A grid line, parameter or grid point. More...

#include <ppl.hh>

Public Types
enum	Kind
	The possible kinds of Grid_Generator objects.

enum	Type { LINE, PARAMETER, POINT }
	The generator type. More...

typedef Expression_Hide_Last< Expression_Hide_Inhomo< Linear_Expression > >	expr_type
	The type of the (adapted) internal expression.

Public Member Functions
	Grid_Generator (Representation r=default_representation)
	Returns the origin of the zero-dimensional space $\Rset^0$ .

	Grid_Generator (const Grid_Generator &g)

	Grid_Generator (const Grid_Generator &g, Representation r)
	Copy constructor with specified representation.

	Grid_Generator (const Grid_Generator &g, dimension_type space_dim)

	Grid_Generator (const Grid_Generator &g, dimension_type space_dim, Representation r)
	Copy constructor with specified space dimension and representation.

	~Grid_Generator ()
	Destructor.

Grid_Generator &	operator= (const Grid_Generator &g)
	Assignment operator.

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

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

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

void	set_space_dimension (dimension_type space_dim)

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

bool	remove_space_dimensions (const Variables_Set &vars)
	Removes all the specified dimensions from the grid generator. More...

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

void	shift_space_dimensions (Variable v, dimension_type n)

Type	type () const
	Returns the generator type of `*this`.

bool	is_line () const
	Returns `true` if and only if `*this` is a line.

bool	is_parameter () const
	Returns `true` if and only if `*this` is a parameter.

bool	is_line_or_parameter () const
	Returns `true` if and only if `*this` is a line or a parameter.

bool	is_point () const
	Returns `true` if and only if `*this` is a point.

bool	is_parameter_or_point () const
	Returns `true` if and only if `*this` row represents a parameter or a point.

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

Coefficient_traits::const_reference	divisor () const
	Returns the divisor of `*this`. 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`.

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

bool	is_equivalent_to (const Grid_Generator &y) const
	Returns `true` if and only if `*this` and `y` are equivalent generators. More...

bool	is_equal_to (const Grid_Generator &y) const
	Returns `true` if `*this` is identical to `y`. More...

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

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

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

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

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

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.

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

void	scale_to_divisor (Coefficient_traits::const_reference d)
	Scales `this` to be represented with a divisor of `d` (if \this is a parameter or point). Does nothing at all on lines. More...

void	set_divisor (Coefficient_traits::const_reference d)
	Sets the divisor of `*this` to `d`. More...

expr_type	expression () const
	Partial read access to the (adapted) internal expression.

Static Public Member Functions
static Grid_Generator	grid_line (const Linear_Expression &e, Representation r=default_representation)
	Returns the line of direction `e`. More...

static Grid_Generator	parameter (const Linear_Expression &e=Linear_Expression::zero(), Coefficient_traits::const_reference d=Coefficient_one(), Representation r=default_representation)

static Grid_Generator	parameter (Representation r)
	Returns the parameter of direction and size `Linear_Expression::zero()` .

static Grid_Generator	parameter (const Linear_Expression &e, Representation r)
	Returns the parameter of direction and size `e` .

static Grid_Generator	grid_point (const Linear_Expression &e=Linear_Expression::zero(), Coefficient_traits::const_reference d=Coefficient_one(), Representation r=default_representation)
	Returns the point at `e` / `d`. More...

static Grid_Generator	grid_point (Representation r)
	Returns the point at `e` .

static Grid_Generator	grid_point (const Linear_Expression &e, Representation r)
	Returns the point at `e` .

static dimension_type	max_space_dimension ()
	Returns the maximum space dimension a Grid_Generator can handle.

static void	initialize ()
	Initializes the class.

static void	finalize ()
	Finalizes the class.

static const Grid_Generator &	zero_dim_point ()
	Returns the origin of the zero-dimensional space $\Rset^0$ .

Static Public Attributes
static const Representation	default_representation = SPARSE
	The representation used for new Grid_Generators. More...

Related Functions
(Note that these are not member functions.)
std::ostream &	operator<< (std::ostream &s, const Grid_Generator &g)
	Output operator. More...

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

Grid_Generator	grid_line (const Linear_Expression &e, Representation r=Grid_Generator::default_representation)
	Shorthand for Grid_Generator::grid_line(const Linear_Expression& e, Representation r).

