Defined in pbr.hpp.

Partitioned binary relations (PBRs) are a generalisation of a bipartitions, and were introduced by Martin and Mazorchuk in [44].

See also: pbr::throw_if_invalid(PBR const&).

Public Types
template<typename T>
using	initializer_list_type = std::initializer_list<std::vector<T>> const&
	Type of constructor argument.

template<typename T>
using	vector_type = std::vector<std::vector<T>> const&
	Type of constructor argument.

Public Member Functions
	PBR ()=delete
	Deleted.

	PBR (initializer_list_type< int32_t > left, initializer_list_type< int32_t > right)
	Construct from adjacencies `1` to `n` and `-1` to `-n`.

	PBR (initializer_list_type< uint32_t > x)
	Construct from adjacencies `0` to `2n - 1`.

	PBR (PBR &&)=default
	Default move constructor.

	PBR (PBR const &)=default
	Default copy constructor.

	PBR (size_t n)
	Construct empty PBR of given degree.

	PBR (vector_type< int32_t > left, vector_type< int32_t > right)
	Construct from adjacencies `1` to `n` and `-1` to `-n`.

	PBR (vector_type< uint32_t > x)
	Construct from adjacencies `0` to `2n - 1`.

std::vector< uint32_t > &	at (size_t i)
	Returns a reference to the points adjacent to a given point, with bounds checking.

std::vector< uint32_t > const &	at (size_t i) const
	Returns a const reference to the points adjacent to a given point, with bounds checking.

size_t	degree () const noexcept
	Returns the degree of a PBR.

size_t	hash_value () const
	Returns a hash value for a PBR.

size_t	number_of_points () const noexcept
	Returns the number of points of a PBR.

bool	operator< (PBR const &that) const
	Compare for less.

PBR &	operator= (PBR &&)=default
	Default move assignment operator.

PBR &	operator= (PBR const &)=default
	Default copy assignment operator.

bool	operator== (PBR const &that) const
	Compare two PBRs for equality.

std::vector< uint32_t > &	operator[] (size_t i)
	Returns a reference to the points adjacent to a given point.

std::vector< uint32_t > const &	operator[] (size_t i) const
	Returns a const reference to the points adjacent to a given point.

void	product_inplace (PBR const &x, PBR const &y, size_t thread_id=0)
	Multiply two PBR objects and store the product in `this`.

void	product_inplace_no_checks (PBR const &x, PBR const &y, size_t thread_id=0)
	Multiply two PBR objects and store the product in `this`.

Related Symbols
(Note that these are not member symbols.)
template<typename Return, typename... T>
enable_if_is_same< Return, PBR >	make (T... args)
	Construct and check a PBR.

bool	operator!= (PBR const &x, PBR const &y)
	Compare two PBRs for inequality.

PBR	operator* (PBR const &x, PBR const &y)
	Multiply two PBRs.

bool	operator<= (PBR const &x, PBR const &y)
	Convenience function that just calls operator< and operator==.

bool	operator> (PBR const &x, PBR const &y)
	Convenience function that just calls operator<.

bool	operator>= (PBR const &x, PBR const &y)
	Convenience function that just calls operator<=.

std::string	to_human_readable_repr (PBR const &x)
	Return a human readable representation of a PBR.

Member Typedef Documentation

◆ initializer_list_type

template<typename T>

using initializer_list_type = std::initializer_list<std::vector<T>> const&

Type of constructor argument.

◆ vector_type

template<typename T>

using vector_type = std::vector<std::vector<T>> const&

Type of constructor argument.

Constructor & Destructor Documentation

◆ PBR() [1/8]

PBR ( )

delete

Deleted. To avoid the situation where the underlying container is not defined, it is not possible to default construct a PBR object.

◆ PBR() [2/8]

PBR ( PBR const & )

default

Default copy constructor.

◆ PBR() [3/8]

PBR ( PBR && )

default

Default move constructor.

◆ PBR() [4/8]

PBR ( vector_type< uint32_t > x )

explicit

Construct from adjacencies 0 to 2n - 1.

The parameter x must be a container of vectors of uint32_t with size \(2n\) for some integer \(n\), and the vector in position \(i\) is the list of points adjacent to \(i\) in the PBR constructed.

Parameters

x	the container of vectors of adjacencies.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Warning: No checks whatsoever on the validity of x are performed.

