map_count_mean.h File Reference

Mean of the counting process of a MAP at resolution t. More...

#include <cstddef>
#include <vector>
#include "line/api/mam/map_moment.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for map_count_mean.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::mam

Functions
template<class T>
std::vector< T >	line::mam::map_count_mean (const Map< T > &m, const std::vector< T > &t)
	Mean of the counting process of a MAP at resolution t.

Detailed Description

Mean of the counting process of a MAP at resolution t.

Templated port of matlab/lib/kpctoolbox/map/map_count_mean.m. The number of arrivals in a window of length t has stationary mean lambda t, with lambda the stationary arrival rate pi D1 e, so the whole function is one linear solve and a product.

ARITHMETIC: exact. No exponential appears, and the mean of the counts is a rational function of the entries of (D0, D1) – which makes it the natural consistency check on the counting-process functions that do need expm (map_count_var, map_count_moment), since M1 from map_count_moment must reproduce this value to the exponential's tolerance.

Definition in file map_count_mean.h.