Arageli: Arageli::polyhedron< T, M, C, CFG

List of all members.


Public Types
typedef C	cone
typedef C::inequation_element_type	inequation_element_type
typedef C::equation_element_type	equation_element_type
typedef C::generatrix_element_type	generatrix_element_type
typedef C::basis_element_type	basis_element_type
typedef C::inequation_type	inequation_type
typedef C::equation_type	equation_type
typedef C::generatrix_type	generatrix_type
typedef C::basis_type	basis_type
typedef C::size_type	size_type
typedef C::dim_type	dim_type
typedef C::difference_type	difference_type
Public Member Functions
	polyhedron ()
	Creates an empty polyhedron in 0-space.
template<typename D>
	polyhedron (const D &dim, const fromempty_t &)
	Creates an empty polyhedron in the space with specified dimention.
template<typename D>
	polyhedron (const D &dim, const fromspace_t &)
	Creates polyhedron as all space with specified dimention.
template<typename M1>
	polyhedron (const M1 &ineqmat, const fromineq_t &)
	Creates polyhedron as a solution of specified inequations set with extended matrix.
template<typename M1>
	polyhedron (const M1 &vert, const fromivert_t &)
	Creates a poytope from vertices each element of which is representable as T.
template<typename M1>
	polyhedron (const M1 &vert, const fromvert_t &)
	Creates a poytope from vertices set.
sideset	sides () const
template<typename M1>
M1	vertices () const
const T &	inequation_matrix (std::size_t i, std::size_t j) const
vector< T >	facet_normal (std::size_t i) const
std::size_t	space_dim () const
Access to valid/normal flags.
bool	is_implicit_valid () const
	If it returns true than implicit representation (inequations and equations) is actual.
bool	is_parametric_valid () const
	If it returns true than parametric representation (generatrices and basis) is actual.
bool	is_all_valid () const
	If it returns true than implicit and parametric representations are both valid.
bool	is_implicit_normal () const
	If it returns true than representation (inequations and equations) is in normal form.
bool	is_parametric_normal () const
	If it returns true than parametric representation (generatrices and basis) is in normal form.
bool	is_all_normal () const
	If it returns true than implicit and parametric representations are both in normal form.
Validation and normalization of the representations.
void	validate_implicit () const
	Make the implicit representation valid.
void	validate_parametric () const
	Make the parametric representation valid.
void	validate_all () const
	Make invalid representation valid.
void	normalize_implicit () const
	Normalize the implicit representation.
void	normalize_parametric () const
	Normalize the parametric representation.
void	normalize_all () const
	Normalize both implicit and parametric representations.
Explicit set of valid/normal flags.
void	set_valid_implicit ()
	Set the valid implicit flag without an actual valid test or validation.
void	set_valid_parametric ()
	Set the valid parametric flag without an actual valid test or validation.
void	set_valid_all ()
	Set the valid both implicit and parametric flags without an actual valid test or validation.
void	set_normal_implicit ()
	Set the normal implicit flag without an actual normal test or normalization.
void	set_normal_parametric ()
	Set the normal parametric flag without an actual normal test or normalization.
void	set_normal_all ()
	Set the normal both implicit and parametric flags without an actual normal test or normalization.

Detailed Description

template<typename T = big_int, typename M = matrix<big_int>, typename C = cone<T, M>, typename CFG = polyhedron_default_config<T, M, C>>
class Arageli::polyhedron< T, M, C, CFG >

The polyhedron in n-dimetion space is represented as a cone Ax >= 0 in (n+1) dimention space and hyperplane x[0] = 1, so the polyhedra is {x : Ax >= 0 & x[0] = 1}. In other words, polyhedron that is completely defined by system Ax >= b, represented as a cone (-b|A)x' >= 0, where x is n-vector and x' is (n+1)-vector.

Member Typedef Documentation