Namespaces
namespace	ag
namespace	aoi
namespace	api
namespace	autosolver
namespace	ba
namespace	cache
namespace	ctmc
namespace	da
namespace	dpfqn
namespace	dqsys
namespace	env
namespace	fes
namespace	fj
namespace	fluid
namespace	http
namespace	infer
namespace	io
namespace	jmt
namespace	lang
namespace	ldes
namespace	ln
namespace	lossn
namespace	lp
namespace	lqn
namespace	lqns
namespace	lsn
namespace	lti
namespace	mam
namespace	mapqn
namespace	mc
namespace	mdd
namespace	me
namespace	mmdp
namespace	moment
namespace	mva
namespace	nc
namespace	npfqn
namespace	opt
namespace	perm
namespace	pfqn
namespace	polling
namespace	qn
namespace	qns
namespace	qsys
namespace	reg
namespace	retrieval
namespace	rng
namespace	sens
namespace	sim
namespace	smc
namespace	sn
namespace	snc
namespace	solvers
namespace	spn
namespace	ssa
namespace	sum
namespace	sym
namespace	tr
namespace	trace
namespace	uq
namespace	util
namespace	wf
namespace	workflow
namespace	ws
namespace	xml

Classes
struct	ApiEntry
struct	AugLagOptions
	Tuning of the outer multiplier iteration. More...
struct	AugLagResult
	Outcome of a constrained solve. More...
struct	AvgTable
	getAvgTable, one row per (station, class) that carries a metric. More...
struct	Bound
	Box constraint on one variable. More...
struct	BoundsTable
	SolverBA(model, method).getBoundsTable(). More...
class	Cache
	Cache(model, name, params). More...
struct	CdfCurve
	One response-time CDF curve: F the CDF value, t the time it is reached. More...
class	ClassSwitch
	ClassSwitch(model, name, C). More...
class	ClosedClass
	ClosedClass(model, name, njobs, refstat, prio). More...
class	Delay
	Delay(model, name): the infinite-server station. More...
class	Error
	Base error for the multiprecision C++ port. More...
class	Fork
	Fork(model, name). More...
class	InputError
	Malformed or inconsistent input (dimensions, negative populations, ...). More...
class	JobClass
	A job class: the index it was given, and the model that owns it. More...
class	Join
	Join(model, name, fork). More...
struct	LevmarOptions
	Tuning of the Levenberg-Marquardt iteration. More...
struct	LevmarResult
	Outcome of a least-squares solve. More...
struct	LsodaOptions
	Integration controls. More...
struct	LsodaSolution
	Result of an integration, mirroring OdeSolution in ode.h. More...
class	LsodaStepper
	One internal step at a time: ODEPACK's itask = 2. More...
struct	LstsqResult
	Outcome of lstsq: the solution and whether the system was rank deficient. More...
class	Matrix
class	MatrixView
struct	NelderMeadOptions
	Tuning of the simplex iteration. More...
struct	NelderMeadResult
	Outcome of a simplex minimization. More...
class	NetworkSolver
	The shared surface of every solver, Python's NetworkSolver. More...
struct	NoConstraints
	A constraint map that returns no constraints; the default for h or g. More...
class	Node
	A node of the model: the index it was given, and the model that owns it. More...
struct	num_traits
struct	num_traits< Complex >
struct	num_traits< double >
struct	num_traits< Rational >
struct	num_traits< Real< D > >
class	NumericError
	The algorithm cannot proceed on this instance (singular matrix, ...). More...
struct	OdeOptions
	Integration controls. More...
struct	OdeSolution
	Result of an integration. More...
class	OpenClass
	OpenClass(model, name, prio). More...
struct	pivot_mag
	The ordered type the pivot search compares in. More...
struct	pivot_mag< std::complex< R > >
	Partial pivoting compares moduli, since the complex field is unordered. More...
class	Place
	Place(model, name): a Petri-net place. More...
class	Queue
	Queue(model, name, strategy). More...
struct	RealSchur
	Real Schur factorization A = Z T Z^T, with Z orthogonal and T upper quasi-triangular: 1 x 1 diagonal blocks for real eigenvalues and 2 x 2 blocks for complex conjugate pairs. More...
struct	RootResult
	Outcome of a scalar solve. More...
class	Router
	Router(model, name): a stateless routing node. More...
class	SelfLoopingClass
	SelfLoopingClass(model, name, njobs, refstat, prio). More...
class	Sink
	Sink(model, name): the external departure node, which holds no jobs. More...
class	SolverBA
	SolverBA: the bounding solver, whose result is a bounds table. More...
class	SolverCTMC
	SolverCTMC: the average table plus the chain it was computed from. More...
class	SolverFLD
	SolverFLD: the fluid solver, which also answers a transient. More...
struct	SolverOptions
	The knobs a solver reads; a negative or empty field keeps the engine default. More...
class	Source
	Source(model, name): the external arrival station. More...
class	Station
	A node that holds jobs and serves them: MATLAB's Station. More...
struct	SvdFactors
	A = U diag(s) Vt, with U (m x m), s of length min(m,n) and Vt (n x n). More...
class	SylvesterFactor
	The Kronecker operator of a FIXED (A,B) pair, factorized once. More...
struct	TranAvg
	getTranAvg: the transient mean queue length per (station, class). More...
class	Transition
	Transition(model, name, params): a Petri-net transition. More...
class	UnsupportedError
	Requested feature or arithmetic mode is not ported yet. More...

Typedefs
typedef lang::Distrib< double >	Distribution
typedef qn::Network< double >	NetworkModel
typedef qn::RoutingMatrix< double >	Routing
typedef lang::Distrib< double >	Dist
using	Complex = std::complex<double>
using	Rational
using	BigInt = boost::multiprecision::cpp_int
template<unsigned Digits10>
using	Real = boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits10>>
using	Real50 = Real<50>
	Precision tiers offered by the CLI's –arith real:<digits> flag.
using	Real100 = Real<100>
using	Real200 = Real<200>
typedef qn::Network< double >	Network
	Network as a user names it: the double model, Python's Network.
typedef qn::RoutingMatrix< double >	RoutingMatrix
	model.init_routing_matrix()'s type, Python's RoutingMatrix.
typedef SolverMVA	MVA
typedef SolverNC	NC
typedef SolverCTMC	CTMC
typedef SolverSSA	SSA
typedef SolverFLD	FLD
typedef SolverFLD	SolverFluid
typedef SolverMAM	MAM
typedef SolverJMT	JMT
typedef SolverLDES	LDES
typedef SolverAUTO	AUTO
typedef SolverBA	BA
using	LsodaRhs = std::function<void(double t, const double* y, double* dydt)>
	The right-hand side dy/dt = f(t, y).