See also: throw_if_invalid(PBR const&)

◆ PBR() [5/8]

PBR ( initializer_list_type< uint32_t > x )

explicit

Construct from adjacencies 0 to 2n - 1.

The parameter x must be a container of vectors of uint32_t with size \(2n\) for some integer \(n\), and the vector in position \(i\) is the list of points adjacent to \(i\) in the PBR constructed.

Parameters

x	the container of vectors of adjacencies.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Warning: No checks whatsoever on the validity of x are performed.

See also: throw_if_invalid(PBR const&)

◆ PBR() [6/8]

PBR ( size_t n )

explicit

Construct empty PBR of given degree.

Parameters

n	the degree.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

◆ PBR() [7/8]

PBR	(	initializer_list_type< int32_t >	left,
		initializer_list_type< int32_t >	right )

Construct from adjacencies 1 to n and -1 to -n.

The parameters left and right should be containers of \(n\) vectors of integer values, so that the vector in position \(i\) of left is the list of points adjacent to \(i\) in the PBR, and the vector in position \(i\) of right is the list of points adjacent to \(n + i\) in the PBR. A negative value \(i\) corresponds to \(n - i\).

Parameters

left	container of adjacencies of `1` to `n`.
right	container of adjacencies of `n` + 1 to `2n`.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Warning: No checks whatsoever on the validity of left or right are performed.

See also: throw_if_invalid(PBR const&) and make(initializer_list_type<int32_t>, initializer_list_type<int32_t>)

◆ PBR() [8/8]

PBR	(	vector_type< int32_t >	left,
		vector_type< int32_t >	right )

Construct from adjacencies 1 to n and -1 to -n.

The parameters left and right should be containers of \(n\) vectors of integer values, so that the vector in position \(i\) of left is the list of points adjacent to \(i\) in the PBR, and the vector in position \(i\) of right is the list of points adjacent to \(n + i\) in the PBR. A negative value \(i\) corresponds to \(n - i\).

Parameters

left	container of adjacencies of `1` to `n`.
right	container of adjacencies of `n` + 1 to `2n`.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Warning: No checks whatsoever on the validity of left or right are performed.

See also: throw_if_invalid(PBR const&) and make(initializer_list_type<int32_t>, initializer_list_type<int32_t>)

Member Function Documentation

◆ at() [1/2]

std::vector< uint32_t > & at ( size_t i )

Returns a reference to the points adjacent to a given point, with bounds checking.

Parameters

i	the point.

Returns: A value reference to a std::vector<uint32_t>.

Exceptions

std::out_of_range if i > number_of_points().

Complexity: Constant.

◆ at() [2/2]

std::vector< uint32_t > const & at ( size_t i ) const

Returns a const reference to the points adjacent to a given point, with bounds checking.

Parameters

i	the point.

Returns: A value const reference to a std::vector<uint32_t>.

Exceptions

std::out_of_range if i > number_of_points().

Complexity: Constant.

◆ degree()

size_t degree ( ) const

noexcept

Returns the degree of a PBR, where the degree of a PBR is half the number of points in the PBR.

Returns: A value of type size_t.

Exceptions: This function is noexcept and is guaranteed never to throw.

Complexity: Constant.

◆ hash_value()

size_t hash_value ( ) const

inline

Returns a hash value for a PBR.

Returns: A hash value for a this.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: Linear in degree().

Note: This value is recomputed every time this function is called.

◆ number_of_points()

size_t number_of_points ( ) const

noexcept

Returns the number of points of a PBR.

Returns: A value of type size_t.

Exceptions: This function is noexcept and is guaranteed never to throw.

Complexity: Constant.

◆ operator<()

bool operator< ( PBR const & that ) const

inline

Compare for less.

Parameters

that	a PBR to compare with.

Returns: true if this is less than that, and false otherwise.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: At worst linear in degree().

◆ operator=()

PBR & operator= ( PBR const & )

default

Default copy assignment operator.

◆ operator==()

bool operator== ( PBR const & that ) const

inline

Compare two PBRs for equality.

Parameters

that	a PBR to compare with.

Returns: true if this equals that, and false otherwise.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: At worst linear in degree().

◆ operator[]() [1/2]

std::vector< uint32_t > & operator[] ( size_t i )

inline

Returns a reference to the points adjacent to a given point.

