template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>
class libsemigroups::StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar >

Defined in matrix.hpp.

This is a class for matrices where both the arithmetic operations in the underlying semiring, and the dimensions of the matrices are known at compile time.

Template Parameters

PlusOp	a stateless type with a call operator of signature `scalar_type operator()(scalar_type, scalar_type)` implementing the addition of the semiring.
ProdOp	a stateless type with a call operator of signature `scalar_type operator()(scalar_type, scalar_type)` implementing the multiplication of the semiring.
ZeroOp	a stateless type with a call operator of signature `scalar_type operator()()` returning the zero of the semiring (the additive identity element).
OneOp	a stateless type with a call operator of signature `scalar_type operator()()` returning the one of the semiring (the multiplicative identity element).
R	the number of rows of the matrix.
C	the number of columns of the matrix.
Scalar	the type of the entries in the matrices (the type of elements in the underlying semiring).

Note: Certain member functions only work for square matrices and some only work for rows.

Public Types
using	const_iterator = typename MatrixCommon::const_iterator
	Alias for const iterators pointing at entries of a matrix.

using	iterator = typename MatrixCommon::iterator
	Alias for iterators pointing at entries of a matrix.

using	One = OneOp
	Alias for the template parameter `OneOp`.

using	Plus = PlusOp
	Alias for the template parameter `PlusOp`.

using	Prod = ProdOp
	Alias for the template parameter `ProdOp`.

using	Row = StaticMatrix<PlusOp, ProdOp, ZeroOp, OneOp, 1, C, Scalar>
	Alias for the type of the rows of a StaticMatrix.

using	RowView = StaticRowView<PlusOp, ProdOp, ZeroOp, OneOp, C, Scalar>
	Alias for the type of row views of a StaticMatrix.

using	scalar_const_reference = typename MatrixCommon::scalar_const_reference
	Alias for const references to the template parameter `Scalar`.

using	scalar_reference = typename MatrixCommon::scalar_reference
	Alias for references to the template parameter `Scalar`.

using	scalar_type = typename MatrixCommon::scalar_type
	Alias for the template parameter `Scalar`.

using	Zero = ZeroOp
	Alias for the template parameter `ZeroOp`.

Public Member Functions
	StaticMatrix ()=default
	Default constructor.

	StaticMatrix (RowView const &rv)
	Construct a row from a row view.

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

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

	StaticMatrix (std::initializer_list< scalar_type > const &c)
	Construct a row (from std::initializer_list).

	StaticMatrix (std::initializer_list< std::initializer_list< scalar_type > > const &m)
	Construct a matrix.

	StaticMatrix (std::vector< std::vector< scalar_type > > const &m)
	Construct a matrix.

scalar_reference	at (size_t r, size_t c)
	Returns a reference to the specified entry of the matrix.

scalar_const_reference	at (size_t r, size_t c) const
	Returns a const reference to the specified entry of the matrix.

iterator	begin () noexcept
	Returns an iterator pointing at the first entry.

const_iterator	cbegin () const noexcept
	Returns a const iterator pointing at the first entry.

const_iterator	cend ()
	Returns a const iterator pointing one beyond the last entry in the matrix.

std::pair< scalar_type, scalar_type >	coords (const_iterator it) const
	Get the coordinates of an iterator.

iterator	end ()
	Returns an iterator pointing one beyond the last entry in the matrix.

size_t	hash_value () const
	Return a hash value of a matrix.

size_t	number_of_cols () const noexcept
	Returns the number of columns of the matrix.

size_t	number_of_rows () const noexcept
	Returns the number of rows of the matrix.

bool	operator!= (RowView const &that) const
	Inequality operator.

bool	operator!= (StaticMatrix const &that) const
	Inequality operator.

scalar_reference	operator() (size_t r, size_t c)
	Returns a reference to the specified entry of the matrix.

scalar_const_reference	operator() (size_t r, size_t c) const
	Returns a const reference to the specified entry of the matrix.

StaticMatrix	operator* (scalar_type a)
	Multiply a matrix by a scalar.

StaticMatrix	operator* (StaticMatrix const &that)
	Returns the product of two matrices.

void	operator*= (scalar_type a)
	Multiplies every entry of a matrix by a scalar in-place.

StaticMatrix	operator+ (scalar_type a)
	Add a scalar to a matrix.

StaticMatrix	operator+ (StaticMatrix const &that)
	Returns the sum of two matrices.

void	operator+= (RowView const &that)
	Add a matrix to another matrix in-place.

void	operator+= (scalar_type a)
	Adds a scalar to every entry of the matrix in-place.

void	operator+= (StaticMatrix const &that)
	Add a matrix to another matrix in-place.

bool	operator< (RowView const &that) const
	Less than operator.

bool	operator< (StaticMatrix const &that) const
	Less than operator.

template<typename U>
bool	operator<= (U const &that) const
	Less than or equal operator.

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

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

bool	operator== (RowView const &that) const
	Equality operator.

bool	operator== (StaticMatrix const &that) const
	Equality operator.

bool	operator> (StaticMatrix const &that) const
	Greater than operator.

template<typename U>
bool	operator>= (U const &that) const
	Greater than or equal operator.

void	product_inplace_no_checks (StaticMatrix const &x, StaticMatrix const &y)
	Multiplies `x` and `y` and stores the result in `this`.

RowView	row (size_t i) const
	Returns a view into a row.

RowView	row_no_checks (size_t i) const
	Returns a view into a row.

template<typename T>
void	rows (T &x) const
	Add row views for every row in the matrix to a container.

scalar_type	scalar_one () const noexcept
	Returns the multiplicative identity of the underlying semiring.

scalar_type	scalar_zero () const noexcept
	Returns the additive identity of the underlying semiring.

semiring_type const *	semiring () const noexcept
	Returns the underlying semiring.

void	swap (StaticMatrix &that) noexcept
	Swaps the contents of `*this` with the contents of `that`.

void	transpose ()
	Transpose a matrix in-place.

void	transpose_no_checks ()
	Transpose a matrix in-place.

Static Public Member Functions
static StaticMatrix	one () const
	Returns an identity matrix.

Constructor & Destructor Documentation

◆ StaticMatrix() [1/7]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix ( std::initializer_list< scalar_type > const & c )

inlineexplicit

Construct a row from an std::initializer_list.

Parameters

c	the values to be copied into the row.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: \(O(n)\) where \(n\) is the size of the row being constructed.

Warning: This constructor only works for rows, i.e. when the template parameter R is 1.

◆ StaticMatrix() [2/7]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix ( std::initializer_list< std::initializer_list< scalar_type > > const & m )

inlineexplicit

Construct a matrix from an std::initializer_list of std::initializer_list.

Parameters

m	the values to be copied into the matrix.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: \(O(mn)\) where \(m\) is the template parameter R and \(n\) is the template parameter C.

Example: Mat m({{1, 1}, {0, 0}});

◆ StaticMatrix() [3/7]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix ( std::vector< std::vector< scalar_type > > const & m )

inlineexplicit

Construct a matrix from an std::vector of std::vector.

Parameters

m	the values to be copied into the matrix.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: \(O(mn)\) where \(m\) is the template parameter R and \(n\) is the template parameter C.

◆ StaticMatrix() [4/7]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix ( RowView const & rv )

inlineexplicit

Construct a row from a row view.

Parameters

rv	the row view.

Exceptions: this function guarantees not to throw a LibsemigroupsException.

Complexity: \(O(n)\) where \(n\) is the size of the row being constructed.

Warning: This constructor will only compile for rows, i.e. when the template parameter R is 1.

◆ StaticMatrix() [5/7]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix ( )

default

Default constructor.

◆ StaticMatrix() [6/7]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & )

default

Default copy constructor.

◆ StaticMatrix() [7/7]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > && )

default

Default move constructor.

Member Function Documentation

◆ at() [1/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

scalar_reference at	(	size_t	r,
		size_t	c )

Returns a reference to the specified entry of the matrix.

Parameters

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

Returns: A value of type scalar_reference.

Exceptions

LibsemigroupsException if r or c is out of bounds.

Complexity: Constant

◆ at() [2/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

scalar_const_reference at	(	size_t	r,
		size_t	c ) const

Returns a const reference to the specified entry of the matrix.

Parameters

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

Returns: A value of type scalar_const_reference.

Exceptions

LibsemigroupsException if r or c is out of bounds.

Complexity: Constant

◆ begin()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

iterator begin ( )

noexcept

This function returns a random access iterator point at the first entry of the matrix.

Returns: A value of type iterator.

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

Complexity: Constant

Warning: The order in which entries in the matrix are iterated over is not specified.

◆ cbegin()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

const_iterator cbegin ( ) const

noexcept

This function returns a const (random access) iterator pointing at the first entry in the matrix.

Returns: A value of type const_iterator.

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

Complexity: Constant

Warning: The order in which entries in the matrix are iterated over is not specified.

◆ cend()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

const_iterator cend ( )

This function returns a const (random access) iterator pointing one passed the last entry of the matrix.

Returns: A value of type const_iterator.

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

Complexity: Constant

Warning: The order in which entries in the matrix are iterated over is not specified.

◆ coords()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

std::pair< scalar_type, scalar_type > coords ( const_iterator it ) const

This function returns a pair containing the row and columns corresponding to a const_iterator pointing into a matrix.

Parameters

it	the const_iterator.

Returns: A value of type std::pair<scalar_type, scalar_type>.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: Constant

◆ end()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

iterator end ( )

Returns: A value of type iterator.

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

Complexity: Constant

Warning: The order in which entries in the matrix are iterated over is not specified.

◆ hash_value()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

size_t hash_value ( ) const

This function returns a hash value for a matrix. The return value is recomputed every time this function is called.

Returns: A hash value for a this.

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

Complexity: \(O(mn)\) where \(m\) is the number_of_rows and \(n\) is number_of_cols.

◆ number_of_cols()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

size_t number_of_cols ( ) const

noexcept

This function returns the number of columns of the matrix.

Returns: A value of type size_t.

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

Complexity: Constant

◆ number_of_rows()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

size_t number_of_rows ( ) const

noexcept

This function returns the number of rows of the matrix.

Returns: A value of type size_t.

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

Complexity: Constant

◆ one()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

static StaticMatrix one ( ) const

static

This function returns an R times R identity matrix.

Returns: The identity matrix with R rows and R columns.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: \(O(n ^ 2)\) where \(n\) is the template parameter R.

◆ operator!=() [1/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

bool operator!= ( RowView const & that ) const

This function returns true if *this is not equal to that; and false otherwise.

Parameters

that	the matrix or row view for comparison.

Returns: The negation of operator==(that).

Complexity: see operator==

◆ operator!=() [2/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

bool operator!= ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & that ) const

This function returns true if *this is not equal to that; and false otherwise.

Parameters

that	the matrix or row view for comparison.

Returns: The negation of operator==(that).

Complexity: see operator==

◆ operator()() [1/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

scalar_reference operator()	(	size_t	r,
		size_t	c )

Returns a reference to the specified entry of the matrix.

Parameters

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

Returns: A value of type scalar_reference.

Exceptions: this function guarantees not to throw a LibsemigroupsException.

Complexity: Constant

Warning: No checks on the validity of the parameters r and c are performed.

◆ operator()() [2/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

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

Returns a const reference to the specified entry of the matrix.

Parameters

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

Returns: A value of type scalar_const_reference.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: Constant

Warning: No checks on the validity of the parameters r and c are performed.

◆ operator*() [1/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix operator* ( scalar_type a )

This function returns the product of the matrix *this and the scalar a.

Parameters

a	the scalar to add.

Returns: The product of *this and a.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Warning: This function does not detect overflows in scalar_type.

◆ operator*() [2/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix operator* ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & that )

This function returns the product of two matrices.

Parameters

that	the matrix to multiply by `this`.

Returns: The product of the two matrices.

Complexity: \(O(mn)\) where \(m\) is number_of_rows and \(m\) is number_of_cols.

Warning: The matrices must be of the same dimensions, although this is not verified.; This function does not detect overflows of scalar_type.

◆ operator*=()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

void operator*= ( scalar_type a )

This function multiplies every entry of a matrix by a scalar in-place.

Parameters

a	the scalar to multiply every entry by.

Complexity: \(O(mn)\) where \(m\) is number_of_rows and \(m\) is number_of_cols.

Warning: This function does not detect overflows of scalar_type.

◆ operator+() [1/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix operator+ ( scalar_type a )

This function returns the sum of the matrix *this and the scalar a.

Parameters

a	the scalar to add.

Returns: The sum of *this and a.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Warning: This function does not detect overflows in scalar_type.

◆ operator+() [2/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix operator+ ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & that )

This function returns the sum of two matrices.

Parameters

that	the matrix to add to `this`.

Returns: The sum of the two matrices.

Complexity: \(O(mn)\) where \(m\) is number_of_rows and \(m\) number_of_cols

Warning: The matrices must be of the same dimensions, although this is not verified.; This function does not detect overflows of scalar_type.

◆ operator+=() [1/3]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

void operator+= ( RowView const & that )

This function adds a matrix (or the row represented by a RowView) to another matrix of the same shape in-place.

Parameters

that	the matrix or row view to add.

Complexity: \(O(mn)\) where \(m\) is number_of_rows and \(m\) is number_of_cols

Warning: The matrices must be of the same dimensions, although this is not checked.; This function does not detect overflows of scalar_type.

◆ operator+=() [2/3]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

void operator+= ( scalar_type a )

This function adds a scalar to every entry of the matrix in-place.

Parameters

a	the scalar_type to add to a StaticMatrix.

Complexity: \(O(mn)\) where \(m\) is number_of_rows and \(m\) is number_of_cols

Warning: This function does not detect overflows of scalar_type.

◆ operator+=() [3/3]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

void operator+= ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & that )

This function adds a matrix (or the row represented by a RowView) to another matrix of the same shape in-place.

Parameters

that	the matrix or row view to add.

Complexity: \(O(mn)\) where \(m\) is number_of_rows and \(m\) is number_of_cols

Warning: The matrices must be of the same dimensions, although this is not checked.; This function does not detect overflows of scalar_type.

◆ operator<() [1/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

bool operator< ( RowView const & that ) const

This operator defines a total order on the set of matrices of the same type.

Parameters

that	the matrix or row view for comparison.

Returns: true if *this is less than that and false if it is not.

Complexity: At worst \(O(mn)\) where \(m\) is number_of_rows and \(n\) is number_of_cols.

◆ operator<() [2/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

bool operator< ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & that ) const

This operator defines a total order on the set of matrices of the same type.

Parameters

that	the matrix or row view for comparison.

Returns: true if *this is less than that and false if it is not.

Complexity: At worst \(O(mn)\) where \(m\) is number_of_rows and \(n\) is number_of_cols.

◆ operator<=()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

template<typename U>

bool operator<= ( U const & that ) const

This operator defines a total order on the set of matrices of the same type.

Template Parameters

U	the type of the argument `that`.

Parameters

that	the matrix or row view for comparison.

Returns: true if *this is less than or equal to that and false if it is not.

Complexity: At worst \(O(mn)\) where \(m\) is number_of_rows and \(n\) is number_of_cols.

◆ operator=() [1/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix & operator= ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > && )

default

Default move assignment operator.

◆ operator=() [2/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

StaticMatrix & operator= ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & )

default

Default copy assignment operator.

◆ operator==() [1/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

bool operator== ( RowView const & that ) const

This function returns true if *this is equal to that; and false otherwise.

Parameters

that	matrix or row view for comparison.

Returns: true if *this and that are equal and false if they are not.

Complexity: At worst \(O(mn)\) where \(m\) is the number of rows and \(n\) is the number of columns of the matrix.

◆ operator==() [2/2]

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

bool operator== ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & that ) const

This function returns true if *this is equal to that; and false otherwise.

Parameters

that	matrix or row view for comparison.

Returns: true if *this and that are equal and false if they are not.

Complexity: At worst \(O(mn)\) where \(m\) is the number of rows and \(n\) is the number of columns of the matrix.

◆ operator>()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

bool operator> ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const & that ) const

This operator defines a total order on the set of matrices of the same type.

Parameters

that	the matrix for comparison.

Returns: true if *this is less than that and false if it is not.

Complexity: At worst \(O(mn)\) where \(m\) is number_of_rows and \(m\) is number_of_cols

◆ operator>=()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

template<typename U>

bool operator>= ( U const & that ) const

This operator defines a total order on the set of matrices of the same type.

Template Parameters

U	the type of the argument `that`.

Parameters

that	the matrix or row view for comparison.

Returns: true if *this is greater than or equal to that and false if it is not.

Complexity: At worst \(O(mn)\) where \(m\) is number_of_rows and \(n\) is number_of_cols.

◆ product_inplace_no_checks()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

void product_inplace_no_checks	(	StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const &	x,
		StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > const &	y )

This function redefines this to be the product of x and y. This is in-place multiplication to avoid allocation of memory for products which do not need to be stored for future use.

Parameters

x	the first matrix to multiply.
y	the second matrix to multiply.

Complexity: \(O(n ^ 3)\) where \(n\) is number_of_rows or number_of_cols.

Warning: This function only applies to matrices with the same number of rows and columns but this isn't verified.

◆ row()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

RowView row ( size_t i ) const

This function returns a RowView into the row with index i.

Parameters

i	the index of the row.

Returns: A value of type RowView.

Exceptions

LibsemigroupsException if i is greater than or equal to number_of_rows.

◆ row_no_checks()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

RowView row_no_checks ( size_t i ) const

This function returns a RowView into the row with index i.

Parameters

i	the index of the row.

Returns: A value of type RowView.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: Constant

Warning: No checks are made on the argument i.

◆ rows()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

template<typename T>

void rows ( T & x ) const

This function adds a RowView for each row in the matrix to the container x.

Template Parameters

T	the type of the container.

Parameters

x	a container.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: \(O(m)\) where \(m\) is the template parameter R.

◆ scalar_one()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

scalar_type scalar_one ( ) const

noexcept

This function returns the multiplicative identity of the underlying semiring of a matrix.

Returns: The multiplicative identity of the semiring, a scalar_type.

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

◆ scalar_zero()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

scalar_type scalar_zero ( ) const

noexcept

This function returns the additive identity of the underlying semiring of a matrix.

Returns: The additive identity of the semiring, a scalar_type.

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

◆ semiring()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

semiring_type const * semiring ( ) const

noexcept

Returns a const pointer to the underlying semiring (if any).

Returns: A value of type Semiring const*.

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

Complexity: Constant

◆ swap()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

void swap ( StaticMatrix< PlusOp, ProdOp, ZeroOp, OneOp, R, C, Scalar > & that )

noexcept

This function swaps the contents of *this with the contents of that.

Parameters

that	the matrix to swap contents with.

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

Complexity: Constant

◆ transpose()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

void transpose ( )

This function transpose a matrix object in-place.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Exceptions

LibsemigroupsException if the matrix isn't square.

Complexity: \(O(mn)\) where \(m\) is number_of_rows and \(n\) is number_of_cols.

◆ transpose_no_checks()

template<typename PlusOp, typename ProdOp, typename ZeroOp, typename OneOp, size_t R, size_t C, typename Scalar>

void transpose_no_checks ( )

This function transpose a matrix object in-place.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: \(O(mn)\) where \(m\) is number_of_rows and \(n\) is number_of_cols.

Warning: This only works when number_of_rows and number_of_cols are equal (i.e. for square matrices), but this is not verified.

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

/Users/jdm/libsemigroups/include/libsemigroups/matrix.hpp

Public Types

Public Member Functions

Static Public Member Functions

Constructor & Destructor Documentation

◆ StaticMatrix() [1/7]

◆ StaticMatrix() [2/7]

◆ StaticMatrix() [3/7]

◆ StaticMatrix() [4/7]

◆ StaticMatrix() [5/7]

◆ StaticMatrix() [6/7]

◆ StaticMatrix() [7/7]

Member Function Documentation

◆ at() [1/2]

◆ at() [2/2]

◆ begin()

◆ cbegin()

◆ cend()

◆ coords()

◆ end()

◆ hash_value()

◆ number_of_cols()

◆ number_of_rows()

◆ one()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator<() [1/2]

◆ operator<() [2/2]

◆ operator<=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator>()

◆ operator>=()

◆ product_inplace_no_checks()

◆ row()

◆ row_no_checks()

◆ rows()

◆ scalar_one()

◆ scalar_zero()

◆ semiring()

◆ swap()

◆ transpose()

◆ transpose_no_checks()