line::spn Namespace Reference

Classes
struct	SpnEnabling
	Unnormalised enabling-degree masses of one mode. More...
struct	SpnInfo
	Everything the caller needs alongside the descriptor. More...
struct	SpnInvariants
	The invariant basis of a net, in place-level coordinates. More...
struct	SpnLpBounds
	The brackets; each vector pair holds the minimum then the maximum. More...
struct	SpnLpMode
	One (transition, mode) pair over place levels. More...
struct	SpnLpOptions
	Options of the relaxation. More...
struct	SpnMetrics
	The stationary measures of Sec. More...
struct	SpnMode
	One (transition, mode) pair of the net, in level coordinates. More...
struct	SpnOptions
	Options of the translation. More...
struct	SpnPfOptions
	Options of the product-form derivation. More...
struct	SpnPfResult
	The product form, and the certificate that it is one. More...
struct	SpnResult
	Descriptor, diagram and metadata returned together. More...

Functions
template<class T>
T	spn_conv (const std::vector< std::vector< long long > > &S, const std::vector< long long > &V, const std::vector< std::vector< T > > &g)
	The normalising constant by convolution over the invariant load vector.
template<class T>
T	spn_conv (const SpnInvariants &inv, const std::vector< std::vector< T > > &g)
	Convolve straight off the invariant basis spn_sinvariants returned.
template<class T>
SpnLpBounds	spn_lpbnd (const qn::NetworkStruct< T > &sn, const SpnLpOptions &options=SpnLpOptions())
	Bracket the mean tokens and the throughputs of a stochastic Petri net.
template<class T>
SpnResult< T >	spn_mdd (const qn::NetworkStruct< T > &sn, const SpnOptions &options=SpnOptions())
	Build the reachable set and Kronecker descriptor of a stochastic Petri net.
template<class T>
SpnMetrics< T >	spn_metrics (const mdd::MddStruct &mdds, const std::vector< std::vector< T > > &g, const SpnInfo< T > &info)
	Every measure of Sec.
template<class T>
SpnPfResult< T >	spn_pf (const qn::NetworkStruct< T > &sn, const SpnPfOptions &options=SpnPfOptions())
	Derive the product form of a stochastic Petri net.
template<class T>
SpnEnabling< T >	spn_rec_enabled (const mdd::MddStruct &mdds, const std::vector< std::vector< T > > &g, const SpnMode< T > &mde, std::size_t nplacelevels)
	Enabling-degree masses of mode mde over the reachable set in mdds.
template<class T>
SpnInvariants	spn_sinvariants (const qn::NetworkStruct< T > &sn, const std::vector< double > &init=std::vector< double >())
	Minimal-support S-invariants and the load vector of a net.

Function Documentation

spn_conv() [1/2]

template<class T>

T line::spn::spn_conv	(	const SpnInvariants &	inv,
		const std::vector< std::vector< T > > &	g )

Convolve straight off the invariant basis spn_sinvariants returned.

Definition at line 125 of file spn_conv.h.

References line::spn::SpnInvariants::S, spn_conv(), and line::spn::SpnInvariants::V.

spn_conv() [2/2]

template<class T>

T line::spn::spn_conv	(	const std::vector< std::vector< long long > > &	S,
		const std::vector< long long > &	V,
		const std::vector< std::vector< T > > &	g )

The normalising constant by convolution over the invariant load vector.

Parameters

S	S[i][p], the minimal-support S-invariants, one row per invariant
V	the load vector S m0, one entry per invariant
g	g[p][i] is g_p(i), the product-form factor of i tokens in place p; its length bounds the marking of place p

Definition at line 105 of file spn_conv.h.

References line::InputError::InputError(), and spn_conv().

Referenced by spn_conv(), and spn_conv().

spn_lpbnd()

template<class T>

SpnLpBounds line::spn::spn_lpbnd	(	const qn::NetworkStruct< T > &	sn,
		const SpnLpOptions &	options = SpnLpOptions() )

Bracket the mean tokens and the throughputs of a stochastic Petri net.

Parameters

sn	a NetworkStruct holding Places and Transitions, single class
options	the relaxation options

Returns

the brackets, per place level and per mode

Definition at line 157 of file spn_lpbnd.h.