Parameters

i	the point.

Returns: A value reference to a std::vector<uint32_t>.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: Constant.

◆ operator[]() [2/2]

std::vector< uint32_t > const & operator[] ( size_t i ) const

inline

Returns a const reference to the points adjacent to a given point.

Parameters

i	the point.

Returns: A value const reference to a std::vector<uint32_t>.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: Constant.

◆ product_inplace()

void product_inplace	(	PBR const &	x,
		PBR const &	y,
		size_t	thread_id = 0 )

Replaces the contents of this by the product of x and y.

The parameter thread_id is required since some temporary storage is required to find the product of x and y. Note that if different threads call this member function with the same value of thread_id then bad things will happen.

Parameters

x	a PBR.
y	a PBR.
thread_id	the index of the calling thread (defaults to `0`).

Exceptions

LibsemigroupsException

if:

the degree() of x is not the same as the degree() of y;
the degree() of *this is not the same as the degree() of x;
one if the addresses &x and &y is the same as that of this; or
either x or y are invalid.

See also: throw_if_invalid.

◆ product_inplace_no_checks()

void product_inplace_no_checks	(	PBR const &	x,
		PBR const &	y,
		size_t	thread_id = 0 )

Replaces the contents of this by the product of x and y.

The parameter thread_id is required since some temporary storage is required to find the product of x and y. Note that if different threads call this member function with the same value of thread_id then bad things will happen.

Parameters

x	a PBR.
y	a PBR.
thread_id	the index of the calling thread (defaults to `0`).

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Warning: No checks are made on whether or not the parameters are compatible. If x and y have different degrees, then bad things will happen.

Friends And Related Symbol Documentation

◆ make()

template<typename Return, typename... T>

enable_if_is_same< Return, PBR > make ( T... args )

Construct and check a PBR.

Template Parameters

Return	the return type. Must satisfy `std::is_same<Return, PBR>`.
T	the types of the arguments.

Parameters

args	the arguments to forward to the PBR constructor.

Returns: A PBR constructed from args and checked.

Exceptions

LibsemigroupsException if libsemigroups::throw_if_invalid(PBR const&) throws when called with the constructed PBR.

Warning: No checks are performed on the validity of args prior to the construction of the PBR object.

See also: PBR.

◆ operator!=()

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

Compare two PBRs for inequality.

Parameters

x	a PBR.
y	a PBR.

Returns: true if this is not equal to that, and false otherwise.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: At worst quadratic in the degree of x and y.

◆ operator*()

PBR operator*	(	PBR const &	x,
		PBR const &	y )

Returns a newly constructed PBR equal to the product of x and y.

Parameters

x	a PBR.
y	a PBR.

Returns: A value of type PBR

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: Cubic in degree().

◆ operator<=()

bool operator<=	(	PBR const &	x,
		PBR const &	y )

Convenience function that just calls operator< and operator==.

◆ operator>()

bool operator>	(	PBR const &	x,
		PBR const &	y )

Convenience function that just calls operator<.

◆ operator>=()

bool operator>=	(	PBR const &	x,
		PBR const &	y )

Convenience function that just calls operator<=.

◆ to_human_readable_repr()

std::string to_human_readable_repr ( PBR const & x )

Return a human readable representation of a PBR.

Parameters

x	the PBR object.

Returns: A value of type std::string.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

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

/Users/jdm/libsemigroups/include/libsemigroups/pbr.hpp

Public Types

Public Member Functions

Related Symbols

Member Typedef Documentation

◆ initializer_list_type

◆ vector_type

Constructor & Destructor Documentation

◆ PBR() [1/8]

◆ PBR() [2/8]

◆ PBR() [3/8]

◆ PBR() [4/8]

◆ PBR() [5/8]

◆ PBR() [6/8]

◆ PBR() [7/8]

◆ PBR() [8/8]

Member Function Documentation

◆ at() [1/2]

◆ at() [2/2]

◆ degree()

◆ hash_value()

◆ number_of_points()

◆ operator<()

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ product_inplace()

◆ product_inplace_no_checks()

Friends And Related Symbol Documentation

◆ make()

◆ operator!=()

◆ operator*()

◆ operator<=()

◆ operator>()

◆ operator>=()

◆ to_human_readable_repr()