Grid_Generator	parameter (const Linear_Expression &e=Linear_Expression::zero(), Coefficient_traits::const_reference d=Coefficient_one(), Representation r=Grid_Generator::default_representation)
	Shorthand for Grid_Generator::parameter(const Linear_Expression& e, Coefficient_traits::const_reference d, Representation r).

Grid_Generator	parameter (Representation r)
	Shorthand for Grid_Generator::parameter(Representation r). More...

Grid_Generator	parameter (const Linear_Expression &e, Representation r)
	Shorthand for Grid_Generator::parameter(const Linear_Expression& e, Representation r).

Grid_Generator	grid_point (const Linear_Expression &e=Linear_Expression::zero(), Coefficient_traits::const_reference d=Coefficient_one(), Representation r=Grid_Generator::default_representation)
	Shorthand for Grid_Generator::grid_point(const Linear_Expression& e, Coefficient_traits::const_reference d, Representation r).

Grid_Generator	grid_point (Representation r)
	Shorthand for Grid_Generator::grid_point(Representation r). More...

Grid_Generator	grid_point (const Linear_Expression &e, Representation r)
	Shorthand for Grid_Generator::grid_point(const Linear_Expression& e, Representation r).

bool	operator== (const Grid_Generator &x, const Grid_Generator &y)
	Returns `true` if and only if `x` is equivalent to `y`. More...

bool	operator!= (const Grid_Generator &x, const Grid_Generator &y)
	Returns `true` if and only if `x` is not equivalent to `y`. More...

std::ostream &	operator<< (std::ostream &s, const Grid_Generator::Type &t)
	Output operator. More...

bool	operator== (const Grid_Generator &x, const Grid_Generator &y)

bool	operator!= (const Grid_Generator &x, const Grid_Generator &y)

Grid_Generator	grid_line (const Linear_Expression &e, Representation r)

Grid_Generator	parameter (const Linear_Expression &e, Coefficient_traits::const_reference d, Representation r)

Grid_Generator	parameter (Representation r)

Grid_Generator	parameter (const Linear_Expression &e, Representation r)

Grid_Generator	grid_point (const Linear_Expression &e, Coefficient_traits::const_reference d, Representation r)

Grid_Generator	grid_point (Representation r)

Grid_Generator	grid_point (const Linear_Expression &e, Representation r)

void	swap (Grid_Generator &x, Grid_Generator &y)

Detailed Description

A grid line, parameter or grid point.

An object of the class Grid_Generator is one of the following:

a grid_line $\vect{l} = (a_0, \ldots, a_{n-1})^\transpose$ ;
a parameter $\vect{q} = (\frac{a_0}{d}, \ldots, \frac{a_{n-1}}{d})^\transpose$ ;
a grid_point $\vect{p} = (\frac{a_0}{d}, \ldots, \frac{a_{n-1}}{d})^\transpose$ ;

where $n$ is the dimension of the space and, for grid_points and parameters, $d > 0$ is the divisor.

How to build a grid generator.: Each type of generator is built by applying the corresponding function (grid_line, parameter or grid_point) to a linear expression; the space dimension of the generator is defined as the space dimension of the corresponding linear expression. Linear expressions used to define a generator should be homogeneous (any constant term will be simply ignored). When defining grid points and parameters, an optional Coefficient argument can be used as a common divisor for all the coefficients occurring in the provided linear expression; the default value for this argument is 1.

: In all the following examples it is assumed that variables x, y and z are defined as follows:
Variable x(0);

Variable y(1);

Variable z(2);

Example 1: The following code builds a grid line with direction and having space dimension :
Grid_Generator l = grid_line(x - y - z);

By definition, the origin of the space is not a line, so that the following code throws an exception:
Grid_Generator l = grid_line(0*x);

Example 2: The following code builds the parameter as the vector $\vect{p} = (1, -1, -1)^\transpose \in \Rset^3$ which has the same direction as the line in Example 1:
Grid_Generator q = parameter(x - y - z);

Note that, unlike lines, for parameters, the length as well as the direction of the vector represented by the code is significant. Thus q is not the same as the parameter q1 defined by
Grid_Generator q1 = parameter(2x - 2y - 2z);

By definition, the origin of the space is not a parameter, so that the following code throws an exception:
Grid_Generator q = parameter(0*x);