References line::qn::TransitionParam< T >::arc_total(), line::spn::SpnLpBounds::bound, line::mam::Map< T >::D1, line::lang::dist_to_map(), line::lp::LpModel< T >::emit_eq(), line::lp::LpModel< T >::emit_ge(), line::lp::LpModel< T >::emit_le(), line::spn::SpnLpMode::enab, line::qn::TransitionParam< T >::enabling, line::spn::SpnLpMode::fire, line::qn::TransitionParam< T >::firing, line::qn::TransitionParam< T >::firingdep, line::qn::TransitionParam< T >::firingproc, line::lang::IMMEDIATE, line::spn::SpnLpMode::inhib, line::qn::TransitionParam< T >::inhibit_total(), line::qn::TransitionParam< T >::inhibiting, line::InputError::InputError(), line::spn::SpnLpBounds::levelname, line::spn::SpnInvariants::m0, line::mam::map_mean(), line::spn::SpnLpBounds::markovian, line::spn::SpnLpMode::mode, line::spn::SpnLpBounds::mode_tput_hi, line::spn::SpnLpBounds::mode_tput_lo, line::spn::SpnLpBounds::mode_util_hi, line::spn::SpnLpBounds::mode_util_lo, line::spn::SpnLpBounds::modes, line::qn::TransitionParam< T >::nmodes, line::qn::TransitionParam< T >::nmodeservers, line::spn::SpnLpBounds::nplacelevels, line::spn::SpnLpBounds::nrows, line::lp::LpModel< T >::num_rows(), line::spn::SpnLpBounds::nvars, line::mam::Map< T >::order(), line::lang::Place, line::spn::SpnLpBounds::place_tput_hi, line::spn::SpnLpBounds::place_tput_lo, line::spn::SpnLpBounds::places, line::spn::SpnLpMode::rate, line::lp::LpModel< T >::row_add(), line::lp::LpModel< T >::row_clear(), line::spn::SpnInvariants::S, line::lp::LpModel< T >::set_bounds(), spn_lpbnd(), spn_sinvariants(), line::qn::TransitionParam< T >::timing, line::spn::SpnLpBounds::tokens_hi, line::spn::SpnLpBounds::tokens_lo, line::spn::SpnLpMode::trans, line::lang::Transition, line::UnsupportedError::UnsupportedError(), and line::spn::SpnInvariants::V.

Referenced by line::ba::solver_ba_spnlp_analyzer(), and spn_lpbnd().

spn_mdd()

template<class T>

SpnResult< T > line::spn::spn_mdd	(	const qn::NetworkStruct< T > &	sn,
		const SpnOptions &	options = SpnOptions() )

Build the reachable set and Kronecker descriptor of a stochastic Petri net.

Parameters

sn	a NetworkStruct holding Places and Transitions
options	translation options

Definition at line 394 of file spn_mdd.h.

References line::mdd::MddEvent< T >::a, line::mdd::MddLocalMatrix< T >::Builder::add(), line::qn::TransitionParam< T >::arc_total(), line::mdd::MddLocalMatrix< T >::Builder::build(), line::mdd::MDD::compact(), line::mam::Map< T >::D0, line::spn::SpnMode< T >::D0, line::mam::Map< T >::D1, line::spn::SpnMode< T >::D1, line::spn::SpnMode< T >::dep, line::spn::SpnResult< T >::desc, line::spn::SpnInfo< T >::descriptor, line::spn::SpnInfo< T >::diagram, line::lang::dist_to_map(), line::mdd::MddDescriptor< T >::domain, line::spn::SpnMode< T >::enab, line::qn::TransitionParam< T >::enabling, line::mdd::MddDescriptor< T >::events, line::spn::SpnInfo< T >::ever_disabled, line::spn::SpnMode< T >::fire, line::qn::TransitionParam< T >::firing, line::qn::TransitionParam< T >::firingdep, line::qn::TransitionParam< T >::firingproc, line::lang::IMMEDIATE, line::spn::SpnResult< T >::info, line::spn::SpnMode< T >::inhib, line::qn::TransitionParam< T >::inhibit_total(), line::qn::TransitionParam< T >::inhibiting, line::spn::SpnInfo< T >::init, line::InputError::InputError(), line::mdd::MDD::insert(), line::mdd::MddDescriptor< T >::invariant_value, line::mdd::MddDescriptor< T >::invariant_weights, line::mdd::MddDescriptor< T >::K, line::spn::SpnInfo< T >::levelkind, line::spn::SpnInfo< T >::levelname, line::mdd::mdd_entry_law(), line::spn::SpnResult< T >::mdds, line::mdd::MDD::member(), line::spn::SpnMode< T >::mode, line::spn::SpnInfo< T >::modes, line::mdd::MddDescriptor< T >::N, line::qn::TransitionParam< T >::nmodes, line::qn::TransitionParam< T >::nmodeservers, line::spn::SpnInfo< T >::nnodes, line::spn::SpnMode< T >::nph, line::spn::SpnInfo< T >::nplacelevels, line::mam::Map< T >::order(), line::spn::SpnInfo< T >::phaseof, line::spn::SpnMode< T >::pie, line::lang::Place, line::spn::SpnInfo< T >::placenames, line::spn::SpnInfo< T >::places, spn_mdd(), line::spn::SpnMode< T >::srv, line::qn::TransitionParam< T >::timing, line::mdd::MDD::to_struct(), line::spn::SpnMode< T >::trans, line::lang::Transition, and line::UnsupportedError::UnsupportedError().

Referenced by spn_mdd(), and spn_pf().

spn_metrics()

template<class T>

SpnMetrics< T > line::spn::spn_metrics	(	const mdd::MddStruct &	mdds,
		const std::vector< std::vector< T > > &	g,
		const SpnInfo< T > &	info )

Every measure of Sec.

3.1 from one diagram and one product form.

Parameters

mdds	the reachable set built by spn_mdd
g	per-level product-form factors g_l(v)
info	the metadata spn_mdd returned alongside the diagram

Definition at line 78 of file spn_metrics.h.

References line::spn::SpnMode< T >::D1, line::spn::SpnMode< T >::dep, line::spn::SpnMode< T >::enab, line::spn::SpnEnabling< T >::eq, line::spn::SpnMetrics< T >::G, line::spn::SpnEnabling< T >::ge, line::spn::SpnMetrics< T >::marginal, line::mdd::mdd_rec(), line::mdd::mdd_rec_marginal(), line::spn::SpnMode< T >::mode, line::spn::SpnMetrics< T >::mode_tput, line::spn::SpnMetrics< T >::mode_util, line::spn::SpnInfo< T >::modes, line::spn::SpnMode< T >::nph, line::spn::SpnInfo< T >::nplacelevels, line::NumericError::NumericError(), line::spn::SpnMetrics< T >::place_tput, line::spn::SpnMetrics< T >::place_util, spn_metrics(), spn_rec_enabled(), line::spn::SpnMode< T >::srv, line::spn::SpnMetrics< T >::tokens, line::spn::SpnMode< T >::trans, and line::UnsupportedError::UnsupportedError().

Referenced by line::nc::solver_nc_spn_analyzer(), and spn_metrics().

spn_pf()

template<class T>

SpnPfResult< T > line::spn::spn_pf	(	const qn::NetworkStruct< T > &	sn,
		const SpnPfOptions &	options = SpnPfOptions() )

Derive the product form of a stochastic Petri net.

Parameters

sn	the network structure of a net holding Places and Transitions
options	tolerances and bounds

Returns

the per-level factors and the certificate

Definition at line 209 of file spn_pf.h.

References line::spn::SpnOptions::bound, line::spn::SpnPfResult< T >::complexes, line::mc::ctmc_solve(), line::spn::SpnPfResult< T >::deficiency, line::spn::SpnOptions::descriptor, line::spn::SpnInfo< T >::diagram, line::mdd::MDD::enumerate(), line::spn::SpnPfResult< T >::g, line::lang::INF, line::InputError::InputError(), line::spn::SpnPfResult< T >::kind, line::spn::SpnPfResult< T >::linkage, line::lstsq(), line::spn::SpnInfo< T >::modes, line::spn::SpnInfo< T >::nnodes, line::spn::SpnInfo< T >::nplacelevels, line::spn::SpnInfo< T >::placenames, line::spn::SpnInfo< T >::places, line::spn::SpnPfResult< T >::residual, line::rref(), line::spn::SpnPfResult< T >::spn, spn_mdd(), spn_pf(), line::spn::SpnPfResult< T >::srank, line::UnsupportedError::UnsupportedError(), line::spn::SpnPfResult< T >::weakly_reversible, line::LstsqResult< T >::x, and line::spn::SpnPfResult< T >::y.

Referenced by line::nc::solver_nc_spn_analyzer(), and spn_pf().

spn_rec_enabled()

template<class T>

SpnEnabling< T > line::spn::spn_rec_enabled	(	const mdd::MddStruct &	mdds,
		const std::vector< std::vector< T > > &	g,
		const SpnMode< T > &	mde,
		std::size_t	nplacelevels )

Enabling-degree masses of mode mde over the reachable set in mdds.

Parameters

mdds	the reachable set built by spn_mdd
g	per-level product-form factors, one vector per level
mde	the mode, as returned in SpnInfo::modes
nplacelevels	how many leading levels are place levels

Definition at line 64 of file spn_rec_enabled.h.

References line::mdd::MddStruct::domain, line::spn::SpnMode< T >::enab, line::spn::SpnEnabling< T >::eq, line::spn::SpnEnabling< T >::ge, line::spn::SpnMode< T >::inhib, line::InputError::InputError(), line::mdd::MddStruct::K, line::spn::SpnEnabling< T >::max_degree, line::mdd::mdd_rec_masked(), and spn_rec_enabled().

Referenced by spn_metrics(), and spn_rec_enabled().

spn_sinvariants()

template<class T>

SpnInvariants line::spn::spn_sinvariants	(	const qn::NetworkStruct< T > &	sn,
		const std::vector< double > &	init = std::vector<double>() )

Minimal-support S-invariants and the load vector of a net.

Parameters

sn	a NetworkStruct holding Places and Transitions
init	initial marking per place level; empty takes it from the reference station of each closed class, as spn_mdd does

Definition at line 110 of file spn_sinvariants.h.

References line::qn::TransitionParam< T >::arc_total(), line::qn::TransitionParam< T >::enabling, line::qn::TransitionParam< T >::firing, line::InputError::InputError(), line::spn::SpnInvariants::m0, line::qn::TransitionParam< T >::nmodes, line::lang::Place, line::spn::SpnInvariants::places, line::spn::SpnInvariants::S, spn_sinvariants(), and line::lang::Transition.

Referenced by spn_lpbnd(), and spn_sinvariants().