aoi_lst_ph.h File Reference

Laplace-Stieltjes transform of a phase-type distribution PH(alpha, T). More...

#include <cstddef>
#include <vector>
#include "line/api/aoi/aoi_types.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/linalg.h"
#include "line/util/lu.h"
#include "line/util/matrix.h"

Include dependency graph for aoi_lst_ph.h:

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Namespaces
namespace	line
namespace	line::aoi

Functions
template<class T>
Lst< T >	line::aoi::aoi_lst_ph (const std::vector< T > &alpha, const Matrix< T > &Tmat)
	Laplace-Stieltjes transform of a phase-type distribution PH(alpha, T).

Detailed Description

Laplace-Stieltjes transform of a phase-type distribution PH(alpha, T).

Templated port of matlab/src/api/aoi/aoi_lst_ph.m, cross-checked against Aoi_lst.ph in jar/src/main/java/jline/api/aoi/Aoi_lst.java (identical).

H*(s) = alpha (s I - T)^{-1} t, t = -T e

MATLAB evaluates it as the linear solve alpha * ((sI - T) \ t) rather than by forming the inverse, and this port does the same through the LU in line/util/lu.h. A linear solve stays in the field, so a PH with rational parameters has an exactly representable transform at every rational s – which makes this the natural exact stand-in for aoi_lst_det, since an Erlang-k with k -> inf approaches a constant while staying rational.

Definition in file aoi_lst_ph.h.