Max-plus matrices

Defined in matrix-class.hpp.

This page describes the functionality for \(n \times n\) matrices over the max-plus semiring for arbitrary dimension \(n\). There are two types of such matrices those whose dimension is known at compile-time, and those where it is not. Both types can be accessed via the alias template MaxPlusMat if N has value 0, then the dimensions can be set at run time, otherwise N is the dimension. The default value of N is 0.

The alias MaxPlusMat is either StaticMatrix, DynamicMatrix (compile-time arithmetic), or DynamicMatrix (run-time arithmetic), please refer to the documentation of these class templates for more details. The only substantial difference in the interface of static and dynamic matrices is that the former can be default constructed and the latter should be constructed using the dimensions.

Example

// default construct an uninitialized 3 x 3 static matrix
[[maybe_unused]] MaxPlusMat<3> m3;
// construct an uninitialized 4 x 4 dynamic matrix
MaxPlusMat<>  m4(4, 4);

Classes
struct	MaxPlusPlus< Scalar >
	Function object for addition in the max-plus semiring. More...
struct	MaxPlusProd< Scalar >
	Function object for multiplication in the max-plus semiring. More...
struct	MaxPlusZero< Scalar >
	Function object for returning the additive identity of the max-plus semiring. More...

Typedefs
template<typename Scalar>
using	DynamicMaxPlusMat
	Alias for dynamic max-plus matrices.
template<size_t R = 0, size_t C = R, typename Scalar = int>
using	MaxPlusMat
	Alias template for max-plus matrices.
template<size_t R, size_t C, typename Scalar>
using	StaticMaxPlusMat
	Alias for static max-plus matrices.

Functions
template<typename Mat>
auto	throw_if_bad_entry (Mat const &, typename Mat::scalar_type val) -> std::enable_if_t< IsMaxPlusMat< Mat > >
	Check that an entry in a max-plus matrix is valid.
template<typename Mat>
auto	throw_if_bad_entry (Mat const &x) -> std::enable_if_t< IsMaxPlusMat< Mat > >
	Check that a max-plus matrix is valid.

Typedef Documentation

DynamicMaxPlusMat

template<typename Scalar>

using DynamicMaxPlusMat

Initial value:

DynamicMatrix<MaxPlusPlus<Scalar>,
                                         MaxPlusProd<Scalar>,
                                         MaxPlusZero<Scalar>,
                                         IntegerZero<Scalar>,
                                         Scalar>

Defined in matrix-class.hpp.

Alias for the type of dynamic max-plus matrices where the dimensions of the matrices can be defined at run time.

Template Parameters

Scalar

the type of the entries in the matrix.

MaxPlusMat

template<size_t R = 0, size_t C = R, typename Scalar = int>

using MaxPlusMat

Initial value:

std::conditional_t<R == 0 || C == 0,
                                       DynamicMaxPlusMat<Scalar>,
                                       StaticMaxPlusMat<R, C, Scalar>>

Defined in matrix-class.hpp.

Alias template for max-plus matrices.

Template Parameters

R	the number of rows. A value of 0 indicates that the value will be set at run time (default: 0).
C	the number of columns. A value of 0 indicates that the value will be set at run time (default: R).
Scalar	the type of the entries in the matrix (default: int).

StaticMaxPlusMat

template<size_t R, size_t C, typename Scalar>

using StaticMaxPlusMat

Initial value:

StaticMatrix<MaxPlusPlus<Scalar>,
                                       MaxPlusProd<Scalar>,
                                       MaxPlusZero<Scalar>,
                                       IntegerZero<Scalar>,
                                       R,
                                       C,
                                       Scalar>

Defined in matrix-class.hpp.

Alias for static max-plus matrices whose arithmetic and dimensions are defined at compile-time.

Template Parameters

R	the number of rows.
C	the number of columns.
Scalar	the type of the entries in the matrix.

Function Documentation

throw_if_bad_entry() [1/2]

template<typename Mat>

auto throw_if_bad_entry	(	Mat const &	,
		typename Mat::scalar_type	val ) -> std::enable_if_t< IsMaxPlusMat< Mat > >

Defined in matrix-exceptions.hpp.

This function can be used to check that an entry in a matrix belongs to the underlying semiring.

Template Parameters

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

Parameters

val	the entry to check.

Exceptions

LibsemigroupsException

if val is POSITIVE_INFINITY.

Deprecated

This function is deprecated and will be removed from libsemigroups in v4.

throw_if_bad_entry() [2/2]

template<typename Mat>

auto throw_if_bad_entry

(

Mat const &

x

)

-> std::enable_if_t< IsMaxPlusMat< Mat > >

Defined in matrix-exceptions.hpp.

This function can be used to check that a matrix contains values in the underlying semiring.

Template Parameters

Mat	the type of the matrix, must satisfy IsMaxPlusMat.

Parameters

x	the matrix to check.

Exceptions

LibsemigroupsException

if x contains POSITIVE_INFINITY.