Reaktoro Namespace Reference

The namespace containing all components of the Reaktoro library. More...

Namespaces
	ChemicalProperty
	The namespace of all chemical property functions.

Classes
class	AqueousMixture
	A type used to describe an aqueous mixture. More...
struct	AqueousMixtureState
	A type used to describe the state of an aqueous mixture. More...
class	AqueousPhase
	A type used to describe an aqueous phase. More...
class	AqueousSpecies
	A type to represent an aqueous species. More...
struct	AqueousSpeciesThermoData
	A type for storing the thermodynamic data of an aqueous species. More...
struct	AqueousSpeciesThermoParamsHKF
	A type for storing the parameters of the HKF equation of state for a aqueous species. More...
class	BilinearInterpolator
	A class used to calculate bilinear interpolation of data in two dimensions. More...
class	ChemicalEditor
	Provides convenient operations to initialize ChemicalSystem and ReactionSystem instances. More...
class	ChemicalField
class	ChemicalModelResult
	The result of a chemical model function that calculates the chemical properties of species. More...
class	ChemicalOutput
	A type used to output sequence of chemical states to a file or terminal. More...
class	ChemicalPlot
	A class used to create plots from sequence of chemical states. More...
class	ChemicalProperties
	A class for querying thermodynamic and chemical properties of a chemical system. More...
class	ChemicalQuantity
	A class that provides a convenient way to retrieve chemical quantities. More...
class	ChemicalScalarBase
	A template base class to represent a chemical scalar and its partial derivatives. More...
class	ChemicalState
	Provides a computational representation of the state of a multiphase chemical system. More...
class	ChemicalSystem
	A class to represent a system and its attributes and properties. More...
class	ChemicalVectorBase
	A template base class to represent a vector of chemical properties and their partial derivatives. More...
class	Composition
	A type that describes temperature in units of K. More...
class	Connectivity
	A type to describe the connectivity of elements, species, and phases in a chemical system. More...
class	CubicEOS
	Defines a cubic equation of state and calculates thermodynamic properties of a fluid phase. More...
struct	DaeOptions
	A struct that defines the options for the DaeSolver. More...
class	DaeProblem
	A class that defines a system of differential-algebraic equations (DAE) problem. More...
class	DaeSolver
	A class for solving differential-algebraic equations (DAE). More...
class	Database
	Provides operations to retrieve physical and thermodynamic data of chemical species. More...
class	DebyeHuckelParams
	A class used to define the parameters in the Debye–Hückel activity model for aqueous mixtures. More...
class	Element
	A type used to define a chemical element and its attributes. More...
class	EquilibriumBalance
	A class that defines the mass balance conditions for equilibrium calculations. More...
class	EquilibriumInverseProblem
	A class used for defining an inverse equilibrium problem. More...
class	EquilibriumInverseSolver
	A class used for solving inverse equilibrium problems. More...
struct	EquilibriumOptions
	The options for the equilibrium calculations. More...
class	EquilibriumPath
	A class that describes a path of equilibrium states. More...
struct	EquilibriumPathOptions
	A struct that describes the options from an equilibrium path calculation. More...
struct	EquilibriumPathResult
	A struct that describes the result of an equilibrium path calculation. More...
class	EquilibriumProblem
	A type that defines an equilibrium problem. More...
class	EquilibriumReactions
	A class that generates a system of equilibrium reactions written in terms of master and secondary species. More...
struct	EquilibriumResult
	A type used to describe the result of an equilibrium calculation. More...
struct	EquilibriumSensitivity
	A type that contains the sensitivity data of the equilibrium state. More...
class	EquilibriumSolver
	A solver class for solving chemical equilibrium calculations. More...
struct	Exception
	Provides a convenient way to initialized an exception with helpful error messages. More...
class	Filter
	A type that describes an optimisation filter. More...
class	FluidMixture
	Provides a computational representation of a fluid (gaseous or liquid) mixture. More...
struct	FluidMixtureState
	A type used to describe the state of a fluid (gaseous or liquid) mixture. More...
class	FluidPhase
	Class that defines a fluid (gaseous or liquid) phase. More...
class	FluidSpecies
	A type to describe the attributes of a fluids (gaseous or liquid) species. More...
struct	FluidSpeciesThermoData
	A type for storing the thermodynamic data of fluid (gaseous or liquid) species. More...
struct	FluidSpeciesThermoParamsHKF
	A type for storing the parameters of the HKF equation of state for a fluid (gaseous or liquid) species. More...
struct	FunctionG
	A type used to describe the function g of the HKF model and its partial temperature and pressure derivatives. More...
class	GaseousPhase
class	Gems
	A wrapper class for Gems code. More...
struct	GemsOptions
	A type that describes the options for Gems. More...
class	GeneralMixture
	Provide a base of implementation for the mixture classes. More...
class	Gnuplot
struct	Hessian
	A type to describe the Hessian of an objective function. More...
class	Interface
	A class used to interface other codes with Reaktoro. More...
class	Interpreter
	Used to interpret json files containing defined calculations. More...
struct	Jacobian
	A type to describe the Jacobian of an equality constraint function. More...
struct	KineticOptions
	A struct to describe the options for a chemical kinetics calculation. More...
struct	KineticOutputOptions
class	KineticPath
	A class that conveniently solves kinetic path calculations. More...
class	KineticProblem
	A type that defines a kinetic problem. More...
class	KineticResult
class	KineticSolver
	A class that represents a solver for chemical kinetics problems. More...
struct	KktMatrix
	A type to represent the left-hand side matrix of a KKT equation. More...
struct	KktOptions
	A type to describe the options for the KKT calculation. More...
struct	KktResult
	A type to describe the result of a KKT calculation. More...
struct	KktSolution
	A type to represent the solution vector of a KKT equation. More...
class	KktSolver
	A type to describe a solver for a KKT equation. More...
struct	KktVector
	A type to represent the right-hand side vector of a KKT equation. More...
class	LagrangeInterpolator
	A class used to calculate interpolation of data in one dimension in any order. More...
class	LiquidPhase
struct	LU
	The class that computes the full pivoting Auxiliary struct for storing the LU decomposition of a matrix A. More...
class	Mesh
	A class that defines the mesh for TransportSolver. More...
struct	MineralCatalyst
struct	MineralMechanism
class	MineralMixture
	Provide a computational representation of a mineral mixture. More...
struct	MineralMixtureState
	A type used to describe the state of a mineral mixture. More...
class	MineralPhase
	Class that defines a mineral phase. More...
class	MineralReaction
class	MineralSpecies
	A type to describe the attributes of a mineral species. More...
struct	MineralSpeciesThermoData
	A type for storing the thermodynamic data of a mineral species. More...
struct	MineralSpeciesThermoParamsHKF
	A type for storing the parameters of the HKF equation of state for a mineral species. More...
struct	MixtureState
	A type used to describe the state of a mixture. More...
struct	NonlinearOptions
	A type that describes the options for the solution of a non-linear problem. More...
struct	NonlinearOutput
	A type that describes the options for the output of a non-linear problem calculation. More...
struct	NonlinearProblem
	A type that describes the non-linear problem. More...
struct	NonlinearResidual
	A type that describes the evaluation result of a non-linear residual function. More...
struct	NonlinearResult
	A type that describes the result of a non-linear problem calculation. More...
class	NonlinearSolver
	A type that implements the Newton algorithm for solving non-linear problems. More...
struct	ObjectiveResult
	A type that describes the result of the evaluation of an objective function. More...
struct	ODEOptions
	A struct that defines the options for the ODESolver. More...
class	ODEProblem
	A class that defines a system of ordinary differential equations (ODE) problem. More...
class	ODESolver
	A wrapper class for CVODE, a library for solving ordinary differential equations. More...
struct	OptimumOptions
	A type that describes the options of a optimisation calculation. More...
struct	OptimumOutputOptions
	A type that describes the options for the output of a optimisation calculation. More...
struct	OptimumParamsActNewton
struct	OptimumParamsIpAction
struct	OptimumParamsIpActive
struct	OptimumParamsIpNewton
struct	OptimumParamsIpOpt
struct	OptimumParamsKarpov
struct	OptimumParamsRefiner
struct	OptimumParamsRegularization
	A type that describes the regularization options for the optimisation calculation. More...
struct	OptimumProblem
	A type that describes the non-linear constrained optimisation problem. More...
struct	OptimumResult
	A type that describes the result of an optimisation calculation. More...
class	OptimumSolver
	The friendly interface to all optimisation algorithms. More...
class	OptimumSolverActNewton
	The class that implements the ActNewton algorithm using an active-set strategy. More...
class	OptimumSolverBase
	The base class for all optimization algorithms. More...
class	OptimumSolverIpAction
	The class that implements the IpAction algorithm using an interior-point method with a null-space KKT formulation. More...
class	OptimumSolverIpActive
	The class that implements the IpActive algorithm using an interior-point method combined with an active-set strategy. More...
class	OptimumSolverIpBounds
	The class that implements the IpBounds algorithm using an interior-point method. More...
class	OptimumSolverIpFeasible
	The class that implements the IpFeasible algorithm using an interior-point method. More...
class	OptimumSolverIpNewton
	The class that implements the IpNewton algorithm using an interior-point method. More...
class	OptimumSolverIpOpt
	The class that implements the IpOpt algorithm using an interior-point method. More...
class	OptimumSolverKarpov
	The class that implements an optimization algorithm based on Karpov's method. More...
class	OptimumSolverRefiner
	The class that implements a refinement operation of the optimal solution. More...
class	OptimumSolverSimplex
	The class that implements the simplex algorithm for linear programming problems. More...
struct	OptimumState
	A type that describes the state of an optimum solution. More...
class	Outputter
	A utility class for printing the progress of iterative calculations. More...
struct	OutputterOptions
class	Partition
	Provide a computational representation of the Partition of a chemical system. More...
class	Phase
	A type used to define a phase and its attributes. More...
struct	PhaseChemicalModelResultBase
	The result of a chemical model function that calculates the chemical properties of species. More...
struct	PhaseThermoModelResultBase
	The result of a thermodynamic model function that calculates the thermodynamic properties of species. More...
class	Phreeqc
class	PhreeqcDatabase
class	PhreeqcEditor
class	Pressure
	A type that describes pressure in units of Pa. More...
class	Reaction
	Provide a computational representation of a chemical reaction. More...
class	ReactionEquation
	Define a type that describes the equation of a reaction. More...
class	ReactionSystem
	A class that represents a system of chemical reactions. More...
struct	ReactionThermoInterpolatedProperties
	A type for storing thermodynamic properties of a reaction over a range of temperatures and pressures. More...
class	ReactiveTransportSolver
	Use this class for solving reactive transport problems. More...
class	Regularizer
	A type that represents a regularized optimization problem. More...
struct	RegularizerOptions
	A type that describes the options for regularizing linear constraints. More...
struct	ResidualEquilibriumConstraints
	A type used to define the result of the evaluation of a system of equilibrium constraints. More...
struct	SmartEquilibriumOptions
	The options for the smart equilibrium calculations. More...
struct	SmartEquilibriumResult
	A type used to describe the result of a smart equilibrium calculation. More...
class	SmartEquilibriumSolver
	A class used to perform equilibrium calculations using machine learning scheme. More...
class	Species
	A type used to describe a species and its attributes. More...
struct	SpeciesElectroState
struct	SpeciesThermoData
	A type for storing the thermodynamic data of general species. More...
struct	SpeciesThermoInterpolatedProperties
	A type for storing thermodynamic properties of a species over a range of temperatures and pressures. More...
struct	SpeciesThermoParamsPhreeqc
	A type for storing Phreeqc parameters of a species. More...
struct	SpeciesThermoState
	Describe the thermodynamic state of a species. More...
class	StringList
	A class for representing a list of strings with special constructors. More...
class	Temperature
	A type that describes temperature in units of K. More...
class	Thermo
	A type to calculate thermodynamic properties of chemical species. More...
class	ThermoModelResult
	The result of a thermodynamic model function that calculates standard thermodynamic properties of species. More...
class	ThermoProperties
	A class used for calculating standard thermodynamic properties of species in a chemical system. More...
class	ThermoScalarBase
	A template base class to represent a thermodynamic scalar and its partial derivatives. More...
class	ThermoVectorBase
	A template base class to represent a vector of thermodynamic scalars and their partial derivatives. More...
class	TransportSolver
	A class for solving advection-diffusion problem. More...
class	TridiagonalMatrix
	A class that defines a Tridiagonal Matrix used on TransportSolver. More...
struct	WaterElectroState
struct	WaterHelmholtzState
struct	WaterThermoState

Typedefs
using	ChemicalScalar = ChemicalScalarBase< double, RowVector >
	A type that represents a chemical property and its derivatives. More...
using	ChemicalScalarRef = ChemicalScalarBase< double &, Eigen::Ref< RowVector, 0, Eigen::InnerStride< Eigen::Dynamic > >>
	A type that represents a chemical property and its derivatives.
using	ChemicalScalarConstRef = ChemicalScalarBase< const double &, Eigen::Ref< const RowVector, 0, Eigen::InnerStride< Eigen::Dynamic > >>
	A type that represents a chemical property and its derivatives.
using	ChemicalVector = ChemicalVectorBase< Vector, Vector, Vector, Matrix >
	A type that represents a vector of chemical properties and their derivatives. More...
using	ChemicalVectorRef = ChemicalVectorBase< VectorRef, VectorRef, VectorRef, MatrixRef >
	A type that represents a vector of chemical properties and their derivatives.
using	ChemicalVectorConstRef = ChemicalVectorBase< VectorConstRef, VectorConstRef, VectorConstRef, MatrixConstRef >
	A type that represents a vector of chemical properties and their derivatives.
using	Index = std::size_t
	Define a type that represents an index.
using	Indices = std::vector< Index >
	Define a type that represents a collection of indices.
using	json = nlohmann::json
using	ThermoScalar = ThermoScalarBase< double >
	A type that defines a scalar thermo property. More...
using	ThermoVector = ThermoVectorBase< Vector, Vector, Vector >
	A type that defines a vector of thermodynamic properties. More...
using	ThermoScalarFunction = std::function< ThermoScalar(Temperature, Pressure)>
using	ThermoVectorFunction = std::function< ThermoVector(Temperature, Pressure)>
using	ChemicalScalarFunction = std::function< ChemicalScalar(Temperature, Pressure, VectorConstRef)>
using	ChemicalVectorFunction = std::function< ChemicalVector(Temperature, Pressure, VectorConstRef)>
template<typename T >
using	Table1D = std::vector< T >
template<typename T >
using	Table2D = std::vector< std::vector< T > >
template<typename T >
using	Table3D = std::vector< std::vector< std::vector< T > >>
using	ThermoVectorRef = ThermoVectorBase< VectorRef, VectorRef, VectorRef >
	A type that defines a vector of thermodynamic properties.
using	ThermoVectorConstRef = ThermoVectorBase< VectorConstRef, VectorConstRef, VectorConstRef >
	A type that defines a vector of thermodynamic properties.
using	Time = std::chrono::time_point< std::chrono::high_resolution_clock >
using	Duration = std::chrono::duration< double >
template<typename Condition >
using	EnableIf = typename std::enable_if< Condition::value, void >::type
template<typename Type >
using	IsScalar = std::is_scalar< Type >
template<typename Type >
using	EnableIfScalar = EnableIf< IsScalar< Type > >
using	ChemicalPropertyFunction = std::function< ChemicalScalar(const ChemicalProperties &)>
	The signature of a function that calculates a single chemical property.
using	ReactionRateFunction = std::function< ChemicalScalar(const ChemicalProperties &)>
	The function signature of the rate of a reaction (in units of mol/s). More...
using	ReactionRateVectorFunction = std::function< ChemicalVector(const ChemicalProperties &)>
	The function signature of the rates of a collection of reactions (in units of mol/s). More...
using	GaseousSpecies = FluidSpecies
using	DaeFunction = std::function< int(double t, VectorConstRef u, VectorConstRef udot, VectorRef F)>
	The function signature of the right-hand side function of a system of ordinary differential equations.
using	DaeJacobian = std::function< int(double t, VectorConstRef u, VectorConstRef udot, MatrixRef J)>
	The function signature of the Jacobian of the right-hand side function of a system of ordinary differential equations.
using	ScalarFunction = std::function< double(VectorConstRef)>
	Define a scalar function type.
using	VectorFunction = std::function< Vector(VectorConstRef)>
	Define a vector function type.
using	Vector = Eigen::VectorXd
using	VectorRef = Eigen::Ref< Eigen::VectorXd >
	< Alias to Eigen type VectorXd. More...
using	VectorStridedRef = Eigen::Ref< Vector, 0, Eigen::InnerStride<> >
	< Alias to Eigen type Ref<VectorXd>.
using	VectorConstRef = Eigen::Ref< const Eigen::VectorXd >
	< Alias to Eigen type Ref<VectorXd>. More...
using	VectorMap = Eigen::Map< Eigen::VectorXd >
	< Alias to Eigen type Ref<const VectorXd>. More...
using	VectorConstMap = Eigen::Map< const Eigen::VectorXd >
	< Alias to Eigen type Map<VectorXd>. More...
using	RowVector = Eigen::RowVectorXd
	< Alias to Eigen type Map<const VectorXd>.
using	RowVectorRef = Eigen::Ref< Eigen::RowVectorXd >
	< Alias to Eigen type RowVectorXd.
using	RowVectorStridedRef = Eigen::Ref< Eigen::RowVectorXd, 0, Eigen::InnerStride<> >
	< Alias to Eigen type Ref<RowVectorXd>.
using	RowVectorConstRef = Eigen::Ref< const Eigen::RowVectorXd >
	< Alias to Eigen type Ref<RowVectorXd>.
using	RowVectorMap = Eigen::Map< Eigen::RowVectorXd >
	< Alias to Eigen type Ref<const RowVectorXd>.
using	RowVectorConstMap = Eigen::Map< const Eigen::RowVectorXd >
	< Alias to Eigen type Map<VectorXd>.
using	Matrix = Eigen::MatrixXd
	Alias to Eigen type MatrixXd.
using	MatrixRef = Eigen::Ref< Eigen::MatrixXd >
	Alias to Eigen type Ref<MatrixXd>. More...
using	MatrixConstRef = Eigen::Ref< const Eigen::MatrixXd >
	Alias to Eigen type Ref<const MatrixXd>. More...
using	MatrixMap = Eigen::Map< Eigen::MatrixXd >
	Alias to Eigen type Map<MatrixXd>. More...
using	MatrixConstMap = Eigen::Map< const Eigen::MatrixXd >
	Alias to Eigen type Map<const MatrixXd>. More...
using	VectorXd = Eigen::VectorXd
	Alias to Eigen type Eigen::VectorXd.
using	VectorXi = Eigen::VectorXi
	Alias to Eigen type Eigen::VectorXd.
using	VectorXdRef = Eigen::Ref< VectorXd >
	Alias to Eigen type Eigen::Ref<VectorXd>.
using	VectorXiRef = Eigen::Ref< VectorXi >
	Alias to Eigen type Eigen::Ref<VectorXi>.
using	VectorXdConstRef = Eigen::Ref< const VectorXd >
	Alias to Eigen type Eigen::Ref<const VectorXd>.
using	VectorXiConstRef = Eigen::Ref< const VectorXi >
	Alias to Eigen type Eigen::Ref<const VectorXi>.
using	VectorXdMap = Eigen::Map< VectorXd >
	Alias to Eigen type Eigen::Map<VectorXd>.
using	VectorXiMap = Eigen::Map< VectorXi >
	Alias to Eigen type Eigen::Map<VectorXi>.
using	VectorXdConstMap = Eigen::Map< const VectorXd >
	Alias to Eigen type Eigen::Map<const VectorXd>.
using	VectorXiConstMap = Eigen::Map< const VectorXi >
	Alias to Eigen type Eigen::Map<const VectorXi>.
using	MatrixXd = Eigen::MatrixXd
	Alias to Eigen type Eigen::MatrixXd.
using	MatrixXi = Eigen::MatrixXi
	Alias to Eigen type Eigen::MatrixXd.
using	MatrixXdRef = Eigen::Ref< MatrixXd >
	Alias to Eigen type Eigen::Ref<MatrixXd>.
using	MatrixXiRef = Eigen::Ref< MatrixXi >
	Alias to Eigen type Eigen::Ref<MatrixXi>.
using	MatrixXdConstRef = Eigen::Ref< const MatrixXd >
	Alias to Eigen type Eigen::Ref<const MatrixXd>.
using	MatrixXiConstRef = Eigen::Ref< const MatrixXi >
	Alias to Eigen type Eigen::Ref<const MatrixXi>.
using	MatrixXdMap = Eigen::Map< MatrixXd >
	Alias to Eigen type Eigen::Map<MatrixXd>.
using	MatrixXiMap = Eigen::Map< MatrixXi >
	Alias to Eigen type Eigen::Map<MatrixXi>.
using	MatrixXdConstMap = Eigen::Map< const MatrixXd >
	Alias to Eigen type Eigen::Map<const MatrixXd>.
using	MatrixXiConstMap = Eigen::Map< const MatrixXi >
	Alias to Eigen type Eigen::Map<const MatrixXi>.
using	PermutationMatrix = Eigen::PermutationMatrix< Eigen::Dynamic, Eigen::Dynamic >
	Define an alias to a permutation matrix type of the Eigen library.
using	N_Vector = struct _generic_N_Vector *
using	ODEFunction = std::function< int(double, VectorConstRef, VectorRef)>
	The function signature of the right-hand side function of a system of ordinary differential equations.
using	ODEJacobian = std::function< int(double, VectorConstRef, MatrixRef)>
	The function signature of the Jacobian of the right-hand side function of a system of ordinary differential equations.
using	CubicRoots = std::tuple< std::complex< double >, std::complex< double >, std::complex< double > >
	Define a type that describes the roots of a cubic equation.
using	SquareRoots = std::tuple< double, double >
	Define a type that describes the roots of a square equation.
using	NonlinearFunction = std::function< NonlinearResidual(VectorConstRef x)>
	A type that describes the functional signature of a non-linear residual function. More...
using	ObjectiveFunction = std::function< ObjectiveResult(VectorConstRef x)>
	A type that describes the functional signature of an objective function. More...
using	AqueousActivityModel = std::function< ChemicalScalar(const AqueousMixtureState &)>
	The signature of a function that calculates the ln activity coefficient of a neutral aqueous species. More...
using	LiquidSpecies = FluidSpecies
using	GaseousMixtureState = FluidMixtureState
using	GaseousMixture = FluidMixture
using	LiquidMixtureState = FluidMixtureState
using	LiquidMixture = FluidMixture
using	ChemicalModel = std::function< void(ChemicalModelResult &, Temperature, Pressure, VectorConstRef)>
	The signature of the chemical model function that calculates the chemical properties of the species in a chemical system.
using	PhaseChemicalModelResult = PhaseChemicalModelResultBase< ChemicalScalarRef, ChemicalVectorRef >
	The chemical properties of the species in a phase.
using	PhaseChemicalModelResultConst = PhaseChemicalModelResultBase< ChemicalScalarConstRef, ChemicalVectorConstRef >
	The chemical properties of the species in a phase (constant).
using	PhaseChemicalModel = std::function< void(PhaseChemicalModelResult &, Temperature, Pressure, VectorConstRef)>
	The signature of the chemical model function that calculates the chemical properties of the species in a phase.
using	PhaseThermoModelResult = PhaseThermoModelResultBase< ThermoVectorRef >
	The thermodynamic properties of the species in a phase.
using	PhaseThermoModelResultConst = PhaseThermoModelResultBase< ThermoVectorConstRef >
	The thermodynamic properties of the species in a phase (constant).
using	PhaseThermoModel = std::function< void(PhaseThermoModelResult &, Temperature, Pressure)>
	The signature of the chemical model function that calculates the thermodynamic properties of the species in a phase.
using	ThermoModel = std::function< void(ThermoModelResult &, Temperature, Pressure)>
	The signature of the thermodynamic model function that calculates the standard thermodynamic properties of the species in a chemical system.
using	GaseousSpeciesThermoParamsHKF = FluidSpeciesThermoParamsHKF
using	LiquidSpeciesThermoParamsHKF = FluidSpeciesThermoParamsHKF
using	GaseousSpeciesThermoData = FluidSpeciesThermoData
using	LiquidSpeciesThermoData = FluidSpeciesThermoData

