The BivariateNormalRand class
Bivariate Gaussian (normal) distribution. More...

#include <bivariate_normal.hpp>

Inheritance diagram for randlib::BivariateNormalRand< RealType >:

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Collaboration diagram for randlib::BivariateNormalRand< RealType >:

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Public Member Functions
	BivariateNormalRand (double location1, double location2, double scale1, double scale2, double correlation)

std::string	Name () const override

void	SetLocations (double location1, double location2)

void	SetCovariance (double scale1, double scale2, double correlation)

DoublePair	GetLocation ()

double	GetFirstLocation () const noexcept

double	GetSecondLocation () const noexcept

double	GetFirstScale () const noexcept

double	GetSecondScale () const noexcept

double	GetCorrelation () const noexcept

double	f (const Pair< RealType > &point) const override

double	logf (const Pair< RealType > &point) const override

double	F (const Pair< RealType > &point) const override

template<std::uniform_random_bit_generator G>
Pair< RealType >	operator() (G &g) const

long double	Correlation () const override

Pair< RealType >	Mode () const override

Public Member Functions inherited from randlib::ContinuousBivariateDistribution< NormalRand< RealType >, NormalRand< RealType >, RealType >
virtual	~ContinuousBivariateDistribution ()

Public Member Functions inherited from randlib::BivariateDistribution< T1, T2, T >
virtual	~BivariateDistribution ()

Pair< T >	MinValue () const override

Pair< T >	MaxValue () const override

virtual LongDoublePair	Mean () const final

virtual LongDoubleTriplet	Covariance () const final

virtual std::pair< T1, T2 >	GetMarginalDistributions () const final

Public Member Functions inherited from randlib::ProbabilityDistribution< Pair< T > >
virtual	~ProbabilityDistribution ()=default

virtual double	F (const Pair< T > &x) const=0

void	CumulativeDistributionFunction (std::span< const Pair< T > > x, std::span< double > y) const

virtual double	S (const Pair< T > &x) const

void	SurvivalFunction (std::span< const Pair< T > > x, std::span< double > y) const

Pair< T >	operator() (G &g) const
	Draws a variate with the given engine through the virtual interface.

Pair< T >	Variate () const
	Uses the engine of this object, so it is not thread-safe for one object; use operator() with one engine per thread instead.

void	Sample (std::span< Pair< T > > outputData) const
	Fills the output with variates drawn with the engine of this object.

void	Sample (G &g, std::span< Pair< T > > outputData) const
	Fills the output with variates drawn with the given engine.

void	Reseed (std::uint64_t seed)

Additional Inherited Members
Public Types inherited from randlib::ProbabilityDistribution< Pair< T > >
using	value_type = Pair< T >

Protected Member Functions inherited from randlib::ContinuousBivariateDistribution< NormalRand< RealType >, NormalRand< RealType >, RealType >
	ContinuousBivariateDistribution ()

Protected Member Functions inherited from randlib::BivariateDistribution< T1, T2, T >
	BivariateDistribution ()

Protected Member Functions inherited from randlib::ProbabilityDistribution< Pair< T > >
std::string	toStringWithPrecision (const double a_value, const int n=6) const

	ProbabilityDistribution ()=default

DefaultEngine &	engine () const

virtual void	sample (detail::EngineRef g, std::span< Pair< T > > outputData) const
	Fills the output with variate(g); distributions with a faster bulk algorithm override it.

fit_error	fitError (FitErrorCode code, const std::string &explanation) const

Protected Attributes inherited from randlib::BivariateDistribution< T1, T2, T >
T1	X {}
	1st marginal distributions

T2	Y {}
	2nd marginal distributions

Static Protected Attributes inherited from randlib::ProbabilityDistribution< Pair< T > >
static constexpr size_t	MAX_ITER_REJECTION
	MAX_ITER_REJECTION upper boundary for maximum amount of iterations in rejection methods one thousand should be enough to be sure there is a bug (or rejection method is too slow to be used)

static constexpr char	POSITIVITY_VIOLATION []

static constexpr char	NON_NEGATIVITY_VIOLATION []

static constexpr char	UPPER_LIMIT_VIOLATION []

static constexpr char	LOWER_LIMIT_VIOLATION []

Detailed Description

template<typename RealType>
class randlib::BivariateNormalRand< RealType >

The BivariateNormalRand class
Bivariate Gaussian (normal) distribution.

