A computer algebra backend. More...

#include <line/api/sym/sym_engine.h>

Inheritance diagram for line::sym::SymEngine:

Public Member Functions
virtual	~SymEngine ()
virtual std::string	name () const =0
	Name of the backing engine, e.g.
virtual bool	isAvailable () const =0
	True if the engine answers a health probe.
virtual CtmcSolution	solveCTMC (const std::vector< std::vector< std::string > > &Q, const std::vector< std::string > &symbols)=0
	Symbolic stationary distribution of a CTMC, pi Q = 0 with sum(pi) = 1.
virtual SymSensitivity	ctmcSensitivity (const std::vector< std::vector< std::string > > &Q, const std::vector< std::string > &symbols, const std::string &theta, const std::vector< std::string > &reward)=0
	Exact parametric sensitivity of a steady-state reward.
virtual CtmcMeasures	ctmcMeasures (const std::vector< std::vector< std::string > > &Q, const std::vector< std::string > &symbols, const std::vector< std::vector< std::string > > &weights, const std::vector< std::string > &names, const std::vector< RatioSpec > &ratios)=0
	Rewrites expressions into a normal form.
virtual Passage	ctmcPassage (const std::vector< std::vector< std::string > > &S, const std::vector< std::string > &s0, const std::vector< std::string > &alpha, const std::string &atom, const std::vector< std::string > &symbols, const std::string &svar, const std::vector< std::string > &want, int nmax)=0
	First passage time into a target set: the transform and the moments.
virtual std::vector< std::string >	simplify (const std::vector< std::string > &exprs, const std::string &form)=0
virtual std::vector< std::string >	diff (const std::vector< std::string > &exprs, const std::string &variable, int order)=0
	Differentiates expressions.
virtual std::vector< double >	eval (const std::vector< std::string > &exprs, const std::map< std::string, double > &assignment)=0
	Substitutes values for symbols and evaluates.
virtual FluidODEs	fluidODEs (const std::vector< std::string > &rhs, const std::vector< std::string > &vars, const std::vector< std::string > &want)=0
	Jacobian, LaTeX form and equilibria of a fluid vector field.

Detailed Description

A computer algebra backend.

Definition at line 131 of file sym_engine.h.

Constructor & Destructor Documentation

◆ ~SymEngine()

virtual line::sym::SymEngine::~SymEngine ( )

inlinevirtual

Definition at line 133 of file sym_engine.h.

Member Function Documentation

◆ ctmcMeasures()

virtual CtmcMeasures line::sym::SymEngine::ctmcMeasures	(	const std::vector< std::vector< std::string > > &	Q,
		const std::vector< std::string > &	symbols,
		const std::vector< std::vector< std::string > > &	weights,
		const std::vector< std::string > &	names,
		const std::vector< RatioSpec > &	ratios )

pure virtual

Rewrites expressions into a normal form.

Parameters

exprs	the expressions
form	one of simplify, factor, together, cancel, expand, latex

Returns: the rewritten expressions, in the input order Stationary distribution and a set of weighted sums of it.

Every mean SolverCTMC reports is a NUMERIC linear functional of pi, so the caller builds one weight vector per measure with no algebra at all and this one round trip returns each w . pi as a rational function: a throughput is pi . depRates, a queue length is pi . stateSpaceAggr, a marginal probability is pi . indicator and a mean reward is pi . r.

Parameters

Q	generator entries as expression strings, row major
symbols	the symbols appearing in Q
weights	one row per measure, each of length Q.size(); entries are parsed in the same field as Q, so an expression is admissible and not only a number
names	a name per weight row, or empty for w0, w1, ...
ratios	ratios of two measures, or empty for none

Implemented in line::sym::SageRestEngine.

◆ ctmcPassage()

virtual Passage line::sym::SymEngine::ctmcPassage	(	const std::vector< std::vector< std::string > > &	S,
		const std::vector< std::string > &	s0,
		const std::vector< std::string > &	alpha,
		const std::string &	atom,
		const std::vector< std::string > &	symbols,
		const std::string &	svar,
		const std::vector< std::string > &	want,
		int	nmax )

pure virtual

First passage time into a target set: the transform and the moments.