Enumerations
enum class	Arith { Double , Exact , Real }

Functions
	LINE_DIST_CTOR (Exp)
	Exp(rate): the exponential law of the given RATE, as Python's Exp.
	LINE_DIST_CTOR (Erlang)
	Erlang(phase_rate, nphases).
	LINE_DIST_CTOR (HyperExp)
	HyperExp(p, lambda1, lambda2).
	LINE_DIST_CTOR (Coxian)
	Coxian(mu, phi).
	LINE_DIST_CTOR (Cox2)
	Cox2(mu1, mu2, phi1).
	LINE_DIST_CTOR (PH)
	PH(alpha, A): a general phase-type law.
	LINE_DIST_CTOR (APH)
	APH(alpha, A): the acyclic phase-type law.
	LINE_DIST_CTOR (MAP)
	MAP(D0, D1).
	LINE_DIST_CTOR (Det)
	Det(t): the deterministic law.
	LINE_DIST_CTOR (Immediate)
	Immediate(): a zero-time transition.
	LINE_DIST_CTOR (Disabled)
	Disabled(): the class is not served here.
	LINE_DIST_CTOR (Uniform)
	Uniform(a, b).
	LINE_DIST_CTOR (Pareto)
	Pareto(shape, scale).
	LINE_DIST_CTOR (Gamma)
	Gamma(shape, scale).
	LINE_DIST_CTOR (Weibull)
	Weibull(scale, shape).
	LINE_DIST_CTOR (Lognormal)
	Lognormal(logmean, logsigma).
	LINE_DIST_CTOR (Normal)
	Normal(mu, sigma).
	LINE_DIST_CTOR (Geometric)
	Geometric(p).
	LINE_DIST_CTOR (Bernoulli)
	Bernoulli(p).
	LINE_DIST_CTOR (Binomial)
	Binomial(n, p).
	LINE_DIST_CTOR (Poisson)
	Poisson(lambda).
	LINE_DIST_CTOR (DiscreteUniform)
	DiscreteUniform(a, b).
	LINE_DIST_CTOR (Zipf)
	Zipf(s, n).
	LINE_DIST_CTOR (DiscreteSampler)
	DiscreteSampler(p, x).
	LINE_DIST_CTOR (Replayer)
	Replayer(samples) / Replayer(samples, path): the trace-driven law.
void	serial_routing (Routing &P, std::size_t r, std::size_t s, const std::vector< std::size_t > &nodes)
	Network.serialRouting(nodes) for one class pair: 1 -> 2 -> ... -> n.
void	serial_routing (Routing &P, std::size_t r, const std::vector< std::size_t > &nodes)
	Network.serialRouting(nodes) on one class of a model.
void	cyclic_routing (Routing &P, std::size_t r, const std::vector< std::size_t > &nodes)
	The same chain closed into a cycle, which is how a closed model circulates.
double	log_bigint (const BigInt &v)
	log(v) for a positive arbitrary-precision integer.
template<class T>
T	num_abs (const T &v)
template<>
double	num_abs< double > (const double &v)
template<class T>
T	num_factorial (unsigned n)
	Factorial as a value of T.
template<class T>
T	num_pow_int (const T &base, unsigned e)
	Integer power, valid in any field (no transcendental requirement).
const char *	arith_name (Arith a)
const std::vector< ApiEntry > &	api_registry ()
	The registry is a function-local static, not a global object, so there is no static-initialization order issue and no mutable global state to guard when the library is called from Python with the GIL released.
const ApiEntry *	find_api (const std::string &name)
bool	api_supports (const ApiEntry &e, Arith a)
	LINE_DECLARE_SOLVER (SolverMVA, "MVA")
	LINE_DECLARE_SOLVER (SolverNC, "NC")
	LINE_DECLARE_SOLVER (SolverMAM, "MAM")
	LINE_DECLARE_SOLVER (SolverSSA, "SSA")
	LINE_DECLARE_SOLVER (SolverJMT, "JMT")
	LINE_DECLARE_SOLVER (SolverLDES, "LDES")
	LINE_DECLARE_SOLVER (SolverAUTO, "AUTO")
template<class T>
AugLagOptions< T >	auglag_defaults ()
	Defaults: rho0 = 10, growth 10, feasibility 1e-10, 50 outer iterations.
template<class T, class F, class H, class G>
AugLagResult< T >	auglag (F f, H h, G g, const std::vector< T > &x0, const std::vector< Bound< T > > &bounds, const AugLagOptions< T > &opt)
	Augmented Lagrangian with a scalar objective and a simplex inner solver.
template<class T, class F, class H, class G>
AugLagResult< T >	auglag (F f, H h, G g, const std::vector< T > &x0, const std::vector< Bound< T > > &bounds)
	auglag with the default tuning.
template<class T, class R, class H, class G>
AugLagResult< T >	auglag_ls (R r, std::size_t m, H h, G g, const std::vector< T > &x0, const AugLagOptions< T > &opt)
	Augmented Lagrangian with a least-squares objective and levmar as the inner solver.
template<class T, class R, class H, class G>
AugLagResult< T >	auglag_ls (R r, std::size_t m, H h, G g, const std::vector< T > &x0)
	auglag_ls with the default tuning.
Rational	rational_from_decimal (const std::string &s)
	The literal as an exact rational, num/10^k with no rounding.
template<class T>
T	num_from_decimal (const std::string &s)
	Parse a decimal literal into T.
template<>
Rational	num_from_decimal< Rational > (const std::string &s)
double	dbl_from_decimal (const std::string &s, double fallback)
	Parse a decimal literal as a plain double (multiplicities, populations, tolerances).
std::vector< std::complex< double > >	eig_values (const Matrix< double > &A)
	Eigenvalues of a general real square matrix, in LAPACK's order.
double	spectral_radius (const Matrix< double > &A)
	Largest modulus over the spectrum, i.e.
double	subdominant_modulus (const Matrix< double > &A)
	Second largest modulus over the spectrum.
std::vector< double >	svd_values (const Matrix< double > &A)
	Singular values in descending order.
RealSchur	schur_decomposition (const Matrix< double > &A)
	Real Schur factorization of a general square matrix (LAPACK dgees, unsorted).
RealSchur	schur_reorder (const RealSchur &s, const std::vector< double > &key)
	Reorder the diagonal blocks of a real Schur form into DESCENDING key order, stably, updating Z so that A = Z T Z^T still holds.
std::size_t	matrix_rank (const Matrix< double > &A)
	Numerical rank at the standard max(m,n) eps sigma_1 threshold.
template<class T>
Matrix< T >	expm (const Matrix< T > &A)
	Matrix exponential exp(A).
template<class T>
Matrix< T >	expm (const Matrix< T > &A, const T &t)
	exp(t A), the form every MAP descriptor actually needs.
void	dft (std::vector< std::complex< double > > &a, bool inverse)
	In-place DFT of a.
template<class T>
LevmarOptions< T >	levmar_defaults ()
	MINPACK-like defaults, with a central-difference step of eps^(1/3).
template<class T, class F>
Matrix< T >	levmar_jacobian_fd (F f, const std::vector< T > &x, std::size_t m, const T &diff_step)
	Central-difference Jacobian of r at x.
template<class T, class F, class J>
LevmarResult< T >	levmar_jac (F f, J jac, const std::vector< T > &x0, std::size_t m, const LevmarOptions< T > &opt)
	Levenberg-Marquardt with a caller-supplied Jacobian.
template<class T, class F>
LevmarResult< T >	levmar (F f, const std::vector< T > &x0, std::size_t m, const LevmarOptions< T > &opt)
	Levenberg-Marquardt with a central-difference Jacobian.
template<class T, class F>
LevmarResult< T >	levmar (F f, const std::vector< T > &x0, std::size_t m)
	levmar with the default tuning.
template<class T>
Matrix< T >	eye (std::size_t n)
	Identity of order n.
template<class T>
Matrix< T >	matmul (const Matrix< T > &A, const Matrix< T > &B)
	Matrix product A B.
template<class T>
std::vector< T >	vecmul (const std::vector< T > &v, const Matrix< T > &A)
	Row vector times matrix, v A.
template<class T>
std::vector< T >	mulvec (const Matrix< T > &A, const std::vector< T > &v)
	Matrix times column vector, A v.
template<class T>
Matrix< T >	inverse (const Matrix< T > &A)
	Inverse by LU with one factorization and n back substitutions.
template<class T>
Matrix< T >	matpow (const Matrix< T > &A, unsigned k)
	Integer matrix power, by repeated squaring.
template<class T>
std::vector< T >	ones (std::size_t n)
	Column vector of ones, the ubiquitous e in MAP algebra.
LsodaSolution	lsoda_integrate_stepwise (const LsodaRhs &f, const std::vector< double > &y0, const std::vector< double > &t_eval, const LsodaOptions &opt)
	Integrate dy/dt = f(t, y) from t_eval.front() through every later entry of t_eval, returning the state at each.
LsodaSolution	lsoda_integrate (const LsodaRhs &f, const std::vector< double > &y0, const std::vector< double > &t_eval, const LsodaOptions &opt=LsodaOptions())
std::vector< double >	lsoda_final (const LsodaRhs &f, const std::vector< double > &y0, double t0, double t1, const LsodaOptions &opt=LsodaOptions())
	Convenience form: integrate from t0 to t1 and report only the end state.
template<class T>
std::vector< std::size_t >	rref (Matrix< T > &A, const T &tol)
	Reduced row echelon form of A, in place, returning the pivot columns.
template<class T>
LstsqResult< T >	lstsq (const Matrix< T > &A, const std::vector< T > &b, const T &tol)
	Least-squares solution of A x = b, minimum-norm when A is rank deficient.
template<class T>
LstsqResult< T >	lstsq (const Matrix< T > &A, const std::vector< T > &b)
	Overload picking the default pivot threshold for the arithmetic in use.
template<class T>
std::vector< std::size_t >	lu_factor (Matrix< T > &A)
	In-place LU of A (n x n).
template<class T>
void	lu_solve (const Matrix< T > &LU, const std::vector< std::size_t > &piv, std::vector< T > &b)
	Solve LUx = Pb in place on b, using the factors from lu_factor.
template<class T>
T	lu_det (const Matrix< T > &A)
	Determinant of a square matrix, by the same partial-pivoting elimination.
template<class T>
std::vector< T >	solve (const Matrix< T > &A, const std::vector< T > &b)
	Convenience: solve Ax = b, leaving A and b untouched.
template<class T, class S>
Matrix< T >	matrix_from (const MatrixView< S > &v)
	Deep copy of a view into an owning matrix, converting the element type.
template<class T>
NelderMeadOptions< T >	nelder_mead_defaults ()
	fminsearch's coefficients and initial simplex, with tighter tolerances.
template<class T>
Bound< T >	bound_free ()
	Unbounded variable.
template<class T>
Bound< T >	bound_lower (const T &lo)
	lo <= x.
template<class T>
Bound< T >	bound_upper (const T &hi)
	x <= hi.
template<class T>
Bound< T >	bound_box (const T &lo, const T &hi)
	lo <= x <= hi.
template<class T, class F>
NelderMeadResult< T >	nelder_mead (F f, const std::vector< T > &x0, const NelderMeadOptions< T > &opt)
	Unconstrained simplex minimization.
template<class T, class F>
NelderMeadResult< T >	nelder_mead (F f, const std::vector< T > &x0)
	nelder_mead with the default tuning.
template<class T, class F>
NelderMeadResult< T >	nelder_mead_box (F f, const std::vector< T > &x0, const std::vector< Bound< T > > &bounds, const NelderMeadOptions< T > &opt)
	Box-constrained simplex minimization by the transformation described in the header comment.
template<class T, class F>
NelderMeadResult< T >	nelder_mead_box (F f, const std::vector< T > &x0, const std::vector< Bound< T > > &bounds)
	nelder_mead_box with the default tuning.
template<class T, class F>
Matrix< T >	ode_numeric_jacobian (const F &f, const T &t, const std::vector< T > &y, const std::vector< T > &fy)
	Numeric Jacobian by central differences.
template<class T, class F, class J>
OdeSolution< T >	ode_rosenbrock4 (const F &f, const J &jac, const T &t0, const T &t1, const std::vector< T > &y0, const OdeOptions< T > &opt)
	Integrate y' = f(t,y) from t0 to t1 with an analytic Jacobian.
template<class T, class F>
OdeSolution< T >	ode_rosenbrock4 (const F &f, const T &t0, const T &t1, const std::vector< T > &y0, const OdeOptions< T > &opt)
	Integrate y' = f(t,y) with a numeric Jacobian by central differences.
template<class T, class F>
std::vector< T >	ode_rosenbrock4_endpoint (const F &f, const T &t0, const T &t1, const std::vector< T > &y0)
	Integrate with the default options and return only the state at t1.
std::vector< std::size_t >	plane_sizes (const std::vector< int > &N)
	Mixed-radix plane sizes: prods[r] = prod_{s<r} (N[s]+1).
std::size_t	population_count (const std::vector< int > &N)
	Number of population vectors n with 0 <= n <= N.
std::size_t	pop_index (const std::vector< int > &n, const std::vector< std::size_t > &prods)
	Index of n in the lattice, 0-based (MATLAB hashpop is 1-based).
bool	next_pop (std::vector< int > &n, const std::vector< int > &N)
	Advance n to the next population vector in the lattice 0 <= n <= N, odometer order with the last class varying fastest.
double	nck (int n, int k)
	Binomial coefficient with a thread-local memo table (mp_pfqn util/nck.c).
double	multichoose (int n, int k)
	Number of multisets of size k from n types, i.e.
template<class T>
T	num_nck (int n, int k)
	Binomial coefficient as a value of T, by the Pascal recurrence.
template<class T, class F>
RootResult< T >	root_bisect (F f, const T &a, const T &b, const T &tol, unsigned maxiter=200)
	Bisection on a bracket with a sign change.
template<class T, class F>
RootResult< T >	root_brent (F f, const T &a0, const T &b0, const T &tol, unsigned maxiter=200)
	Brent's method on a bracket with a sign change.
template<class T, class F, class DF>
RootResult< T >	root_newton (F f, DF df, const T &x0, const T &tol, unsigned maxiter=200)
	Plain Newton from a starting point.
template<class T, class F, class DF>
RootResult< T >	root_newton_safe (F f, DF df, const T &a0, const T &b0, const T &tol, unsigned maxiter=200)
	Newton safeguarded by a bracket with a sign change: the Newton step is used only when it stays inside the bracket and at least halves it, otherwise the step is a bisection.
template<class T, class F>
void	bracket_expand (F f, const T &a, T &b, unsigned maxdoubling=200)
	Expand a bracket to the right until f changes sign, doubling the upper end.
SvdFactors	svd_full (const Matrix< double > &A)
	Full SVD of a real matrix, singular values in descending order.
Matrix< double >	pinv (const Matrix< double > &A)
	Moore-Penrose pseudo-inverse, A^+ = V diag(1/s_i) U^T over the singular values above max(m,n) eps sigma_1, which is MATLAB's default pinv tolerance.
template<class T>
Matrix< T >	sylvester_solve (const Matrix< T > &A, const Matrix< T > &B, const Matrix< T > &C)
	Solve A X + X B = C for X.
template<class T>
Matrix< T >	lyap_solve (const Matrix< T > &A, const Matrix< T > &B, const Matrix< T > &C)
	MATLAB lyap(A,B,C) solves A X + X B + C = 0, i.e.
Matrix< double >	sylvester_schur (const Matrix< double > &A, const Matrix< double > &B, const Matrix< double > &C)
	A X + X B = C by Bartels-Stewart, at double.
Matrix< double >	lyap_schur (const Matrix< double > &A, const Matrix< double > &B, const Matrix< double > &C)
	MATLAB lyap(A,B,C) at double via Bartels-Stewart: A X + X B + C = 0.

Typedef Documentation

◆ AUTO

typedef SolverAUTO line::AUTO

Definition at line 182 of file solver.h.

◆ BA

typedef SolverBA line::BA

Definition at line 183 of file solver.h.

◆ BigInt

using line::BigInt = boost::multiprecision::cpp_int

Definition at line 78 of file number.h.

◆ Complex

using line::Complex = std::complex<double>

Definition at line 43 of file complex_number.h.

◆ CTMC

typedef SolverCTMC line::CTMC

Definition at line 175 of file solver.h.

◆ Dist

typedef lang::Distrib<double> line::Dist

Definition at line 53 of file nodes.h.

◆ Distribution

typedef lang::Distrib<double> line::Distribution

Definition at line 42 of file distributions.h.

◆ FLD

typedef SolverFLD line::FLD

Definition at line 177 of file solver.h.

◆ JMT

typedef SolverJMT line::JMT

Definition at line 180 of file solver.h.

◆ LDES

typedef SolverLDES line::LDES

Definition at line 181 of file solver.h.

◆ LsodaRhs

using line::LsodaRhs = std::function<void(double t, const double* y, double* dydt)>

The right-hand side dy/dt = f(t, y).

y and dydt are plain 0-based arrays of length neq. The vendored solver keeps its state 1-based internally, as the Fortran original did, and hands the callback pointers already offset past the unused slot, so nothing here has to know about that.

Definition at line 54 of file lsoda.h.

◆ MAM

typedef SolverMAM line::MAM

Definition at line 179 of file solver.h.

◆ MVA

typedef SolverMVA line::MVA

Definition at line 173 of file solver.h.

◆ NC

typedef SolverNC line::NC

Definition at line 174 of file solver.h.

◆ Network

typedef qn::Network<double> line::Network

Network as a user names it: the double model, Python's Network.

Definition at line 53 of file solver.h.

◆ NetworkModel

typedef qn::Network<double> line::NetworkModel

Definition at line 51 of file nodes.h.

◆ Rational

using line::Rational

Initial value:

boost::multiprecision::number<boost::multiprecision::cpp_rational_backend,

boost::multiprecision::et_off>

Definition at line 76 of file number.h.

◆ Real

template<unsigned Digits10>

using line::Real = boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits10>>

Definition at line 80 of file number.h.

◆ Real100

using line::Real100 = Real<100>

Definition at line 85 of file number.h.

◆ Real200

using line::Real200 = Real<200>

Definition at line 86 of file number.h.

◆ Real50

using line::Real50 = Real<50>

Precision tiers offered by the CLI's –arith real:<digits> flag.

Definition at line 84 of file number.h.

◆ Routing

typedef qn::RoutingMatrix<double> line::Routing

Definition at line 52 of file nodes.h.

◆ RoutingMatrix

typedef qn::RoutingMatrix<double> line::RoutingMatrix

model.init_routing_matrix()'s type, Python's RoutingMatrix.

Definition at line 55 of file solver.h.

◆ SolverFluid

typedef SolverFLD line::SolverFluid

Definition at line 178 of file solver.h.

◆ SSA

typedef SolverSSA line::SSA

Definition at line 176 of file solver.h.

Enumeration Type Documentation

◆ Arith

enum class line::Arith

strong

Enumerator
Double
Exact
Real

Definition at line 26 of file registry.h.

Function Documentation

◆ api_registry()

const std::vector< ApiEntry > & line::api_registry ( )

inline

The registry is a function-local static, not a global object, so there is no static-initialization order issue and no mutable global state to guard when the library is called from Python with the GIL released.

Definition at line 49 of file registry.h.

References api_registry(), Double, Exact, and Real.

Referenced by api_registry(), and find_api().

◆ api_supports()

bool line::api_supports	(	const ApiEntry &	e,
		Arith	a )

inline

Definition at line 1684 of file registry.h.

References api_supports(), and line::ApiEntry::arith.

Referenced by line::reg::api_invoke(), and api_supports().

◆ arith_name()

const char * line::arith_name ( Arith a )

inline

Definition at line 28 of file registry.h.

References arith_name(), Double, Exact, and Real.

Referenced by line::reg::api_invoke(), and arith_name().

◆ auglag() [1/2]

template<class T, class F, class H, class G>

AugLagResult< T > line::auglag	(	F	f,
		H	h,
		G	g,
		const std::vector< T > &	x0,
		const std::vector< Bound< T > > &	bounds )

auglag with the default tuning.

Definition at line 215 of file auglag.h.

References auglag(), and auglag_defaults().

◆ auglag() [2/2]

template<class T, class F, class H, class G>

AugLagResult< T > line::auglag	(	F	f,
		H	h,
		G	g,
		const std::vector< T > &	x0,
		const std::vector< Bound< T > > &	bounds,
		const AugLagOptions< T > &	opt )

Augmented Lagrangian with a scalar objective and a simplex inner solver.

Parameters

f	objective, x -> T
h	equality constraints, x -> vector (empty for none)
g	inequality constraints g(x) <= 0, x -> vector (empty for none)
x0	starting point
bounds	one Bound per variable; pass all-free bounds for none
opt	tuning

Definition at line 141 of file auglag.h.

References auglag(), line::AugLagResult< T >::converged, line::NelderMeadResult< T >::converged, line::AugLagResult< T >::fval, line::InputError::InputError(), line::AugLagResult< T >::lambda, line::AugLagResult< T >::mu, nelder_mead_box(), line::AugLagResult< T >::outer_iterations, line::AugLagResult< T >::violation, line::AugLagResult< T >::x, and line::NelderMeadResult< T >::x.

Referenced by line::mam::amap2_adjust_gamma(), auglag(), auglag(), line::mam::map_anfit_lsq(), and line::mam::maph2m_fit_multiclass().

◆ auglag_defaults()

template<class T>

AugLagOptions< T > line::auglag_defaults ( )

Defaults: rho0 = 10, growth 10, feasibility 1e-10, 50 outer iterations.

Definition at line 81 of file auglag.h.

References auglag_defaults(), line::AugLagOptions< T >::ctol, line::AugLagOptions< T >::inner_lm, line::AugLagOptions< T >::inner_nm, levmar_defaults(), line::AugLagOptions< T >::max_outer, nelder_mead_defaults(), line::AugLagOptions< T >::rho0, line::AugLagOptions< T >::rho_factor, line::AugLagOptions< T >::rho_max, and line::AugLagOptions< T >::shrink.

Referenced by line::mam::amap2_adjust_gamma(), line::mam::aph2_adjust_opt_char(), line::mam::aph2_adjust_opt_param(), auglag(), auglag_defaults(), auglag_ls(), line::mam::m3pp22_fitc_approx_cov(), line::mam::m3pp2m_fitc_approx(), line::mam::m3pp2m_fitc_approx_ag(), line::mam::m3pp2m_fitc_approx_ag_multiclass(), line::mam::map_anfit_lsq(), and line::mam::mmpp2_fitc_approx().

◆ auglag_ls() [1/2]

template<class T, class R, class H, class G>

AugLagResult< T > line::auglag_ls	(	R	r,
		std::size_t	m,
		H	h,
		G	g,
		const std::vector< T > &	x0 )

auglag_ls with the default tuning.

Definition at line 320 of file auglag.h.

References auglag_defaults(), and auglag_ls().

◆ auglag_ls() [2/2]

template<class T, class R, class H, class G>

AugLagResult< T > line::auglag_ls	(	R	r,
		std::size_t	m,
		H	h,
		G	g,
		const std::vector< T > &	x0,
		const AugLagOptions< T > &	opt )

Augmented Lagrangian with a least-squares objective and levmar as the inner solver.

The augmented Lagrangian of a sum of squares is itself a sum of squares up to an additive constant, because lambda h + (rho/2) h^2 = (rho/2)(h + lambda/rho)^2 - lambda^2/(2 rho) (1/(2 rho)) max(0, mu + rho g)^2 = (rho/2) max(0, g + mu/rho)^2 so the inner problem is handed to levmar with the extended residual [ r(x) ; sqrt(rho/2) (h + lambda/rho) ; sqrt(rho/2) max(0, g + mu/rho) ]. The dropped constants do not move the minimizer. The max(.) makes the extended residual only piecewise smooth, which the finite-difference Jacobian tolerates because an inequality is either active or inactive over a whole differencing step except on a measure-zero set of iterates.

Bounds are NOT supported here (levmar is unconstrained): express them as inequality rows of g, which is what the callers in line/api/mam do.

Parameters

r	residual map, x -> vector of length m; the objective is sum r_i^2
m	number of residuals
h	equality constraints
g	inequality constraints g(x) <= 0
x0	starting point
opt	tuning

Definition at line 246 of file auglag.h.

References auglag_ls(), line::AugLagResult< T >::converged, line::LevmarResult< T >::converged, line::AugLagResult< T >::fval, line::InputError::InputError(), line::AugLagResult< T >::lambda, levmar(), line::AugLagResult< T >::mu, line::AugLagResult< T >::outer_iterations, line::AugLagResult< T >::violation, line::AugLagResult< T >::x, and line::LevmarResult< T >::x.

Referenced by line::mam::aph2_adjust_opt_char(), line::mam::aph2_adjust_opt_param(), auglag_ls(), auglag_ls(), and line::mam::mmpp2_fitc_approx().

◆ bound_box()

template<class T>

Bound< T > line::bound_box	(	const T &	lo,
		const T &	hi )

lo <= x <= hi.

Definition at line 146 of file neldermead.h.

References bound_box(), line::Bound< T >::has_hi, line::Bound< T >::has_lo, line::Bound< T >::hi, and line::Bound< T >::lo.

Referenced by line::mam::amap2_adjust_gamma(), and bound_box().

◆ bound_free()

template<class T>

Bound< T > line::bound_free ( )

Unbounded variable.

Definition at line 122 of file neldermead.h.

References line::Bound< T >::Bound(), and bound_free().

Referenced by bound_free().

◆ bound_lower()

template<class T>

Bound< T > line::bound_lower ( const T & lo )

lo <= x.

Definition at line 128 of file neldermead.h.

References bound_lower(), line::Bound< T >::has_lo, and line::Bound< T >::lo.

Referenced by line::mam::amap2_adjust_gamma(), and bound_lower().

◆ bound_upper()

template<class T>

Bound< T > line::bound_upper ( const T & hi )

x <= hi.

Definition at line 137 of file neldermead.h.

References bound_upper(), line::Bound< T >::has_hi, and line::Bound< T >::hi.

Referenced by bound_upper().

◆ bracket_expand()

template<class T, class F>

void line::bracket_expand	(	F	f,
		const T &	a,
		T &	b,
		unsigned	maxdoubling = 200 )

Expand a bracket to the right until f changes sign, doubling the upper end.

Used by the TTL cache fixed points, where the residual is monotone in the characteristic time but no upper bound is known a priori.

Exceptions

NumericError if no sign change is found before the cap

Definition at line 357 of file rootfind.h.

References bracket_expand(), and line::NumericError::NumericError().

Referenced by bracket_expand(), and line::cache::cache_t_lrum_map().

◆ cyclic_routing()

void line::cyclic_routing	(	Routing &	P,
		std::size_t	r,
		const std::vector< std::size_t > &	nodes )

inline

The same chain closed into a cycle, which is how a closed model circulates.

Definition at line 297 of file nodes.h.

References cyclic_routing(), serial_routing(), and line::qn::RoutingMatrix< T >::set().

Referenced by cyclic_routing().

◆ dbl_from_decimal()

double line::dbl_from_decimal	(	const std::string &	s,
		double	fallback )

inline

Parse a decimal literal as a plain double (multiplicities, populations, tolerances).

Definition at line 120 of file decimal.h.

References dbl_from_decimal().

Referenced by dbl_from_decimal(), and line::lqn::read_lqnx_model().

◆ dft()

void line::dft	(	std::vector< std::complex< double > > &	a,
		bool	inverse )

inline

In-place DFT of a.

inverse selects the +i sign and the 1/n scaling, so the pair matches MATLAB's fft and ifft.

Definition at line 120 of file fft.h.

References dft(), and inverse().

Referenced by dft().

◆ eig_values()

std::vector< std::complex< double > > line::eig_values ( const Matrix< double > & A )

inline

Eigenvalues of a general real square matrix, in LAPACK's order.

Definition at line 59 of file eig.h.

References line::Matrix< T >::cols(), eig_values(), line::InputError::InputError(), line::NumericError::NumericError(), line::Matrix< T >::rows(), and line::UnsupportedError::UnsupportedError().

Referenced by line::cache::cache_rmf_lna(), line::mc::ctmc_saddlepoint_perron(), eig_values(), line::fluid::fluid_lyapunov(), line::mam::map_gamma2(), line::smc::max_eig(), spectral_radius(), and subdominant_modulus().

◆ expm() [1/2]

template<class T>

Matrix< T > line::expm ( const Matrix< T > & A )

Matrix exponential exp(A).

Parameters

A	square matrix

Returns: exp(A), by scaling and squaring with a Pade approximant whose degree and scaling are chosen for the working precision of T

Definition at line 141 of file expm.h.

References line::Matrix< T >::cols(), expm(), eye(), line::InputError::InputError(), matmul(), line::NumericError::NumericError(), and line::Matrix< T >::rows().

Referenced by line::fluid::aoi_cdf(), line::cache::cache_lrum_map_levelstats(), line::mc::ctmc_passage_time(), line::mc::ctmc_saddlepoint(), line::lang::dist_cdf(), expm(), expm(), line::mam::map_acfc(), line::mam::map_cdf(), line::mam::map_count_moment(), line::mam::map_count_var(), line::mam::map_pdf(), line::mam::map_varcount(), line::mam::MeSampler< T >::MeSampler(), line::mam::mfq_ld_distr(), line::mam::mfq_ld_solve(), line::mam::mmap_count_var(), line::qsys::qsys_mapphc(), line::qsys::qsys_mg1_ps(), and line::mam::solver_mam_ldqbd_transient().

◆ expm() [2/2]

template<class T>

Matrix< T > line::expm	(	const Matrix< T > &	A,
		const T &	t )

exp(t A), the form every MAP descriptor actually needs.

Definition at line 198 of file expm.h.

References line::Matrix< T >::cols(), expm(), and line::Matrix< T >::rows().

◆ eye()

template<class T>

Matrix< T > line::eye ( std::size_t n )

Identity of order n.

Definition at line 28 of file linalg.h.

References eye().

