M3PP(2, m) fitted to counting-process characteristics with an optimized per-class split (matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx.m, matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx_ag.m, matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx_ag_multiclass.m). More...

#include <cstddef>
#include <vector>
#include "line/api/mam/map_fit_detail.h"
#include "line/api/mam/map_moment.h"
#include "line/api/mam/map_transform.h"
#include "line/api/mam/mmap_lambda.h"
#include "line/api/mam/mmpp2_fitc_approx.h"
#include "line/num/number.h"
#include "line/util/auglag.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for m3pp2m_fitc_approx.h:

Classes
struct	line::mam::M3pp2mFitcApproxResult< T >
	Result of the optimization-based M3PP(2, m) fits. More...

Namespaces
namespace	line
	Conservation laws of a layered queueing network, enumerated from its structure.
namespace	line::mam

Functions
template<class T>
Mmap< T >	line::mam::m3pp2m_assemble (const Map< T > &base, const std::vector< T > &q1, const std::vector< T > &q2)
	Assemble the M3PP from an underlying MAP and the per-phase marking probabilities.
template<class T>
M3pp2mFitcApproxResult< T >	line::mam::m3pp2m_fitc_approx (const T &a, const T &bt1, const T &bt2, const T &binf, const T &m3t2, const T &t1, const T &t2, const std::vector< T > &ai, const std::vector< T > &dvt3, const T &t3, const std::vector< Bound< T > > &bounds, const AugLagOptions< T > &opt)
	m3pp2m_fitc_approx: fit the underlying MMPP(2) by optimization, then split the classes on their variance DIFFERENCES at t3.
template<class T>
M3pp2mFitcApproxResult< T >	line::mam::m3pp2m_fitc_approx (const T &a, const T &bt1, const T &bt2, const T &binf, const T &m3t2, const T &t1, const T &t2, const std::vector< T > &ai, const std::vector< T > &dvt3, const T &t3)
	m3pp2m_fitc_approx with no box on the free variables and the default tuning.
template<class T>
M3pp2mFitcApproxResult< T >	line::mam::m3pp2m_fitc_approx_ag_multiclass (const Map< T > &mmpp, const std::vector< T > &ai, const std::vector< T > &gt3, const T &t3, const std::vector< Bound< T > > &bounds, const AugLagOptions< T > &opt)
	m3pp2m_fitc_approx_ag_multiclass: split a GIVEN MMPP(2) into m classes on their variance-plus-covariance at t3.
template<class T>
M3pp2mFitcApproxResult< T >	line::mam::m3pp2m_fitc_approx_ag_multiclass (const Map< T > &mmpp, const std::vector< T > &ai, const std::vector< T > &gt3, const T &t3)
	m3pp2m_fitc_approx_ag_multiclass with no box and the default tuning.
template<class T>
M3pp2mFitcApproxResult< T >	line::mam::m3pp2m_fitc_approx_ag (const T &a, const T &bt1, const T &bt2, const T &binf, const T &m3t2, const T &t1, const T &t2, const std::vector< T > &ai, const std::vector< T > &gt3, const T &t3, const std::vector< Bound< T > > &bounds, const AugLagOptions< T > &opt)
	m3pp2m_fitc_approx_ag: fit the underlying MMPP(2) by optimization, then apply the 'ag' per-class split.
template<class T>
M3pp2mFitcApproxResult< T >	line::mam::m3pp2m_fitc_approx_ag (const T &a, const T &bt1, const T &bt2, const T &binf, const T &m3t2, const T &t1, const T &t2, const std::vector< T > &ai, const std::vector< T > &gt3, const T &t3)
	m3pp2m_fitc_approx_ag with no box and the default tuning.

Detailed Description

M3PP(2, m) fitted to counting-process characteristics with an optimized per-class split (matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx.m, matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx_ag.m, matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx_ag_multiclass.m).

The underlying MMPP(2) comes from mmpp2_fitc_approx. The per-class split is then a pair of per-phase marking probabilities (q1i, q2i) per class, each an AFFINE function of the class rate ai (matched exactly) and of one free per-class quantity:

the non-'ag' variant frees dvi, the difference between the variance of class i and that of all other classes combined at resolution t3;
the 'ag' variant frees gi, the sum of the variance of class i and its covariance with all other classes combined at t3. Since m3pp2m_fitc.h can match only m - 1 of those exactly (the last class absorbs the remainder), the reference instead asks for the least-squares compromise over ALL m classes, subject to the marking probabilities being non-negative and summing to one in each phase. That is a quadratic program:

min sum_i (x_i / target_i - 1)^2 s.t. q1i(x_i) >= 0, q2i(x_i) >= 0 for every class i sum_i q1i(x_i) = 1, sum_i q2i(x_i) = 1

(the reference writes the objective as 1/2 x'Hx + f'x with H = diag(2/t_i^2) and f_i = -2/t_i, which is the expansion of the sum above minus the constant m; its reported fit_error = fx + m is therefore exactly the sum above, and that is what M3pp2mFitcApproxResult::class_objective holds).

Because the two coefficients q1i_dvi and q2i_dvi do not depend on i, both equality rows constrain only sum_i x_i; they have rank one and, as the algebra of the reference guarantees, a consistent right-hand side, so the program is a single equality plus 2m inequalities.

ACCEPTANCE CONTRACT (see line/util/auglag.h). MATLAB solves the QP with quadprog (interior-point-convex) or the bundled Goldfarb-Idnani QP; the JAR uses OSQP. This port uses the augmented Lagrangian with a Levenberg-Marquardt inner solver on the residual (x_i/target_i - 1). The iterates do not match any of them. What is guaranteed and tested is the specification:

the returned MMAP is valid – sum_i Dc_i = D1 and every Dc_i non-negative to the toolbox feasibility tolerance 1e-8, and the underlying (D0, D1) passes map_isfeasible (see mmap_isfeasible_tol);
the per-class rates are matched exactly, by construction;
the achieved objective (the reference's fit_error) is returned so it can be compared against any other QP solver's on the same input;
when the requested per-class targets are those of an actual M3PP(2, m), the objective reaches zero and the achieved targets, recomputed independently with mmap_count_var, reproduce the requested ones.

The box is UNCONSTRAINED by default (lb = -inf), as in both MATLAB files. The free variables are variance DIFFERENCES, routinely negative, and the equality row fixes their sum, which is negative on ordinary inputs: for the MMPP(2) l1 = 2, l2 = 0.5, r1 = 0.3, r2 = 0.7 at t3 = 1 it forces sum_i x_i = -1.8976, so a positive lower bound empties the feasible set. Optional bounds are exposed for a caller that wants them.

DIVERGENCE FROM THE JAR: M3pp2m_fitc_approx.java and M3pp2m_fitc_approx_ag_multiclass.java add 2m further inequality rows (q1i <= 1, q2i <= 1) that neither MATLAB file has, and then project the solution post hoc with max(0, q) followed by a row renormalization. The extra rows can make a program infeasible that MATLAB solves, and the projection silently changes the fitted per-class rates. This port follows MATLAB: 2m rows, no post-hoc projection, and the infeasibility of the result reported through M3pp2mFitcApproxResult::feasible rather than repaired.

Gated on transcendental arithmetic.

Definition in file m3pp2m_fitc_approx.h.

Classes

Namespaces

Functions

Detailed Description