PTransfBase< Scalar, Container >

template<typename Scalar, typename Container>
class libsemigroups::PTransfBase< Scalar, Container >

This is a class template for partial transformations that collects all the common aspects of the subclasses StaticPTransf and DynamicPTransf. It is not intended that instance of this class are actually constructed, only its derived classes.

Template Parameters

Scalar	the type of image values (must be an unsigned integer type).
Container	the type of the container holding the image values.

Inheritance diagram for PTransfBase< Scalar, Container >:

Public Types
using	const_iterator = typename Container::const_iterator
	Type of const iterators point to image values.
using	container_type = Container
	Type of the underlying container.
using	iterator = typename Container::iterator
	Type of iterators point to image values.
using	point_type = Scalar
	Type of the image values.

Public Member Functions
	PTransfBase ()=default
	Default constructor.
	PTransfBase (Container &&cont)
	Construct from a container of images.
	PTransfBase (Container const &cont)
	Construct from a container of images.
template<typename Iterator>
	PTransfBase (Iterator first, Iterator last)
	Construct from a range of images.
	PTransfBase (PTransfBase &&)=default
	Default move constructor.
	PTransfBase (PTransfBase const &)=default
	Default copy constructor.
	PTransfBase (std::initializer_list< Scalar > cont)
	Construct from a container of images.
point_type &	at (size_t i)
	Get a reference to the image of a point.
point_type const &	at (size_t i) const
	Get a const reference to the image of a point.
const_iterator	begin () const noexcept
	Returns a const_iterator (random access iterator) pointing at the first image value.
iterator	begin () noexcept
	Returns an iterator (random access iterator) pointing at the first image value.
const_iterator	cbegin () const noexcept
	Returns a const_iterator (random access iterator) pointing at the first image value.
const_iterator	cend () const noexcept
	Returns a const_iterator (random access iterator) pointing one past the last image value.
size_t	degree () const noexcept
	Returns the degree of a partial transformation.
const_iterator	end () const noexcept
	Returns a const_iterator (random access iterator) pointing one past the last image value.
iterator	end () noexcept
	Returns an iterator (random access iterator) pointing one past the last image value.
size_t	hash_value () const
	Returns a hash value.
bool	operator!= (PTransfBase const &that) const
	Compare for inequality.
template<typename Subclass>
Subclass	operator* (Subclass const &that) const
	Multiply by another partial transformation.
bool	operator< (PTransfBase const &that) const
	Compare for less.
bool	operator<= (PTransfBase const &that) const
	Compare for less than or equal.
PTransfBase &	operator= (PTransfBase &&)=default
	Default move assignment operator.
PTransfBase &	operator= (PTransfBase const &)=default
	Default copy assignment operator.
bool	operator== (PTransfBase const &that) const
	Compare for equality.
bool	operator> (PTransfBase const &that) const
	Compare for greater.
bool	operator>= (PTransfBase const &that) const
	Compare for greater than or equal.
point_type &	operator[] (size_t i)
	Get a reference to the image of a point.
point_type const &	operator[] (size_t i) const
	Get a const reference to the image of a point.
size_t	rank () const
	Returns the number of distinct image values.
void	swap (PTransfBase &that) noexcept
	Swap with another partial transformation.

Static Public Member Functions
template<typename Subclass, typename OtherContainer = Container>
static Subclass	make (OtherContainer &&cont)
	Construct from universal reference container and check.
template<typename Subclass, typename OtherScalar>
static Subclass	make (std::initializer_list< OtherScalar > cont)
	Construct from std::initializer_list and check.
template<typename Subclass>
static Subclass	one (size_t N)
	Returns the identity transformation on the given number of points.
static point_type	undef () noexcept
	Returns the value used to represent "undefined".

Member Typedef Documentation

const_iterator

template<typename Scalar, typename Container>

using const_iterator = typename Container::const_iterator

Type of const iterators point to image values.

container_type

template<typename Scalar, typename Container>

using container_type = Container

Type of the underlying container.

iterator

template<typename Scalar, typename Container>

using iterator = typename Container::iterator

Type of iterators point to image values.

point_type

template<typename Scalar, typename Container>

using point_type = Scalar

Also the template parameter Scalar.

Constructor & Destructor Documentation

PTransfBase() [1/7]

template<typename Scalar, typename Container>

PTransfBase ( )

default

Constructs an uninitialized partial transformation of degree 0.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Constant.

PTransfBase() [2/7]

template<typename Scalar, typename Container>

PTransfBase ( Container const & cont )

inlineexplicit

Constructs a partial transformation initialized using the container cont as follows: the image of the point i under the partial transformation is the value in position i of the container cont.

Parameters

cont	the container.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in the size of the container cont.

Warning

No checks on the validity of cont are performed.