Enumerations
enum	PhaseType { Solid, Liquid, Gas, Plasma }
	A type to define the possible state of matter of a phase.
enum	GibbsHessian { Exact, ExactDiagonal, Approximation, ApproximationDiagonal }
	The options for the description of the Hessian of the Gibbs energy function. More...
enum	ODEStepMode { Adams, BDF }
	The linear multistep method to be used in ODESolver.
enum	ODEIterationMode { Functional, Newton }
	The type of nonlinear solver iteration to be used in ODESolver.
enum	KktMethod {   PartialPivLU, FullPivLU, Nullspace, Rangespace,   Automatic }
	An enumeration of possible methods for the solution of a KKT equation. More...
enum	OptimumMethod {   IpAction, IpActive, IpNewton, IpOpt,   Karpov, Refiner, Simplex, ActNewton }
	The method used for the optimisation calculationss.
enum	StepMode { Conservative, Aggressive }
	The available stepping modes for some optimization algorithms. More...
enum	StateOfMatter { Solid, Liquid, Gas, Plasma }
	A type to define the possible states of matter of a phase or substance.
enum	PhaseIdentificationMethod { None, VolumeMethod, IsothermalCompressibilityMethods, GibbsEnergyAndEquationOfStateMethod }
	Defines the enumeration of available phase identification methods.