Example 3: The following code builds the grid point $\vect{p} = (1, 0, 2)^\transpose \in \Rset^3$ :
Grid_Generator p = grid_point(1*x + 0*y + 2*z);

The same effect can be obtained by using the following code:
Grid_Generator p = grid_point(x + 2*z);

Similarly, the origin $\vect{0} \in \Rset^3$ can be defined using either one of the following lines of code:
Grid_Generator origin3 = grid_point(0*x + 0*y + 0*z);

Grid_Generator origin3_alt = grid_point(0*z);

Note however that the following code would have defined a different point, namely $\vect{0} \in \Rset^2$ :
Grid_Generator origin2 = grid_point(0*y);

The following two lines of code both define the only grid point having space dimension zero, namely $\vect{0} \in \Rset^0$ . In the second case we exploit the fact that the first argument of the function point is optional.
Grid_Generator origin0 = Generator::zero_dim_point();

Grid_Generator origin0_alt = grid_point();

Example 4: The grid point $\vect{p}$ specified in Example 3 above can also be obtained with the following code, where we provide a non-default value for the second argument of the function grid_point (the divisor):
Grid_Generator p = grid_point(2*x + 0*y + 4*z, 2);

Obviously, the divisor can be used to specify points having some non-integer (but rational) coordinates. For instance, the grid point $\vect{p1} = (-1.5, 3.2, 2.1)^\transpose \in \Rset^3$ can be specified by the following code:
Grid_Generator p1 = grid_point(-15*x + 32*y + 21*z, 10);

If a zero divisor is provided, an exception is thrown.

Example 5: Parameters, like grid points can have a divisor. For instance, the parameter $\vect{q} = (1, 0, 2)^\transpose \in \Rset^3$ can be defined:
Grid_Generator q = parameter(2*x + 0*y + 4*z, 2);

Also, the divisor can be used to specify parameters having some non-integer (but rational) coordinates. For instance, the parameter $\vect{q} = (-1.5, 3.2, 2.1)^\transpose \in \Rset^3$ can be defined:
Grid_Generator q = parameter(-15*x + 32*y + 21*z, 10);

If a zero divisor is provided, an exception is thrown.

How to inspect a grid generator: Several methods are provided to examine a grid generator and extract all the encoded information: its space dimension, its type and the value of its integer coefficients and the value of the denominator.

Example 6: The following code shows how it is possible to access each single coefficient of a grid generator. If g1 is a grid point having coordinates $(a_0, \ldots, a_{n-1})^\transpose$ , we construct the parameter g2 having coordinates $(a_0, 2 a_1, \ldots, (i+1)a_i, \ldots, n a_{n-1})^\transpose$ .
if (g1.is_point()) {

cout << "Grid point g1: " << g1 << endl;

Linear_Expression e;

for (dimension_type i = g1.space_dimension(); i-- > 0; )

e += (i + 1) * g1.coefficient(Variable(i)) * Variable(i);

Grid_Generator g2 = parameter(e, g1.divisor());

cout << "Parameter g2: " << g2 << endl;

}

else

cout << "Grid generator g1 is not a grid point." << endl;

Therefore, for the grid point
Grid_Generator g1 = grid_point(2*x - y + 3*z, 2);

we would obtain the following output:
Grid point g1: p((2*A - B + 3*C)/2)

Parameter g2: parameter((2*A - 2*B + 9*C)/2)

When working with grid points and parameters, be careful not to confuse the notion of coefficient with the notion of coordinate: these are equivalent only when the divisor is 1.

Constructor & Destructor Documentation

Parma_Polyhedra_Library::Grid_Generator::Grid_Generator ( const Grid_Generator & g )

inline

Ordinary copy constructor. The new Grid_Generator will have the same representation as g.

Parma_Polyhedra_Library::Grid_Generator::Grid_Generator	(	const Grid_Generator &	g,
		dimension_type	space_dim
	)

inline

Copy constructor with specified space dimension. The new Grid_Generator will have the same representation as g.

Member Function Documentation

static Grid_Generator Parma_Polyhedra_Library::Grid_Generator::grid_line	(	const Linear_Expression &	e,
		Representation	r = `default_representation`
	)

static

Returns the line of direction e.