Referenced by line::fluid::aoi_solve_bufferless(), line::fluid::aoi_solve_singlebuffer(), line::cache::cache_lrum_map_levelstats(), line::mam::dmap_geo_mul_sum(), line::mam::dmap_moment(), expm(), eye(), line::fj::fj_compute_pi(), line::fj::fj_compute_t(), line::fj::fj_compute_t_nare(), line::fj::fj_dist2fj(), line::fluid::fluid_drift_jacobian(), line::smc::gim1_pi_etaqa(), line::smc::gim1_qlen_etaqa(), line::mam::krons(), line::mam::mam_transient2(), line::mam::mam_transient2_open(), line::mam::map_joint(), matpow(), line::mam::mfq_fluflu_sojourn(), line::mam::mfq_fundamental(), line::mam::mfq_multiregime(), line::mam::mfq_prio_queue(), line::smc::mg1_cr(), line::smc::mg1_eg(), line::smc::mg1_fi(), line::mam::mmap3k_fit(), line::mam::mmap_max(), line::mam::mmap_max(), line::mam::mmap_modulate(), line::mam::mmapph1fcfs_ncdistr(), line::mam::mmapph1fcfs_ncmean(), line::mam::qbd_bmapbmap1(), line::mam::qbd_depproc_jointmom(), line::mam::qbd_fundmat(), line::mam::qbd_fundmat_laplace(), line::mam::qbd_mapmap1_blocks(), line::mam::qbd_pi(), line::mam::qbd_qlen_factmoment(), line::mam::qbd_R_logred(), line::mam::qbd_rap(), line::mam::qbd_raprap1(), line::qsys::qsys_dmc(), line::qsys::qsys_mapd1(), line::qsys::qsys_mapdc(), line::qsys::qsys_mapg1k(), line::qsys::qsys_mapphc(), line::mam::solver_mam_bmap_map_1_blocks(), line::mam::solver_mam_map_bmap_1_blocks(), and line::mam::solver_mam_transient_qbd().

◆ find_api()

const ApiEntry * line::find_api ( const std::string & name )

inline

Definition at line 1677 of file registry.h.

References api_registry(), and find_api().

Referenced by line::reg::api_invoke(), and find_api().

◆ inverse()

template<class T>

Matrix< T > line::inverse ( const Matrix< T > & A )

Inverse by LU with one factorization and n back substitutions.

Definition at line 72 of file linalg.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), inverse(), lu_factor(), lu_solve(), and line::Matrix< T >::rows().

◆ levmar() [1/2]

template<class T, class F>

LevmarResult< T > line::levmar	(	F	f,
		const std::vector< T > &	x0,
		std::size_t	m )

levmar with the default tuning.

Definition at line 320 of file levmar.h.

References levmar(), and levmar_defaults().

◆ levmar() [2/2]

template<class T, class F>

LevmarResult< T > line::levmar	(	F	f,
		const std::vector< T > &	x0,
		std::size_t	m,
		const LevmarOptions< T > &	opt )

Levenberg-Marquardt with a central-difference Jacobian.

Parameters

f	residual map, x -> vector of length m
x0	starting point
m	number of residuals
opt	tuning

Definition at line 301 of file levmar.h.

References line::LevmarResult< T >::evaluations, levmar(), levmar_jac(), and levmar_jacobian_fd().

Referenced by auglag_ls(), levmar(), and levmar().

◆ levmar_defaults()

template<class T>

LevmarOptions< T > line::levmar_defaults ( )

MINPACK-like defaults, with a central-difference step of eps^(1/3).

Definition at line 77 of file levmar.h.

References line::LevmarOptions< T >::diff_step, line::LevmarOptions< T >::ftol, line::LevmarOptions< T >::gtol, line::LevmarOptions< T >::lambda0, line::LevmarOptions< T >::lambda_decrease, line::LevmarOptions< T >::lambda_increase, line::LevmarOptions< T >::lambda_max, levmar_defaults(), line::LevmarOptions< T >::max_iter, and line::LevmarOptions< T >::xtol.

Referenced by auglag_defaults(), levmar(), and levmar_defaults().

◆ levmar_jac()

template<class T, class F, class J>

LevmarResult< T > line::levmar_jac	(	F	f,
		J	jac,
		const std::vector< T > &	x0,
		std::size_t	m,
		const LevmarOptions< T > &	opt )

Levenberg-Marquardt with a caller-supplied Jacobian.

Parameters

f	residual map, x -> vector of length m
jac	Jacobian map, x -> m x n Matrix
x0	starting point
m	number of residuals
opt	tuning

Definition at line 168 of file levmar.h.

References line::Matrix< T >::cols(), line::LevmarResult< T >::converged, line::LevmarResult< T >::evaluations, line::InputError::InputError(), line::LevmarResult< T >::iterations, levmar_jac(), num_abs(), line::LevmarResult< T >::residual, line::Matrix< T >::rows(), solve(), line::LevmarResult< T >::ssq, and line::LevmarResult< T >::x.

Referenced by levmar(), and levmar_jac().

◆ levmar_jacobian_fd()

template<class T, class F>

Matrix< T > line::levmar_jacobian_fd	(	F	f,
		const std::vector< T > &	x,
		std::size_t	m,
		const T &	diff_step )

Central-difference Jacobian of r at x.

The step for component j is diff_step * max(|x_j|, 1), so a variable of any magnitude gets a meaningful perturbation and a variable at zero still gets one.

Parameters

f	residual map, x -> vector of length m
x	evaluation point
m	number of residuals
diff_step	relative differencing step

Returns: the m x n Jacobian

Definition at line 133 of file levmar.h.

References line::InputError::InputError(), levmar_jacobian_fd(), and num_abs().

Referenced by levmar(), and levmar_jacobian_fd().

◆ LINE_DECLARE_SOLVER() [1/7]

line::LINE_DECLARE_SOLVER	(	SolverAUTO	,
		"AUTO"	)

References LINE_DECLARE_SOLVER().

◆ LINE_DECLARE_SOLVER() [2/7]

line::LINE_DECLARE_SOLVER	(	SolverJMT	,
		"JMT"	)

References LINE_DECLARE_SOLVER().

◆ LINE_DECLARE_SOLVER() [3/7]

line::LINE_DECLARE_SOLVER	(	SolverLDES	,
		"LDES"	)

References LINE_DECLARE_SOLVER().

◆ LINE_DECLARE_SOLVER() [4/7]

line::LINE_DECLARE_SOLVER	(	SolverMAM	,
		"MAM"	)

References LINE_DECLARE_SOLVER().

◆ LINE_DECLARE_SOLVER() [5/7]

line::LINE_DECLARE_SOLVER	(	SolverMVA	,
		"MVA"	)

References LINE_DECLARE_SOLVER().

Referenced by LINE_DECLARE_SOLVER(), LINE_DECLARE_SOLVER(), LINE_DECLARE_SOLVER(), LINE_DECLARE_SOLVER(), LINE_DECLARE_SOLVER(), LINE_DECLARE_SOLVER(), and LINE_DECLARE_SOLVER().

◆ LINE_DECLARE_SOLVER() [6/7]

line::LINE_DECLARE_SOLVER	(	SolverNC	,
		"NC"	)

References LINE_DECLARE_SOLVER().

◆ LINE_DECLARE_SOLVER() [7/7]

line::LINE_DECLARE_SOLVER	(	SolverSSA	,
		"SSA"	)

References LINE_DECLARE_SOLVER().

◆ LINE_DIST_CTOR() [1/25]

line::LINE_DIST_CTOR ( APH )

APH(alpha, A): the acyclic phase-type law.

APH.fitMeanAndSCV(mean, scv).

APH.fitCentral(mean, scv, skew).

Definition at line 124 of file distributions.h.

References line::lang::aph_fit_central(), line::lang::aph_fit_mean_scv(), LINE_DIST_CTOR(), and line::lang::Distrib< T >::phase_type().

◆ LINE_DIST_CTOR() [2/25]

line::LINE_DIST_CTOR ( Bernoulli )

Bernoulli(p).

Definition at line 206 of file distributions.h.

References line::lang::Distrib< T >::bernoulli(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [3/25]

line::LINE_DIST_CTOR ( Binomial )

Binomial(n, p).

Definition at line 211 of file distributions.h.

References line::lang::Distrib< T >::binomial(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [4/25]

line::LINE_DIST_CTOR ( Cox2 )

Cox2(mu1, mu2, phi1).

Cox2.fitCentral(mean, scv, skew).

Definition at line 106 of file distributions.h.

References line::lang::Distrib< T >::cox2(), line::lang::cox2_fit_central(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [5/25]

line::LINE_DIST_CTOR ( Coxian )

Coxian(mu, phi).

Coxian.fitMeanAndSCV(mean, scv).

Coxian.fitCentral(mean, scv, skew).

Definition at line 91 of file distributions.h.

References line::lang::Distrib< T >::coxian(), line::lang::coxian_fit_central(), line::lang::coxian_fit_mean_scv(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [6/25]

line::LINE_DIST_CTOR ( Det )

Det(t): the deterministic law.

Definition at line 146 of file distributions.h.

References line::lang::Distrib< T >::det(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [7/25]

line::LINE_DIST_CTOR ( Disabled )

Disabled(): the class is not served here.

Definition at line 156 of file distributions.h.

References line::lang::Distrib< T >::disabled_dist(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [8/25]

line::LINE_DIST_CTOR ( DiscreteSampler )

DiscreteSampler(p, x).

Definition at line 233 of file distributions.h.

References line::lang::Distrib< T >::discrete_sampler(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [9/25]

line::LINE_DIST_CTOR ( DiscreteUniform )

DiscreteUniform(a, b).

Definition at line 221 of file distributions.h.

References line::lang::Distrib< T >::discrete_uniform(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [10/25]

line::LINE_DIST_CTOR ( Erlang )

Erlang(phase_rate, nphases).

Erlang.fitMeanAndSCV(mean, scv).

Erlang.fitMeanAndOrder(mean, k).

Definition at line 58 of file distributions.h.

References line::lang::Distrib< T >::erlang(), line::lang::Distrib< T >::erlang_fit(), line::lang::erlang_fit_mean_order(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [11/25]

line::LINE_DIST_CTOR ( Exp )

Exp(rate): the exponential law of the given RATE, as Python's Exp.

Exp.fitMean(mean).

Exp.fitRate(rate).

Definition at line 49 of file distributions.h.

References line::lang::Distrib< T >::exp_rate(), and LINE_DIST_CTOR().

Referenced by LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), LINE_DIST_CTOR(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [12/25]

line::LINE_DIST_CTOR ( Gamma )

Gamma(shape, scale).

Gamma.fitMeanAndSCV(mean, scv).

Definition at line 175 of file distributions.h.

References line::lang::Distrib< T >::gamma_dist(), line::lang::gamma_fit_mean_scv(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [13/25]

line::LINE_DIST_CTOR ( Geometric )

Geometric(p).

Definition at line 201 of file distributions.h.

References line::lang::Distrib< T >::geometric(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [14/25]

line::LINE_DIST_CTOR ( HyperExp )

HyperExp(p, lambda1, lambda2).

HyperExp.fitMeanAndSCV(mean, scv).

HyperExp.fitMeanAndSCVBalanced(mean, scv).

Definition at line 73 of file distributions.h.

References line::lang::Distrib< T >::hyperexp(), line::lang::hyperexp_fit_mean_scv(), line::lang::hyperexp_fit_mean_scv_balanced(), line::lang::Distrib< T >::hyperexp_n(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [15/25]

line::LINE_DIST_CTOR ( Immediate )

Immediate(): a zero-time transition.

Definition at line 151 of file distributions.h.

References line::lang::Distrib< T >::immediate(), and LINE_DIST_CTOR().

◆ LINE_DIST_CTOR() [16/25]

line::LINE_DIST_CTOR ( Lognormal )

Lognormal(logmean, logsigma).

Definition at line 189 of file distributions.h.

References LINE_DIST_CTOR(), and line::lang::Distrib< T >::lognormal().

◆ LINE_DIST_CTOR() [17/25]

line::LINE_DIST_CTOR ( MAP )

MAP(D0, D1).

Definition at line 139 of file distributions.h.

References LINE_DIST_CTOR(), line::lang::MAP, and line::lang::Distrib< T >::map_dist().

◆ LINE_DIST_CTOR() [18/25]

line::LINE_DIST_CTOR ( Normal )

Normal(mu, sigma).

Definition at line 196 of file distributions.h.

References LINE_DIST_CTOR(), and line::lang::Distrib< T >::normal().

◆ LINE_DIST_CTOR() [19/25]

line::LINE_DIST_CTOR ( Pareto )

Pareto(shape, scale).

Pareto.fitMeanAndSCV(mean, scv).

Definition at line 166 of file distributions.h.

References LINE_DIST_CTOR(), line::lang::Distrib< T >::pareto(), and line::lang::pareto_fit_mean_scv().

◆ LINE_DIST_CTOR() [20/25]

line::LINE_DIST_CTOR ( PH )

PH(alpha, A): a general phase-type law.

