line::SylvesterFactor< T > Class Template Reference

The Kronecker operator of a FIXED (A,B) pair, factorized once. More...

#include <line/util/sylvester.h>

Public Member Functions
	SylvesterFactor (const Matrix< T > &A, const Matrix< T > &B)
Matrix< T >	solve_sylvester (const Matrix< T > &C) const
	Solve A X + X B = C.
Matrix< T >	solve_lyap (const Matrix< T > &C) const
	Solve A X + X B + C = 0, MATLAB's lyap(A,B,C).

Detailed Description

template<class T>
class line::SylvesterFactor< T >

The Kronecker operator of a FIXED (A,B) pair, factorized once.

The MMAP[K]/PH[K]/1 queue-length recursion solves a chain of Sylvester equations that share A and B and differ only in the right-hand side, one per queue-length level. Refactorizing per level would make the recursion cubic in the level count for no reason.

Definition at line 60 of file sylvester.h.

Constructor & Destructor Documentation

SylvesterFactor()

template<class T>

line::SylvesterFactor< T >::SylvesterFactor ( const Matrix< T > & A, const Matrix< T > & B )

inline

Definition at line 62 of file sylvester.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), line::lu_factor(), and line::Matrix< T >::Matrix().

Referenced by line::lyap_solve(), and line::sylvester_solve().

Member Function Documentation

solve_lyap()

template<class T>

Matrix< T > line::SylvesterFactor< T >::solve_lyap ( const Matrix< T > & C ) const

inline

Solve A X + X B + C = 0, MATLAB's lyap(A,B,C).

Definition at line 94 of file sylvester.h.

References line::Matrix< T >::cols(), line::Matrix< T >::rows(), and solve_sylvester().

Referenced by line::mam::mmapph1fcfs_ncdistr(), and line::mam::mmapph1fcfs_ncmean().

solve_sylvester()

template<class T>

Matrix< T > line::SylvesterFactor< T >::solve_sylvester ( const Matrix< T > & C ) const

inline

Solve A X + X B = C.

Definition at line 78 of file sylvester.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), line::lu_solve(), and line::Matrix< T >::rows().

Referenced by solve_lyap().

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

• include/line/util/sylvester.h