Functions
auto	amount (double value, Index nspecies, Index ispecies) -> ChemicalScalarBase< double, decltype(tr(unit(nspecies, ispecies)))>
	Return a ChemicalScalar representation of a mole amount of a species. More...
template<typename V , typename N >
auto	operator+ (const ChemicalScalarBase< V, N > &l) -> ChemicalScalarBase< V, N >
template<typename V , typename N >
auto	operator- (const ChemicalScalarBase< V, N > &l) -> ChemicalScalarBase< double, decltype(-l.ddn)>
template<typename VL , typename NL , typename VR , typename NR >
auto	operator+ (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalScalarBase< double, decltype(l.ddn+r.ddn)>
template<typename VL , typename NL , typename VR >
auto	operator+ (const ChemicalScalarBase< VL, NL > &l, const ThermoScalarBase< VR > &r) -> ChemicalScalarBase< double, decltype(l.ddn)>
template<typename VL , typename VR , typename NR >
auto	operator+ (const ThermoScalarBase< VL > &l, const ChemicalScalarBase< VR, NR > &r) -> decltype(r+l)
template<typename V , typename N >
auto	operator+ (const ChemicalScalarBase< V, N > &l, double r) -> ChemicalScalarBase< double, decltype(l.ddn)>
template<typename V , typename N >
auto	operator+ (double l, const ChemicalScalarBase< V, N > &r) -> decltype(r+l)
template<typename VL , typename NL , typename VR , typename NR >
auto	operator- (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalScalarBase< double, decltype(l.ddn - r.ddn)>
template<typename VL , typename NL , typename VR >
auto	operator- (const ChemicalScalarBase< VL, NL > &l, const ThermoScalarBase< VR > &r) -> ChemicalScalarBase< double, decltype(l.ddn)>
template<typename VL , typename VR , typename NR >
auto	operator- (const ThermoScalarBase< VL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalScalarBase< double, decltype(-r.ddn)>
template<typename V , typename N >
auto	operator- (const ChemicalScalarBase< V, N > &l, double r) -> ChemicalScalarBase< double, decltype(l.ddn)>
template<typename V , typename N >
auto	operator- (double l, const ChemicalScalarBase< V, N > &r) -> ChemicalScalarBase< double, decltype(-r.ddn)>
template<typename V , typename N >
auto	operator* (double l, const ChemicalScalarBase< V, N > &r) -> ChemicalScalarBase< double, decltype(l *r.ddn)>
template<typename V , typename N >
auto	operator* (const ChemicalScalarBase< V, N > &l, double r) -> decltype(r *l)
template<typename VL , typename VR , typename NR >
auto	operator* (const ThermoScalarBase< VL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalScalarBase< double, decltype(l.val *r.ddn)>
template<typename VL , typename NL , typename VR >
auto	operator* (const ChemicalScalarBase< VL, NL > &l, const ThermoScalarBase< VR > &r) -> decltype(r *l)
template<typename VL , typename NL , typename VR , typename NR >
auto	operator* (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalScalarBase< double, decltype(l.val *r.ddn+l.ddn *r.val)>
template<typename V , typename N >
auto	operator/ (double l, const ChemicalScalarBase< V, N > &r) -> ChemicalScalarBase< double, decltype(double() *r.ddn)>
template<typename V , typename N >
auto	operator/ (const ChemicalScalarBase< V, N > &l, double r) -> decltype((1.0/r) *l)
template<typename VL , typename VR , typename NR >
auto	operator/ (const ThermoScalarBase< VL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalScalarBase< double, decltype(-(l.val *r.ddn) *double())>
template<typename VL , typename NL , typename VR >
auto	operator/ (const ChemicalScalarBase< VL, NL > &l, const ThermoScalarBase< VR > &r) -> ChemicalScalarBase< double, decltype(l.ddn/r.val)>
template<typename VL , typename NL , typename VR , typename NR >
auto	operator/ (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalScalarBase< double, decltype((l.ddn *r.val - l.val *r.ddn) *double())>
template<typename VL , typename NL , typename VR , typename NR >
auto	operator< (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> bool
template<typename V , typename N >
auto	operator< (const ChemicalScalarBase< V, N > &l, double r) -> bool
template<typename V , typename N >
auto	operator< (double l, const ChemicalScalarBase< V, N > &r) -> bool
template<typename VL , typename NL , typename VR , typename NR >
auto	operator<= (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> bool
template<typename V , typename N >
auto	operator<= (const ChemicalScalarBase< V, N > &l, double r) -> bool
template<typename V , typename N >
auto	operator<= (double l, const ChemicalScalarBase< V, N > &r) -> bool
template<typename VL , typename NL , typename VR , typename NR >
auto	operator> (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> bool
template<typename V , typename N >
auto	operator> (const ChemicalScalarBase< V, N > &l, double r) -> bool
template<typename V , typename N >
auto	operator> (double l, const ChemicalScalarBase< V, N > &r) -> bool
template<typename VL , typename NL , typename VR , typename NR >
auto	operator>= (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> bool
template<typename V , typename N >
auto	operator>= (const ChemicalScalarBase< V, N > &l, double r) -> bool
template<typename V , typename N >
auto	operator>= (double l, const ChemicalScalarBase< V, N > &r) -> bool
template<typename VL , typename NL , typename VR , typename NR >
auto	operator== (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> bool
template<typename V , typename N >
auto	operator== (const ChemicalScalarBase< V, N > &l, double r) -> bool
template<typename V , typename N >
auto	operator== (double l, const ChemicalScalarBase< V, N > &r) -> bool
template<typename VL , typename NL , typename VR , typename NR >
auto	operator!= (const ChemicalScalarBase< VL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> bool
template<typename V , typename N >
auto	operator!= (const ChemicalScalarBase< V, N > &l, double r) -> bool
template<typename V , typename N >
auto	operator!= (double l, const ChemicalScalarBase< V, N > &r) -> bool
auto	operator<< (std::ostream &out, const ChemicalScalar &scalar) -> std::ostream &
template<typename V , typename N >
auto	abs (const ChemicalScalarBase< V, N > &l) -> ChemicalScalarBase< double, decltype(double() *l.ddn)>
template<typename V , typename N >
auto	sqrt (const ChemicalScalarBase< V, N > &l) -> ChemicalScalarBase< double, decltype(double() *l.ddn)>
template<typename V , typename N >
auto	pow (const ChemicalScalarBase< V, N > &l, double power) -> ChemicalScalarBase< double, decltype(double() *l.ddn)>
template<typename V , typename N >
auto	exp (const ChemicalScalarBase< V, N > &l) -> ChemicalScalarBase< double, decltype(double() *l.ddn)>
template<typename V , typename N >
auto	log (const ChemicalScalarBase< V, N > &l) -> ChemicalScalarBase< double, decltype(double() *l.ddn)>
template<typename V , typename N >
auto	log10 (const ChemicalScalarBase< V, N > &l) -> decltype(log(l)/1.0)
template<typename V , typename T , typename P , typename N >
auto	zeros (const ChemicalVectorBase< V, T, P, N > &v) -> ChemicalVectorBase< decltype(zeros(0)), decltype(zeros(0)), decltype(zeros(0)), decltype(zeros(0, 0))>
	Return a ChemicalVectorBase expression representing zeros with same dimension of given vector.
template<typename V , typename T , typename P , typename N >
auto	ones (const ChemicalVectorBase< V, T, P, N > &v) -> ChemicalVectorBase< decltype(ones(0)), decltype(zeros(0)), decltype(zeros(0)), decltype(zeros(0, 0))>
	Return a ChemicalVectorBase expression representing ones with same dimension of given vector.
template<typename V , typename T , typename P , typename N >
auto	operator<< (std::ostream &out, const ChemicalVectorBase< V, T, P, N > &r) -> std::ostream &
template<typename V , typename T , typename P , typename N >
auto	operator+ (const ChemicalVectorBase< V, T, P, N > &r) -> ChemicalVectorBase< V, T, P, N >
template<typename V , typename T , typename P , typename N >
auto	operator- (const ChemicalVectorBase< V, T, P, N > &r) -> ChemicalVectorBase< decltype(-r.val), decltype(-r.ddT), decltype(-r.ddP), decltype(-r.ddn)>
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator+ (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> ChemicalVectorBase< decltype(l.val+r.val), decltype(l.ddT+r.ddT), decltype(l.ddP+r.ddP), decltype(l.ddn+r.ddn)>
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR >
auto	operator+ (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> ChemicalVectorBase< decltype(l.val+r.val), decltype(l.ddT+r.ddT), decltype(l.ddP+r.ddP), decltype(l.ddn)>
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR , typename NR >
auto	operator+ (const ThermoVectorBase< VL, TL, PL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> decltype(r+l)
template<typename VL , typename TL , typename PL , typename NL , typename VR >
auto	operator+ (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ThermoScalarBase< VR > &r) -> ChemicalVectorBase< decltype(l.val+r.val *ones(l.size())), decltype(l.ddT+r.ddT *ones(l.size())), decltype(l.ddP+r.ddP *ones(l.size())), decltype(l.ddn)>
template<typename VL , typename VR , typename TR , typename PR , typename NR >
auto	operator+ (const ThermoScalarBase< VL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> decltype(r+l)
template<typename V , typename T , typename P , typename N , typename Derived >
auto	operator+ (const ChemicalVectorBase< V, T, P, N > &l, const Eigen::MatrixBase< Derived > &r) -> ChemicalVectorBase< decltype(l.val+r), T, P, N >
template<typename V , typename T , typename P , typename N , typename Derived >
auto	operator+ (const Eigen::MatrixBase< Derived > &l, const ChemicalVectorBase< V, T, P, N > &r) -> decltype(r+l)
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator- (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> ChemicalVectorBase< decltype(l.val - r.val), decltype(l.ddT - r.ddT), decltype(l.ddP - r.ddP), decltype(l.ddn - r.ddn)>
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR >
auto	operator- (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> ChemicalVectorBase< decltype(l.val - r.val), decltype(l.ddT - r.ddT), decltype(l.ddP - r.ddP), decltype(l.ddn)>
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR , typename NR >
auto	operator- (const ThermoVectorBase< VL, TL, PL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> decltype(-(r - l))
template<typename VL , typename TL , typename PL , typename NL , typename VR >
auto	operator- (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ThermoScalarBase< VR > &r) -> ChemicalVectorBase< decltype(l.val - r.val *ones(l.size())), decltype(l.ddT - r.ddT *ones(l.size())), decltype(l.ddP - r.ddP *ones(l.size())), decltype(l.ddn)>
template<typename VL , typename VR , typename TR , typename PR , typename NR >
auto	operator- (const ThermoScalarBase< VL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> decltype(r+l)
template<typename V , typename T , typename P , typename N , typename Derived >
auto	operator- (const ChemicalVectorBase< V, T, P, N > &l, const Eigen::MatrixBase< Derived > &r) -> ChemicalVectorBase< decltype(l.val - r), T, P, N >
template<typename V , typename T , typename P , typename N , typename Derived >
auto	operator- (const Eigen::MatrixBase< Derived > &l, const ChemicalVectorBase< V, T, P, N > &r) -> decltype(-(r - l))
template<typename V , typename T , typename P , typename N >
auto	operator* (double l, const ChemicalVectorBase< V, T, P, N > &r) -> ChemicalVectorBase< decltype(l *r.val), decltype(l *r.ddT), decltype(l *r.ddP), decltype(l *r.ddn)>
template<typename V , typename T , typename P , typename N >
auto	operator* (const ChemicalVectorBase< V, T, P, N > &l, double r) -> decltype(r *l)
template<typename VL , typename VR , typename T , typename P , typename N >
auto	operator* (const ThermoScalarBase< VL > &l, const ChemicalVectorBase< VR, T, P, N > &r) -> ChemicalVectorBase< decltype(l.val *r.val), decltype(l.val *r.ddT+l.ddT *r.val), decltype(l.val *r.ddP+l.ddP *r.val), decltype(l.val *r.ddn)>
template<typename VL , typename VR , typename T , typename P , typename N >
auto	operator* (const ChemicalVectorBase< VL, T, P, N > &l, const ThermoScalarBase< VR > &r) -> decltype(r *l)
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename NR >
auto	operator* (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalVectorBase< decltype(l.val *r.val), decltype(l.val *r.ddT+l.ddT *r.val), decltype(l.val *r.ddP+l.ddP *r.val), decltype(l.val *r.ddn+l.ddn *r.val)>
template<typename VL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator* (const ChemicalScalarBase< VL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> decltype(r *l)
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator% (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> ChemicalVectorBase< decltype(diag(l.val) *r.val), decltype(diag(l.val) *r.ddT+diag(r.val) *l.ddT), decltype(diag(l.val) *r.ddP+diag(r.val) *l.ddP), decltype(diag(l.val) *r.ddn+diag(r.val) *l.ddn)>
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR , typename NR >
auto	operator% (const ThermoVectorBase< VL, TL, PL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> ChemicalVectorBase< decltype(diag(l.val) *r.val), decltype(diag(l.val) *r.ddT+diag(r.val) *l.ddT), decltype(diag(l.val) *r.ddP+diag(r.val) *l.ddP), decltype(diag(l.val) *r.ddn)>
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR >
auto	operator% (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> decltype(r % l)
template<typename V , typename T , typename P , typename N , typename Derived >
auto	operator% (const Eigen::MatrixBase< Derived > &l, const ChemicalVectorBase< V, T, P, N > &r) -> ChemicalVectorBase< decltype(diag(l) *r.val), decltype(diag(l) *r.ddT), decltype(diag(l) *r.ddP), decltype(diag(l) *r.ddn)>
template<typename VL , typename TL , typename PL , typename NL , typename Derived >
auto	operator% (const ChemicalVectorBase< VL, TL, PL, NL > &l, const Eigen::MatrixBase< Derived > &r) -> decltype(r % l)
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator/ (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> ChemicalVector
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator/ (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> ChemicalVector
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename NR >
auto	operator/ (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalScalarBase< VR, NR > &r) -> ChemicalVector
template<typename VL , typename VR , typename T , typename P , typename N >
auto	operator/ (const ChemicalVectorBase< VL, T, P, N > &l, const ThermoScalarBase< VR > &r) -> ChemicalVectorBase< decltype(l.val/r.val), decltype(double() *(l.ddT *r.val - l.val *r.ddT)), decltype(double() *(l.ddP *r.val - l.val *r.ddP)), decltype(double() *(l.ddn *r.val))>
template<typename V , typename T , typename P , typename N >
auto	operator/ (const ChemicalVectorBase< V, T, P, N > &l, double r) -> decltype((1.0/r) *l)
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator< (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> bool
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator<= (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> bool
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator> (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> bool
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator>= (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> bool
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator== (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> bool
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	operator!= (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> bool
template<typename V , typename T , typename P , typename N >
auto	row (ChemicalVectorBase< V, T, P, N > &vec, Index irow) -> ChemicalScalarBase< decltype(vec.val[irow]), decltype(vec.ddn.row(irow))>
	Return a ChemicalScalarBase with reference to the chemical scalar in a given row.
template<typename V , typename T , typename P , typename N >
auto	row (const ChemicalVectorBase< V, T, P, N > &vec, Index irow) -> ChemicalScalarBase< decltype(vec.val[irow]), decltype(vec.ddn.row(irow))>
	Return a ChemicalScalarBase with const reference to the chemical scalar in a given row.
template<typename V , typename T , typename P , typename N >
auto	row (ChemicalVectorBase< V, T, P, N > &vec, Index irow, Index icol, Index ncols) -> ChemicalScalarBase< decltype(vec.val[irow]), decltype(vec.ddn.row(irow).segment(icol, ncols))>
	Return a reference of a row of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	row (const ChemicalVectorBase< V, T, P, N > &vec, Index irow, Index icol, Index ncols) -> ChemicalScalarBase< decltype(vec.val[irow]), decltype(vec.ddn.row(irow).segment(icol, ncols))>
	Return a const reference of a row of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	rows (ChemicalVectorBase< V, T, P, N > &vec, Index irow, Index nrows) -> ChemicalVectorBase< decltype(rows(vec.val, irow, nrows)), decltype(rows(vec.ddT, irow, nrows)), decltype(rows(vec.ddP, irow, nrows)), decltype(rows(vec.ddn, irow, nrows))>
	Return a reference of a sequence of rows of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	rows (const ChemicalVectorBase< V, T, P, N > &vec, Index irow, Index nrows) -> ChemicalVectorBase< decltype(rows(vec.val, irow, nrows)), decltype(rows(vec.ddT, irow, nrows)), decltype(rows(vec.ddP, irow, nrows)), decltype(rows(vec.ddn, irow, nrows))>
	Return a const reference of a sequence of rows of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	rows (ChemicalVectorBase< V, T, P, N > &vec, Index irow, Index icol, Index nrows, Index ncols) -> ChemicalVectorBase< decltype(rows(vec.val, irow, nrows)), decltype(rows(vec.ddT, irow, nrows)), decltype(rows(vec.ddP, irow, nrows)), decltype(block(vec.ddn, irow, icol, nrows, ncols))>
	Return a reference of a sequence of rows of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	rows (const ChemicalVectorBase< V, T, P, N > &vec, Index irow, Index icol, Index nrows, Index ncols) -> ChemicalVectorBase< decltype(rows(vec.val, irow, nrows)), decltype(rows(vec.ddT, irow, nrows)), decltype(rows(vec.ddP, irow, nrows)), decltype(block(vec.ddn, irow, icol, nrows, ncols))>
	Return a const reference of a sequence of rows of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	rows (ChemicalVectorBase< V, T, P, N > &vec, const Indices &irows) -> ChemicalVectorBase< decltype(rows(vec.val, irows)), decltype(rows(vec.ddT, irows)), decltype(rows(vec.ddP, irows)), decltype(rows(vec.ddn, irows))>
	Return a reference of some rows of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	rows (const ChemicalVectorBase< V, T, P, N > &vec, const Indices &irows) -> ChemicalVectorBase< decltype(rows(vec.val, irows)), decltype(rows(vec.ddT, irows)), decltype(rows(vec.ddP, irows)), decltype(rows(vec.ddn, irows))>
	Return a const reference of some rows of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	rows (ChemicalVectorBase< V, T, P, N > &vec, const Indices &irows, const Indices &icols) -> ChemicalVectorBase< decltype(rows(vec.val, irows)), decltype(rows(vec.ddT, irows)), decltype(rows(vec.ddP, irows)), decltype(submatrix(vec.ddn, irows, icols))>
	Return a reference of some rows and cols of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	rows (const ChemicalVectorBase< V, T, P, N > &vec, const Indices &irows, const Indices &icols) -> ChemicalVectorBase< decltype(rows(vec.val, irows)), decltype(rows(vec.ddT, irows)), decltype(rows(vec.ddP, irows)), decltype(submatrix(vec.ddn, irows, icols))>
	Return a const reference of some rows and cols of this ChemicalVectorBase instance.
template<typename V , typename T , typename P , typename N >
auto	abs (const ChemicalVectorBase< V, T, P, N > &l) -> ChemicalVector
template<typename V , typename T , typename P , typename N >
auto	sqrt (const ChemicalVectorBase< V, T, P, N > &l) -> ChemicalVector
template<typename V , typename T , typename P , typename N >
auto	pow (const ChemicalVectorBase< V, T, P, N > &l, double power) -> ChemicalVector
template<typename V , typename T , typename P , typename N >
auto	exp (const ChemicalVectorBase< V, T, P, N > &l) -> ChemicalVector
template<typename V , typename T , typename P , typename N >
auto	log (const ChemicalVectorBase< V, T, P, N > &l) -> ChemicalVector
template<typename V , typename T , typename P , typename N >
auto	log10 (const ChemicalVectorBase< V, T, P, N > &l) -> decltype(log(l)/double())
template<typename V , typename T , typename P , typename N >
auto	min (const ChemicalVectorBase< V, T, P, N > &r) -> double
template<typename V , typename T , typename P , typename N >
auto	max (const ChemicalVectorBase< V, T, P, N > &r) -> double
template<typename V , typename T , typename P , typename N >
auto	sum (const ChemicalVectorBase< V, T, P, N > &r) -> ChemicalScalarBase< double, decltype(r.ddn.colwise().sum())>
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	dot (const ChemicalVectorBase< VL, TL, PL, NL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> ChemicalScalarBase< double, decltype(tr(l.val) *r.ddn+tr(r.val) *l.ddn)>
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	dot (const ThermoVectorBase< VL, TL, PL > &l, const ChemicalVectorBase< VR, TR, PR, NR > &r) -> ChemicalScalarBase< double, decltype(tr(l.val) *r.ddn)>
template<typename VL , typename TL , typename PL , typename NL , typename VR , typename TR , typename PR , typename NR >
auto	dot (const ChemicalVectorBase< VR, TR, PR, NR > &l, const ThermoVectorBase< VL, TL, PL > &r) -> decltype(dot(r, l))
template<typename V , typename T , typename P , typename N , typename Derived >
auto	dot (const Eigen::MatrixBase< Derived > &l, const ChemicalVectorBase< V, T, P, N > &r) -> ChemicalScalarBase< double, decltype(tr(l) *r.ddn)>
template<typename V , typename T , typename P , typename N , typename Derived >
auto	dot (const ChemicalVectorBase< V, T, P, N > &l, const Eigen::MatrixBase< Derived > &r) -> decltype(dot(r, l))
template<typename Scalar >
auto	convertCelsiusToKelvin (Scalar T) -> decltype(T+273.15)
	Converts temperature from celsius to kelvin.
template<typename Scalar >
auto	convertKelvinToCelsius (Scalar T) -> decltype(T - 273.15)
	Converts temperature from kelvin to celsius.
template<typename Scalar >
auto	convertPascalToKiloPascal (Scalar P) -> decltype(P *1.0e-3)
	Converts pressure from pascal to kilo pascal.
template<typename Scalar >
auto	convertPascalToMegaPascal (Scalar P) -> decltype(P *1.0e-6)
	Converts pressure from pascal to mega pascal.
template<typename Scalar >
auto	convertPascalToBar (Scalar P) -> decltype(P *1.0e-5)
	Converts pressure from pascal to bar.
template<typename Scalar >
auto	convertKiloPascalToPascal (Scalar P) -> decltype(P *1.0e+3)
	Converts pressure from kilo pascal to pascal.
template<typename Scalar >
auto	convertKiloPascalToMegaPascal (Scalar P) -> decltype(P *1.0e-3)
	Converts pressure from kilo pascal to mega pascal.
template<typename Scalar >
auto	convertKiloPascalToBar (Scalar P) -> decltype(P *1.0e-2)
	Converts pressure from kilo pascal to bar.
template<typename Scalar >
auto	convertMegaPascalToPascal (Scalar P) -> decltype(P *1.0e+6)
	Converts pressure from mega pascal to pascal.
template<typename Scalar >
auto	convertMegaPascalToKiloPascal (Scalar P) -> decltype(P *1.0e+3)
	Converts pressure from mega pascal to kilo pascal.
template<typename Scalar >
auto	convertMegaPascalToBar (Scalar P) -> decltype(P *1.0e+1)
	Converts pressure from mega pascal to bar.
template<typename Scalar >
auto	convertBarToPascal (Scalar P) -> decltype(P *1.0e+5)
	Converts pressure from bar to pascal.
template<typename Scalar >
auto	convertBarToKiloPascal (Scalar P) -> decltype(P *1.0e+2)
	Converts pressure from bar to kilo pascal.
template<typename Scalar >
auto	convertBarToMegaPascal (Scalar P) -> decltype(P *1.0e-1)
	Converts pressure from bar to mega pascal.
template<typename Scalar >
auto	convertBarToAtm (Scalar P) -> decltype(P *0.986923267)
	Convert pressure from bar to atm.
template<typename Scalar >
auto	convertCubicCentimeterToCubicMeter (Scalar V) -> decltype(V *1.0e-6)
	Converts volume from cm3 to m3.
template<typename Scalar >
auto	convertCubicMeterToCubicCentimeter (Scalar V) -> decltype(V *1.0e+6)
	Converts volume from m3 to cm3.
template<typename Scalar >
auto	convertCubicMeterToLiter (Scalar V) -> decltype(V *1.0e+3)
	Converts volume from m3 to liter.
template<typename Scalar >
auto	convertLiterToCubicMeter (Scalar V) -> decltype(V *1.0e-3)
	Converts volume from liter to m3.
auto	elements () -> std::vector< std::string >
	Return a vector of all known 116 chemical elements.
auto	elements (std::string formula) -> std::map< std::string, double >
	Determine. More...
auto	atomicMass (std::string element) -> double
	Return the atomic mass of a chemical element (in units of kg/mol). More...
auto	molarMass (const std::map< std::string, double > &compound) -> double
	Calculate the molar mass of a chemical compound (in units of kg/mol). More...
auto	molarMass (std::string formula) -> double
	Calculate the molar mass of a chemical compound (in units of kg/mol). More...
auto	charge (const std::string &formula) -> double
	Extract the electrical charge of a chemical formula. More...
auto	interpolate (const std::vector< double > &temperatures, const std::vector< double > &pressures, const std::vector< ThermoScalar > &scalars) -> ThermoScalarFunction
auto	interpolate (const std::vector< double > &temperatures, const std::vector< double > &pressures, const ThermoScalarFunction &f) -> ThermoScalarFunction
auto	interpolate (const std::vector< double > &temperatures, const std::vector< double > &pressures, const std::vector< ThermoScalarFunction > &fs) -> ThermoVectorFunction
auto	alternativeWaterNames () -> std::vector< std::string > &
	Return a collection of alternative names to the given species name. More...
auto	alternativeChargedSpeciesNames (std::string name) -> std::vector< std::string > &
	Return a collection of alternative names to the given charged species name. More...
auto	alternativeNeutralSpeciesNames (std::string name) -> std::vector< std::string > &
	Return a collection of alternative names to the given neutral species name. More...
auto	conventionalWaterName () -> std::string
	Return the conventional water name, which is H2O(l).
auto	conventionalChargedSpeciesName (std::string name) -> std::string
	Return the conventional charged species name adopted in Reaktoro. More...
auto	conventionalNeutralSpeciesName (std::string name) -> std::string
	Return the conventional neutral species name adopted in Reaktoro. More...
auto	isAlternativeWaterName (std::string trial) -> bool
	Return true if a trial name is an alternative to a water species name. More...
auto	isAlternativeChargedSpeciesName (std::string trial, std::string name) -> bool
	Return true if a trial name is an alternative to a given charged species name. More...
auto	isAlternativeNeutralSpeciesName (std::string trial, std::string name) -> bool
	Return true if a trial name is an alternative to a given neutral species name. More...
auto	splitChargedSpeciesName (std::string name) -> std::pair< std::string, double >
	Return a pair with the base name of a charged species and its electrical charge. More...
auto	baseNameChargedSpecies (std::string name) -> std::string
	Return the name of a charged species without charge suffix. More...
auto	baseNameNeutralSpecies (std::string name) -> std::string
	Return the name of a neutral species without suffix (aq). More...
auto	chargeInSpeciesName (std::string name) -> double
	Return the electrical charge in a species name. More...
template<typename Ret , typename... Args>
auto	memoize (std::function< Ret(Args...)> f) -> std::function< Ret(Args...)>
template<typename Ret , typename... Args>
auto	memoizeLast (std::function< Ret(Args...)> f) -> std::function< Ret(Args...)>
template<typename Ret , typename... Args>
auto	memoizeLastPtr (std::function< Ret(Args...)> f) -> std::shared_ptr< std::function< Ret(Args...)>>
template<typename Ret , typename... Args>
auto	dereference (const std::shared_ptr< std::function< Ret(Args...)>> &f) -> std::function< Ret(Args...)>
auto	parseReaction (std::string equation) -> std::map< std::string, double >
	Parse a reaction equation.
auto	operator<< (std::ostream &out, const ReactionEquation &equation) -> std::ostream &
	Output a ReactionEquation instance.
auto	begin (const Reaktoro::ReactionEquation &equation) -> decltype(equation.equation().begin())
	Return begin const iterator of a ReactionEquation instance.
auto	begin (Reaktoro::ReactionEquation &equation) -> decltype(equation.equation().begin())
	Return begin iterator of a ReactionEquation instance.
auto	end (const Reaktoro::ReactionEquation &equation) -> decltype(equation.equation().end())
	Return end const iterator of a ReactionEquation instance.
auto	end (Reaktoro::ReactionEquation &equation) -> decltype(equation.equation().end())
	Return end iterator of a ReactionEquation instance.
template<typename T >
auto	index (const T &value, const std::vector< T > &values) -> Index
	Find the index of a value in a container of values.
auto	index (const std::string &word, const std::vector< std::string > &strings) -> Index
	Find the index of the word in the container of strings.
template<typename NamedValues >
auto	index (const std::string &name, const NamedValues &values) -> Index
	Return the index of an entry in a container.
template<typename NamedValue , typename NamedValues >
auto	index (const NamedValue &value, const NamedValues &values) -> Index
	Return the index of an entry in a container.
template<typename Names , typename NamedValues >
auto	indexAny (const Names &names, const NamedValues &values) -> Index
	Return the index of the first entry in a container of named values with any of the given names.
template<typename NamedValues >
auto	indices (const std::vector< std::string > &names, const NamedValues &values) -> Indices
	Return the indices of some entries in a container.
template<typename NamedValues >
auto	indices (const NamedValues &subvalues, const NamedValues &values) -> Indices
	Return the indices of some entries in a container.
auto	indices (const std::vector< std::string > &words, const std::vector< std::string > &strings) -> Indices
	Find the indices of the words in the container of strings
template<typename Container >
auto	contained (const Container &values1, const Container &values2) -> bool
	Check if a value is contained in a container of values. More...
template<typename NamedValues >
auto	contained (const std::string &name, const NamedValues &values) -> bool
	Return true if a named value is in a set of values.
template<typename T >
auto	unify (const std::vector< T > &values1, const std::vector< T > &values2) -> std::vector< T >
	Determine the union of two containers.
template<typename T >
auto	intersect (const std::vector< T > &values1, const std::vector< T > &values2) -> std::vector< T >
	Determine the intersection of two containers.
template<typename T >
auto	difference (const std::vector< T > &values1, const std::vector< T > &values2) -> std::vector< T >
	Determine the difference of two containers.
template<typename T >
auto	emptyIntersection (const std::vector< T > &values1, const std::vector< T > &values2) -> bool
	Check if two containers have empty intersection.
template<typename T >
auto	emptyDifference (const std::vector< T > &values1, const std::vector< T > &values2) -> bool
	Check if two containers have empty difference.
template<typename Container >
auto	equal (const Container &values1, const Container &values2) -> bool
	Check if two containers are equal.
template<typename Container >
auto	isunique (Container values) -> bool
	Check if a container has unique values.
template<typename T >
auto	unique (std::vector< T > values) -> std::vector< T >
	Create a container with unique values from another.
template<typename T >
auto	range (T first, T last, T step) -> std::vector< T >
	Return a range of values. More...
template<typename T >
auto	range (T first, T last) -> std::vector< T >
	Return a range of values with unit step. More...
template<typename T >
auto	range (T last) -> std::vector< T >
	Return a range of values starting from zero and increasing by one. More...
template<typename T , typename Predicate >
auto	filter (const std::vector< T > &values, Predicate predicate) -> std::vector< T >
	Filter the values that pass on the predicate.
template<typename T , typename Predicate >
auto	remove (const std::vector< T > &values, Predicate predicate) -> std::vector< T >
	Remove the values that pass on the predicate.
template<typename T >
auto	extract (const std::vector< T > &values, const Indices &indices) -> std::vector< T >
	Extract values from a vector given a list of indices. More...
template<typename Container >
auto	minValue (const Container &values) -> typename Container::value_type
	Return the minimum value in a STL compatible container.
template<typename Container >
auto	maxValue (const Container &values) -> typename Container::value_type
	Return the maximum value in a STL compatible container.
template<typename Container , typename = typename std::enable_if<!std::is_same<typename Container::value_type, std::string>::value>::type>
auto	contained (const typename Container::value_type &value, const Container &values) -> bool
	StringList::operator const std::vector< std::string > & () const
auto	begin (const StringList &strings) -> decltype(strings.strings().begin())
	Return begin const iterator of a StringList instance.
auto	begin (StringList &strings) -> decltype(strings.strings().begin())
	Return begin iterator of a StringList instance.
auto	end (const StringList &strings) -> decltype(strings.strings().end())
	Return end const iterator of a StringList instance.
auto	end (StringList &strings) -> decltype(strings.strings().end())
	Return end iterator of a StringList instance.
auto	lowercase (std::string str) -> std::string
	Return a string with lower case characters.
auto	uppercase (std::string str) -> std::string
	Return a string with upper case characters.
auto	leftTrim (std::string &str) -> std::string &
	Trim the string from start (taken from http://stackoverflow.com/questions/216823/whats-the-best-way-to-trim-stdstring)
auto	rightTrim (std::string &str) -> std::string &
	Trim the string from end (taken from http://stackoverflow.com/questions/216823/whats-the-best-way-to-trim-stdstring)
auto	trim (std::string &str) -> std::string &
	Trim the string from both ends (taken from http://stackoverflow.com/questions/216823/whats-the-best-way-to-trim-stdstring)
auto	split (const std::string &str, const std::string &delims, std::function< std::string &(std::string &)> transform) -> std::vector< std::string >
	Split the string on every occurrence of the specified delimiters.
auto	split (const std::string &str, const std::string &delims=" ") -> std::vector< std::string >
	Split the string on every occurrence of the specified delimiters.
auto	splitrim (const std::string &str, const std::string &delims=" ") -> std::vector< std::string >
	Split the string on every occurrence of the specified delimiters and trim each word.
auto	join (const std::vector< std::string > &strs, std::string delim=" ") -> std::string
	Join several strings into one.
auto	tofloat (const std::string &str) -> double
	Convert the string into a floating point number.
auto	tofloats (const std::string &str, const std::string &delims=" ") -> std::vector< double >
	Convert the string into a list of floating point numbers.
template<typename T >
auto	table1D (unsigned dim1) -> Table1D< T >
template<typename T >
auto	table2D (unsigned dim1, unsigned dim2) -> Table2D< T >
template<typename T >
auto	table3D (unsigned dim1, unsigned dim2, unsigned dim3) -> Table3D< T >
template<typename V >
auto	operator+ (const ThermoScalarBase< V > &l) -> ThermoScalarBase< double >
template<typename VL , typename VR >
auto	operator+ (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> ThermoScalarBase< double >
template<typename V >
auto	operator+ (double l, const ThermoScalarBase< V > &r) -> ThermoScalarBase< double >
template<typename V >
auto	operator+ (const ThermoScalarBase< V > &l, double r) -> ThermoScalarBase< double >
template<typename V >
auto	operator- (const ThermoScalarBase< V > &l) -> ThermoScalarBase< double >
template<typename VL , typename VR >
auto	operator- (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> ThermoScalarBase< double >
template<typename V >
auto	operator- (const ThermoScalarBase< V > &l, double r) -> ThermoScalarBase< double >
template<typename V >
auto	operator- (double l, const ThermoScalarBase< V > &r) -> ThermoScalarBase< double >
template<typename VL , typename VR >
auto	operator* (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> ThermoScalarBase< double >
template<typename V >
auto	operator* (double l, const ThermoScalarBase< V > &r) -> ThermoScalarBase< double >
template<typename V >
auto	operator* (const ThermoScalarBase< V > &l, double r) -> ThermoScalarBase< double >
template<typename VL , typename VR >
auto	operator/ (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> ThermoScalarBase< double >
template<typename V >
auto	operator/ (double l, const ThermoScalarBase< V > &r) -> ThermoScalarBase< double >
template<typename V >
auto	operator/ (const ThermoScalarBase< V > &l, double r) -> ThermoScalarBase< double >
template<typename VL , typename VR >
auto	operator< (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> bool
template<typename VL , typename VR >
auto	operator<= (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> bool
template<typename VL , typename VR >
auto	operator> (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> bool
template<typename VL , typename VR >
auto	operator>= (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> bool
template<typename VL , typename VR >
auto	operator== (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> bool
template<typename VL , typename VR >
auto	operator!= (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &r) -> bool
template<typename V >
auto	operator< (double l, const ThermoScalarBase< V > &r) -> bool
template<typename V >
auto	operator< (const ThermoScalarBase< V > &l, double r) -> bool
template<typename V >
auto	operator<= (double l, const ThermoScalarBase< V > &r) -> bool
template<typename V >
auto	operator<= (const ThermoScalarBase< V > &l, double r) -> bool
template<typename V >
auto	operator> (double l, const ThermoScalarBase< V > &r) -> bool
template<typename V >
auto	operator> (const ThermoScalarBase< V > &l, double r) -> bool
template<typename V >
auto	operator>= (double l, const ThermoScalarBase< V > &r) -> bool
template<typename V >
auto	operator>= (const ThermoScalarBase< V > &l, double r) -> bool
template<typename V >
auto	operator== (double l, const ThermoScalarBase< V > &r) -> bool
template<typename V >
auto	operator== (const ThermoScalarBase< V > &l, double r) -> bool
template<typename V >
auto	operator!= (double l, const ThermoScalarBase< V > &r) -> bool
template<typename V >
auto	operator!= (const ThermoScalarBase< V > &l, double r) -> bool
template<typename V >
auto	operator<< (std::ostream &out, const ThermoScalarBase< V > &scalar) -> std::ostream &
template<typename V >
auto	abs (const ThermoScalarBase< V > &l) -> ThermoScalarBase< double >
template<typename V >
auto	sqrt (const ThermoScalarBase< V > &l) -> ThermoScalarBase< double >
template<typename V >
auto	pow (const ThermoScalarBase< V > &l, double power) -> ThermoScalarBase< double >
template<typename VL , typename VR >
auto	pow (const ThermoScalarBase< VL > &l, const ThermoScalarBase< VR > &power) -> ThermoScalarBase< double >
template<typename V >
auto	exp (const ThermoScalarBase< V > &l) -> ThermoScalarBase< double >
template<typename V >
auto	log (const ThermoScalarBase< V > &l) -> ThermoScalarBase< double >
template<typename V >
auto	log10 (const ThermoScalarBase< V > &l) -> ThermoScalarBase< double >
template<typename V , typename T , typename P >
auto	zeros (const ThermoVectorBase< V, T, P > &v) -> ThermoVectorBase< decltype(zeros(0)), decltype(zeros(0)), decltype(zeros(0))>
