Defined in bmat8.hpp.

This class represents 8 x 8 matrices over the boolean semiring. The functions for these small matrices over the boolean semiring are more optimised than the generic functions for boolean matrices. Note that all BMat8 are represented internally as an 8 x 8 matrix; any entries not defined by the user are taken to be 0. This does not affect the results of any calculations.

Public Member Functions
	BMat8 () noexcept=default
	Default constructor.

constexpr	BMat8 (BMat8 &&) noexcept=default
	Default move constructor.

constexpr	BMat8 (BMat8 const &) noexcept=default
	Default copy constructor.

	BMat8 (std::vector< std::vector< bool > > const &mat)
	A constructor.

constexpr	BMat8 (uint64_t mat) noexcept
	Construct from an integer.

uint8_t	at (size_t r) const
	Access a row of a BMat8 (with bound checks).

BitRef	at (size_t r, size_t c)
	Access entries in a matrix (with bound checks).

bool	at (size_t r, size_t c) const
	Access entries in a matrix (with bound checks).

constexpr bool	operator!= (BMat8 const &that) const noexcept
	Inequality operator.

constexpr uint8_t	operator() (size_t r) const noexcept
	Access a row of a BMat8 (no bound checks).

constexpr BitRef	operator() (size_t r, size_t c)
	Access entries in a matrix (no bound checks).

constexpr bool	operator() (size_t r, size_t c) const noexcept
	Access entries in a matrix (no bound checks).

BMat8	operator* (BMat8 const &that) const noexcept
	Returns the matrix product of `this` and `that`.

constexpr BMat8	operator* (bool scalar) const noexcept
	Multiply a BMat8 by a scalar.

BMat8 &	operator*= (BMat8 const &that) noexcept
	Multiply `this` by `that` in-place.

constexpr BMat8 &	operator*= (bool scalar) noexcept
	Multiply a BMat8 by a scalar (in-place).

constexpr BMat8	operator+ (BMat8 const &that) const noexcept
	Sum BMat8 objects.

constexpr BMat8 &	operator+= (BMat8 const &that) noexcept
	Sum BMat8 objects (in-place).

constexpr bool	operator< (BMat8 const &that) const noexcept
	Less than operator.

constexpr bool	operator<= (BMat8 const &that) const noexcept
	Less than or equal operator.

constexpr BMat8 &	operator= (BMat8 &&) noexcept=default
	Default move assignment operator.

constexpr BMat8 &	operator= (BMat8 const &) noexcept=default
	Default copy assignment operator.

constexpr bool	operator== (BMat8 const &that) const noexcept
	Equality operator.

constexpr bool	operator> (BMat8 const &that) const noexcept
	Greater than operator.

constexpr bool	operator>= (BMat8 const &that) const noexcept
	Greater than or equal operator.

void	swap (BMat8 &that) noexcept
	Swaps `this` with `that`.

constexpr uint64_t	to_int () const noexcept
	Returns the integer representation of `this`.

Constructor & Destructor Documentation

◆ BMat8() [1/5]

BMat8 ( )

defaultnoexcept

There is no guarantee about the contents of the matrix constructed.

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

Complexity: Constant.

◆ BMat8() [2/5]

BMat8 ( uint64_t mat )

inlineexplicitconstexprnoexcept

This constructor initializes a BMat8 to have rows equal to the 8 chunks, of 8 bits each, of the binary representation of mat.

Parameters

mat	the integer representation of the matrix being constructed.

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

Complexity: Constant.

◆ BMat8() [3/5]

BMat8 ( std::vector< std::vector< bool > > const & mat )

explicit

This constructor initializes a matrix where the rows of the matrix are the vectors in mat.

Parameters

mat	the vector of vectors representation of the matrix being constructed.

Exceptions

LibsemigroupsException	if `mat` has 0 rows.
LibsemigroupsException	if `mat` has more than 8 rows.
LibsemigroupsException	if the rows of `mat` are not all of the same length.

