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 $2 n$ 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 $2 n$ 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()