.hh.

friend class Generator

friend

Definition at line 827 of file Linear_Expression_defs.hh.

friend class Grid

friend

Definition at line 822 of file Linear_Expression_defs.hh.

friend class Grid_Generator

friend

Definition at line 826 of file Linear_Expression_defs.hh.

template<typename Row >

friend class Linear_Expression_Impl

friend

Definition at line 815 of file Linear_Expression_defs.hh.

template<typename T >

friend class Linear_System

friend

Definition at line 844 of file Linear_Expression_defs.hh.

friend class MIP_Problem

friend

Definition at line 833 of file Linear_Expression_defs.hh.

void neg_assign ( Linear_Expression & e )

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::negate().

                                  {
   e.impl->negate();
 }

void neg_assign ( Linear_Expression & e )

friend

Referenced by Parma_Polyhedra_Library::PIP_Tree_Node::Artificial_Parameter::Artificial_Parameter().

template<typename T >

friend class Octagonal_Shape

friend

Definition at line 842 of file Linear_Expression_defs.hh.

friend class Octagonal_Shape_Helper

friend

Definition at line 837 of file Linear_Expression_defs.hh.

Linear_Expression operator*	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

Linear_Expression operator*	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

Linear_Expression operator*	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

                                                                            {
   Linear_Expression x = e;
   x *= n;
   return x;
 }

Linear_Expression operator*	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

                                            {
   return e * n;
 }

Linear_Expression operator*	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

friend

Linear_Expression operator*	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

friend

Linear_Expression & operator*=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

Linear_Expression & operator*=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

References impl.

                                                                       {
   *e.impl *= n;
   return e;
 }

Linear_Expression& operator*=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

friend

Linear_Expression operator+	(	const Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

Linear_Expression operator+	(	Variable	v,
		Variable	w
	)

Linear_Expression operator+	(	Variable	v,
		const Linear_Expression &	e
	)

Linear_Expression operator+	(	const Linear_Expression &	e,
		Variable	v
	)

Linear_Expression operator+	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

Linear_Expression operator+	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

Linear_Expression operator+ ( const Linear_Expression & e )

                                       {
   return e;
 }

Linear_Expression operator+	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

                                                                            {
   Linear_Expression x = e;
   x += n;
   return x;
 }

Linear_Expression operator+	(	const Linear_Expression &	e,
		const Variable	v
	)

                                                         {
   Linear_Expression x = e;
   x += v;
   return x;
 }

Linear_Expression operator+	(	const Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

References space_dimension().

                                                                     {
   if (e1.space_dimension() >= e2.space_dimension()) {
     Linear_Expression e = e1;
     e += e2;
     return e;
   }
   else {
     Linear_Expression e = e2;
     e += e1;
     return e;
   }
 }

Linear_Expression operator+	(	const Variable	v,
		const Linear_Expression &	e
	)

                                                         {
   return e + v;
 }

Linear_Expression operator+	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

                                            {
   return e + n;
 }

Linear_Expression operator+	(	const Variable	v,
		const Variable	w
	)

References max_space_dimension(), and Parma_Polyhedra_Library::Variable::space_dimension().

                                               {
   const dimension_type v_space_dim = v.space_dimension();
   const dimension_type w_space_dim = w.space_dimension();
   const dimension_type space_dim = std::max(v_space_dim, w_space_dim);
   if (space_dim > Linear_Expression::max_space_dimension()) {
     throw std::length_error("Linear_Expression "
                             "PPL::operator+(v, w):\n"
                             "v or w exceed the maximum allowed "
                             "space dimension.");
   }
   if (v_space_dim >= w_space_dim) {
     Linear_Expression e(v);
     e += w;
     return e;
   }
   else {
     Linear_Expression e(w);
     e += v;
     return e;
   }
 }

Linear_Expression operator+	(	const Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

friend

Linear_Expression operator+	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

friend

Linear_Expression operator+	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

friend

Linear_Expression operator+	(	Variable	v,
		const Linear_Expression &	e
	)

friend

Linear_Expression operator+	(	Variable	v,
		Variable	w
	)

friend

Linear_Expression & operator+=	(	Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

Linear_Expression & operator+=	(	Linear_Expression &	e,
		Variable	v
	)

Exceptions

std::length_error Thrown if the space dimension of v exceeds Linear_Expression::max_space_dimension().

Linear_Expression & operator+=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

Linear_Expression & operator+=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

References impl.

                                                                       {
   *e.impl += n;
   return e;
 }

Linear_Expression & operator+=	(	Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

References impl.

                                                                {
   *e1.impl += *e2.impl;
   return e1;
 }

Linear_Expression & operator+=	(	Linear_Expression &	e,
		const Variable	v
	)

References impl.

