pfqn_nrl.h File Reference

Norlund-Rice inversion of the normalizing constant, in its logistic (NRL) and probit (NRP) substitutions. More...

#include <cmath>
#include <cstddef>
#include <functional>
#include <vector>
#include "line/api/pfqn/infradius_h.h"
#include "line/api/pfqn/laplaceapprox.h"
#include "line/api/pfqn/pfqn_asympt_common.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for pfqn_nrl.h:

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Namespaces
namespace	line
namespace	line::pfqn

Functions
template<class T>
T	line::pfqn::pfqn_nrl (const Matrix< T > &L, const std::vector< T > &N, const std::vector< T > &Z, const Matrix< T > &alpha)
	Norlund-Rice logit approximation of log G.
template<class T>
T	line::pfqn::pfqn_nrp (const Matrix< T > &L, const std::vector< T > &N, const std::vector< T > &Z, const Matrix< T > &alpha)
	Norlund-Rice probit approximation of log G.

Detailed Description

Norlund-Rice inversion of the normalizing constant, in its logistic (NRL) and probit (NRP) substitutions.

Templated port of matlab/src/api/pfqn/pfqn_nrl.m and pfqn_nrp.m. Both scale the demands column-wise into [0,1], apply the Laplace approximation of laplaceapprox.m to the corresponding infradius integrand at the origin, and undo the scaling with sum_r N_r log Lmax_r. The two differ only in the change of variable, so they are ported together.

THE CURVATURE TERM IS HALF THE LOG-DETERMINANT, and it is the single thing most worth checking when a ported value disagrees with MATLAB here. Both routines consume laplaceapprox's logI, which is log(I) and therefore carries -(1/2) log det(-H); using the full log-determinant instead shifts every value by (1/2) log det(-H) with no other symptom. On the single-class model L = [1/2, 1/3, 1/5], N = 5, Z = 0 that shift is 0.347 nats, turning the correct -2.1159 into -1.7694, both of which look plausible next to the exact -1.9951.

DELAY. A non-zero think time is appended as one more station whose rate row is 1, 2, ..., Ntot, i.e. an infinite server, exactly as in the reference.

ARITHMETIC. A Laplace approximation of a contour integral, so gated on num_traits<T>::has_transcendental. pfqn_nrp additionally carries the double-precision ceiling of the normal CDF; see infradius_h.h.

Definition in file pfqn_nrl.h.