	Return a ThermoVectorBase expression representing zeros with same dimension of given vector.
template<typename V , typename T , typename P >
auto	ones (const ThermoVectorBase< V, T, P > &v) -> ThermoVectorBase< decltype(ones(0)), decltype(zeros(0)), decltype(zeros(0))>
	Return a ThermoVectorBase expression representing ones with same dimension of given vector.
template<typename V , typename T , typename P >
auto	operator<< (std::ostream &out, const ThermoVectorBase< V, T, P > &a) -> std::ostream &
template<typename V , typename T , typename P >
auto	operator+ (const ThermoVectorBase< V, T, P > &l) -> ThermoVectorBase< V, T, P >
template<typename V , typename T , typename P >
auto	operator- (const ThermoVectorBase< V, T, P > &l) -> ThermoVectorBase< decltype(-l.val), decltype(-l.ddT), decltype(-l.ddP)>
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator+ (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> ThermoVectorBase< decltype(l.val+r.val), decltype(l.ddT+r.ddT), decltype(l.ddP+r.ddP)>
template<typename V , typename T , typename P >
auto	operator+ (const ThermoVectorBase< V, T, P > &l, VectorConstRef r) -> ThermoVectorBase< decltype(l.val+r), T, P >
template<typename V , typename T , typename P >
auto	operator+ (VectorConstRef l, const ThermoVectorBase< V, T, P > &r) -> decltype(r+l)
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator- (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> ThermoVectorBase< decltype(l.val - r.val), decltype(l.ddT - r.ddT), decltype(l.ddP - r.ddP)>
template<typename V , typename T , typename P >
auto	operator- (const ThermoVectorBase< V, T, P > &l, VectorConstRef r) -> ThermoVectorBase< decltype(l.val - r), T, P >
template<typename V , typename T , typename P >
auto	operator- (VectorConstRef l, const ThermoVectorBase< V, T, P > &r) -> decltype(-(r - l))
template<typename V , typename T , typename P >
auto	operator* (double l, const ThermoVectorBase< V, T, P > &r) -> ThermoVectorBase< decltype(l *r.val), decltype(l *r.ddT), decltype(l *r.ddP)>
template<typename V , typename T , typename P >
auto	operator* (const ThermoVectorBase< V, T, P > &l, double r) -> decltype(r *l)
template<typename VL , typename V , typename T , typename P >
auto	operator* (const ThermoScalarBase< VL > &l, const ThermoVectorBase< V, T, P > &r) -> ThermoVectorBase< decltype(l.val *r.val), decltype(l.val *r.ddT+l.ddT *r.val), decltype(l.val *r.ddP+l.ddP *r.val)>
template<typename V , typename T , typename P , typename VR >
auto	operator* (const ThermoVectorBase< V, T, P > &l, const ThermoScalarBase< VR > &r) -> decltype(r *l)
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator% (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> ThermoVectorBase< decltype(diag(l.val) *r.val), decltype(diag(l.val) *r.ddT+diag(r.val) *l.ddT), decltype(diag(l.val) *r.ddP+diag(r.val) *l.ddP)>
template<typename V , typename T , typename P >
auto	operator% (VectorConstRef l, const ThermoVectorBase< V, T, P > &r) -> ThermoVectorBase< decltype(diag(l) *r.val), decltype(diag(l) *r.ddT), decltype(diag(l) *r.ddP)>
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator% (const ThermoVectorBase< VL, TL, PL > &l, VectorConstRef r) -> decltype(r % l)
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator/ (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> ThermoVector
template<typename V , typename T , typename P , typename VR >
auto	operator/ (const ThermoVectorBase< V, T, P > &l, const ThermoScalarBase< VR > &r) -> ThermoVectorBase< decltype(l.val/r.val), decltype(double() *(l.ddT *r.val - l.val *r.ddT)), decltype(double() *(l.ddP *r.val - l.val *r.ddP))>
template<typename V , typename T , typename P >
auto	operator/ (const ThermoVectorBase< V, T, P > &l, double r) -> decltype((1.0/r) *l)
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator< (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> bool
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator<= (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> bool
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator> (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> bool
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator>= (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> bool
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator== (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> bool
template<typename VL , typename TL , typename PL , typename VR , typename TR , typename PR >
auto	operator!= (const ThermoVectorBase< VL, TL, PL > &l, const ThermoVectorBase< VR, TR, PR > &r) -> bool
template<typename V , typename T , typename P >
auto	row (ThermoVectorBase< V, T, P > &vec, Index irow) -> ThermoScalarBase< decltype(vec.val[irow])>
	Return a reference of a row of this ThermoVectorBase instance.
template<typename V , typename T , typename P >
auto	row (const ThermoVectorBase< V, T, P > &vec, Index irow) -> ThermoScalarBase< decltype(vec.val[irow])>
	Return a const reference of a row of this ThermoVectorBase instance.
template<typename V , typename T , typename P >
auto	rows (ThermoVectorBase< V, T, P > &vec, Index irow, Index nrows) -> ThermoVectorBase< decltype(vec.val.segment(irow, nrows)), decltype(vec.ddT.segment(irow, nrows)), decltype(vec.ddP.segment(irow, nrows))>
	Return a reference of a sequence of rows of this ThermoVectorBase instance.
template<typename V , typename T , typename P >
auto	rows (const ThermoVectorBase< V, T, P > &vec, Index irow, Index nrows) -> ThermoVectorBase< decltype(vec.val.segment(irow, nrows)), decltype(vec.ddT.segment(irow, nrows)), decltype(vec.ddP.segment(irow, nrows))>
	Return a const reference of a sequence of rows of this ThermoVectorBase instance.
template<typename V , typename T , typename P >
auto	rows (ThermoVectorBase< V, T, P > &vec, const Indices &irows) -> ThermoVectorBase< decltype(Reaktoro::rows(vec.val, irows)), decltype(Reaktoro::rows(vec.ddT, irows)), decltype(Reaktoro::rows(vec.ddP, irows))>
	Return a reference of some rows of this ThermoVectorBase instance.
template<typename V , typename T , typename P >
auto	rows (const ThermoVectorBase< V, T, P > &vec, const Indices &irows) -> ThermoVectorBase< decltype(Reaktoro::rows(vec.val, irows)), decltype(Reaktoro::rows(vec.ddT, irows)), decltype(Reaktoro::rows(vec.ddP, irows))>
	Return a const reference of some rows of this ThermoVectorBase instance.
template<typename V , typename T , typename P >
auto	abs (const ThermoVectorBase< V, T, P > &l) -> ThermoVector
template<typename V , typename T , typename P >
auto	sqrt (const ThermoVectorBase< V, T, P > &l) -> ThermoVector
template<typename V , typename T , typename P >
auto	pow (const ThermoVectorBase< V, T, P > &l, double power) -> ThermoVector
template<typename V , typename T , typename P >
auto	exp (const ThermoVectorBase< V, T, P > &l) -> ThermoVector
template<typename V , typename T , typename P >
auto	log (const ThermoVectorBase< V, T, P > &l) -> ThermoVector
template<typename V , typename T , typename P >
auto	log10 (const ThermoVectorBase< V, T, P > &l) -> ThermoVector
auto	time () -> Time
	Return the time point now. More...
auto	elapsed (const Time &end, const Time &begin) -> double
	Return the elapsed time between two time points (in units of s) More...
auto	elapsed (const Time &begin) -> double
	Return the elapsed time between a time point and now (in units of s) More...
auto	operator<< (std::ostream &out, const ChemicalState &state) -> std::ostream &
	Outputs a ChemicalState instance.
auto	operator+ (const ChemicalState &l, const ChemicalState &r) -> ChemicalState
	Add two ChemicalState instances.
auto	operator* (double scalar, const ChemicalState &state) -> ChemicalState
	Multiply a ChemicalState instance by a scalar (from the left).
auto	operator* (const ChemicalState &state, double scalar) -> ChemicalState
	Multiply a ChemicalState instance by a scalar (from the right).
auto	operator<< (std::ostream &out, const ChemicalSystem &system) -> std::ostream &
	Output a ChemicalSystem instance.
auto	operator< (const Element &lhs, const Element &rhs) -> bool
	Compare two Element instances for less than.
auto	operator== (const Element &lhs, const Element &rhs) -> bool
	Compare two Element instances for equality.
auto	operator< (const Phase &lhs, const Phase &rhs) -> bool
	Compare two Phase instances for less than.
auto	operator== (const Phase &lhs, const Phase &rhs) -> bool
	Compare two Phase instances for equality.
auto	operator< (const Reaction &lhs, const Reaction &rhs) -> bool
	Compare two Reaction instances for less than.
auto	operator== (const Reaction &lhs, const Reaction &rhs) -> bool
	Compare two Reaction instances for equality.
auto	operator<< (std::ostream &out, const ReactionSystem &reactions) -> std::ostream &
auto	operator< (const Species &lhs, const Species &rhs) -> bool
	Compare two Species instances for less than.
auto	operator== (const Species &lhs, const Species &rhs) -> bool
	Compare two Species instances for equality.
template<typename NamedValues >
auto	names (const NamedValues &values) -> std::vector< std::string >
	Return the names of the entries in a container.
template<typename ChargedValues >
auto	charges (const ChargedValues &values) -> Vector
	Return the electrical charges of all species in a list of species.
template<typename SpeciesValues >
auto	molarMasses (const SpeciesValues &species) -> Vector
	Return the molar masses of all species in a list of species (in units of kg/mol)
auto	moleFractions (Composition n) -> ChemicalVector
	Return the mole fractions of the species.
template<typename SpeciesValues >
auto	charges (const SpeciesValues &species) -> Vector
auto	equilibrate (ChemicalState &state) -> EquilibriumResult
	Equilibrate a chemical state instance. More...
auto	equilibrate (ChemicalState &state, const Partition &partition) -> EquilibriumResult
	Equilibrate a chemical state instance. More...
auto	equilibrate (ChemicalState &state, const EquilibriumOptions &options) -> EquilibriumResult
	Equilibrate a chemical state instance with equilibrium options. More...
auto	equilibrate (ChemicalState &state, const Partition &partition, const EquilibriumOptions &options) -> EquilibriumResult
	Equilibrate a chemical state instance with equilibrium options. More...
auto	equilibrate (ChemicalState &state, const EquilibriumProblem &problem) -> EquilibriumResult
	Equilibrate a chemical state instance with an equilibrium problem. More...
auto	equilibrate (ChemicalState &state, const EquilibriumProblem &problem, const EquilibriumOptions &options) -> EquilibriumResult
	Equilibrate a chemical state instance with an equilibrium problem. More...
auto	equilibrate (const EquilibriumProblem &problem) -> ChemicalState
	Equilibrate a chemical state instance with an equilibrium problem. More...
auto	equilibrate (const EquilibriumProblem &problem, const EquilibriumOptions &options) -> ChemicalState
	Equilibrate a chemical state instance with an equilibrium problem. More...
auto	equilibrate (ChemicalState &state, const EquilibriumInverseProblem &problem) -> EquilibriumResult
	Equilibrate a chemical state instance with an equilibrium inverse problem. More...
auto	equilibrate (ChemicalState &state, const EquilibriumInverseProblem &problem, const EquilibriumOptions &options) -> EquilibriumResult
	Equilibrate a chemical state instance with an equilibrium inverse problem. More...
auto	equilibrate (const EquilibriumInverseProblem &problem) -> ChemicalState
	Equilibrate a chemical state instance with an equilibrium inverse problem. More...
auto	equilibrate (const EquilibriumInverseProblem &problem, const EquilibriumOptions &options) -> ChemicalState
	Equilibrate a chemical state instance with an equilibrium inverse problem. More...
auto	operator<< (std::ostream &out, const BilinearInterpolator &interpolator) -> std::ostream &
	Output a BilinearInterpolator instance.
auto	derivativeForward (const ScalarFunction &f, VectorConstRef x) -> Vector
	Calculate the partial derivatives of a scalar function using a 1st-order forward finite difference scheme. More...
auto	derivativeBackward (const ScalarFunction &f, VectorConstRef x) -> Vector
	Calculate the partial derivatives of a scalar function using a 1st-order backward finite difference scheme. More...
auto	derivativeCentral (const ScalarFunction &f, VectorConstRef x) -> Vector
	Calculate the partial derivatives of a scalar function using a 2nd-order central finite difference scheme. More...
auto	derivativeForward (const VectorFunction &f, VectorConstRef x) -> Matrix
	Calculate the partial derivatives of a vector function using a 1st-order forward finite difference scheme. More...
auto	derivativeBackward (const VectorFunction &f, VectorConstRef x) -> Matrix
	Calculate the partial derivatives of a vector function using a 1st-order backward finite difference scheme. More...
auto	derivativeCentral (const VectorFunction &f, VectorConstRef x) -> Matrix
	Calculate the partial derivatives of a vector function using a 2nd-order central finite difference scheme. More...
auto	linearlyIndependentCols (MatrixConstRef A) -> Indices
	Determine the set of linearly independent columns in a matrix using a column pivoting QR algorithm. More...
auto	linearlyIndependentRows (MatrixConstRef A) -> Indices
	Determine the set of linearly independent rows in a matrix. More...
auto	linearlyIndependentCols (MatrixConstRef A, MatrixRef B) -> Indices
	Determine the set of linearly independent columns in a matrix. More...
auto	linearlyIndependentRows (MatrixConstRef A, MatrixRef B) -> Indices
	Determine the set of linearly independent rows in a matrix. More...
auto	inverseShermanMorrison (MatrixConstRef invA, VectorConstRef D) -> Matrix
	Calculate the inverse of A + D where inv(A) is already known and D is a diagonal matrix. More...
auto	farey (double x, unsigned maxden) -> std::tuple< long, long >
	Return the numerator and denominator of the rational number closest to x. More...
auto	rationalize (double x, unsigned maxden) -> std::tuple< long, long >
	Calculates the rational number that approximates a given real number. More...
auto	cleanRationalNumbers (double *vals, long size, long maxden=6) -> void
	Clean an array that is known to have rational numbers from round-off errors. More...
auto	cleanRationalNumbers (MatrixRef A, long maxden=6) -> void
	Clean a matrix that is known to have rational numbers from round-off errors. More...
template<typename VectorTypeX , typename VectorTypeY >
auto	dot3p_ (const VectorTypeX &x, const VectorTypeY &y, double s) -> double
auto	dot3p (VectorConstRef x, VectorConstRef y, double s) -> double
	Return the dot product s + dot(x, y) of two vectors with triple-precision.
auto	residual3p (MatrixConstRef A, VectorConstRef x, VectorConstRef b) -> Vector
	Return the residual of the equation A*x - b with triple-precision.
auto	zeros (Index rows) -> decltype(Vector::Zero(rows))
	Return an expression of a zero vector. More...
auto	ones (Index rows) -> decltype(Vector::Ones(rows))
	Return an expression of a vector with entries equal to one. More...
auto	random (Index rows) -> decltype(Vector::Random(rows))
	Return an expression of a vector with random entries. More...
auto	linspace (Index rows, double start, double stop) -> decltype(Vector::LinSpaced(rows, start, stop))
	Return a linearly spaced vector. More...
auto	unit (Index rows, Index i) -> decltype(Vector::Unit(rows, i))
	Return an expression of a unit vector. More...
auto	zeros (Index rows, Index cols) -> decltype(Matrix::Zero(rows, cols))
	Return an expression of a zero matrix. More...
auto	ones (Index rows, Index cols) -> decltype(Matrix::Ones(rows, cols))
	Return an expression of a matrix with entries equal to one. More...
auto	random (Index rows, Index cols) -> decltype(Matrix::Random(rows, cols))
	Return an expression of a matrix with random entries. More...
auto	identity (Index rows, Index cols) -> decltype(Matrix::Identity(rows, cols))
	Return an expression of an identity matrix. More...
template<typename Derived >
auto	rows (Eigen::MatrixBase< Derived > &mat, Index start, Index num) -> decltype(mat.middleRows(start, num))
	Return a view of a sequence of rows of a matrix. More...
template<typename Derived >
auto	rows (const Eigen::MatrixBase< Derived > &mat, Index start, Index num) -> decltype(mat.middleRows(start, num))
	Return a view of a sequence of rows of a matrix. More...
template<typename Derived , typename Indices >
auto	rows (Eigen::MatrixBase< Derived > &mat, const Indices &irows) -> decltype(mat(irows, Eigen::all))
	Return a view of some rows of a matrix. More...
template<typename Derived , typename Indices >
auto	rows (const Eigen::MatrixBase< Derived > &mat, const Indices &irows) -> decltype(mat(irows, Eigen::all))
	Return a const view of some rows of a matrix. More...
template<typename Derived >
auto	cols (Eigen::MatrixBase< Derived > &mat, Index start, Index num) -> decltype(mat.middleCols(start, num))
	Return a view of a sequence of columns of a matrix. More...
template<typename Derived >
auto	cols (const Eigen::MatrixBase< Derived > &mat, Index start, Index num) -> decltype(mat.middleCols(start, num))
	Return a view of a sequence of columns of a matrix. More...
template<typename Derived , typename Indices >
auto	cols (Eigen::MatrixBase< Derived > &mat, const Indices &icols) -> decltype(mat(Eigen::all, icols))
	Return a view of some columns of a matrix. More...
template<typename Derived , typename Indices >
auto	cols (const Eigen::MatrixBase< Derived > &mat, const Indices &icols) -> decltype(mat(Eigen::all, icols))
	Return a const view of some columns of a matrix. More...
template<typename Derived >
auto	segment (Eigen::MatrixBase< Derived > &vec, Index irow, Index nrows) -> decltype(vec.segment(irow, nrows))
	Return a view of some rows and columns of a matrix. More...
template<typename Derived >
auto	segment (const Eigen::MatrixBase< Derived > &vec, Index irow, Index nrows) -> decltype(vec.segment(irow, nrows))
	Return a view of some rows and columns of a matrix. More...
template<typename Derived >
auto	block (Eigen::MatrixBase< Derived > &mat, Index irow, Index icol, Index nrows, Index ncols) -> decltype(mat.block(irow, icol, nrows, ncols))
	Return a view of some rows and columns of a matrix. More...
template<typename Derived >
auto	block (const Eigen::MatrixBase< Derived > &mat, Index irow, Index icol, Index nrows, Index ncols) -> decltype(mat.block(irow, icol, nrows, ncols))
	Return a view of some rows and columns of a matrix. More...
template<typename Derived , typename Indices >
auto	submatrix (Eigen::MatrixBase< Derived > &mat, const Indices &irows, const Indices &icols) -> decltype(mat(irows, icols))
	Return a view of some rows and columns of a matrix. More...
template<typename Derived , typename Indices >
auto	submatrix (const Eigen::MatrixBase< Derived > &mat, const Indices &irows, const Indices &icols) -> decltype(mat(irows, icols))
	Return a const view of some rows and columns of a matrix. More...
template<typename Scalar , int Rows, int Cols, int Options, int MaxRows, int MaxCols>
auto	blockmap (Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &mat, Index row, Index col, Index nrows, Index ncols) -> Eigen::Map< Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols >, Eigen::Unaligned, Eigen::Stride< Rows, Cols >>
	Return a block mapped view of a matrix. More...
template<typename Scalar , int Rows, int Cols, int Options, int MaxRows, int MaxCols>
auto	blockmap (const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &mat, Index row, Index col, Index nrows, Index ncols) -> Eigen::Map< const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols >, Eigen::Unaligned, Eigen::Stride< Rows, Cols >>
	Return a const block mapped view of a matrix. More...
template<typename Scalar , int Rows, int Cols, int Options, int MaxRows, int MaxCols>
auto	rowsmap (Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &mat, Index row, Index nrows) -> Eigen::Map< Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols >, Eigen::Unaligned, Eigen::Stride< Rows, Cols >>
	Return a mapped view of a sequence of rows of a matrix. More...
template<typename Scalar , int Rows, int Cols, int Options, int MaxRows, int MaxCols>
auto	rowsmap (const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &mat, Index row, Index nrows) -> Eigen::Map< const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols >, Eigen::Unaligned, Eigen::Stride< Rows, Cols >>
	Return a const mapped view of a sequence of rows of a matrix. More...
template<typename Scalar , int Rows, int Cols, int Options, int MaxRows, int MaxCols>
auto	colsmap (Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &mat, Index col, Index ncols) -> Eigen::Map< Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols >, Eigen::Unaligned, Eigen::Stride< Rows, Cols >>
	Return a mapped view of a sequence of columns of a matrix. More...
template<typename Scalar , int Rows, int Cols, int Options, int MaxRows, int MaxCols>
auto	colsmap (const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &mat, Index col, Index ncols) -> Eigen::Map< const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols >, Eigen::Unaligned, Eigen::Stride< Rows, Cols >>
	Return a const mapped view of a sequence of columns of a matrix. More...
template<typename Derived >
auto	tr (Eigen::MatrixBase< Derived > &mat) -> decltype(mat.transpose())
	Return the transpose of the matrix.
template<typename Derived >
auto	tr (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.transpose())
	Return the transpose of the matrix.
template<typename Derived >
auto	inv (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.cwiseInverse())
	Return the component-wise inverse of the matrix.
template<typename Derived >
auto	diag (const Eigen::MatrixBase< Derived > &vec) -> decltype(vec.asDiagonal())
	Return a diagonal matrix representation of a vector.
template<typename Derived >
auto	diagonal (Eigen::MatrixBase< Derived > &mat) -> decltype(mat.diagonal())
	Return a vector representation of the diagonal of a matrix.
template<typename Derived >
auto	diagonal (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.diagonal())
	Return a vector representation of the diagonal of a matrix.
template<int p, typename Derived >
auto	norm (const Eigen::MatrixBase< Derived > &mat) -> double
	Return the Lp norm of a matrix.
template<typename Derived >
auto	norm (const Eigen::MatrixBase< Derived > &mat) -> double
	Return the L2 norm of a matrix.
template<typename Derived >
auto	norminf (const Eigen::MatrixBase< Derived > &mat) -> double
	Return the L-inf norm of a matrix.
template<typename Derived >
auto	sum (const Eigen::DenseBase< Derived > &mat) -> typename Derived::Scalar
	Return the sum of the components of a matrix.
template<typename DerivedLHS , typename DerivedRHS >
auto	dot (const Eigen::MatrixBase< DerivedLHS > &lhs, const Eigen::MatrixBase< DerivedRHS > &rhs) -> decltype(lhs.dot(rhs))
	Return the dot product of two matrices.
template<typename Derived >
auto	min (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.minCoeff())
	Return the minimum component of a matrix.
template<typename DerivedLHS , typename DerivedRHS >
auto	min (const Eigen::MatrixBase< DerivedLHS > &lhs, const Eigen::MatrixBase< DerivedRHS > &rhs) -> decltype(lhs.cwiseMin(rhs))
	Return the component-wise minimum of two matrices.
template<typename Derived >
auto	max (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.maxCoeff())
	Return the maximum component of a matrix.
template<typename DerivedLHS , typename DerivedRHS >
auto	max (const Eigen::MatrixBase< DerivedLHS > &lhs, const Eigen::MatrixBase< DerivedRHS > &rhs) -> decltype(lhs.cwiseMax(rhs))
	Return the component-wise maximum of two matrices.
template<typename DerivedLHS , typename DerivedRHS >
auto	operator% (const Eigen::MatrixBase< DerivedLHS > &lhs, const Eigen::MatrixBase< DerivedRHS > &rhs) -> decltype(lhs.cwiseProduct(rhs))
	Return the component-wise multiplication of two matrices.
template<typename DerivedLHS , typename DerivedRHS >
auto	operator/ (const Eigen::MatrixBase< DerivedLHS > &lhs, const Eigen::MatrixBase< DerivedRHS > &rhs) -> decltype(lhs.cwiseQuotient(rhs))
	Return the component-wise division of two matrices.
template<typename Derived >
auto	operator/ (const typename Derived::Scalar &scalar, const Eigen::MatrixBase< Derived > &mat) -> decltype(scalar *mat.cwiseInverse())
	Return the component-wise division of two matrices.
template<typename Derived >
auto	operator+ (const typename Derived::Scalar &scalar, const Eigen::MatrixBase< Derived > &mat) -> decltype((scalar+mat.array()).matrix())
	Return the component-wise division of two matrices.
template<typename Derived >
auto	operator+ (const Eigen::MatrixBase< Derived > &mat, const typename Derived::Scalar &scalar) -> decltype((scalar+mat.array()).matrix())
	Return the component-wise division of two matrices.
template<typename Derived >
auto	operator- (const typename Derived::Scalar &scalar, const Eigen::MatrixBase< Derived > &mat) -> decltype((scalar - mat.array()).matrix())
	Return the component-wise division of two matrices.
template<typename Derived >
auto	operator- (const Eigen::MatrixBase< Derived > &mat, const typename Derived::Scalar &scalar) -> decltype((mat.array() - scalar).matrix())
	Return the component-wise division of two matrices.
template<typename Derived >
auto	abs (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.cwiseAbs())
	Return the component-wise absolute entries of a matrix.
template<typename Derived >
auto	sqrt (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.cwiseSqrt())
	Return the component-wise square root of a matrix.
template<typename Derived >
auto	pow (const Eigen::MatrixBase< Derived > &mat, double power) -> decltype(mat.array().pow(power))
	Return the component-wise exponential of a matrix.
template<typename Derived >
auto	exp (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.array().exp().matrix())
	Return the component-wise natural exponential of a matrix.
template<typename Derived >
auto	log (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.array().log().matrix())
	Return the component-wise natural log of a matrix.
template<typename Derived >
auto	log10 (const Eigen::MatrixBase< Derived > &mat) -> decltype(mat.array().log10().matrix())
	Return the component-wise log10 of a matrix.
auto	constants (Index rows, double val) -> decltype(Vector::Constant(rows, val))
auto	unitcol (Index rows, Index i) -> decltype(unit(rows, i))
auto	unitrow (Index cols, Index i) -> decltype(RowVector::Unit(cols, i))
int	CVODEStep (const ODEStepMode &step)
int	CVODEIteration (const ODEIterationMode &iteration)
int	CVODEMaxStepOrder (const ODEOptions &options)
int	CVODEFunction (realtype t, N_Vector y, N_Vector ydot, void *user_data)
int	CVODEJacobian (long int N, realtype t, N_Vector y, N_Vector fy, DlsMat J, void *user_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3)
auto	cardano (double a, double b, double c, double d) -> CubicRoots
	Calculate the roots of a cubic equation using Cardano's method. More...
auto	newton (const std::function< std::tuple< double, double >(double)> &f, double x0, double epsilon, unsigned maxiter) -> double
	Calculate the root of a non-linear function using Newton's method. More...
auto	newton (const std::function< void(VectorConstRef, VectorRef, MatrixRef)> &f, VectorConstRef x0, double epsilon, unsigned maxiter) -> Vector
	Calculate the root of a non-linear multi-dimensional function using Newton's method. More...
auto	realRoots (const CubicRoots &roots) -> std::vector< double >
	Return all real roots of a group of roots. More...
auto	operator* (const Hessian &H, VectorConstRef x) -> Vector
	Return the multiplication of a Hessian matrix and a vector.
auto	isfinite (const ObjectiveResult &f) -> bool
	Returns true if the evaluation of a objective function has finite value and gradient.
auto	largestStep (VectorConstRef p, VectorConstRef dp) -> double
	Compute the largest step length \(\alpha\) such that \(\mathbf{p} + \alpha\Delta\mathbf{p}\) is on the lower bound \(\mathbf{x}_l=\mathbf{0}\). More...
auto	fractionToTheBoundary (VectorConstRef p, VectorConstRef dp, double tau) -> double
auto	fractionToTheBoundary (VectorConstRef p, VectorConstRef dp, double tau, Index &ilimiting) -> double
auto	fractionToTheBoundary (VectorConstRef p, VectorConstRef dp, MatrixConstRef C, VectorConstRef r, double tau) -> double
auto	fractionToTheLowerBoundary (VectorConstRef p, VectorConstRef dp, VectorConstRef lower, double tau) -> double
auto	lessThan (double a, double b, double baseval) -> bool
	Compute the fraction-to-the-boundary step length given by: More...
auto	greaterThan (double a, double b, double baseval) -> bool
	Check if a float number is greater than another by a base value. More...
auto	infinity () -> double
	Return the floating-point representation of positive infinity.
auto	bfgs () -> std::function< Matrix(VectorConstRef, VectorConstRef)>
	Return an inverse Hessian function based on the BFGS Hessian approximation.
auto	minimizeGoldenSectionSearch (const std::function< double(double)> &f, double tol) -> double
auto	minimizeGoldenSectionSearch (const std::function< double(double)> &f, double a, double b, double tol=1e-5) -> double
	Calculate the minimum of a single variable function using the Golden Section Search algorithm.
auto	minimizeBrent (const std::function< double(double)> &f, double min, double max, double tolerance=1e-5, unsigned maxiters=100) -> double
	Calculate the minimum of a single variable function using the Brent algorithm.
auto	aqueousActivityModelDrummondCO2 (const AqueousMixture &mixture) -> AqueousActivityModel
	Create the function for the calculation of ln activity coefficient of CO2(aq), based on the model of Drummond (1981). More...
auto	aqueousActivityModelDuanSunCO2 (const AqueousMixture &mixture) -> AqueousActivityModel
	Create the function for the calculation of ln activity coefficient of CO2(aq), based on the model of Duan and Sun (2003) The model is documented in the paper Duan, Z., Sun, R. More...
auto	aqueousActivityModelRumpfCO2 (const AqueousMixture &mixture) -> AqueousActivityModel
	Create the function for the calculation of ln activity coefficient of CO2(aq), based on the model of Rumpf et al. More...
auto	aqueousActivityModelSetschenow (const AqueousMixture &mixture, double b) -> AqueousActivityModel
	Create the aqueous activity function of a neutral species based on the Setschenow model. More...
auto	database (std::string name) -> std::string
	Return the contents of a built-in database as a string. More...
auto	databases () -> std::vector< std::string >
	Return the list of names of all built-in databases.
auto	sanityCheckInteractionParamsFunction (const unsigned &nspecies, const CubicEOS::InteractionParamsFunction &func) -> void
	Sanity check free function to verify if BIPs matrices have proper dimensions. More...
auto	identifyPhaseUsingVolume (const ThermoScalar &temperature, const ThermoScalar &pressure, const ChemicalScalar &Z, const ChemicalScalar &b) -> PhaseType
	Return a PhaseType that says if the phase is a Liquid or Gas based on Volume Method. More...
auto	identifyPhaseUsingIsothermalCompressibility (const ThermoScalar &temperature, const ThermoScalar &pressure, const ChemicalScalar &Z) -> PhaseType
	Return a PhaseType that says if the phase is a Liquid or Gas based on Isothermal Compressibility. More...
auto	pressureComparison (const ThermoScalar &Pressure, const ThermoScalar &Temperature, const ChemicalScalar &amix, const ChemicalScalar &bmix, const ChemicalScalar &A, const ChemicalScalar &B, const ChemicalScalar &C, const double epsilon, const double sigma) -> PhaseType
auto	gibbsResidualEnergyComparison (const ThermoScalar &pressure, const ThermoScalar &temperature, const ChemicalScalar &amix, const ChemicalScalar &bmix, const ChemicalScalar &A, const ChemicalScalar &B, const ChemicalScalar &Z_min, const ChemicalScalar &Z_max, const double epsilon, const double sigma) -> PhaseType
auto	identifyPhaseUsingGibbsEnergyAndEos (const ThermoScalar &pressure, const ThermoScalar &temperature, const ChemicalScalar &amix, const ChemicalScalar &bmix, const ChemicalScalar &A, const ChemicalScalar &B, const ChemicalScalar &C, std::vector< ChemicalScalar > Zs, const double epsilon, const double sigma) -> PhaseType
	Return a PhaseType that says if the phase is a Liquid or Gas based on gibbs residual energy and equation of state. More...
auto	operator== (const MixtureState &l, const MixtureState &r) -> bool
	Compare two MixtureState instances for equality.
auto	aqueousChemicalModelDebyeHuckel (const AqueousMixture &mixture, const DebyeHuckelParams &params) -> PhaseChemicalModel
	Return an equation of state for an aqueous phase based on the Debye–Hückel activity model. More...
auto	aqueousChemicalModelHKF (const AqueousMixture &mixture) -> PhaseChemicalModel
	Return an equation of state for an aqueous phase based on HKF model. More...
auto	aqueousChemicalModelIdeal (const AqueousMixture &mixture) -> PhaseChemicalModel
	Return an equation of state for an aqueous phase based on the ideal model. More...
auto	aqueousChemicalModelPitzerHMW (const AqueousMixture &mixture) -> PhaseChemicalModel
	Return an equation of state for an aqueous phase based on a Pitzer model. More...
auto	fluidChemicalModelCubicEOS (const FluidMixture &mixture, PhaseType phase_type, CubicEOS::Params params) -> PhaseChemicalModel
	Set the chemical model of the phase with a Cubic equation of state. More...
auto	fluidChemicalModelIdeal (const FluidMixture &mixture) -> PhaseChemicalModel
	Return an equation of state for a gaseous phase based on the ideal model. More...
auto	fluidChemicalModelSpycherPruessEnnis (const FluidMixture &mixture) -> PhaseChemicalModel
	Return a chemical model function for a gaseous phase based on the Spycher et al. More...
auto	fluidChemicalModelSpycherReed (const FluidMixture &mixture) -> PhaseChemicalModel
	Return a chemical model function for a gaseous phase based on the Spycher and Reed (1988) model. More...
auto	mineralChemicalModelIdeal (const MineralMixture &mixture) -> PhaseChemicalModel
	Return an equation of state for a mineral phase based on the ideal model. More...
auto	mineralChemicalModelRedlichKister (const MineralMixture &mixture, double a0, double a1, double a2) -> PhaseChemicalModel
	Return an equation of state for a binary mineral solid solution based on Redlich-Kister model. More...
auto	functionG (Temperature T, Pressure P, const WaterThermoState &wts) -> FunctionG
	Calculate the function g of the HKF model.
auto	speciesElectroStateHKF (const FunctionG &g, const AqueousSpecies &species) -> SpeciesElectroState
	Calculate the electrostatic state of the aqueous species using the g-function state.
auto	speciesElectroStateHKF (Temperature T, Pressure P, const AqueousSpecies &species) -> SpeciesElectroState
	Calculate the electrostatic state of the aqueous species using the HKF model.
auto	speciesThermoStateSolventHKF (Temperature T, Pressure P, const WaterThermoState &wts) -> SpeciesThermoState
	Calculate the thermodynamic state of solvent water using the HKF model.
auto	speciesThermoStateSoluteHKF (Temperature T, Pressure P, const AqueousSpecies &species, const SpeciesElectroState &aes, const WaterElectroState &wes) -> SpeciesThermoState
	Calculate the thermodynamic state of an aqueous solute using the HKF model.
auto	speciesThermoStateHKF (Temperature T, Pressure P, const AqueousSpecies &species) -> SpeciesThermoState
	Calculate the thermodynamic state of an aqueous species using the HKF model.
auto	speciesThermoStateHKF (Temperature T, Pressure P, const FluidSpecies &species) -> SpeciesThermoState
	Calculate the thermodynamic state of a fluid species using the HKF model.
auto	speciesThermoStateHKF (Temperature T, Pressure P, const MineralSpecies &species) -> SpeciesThermoState
	Calculate the thermodynamic state of a mineral species using the HKF model.
auto	operator< (const MineralCatalyst &lhs, const MineralCatalyst &rhs) -> bool
	Compare two MineralCatalyst instances for less than.
auto	operator== (const MineralCatalyst &lhs, const MineralCatalyst &rhs) -> bool
	Compare two MineralCatalyst instances for equality.
auto	operator< (const MineralMechanism &lhs, const MineralMechanism &rhs) -> bool
	Compare two MineralMechanism instances for less than.
auto	operator== (const MineralMechanism &lhs, const MineralMechanism &rhs) -> bool
	Compare two MineralMechanism instances for equality.
auto	molarSurfaceArea (const MineralReaction &reaction, const ChemicalSystem &system) -> double
	Calculate the molar surface area of a mineral (in units of m2/mol) More...
auto	createReaction (const MineralReaction &mineralrxn, const ChemicalSystem &system) -> Reaction
auto	waterElectroStateJohnsonNorton (Temperature T, Pressure P, const WaterThermoState &wts) -> WaterElectroState
	Calculate the electrostatic state of water using the model of Johnson and Norton (1991). More...
auto	waterHelmholtzStateHGK (Temperature T, ThermoScalar D) -> WaterHelmholtzState
	Calculate the Helmholtz free energy state of water using the Haar–Gallagher–Kell (1984) equation of state. More...
auto	waterHelmholtzStateWagnerPruss (Temperature T, ThermoScalar D) -> WaterHelmholtzState
	Calculate the Helmholtz free energy state of water using the Wagner and Pruss (1995) equation of state. More...
auto	waterThermoStateHGK (Temperature T, Pressure P, StateOfMatter stateofmatter) -> WaterThermoState
	Calculate the thermodynamic state of water using the Haar–Gallagher–Kell (1984) equation of state. More...
auto	waterThermoStateWagnerPruss (Temperature T, Pressure P, StateOfMatter stateofmatter) -> WaterThermoState
	Calculate the thermodynamic state of water using the Wagner and Pruss (1995) equation of state. More...
auto	waterThermoState (Temperature T, Pressure P, const WaterHelmholtzState &whs) -> WaterThermoState
	Calculate the thermodynamic state of water. More...
template<typename HelmholtsModel >
auto	waterDensity (Temperature T, Pressure P, const HelmholtsModel &model, StateOfMatter stateofmatter) -> ThermoScalar
auto	waterDensityHGK (Temperature T, Pressure P, StateOfMatter stateofmatter) -> ThermoScalar
	Calculate the density of water using the Haar–Gallagher–Kell (1984) equation of state. More...
auto	waterLiquidDensityHGK (Temperature T, Pressure P) -> ThermoScalar
	Calculate the density of liquid water using the Haar–Gallagher–Kell (1984) equation of state. More...
auto	waterVaporDensityHGK (Temperature T, Pressure P) -> ThermoScalar
	Calculate the density of vapor water using the Haar–Gallagher–Kell (1984) equation of state. More...
auto	waterDensityWagnerPruss (Temperature T, Pressure P, StateOfMatter stateofmatter) -> ThermoScalar
	Calculate the density of water using the Wagner and Pruss (1995) equation of state. More...
auto	waterLiquidDensityWagnerPruss (Temperature T, Pressure P) -> ThermoScalar
	Calculate the density of liquid water using the Wagner and Pruss (1995) equation of state. More...
auto	waterVaporDensityWagnerPruss (Temperature T, Pressure P) -> ThermoScalar
	Calculate the density of vapor water using the Wagner and Pruss (1995) equation of state. More...
template<typename HelmholtzModel >
auto	waterPressure (Temperature T, ThermoScalar D, const HelmholtzModel &model) -> ThermoScalar
auto	waterPressureHGK (Temperature T, ThermoScalar D) -> ThermoScalar
	Calculate the pressure of water using the Haar–Gallagher–Kell (1984) equation of state. More...
auto	waterPressureWagnerPruss (Temperature T, ThermoScalar D) -> ThermoScalar
	Calculate the pressure of water using the Wagner and Pruss (1995) equation of state. More...
auto	waterSaturatedPressureWagnerPruss (Temperature T) -> ThermoScalar
	Calculate the saturated pressure of water using the Wagner and Pruss (1995) equation of state. More...
auto	waterSaturatedLiquidDensityWagnerPruss (Temperature T) -> ThermoScalar
	Calculate the saturated liquid-density of water using the Wagner and Pruss (1995) equation of state. More...
auto	waterSaturatedVapourDensityWagnerPruss (Temperature T) -> ThermoScalar
	Calculate the saturated vapour-density of water using the Wagner and Pruss (1995) equation of state. More...

Variables
constexpr auto	universalGasConstant = 8.3144621
	The universal gas constant (in units of J/(mol*K))
constexpr auto	faradayConstant = 96485.3329
	The Faraday constant (in units of C/mol)
constexpr auto	jouleToCalorie = 0.239005736
	The constant factor that converts joule to calorie.
constexpr auto	calorieToJoule = 4.184
	The constant factor that converts calorie to joule.
constexpr auto	barToPascal = 1.0e+05
	The conversion factor from bar to pascal.
constexpr auto	cubicCentimeterToCubicMeter = 1.0e-06
	The conversion factor from cubic centimeters to cubic meters.
constexpr auto	cubicMeterToCubicCentimeter = 1.0e+06
	The conversion factor from cubic meters to cubic centimeters.
const double	waterMolarMass = 0.018015268
	The molar mass of water in units of kg/mol.
const double	waterCriticalTemperature = 647.096
	The critical temperature of water in units of K.
const double	waterCriticalPressure = 22.064e+06
	The critical pressure of water in units of Pa.
const double	waterCriticalDensity = 322.0
	The critical density of water in units of kg/m3.
const double	waterTriplePointTemperature = 273.16
	The triple point temperature of water in units of K.
const double	waterTriplePointPressure = 611.655
	The triple point pressure of water in units of Pa.
const double	waterTriplePointDensityLiquid = 999.793
	The triple point liquid-density of water in units of kg/m3.
const double	waterTriplePointDensityVapour = 0.00485458
	The triple point vapour-density of water in units of kg/m3.