With A the complement of the target, S = Q(A,A) the sub-generator, s0 = -S*1 the exit vector and alpha the initial law restricted to A, following Harrison and Knottenbelt (2002),

L(s) = alpha (sI - S)^-1 s0 + atom        Eqs. 1-2
(-S) M(n) = n M(n-1),  M(0) = 1           Eq. 3

THE MOMENTS COME FROM THE RECURSION, not from differentiating L: it carries no transform symbol, stays in the same fraction field and is nmax right solves against one matrix. Differentiating would leave the fraction field, and the evaluation at s = 0 can hit 0/0 where a factor of s failed to cancel.

Parameters

S	the sub-generator on the non-target states, row major
s0	the exit vector -S*1
alpha	the initial law restricted to the non-target states
atom	the initial mass already inside the target set
symbols	the rate symbols appearing in S
svar	the transform symbol; adjoined to the field only when a transform is asked for, and required to differ from every rate symbol
want	any of lst, lstall, moments, momall
nmax	highest moment order, at least 1

Implemented in line::sym::SageRestEngine.

◆ ctmcSensitivity()

virtual SymSensitivity line::sym::SymEngine::ctmcSensitivity	(	const std::vector< std::vector< std::string > > &	Q,
		const std::vector< std::string > &	symbols,
		const std::string &	theta,
		const std::vector< std::string > &	reward )

pure virtual

Exact parametric sensitivity of a steady-state reward.

Parameters

Q	generator entries as expression strings, row major
symbols	the symbols appearing in Q
theta	the symbol to differentiate with respect to
reward	reward rate per state, empty for the distribution alone

Returns: the sensitivity of the distribution and, if a reward is given, of its mean

Implemented in line::sym::SageRestEngine.

◆ diff()

virtual std::vector< std::string > line::sym::SymEngine::diff	(	const std::vector< std::string > &	exprs,
		const std::string &	variable,
		int	order )

pure virtual

Differentiates expressions.

Parameters

exprs	the expressions
variable	the differentiation variable
order	the order of the derivative, at least 1

Returns: the derivatives, in the input order

Implemented in line::sym::SageRestEngine.

◆ eval()

virtual std::vector< double > line::sym::SymEngine::eval	(	const std::vector< std::string > &	exprs,
		const std::map< std::string, double > &	assignment )

pure virtual

Substitutes values for symbols and evaluates.

Parameters

exprs	the expressions
assignment	value of each symbol

Returns: the numeric values, NaN where a free symbol remains

Implemented in line::sym::SageRestEngine.

◆ fluidODEs()

virtual FluidODEs line::sym::SymEngine::fluidODEs	(	const std::vector< std::string > &	rhs,
		const std::vector< std::string > &	vars,
		const std::vector< std::string > &	want )

pure virtual

Jacobian, LaTeX form and equilibria of a fluid vector field.

Parameters

rhs	the right hand side of dx/dt, one expression per state variable
vars	the state variable names
want	any of jacobian, latex, equilibria

Returns: the requested items

Implemented in line::sym::SageRestEngine.

◆ isAvailable()

virtual bool line::sym::SymEngine::isAvailable ( ) const

pure virtual

True if the engine answers a health probe.

Implemented in line::sym::SageRestEngine.

◆ name()

virtual std::string line::sym::SymEngine::name ( ) const

pure virtual

Name of the backing engine, e.g.

"sage".

Implemented in line::sym::SageRestEngine.

◆ simplify()

virtual std::vector< std::string > line::sym::SymEngine::simplify	(	const std::vector< std::string > &	exprs,
		const std::string &	form )

pure virtual

Implemented in line::sym::SageRestEngine.

◆ solveCTMC()

virtual CtmcSolution line::sym::SymEngine::solveCTMC	(	const std::vector< std::vector< std::string > > &	Q,
		const std::vector< std::string > &	symbols )

pure virtual

Symbolic stationary distribution of a CTMC, pi Q = 0 with sum(pi) = 1.

Parameters

Q	generator entries as expression strings, row major and square
symbols	the symbols appearing in Q, e.g. x1..xE

Returns: the solution, with pi also split over a common denominator

Implemented in line::sym::SageRestEngine.

The documentation for this class was generated from the following file:

include/line/api/sym/sym_engine.h

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ ~SymEngine()

Member Function Documentation

◆ ctmcMeasures()

◆ ctmcPassage()

◆ ctmcSensitivity()

◆ diff()

◆ eval()

◆ fluidODEs()

◆ isAvailable()

◆ name()

◆ simplify()

◆ solveCTMC()