fj_gk_bound.h File Reference

G(K) factors for the standardized-maximum approximation X_K^max ~ mu + sigma G(K). More...

#include "line/api/fj/fj_harmonic.h"
#include "line/api/fj/fj_types.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for fj_gk_bound.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::fj

Functions
template<class T>
FJGKBoundResult< T >	line::fj::fj_gk_bound (unsigned K)
	G(K) factors for the standardized-maximum approximation X_K^max ~ mu.
template<class T>
T	line::fj::fj_gk_bound (unsigned K, FJDistType type)
	Single-family accessor, matching MATLAB's 'exp'/'uniform'/'evd'/'bound' modes.

Detailed Description

G(K) factors for the standardized-maximum approximation X_K^max ~ mu + sigma G(K).

Templated port of matlab/src/api/fj/fj_gk_bound.m. The JAR carries the same four values in jline.api.fj.GKBoundResult, computed inside FJ_xmax.fj_xmax_approx (identical formulas).

exponential: G(K) = H_K - 1 uniform: G(K) = sqrt(3) (K-1)/(K+1) evd: G(K) = sqrt(6) ln(K) / pi upper bound: G(K) = (K-1)/sqrt(2K-1) (David 1970)

static_assert(num_traits<T>::has_transcendental) – three of the four involve sqrt or log, so the struct as a whole is only defined for the inexact number types. The exponential entry alone is rational and is reachable exactly through fj_harmonic.

Definition in file fj_gk_bound.h.