Exceptions

std::invalid_argument Thrown if the homogeneous part of e represents the origin of the vector space.

static Grid_Generator Parma_Polyhedra_Library::Grid_Generator::parameter	(	const Linear_Expression &	e = `Linear_Expression::zero()`,
		Coefficient_traits::const_reference	d = `Coefficient_one()`,
		Representation	r = `default_representation`
	)

static

Returns the parameter of direction e and size e/d, with the same representation as e.

Both e and d are optional arguments, with default values Linear_Expression::zero() and Coefficient_one(), respectively.

Exceptions

std::invalid_argument Thrown if d is zero.

static Grid_Generator Parma_Polyhedra_Library::Grid_Generator::grid_point	(	const Linear_Expression &	e = `Linear_Expression::zero()`,
		Coefficient_traits::const_reference	d = `Coefficient_one()`,
		Representation	r = `default_representation`
	)

static

Returns the point at e / d.

Both e and d are optional arguments, with default values Linear_Expression::zero() and Coefficient_one(), respectively.

Exceptions

std::invalid_argument Thrown if d is zero.

void Parma_Polyhedra_Library::Grid_Generator::set_space_dimension ( dimension_type space_dim )

inline

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

bool Parma_Polyhedra_Library::Grid_Generator::remove_space_dimensions ( const Variables_Set & vars )

Removes all the specified dimensions from the grid generator.

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

Always returns true. The return value is needed for compatibility with the Generator class.

void Parma_Polyhedra_Library::Grid_Generator::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.

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

inline

Returns the coefficient of v in *this.

Exceptions

std::invalid_argument Thrown if the index of v is greater than or equal to the space dimension of *this.

Coefficient_traits::const_reference Parma_Polyhedra_Library::Grid_Generator::divisor ( ) const

inline

Returns the divisor of *this.

Exceptions

std::invalid_argument Thrown if *this is a line.

bool Parma_Polyhedra_Library::Grid_Generator::is_equivalent_to ( const Grid_Generator & y ) const

Returns true if and only if *this and y are equivalent generators.

Generators having different space dimensions are not equivalent.

bool Parma_Polyhedra_Library::Grid_Generator::is_equal_to ( const Grid_Generator & y ) const

Returns true if *this is identical to y.

This is faster than is_equivalent_to(), but it may return `false' even for equivalent generators.

void Parma_Polyhedra_Library::Grid_Generator::scale_to_divisor ( Coefficient_traits::const_reference d )

Scales *this to be represented with a divisor of d (if \*this is a parameter or point). Does nothing at all on lines.

It is assumed that d is a multiple of the current divisor and different from zero. The behavior is undefined if the assumption does not hold.

void Parma_Polyhedra_Library::Grid_Generator::set_divisor ( Coefficient_traits::const_reference d )

inline

Sets the divisor of *this to d.

Exceptions

std::invalid_argument Thrown if *this is a line.

Friends And Related Function Documentation

std::ostream & operator<<	(	std::ostream &	s,
		const Grid_Generator &	g
	)

void swap	(	Grid_Generator &	x,
		Grid_Generator &	y
	)

Grid_Generator parameter ( Representation r )

Grid_Generator grid_point ( Representation r )

bool operator==	(	const Grid_Generator &	x,
		const Grid_Generator &	y
	)

bool operator!=	(	const Grid_Generator &	x,
		const Grid_Generator &	y
	)

std::ostream & operator<<	(	std::ostream &	s,
		const Grid_Generator::Type &	t
	)

bool operator==	(	const Grid_Generator &	x,
		const Grid_Generator &	y
	)

bool operator!=	(	const Grid_Generator &	x,
		const Grid_Generator &	y
	)

Grid_Generator grid_line	(	const Linear_Expression &	e,
		Representation	r
	)

Grid_Generator parameter	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	d,
		Representation	r
	)

Grid_Generator parameter	(	const Linear_Expression &	e,
		Representation	r
	)

Grid_Generator grid_point	(	const Linear_Expression &	e,
		Coefficient_traits::const_reference	d,
		Representation	r
	)

Grid_Generator grid_point	(	const Linear_Expression &	e,
		Representation	r
	)

void swap	(	Grid_Generator &	x,
		Grid_Generator &	y
	)

const Representation Parma_Polyhedra_Library::Grid_Generator::default_representation = SPARSE

static

The representation used for new Grid_Generators.

Note: The copy constructor and the copy constructor with specified size use the representation of the original object, so that it is indistinguishable from the original object.

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

ppl.hh

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Related Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation