map_acfc.h File Reference

Autocorrelation of the counting process of a MAP at a given timescale. More...

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

Include dependency graph for map_acfc.h:

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Namespaces
namespace	line
namespace	line::mam

Functions
template<class T>
std::vector< T >	line::mam::map_acfc (const Map< T > &m, const std::vector< unsigned > &kset, const T &u)
	Autocorrelation of the counting process of a MAP at a given timescale.

Detailed Description

Autocorrelation of the counting process of a MAP at a given timescale.

Templated port of matlab/lib/kpctoolbox/map/map_acfc.m. With Q = D0 + D1, pi the stationary phase vector, u the slot length and tmp = (e pi - Q)^-1,

rho(k) = PRE exp(Q (k-1) u) POST / Var[N(u)], PRE = pi D1 (I - exp(Q u)), POST = (I - exp(Q u)) tmp^2 D1 e,

i.e. the lag-k covariance of the numbers of arrivals in consecutive windows of length u, normalized by their common variance (map_varcount). This is the counting-process autocorrelation, not the inter-arrival autocorrelation map_acf, and the two are different functions of the same MAP: a renewal process has zero inter-arrival autocorrelation at every lag but a nonzero count autocorrelation unless it is Poisson.

ARITHMETIC: transcendental, three matrix exponentials per lag.

The JAR has no counterpart of this function.

Definition in file map_acfc.h.