Notation: X ~ N(μ1, μ2, σ1, ρ, σ2)

Constructor & Destructor Documentation

◆ BivariateNormalRand()

template<typename RealType >

randlib::BivariateNormalRand< RealType >::BivariateNormalRand	(	double	location1,
		double	location2,
		double	scale1,
		double	scale2,
		double	correlation
	)

Member Function Documentation

◆ Correlation()

template<typename RealType >

long double randlib::BivariateNormalRand< RealType >::Correlation ( ) const

overridevirtual

Implements randlib::BivariateDistribution< T1, T2, T >.

◆ f()

template<typename RealType >

double randlib::BivariateNormalRand< RealType >::f ( const Pair< RealType > & point ) const

overridevirtual

f(x, y) = δ(xAdj - yAdj)

f(x, y) = δ(xAdj + yAdj)

Implements randlib::ContinuousBivariateDistribution< NormalRand< RealType >, NormalRand< RealType >, RealType >.

◆ F()

template<typename RealType >

double randlib::BivariateNormalRand< RealType >::F ( const Pair< RealType > & point ) const

override

F(x, y) = F(x)F(y)

Unnumbered equation between (3) and (4) in Section 2.2 of Genz (2004), integrating in terms of theta between asin(ρ) and +/- π/2

Integrand is exp(-(x^2 + y^2 - 2xysin(θ)) / (2cos(θ)^2))

◆ GetCorrelation()

template<typename RealType >

double randlib::BivariateNormalRand< RealType >::GetCorrelation ( ) const

inlinenoexcept

◆ GetFirstLocation()

template<typename RealType >

double randlib::BivariateNormalRand< RealType >::GetFirstLocation ( ) const

inlinenoexcept

◆ GetFirstScale()

template<typename RealType >

double randlib::BivariateNormalRand< RealType >::GetFirstScale ( ) const

inlinenoexcept

◆ GetLocation()

template<typename RealType >

DoublePair randlib::BivariateNormalRand< RealType >::GetLocation ( )

inline

◆ GetSecondLocation()

template<typename RealType >

double randlib::BivariateNormalRand< RealType >::GetSecondLocation ( ) const

inlinenoexcept

◆ GetSecondScale()

template<typename RealType >

double randlib::BivariateNormalRand< RealType >::GetSecondScale ( ) const

inlinenoexcept

◆ logf()

template<typename RealType >

double randlib::BivariateNormalRand< RealType >::logf ( const Pair< RealType > & point ) const

overridevirtual

log(f(x, y)) = log(f(x)) + log(f(y))

log(f(x, y)) = log(δ(xAdj - yAdj))

log(f(x, y)) = log(δ(xAdj + yAdj))

Implements randlib::ContinuousBivariateDistribution< NormalRand< RealType >, NormalRand< RealType >, RealType >.

◆ Mode()

template<typename RealType >

Pair< RealType > randlib::BivariateNormalRand< RealType >::Mode ( ) const

overridevirtual

Implements randlib::BivariateDistribution< T1, T2, T >.

◆ Name()

template<typename RealType >

std::string randlib::BivariateNormalRand< RealType >::Name ( ) const

overridevirtual

Returns: title of distribution, for instance "Normal(0, 1)"

Implements randlib::ProbabilityDistribution< Pair< T > >.

◆ operator()()

template<typename RealType >

template<std::uniform_random_bit_generator G>

Pair< RealType > randlib::BivariateNormalRand< RealType >::operator() ( G & g ) const

◆ SetCovariance()

template<typename RealType >

void randlib::BivariateNormalRand< RealType >::SetCovariance	(	double	scale1,
		double	scale2,
		double	correlation
	)

◆ SetLocations()

template<typename RealType >

void randlib::BivariateNormalRand< RealType >::SetLocations	(	double	location1,
		double	location2
	)

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

bivariate_normal.hpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BivariateNormalRand()

Member Function Documentation

◆ Correlation()

◆ f()

◆ F()

◆ GetCorrelation()

◆ GetFirstLocation()

◆ GetFirstScale()

◆ GetLocation()

◆ GetSecondLocation()

◆ GetSecondScale()

◆ logf()

◆ Mode()

◆ Name()

◆ operator()()

◆ SetCovariance()

◆ SetLocations()