Definition at line 117 of file distributions.h.

References LINE_DIST_CTOR(), and line::lang::Distrib< T >::phase_type().

◆ LINE_DIST_CTOR() [21/25]

line::LINE_DIST_CTOR ( Poisson )

Poisson(lambda).

Definition at line 216 of file distributions.h.

References LINE_DIST_CTOR(), and line::lang::Distrib< T >::poisson().

◆ LINE_DIST_CTOR() [22/25]

line::LINE_DIST_CTOR ( Replayer )

Replayer(samples) / Replayer(samples, path): the trace-driven law.

Definition at line 243 of file distributions.h.

References LINE_DIST_CTOR(), line::lang::Distrib< T >::replayer(), and line::lang::Distrib< T >::replayer_from().

◆ LINE_DIST_CTOR() [23/25]

line::LINE_DIST_CTOR ( Uniform )

Uniform(a, b).

Definition at line 161 of file distributions.h.

References LINE_DIST_CTOR(), and line::lang::Distrib< T >::uniform().

◆ LINE_DIST_CTOR() [24/25]

line::LINE_DIST_CTOR ( Weibull )

Weibull(scale, shape).

Definition at line 184 of file distributions.h.

References LINE_DIST_CTOR(), and line::lang::Distrib< T >::weibull().

◆ LINE_DIST_CTOR() [25/25]

line::LINE_DIST_CTOR ( Zipf )

Zipf(s, n).

Definition at line 228 of file distributions.h.

References LINE_DIST_CTOR(), and line::lang::Distrib< T >::zipf().

◆ log_bigint()

double line::log_bigint ( const BigInt & v )

inline

log(v) for a positive arbitrary-precision integer.

Keeps only the leading 53 bits of the mantissa and accounts for the discarded bits in the exponent, so the result is finite for values far outside the double range.

Definition at line 97 of file number.h.

References log_bigint().

Referenced by line::num_traits< Rational >::log_as_double(), and log_bigint().

◆ lsoda_final()

std::vector< double > line::lsoda_final	(	const LsodaRhs &	f,
		const std::vector< double > &	y0,
		double	t0,
		double	t1,
		const LsodaOptions &	opt = LsodaOptions() )

inline

Convenience form: integrate from t0 to t1 and report only the end state.

Definition at line 435 of file lsoda.h.

References line::LsodaSolution::final_state(), lsoda_final(), and lsoda_integrate().

Referenced by lsoda_final().

◆ lsoda_integrate()

LsodaSolution line::lsoda_integrate	(	const LsodaRhs &	f,
		const std::vector< double > &	y0,
		const std::vector< double > &	t_eval,
		const LsodaOptions &	opt = LsodaOptions() )

inline

Definition at line 178 of file lsoda.h.

References line::LsodaSolution::f_evals, line::InputError::InputError(), line::LsodaSolution::istate, line::LsodaSolution::jacobians, lsoda_integrate(), lsoda_integrate_stepwise(), line::LsodaSolution::method, line::LsodaSolution::steps, line::LsodaSolution::success, line::LsodaSolution::t, and line::LsodaSolution::y.

Referenced by line::cache::cache_miss_rmf_expansion_transient(), line::fluid::fluid_integrate_grid(), line::fluid::fluid_integrate_leg(), lsoda_final(), and lsoda_integrate().

◆ lsoda_integrate_stepwise()

LsodaSolution line::lsoda_integrate_stepwise	(	const LsodaRhs &	f,
		const std::vector< double > &	y0,
		const std::vector< double > &	t_eval,
		const LsodaOptions &	opt )

inline

Integrate dy/dt = f(t, y) from t_eval.front() through every later entry of t_eval, returning the state at each.

lsoda_integrate on the same output grid, driven one accepted step at a time so LsodaOptions::step_stop can end a window early.

t_eval must be non-empty and non-decreasing; its first entry is the initial time and is reported back unchanged with y0. This is the tspan form the fluid analyzers use, so one call covers both "give me the steady state at T" (two entries) and "give me the transient" (many).

A solver failure is reported, not thrown: success is false and istate carries LSODA's own code, because the fluid iteration treats a step that did not converge as a signal to shorten the horizon rather than as an error. The stepwise driver behind LsodaOptions::step_stop; defined below, after LsodaStepper, which it drives. Declared here so lsoda_integrate can hand off to it without moving either function.

ONE STEPPER PER OUTPUT INTERVAL, and that is what keeps the grid honest. itask = 2 may carry t PAST the interval's end, so each interval is stepped until the stepper reports it is done and then settle_at_end interpolates back onto the requested instant through the same history – exactly what a continuation call with itask = 1 does. The restart between intervals costs a little accuracy against the single itask = 1 call, which is why this driver is NOT the default: only a caller that asked for a stop test pays for it, and the fluid windows that do hand over a two-entry grid, i.e. one interval.

WHEN THE TEST FIRES the state is held for the WHOLE remaining grid rather than the trajectory being truncated. The test says the drift is zero to double precision, so y is that state for every later t and the held values are exact, not padded: a caller reading final_state() or a transient grid cannot tell this window from one that was stepped to its end, which is the point – an early return must not read as a failure to any of them.

Definition at line 379 of file lsoda.h.

References line::LsodaSolution::f_evals, line::LsodaStepper::f_evals(), line::LsodaStepper::failed(), line::LsodaSolution::istate, line::LsodaStepper::istate(), line::LsodaSolution::jacobians, lsoda_integrate_stepwise(), line::LsodaStepper::settle_at_end(), line::LsodaStepper::step(), line::LsodaSolution::steps, line::LsodaStepper::steps(), line::LsodaSolution::success, line::LsodaSolution::t, line::LsodaStepper::t(), line::LsodaStepper::t_end(), line::LsodaSolution::y, and line::LsodaStepper::y().

Referenced by lsoda_integrate(), and lsoda_integrate_stepwise().

◆ lstsq() [1/2]

template<class T>

LstsqResult< T > line::lstsq	(	const Matrix< T > &	A,
		const std::vector< T > &	b )

Overload picking the default pivot threshold for the arithmetic in use.

Definition at line 213 of file lstsq.h.

References lstsq().

◆ lstsq() [2/2]

template<class T>

LstsqResult< T > line::lstsq	(	const Matrix< T > &	A,
		const std::vector< T > &	b,
		const T &	tol )

Least-squares solution of A x = b, minimum-norm when A is rank deficient.

Parameters

A	(m x n), any shape
b	(m)
tol	pivot threshold; pass 0 for the exact rank

Definition at line 152 of file lstsq.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), lstsq(), line::LstsqResult< T >::rank, line::LstsqResult< T >::rankdef, line::Matrix< T >::rows(), rref(), solve(), and line::LstsqResult< T >::x.

Referenced by line::fj::fj_boundary_solve(), line::fluid::fluid_dae_hold_multipliers(), line::fluid::fluid_dae_newton(), lstsq(), lstsq(), line::pfqn::pfqn_procomom(), line::spn::spn_pf(), and line::smc::stat().

◆ lu_det()

template<class T>

T line::lu_det ( const Matrix< T > & A )

Determinant of a square matrix, by the same partial-pivoting elimination.

SINGULAR IS A VALUE HERE, NOT AN ERROR, which is why this does not go through lu_factor: that one throws on a zero pivot because every caller of it is solving a system, where a zero pivot means the question has no answer. A determinant of a singular matrix is zero, a perfectly good answer, and Cramer's rule needs it – MarkovProcess.getProbState forms a numerator matrix that IS singular whenever the state has probability zero.

The sign comes from the parity of the row swaps, so it is exact even where the product of the pivots is not.

Definition at line 122 of file lu.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), lu_det(), line::pivot_mag< T >::of(), and line::Matrix< T >::rows().

Referenced by line::lang::processes::get_prob_state(), and lu_det().

◆ lu_factor()

template<class T>

std::vector< std::size_t > line::lu_factor ( Matrix< T > & A )

In-place LU of A (n x n).

Returns the row permutation; A holds L (unit diagonal, implicit) below and U on and above the diagonal.

Definition at line 48 of file lu.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), lu_factor(), line::NumericError::NumericError(), line::pivot_mag< T >::of(), and line::Matrix< T >::rows().

Referenced by line::aoi::aoi_lst_ph(), line::mc::ctmc_solve_reducible_blkdecomp(), line::mc::ctmc_stochcomp(), line::lang::dmap_refresh_moments(), line::infer::infer_lqn_ekf(), inverse(), lu_factor(), ode_rosenbrock4(), line::pfqn::pfqn_bk(), line::pfqn::pfqn_comomrm_orig(), line::api::lqn::ph_moments(), line::retrieval::retrieval_fpi_latency(), solve(), and line::SylvesterFactor< T >::SylvesterFactor().

◆ lu_solve()

template<class T>

void line::lu_solve	(	const Matrix< T > &	LU,
		const std::vector< std::size_t > &	piv,
		std::vector< T > &	b )

Solve LUx = Pb in place on b, using the factors from lu_factor.

The whole permutation must be applied to b BEFORE any elimination. lu_factor swaps entire rows, multiplier columns included, so LU(i,k) is the multiplier of the row that ends up at position i. Interleaving the swaps with the forward updates – swap b[k], then update b[i] with LU(i,k) – pairs the row identity at step k with a final-order multiplier whenever a later step moves that row, and silently returns a wrong solution. It does so without any warning sign: the factorization still satisfies LU = PA and the pivots are all healthy. The failure needs a pivot sequence that moves an already-eliminated row, which diagonally dominant matrices rarely produce, so it hides until a generator with a small leading diagonal is solved.

Definition at line 94 of file lu.h.

References line::InputError::InputError(), lu_solve(), and line::Matrix< T >::rows().

Referenced by line::aoi::aoi_lst_ph(), line::mc::ctmc_solve_reducible_blkdecomp(), line::mc::ctmc_stochcomp(), line::lang::dmap_refresh_moments(), line::infer::infer_lqn_ekf(), inverse(), lu_solve(), ode_rosenbrock4(), line::pfqn::pfqn_comomrm_orig(), line::api::lqn::ph_moments(), line::retrieval::retrieval_fpi_latency(), solve(), and line::SylvesterFactor< T >::solve_sylvester().

◆ lyap_schur()

Matrix< double > line::lyap_schur	(	const Matrix< double > &	A,
		const Matrix< double > &	B,
		const Matrix< double > &	C )

inline

MATLAB lyap(A,B,C) at double via Bartels-Stewart: A X + X B + C = 0.

Definition at line 200 of file sylvester.h.

References line::Matrix< T >::cols(), lyap_schur(), line::Matrix< T >::rows(), and sylvester_schur().

Referenced by line::fj::fj_compute_pi(), line::fj::fj_compute_t(), and lyap_schur().

◆ lyap_solve()

template<class T>

Matrix< T > line::lyap_solve	(	const Matrix< T > &	A,
		const Matrix< T > &	B,
		const Matrix< T > &	C )

MATLAB lyap(A,B,C) solves A X + X B + C = 0, i.e.

sylvester_solve(A, B, -C).

Definition at line 123 of file sylvester.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), lyap_solve(), line::Matrix< T >::rows(), and line::SylvesterFactor< T >::SylvesterFactor().

Referenced by line::cache::cache_rmf_lna(), lyap_solve(), and line::mam::map_optim_dist().

◆ matmul()

template<class T>

Matrix< T > line::matmul	(	const Matrix< T > &	A,
		const Matrix< T > &	B )

Matrix product A B.

Definition at line 36 of file linalg.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), matmul(), and line::Matrix< T >::rows().

