Min-plus matrices

Defined in matrix.hpp.

This page describes the functionality for \(n \times n\) matrices over the min-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 MinPlusMat: 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 MinPlusMat 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
MinPlusMat<3> m;
// construct an uninitialized 4 x 4 dynamic matrix
MinPlusMat<> m(4, 4);

Classes
struct	MinPlusPlus< Scalar >
	Function object for addition in the min-plus semiring. More...
struct	MinPlusProd< Scalar >
	Function object for multiplication in the min-plus semiring. More...
struct	MinPlusZero< Scalar >
	Function object for returning the additive identity of the min-plus semiring. More...

Typedefs
template<typename Scalar>
using	DynamicMinPlusMat
	Alias for dynamic min-plus matrices.
template<size_t R = 0, size_t C = R, typename Scalar = int>
using	MinPlusMat
	Alias template for min-plus matrices.
template<size_t R, size_t C, typename Scalar>
using	StaticMinPlusMat
	Alias for static min-plus matrices.

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

Typedef Documentation

DynamicMinPlusMat

template<typename Scalar>

using DynamicMinPlusMat

Initial value:

 DynamicMatrix<MinPlusPlus<Scalar>,
                                          MinPlusProd<Scalar>,
                                          MinPlusZero<Scalar>,
                                          IntegerZero<Scalar>,
                                          Scalar>

Defined in matrix.hpp.

Alias for the type of dynamic min-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.

MinPlusMat

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

using MinPlusMat

Initial value:

 std::conditional_t<R == 0 || C == 0,
                                        DynamicMinPlusMat<Scalar>,
                                        StaticMinPlusMat<R, C, Scalar>>

Defined in matrix.hpp.

Alias template for min-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).

StaticMinPlusMat

template<size_t R, size_t C, typename Scalar>

using StaticMinPlusMat

Initial value:

 StaticMatrix<MinPlusPlus<Scalar>,
                                        MinPlusProd<Scalar>,
                                        MinPlusZero<Scalar>,
                                        IntegerZero<Scalar>,
                                        R,
                                        C,
                                        Scalar>

Defined in matrix.hpp.

Alias for static min-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>

std::enable_if_t< IsMinPlusMat< Mat > > throw_if_bad_entry	(	Mat const &	,
		typename Mat::scalar_type	val )

Defined in matrix.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 IsMinPlusMat<Mat>.

Parameters

val	the entry to check.

Exceptions

LibsemigroupsException

if val is NEGATIVE_INFINITY.

throw_if_bad_entry() [2/2]

template<typename Mat>

std::enable_if_t< IsMinPlusMat< Mat > > throw_if_bad_entry

(

Mat const &

x

)

Defined in matrix.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 IsMinPlusMat.

Parameters

x	the matrix to check.

Exceptions

LibsemigroupsException

if x contains NEGATIVE_INFINITY.