Complexity: Constant.

◆ BMat8() [4/5]

BMat8 ( BMat8 const & )

constexprdefaultnoexcept

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

Complexity: Constant.

◆ BMat8() [5/5]

BMat8 ( BMat8 && )

constexprdefaultnoexcept

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

Complexity: Constant.

Member Function Documentation

◆ at() [1/3]

uint8_t at ( size_t r ) const

nodiscard

Returns the row with index r in the matrix represented as a uint8_t.

Parameters

r	the index of the row.

Returns: A row of the matrix.

Exceptions

LibsemigroupsException if r is out of bounds (i.e. \(>= 8\)).

Complexity: Constant.

Note: Note that since all matrices are internally represented as 8 x 8, it is possible to access entries that you might not believe exist.

See also: operator()(size_t) const rows, and to_vector.

◆ at() [2/3]

BitRef at	(	size_t	r,
		size_t	c )

nodiscard

Returns a reference to the entry in the row r and column c.

Parameters

r	the row.
c	the column.

Exceptions

LibsemigroupsException if r or c is out of bounds.

Complexity: Constant.

See also: operator()()

◆ at() [3/3]

bool at	(	size_t	r,
		size_t	c ) const

nodiscard

Returns the value of the entry in the row r and column c.

Parameters

r	the row.
c	the column.

Exceptions

LibsemigroupsException if r or c is out of bounds.

Complexity: Constant.

See also: operator()()

◆ operator!=()

bool operator!= ( BMat8 const & that ) const

inlinenodiscardconstexprnoexcept

Returns true if this does not equal that

This function checks the mathematical inequality of two BMat8 objects.

Parameters

that	the BMat8 for comparison.

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

Complexity: Constant.

◆ operator()() [1/3]

uint8_t operator() ( size_t r ) const

inlinenodiscardconstexprnoexcept

Returns the row with index r in the matrix represented as a uint8_t.

Parameters

r	the index of the row.

Returns: A row of the matrix.

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

Complexity: Constant.

Note: Note that since all matrices are internally represented as 8 x 8, it is possible to access entries that you might not believe exist.

Warning: No checks on the parameter r are performed.

See also: at, rows, and to_vector.

◆ operator()() [2/3]

BitRef operator()	(	size_t	r,
		size_t	c )

inlinenodiscardconstexpr

Returns a reference to the entry in the matrix in row r and column c.

Parameters

r	the index of the row.
c	the index of the column.

Returns: A reference to the entry.

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

Complexity: Constant.

Note: Note that since all matrices are internally represented as 8 x 8, it is possible to access entries that you might not believe exist.

Warning: No checks on the parameters r and c are performed, if r or c is greater than 7, then bad things will happen.

See also: at

◆ operator()() [3/3]

bool operator()	(	size_t	r,
		size_t	c ) const

inlinenodiscardconstexprnoexcept

Returns the entry in the matrix in row r and column c.

Parameters

r	the index of the row.
c	the index of the column.

Returns: A bool.

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

Complexity: Constant.

Note: Note that since all matrices are internally represented as 8 x 8, it is possible to access entries that you might not believe exist.

Warning: No checks on the parameters r and c are performed, if r or c is greater than 7, then bad things will happen.

See also: at

◆ operator*() [1/2]

BMat8 operator* ( BMat8 const & that ) const

nodiscardnoexcept

This function returns the standard matrix product (over the boolean semiring) of two BMat8 objects. Uses the technique given here.

Parameters

that	the matrix we want to multiply by `this`.

Returns: A BMat8.

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

Complexity: Constant.

◆ operator*() [2/2]

BMat8 operator* ( bool scalar ) const

inlinenodiscardconstexprnoexcept

This function returns the product of a BMat8 object and the boolean scalar value scalar.

Parameters

scalar the scalar.

Returns: A BMat8.

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

Complexity: Constant.