Referenced by line::cache::cache_lrum_map_levelstats(), line::cache::cache_miss_rmf(), line::mam::dmap_exp_mul_int(), line::mam::dmap_geo_mul_sum(), expm(), line::fj::fj_compute_pi(), line::fj::fj_compute_t(), line::fj::fj_compute_t_nare(), line::fluid::fluid_eliminate_immediate(), line::fluid::fluid_lyapunov(), line::fluid::fluid_refine_meanfield(), line::smc::gim1_pi_etaqa(), line::smc::gim1_qlen_etaqa(), line::mam::ldqbd_pi(), line::mam::ldqbd_R(), line::mam::mam_bgchain_station(), line::mam::mam_transient2(), line::mam::mam_transient2_open(), line::mam::map_acfc(), line::mam::map_compute_R(), line::mam::map_compute_R_quadratic(), line::mam::map_compute_R_residual(), line::mam::map_embedded(), line::mam::map_exp_mul_int(), line::mam::map_geo_mul_sum(), line::mam::map_isfeasible(), line::mam::map_joint(), line::mam::map_stochcomp(), line::mam::map_varcount(), matmul(), matpow(), line::mam::mfq_fluflu_sojourn(), line::mam::mfq_fundamental(), line::mam::mfq_general_solve(), line::mam::mfq_ld_solve(), line::mam::mfq_multiregime(), line::mam::mfq_prio_queue(), line::mam::mfq_sojourn(), line::smc::mg1_cr(), line::smc::mg1_eg(), line::smc::mg1_fi(), line::smc::mg1_pi_etaqa(), line::mam::mmap3k_fit(), line::mam::mmap_pie(), line::mam::mmapph1fcfs_ncdistr(), line::mam::mmapph1fcfs_ncmean(), line::npfqn::npfqn_bnd_bpt(), line::npfqn::npfqn_traffic_rqt(), line::fluid::petri::petri_jacobian(), line::pfqn::pfqn_procomom2(), line::mam::ph2hyper(), line::mam::qbd_fundmat(), line::mam::qbd_fundmat_laplace(), line::mam::qbd_G_residual(), line::mam::qbd_mapmap1(), line::mam::qbd_pi(), line::mam::qbd_qlen_factmoment(), line::mam::qbd_R(), line::mam::qbd_R_logred(), line::mam::qbd_R_residual(), line::mam::qbd_rap(), line::mam::qbd_rg(), line::qsys::qsys_bmapm1(), line::qsys::qsys_dmc(), line::qsys::qsys_mapd1(), line::qsys::qsys_mapdc(), line::qsys::qsys_mapg1k(), line::qsys::qsys_mapmc(), line::qsys::qsys_mapphc(), line::qsys::qsys_mmapgk1(), line::qsys::qsys_phmc(), line::ba::solver_ba_bpt(), line::ba::solver_ba_snc_envelopes(), line::mva::solver_rqna(), and sylvester_schur().

◆ matpow()

template<class T>

Matrix< T > line::matpow	(	const Matrix< T > &	A,
		unsigned	k )

Integer matrix power, by repeated squaring.

Definition at line 89 of file linalg.h.

References line::Matrix< T >::cols(), eye(), line::InputError::InputError(), matmul(), matpow(), and line::Matrix< T >::rows().

Referenced by line::mam::map_acf(), line::mam::map_ccdf_derivative(), line::mam::map_joint(), line::mam::map_jointpdf_derivative(), line::mam::map_moment(), matpow(), line::mam::mmap_backward_moment(), line::mam::mmap_cross_moment(), line::mam::mmap_forward_moment(), line::mam::qbd_depproc_jointmom(), and line::mam::qbd_qlen_factmoment().

◆ matrix_from()

template<class T, class S>

Matrix< T > line::matrix_from ( const MatrixView< S > & v )

Deep copy of a view into an owning matrix, converting the element type.

Definition at line 130 of file matrix.h.

References line::MatrixView< T >::cols(), matrix_from(), and line::MatrixView< T >::rows().

Referenced by matrix_from().

◆ matrix_rank()

std::size_t line::matrix_rank ( const Matrix< double > & A )

inline

Numerical rank at the standard max(m,n) eps sigma_1 threshold.

Definition at line 329 of file eig.h.

References line::Matrix< T >::cols(), matrix_rank(), line::Matrix< T >::rows(), and svd_values().

Referenced by matrix_rank(), line::smc::mg1_eg(), and line::smc::mg1_pi_etaqa().

◆ multichoose()

double line::multichoose	(	int	n,
		int	k )

inline

Number of multisets of size k from n types, i.e.

C(n+k-1, k).

Definition at line 79 of file population.h.

References multichoose(), and nck().

Referenced by multichoose().

◆ mulvec()

template<class T>

std::vector< T > line::mulvec	(	const Matrix< T > &	A,
		const std::vector< T > &	v )

Matrix times column vector, A v.

Definition at line 62 of file linalg.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), mulvec(), and line::Matrix< T >::rows().

Referenced by line::aoi::aoi_lst_ph(), line::mam::dmap_moment(), line::fj::fj_return_per(), line::mam::map_acf(), line::mam::map_acfc(), line::mam::map_count_var(), line::mam::map_m1ps_h_recursive(), line::mam::map_pdf(), line::mam::map_varcount(), line::mam::mfq_general_solve(), line::mam::mfq_prio_queue(), line::mam::mmap_count_var(), line::mam::mmapph1fcfs_stdistr_ph(), mulvec(), line::mam::qbd_caudal(), line::mam::qbd_R_logred(), line::mam::qbd_rap(), line::qsys::qsys_bmapphnn_retrial(), line::qsys::qsys_dmc(), line::qsys::qsys_mapd1(), line::qsys::qsys_mapg1k(), line::qsys::qsys_mapmc(), line::qsys::qsys_mapphc(), line::qsys::qsys_mmapg1k(), line::qsys::qsys_mmapgk1(), and line::qsys::qsys_phmc().

◆ nck()

double line::nck	(	int	n,
		int	k )

inline

Binomial coefficient with a thread-local memo table (mp_pfqn util/nck.c).

Definition at line 69 of file population.h.

References nck().

Referenced by multichoose(), nck(), line::pfqn::pfqn_cub_evals(), and line::pfqn::pfqn_nc().

◆ nelder_mead() [1/2]

template<class T, class F>

NelderMeadResult< T > line::nelder_mead	(	F	f,
		const std::vector< T > &	x0 )

nelder_mead with the default tuning.

Definition at line 356 of file neldermead.h.

References nelder_mead(), and nelder_mead_defaults().

◆ nelder_mead() [2/2]

template<class T, class F>

NelderMeadResult< T > line::nelder_mead	(	F	f,
		const std::vector< T > &	x0,
		const NelderMeadOptions< T > &	opt )

Unconstrained simplex minimization.

Parameters

f	objective, x -> T
x0	starting point, which becomes vertex 0 of the simplex
opt	tuning

Definition at line 224 of file neldermead.h.

References line::NelderMeadResult< T >::converged, line::NelderMeadResult< T >::evaluations, line::NelderMeadResult< T >::fval, line::InputError::InputError(), line::NelderMeadResult< T >::iterations, nelder_mead(), num_abs(), and line::NelderMeadResult< T >::x.

Referenced by nelder_mead(), nelder_mead(), and nelder_mead_box().

◆ nelder_mead_box() [1/2]

template<class T, class F>

NelderMeadResult< T > line::nelder_mead_box	(	F	f,
		const std::vector< T > &	x0,
		const std::vector< Bound< T > > &	bounds )

nelder_mead_box with the default tuning.

Definition at line 428 of file neldermead.h.

References nelder_mead_box(), and nelder_mead_defaults().

◆ nelder_mead_box() [2/2]

template<class T, class F>

NelderMeadResult< T > line::nelder_mead_box	(	F	f,
		const std::vector< T > &	x0,
		const std::vector< Bound< T > > &	bounds,
		const NelderMeadOptions< T > &	opt )

Box-constrained simplex minimization by the transformation described in the header comment.

Every point at which f is evaluated satisfies the bounds.

Parameters

f	objective, x -> T, called only at feasible x
x0	starting point, clamped into the box if it is outside
bounds	one Bound per variable
opt	tuning

Definition at line 370 of file neldermead.h.

References line::NelderMeadResult< T >::converged, line::NelderMeadResult< T >::evaluations, line::NelderMeadResult< T >::fval, line::InputError::InputError(), line::NelderMeadResult< T >::iterations, nelder_mead(), nelder_mead_box(), and line::NelderMeadResult< T >::x.

Referenced by line::mam::amap2_adjust_gamma(), auglag(), line::api::infer_fmlps(), line::api::infer_mlps(), nelder_mead_box(), and nelder_mead_box().

◆ nelder_mead_defaults()

template<class T>

NelderMeadOptions< T > line::nelder_mead_defaults ( )

fminsearch's coefficients and initial simplex, with tighter tolerances.

Definition at line 79 of file neldermead.h.

References line::NelderMeadOptions< T >::alpha, line::NelderMeadOptions< T >::ftol, line::NelderMeadOptions< T >::gamma, line::NelderMeadOptions< T >::max_eval, line::NelderMeadOptions< T >::max_iter, nelder_mead_defaults(), line::NelderMeadOptions< T >::rho, line::NelderMeadOptions< T >::sigma, line::NelderMeadOptions< T >::step_abs, line::NelderMeadOptions< T >::step_rel, and line::NelderMeadOptions< T >::xtol.

Referenced by line::mam::amap2_adjust_gamma(), auglag_defaults(), nelder_mead(), nelder_mead_box(), and nelder_mead_defaults().

◆ next_pop()

bool line::next_pop	(	std::vector< int > &	n,
		const std::vector< int > &	N )

inline

Advance n to the next population vector in the lattice 0 <= n <= N, odometer order with the last class varying fastest.

Returns false once the lattice is exhausted, leaving n at all-zero.

Definition at line 56 of file population.h.

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

Referenced by line::pfqn::cd_peak_scaling(), line::fes::fes_compute_throughputs(), next_pop(), line::pfqn::pfqn_ca(), line::pfqn::pfqn_conv(), line::pfqn::pfqn_gld(), line::pfqn::pfqn_lcfsqn_ca(), line::pfqn::pfqn_lcfsqn_mva(), line::pfqn::pfqn_mva(), line::pfqn::pfqn_mva_ilock(), line::pfqn::pfqn_mvald(), line::pfqn::pfqn_mvaldmx(), line::pfqn::pfqn_perm(), line::pfqn::pfqn_schmidt(), and line::pfqn::pfqn_schmidt_ext().

◆ num_abs()

template<class T>

T line::num_abs ( const T & v )

inline

Definition at line 172 of file number.h.

References num_abs().

Referenced by line::mam::amap2_adjust_gamma(), line::mam::amap2_fit_gamma(), line::mam::amap2_fitall_gamma(), line::mam::aph2_fitall(), line::mam::aph_fit(), line::cache::cache_lrum_map_levelstats(), line::cache::cache_miss_asy(), line::cache::cache_mva_miss(), line::cache::cache_prob_erec(), line::cache::cache_prob_spm(), line::cache::cache_spm(), line::cache::cache_t_lrum_map(), line::cache::cache_ttl_lrua(), line::cache::cache_xi_fp(), line::cache::cache_xi_iter(), line::wf::calculate_branch_diversity(), line::mc::ctmc_foxglynn(), line::mc::ctmc_isfeasible(), line::mc::ctmc_maxabs(), line::mc::ctmc_saddlepoint(), line::mc::ctmc_solve_reducible_blkdecomp(), line::lang::processes::default_uniformization_rate(), line::wf::detect_branches(), line::mam::dmap_isfeasible(), line::env::env_ctmc_decompose(), line::fes::fes_build_isolated(), line::fj::fj_tail_forktail(), line::pfqn::grnmol(), line::mam::hyperexp_fit_longtail_k(), line::infer::infer_gibbs(), line::infer::infer_lqn(), line::infer::infer_lqn_jacobian(), line::pfqn::laplaceapprox(), levmar_jac(), levmar_jacobian_fd(), line::mam::m3pp22_fitc_approx_cov(), line::mam::m3pp22_fitc_approx_cov_multiclass(), line::mam::m3pp2m_fitc(), line::mam::m3pp2m_fitc_approx(), line::mam::m3pp2m_fitc_approx_ag(), line::mam::m3pp2m_fitc_approx_ag_multiclass(), line::mam::mamap22_fit_bs_multiclass(), line::mam::mamap22_fit_fs_multiclass(), line::mam::mamap2m_fit_fb_multiclass(), line::mam::map2_fit(), line::mam::map2mmpp(), line::mam::map_compute_R(), line::mam::map_compute_R_quadratic(), line::mam::map_compute_R_residual(), line::mam::map_gamma_full(), line::mam::map_isfeasible(), line::mam::map_m1ps_cdfrespt(), line::mam::map_m1ps_h_recursive(), line::mam::map_m1ps_sojourn(), line::mam::map_mmpp2(), line::mam::maph2m_fit_multiclass(), line::me::me_cqn(), line::me::me_oqn(), line::mam::mfq_general_solve(), line::mam::mfq_ld_solve(), line::mam::mmap2k_fit(), line::mam::mmap_isfeasible_tol(), line::mam::mmdp_isfeasible(), line::mam::mmpp2_fitc(), nelder_mead(), line::npfqn::npfqn_feedback_elim(), num_abs(), num_abs< double >(), ode_numeric_jacobian(), ode_rosenbrock4(), line::pivot_mag< T >::of(), line::pfqn::pfqn_bk(), line::pfqn::pfqn_lap(), line::pfqn::pfqn_ldbcmp(), line::pfqn::pfqn_le_fpi(), line::pfqn::pfqn_le_fpiZ(), line::pfqn::pfqn_marie(), line::pfqn::pfqn_momlin(), line::pfqn::pfqn_mvaoi_marg(), line::pfqn::pfqn_mwrbb(), line::pfqn::pfqn_propfair(), line::pfqn::pfqn_rd(), line::pfqn::pfqn_sens_linearizer(), line::pfqn::pfqn_sens_mom(), line::pfqn::pfqn_sens_mva(), line::pfqn::pfqn_sens_mvaldmx(), line::mam::ph2hyper(), line::mam::qbd_depproc_residual(), line::mam::qbd_R_logred(), line::qsys::qsys_gg1(), line::qsys::qsys_ggnm_diffusion(), line::qsys::qsys_gig1_approx_myskja2(), line::qsys::qsys_gigk_approx_whitt(), line::qsys::qsys_hh1_lindley(), line::qsys::qsys_mapd1(), line::qsys::qsys_mapdc(), line::qsys::qsys_mapg1k(), line::qsys::qsys_mg1_fb(), line::qsys::qsys_mg1_lrpt(), line::qsys::qsys_mg1_psjf(), line::qsys::qsys_mm1_dps(), line::qsys::qsys_mm1_tandem_lindley(), line::qsys::qsys_mmcc_retrial_fp(), line::qsys::qsys_phmc(), root_brent(), root_newton(), rref(), line::sim::sim_asymvar_ctmc(), line::sim::sim_quest_heuristic_ci(), line::sim::sim_runlength(), line::mam::solver_mam_basic(), line::mam::solver_mna_closed(), line::mva::solver_mva_cache_analyzer(), line::sum::sum_closed(), line::trace::trace_summary(), and line::wf::validate_branch_pattern().