                                                    {
   *e.impl += v;
   return e;
 }

Linear_Expression& operator+=	(	Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

friend

Linear_Expression& operator+=	(	Linear_Expression &	e,
		Variable	v
	)

friend

Linear_Expression& operator+=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

friend

Linear_Expression operator- ( const Linear_Expression & e )

Linear_Expression operator-	(	const Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

Linear_Expression operator-	(	Variable	v,
		Variable	w
	)

Linear_Expression operator-	(	Variable	v,
		const Linear_Expression &	e
	)

Linear_Expression operator-	(	const Linear_Expression &	e,
		Variable	v
	)

Linear_Expression operator-	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

Linear_Expression operator-	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

Linear_Expression operator-	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

                                                                            {
   Linear_Expression x = e;
   x -= n;
   return x;
 }

Linear_Expression operator-	(	const Variable	v,
		const Variable	w
	)

References max_space_dimension(), and Parma_Polyhedra_Library::Variable::space_dimension().

                                               {
   const dimension_type v_space_dim = v.space_dimension();
   const dimension_type w_space_dim = w.space_dimension();
   const dimension_type space_dim = std::max(v_space_dim, w_space_dim);
   if (space_dim > Linear_Expression::max_space_dimension()) {
     throw std::length_error("Linear_Expression "
                             "PPL::operator+(v, w):\n"
                             "v or w exceed the maximum allowed "
                             "space dimension.");
   }
   if (v_space_dim >= w_space_dim) {
     Linear_Expression e(v);
     e -= w;
     return e;
   }
   else {
     Linear_Expression e(w.space_dimension(), true);
     e -= w;
     e += v;
     return e;
   }
 }

Linear_Expression operator- ( const Linear_Expression & e )

References Parma_Polyhedra_Library::neg_assign().

                                       {
   Linear_Expression r(e);
   neg_assign(r);
   return r;
 }

Linear_Expression operator-	(	const Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

References Parma_Polyhedra_Library::neg_assign(), and space_dimension().

                                                                     {
   if (e1.space_dimension() >= e2.space_dimension()) {
     Linear_Expression e = e1;
     e -= e2;
     return e;
   }
   else {
     Linear_Expression e = e2;
     neg_assign(e);
     e += e1;
     return e;
   }
 }

Linear_Expression operator-	(	const Variable	v,
		const Linear_Expression &	e
	)

References negate(), Parma_Polyhedra_Library::Variable::space_dimension(), and space_dimension().

                                                         {
   Linear_Expression result(e, std::max(v.space_dimension(), e.space_dimension()));
   result.negate(0, e.space_dimension() + 1);
   result += v;
   return result;
 }

Linear_Expression operator-	(	const Linear_Expression &	e,
		const Variable	v
	)

References Parma_Polyhedra_Library::Variable::space_dimension(), and space_dimension().

                                                         {
   Linear_Expression result(e, std::max(v.space_dimension(), e.space_dimension()));
   result -= v;
   return result;
 }

Linear_Expression operator-	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

References Parma_Polyhedra_Library::neg_assign().

                                            {
   Linear_Expression result(e);
   neg_assign(result);
   result += n;
   return result;
 }

Linear_Expression operator- ( const Linear_Expression & e )

friend

Linear_Expression operator-	(	const Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

friend

Linear_Expression operator-	(	Variable	v,
		Variable	w
	)

friend

Linear_Expression operator-	(	Coefficient_traits::const_reference	n,
		const Linear_Expression &	e
	)

friend

Linear_Expression operator-	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

friend

Linear_Expression operator-	(	Variable	v,
		const Linear_Expression &	e
	)

friend

Linear_Expression operator-	(	const Linear_Expression &	e,
		Variable	v
	)

friend

Linear_Expression & operator-=	(	Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

Linear_Expression & operator-=	(	Linear_Expression &	e,
		Variable	v
	)

Exceptions

std::length_error Thrown if the space dimension of v exceeds Linear_Expression::max_space_dimension().

Linear_Expression & operator-=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

Linear_Expression & operator-=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

References impl.

                                                                       {
   *e.impl -= n;
   return e;
 }

Linear_Expression & operator-=	(	Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

References impl.

                                                                {
   *e1.impl -= *e2.impl;
   return e1;
 }

Linear_Expression & operator-=	(	Linear_Expression &	e,
		const Variable	v
	)

References impl.

                                                    {
   *e.impl -= v;
   return e;
 }

Linear_Expression& operator-=	(	Linear_Expression &	e1,
		const Linear_Expression &	e2
	)

friend

Linear_Expression& operator-=	(	Linear_Expression &	e,
		Variable	v
	)

friend

Linear_Expression& operator-=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

friend

Linear_Expression & operator/=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

Linear_Expression & operator/=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

References impl.