◆ operator*=() [1/2]

BMat8 & operator*= ( BMat8 const & that )

noexcept

This function replaces the value of this by the standard matrix product (over the boolean semiring) of this and that.

Parameters

that	the matrix we want to multiply by `this`.

Returns: A reference to *this.

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

Complexity: Constant.

◆ operator*=() [2/2]

BMat8 & operator*= ( bool scalar )

inlineconstexprnoexcept

This function returns the product of a BMat8 object and the boolean scalar value scalar.

Parameters

scalar the scalar.

Returns: A reference to this.

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

Complexity: Constant.

◆ operator+()

BMat8 operator+ ( BMat8 const & that ) const

inlinenodiscardconstexprnoexcept

This function returns the sum of two BMat8 objects.

Parameters

that	the BMat8 to add.

Returns: The sum of *this and that.

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

Complexity: Constant.

◆ operator+=()

BMat8 & operator+= ( BMat8 const & that )

inlineconstexprnoexcept

This function adds that to *this in-place.

Parameters

that	the BMat8 to add.

Returns: A reference to *this.

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

Complexity: Constant.

◆ operator<()

bool operator< ( BMat8 const & that ) const

inlinenodiscardconstexprnoexcept

Returns true if this is less than that.

This function checks whether a BMat8 objects is less than another; where the order is defined by to_int.

Parameters

that	the BMat8 for comparison.

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

Complexity: Constant.

◆ operator<=()

bool operator<= ( BMat8 const & that ) const

inlinenodiscardconstexprnoexcept

Returns true if this is less than or equal to that.

This function checks whether a BMat8 objects is less or equal than another; where the order is defined by to_int.

Parameters

that	the BMat8 for comparison.

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

Complexity: Constant.

◆ operator=() [1/2]

BMat8 & operator= ( BMat8 && )

constexprdefaultnoexcept

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

Complexity: Constant.

◆ operator=() [2/2]

BMat8 & operator= ( BMat8 const & )

constexprdefaultnoexcept

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

Complexity: Constant.

◆ operator==()

bool operator== ( BMat8 const & that ) const

inlinenodiscardconstexprnoexcept

Returns true if this equals that.

This function checks the mathematical equality of two BMat8 objects.

Parameters

that	the BMat8 for comparison.

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

Complexity: Constant.

◆ operator>()

bool operator> ( BMat8 const & that ) const

inlinenodiscardconstexprnoexcept

Returns true if this is greater than that.

This function checks whether a BMat8 objects is greater than another; where the order is defined by to_int.

Parameters

that	the BMat8 for comparison.

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

Complexity: Constant.

◆ operator>=()

bool operator>= ( BMat8 const & that ) const

inlinenodiscardconstexprnoexcept

Returns true if this is greater than or equal to that.

This function checks whether a BMat8 objects is greater or equal than another; where the order is defined by to_int.

Parameters

that	the BMat8 for comparison.

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

Complexity: Constant.

◆ swap()

void swap ( BMat8 & that )

inlinenoexcept

This function swaps the values of this and that.

Parameters

that	the BMat8 to swap `this` with.

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

Complexity: Constant.

◆ to_int()

uint64_t to_int ( ) const

inlinenodiscardconstexprnoexcept

Returns an unsigned integer obtained by interpreting an 8 x 8 BMat8 as a sequence of 64 bits (reading rows left to right, from top to bottom) and then realising this sequence as an unsigned int.

Returns: A uint64_t.

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

Complexity: Constant.

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

/Users/jdm/libsemigroups/include/libsemigroups/bmat8.hpp

Public Member Functions

Constructor & Destructor Documentation

◆ BMat8() [1/5]

◆ BMat8() [2/5]

◆ BMat8() [3/5]

◆ BMat8() [4/5]

◆ BMat8() [5/5]

Member Function Documentation

◆ at() [1/3]

◆ at() [2/3]

◆ at() [3/3]

◆ operator!=()

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator<()

◆ operator<=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator>()

◆ operator>=()

◆ swap()

◆ to_int()