◆ num_abs< double >()

template<>

double line::num_abs< double > ( const double & v )

inline

Definition at line 178 of file number.h.

References num_abs().

◆ num_factorial()

template<class T>

T line::num_factorial ( unsigned n )

inline

Factorial as a value of T.

Exact for Rational and for BigInt-backed types.

Definition at line 184 of file number.h.

References num_factorial().

◆ num_from_decimal()

template<class T>

T line::num_from_decimal ( const std::string & s )

Parse a decimal literal into T.

Rational reconstructs num/10^k from the digits; every other backend uses strtod, matching what MATLAB's str2double and Java's Double.parseDouble do.

Definition at line 110 of file decimal.h.

References num_from_decimal().

Referenced by num_from_decimal(), num_from_decimal< Rational >(), and line::lqn::read_lqnx_model().

◆ num_from_decimal< Rational >()

template<>

Rational line::num_from_decimal< Rational > ( const std::string & s )

inline

Definition at line 115 of file decimal.h.

References num_from_decimal(), and rational_from_decimal().

◆ num_nck()

template<class T>

T line::num_nck	(	int	n,
		int	k )

Binomial coefficient as a value of T, by the Pascal recurrence.

Exact for the rational backend at any n, unlike the double version above, which loses integrality once C(n,k) exceeds 2^53.

Definition at line 87 of file population.h.

References num_nck().

Referenced by line::moment::moment_binomial_from_negbinomial(), line::moment::moment_binotrans(), line::moment::moment_binotransinv(), line::moment::moment_central_from_raw(), line::moment::moment_cumulant_from_raw(), line::moment::moment_housematrix(), line::moment::moment_joint_central_from_raw_mean(), line::moment::moment_joint_raw_from_central(), line::moment::moment_negbinomial_from_binomial(), line::moment::moment_raw_from_central(), num_nck(), and line::pfqn::pfqn_schmidt_ext().

◆ num_pow_int()

template<class T>

T line::num_pow_int	(	const T &	base,
		unsigned	e )

inline

Integer power, valid in any field (no transcendental requirement).

Definition at line 192 of file number.h.

References num_pow_int().

◆ ode_numeric_jacobian()

template<class T, class F>

Matrix< T > line::ode_numeric_jacobian	(	const F &	f,
		const T &	t,
		const std::vector< T > &	y,
		const std::vector< T > &	fy )

Numeric Jacobian by central differences.

The increment is eps^(1/3) scaled by the magnitude of the component, which is the standard balance for a central difference: the truncation error is O(delta^2) and the cancellation error O(eps/delta), and the two meet at delta ~ eps^(1/3), giving about two thirds of the digits of T. A one-sided difference would cost one fewer evaluation per column and half the digits; the extra accuracy matters here because the Jacobian of a stiff problem is what the whole stability of the step rests on.

Definition at line 263 of file ode.h.

References line::InputError::InputError(), num_abs(), and ode_numeric_jacobian().

Referenced by ode_numeric_jacobian(), and ode_rosenbrock4().

◆ ode_rosenbrock4() [1/2]

template<class T, class F, class J>

OdeSolution< T > line::ode_rosenbrock4	(	const F &	f,
		const J &	jac,
		const T &	t0,
		const T &	t1,
		const std::vector< T > &	y0,
		const OdeOptions< T > &	opt )

Integrate y' = f(t,y) from t0 to t1 with an analytic Jacobian.

Parameters

f	right-hand side, std::vector<T> f(const T& t, const std::vector<T>& y)
jac	Jacobian, Matrix<T> jac(const T& t, const std::vector<T>& y)
t0	initial time
t1	final time; t1 > t0 is required (this is an initial value problem marched forwards, and a backwards request is an input error rather than a silently reversed integration)
y0	initial state
opt	tolerances and step bounds

Definition at line 304 of file ode.h.

References line::Matrix< T >::cols(), line::OdeSolution< T >::f_evals, line::InputError::InputError(), line::OdeSolution< T >::jacobians, lu_factor(), lu_solve(), num_abs(), line::NumericError::NumericError(), ode_rosenbrock4(), line::OdeSolution< T >::rejected, line::Matrix< T >::rows(), line::OdeSolution< T >::steps, line::OdeSolution< T >::t, and line::OdeSolution< T >::y.

Referenced by line::cache::cache_miss_rmf_transient(), line::cache::cache_rrm_meanfield(), line::fluid::fluid_ode_solve_stiff(), ode_rosenbrock4(), ode_rosenbrock4(), ode_rosenbrock4_endpoint(), and line::fluid::petri::solver_fluid_petri().

◆ ode_rosenbrock4() [2/2]

template<class T, class F>

OdeSolution< T > line::ode_rosenbrock4	(	const F &	f,
		const T &	t0,
		const T &	t1,
		const std::vector< T > &	y0,
		const OdeOptions< T > &	opt )

Integrate y' = f(t,y) with a numeric Jacobian by central differences.

Definition at line 484 of file ode.h.

References ode_numeric_jacobian(), and ode_rosenbrock4().

◆ ode_rosenbrock4_endpoint()

template<class T, class F>

std::vector< T > line::ode_rosenbrock4_endpoint	(	const F &	f,
		const T &	t0,
		const T &	t1,
		const std::vector< T > &	y0 )

Integrate with the default options and return only the state at t1.

Definition at line 496 of file ode.h.

References ode_rosenbrock4(), and ode_rosenbrock4_endpoint().

Referenced by line::mam::map_pntquad(), and ode_rosenbrock4_endpoint().

◆ ones()

template<class T>

std::vector< T > line::ones ( std::size_t n )

Column vector of ones, the ubiquitous e in MAP algebra.

Definition at line 104 of file linalg.h.

References ones().

◆ pinv()

Matrix< double > line::pinv ( const Matrix< double > & A )

inline

Moore-Penrose pseudo-inverse, A^+ = V diag(1/s_i) U^T over the singular values above max(m,n) eps sigma_1, which is MATLAB's default pinv tolerance.

Definition at line 93 of file svd.h.

References line::Matrix< T >::cols(), pinv(), line::Matrix< T >::rows(), line::SvdFactors::s, svd_full(), line::SvdFactors::U, and line::SvdFactors::Vt.

Referenced by pinv(), and line::api::sn_pn_firing_rates().

◆ plane_sizes()

std::vector< std::size_t > line::plane_sizes ( const std::vector< int > & N )

inline

Mixed-radix plane sizes: prods[r] = prod_{s<r} (N[s]+1).

Definition at line 27 of file population.h.

References plane_sizes().

Referenced by line::pfqn::pfqn_ca(), line::pfqn::pfqn_conv(), line::pfqn::pfqn_gld(), line::pfqn::pfqn_lcfsqn_ca(), line::pfqn::pfqn_lcfsqn_mva(), line::pfqn::pfqn_mva(), line::pfqn::pfqn_mva_ilock(), line::pfqn::pfqn_mvald(), line::pfqn::pfqn_mvaldmx(), line::pfqn::pfqn_schmidt(), line::pfqn::pfqn_schmidt_ext(), line::pfqn::pfqn_sens_mvaldmx(), and plane_sizes().

◆ pop_index()

std::size_t line::pop_index	(	const std::vector< int > &	n,
		const std::vector< std::size_t > &	prods )

inline

Index of n in the lattice, 0-based (MATLAB hashpop is 1-based).

Definition at line 45 of file population.h.

References pop_index().

Referenced by line::pfqn::pfqn_ca(), line::pfqn::pfqn_conv(), line::pfqn::pfqn_gld(), line::pfqn::pfqn_lcfsqn_ca(), line::pfqn::pfqn_lcfsqn_mva(), line::pfqn::pfqn_mva(), line::pfqn::pfqn_mva_ilock(), line::pfqn::pfqn_mvald(), line::pfqn::pfqn_mvaldmx(), line::pfqn::pfqn_schmidt(), line::pfqn::pfqn_schmidt_ext(), and pop_index().

◆ population_count()

std::size_t line::population_count ( const std::vector< int > & N )

inline

Number of population vectors n with 0 <= n <= N.

Definition at line 38 of file population.h.

References population_count().

Referenced by line::pfqn::pfqn_ca(), line::pfqn::pfqn_conv(), line::pfqn::pfqn_gld(), line::pfqn::pfqn_lcfsqn_ca(), line::pfqn::pfqn_lcfsqn_mva(), line::pfqn::pfqn_mva(), line::pfqn::pfqn_mva_ilock(), line::pfqn::pfqn_mvald(), line::pfqn::pfqn_mvaldmx(), line::pfqn::pfqn_schmidt(), line::pfqn::pfqn_schmidt_ext(), line::pfqn::pfqn_sens_dmva(), line::pfqn::pfqn_sens_mom(), line::pfqn::pfqn_sens_mva(), line::pfqn::pfqn_sens_mvaldmx(), line::pfqn::pfqn_sens_respt(), and population_count().

◆ rational_from_decimal()

Rational line::rational_from_decimal ( const std::string & s )

inline

The literal as an exact rational, num/10^k with no rounding.

Definition at line 84 of file decimal.h.

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

Referenced by num_from_decimal< Rational >(), and rational_from_decimal().

◆ root_bisect()

template<class T, class F>

RootResult< T > line::root_bisect	(	F	f,
		const T &	a,
		const T &	b,
		const T &	tol,
		unsigned	maxiter = 200 )

Bisection on a bracket with a sign change.

Parameters

f	callable T -> T
a,b	bracket endpoints, in either order
tol	absolute width of the final bracket
maxiter	iteration cap

Exceptions

InputError if f(a) and f(b) have the same sign and neither is a root

Definition at line 70 of file rootfind.h.

References line::RootResult< T >::bracket_width, line::RootResult< T >::converged, line::InputError::InputError(), line::RootResult< T >::iterations, line::RootResult< T >::root, root_bisect(), and line::RootResult< T >::value.

Referenced by line::cache::cache_t_lrum_map(), line::cache::cache_ttl_lrua(), and root_bisect().

◆ root_brent()

template<class T, class F>

RootResult< T > line::root_brent	(	F	f,
		const T &	a0,
		const T &	b0,
		const T &	tol,
		unsigned	maxiter = 200 )

Brent's method on a bracket with a sign change.

Falls back to bisection whenever the interpolated step is not a strict improvement, so the bracket is never lost.

Definition at line 130 of file rootfind.h.

References line::RootResult< T >::bracket_width, line::RootResult< T >::converged, line::InputError::InputError(), line::RootResult< T >::iterations, num_abs(), line::RootResult< T >::root, root_brent(), and line::RootResult< T >::value.