Detailed Description

The namespace containing all components of the Reaktoro library.

Typedef Documentation

ChemicalScalar

typedef ChemicalScalarBase< double, RowVector > ChemicalScalar

A type that represents a chemical property and its derivatives.

A chemical scalar is a quantity that depends on temperature, pressure, and mole amounts of species. A ChemicalScalar holds not only its value, but also its temperature, pressure, and mole partial derivatives.

See also

ThermoScalar, ChemicalVector, ThermoVector

ChemicalVector

typedef ChemicalVectorBase< Vector, Vector, Vector, Matrix > ChemicalVector

A type that represents a vector of chemical properties and their derivatives.

A chemical scalar is a quantity that depends on temperature, pressure, and mole amounts of species. A ChemicalScalar holds not only its value, but also its partial derivatives with respect to temperature, pressure, and species amounts. A ChemicalVector is a vector representation of a collection of ChemicalScalar instances.

See also

ThermoVector, ThermoScalar, ChemicalScalar

ThermoScalar

typedef ThermoScalarBase< double > ThermoScalar

A type that defines a scalar thermo property.

A thermo property means here any property that depends on temperature and pressure. A ThermoScalar instance not only holds the value of the thermo property, but also is partial temperature and pressure derivatives.

See also

ChemicalVector

ThermoVector

typedef ThermoVectorBase< Vector, Vector, Vector > ThermoVector

A type that defines a vector of thermodynamic properties.

A thermo property means here any property that depends on temperature and pressure. A ThermoVector instance not only holds the values of the thermo properties, but also their partial temperature and pressure derivatives.

See also

ThermoScalar, ChemicalScalar, ChemicalVector

VectorRef

typedef Eigen::Ref< VectorXd > VectorRef

< Alias to Eigen type VectorXd.

Alias to Eigen type Eigen::Ref<VectorXd>.

VectorConstRef

typedef Eigen::Ref< const VectorXd > VectorConstRef

< Alias to Eigen type Ref<VectorXd>.

Alias to Eigen type Eigen::Ref<const VectorXd>.

VectorMap

typedef Eigen::Map< VectorXd > VectorMap

< Alias to Eigen type Ref<const VectorXd>.

Alias to Eigen type Eigen::Map<VectorXd>.

VectorConstMap

typedef Eigen::Map< const VectorXd > VectorConstMap

< Alias to Eigen type Map<VectorXd>.

Alias to Eigen type Eigen::Map<const VectorXd>.

MatrixRef

typedef Eigen::Ref< MatrixXd > MatrixRef

Alias to Eigen type Ref<MatrixXd>.

Alias to Eigen type Eigen::Ref<MatrixXd>.

MatrixConstRef

typedef Eigen::Ref< const MatrixXd > MatrixConstRef

Alias to Eigen type Ref<const MatrixXd>.

Alias to Eigen type Eigen::Ref<const MatrixXd>.

MatrixMap

typedef Eigen::Map< MatrixXd > MatrixMap

Alias to Eigen type Map<MatrixXd>.

Alias to Eigen type Eigen::Map<MatrixXd>.

MatrixConstMap

typedef Eigen::Map< const MatrixXd > MatrixConstMap

Alias to Eigen type Map<const MatrixXd>.

Alias to Eigen type Eigen::Map<const MatrixXd>.

NonlinearFunction

using NonlinearFunction = std::function<NonlinearResidual(VectorConstRef x)>

A type that describes the functional signature of a non-linear residual function.

Parameters

x	The vector of variables

Returns

The residual of the non-linear function evaluated at x

ObjectiveFunction

using ObjectiveFunction = std::function<ObjectiveResult(VectorConstRef x)>

A type that describes the functional signature of an objective function.

Parameters

x	The vector of primal variables

Returns

The objective function evaluated at x

AqueousActivityModel

using AqueousActivityModel = std::function<ChemicalScalar(const AqueousMixtureState&)>

The signature of a function that calculates the ln activity coefficient of a neutral aqueous species.

See also

AqueousMixtureState, ChemicalScalar

Enumeration Type Documentation

GibbsHessian

enum GibbsHessian

strong

The options for the description of the Hessian of the Gibbs energy function.

Enumerator
Exact	The Hessian of the Gibbs energy function is H = H(exact).
ExactDiagonal	The Hessian of the Gibbs energy function is H = diag(H(exact)).
Approximation	The Hessian of the Gibbs energy function is H = d(ln(x))/dn, where x is the mole fractions of the species.
ApproximationDiagonal	The Hessian of the Gibbs energy function is H = diag(d(ln(x))/dn), where x is the mole fractions of the species.

KktMethod

enum KktMethod

strong

An enumeration of possible methods for the solution of a KKT equation.

Enumerator
PartialPivLU	Use a partial pivoting LU algorithm on the full KKT equation. This can only be used for dense Hessian matrices.
FullPivLU	Use a full pivoting LU algorithm on the full KKT equation. This can only be used for dense Hessian matrices.
Nullspace	Use a nullspace method to solve the KKT equation. This method is advisable when there are many equality constraints and these are linear so that their gradient is constant.
Rangespace	Use a rangespace method to solve the KKT equation. This method is advisable when the Hessian matrix can be easily inverted such as a quasi-Newton approximation or a diagonal matrix.
Automatic	Use a method that fits better to the type of KKT equation. This option will ensure that a rangespace method is used when the Hessian matrix is diagonal or its inverse is available. It will use a PartialPivLU method for dense KKT equations.

StepMode

enum StepMode

The available stepping modes for some optimization algorithms.

Enumerator
Conservative	Use convervative step in which its direction is not changed.
Aggressive	Use aggressive step that results in faster approach of variables to the bounds.

Function Documentation

amount()

auto Reaktoro::amount ( double  value, Index  nspecies, Index  ispecies  ) -> ChemicalScalarBase<double, decltype(tr(unit(nspecies, ispecies)))>

inline

Return a ChemicalScalar representation of a mole amount of a species.

Parameters

value	The mole amount of the species.
nspecies	The number of species in the system.
ispecies	The index of the species in the system.

elements()

auto elements

(

std::string

formula

)

-> std::map< std::string, double >

Determine.

the elemental composition of a chemical compound.

Parameters

compound

The formula of the chemical compound

Returns

The elemental composition of the chemical compound

atomicMass()

auto atomicMass

(

std::string

element

)

-> double

Return the atomic mass of a chemical element (in units of kg/mol).

Parameters

element

The symbol of the chemical element

Returns

The atomic mass of the chemical element

molarMass() [1/2]

auto molarMass

(

const std::map< std::string, double > &

compound

)

-> double

Calculate the molar mass of a chemical compound (in units of kg/mol).

Parameters

compound

The elements and their stoichiometries that compose the chemical compound

Returns

The molar mass of the chemical compound

molarMass() [2/2]

auto molarMass

(

std::string

formula

)

-> double

Calculate the molar mass of a chemical compound (in units of kg/mol).

Parameters

compound

The formula of the chemical compound

Returns

The molar mass of the chemical compound

charge()

auto charge

(

const std::string &

formula

)

-> double

Extract the electrical charge of a chemical formula.

The chemical formula of a species can be represented by string with the following formats:

std::string formula1 = "Na+";   // species: Na+
std::string formula2 = "Ca++";  // species: Ca++
std::string formula3 = "OH-";   // species: OH-
std::string formula4 = "CO3--"; // species: CO3--
std::string formula5 = "H+";    // species: H+

The number 1 is optional when the species has one negative or positive electrical charge.

Parameters

formula

The chemical formula of a species

Returns

The electrical charge of the species

alternativeWaterNames()

auto alternativeWaterNames

(

)

-> std::vector< std::string > &

Return a collection of alternative names to the given species name.

Parameters

name	The name of the species.

alternativeChargedSpeciesNames()

auto alternativeChargedSpeciesNames

(

std::string

name

)

-> std::vector< std::string > &

Return a collection of alternative names to the given charged species name.

The argument name must follow the naming convention H+, Ca++, Cl-, HCO3-, CO3--, and so forth. That is it, the charge is given as a suffix with as much - or + as the number of charges.

Parameters

name	The name of the charged species.

alternativeNeutralSpeciesNames()

auto alternativeNeutralSpeciesNames

(

std::string

name

)

-> std::vector< std::string > &

Return a collection of alternative names to the given neutral species name.

The argument name must follow the naming convention CO2(aq), CaCO3(aq), NaCl(aq), and so forth. That is, the neutral species name has the suffix (aq).

Parameters

name	The name of the neutral species.

conventionalChargedSpeciesName()

auto conventionalChargedSpeciesName

(

std::string

name

)

-> std::string

Return the conventional charged species name adopted in Reaktoro.

This method will return the conventional charged species name adopted in Reaktoro. For example, Ca+2 results in Ca++, CO3-2 results in CO3--, Mg[+2] results in Mg++, and so forth.

Parameters

name	The name of a charged species.

conventionalNeutralSpeciesName()

auto conventionalNeutralSpeciesName

(

std::string

name

)

-> std::string

Return the conventional neutral species name adopted in Reaktoro.

This method will return the conventional neutral species name adopted in Reaktoro. For example, CO2 results in CO2(aq), CaCO3@ results in CaCO3(aq), NaCl,aq results in NaCl(aq), and so forth.

Parameters

name	The name of a charged species.

isAlternativeWaterName()

auto isAlternativeWaterName

(

std::string

trial

)

-> bool

Return true if a trial name is an alternative to a water species name.

Parameters

trial

The trial name that is being checked as an alternative to H2O(l)

isAlternativeChargedSpeciesName()

auto isAlternativeChargedSpeciesName	(	std::string	trial,
		std::string	name
	)		-> bool

Return true if a trial name is an alternative to a given charged species name.

Parameters

trial	The trial name that is being checked as an alternative to name
name	The name of the charged species with convention H+, Ca++, CO3--, etc.

isAlternativeNeutralSpeciesName()

auto isAlternativeNeutralSpeciesName	(	std::string	trial,
		std::string	name
	)		-> bool

Return true if a trial name is an alternative to a given neutral species name.

Parameters

trial	The trial name that is being checked as an alternative to name
name	The name of the neutral species with convention CO2(aq), CaCO3(aq).

splitChargedSpeciesName()

auto splitChargedSpeciesName

(

std::string

name

)

-> std::pair< std::string, double >

Return a pair with the base name of a charged species and its electrical charge.

The name of the charge species has to have the following naming conventions: Ca++, Ca+2, and Ca[2+], or Na+, Na[+], or CO3–, CO3-2, and CO3[2-].

Parameters

name	The name of the charged species.

baseNameChargedSpecies()

auto baseNameChargedSpecies

(

std::string

name

)

-> std::string

Return the name of a charged species without charge suffix.

The name of the charge species has to have the following naming conventions: Ca++, Ca+2, and Ca[2+], or Na+, Na[+], or CO3–, CO3-2, and CO3[2-].

Parameters

name	The name of the charged species.

baseNameNeutralSpecies()

auto baseNameNeutralSpecies

(

std::string

name

)

-> std::string

Return the name of a neutral species without suffix (aq).

Parameters

name	The name of the charged species.

chargeInSpeciesName()

auto chargeInSpeciesName

(

std::string

name

)

-> double

Return the electrical charge in a species name.

The charge in the species name must be represended as H+, Ca++, HCO3-, CO3--, SO4--, and so forth.

Parameters

name	The name of the species

contained()

auto contained	(	const Container &	values1,
		const Container &	values2
	)		-> bool

Check if a value is contained in a container of values.

Check if a container of values is contained in another

range() [1/3]

auto range	(	T	first,
		T	last,
		T	step
	)		-> std::vector<T>

Return a range of values.

Parameters

begin	The begin of the sequence
end	The past-the-end entry of the sequence
step	The step of the sequence

range() [2/3]

auto range	(	T	first,
		T	last
	)		-> std::vector<T>

Return a range of values with unit step.

Parameters

begin	The begin of the sequence
end	The past-the-end entry of the sequence

range() [3/3]

auto range

(

T

last

)

-> std::vector<T>

Return a range of values starting from zero and increasing by one.

Parameters

The	size of the sequence

extract()

auto extract	(	const std::vector< T > &	values,
		const Indices &	indices
	)		-> std::vector<T>

Extract values from a vector given a list of indices.

Parameters

values	The values from which a extraction will be performed
indices	The indices of the values to be extracted

Returns

The extracted values

time()

auto time

(

)

-> Time

Return the time point now.

See also

elapsed

elapsed() [1/2]

auto elapsed	(	const Time &	end,
		const Time &	begin
	)		-> double

Return the elapsed time between two time points (in units of s)

Parameters

end	The end time point
end	The begin time point

Returns

The elapsed time between end and begin in seconds

elapsed() [2/2]

auto elapsed

(

const Time &

begin

)

-> double

Return the elapsed time between a time point and now (in units of s)

Parameters

end	The begin time point

Returns

The elapsed time between now and begin in seconds

equilibrate() [1/12]

auto equilibrate

(

ChemicalState &

state

)

-> EquilibriumResult

Equilibrate a chemical state instance.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [2/12]

auto equilibrate	(	ChemicalState &	state,
		const Partition &	partition
	)		-> EquilibriumResult

Equilibrate a chemical state instance.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [3/12]

auto equilibrate	(	ChemicalState &	state,
		const EquilibriumOptions &	options
	)		-> EquilibriumResult

Equilibrate a chemical state instance with equilibrium options.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [4/12]

auto equilibrate	(	ChemicalState &	state,
		const Partition &	partition,
		const EquilibriumOptions &	options
	)		-> EquilibriumResult

Equilibrate a chemical state instance with equilibrium options.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [5/12]

auto equilibrate	(	ChemicalState &	state,
		const EquilibriumProblem &	problem
	)		-> EquilibriumResult

Equilibrate a chemical state instance with an equilibrium problem.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [6/12]

auto equilibrate	(	ChemicalState &	state,
		const EquilibriumProblem &	problem,
		const EquilibriumOptions &	options
	)		-> EquilibriumResult

Equilibrate a chemical state instance with an equilibrium problem.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [7/12]

auto equilibrate

(

const EquilibriumProblem &

problem

)

-> ChemicalState

Equilibrate a chemical state instance with an equilibrium problem.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [8/12]

auto equilibrate	(	const EquilibriumProblem &	problem,
		const EquilibriumOptions &	options
	)		-> ChemicalState

Equilibrate a chemical state instance with an equilibrium problem.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [9/12]

auto equilibrate	(	ChemicalState &	state,
		const EquilibriumInverseProblem &	problem
	)		-> EquilibriumResult

Equilibrate a chemical state instance with an equilibrium inverse problem.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [10/12]

auto equilibrate	(	ChemicalState &	state,
		const EquilibriumInverseProblem &	problem,
		const EquilibriumOptions &	options
	)		-> EquilibriumResult

Equilibrate a chemical state instance with an equilibrium inverse problem.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [11/12]

auto equilibrate

(

const EquilibriumInverseProblem &

problem

)

-> ChemicalState

Equilibrate a chemical state instance with an equilibrium inverse problem.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

equilibrate() [12/12]

auto equilibrate	(	const EquilibriumInverseProblem &	problem,
		const EquilibriumOptions &	options
	)		-> ChemicalState

Equilibrate a chemical state instance with an equilibrium inverse problem.

Warning

This function is intended for convenience only! For performance critical applications, use class EquilibriumSolver.

derivativeForward() [1/2]

auto derivativeForward	(	const ScalarFunction &	f,
		VectorConstRef	x
	)		-> Vector

Calculate the partial derivatives of a scalar function using a 1st-order forward finite difference scheme.

Parameters

f	The scalar function as an instance of ScalarFunction
x	The point where the derivative is calculated

Returns

The partial derivatives of the scalar function

derivativeBackward() [1/2]

auto derivativeBackward	(	const ScalarFunction &	f,
		VectorConstRef	x
	)		-> Vector

Calculate the partial derivatives of a scalar function using a 1st-order backward finite difference scheme.

Parameters

f	The scalar function as an instance of ScalarFunction
x	The point where the derivative is calculated

Returns

The partial derivatives of the scalar function

derivativeCentral() [1/2]

auto derivativeCentral	(	const ScalarFunction &	f,
		VectorConstRef	x
	)		-> Vector

Calculate the partial derivatives of a scalar function using a 2nd-order central finite difference scheme.

Parameters

f	The scalar function as an instance of ScalarFunction
x	The point where the derivative is calculated

Returns

The partial derivatives of the scalar function

derivativeForward() [2/2]

auto derivativeForward	(	const VectorFunction &	f,
		VectorConstRef	x
	)		-> Matrix

Calculate the partial derivatives of a vector function using a 1st-order forward finite difference scheme.

Parameters

f	The scalar function as an instance of ScalarFunction
x	The point where the derivative is calculated

Returns

The partial derivatives of the scalar function

derivativeBackward() [2/2]

auto derivativeBackward	(	const VectorFunction &	f,
		VectorConstRef	x
	)		-> Matrix

Calculate the partial derivatives of a vector function using a 1st-order backward finite difference scheme.

Parameters

f	The scalar function as an instance of ScalarFunction
x	The point where the derivative is calculated

Returns

The partial derivatives of the scalar function

derivativeCentral() [2/2]

auto derivativeCentral	(	const VectorFunction &	f,
		VectorConstRef	x
	)		-> Matrix

Calculate the partial derivatives of a vector function using a 2nd-order central finite difference scheme.

Parameters

f	The scalar function as an instance of ScalarFunction
x	The point where the derivative is calculated

Returns

The partial derivatives of the scalar function

linearlyIndependentCols() [1/2]

auto linearlyIndependentCols

(

MatrixConstRef

A

)

-> Indices

Determine the set of linearly independent columns in a matrix using a column pivoting QR algorithm.

Parameters

A	The matrix whose linearly independent columns must be found

Returns

The indices of the linearly independent columns

linearlyIndependentRows() [1/2]

auto linearlyIndependentRows

(

MatrixConstRef

A

)

-> Indices

Determine the set of linearly independent rows in a matrix.

Parameters

A	The matrix whose linearly independent rows must be found

Returns

The indices of the linearly independent rows

linearlyIndependentCols() [2/2]

auto linearlyIndependentCols	(	MatrixConstRef	A,
		MatrixRef	B
	)		-> Indices

Determine the set of linearly independent columns in a matrix.

Parameters

[in]	A	The matrix whose linearly independent columns must be found
[out]	B	The matrix composed by linearly independent columns only

Returns

The indices of the linearly independent columns

linearlyIndependentRows() [2/2]

auto linearlyIndependentRows	(	MatrixConstRef	A,
		MatrixRef	B
	)		-> Indices

Determine the set of linearly independent rows in a matrix.

Parameters

[in]	A	The matrix whose linearly independent rows must be found
[out]	B	The matrix composed by linearly independent rows only

Returns

The indices of the linearly independent rows

inverseShermanMorrison()

auto inverseShermanMorrison	(	MatrixConstRef	invA,
		VectorConstRef	D
	)		-> Matrix

Calculate the inverse of A + D where inv(A) is already known and D is a diagonal matrix.

Parameters

invA[in,out]	The inverse of the matrix A and the final inverse of A + D
D	The diagonal matrix D

farey()

auto Reaktoro::farey	(	double	x,
		unsigned	maxden
	)		-> std::tuple<long, long>

Return the numerator and denominator of the rational number closest to x.

This methods expects 0 <= x <= 1.

Parameters

x	The number for which the closest rational number is sought.
maxden	The maximum denominator that the rational number can have.

rationalize()

auto rationalize	(	double	x,
		unsigned	maxden
	)		-> std::tuple< long, long >

Calculates the rational number that approximates a given real number.

The algorithm is based on Farey sequence as shown here.

Parameters

x	The real number.
maxden	The maximum denominator.

Returns

A tuple containing the numerator and denominator.

cleanRationalNumbers() [1/2]

auto cleanRationalNumbers	(	double *	vals,
		long	size,
		long	maxden = 6
	)		-> void

Clean an array that is known to have rational numbers from round-off errors.

Parameters

vals[in,out]	The values to be cleaned
maxden	The maximum known denominator in the array with rational numbers

cleanRationalNumbers() [2/2]

auto cleanRationalNumbers	(	MatrixRef	A,
		long	maxden = 6
	)		-> void

Clean a matrix that is known to have rational numbers from round-off errors.

Parameters

A[in,out]	The matrix to be cleaned
maxden	The maximum known denominator in the matrix with rational numbers

zeros() [1/2]

auto zeros ( Index  rows ) -> decltype(Vector::Zero(rows))

inline

Return an expression of a zero vector.

Parameters

rows	The number of rows

Returns

The expression of a zero vector

ones() [1/2]

auto ones ( Index  rows ) -> decltype(Vector::Ones(rows))

inline

Return an expression of a vector with entries equal to one.

Parameters

rows	The number of rows

Returns

The expression of a vector with entries equal to one

random() [1/2]

auto random ( Index  rows ) -> decltype(Vector::Random(rows))

inline

Return an expression of a vector with random entries.

Parameters

rows	The number of rows

Returns

The expression of a vector with random entries equal to one

linspace()

auto linspace ( Index  rows, double  start, double  stop  ) -> decltype(Vector::LinSpaced(rows, start, stop))

inline

Return a linearly spaced vector.

Parameters

rows	The number of rows
start	The start of the sequence
stop	The stop of the sequence

Returns

The expression of a vector with linearly spaced entries

unit()

auto unit ( Index  rows, Index  i  ) -> decltype(Vector::Unit(rows, i))

inline

Return an expression of a unit vector.

Parameters

rows	The number of rows
i	The index at which the component is one

Returns

The expression of a unit vector

zeros() [2/2]

auto zeros ( Index  rows, Index  cols  ) -> decltype(Matrix::Zero(rows, cols))

inline

Return an expression of a zero matrix.

Parameters

rows	The number of rows
cols	The number of columns

Returns

The expression of a zero matrix

ones() [2/2]

auto ones ( Index  rows, Index  cols  ) -> decltype(Matrix::Ones(rows, cols))

inline

Return an expression of a matrix with entries equal to one.

Parameters

rows	The number of rows
cols	The number of columns

Returns

The expression of a matrix with entries equal to one

random() [2/2]

auto random ( Index  rows, Index  cols  ) -> decltype(Matrix::Random(rows, cols))

inline

Return an expression of a matrix with random entries.

Parameters

rows	The number of rows
cols	The number of columns

Returns

The expression of a matrix with random entries

identity()

auto identity ( Index  rows, Index  cols  ) -> decltype(Matrix::Identity(rows, cols))

inline

Return an expression of an identity matrix.

Parameters

rows	The number of rows
cols	The number of columns

Returns

The expression of an identity matrix

rows() [1/4]

auto rows	(	Eigen::MatrixBase< Derived > &	mat,
		Index	start,
		Index	num
	)		-> decltype(mat.middleRows(start, num))

Return a view of a sequence of rows of a matrix.

Parameters

start	The row index of the start of the sequence
num	The number of rows in the sequence

rows() [2/4]

auto rows	(	const Eigen::MatrixBase< Derived > &	mat,
		Index	start,
		Index	num
	)		-> decltype(mat.middleRows(start, num))

Return a view of a sequence of rows of a matrix.

Parameters

start	The row index of the start of the sequence
num	The number of rows in the sequence

rows() [3/4]

auto rows	(	Eigen::MatrixBase< Derived > &	mat,
		const Indices &	irows
	)		-> decltype(mat(irows, Eigen::all))

Return a view of some rows of a matrix.

Parameters

mat	The matrix for which the view is created
irows	The indices of the rows of the matrix

rows() [4/4]

auto rows	(	const Eigen::MatrixBase< Derived > &	mat,
		const Indices &	irows
	)		-> decltype(mat(irows, Eigen::all))

Return a const view of some rows of a matrix.

Parameters

mat	The matrix for which the view is created
irows	The indices of the rows of the matrix

cols() [1/4]

auto cols	(	Eigen::MatrixBase< Derived > &	mat,
		Index	start,
		Index	num
	)		-> decltype(mat.middleCols(start, num))

Return a view of a sequence of columns of a matrix.

Parameters

start	The column index of the start of the sequence
num	The number of columns in the sequence

cols() [2/4]

auto cols	(	const Eigen::MatrixBase< Derived > &	mat,
		Index	start,
		Index	num
	)		-> decltype(mat.middleCols(start, num))

Return a view of a sequence of columns of a matrix.

Parameters

start	The column index of the start of the sequence
num	The number of columns in the sequence

cols() [3/4]

auto cols	(	Eigen::MatrixBase< Derived > &	mat,
		const Indices &	icols
	)		-> decltype(mat(Eigen::all, icols))

Return a view of some columns of a matrix.

Parameters

mat	The matrix for which the view is created
icols	The indices of the columns of the matrix

cols() [4/4]

auto cols	(	const Eigen::MatrixBase< Derived > &	mat,
		const Indices &	icols
	)		-> decltype(mat(Eigen::all, icols))

Return a const view of some columns of a matrix.

Parameters

mat	The matrix for which the view is created
icols	The indices of the columns of the matrix

segment() [1/2]

auto segment	(	Eigen::MatrixBase< Derived > &	vec,
		Index	irow,
		Index	nrows
	)		-> decltype(vec.segment(irow, nrows))

Return a view of some rows and columns of a matrix.

Parameters

mat	The matrix for which the view is created
irows	The indices of the rows of the matrix
icols	The indices of the columns of the matrix

segment() [2/2]

auto segment	(	const Eigen::MatrixBase< Derived > &	vec,
		Index	irow,
		Index	nrows
	)		-> decltype(vec.segment(irow, nrows))

Return a view of some rows and columns of a matrix.

Parameters

mat	The matrix for which the view is created
irows	The indices of the rows of the matrix
icols	The indices of the columns of the matrix

block() [1/2]

auto block	(	Eigen::MatrixBase< Derived > &	mat,
		Index	irow,
		Index	icol,
		Index	nrows,
		Index	ncols
	)		-> decltype(mat.block(irow, icol, nrows, ncols))

Return a view of some rows and columns of a matrix.

Parameters

mat	The matrix for which the view is created
irows	The indices of the rows of the matrix
icols	The indices of the columns of the matrix

block() [2/2]

auto block	(	const Eigen::MatrixBase< Derived > &	mat,
		Index	irow,
		Index	icol,
		Index	nrows,
		Index	ncols
	)		-> decltype(mat.block(irow, icol, nrows, ncols))

Return a view of some rows and columns of a matrix.

Parameters

mat	The matrix for which the view is created
irows	The indices of the rows of the matrix
icols	The indices of the columns of the matrix

submatrix() [1/2]

auto submatrix	(	Eigen::MatrixBase< Derived > &	mat,
		const Indices &	irows,
		const Indices &	icols
	)		-> decltype(mat(irows, icols))

Return a view of some rows and columns of a matrix.

Parameters

mat	The matrix for which the view is created
irows	The indices of the rows of the matrix
icols	The indices of the columns of the matrix

submatrix() [2/2]

auto submatrix	(	const Eigen::MatrixBase< Derived > &	mat,
		const Indices &	irows,
		const Indices &	icols
	)		-> decltype(mat(irows, icols))

Return a const view of some rows and columns of a matrix.

Parameters

mat	The matrix for which the view is created
irows	The indices of the rows of the matrix
icols	The indices of the columns of the matrix

blockmap() [1/2]

auto Reaktoro::blockmap	(	Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &	mat,
		Index	row,
		Index	col,
		Index	nrows,
		Index	ncols
	)		-> Eigen::Map<Eigen::Matrix<Scalar,Rows,Cols,Options,MaxRows,MaxCols>, Eigen::Unaligned, Eigen::Stride<Rows,Cols>>

Return a block mapped view of a matrix.

Parameters

mat	The matrix from which the mapped view is created.
row	The index of the row at which the view starts.
col	The index of the column at which the view starts.
nrows	The number of rows of the mapped view.
ncols	The number of columns of the mapped view.

blockmap() [2/2]

auto Reaktoro::blockmap	(	const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &	mat,
		Index	row,
		Index	col,
		Index	nrows,
		Index	ncols
	)		-> Eigen::Map<const Eigen::Matrix<Scalar,Rows,Cols,Options,MaxRows,MaxCols>, Eigen::Unaligned, Eigen::Stride<Rows,Cols>>

Return a const block mapped view of a matrix.

Parameters

mat	The matrix from which the mapped view is created.
row	The index of the row at which the view starts.
col	The index of the column at which the view starts.
nrows	The number of rows of the mapped view.
ncols	The number of columns of the mapped view.

rowsmap() [1/2]

auto Reaktoro::rowsmap	(	Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &	mat,
		Index	row,
		Index	nrows
	)		-> Eigen::Map<Eigen::Matrix<Scalar,Rows,Cols,Options,MaxRows,MaxCols>, Eigen::Unaligned, Eigen::Stride<Rows,Cols>>

Return a mapped view of a sequence of rows of a matrix.

Parameters

mat	The matrix from which the mapped view is created.
row	The index of the row at which the view starts.
nrows	The number of rows of the mapped view.

rowsmap() [2/2]

auto Reaktoro::rowsmap	(	const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &	mat,
		Index	row,
		Index	nrows
	)		-> Eigen::Map<const Eigen::Matrix<Scalar,Rows,Cols,Options,MaxRows,MaxCols>, Eigen::Unaligned, Eigen::Stride<Rows,Cols>>

Return a const mapped view of a sequence of rows of a matrix.

Parameters

mat	The matrix from which the mapped view is created.
row	The index of the row at which the view starts.
nrows	The number of rows of the mapped view.

colsmap() [1/2]

auto Reaktoro::colsmap	(	Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &	mat,
		Index	col,
		Index	ncols
	)		-> Eigen::Map<Eigen::Matrix<Scalar,Rows,Cols,Options,MaxRows,MaxCols>, Eigen::Unaligned, Eigen::Stride<Rows,Cols>>

Return a mapped view of a sequence of columns of a matrix.

Parameters

mat	The matrix from which the mapped view is created.
row	The index of the row at which the view starts.
col	The index of the column at which the view starts.
nrows	The number of rows of the mapped view.
ncols	The number of columns of the mapped view.

colsmap() [2/2]

auto Reaktoro::colsmap	(	const Eigen::Matrix< Scalar, Rows, Cols, Options, MaxRows, MaxCols > &	mat,
		Index	col,
		Index	ncols
	)		-> Eigen::Map<const Eigen::Matrix<Scalar,Rows,Cols,Options,MaxRows,MaxCols>, Eigen::Unaligned, Eigen::Stride<Rows,Cols>>

Return a const mapped view of a sequence of columns of a matrix.

Parameters

mat	The matrix from which the mapped view is created.
row	The index of the row at which the view starts.
col	The index of the column at which the view starts.
nrows	The number of rows of the mapped view.
ncols	The number of columns of the mapped view.

cardano()

auto cardano	(	double	a,
		double	b,
		double	c,
		double	d
	)		-> CubicRoots

Calculate the roots of a cubic equation using Cardano's method.

The calculation uses the approach presented in: Nickalls, R. W. D. (2012). A New Approach to Solving the Cubic: Cardan’s Solution Revealed. The Mathematical Gazette, 77(480), 354–359 to solve the cubic equation: \( ax^{3}+bx^{2}+cx+d=0 \).

Parameters

a	The coefficient a of the cubic equation
b	The coefficient b of the cubic equation
c	The coefficient c of the cubic equation
d	The coefficient d of the cubic equation

Returns

The three roots \( (r_1, r_2, r_3) \) that solve the cubic equation, where \( |r_1| \geq |r_2| \geq |r_3| \). If they are all real, they are returned in descending order (the first element is the highest).

newton() [1/2]

auto newton	(	const std::function< std::tuple< double, double >(double)> &	f,
		double	x0,
		double	epsilon,
		unsigned	maxiter
	)		-> double

Calculate the root of a non-linear function using Newton's method.

Parameters

f	The function that returns a pair of \( f(x) \) and \( f^{\prime}(x) \).
x0	The initial guess for the iterative root calculation.
epsilon	The tolerance used in \( |f(x)| < \epsilon \) to check convergence.
maxiter	The maximum number of iterations.

newton() [2/2]

auto newton	(	const std::function< void(VectorConstRef, VectorRef, MatrixRef)> &	f,
		VectorConstRef	x0,
		double	epsilon,
		unsigned	maxiter
	)		-> Vector

Calculate the root of a non-linear multi-dimensional function using Newton's method.

Parameters

f	The function that returns \( f(x) \) and \( J(x) \).
x0	The initial guess for the iterative root calculation.
epsilon	The tolerance used in \( |f(x)| < \epsilon \) to check convergence.
maxiter	The maximum number of iterations.

realRoots()

auto realRoots

(

const CubicRoots &

roots

)

-> std::vector< double >

Return all real roots of a group of roots.

Parameters

roots

CubicRoots with of complex and real roots

Returns

A vector with all real roots

largestStep()

auto largestStep	(	VectorConstRef	p,
		VectorConstRef	dp
	)		-> double

Compute the largest step length \(\alpha\) such that \(\mathbf{p} + \alpha\Delta\mathbf{p}\) is on the lower bound \(\mathbf{x}_l=\mathbf{0}\).

Parameters

p	The point \(\mathbf{p}\)
dp	The step \(\Delta\mathbf{p}\)

lessThan()

auto lessThan	(	double	a,
		double	b,
		double	baseval
	)		-> bool

Compute the fraction-to-the-boundary step length given by:

\[\alpha_{\mathrm{max}}=\max\{\alpha\in(0,1]:\mathbf{p}+\alpha\Delta\mathbf{p}\geq(1-\tau)\mathbf{p}\}@f.] @param p The point @f$\mathbf{p}@f$ @param dp The step @f$\Delta\mathbf{p}@f$ @param tau The fraction-to-the-boundary parameter @f$\tau@f$ auto fractionToTheBoundary(VectorConstRef p, VectorConstRef dp, double tau) -> double; Compute the fraction-to-the-boundary step length given by: @f[\alpha_{\mathrm{max}}=\max\{\alpha\in(0,1]:\mathbf{p}+\alpha\Delta\mathbf{p}\geq(1-\tau)\mathbf{p}\}@f.] @param p The point @f$\mathbf{p}@f$ @param dp The step @f$\Delta\mathbf{p}@f$ @param tau The fraction-to-the-boundary parameter @f$\tau@f$ @param ilimiting The index of the limiting variable auto fractionToTheBoundary(VectorConstRef p, VectorConstRef dp, double tau, Index& ilimiting) -> double; Compute the fraction-to-the-boundary step length given by: @f[\alpha_{\mathrm{max}}=\max\{\alpha\in(0,1]:\alpha C\Delta\mathbf{p}\geq-\tau C\mathbf{p}+\mathbf{r}\}@f.] @param p The point @f$\mathbf{p}@f$ @param dp The step @f$\Delta\mathbf{p}@f$ @param C The left-hand side matrix that defines the inequality constraint @f$C\mathbf{p}\geq\mathbf{r}@f$ @param r The right-hand side vector that defines the inequality constraint @f$C\mathbf{p}\geq\mathbf{r}@f$ @param tau The fraction-to-the-boundary parameter @f$\tau@f$ auto fractionToTheBoundary(VectorConstRef p, VectorConstRef dp, MatrixConstRef C, VectorConstRef r, double tau) -> double; Compute the fraction-to-the-boundary step length given by: @f[\alpha_{\mathrm{max}}=\max\{\alpha\in(0,1]:\mathbf{p}+\alpha\Delta\mathbf{p}\geq(1-\tau)\mathbf{p}\}@f.] @param p The point @f$\mathbf{p}@f$ @param dp The step @f$\Delta\mathbf{p}@f$ @param lower The lower bound for the step @f$\Delta\mathbf{p}@f$ @param tau The fraction-to-the-boundary parameter @f$\tau@f$ auto fractionToTheLowerBoundary(VectorConstRef p, VectorConstRef dp, VectorConstRef lower, double tau) -> double; Check if a float number is less than another by a base value. This method is particularly useful when comparing two float numbers where round-off errors can compromise the checking. The following is used for the comparison: @f[a < b + 10\epsilon \mathrm{baseval}\]

, where \(\epsilon\) is the machine double precision.