                                                                       {
   *e.impl /= n;
   return e;
 }

Linear_Expression& operator/=	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n
	)

friend

std::ostream & operator<<	(	std::ostream &	s,
		const Linear_Expression &	e
	)

std::ostream & operator<<	(	std::ostream &	s,
		const Linear_Expression &	e
	)

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::print().

                                                       {
   e.impl->print(s);
   return s;
 }

std::ostream& Parma_Polyhedra_Library::IO_Operators::operator<<	(	std::ostream &	s,
		const Linear_Expression &	e
	)

friend

friend class PIP_Problem

friend

Definition at line 830 of file Linear_Expression_defs.hh.

friend class PIP_Tree_Node

friend

Definition at line 825 of file Linear_Expression_defs.hh.

friend class Polyhedron

friend

Definition at line 824 of file Linear_Expression_defs.hh.

friend class Scalar_Products

friend

Definition at line 832 of file Linear_Expression_defs.hh.

void sub_mul_assign	(	Linear_Expression &	e1,
		Coefficient_traits::const_reference	factor,
		const Linear_Expression &	e2
	)

Definition at line 408 of file Linear_Expression_inlines.hh.

                                                  {
   e1.impl->sub_mul_assign(factor, *e2.impl);
 }

Linear_Expression & sub_mul_assign	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n,
		Variable	v
	)

Linear_Expression & sub_mul_assign	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n,
		const Variable	v
	)

References impl, and Parma_Polyhedra_Library::Linear_Expression_Interface::sub_mul_assign().

                                       {
   e.impl->sub_mul_assign(n, v);
   return e;
 }

Linear_Expression& sub_mul_assign	(	Linear_Expression &	e,
		Coefficient_traits::const_reference	n,
		Variable	v
	)

friend

void sub_mul_assign	(	Linear_Expression &	e1,
		Coefficient_traits::const_reference	factor,
		const Linear_Expression &	e2
	)

friend

Definition at line 408 of file Linear_Expression_inlines.hh.

                                                  {
   e1.impl->sub_mul_assign(factor, *e2.impl);
 }

void swap	(	Linear_Expression &	x,
		Linear_Expression &	y
	)

References m_swap().

                                                  {
   x.m_swap(y);
 }

void swap	(	Linear_Expression &	x,
		Linear_Expression &	y
	)

Referenced by Linear_Expression(), Parma_Polyhedra_Library::Linear_Expression::const_iterator::m_swap(), m_swap(), operator=(), and Parma_Polyhedra_Library::Linear_Expression::const_iterator::operator=().

friend class Termination_Helpers

friend

Definition at line 838 of file Linear_Expression_defs.hh.

Member Data Documentation

const Representation Parma_Polyhedra_Library::Linear_Expression::default_representation = SPARSE

static

Definition at line 291 of file Linear_Expression_defs.hh.

Linear_Expression_Interface* Parma_Polyhedra_Library::Linear_Expression::impl

private

Definition at line 656 of file Linear_Expression_defs.hh.

Referenced by add_mul_assign(), Parma_Polyhedra_Library::add_mul_assign(), all_homogeneous_terms_are_zero(), all_zeroes(), all_zeroes_except(), ascii_dump(), ascii_load(), begin(), coefficient(), Parma_Polyhedra_Library::compare(), end(), external_memory_in_bytes(), gcd(), get(), have_a_common_variable(), inhomogeneous_term(), is_equal_to(), is_zero(), last_nonzero(), linear_combine(), linear_combine_lax(), Linear_Expression(), lower_bound(), m_swap(), neg_assign(), negate(), normalize(), num_zeroes(), operator*=(), operator+=(), operator-=(), operator/=(), operator<<(), permute_space_dimensions(), remove_space_dimensions(), representation(), scalar_product_assign(), scalar_product_sign(), set(), set_space_dimension(), shift_space_dimensions(), sign_normalize(), space_dimension(), sub_mul_assign(), Parma_Polyhedra_Library::sub_mul_assign(), swap_space_dimensions(), and ~Linear_Expression().

const PPL::Linear_Expression * Parma_Polyhedra_Library::Linear_Expression::zero_p = 0

staticprivate

Holds (between class initialization and finalization) a pointer to the (zero-dimension space) constant 0.

Definition at line 654 of file Linear_Expression_defs.hh.

Referenced by zero().

The documentation for this class was generated from the following files:

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Static Private Attributes

Friends

Related Functions

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation