Matrices

This page contains links to the documentation of the functionality in libsemigroups for matrices.

There are several different classes in libsemigroups for representing matrices over various semirings. There are up to three different representations for every type of matrix:

1. those whose dimension and arithmetic operations can be defined at compile time: StaticMatrix;
2. those whose arithmetic operation can be defined at compile time but whose dimensions can be set at run time: DynamicMatrix (with compile-time arithmetic);
3. those whose arithmetic operations and dimensions can be set at run time: DynamicMatrix (with run-time arithmetic).

It's unlikely that you will want to use the classes described on this page directly, but rather through the aliases described on the other matrix pages (such as, for example, BMat).

Warning

All of the matrices in libsemigroups have entries that are integer types, and the code does not currently attempt to detect overflows.

Over specific semirings

The following matrix classes are provided which define matrices over some specific semirings:

• Boolean matrices
• Integer matrices
• Max-plus matrices
• Min-plus matrices
• Truncated max-plus matrices
• Truncated min-plus matrices
• Matrices over the natural numbers mod (t = t + p)
• Projective max-plus matrices

Over arbitrary semirings

The following general matrix classes are provided which can be used to define matrices over arbitrary semirings:

• DynamicMatrix (with compile-time arithmetic)
• DynamicMatrix (with run-time arithmetic)
• StaticMatrix

Row views

A row view is a lightweight representation of a row of a matrix. The following row view classes are provided:

• DynamicRowView (compile-time arithmetic)
• DynamicRowView (run-time arithmetic)
• StaticRowView

Adapters

There are various specialisations of the adapters described on this page for the matrices described on this page:

• Adapters for other matrices
• Adapters for BMat
• Adapters for BMat8

Topics
	make<Matrix>
	Safely construct a Matrix instance.

Namespaces
namespace	libsemigroups::matrix
	Namespace for helper functions for matrices.

Functions
template<typename Mat>
auto	operator* (typename Mat::scalar_type a, Mat const &x) -> std::enable_if_t< IsMatrix< Mat >, Mat >
	Multiply a matrix by a scalar.
template<typename Mat>
auto	operator+ (typename Mat::scalar_type a, Mat const &x) -> std::enable_if_t< IsMatrix< Mat >, Mat >
	Add a scalar to a matrix.
template<typename S, typename T>
std::ostringstream &	operator<< (std::ostringstream &os, detail::RowViewCommon< S, T > const &x)
	Insertion operator for row views.
template<typename Mat>
auto	operator<< (std::ostringstream &os, Mat const &x) -> std::enable_if_t< IsMatrix< Mat >, std::ostringstream & >
	Insertion operator for matrices.
template<typename Mat>
auto	to_human_readable_repr (Mat const &x, std::string const &prefix, std::string const &short_name="", std::string const &braces="{}", size_t max_width=72) -> std::enable_if_t< IsMatrix< Mat >, std::string >
	Returns a human readable representation of a matrix.

Variables
template<typename T>
constexpr bool	IsDynamicMatrix = IsMatrix<T> && !IsStaticMatrix<T>
	Helper variable template.
template<typename T>
static constexpr bool	IsIntMat = detail::IsIntMatHelper<T>::value
	Helper variable template.
template<typename T>
constexpr bool	IsMatrix = detail::IsMatrixHelper<T>::value
	Helper variable template.
template<typename T>
static constexpr bool	IsMatWithSemiring = detail::IsMatWithSemiringHelper<T>::value
	Helper variable template.
template<typename T>
static constexpr bool	IsMaxPlusMat = detail::IsMaxPlusMatHelper<T>::value
	Helper variable template.
template<typename T>
static constexpr bool	IsMinPlusMat = detail::IsMinPlusMatHelper<T>::value
	Helper variable template.
template<typename T>
constexpr bool	IsStaticMatrix = detail::IsStaticMatrixHelper<T>::value
	Helper variable template.

Function Documentation

operator*()

template<typename Mat>

auto operator*	(	typename Mat::scalar_type	a,
		Mat const &	x ) -> std::enable_if_t<IsMatrix<Mat>, Mat>

This function returns the product of the matrix x and the scalar a.

Template Parameters

Mat	the type of the 2nd argument, must satisfy IsMatrix<Mat>.

Parameters

a	the scalar to multiply.
x	the matrix.

Returns

The product of a and x.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Warning

This function does not detect overflows of Mat::scalar_type.

operator+()

template<typename Mat>

auto operator+	(	typename Mat::scalar_type	a,
		Mat const &	x ) -> std::enable_if_t<IsMatrix<Mat>, Mat>

This function returns the sum of the matrix x and the scalar a.

Template Parameters

Mat	the type of the 2nd argument, must satisfy IsMatrix<Mat>.

Parameters

a	the scalar to add.
x	the matrix.

Returns

The sum of a and x.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Warning

This function does not detect overflows of Mat::scalar_type.

operator<<() [1/2]

template<typename S, typename T>

std::ostringstream & operator<<	(	std::ostringstream &	os,
		detail::RowViewCommon< S, T > const &	x )

This function inserts a human readable representation of a row view into the string stream os.

Parameters

os	the string stream.
x	the row view.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

operator<<() [2/2]

template<typename Mat>

auto operator<<	(	std::ostringstream &	os,
		Mat const &	x ) -> std::enable_if_t<IsMatrix<Mat>, std::ostringstream&>

This function inserts a human readable representation of a matrix into the string stream os.

Template Parameters

Mat	the type of the argument x, must satisfy IsMatrix<Mat>.

Parameters

os	the string stream.
x	the matrix.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

to_human_readable_repr()

template<typename Mat>

auto to_human_readable_repr	(	Mat const &	x,
		std::string const &	prefix,
		std::string const &	short_name = "",
		std::string const &	braces = "{}",
		size_t	max_width = 72 ) -> std::enable_if_t<IsMatrix<Mat>, std::string>

This function returns a human readable representation of a matrix.

Template Parameters

Mat	the type of the matrix, must satisfy IsMatrix<Mat>.

Parameters

x	the matrix.
prefix	the prefix for the returned string.
short_name	the short name of the type of matrix (default: "").
braces	the braces to use to delineate rows (default: "{}").
max_width	the maximum width of the returned representation (default: 72).

Exceptions

LibsemigroupsException

if braces does not have size 2.

Variable Documentation

IsDynamicMatrix

template<typename T>

bool IsDynamicMatrix = IsMatrix<T> && !IsStaticMatrix<T>

constexpr

Defined in matrix.hpp.

This variable has value true if the template parameter T is DynamicMatrix; and false otherwise.

Template Parameters

T	the type to check.

IsIntMat

template<typename T>

bool IsIntMat = detail::IsIntMatHelper<T>::value

staticconstexpr

Defined in matrix.hpp.

This variable has value true if the template parameter T is IntMat; and false otherwise.

Template Parameters

T	the type to check.

IsMatrix

template<typename T>

bool IsMatrix = detail::IsMatrixHelper<T>::value

constexpr

Defined in matrix.hpp.

This variable has value true if the template parameter T is derived from any of DynamicMatrix (with compile-time arithmetic), DynamicMatrix (with run-time arithmetic), or StaticMatrix; and false otherwise.

Template Parameters

T	the type to check.

IsMatWithSemiring

template<typename T>

bool IsMatWithSemiring = detail::IsMatWithSemiringHelper<T>::value

staticconstexpr

Defined in matrix.hpp.

This variable has value true if the template parameter T is DynamicMatrix<Semiring, Scalar>; and false otherwise.

Template Parameters

T	the type to check.

IsMaxPlusMat

template<typename T>

bool IsMaxPlusMat = detail::IsMaxPlusMatHelper<T>::value

staticconstexpr

Defined in matrix.hpp.

This variable has value true if the template parameter T is MaxPlusMat; and false otherwise.

Template Parameters

T	the type to check.

IsMinPlusMat

template<typename T>

bool IsMinPlusMat = detail::IsMinPlusMatHelper<T>::value

staticconstexpr

Defined in matrix.hpp.

This variable has value true if the template parameter T is MinPlusMat; and false otherwise.

Template Parameters

T	the type to check.

IsStaticMatrix

template<typename T>

bool IsStaticMatrix = detail::IsStaticMatrixHelper<T>::value

constexpr

Defined in matrix.hpp.

This variable has value true if the template parameter T is StaticMatrix; and false otherwise.

Template Parameters

T	the type to check.