See also

make

PTransfBase() [3/7]

template<typename Scalar, typename Container>

PTransfBase ( Container && cont )

inlineexplicit

Constructs a partial transformation initialized using the container cont as follows: the image of the point i under the partial transformation is the value in position i of the container cont.

Parameters

cont	the container.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in the size of the container cont.

Warning

No checks on the validity of cont are performed.

See also

make

PTransfBase() [4/7]

template<typename Scalar, typename Container>

template<typename Iterator>

PTransfBase ( Iterator first, Iterator last )

inlineexplicit

Constructs a partial transformation initialized using the iterators first and last as follows: the image of the point i under the partial transformation at first + i.

The values pointed at by iterators of type Iterator must be convertible to point_type or equal to UNDEFINED.

Parameters

first	iterator pointing at the first image point.
last	iterator pointing one beyond the last image point.

Complexity

Linear in the size of the container cont.

Warning

No checks on the validity of cont are performed.

See also

make

PTransfBase() [5/7]

template<typename Scalar, typename Container>

PTransfBase ( std::initializer_list< Scalar > cont )

inline

Constructs a partial transformation initialized using the container cont as follows: the image of the point i under the partial transformation is the value in position i of the container cont.

Parameters

cont	the container.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in the size of the container cont.

Warning

No checks on the validity of cont are performed.

See also

make

PTransfBase() [6/7]

template<typename Scalar, typename Container>

PTransfBase ( PTransfBase< Scalar, Container > const & )

default

Default copy constructor

PTransfBase() [7/7]

template<typename Scalar, typename Container>

PTransfBase ( PTransfBase< Scalar, Container > && )

default

Default move constructor

Member Function Documentation

at() [1/2]

template<typename Scalar, typename Container>

point_type & at ( size_t i )

inlinenodiscard

Returns a reference to the image of i.

Parameters

i	the point.

Returns

A reference to a point_type.

Exceptions

std::out_of_range

if i is out of range.

Complexity

Constant.

at() [2/2]

template<typename Scalar, typename Container>

point_type const & at ( size_t i ) const

inlinenodiscard

Returns a const reference to the image of i.

Parameters

i	the point.

Returns

A const reference to a point_type.

Exceptions

std::out_of_range

if i is out of range.

Complexity

Constant.

begin() [1/2]

template<typename Scalar, typename Container>

const_iterator begin ( ) const

inlinenodiscardnoexcept

Returns

A const iterator to the first image value.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

begin() [2/2]

template<typename Scalar, typename Container>

iterator begin ( )

inlinenodiscardnoexcept

Returns

An iterator to the first image value.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

cbegin()

template<typename Scalar, typename Container>

const_iterator cbegin ( ) const

inlinenodiscardnoexcept

Returns

A const iterator to the first image value.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

cend()

template<typename Scalar, typename Container>

const_iterator cend ( ) const

inlinenodiscardnoexcept

Returns

A const iterator pointing one past the last image value.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

degree()

template<typename Scalar, typename Container>

size_t degree ( ) const

inlinenodiscardnoexcept

The degree of a partial transformation is the number of points used in its definition, which is equal to the size of the underlying container.

Returns

A value of type size_t.

Exceptions

This function is noexcept and is guaranteed never to throw.

end() [1/2]

template<typename Scalar, typename Container>

const_iterator end ( ) const

inlinenodiscardnoexcept

Returns

A const iterator pointing one past the last image value.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

end() [2/2]

template<typename Scalar, typename Container>

iterator end ( )

inlinenodiscardnoexcept

Returns

An iterator pointing one past the last image value.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

hash_value()

template<typename Scalar, typename Container>

size_t hash_value ( ) const

inlinenodiscard

Returns

A value of type size_t.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in degree().

make() [1/2]

template<typename Scalar, typename Container>

template<typename Subclass, typename OtherContainer = Container>

static Subclass make ( OtherContainer && cont )

staticnodiscard

Constructs a partial transformation initialized using the container cont as follows: the image of the point i under the partial transformation is the value in position i of the container cont.

Template Parameters

Subclass	the type of the return value.
OtherContainer	universal reference for the type of the container (default: Container).

Parameters

cont	the container.

Exceptions

LibsemigroupsException

if any of the following hold: the size of cont is incompatible with container_type. any value in cont exceeds cont.size() and is not equal to UNDEFINED.

Complexity

Linear in the size of the container cont.

make() [2/2]

template<typename Scalar, typename Container>

template<typename Subclass, typename OtherScalar>

static Subclass make ( std::initializer_list< OtherScalar > cont )

staticnodiscard

Constructs a partial transformation initialized using the container cont as follows: the image of the point i under the partial transformation is the value in position i of the container cont.

Template Parameters

Subclass	the type of the return value.
OtherScalar	the type of the points in cont.

Parameters

cont	the initializer list.

Exceptions

LibsemigroupsException

if any of the following hold: the size of cont is incompatible with container_type. any value in cont exceeds cont.size() and is not equal to UNDEFINED.

Complexity

Linear in the size of the container cont.

one()

template<typename Scalar, typename Container>

template<typename Subclass>

static Subclass one ( size_t N )

inlinestaticnodiscard

This function returns a newly constructed partial transformation with degree equal to the degree of N that fixes every value from 0 to N - 1.

Template Parameters

Subclass

the return type.

Parameters

N	the degree of the identity being constructed.

Returns

A value of type Subclass.

operator!=()

template<typename Scalar, typename Container>

bool operator!= ( PTransfBase< Scalar, Container > const & that ) const

inlinenodiscard

Returns true if *this does not equal that by comparing the image values of *this and that.

Parameters

that	the partial transformation for comparison.

Returns

A value of type bool.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

At worst linear in degree().

operator*()

template<typename Scalar, typename Container>

template<typename Subclass>

Subclass operator* ( Subclass const & that ) const

inlinenodiscard

Returns a newly constructed partial transformation holding the product of *this and that.

Template Parameters

Subclass

the return type.

Parameters

that	a partial transformation.

Returns

A value of type Subclass.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in degree().

Warning

This function does not check its arguments. In particular, if *this and that have different degrees, then bad things may happen.

operator<()

template<typename Scalar, typename Container>

bool operator< ( PTransfBase< Scalar, Container > const & that ) const

inlinenodiscard

Returns true if *this is less than that by comparing the image values of *this and that.

Parameters

that	the partial transformation for comparison.

Returns

A value of type bool.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

At worst linear in degree().

operator<=()

template<typename Scalar, typename Container>

bool operator<= ( PTransfBase< Scalar, Container > const & that ) const

inlinenodiscard

Returns true if *this is less than or equal to that by comparing the image values of *this and that.

Parameters

that	the partial transformation for comparison.

Returns

A value of type bool.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

At worst linear in degree().

operator=() [1/2]

template<typename Scalar, typename Container>

PTransfBase & operator= ( PTransfBase< Scalar, Container > && )

default

Default move assignment operator.

operator=() [2/2]

template<typename Scalar, typename Container>

PTransfBase & operator= ( PTransfBase< Scalar, Container > const & )

default

Default copy assignment operator.

operator==()

template<typename Scalar, typename Container>

bool operator== ( PTransfBase< Scalar, Container > const & that ) const

inlinenodiscard

Returns true if *this equals that by comparing the image values of *this and that.

Parameters

that	the partial transformation for comparison.

Returns

A value of type bool.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

At worst linear in degree().

operator>()

template<typename Scalar, typename Container>

bool operator> ( PTransfBase< Scalar, Container > const & that ) const

inlinenodiscard

Returns true if *this is greater than that by comparing the image values of *this and that.

Parameters

that	the partial transformation for comparison.

Returns

A value of type bool.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

At worst linear in degree().

operator>=()

template<typename Scalar, typename Container>

bool operator>= ( PTransfBase< Scalar, Container > const & that ) const

inlinenodiscard

Returns true if *this is greater than or equal to that by comparing the image values of *this and that.

Parameters

that	the partial transformation for comparison.

Returns

A value of type bool.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

At worst linear in degree().

operator[]() [1/2]

template<typename Scalar, typename Container>

point_type & operator[] ( size_t i )

inlinenodiscard

Returns a reference to the image of i.

Parameters

i	the point.

Returns

A reference to a point_type.

Complexity

Constant.

Warning

No bound checks are performed on i.

operator[]() [2/2]

template<typename Scalar, typename Container>

point_type const & operator[] ( size_t i ) const

inlinenodiscard

Returns a const reference to the image of i.

Parameters

i	the point.

Returns

A const reference to a point_type.

Complexity

Constant.

Warning

No bound checks are performed on i.

rank()

template<typename Scalar, typename Container>

size_t rank ( ) const

inlinenodiscard

The rank of a partial transformation is the number of its distinct image values, not including UNDEFINED.

Returns

A value of type size_t.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in degree().

swap()

template<typename Scalar, typename Container>

void swap ( PTransfBase< Scalar, Container > & that )

inlinenoexcept

Parameters

that	the partial transformation to swap with.

Exceptions

This function is noexcept and is guaranteed never to throw.

undef()

template<typename Scalar, typename Container>

static point_type undef ( )

inlinestaticnodiscardnoexcept

This static function returns the value of type point_type used to represent an "undefined" value.

Returns

A value of type point_type.

Exceptions

This function is noexcept and is guaranteed never to throw.

---

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

• /Users/jdm/libsemigroups/include/libsemigroups/transf.hpp