Parameters

a	The left-hand side value
b	The right-hand side value
baseval	The base value for the comparison

greaterThan()

auto greaterThan	(	double	a,
		double	b,
		double	baseval
	)		-> bool

Check if a float number is greater than another by a base value.

This method is particularly useful when comparing two float numbers where round-off errors can compromise the checking. The following is used for the comparison:

\[a > b - 10\epsilon \mathrm{baseval}\]

, where \(\epsilon\) is the machine double precision.

Parameters

a	The left-hand side value
b	The right-hand side value
baseval	The base value for the comparison

aqueousActivityModelDrummondCO2()

auto aqueousActivityModelDrummondCO2

(

const AqueousMixture &

mixture

)

-> AqueousActivityModel

Create the function for the calculation of ln activity coefficient of CO₂(aq), based on the model of Drummond (1981).

The model is documented in the paper Drummond, S. E. (1981). Boiling and mixing of hydrothermal fluids: chemical effects on mineral precipitation. Pennsylvania State University.

Parameters

mixture

The aqueous mixture instance

Returns

The aqueous activity function of species CO2(aq)

See also

AqueousMixture, AqueousActivityModel

aqueousActivityModelDuanSunCO2()

auto aqueousActivityModelDuanSunCO2

(

const AqueousMixture &

mixture

)

-> AqueousActivityModel

Create the function for the calculation of ln activity coefficient of CO₂(aq), based on the model of Duan and Sun (2003) The model is documented in the paper Duan, Z., Sun, R.

(2003). An improved model calculating CO2 solubility in pure water and aqueous NaCl mixtures from 273 to 533 K and from 0 to 2000 bar. Chemical Geology, 193(3-4), 257–271.

Parameters

mixture

The aqueous mixture instance

See also

AqueousMixture, AqueousActivityModel

aqueousActivityModelRumpfCO2()

auto aqueousActivityModelRumpfCO2

(

const AqueousMixture &

mixture

)

-> AqueousActivityModel

Create the function for the calculation of ln activity coefficient of CO₂(aq), based on the model of Rumpf et al.

(1994). The model is documented in the paper *Rumpf, B., Nicolaisen, H., Ocal, C., & Maurer, G. (1994). Solubility of carbon dioxide in aqueous mixtures of sodium chloride: Experimental results and correlation. Journal of Solution Chemistry,

Parameters

mixture

The aqueous mixture instance

See also

AqueousMixture, AqueousActivityModel

aqueousActivityModelSetschenow()

auto aqueousActivityModelSetschenow	(	const AqueousMixture &	mixture,
		double	b
	)		-> AqueousActivityModel

Create the aqueous activity function of a neutral species based on the Setschenow model.

Parameters

mixture	The aqueous mixture instance containing the aqueous species
b	The Setschenow constant

Returns

The aqueous activity function of the aqueous species

See also

AqueousMixture, AqueousActivityModel

database()

auto database

(

std::string

name

)

-> std::string

Return the contents of a built-in database as a string.

This method searches among all built-in databases and return the database file as a string. If the given database name is not found, an empty string is returned.

Parameters

name	The name of the database.

See also

databases

sanityCheckInteractionParamsFunction()

auto Reaktoro::sanityCheckInteractionParamsFunction	(	const unsigned &	nspecies,
		const CubicEOS::InteractionParamsFunction &	func
	)		-> void

Sanity check free function to verify if BIPs matrices have proper dimensions.

Considering that the phase has n species, the BIP matrices k, kT and kTT should have (n, n) as dimensions.

See also

CubicEOS::setInteractionParamsFunction

identifyPhaseUsingVolume()

auto identifyPhaseUsingVolume	(	const ThermoScalar &	temperature,
		const ThermoScalar &	pressure,
		const ChemicalScalar &	Z,
		const ChemicalScalar &	b
	)		-> PhaseType

Return a PhaseType that says if the phase is a Liquid or Gas based on Volume Method.

Parameters

Temperature	Phase temperature
Pressure	Phase pressure
Z	Phase compressibility factor

Returns

The type of the phase

Reference: Bennett, J. and Schmidt, K.A., 2016. Comparison of Phase Identification Methods Used in Oil Industry Flow Simulations. Energy & Fuels, 31(4), pp.3370-3379.

identifyPhaseUsingIsothermalCompressibility()

auto identifyPhaseUsingIsothermalCompressibility	(	const ThermoScalar &	temperature,
		const ThermoScalar &	pressure,
		const ChemicalScalar &	Z
	)		-> PhaseType

Return a PhaseType that says if the phase is a Liquid or Gas based on Isothermal Compressibility.

Parameters

Temperature	Phase temperature
Pressure	Phase pressure
Z	Phase compressibility factor

Returns

The type of the phase

Reference: Bennett, J. and Schmidt, K.A., 2016. Comparison of Phase Identification Methods Used in Oil Industry Flow Simulations. Energy & Fuels, 31(4), pp.3370-3379.

identifyPhaseUsingGibbsEnergyAndEos()

auto identifyPhaseUsingGibbsEnergyAndEos	(	const ThermoScalar &	pressure,
		const ThermoScalar &	temperature,
		const ChemicalScalar &	amix,
		const ChemicalScalar &	bmix,
		const ChemicalScalar &	A,
		const ChemicalScalar &	B,
		const ChemicalScalar &	C,
		std::vector< ChemicalScalar >	Zs,
		const double	epsilon,
		const double	sigma
	)		-> PhaseType

Return a PhaseType that says if the phase is a Liquid or Gas based on gibbs residual energy and equation of state.

Parameters

pressure	Phase pressure
temperature	Phase temperature
amix	attractive parameter
Zs	Z-roots, as calculated by the cubic EOS. Must have size 1 or 2 here. If size(Z) == 2, the values od Gibbs residual energy are compared. It is a liquid phase if Gibbs residual energy of Z_min is the smallest and gaseous if Gibbs residual energy of Z_max is the smallest. If size(Z) == 1, the pressue is compared with the local P_min and local P_max of the EoS. It is a liquid phase if P \textgreater P_min and gaseous if P \textless Pmax.

Returns

The type of the phase

Reference: Bennett, J. and Schmidt, K.A., 2016. Comparison of Phase Identification Methods Used in Oil Industry Flow Simulations. Energy & Fuels, 31(4), pp.3370-3379.

aqueousChemicalModelDebyeHuckel()

auto aqueousChemicalModelDebyeHuckel	(	const AqueousMixture &	mixture,
		const DebyeHuckelParams &	params
	)		-> PhaseChemicalModel

Return an equation of state for an aqueous phase based on the Debye–Hückel activity model.

Parameters

mixture	The aqueous mixture instance
params	The parameters for the Debye–Hückel activity model.

Returns

The activity model function for the aqueous phase

See also

AqueousMixture, DebyeHuckelParams, PhaseChemicalModel

aqueousChemicalModelHKF()

auto aqueousChemicalModelHKF

(

const AqueousMixture &

mixture

)

-> PhaseChemicalModel

Return an equation of state for an aqueous phase based on HKF model.

The HKF model implemented here was documented in:

• Helgeson, H. C., Kirkham, D. H., Flowers, G. C. (1981). Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures: IV. Calculation of activity coefficients, osmotic coefficients, and apparent molal and standard and relative partial molal properties to 600°C. American Journal of Science, 281(10), 1249–1516.

  Parameters

  mixture

  The aqueous mixture

  Returns

  The equation of state function for the aqueous phase

  See also

  AqueousMixture, PhaseChemicalModel

aqueousChemicalModelIdeal()

auto aqueousChemicalModelIdeal

(

const AqueousMixture &

mixture

)

-> PhaseChemicalModel

Return an equation of state for an aqueous phase based on the ideal model.

Parameters

mixture

The aqueous mixture

Returns

The equation of state function for the aqueous phase

See also

AqueousMixture, PhaseChemicalModel

aqueousChemicalModelPitzerHMW()

auto aqueousChemicalModelPitzerHMW

(

const AqueousMixture &

mixture

)

-> PhaseChemicalModel

Return an equation of state for an aqueous phase based on a Pitzer model.

The implementation of this Pitzer model was taken from the following references:

1. Harvie, C.E., Møller, N., Weare, J.H. (1984). The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25°C. Geochimica et Cosmochimica Acta, 48(4), 723–751.
2. Harvie, C.E., Weare, J.H. (1980). The prediction of mineral soluhilities in natural waters: the system from zero to high concentration at 25°C. Geochimica et Cosmochimica Acta, 44(7), 981–997.
3. Pitzer, K. S. (1975). Thermodynamics of electrolytes. V. effects of higher-order electrostatic terms. Journal of Solution Chemistry, 4(3), 249–265.

   Parameters

   mixture

   The aqueous mixture

   Returns

   The equation of state function for the aqueous phase

   See also

   AqueousMixture, PhaseChemicalModel

fluidChemicalModelCubicEOS()

auto fluidChemicalModelCubicEOS	(	const FluidMixture &	mixture,
		PhaseType	phase_type,
		CubicEOS::Params	params
	)		-> PhaseChemicalModel

Set the chemical model of the phase with a Cubic equation of state.

See also

FluidPhase::setChemicalModelCubicEOS

fluidChemicalModelIdeal()

auto fluidChemicalModelIdeal

(

const FluidMixture &

mixture

)

-> PhaseChemicalModel

Return an equation of state for a gaseous phase based on the ideal model.

This model only supports a gaseous phase. Using it in a FluidPhase that is not a PhaseType::Gas will result in a runtime error.

Parameters

mixture

The fluid mixture

Returns

The equation of state function for the fluid phase

See also

FluidMixture, FluidChemicalModel

fluidChemicalModelSpycherPruessEnnis()

auto fluidChemicalModelSpycherPruessEnnis

(

const FluidMixture &

mixture

)

-> PhaseChemicalModel

Return a chemical model function for a gaseous phase based on the Spycher et al.

(2003) model. This model only supports a gaseous phase with species CO2(g) and H2O(g). The model is documented in: Spycher, N., Pruess, K., Ennis-King, J. (2003). CO2-H2O mixtures in the geological sequestration of CO2. I. Assessment and calculation of mutual solubilities from 12 to 100°C and up to 600 bar. Geochimica et Cosmochimica Acta, 67(16), 3015–3031.

Parameters

mixture

The gaseous mixture instance

See also

FluidMixture, PhaseChemicalModel

fluidChemicalModelSpycherReed()

auto fluidChemicalModelSpycherReed

(

const FluidMixture &

mixture

)

-> PhaseChemicalModel

Return a chemical model function for a gaseous phase based on the Spycher and Reed (1988) model.

This model only supports the gaseous species H2O(g), CO2(g), and CH4(g).

Reference: Spycher, N., Reed, M. (1988). Fugacity coefficients of H2, CO2, CH4, H2O and of H2O–CO2–CH4 mixtures: A virial equation treatment for moderate pressures and temperatures applicable to calculations of hydrothermal boiling. Geochimica et Cosmochimica Acta, 52(3), 739–749.

Parameters

mixture

The gaseous mixture instance

See also

GaseousMixture

mineralChemicalModelIdeal()

auto mineralChemicalModelIdeal

(

const MineralMixture &

mixture

)

-> PhaseChemicalModel

Return an equation of state for a mineral phase based on the ideal model.

Parameters

mixture

The mineral mixture

Returns

The equation of state function for the mineral phase

See also

MineralMixture, MineralChemicalModel

mineralChemicalModelRedlichKister()

auto mineralChemicalModelRedlichKister	(	const MineralMixture &	mixture,
		double	a0,
		double	a1,
		double	a2
	)		-> PhaseChemicalModel

Return an equation of state for a binary mineral solid solution based on Redlich-Kister model.

The Redlich-Kister model calculates the activity coefficient of the end-members in a solid solution using the equations:

\[\ln\gamma_{1}=x_{2}^{2}[a_{0}+a_{1}(3x_{1}-x_{2})+a_{2}(x_{1}-x_{2})(5x_{1}-x_{2})]\]

and

\[\ln\gamma_{2}=x_{1}^{2}[a_{0}-a_{1}(3x_{2}-x_{1})+a_{2}(x_{2}-x_{1})(5x_{2}-x_{1})]\]

. The parameters \(a_0\), \(a_1\), and \(a_2\) must be provided. Set them to zero if not needed.

Parameters

mixture	The mineral mixture
a0	The Redlich-Kister parameter a0
a1	The Redlich-Kister parameter a1
a2	The Redlich-Kister parameter a2

Returns

The equation of state function for the mineral phase

See also

MineralMixture, MineralChemicalModel

molarSurfaceArea()

auto Reaktoro::molarSurfaceArea	(	const MineralReaction &	reaction,
		const ChemicalSystem &	system
	)		-> double

Calculate the molar surface area of a mineral (in units of m2/mol)

Parameters

reaction	The mineral reaction instance
system	The chemical system instance

Returns

The molar surface area of the mineral (in units of m2/mol)

waterElectroStateJohnsonNorton()

auto waterElectroStateJohnsonNorton	(	Temperature	T,
		Pressure	P,
		const WaterThermoState &	wts
	)		-> WaterElectroState

Calculate the electrostatic state of water using the model of Johnson and Norton (1991).

References:

• Johnson, J. W., Norton, D. (1991). Critical phenomena in hydrothermal systems; state, thermodynamic, electrostatic, and transport properties of H2O in the critical region. American Journal of Science, 291(6), 541–648. doi

waterHelmholtzStateHGK()

auto waterHelmholtzStateHGK	(	Temperature	T,
		ThermoScalar	D
	)		-> WaterHelmholtzState

Calculate the Helmholtz free energy state of water using the Haar–Gallagher–Kell (1984) equation of state.

Parameters

T	The temperature of water (in units of K)
D	The density of water (in units of kg/m3)

Returns

The Helmholtz free energy state of water

See also

WaterHelmholtzState

waterHelmholtzStateWagnerPruss()

auto waterHelmholtzStateWagnerPruss	(	Temperature	T,
		ThermoScalar	D
	)		-> WaterHelmholtzState

Calculate the Helmholtz free energy state of water using the Wagner and Pruss (1995) equation of state.

Parameters

T	The temperature of water (in units of K)
D	The density of water (in units of kg/m3)

Returns

The Helmholtz free energy state of water

See also

WaterHelmholtzState

waterThermoStateHGK()

auto waterThermoStateHGK	(	Temperature	T,
		Pressure	P,
		StateOfMatter	stateofmatter
	)		-> WaterThermoState

Calculate the thermodynamic state of water using the Haar–Gallagher–Kell (1984) equation of state.

References:

• Haar, L., Gallagher, J. S., Kell, G. S. (1984). NBS/NRC Steam Tables: Thermodynamic and Transport Properties and Computer Program for Vapor and Liquid States of Water in SI Units. New York: Hemisphere Publishing Corporation.

  Parameters

  T	The temperature of water (in units of K)
  P	The pressure of water (in units of Pa)

  Returns

  The thermodynamic state of water

  See also

  WaterThermoState

waterThermoStateWagnerPruss()

auto waterThermoStateWagnerPruss	(	Temperature	T,
		Pressure	P,
		StateOfMatter	stateofmatter
	)		-> WaterThermoState

Calculate the thermodynamic state of water using the Wagner and Pruss (1995) equation of state.

References:

• Wagner, W., Pruss, A. (1999). The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. Journal of Physical and Chemical Reference Data, 31(2), 387. doi

  Parameters

  T	The temperature of water (in units of K)
  P	The pressure of water (in units of Pa)

  Returns

  The thermodynamic state of water

  See also

  WaterThermoState

waterThermoState()

auto waterThermoState	(	Temperature	T,
		Pressure	P,
		const WaterHelmholtzState &	whs
	)		-> WaterThermoState

Calculate the thermodynamic state of water.

This is a general method that uses the Helmholtz free energy state of water, as an instance of WaterHelmholtzState, to completely resolve its thermodynamic state.

Parameters

T	The temperature of water (in units of K)
P	The pressure of water (in units of Pa)
whs	The Helmholtz free energy state of water

Returns

The thermodynamic state of water

See also

WaterHelmholtzState, WaterThermoState

waterDensityHGK()

auto waterDensityHGK	(	Temperature	T,
		Pressure	P,
		StateOfMatter	stateofmatter
	)		-> ThermoScalar

Calculate the density of water using the Haar–Gallagher–Kell (1984) equation of state.

Parameters

T	The temperature of water (in units of K)
P	The pressure of water (in units of Pa)

Returns

The density of liquid water (in units of kg/m3)

waterLiquidDensityHGK()

auto waterLiquidDensityHGK	(	Temperature	T,
		Pressure	P
	)		-> ThermoScalar

Calculate the density of liquid water using the Haar–Gallagher–Kell (1984) equation of state.

Parameters

T	The temperature of water (in units of K)
P	The pressure of water (in units of Pa)

Returns

The density of liquid water (in units of kg/m3)

waterVaporDensityHGK()

auto waterVaporDensityHGK	(	Temperature	T,
		Pressure	P
	)		-> ThermoScalar

Calculate the density of vapor water using the Haar–Gallagher–Kell (1984) equation of state.

Parameters

T	The temperature of water (in units of K)
P	The pressure of water (in units of Pa)

Returns

The density of water (in units of kg/m3)

waterDensityWagnerPruss()

auto waterDensityWagnerPruss	(	Temperature	T,
		Pressure	P,
		StateOfMatter	stateofmatter
	)		-> ThermoScalar

Calculate the density of water using the Wagner and Pruss (1995) equation of state.

Parameters

T	The temperature of water (in units of K)
P	The pressure of water (in units of Pa)

Returns

The density of liquid water (in units of kg/m3)

waterLiquidDensityWagnerPruss()

auto waterLiquidDensityWagnerPruss	(	Temperature	T,
		Pressure	P
	)		-> ThermoScalar

Calculate the density of liquid water using the Wagner and Pruss (1995) equation of state.

Parameters

T	The temperature of water (in units of K)
P	The pressure of water (in units of Pa)

Returns

The density of liquid water (in units of kg/m3)

waterVaporDensityWagnerPruss()

auto waterVaporDensityWagnerPruss	(	Temperature	T,
		Pressure	P
	)		-> ThermoScalar

Calculate the density of vapor water using the Wagner and Pruss (1995) equation of state.

Parameters

T	The temperature of water (in units of K)
P	The pressure of water (in units of Pa)

Returns

The density of water (in units of kg/m3)

waterPressureHGK()

auto waterPressureHGK	(	Temperature	T,
		ThermoScalar	D
	)		-> ThermoScalar

Calculate the pressure of water using the Haar–Gallagher–Kell (1984) equation of state.

Parameters

T	The temperature of water (in units of K)
D	The density of water (in units of kg/m3)

Returns

The pressure of water (in units of Pa)

waterPressureWagnerPruss()

auto waterPressureWagnerPruss	(	Temperature	T,
		ThermoScalar	D
	)		-> ThermoScalar

Calculate the pressure of water using the Wagner and Pruss (1995) equation of state.

Parameters

T	The temperature of water (in units of K)
D	The density of water (in units of kg/m3)

Returns

The pressure of water (in units of Pa)

waterSaturatedPressureWagnerPruss()

auto waterSaturatedPressureWagnerPruss

(

Temperature

T

)

-> ThermoScalar

Calculate the saturated pressure of water using the Wagner and Pruss (1995) equation of state.

Parameters

T	The temperature of water (in units of K)

Returns

The saturated pressure of water (in units of Pa)

waterSaturatedLiquidDensityWagnerPruss()

auto waterSaturatedLiquidDensityWagnerPruss

(

Temperature

T

)

-> ThermoScalar

Calculate the saturated liquid-density of water using the Wagner and Pruss (1995) equation of state.

Parameters

T	The temperature of water (in units of K)

Returns

The saturated liquid-density of water (in units of kg/m3)

waterSaturatedVapourDensityWagnerPruss()

auto waterSaturatedVapourDensityWagnerPruss

(

Temperature

T

)

-> ThermoScalar

Calculate the saturated vapour-density of water using the Wagner and Pruss (1995) equation of state.

Parameters

T	The temperature of water (in units of K)

Returns

The saturated vapour-density of water (in units of kg/m3)