Referenced by line::fj::fj_tail_forktail(), line::fj::fj_tail_ordstat(), line::qsys::qsys_tandem_ub_ciucu(), root_brent(), and line::mva::solver_mva_qsys_analyzer().

◆ root_newton()

template<class T, class F, class DF>

RootResult< T > line::root_newton	(	F	f,
		DF	df,
		const T &	x0,
		const T &	tol,
		unsigned	maxiter = 200 )

Plain Newton from a starting point.

The only method here that can find a root of even multiplicity, where f does not change sign and no bracket exists; convergence is then linear rather than quadratic.

Parameters

f	callable T -> T
df	callable T -> T, the derivative
x0	starting point of the iteration
tol	convergence tolerance on the Newton step
maxiter	iteration cap (default 200)

Exceptions

NumericError if the derivative vanishes at an iterate

Definition at line 247 of file rootfind.h.

References line::RootResult< T >::bracket_width, line::RootResult< T >::converged, line::RootResult< T >::iterations, num_abs(), line::NumericError::NumericError(), line::RootResult< T >::root, root_newton(), and line::RootResult< T >::value.

Referenced by root_newton().

◆ root_newton_safe()

template<class T, class F, class DF>

RootResult< T > line::root_newton_safe	(	F	f,
		DF	df,
		const T &	a0,
		const T &	b0,
		const T &	tol,
		unsigned	maxiter = 200 )

Newton safeguarded by a bracket with a sign change: the Newton step is used only when it stays inside the bracket and at least halves it, otherwise the step is a bisection.

Never diverges and never leaves the bracket.

Definition at line 285 of file rootfind.h.

References line::RootResult< T >::bracket_width, line::RootResult< T >::converged, line::InputError::InputError(), line::RootResult< T >::iterations, line::RootResult< T >::root, root_newton_safe(), and line::RootResult< T >::value.

Referenced by root_newton_safe().

◆ rref()

template<class T>

std::vector< std::size_t > line::rref	(	Matrix< T > &	A,
		const T &	tol )

Reduced row echelon form of A, in place, returning the pivot columns.

Rows beyond the returned rank are identically zero.

Definition at line 110 of file lstsq.h.

References line::Matrix< T >::cols(), num_abs(), line::Matrix< T >::rows(), and rref().

Referenced by lstsq(), rref(), and line::spn::spn_pf().

◆ schur_decomposition()

RealSchur line::schur_decomposition ( const Matrix< double > & A )

inline

Real Schur factorization of a general square matrix (LAPACK dgees, unsorted).

The Schur form is the right basis for splitting a spectrum into invariant subspaces, which is what a multi-regime fluid queue needs: the eigenvector basis exists only for a diagonalizable matrix and is complex whenever the spectrum is, while Z is orthogonal and real for every real A.

Definition at line 182 of file eig.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), line::NumericError::NumericError(), line::Matrix< T >::rows(), schur_decomposition(), line::RealSchur::T, line::UnsupportedError::UnsupportedError(), and line::RealSchur::Z.

Referenced by line::fluid::aoi_solve_singlebuffer(), line::fj::fj_compute_t_nare(), line::mam::mfq_multiregime(), schur_decomposition(), and sylvester_schur().

◆ schur_reorder()

RealSchur line::schur_reorder	(	const RealSchur &	s,
		const std::vector< double > &	key )

inline

Reorder the diagonal blocks of a real Schur form into DESCENDING key order, stably, updating Z so that A = Z T Z^T still holds.

This is MATLAB's ordschur with a CLUSTER-NUMBER select vector, whose documented behaviour is that clusters appear in descending order of the cluster number. The key is given per diagonal ENTRY; for a 2 x 2 block the key of its first row is used and the second is ignored, which is the same requirement MATLAB imposes (a select vector must be constant on a block, and a caller that splits one is asking for a factorization that does not exist over the reals).

WHY dtrexc AND NOT dtrsen. dtrsen splits a spectrum into TWO clusters, the selected one and the rest, so an ordering into three or more classes needs it applied recursively to trailing submatrices, with the accumulated Q and the shifting block boundaries tracked by hand at every level. dtrexc moves ONE diagonal block from position ifst to position ilst and updates Q itself, so an arbitrary key ordering is a stable selection sort over blocks with no submatrix bookkeeping at all. It also refuses to split a 2 x 2 block rather than silently producing a complex pair astride a boundary, which is the failure that would otherwise be discovered downstream as a complex "real" subspace.

Parameters

s	a real Schur factorization, typically from schur_decomposition
key	one value per diagonal entry; blocks are sorted descending by it

Definition at line 248 of file eig.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), line::NumericError::NumericError(), line::Matrix< T >::rows(), schur_reorder(), line::RealSchur::T, line::UnsupportedError::UnsupportedError(), and line::RealSchur::Z.

Referenced by line::fluid::aoi_solve_singlebuffer(), line::fj::fj_compute_t_nare(), line::mam::mfq_multiregime(), and schur_reorder().

◆ serial_routing() [1/2]

void line::serial_routing	(	Routing &	P,
		std::size_t	r,
		const std::vector< std::size_t > &	nodes )

inline

Network.serialRouting(nodes) on one class of a model.

Definition at line 292 of file nodes.h.

References serial_routing().

◆ serial_routing() [2/2]

void line::serial_routing	(	Routing &	P,
		std::size_t	r,
		std::size_t	s,
		const std::vector< std::size_t > &	nodes )

inline

Network.serialRouting(nodes) for one class pair: 1 -> 2 -> ... -> n.

Definition at line 286 of file nodes.h.

References serial_routing(), and line::qn::RoutingMatrix< T >::set().

Referenced by cyclic_routing(), serial_routing(), and serial_routing().

◆ solve()

template<class T>

std::vector< T > line::solve	(	const Matrix< T > &	A,
		const std::vector< T > &	b )

Convenience: solve Ax = b, leaving A and b untouched.

Definition at line 158 of file lu.h.

References lu_factor(), lu_solve(), and solve().

◆ spectral_radius()

double line::spectral_radius ( const Matrix< double > & A )

inline

Largest modulus over the spectrum, i.e.

the spectral radius.

Definition at line 97 of file eig.h.

References eig_values(), and spectral_radius().

Referenced by line::mam::qbd_rap(), and spectral_radius().

◆ subdominant_modulus()

double line::subdominant_modulus ( const Matrix< double > & A )

inline

Second largest modulus over the spectrum.

This is the quantity the NCD machinery needs (ctmc_courtois's epsMAX is built from the subdominant eigenvalue of each diagonal block); returns 0 when the matrix is 1 x 1.

Definition at line 111 of file eig.h.

References eig_values(), and subdominant_modulus().

Referenced by subdominant_modulus().

◆ svd_full()

SvdFactors line::svd_full ( const Matrix< double > & A )

inline

Full SVD of a real matrix, singular values in descending order.

Definition at line 48 of file svd.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), line::NumericError::NumericError(), line::Matrix< T >::rows(), line::SvdFactors::s, svd_full(), line::SvdFactors::U, line::UnsupportedError::UnsupportedError(), and line::SvdFactors::Vt.

Referenced by line::fluid::fluid_refine_meanfield(), pinv(), and svd_full().

◆ svd_values()

std::vector< double > line::svd_values ( const Matrix< double > & A )

inline

Singular values in descending order.

Definition at line 128 of file eig.h.

References line::Matrix< T >::cols(), line::NumericError::NumericError(), line::Matrix< T >::rows(), svd_values(), and line::UnsupportedError::UnsupportedError().

Referenced by line::fluid::fluid_refine_meanfield(), matrix_rank(), line::smc::mg1_cr(), line::mam::qbd_rap(), and svd_values().

◆ sylvester_schur()

Matrix< double > line::sylvester_schur	(	const Matrix< double > &	A,
		const Matrix< double > &	B,
		const Matrix< double > &	C )

inline

A X + X B = C by Bartels-Stewart, at double.

WHY THIS EXISTS BESIDE THE KRONECKER SOLVER ABOVE. The Kronecker form is the only one available in an arbitrary field, and its O((n m)^3) cost is acceptable for the phase-space matrices the MMAP queue recursion passes. The FJ_codes fork-join engine passes matrices of order (C + 1) * m^2 * ma with C defaulting to 100, i.e. n and m in the hundreds to low thousands: the Kronecker operator of an 800 x 800 pair is 640000 square, which is 3 TB of LU. Bartels-Stewart is O(n^3 + m^3) and factorizes the same problem in fractions of a second, at the price of a real Schur factorization – LAPACK, hence double only, exactly as util/eig.h is.

A X + X B = C is solved as Ta Y + Y Tb = Za' C Zb with A = Za Ta Za' and B = Zb Tb Zb' real Schur, the quasi-triangular core done by dtrsyl, and X = Za Y Zb'. dtrsyl's scale guards against overflow when the two spectra nearly collide; it is divided out here, and a scale of zero means the equation has no solution, which is reported by name rather than returned as an infinity.

Definition at line 149 of file sylvester.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), matmul(), line::NumericError::NumericError(), line::Matrix< T >::rows(), schur_decomposition(), sylvester_schur(), line::RealSchur::T, line::Matrix< T >::transpose(), line::UnsupportedError::UnsupportedError(), and line::RealSchur::Z.

Referenced by line::fj::fj_compute_pi(), lyap_schur(), and sylvester_schur().

◆ sylvester_solve()

template<class T>

Matrix< T > line::sylvester_solve	(	const Matrix< T > &	A,
		const Matrix< T > &	B,
		const Matrix< T > &	C )

Solve A X + X B = C for X.

Parameters

A	n x n
B	m x m
C	n x m

Definition at line 115 of file sylvester.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), line::Matrix< T >::rows(), sylvester_solve(), and line::SylvesterFactor< T >::SylvesterFactor().

Referenced by line::fluid::fluid_lyapunov(), and sylvester_solve().

◆ vecmul()

template<class T>

std::vector< T > line::vecmul	(	const std::vector< T > &	v,
		const Matrix< T > &	A )

Row vector times matrix, v A.

Definition at line 50 of file linalg.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), line::Matrix< T >::rows(), and vecmul().

Namespaces

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ AUTO

◆ BA

◆ BigInt

◆ Complex

◆ CTMC

◆ Dist

◆ Distribution

◆ FLD

◆ JMT

◆ LDES

◆ LsodaRhs

◆ MAM

◆ MVA

◆ NC

◆ Network

◆ NetworkModel

◆ Rational

◆ Real

◆ Real100

◆ Real200

◆ Real50

◆ Routing

◆ RoutingMatrix

◆ SolverFluid

◆ SSA

Enumeration Type Documentation

◆ Arith

Function Documentation

◆ api_registry()

◆ api_supports()

◆ arith_name()

◆ auglag() [1/2]

◆ auglag() [2/2]

◆ auglag_defaults()

◆ auglag_ls() [1/2]

◆ auglag_ls() [2/2]

◆ bound_box()

◆ bound_free()

◆ bound_lower()

◆ bound_upper()

◆ bracket_expand()

◆ cyclic_routing()

◆ dbl_from_decimal()

◆ dft()

◆ eig_values()

◆ expm() [1/2]

◆ expm() [2/2]

◆ eye()

◆ find_api()

◆ inverse()

◆ levmar() [1/2]

◆ levmar() [2/2]

◆ levmar_defaults()

◆ levmar_jac()

◆ levmar_jacobian_fd()

◆ LINE_DECLARE_SOLVER() [1/7]

◆ LINE_DECLARE_SOLVER() [2/7]

◆ LINE_DECLARE_SOLVER() [3/7]

◆ LINE_DECLARE_SOLVER() [4/7]

◆ LINE_DECLARE_SOLVER() [5/7]

◆ LINE_DECLARE_SOLVER() [6/7]

◆ LINE_DECLARE_SOLVER() [7/7]

◆ LINE_DIST_CTOR() [1/25]

◆ LINE_DIST_CTOR() [2/25]

◆ LINE_DIST_CTOR() [3/25]

◆ LINE_DIST_CTOR() [4/25]

◆ LINE_DIST_CTOR() [5/25]

◆ LINE_DIST_CTOR() [6/25]

◆ LINE_DIST_CTOR() [7/25]

◆ LINE_DIST_CTOR() [8/25]

◆ LINE_DIST_CTOR() [9/25]

◆ LINE_DIST_CTOR() [10/25]

◆ LINE_DIST_CTOR() [11/25]

◆ LINE_DIST_CTOR() [12/25]