A class used to generate a Beta distribution. More...

#include <Beta.h>

Inheritance diagram for Beta:

Public Types
typedef DataFileName	DataFileParameterType

Public Member Functions
	Beta (const InputParameters &parameters)

virtual Real	pdf (const Real &x) const override

virtual Real	cdf (const Real &x) const override

virtual Real	quantile (const Real &p) const override

virtual Real	median () const

virtual bool	enabled () const

std::shared_ptr< MooseObject >	getSharedPtr ()

std::shared_ptr< const MooseObject >	getSharedPtr () const

MooseApp &	getMooseApp () const

const std::string &	type () const

virtual const std::string &	name () const

std::string	typeAndName () const

std::string	errorPrefix (const std::string &error_type) const

void	callMooseError (std::string msg, const bool with_prefix) const

MooseObjectParameterName	uniqueParameterName (const std::string &parameter_name) const

const InputParameters &	parameters () const

MooseObjectName	uniqueName () const

const T &	getParam (const std::string &name) const

std::vector< std::pair< T1, T2 > >	getParam (const std::string &param1, const std::string &param2) const

const T *	queryParam (const std::string &name) const

const T &	getRenamedParam (const std::string &old_name, const std::string &new_name) const

T	getCheckedPointerParam (const std::string &name, const std::string &error_string="") const

bool	isParamValid (const std::string &name) const

bool	isParamSetByUser (const std::string &nm) const

void	paramError (const std::string &param, Args... args) const

void	paramWarning (const std::string &param, Args... args) const

void	paramInfo (const std::string &param, Args... args) const

void	connectControllableParams (const std::string &parameter, const std::string &object_type, const std::string &object_name, const std::string &object_parameter) const

void	mooseError (Args &&... args) const

void	mooseErrorNonPrefixed (Args &&... args) const

void	mooseDocumentedError (const std::string &repo_name, const unsigned int issue_num, Args &&... args) const

void	mooseWarning (Args &&... args) const

void	mooseWarningNonPrefixed (Args &&... args) const

void	mooseDeprecated (Args &&... args) const

void	mooseInfo (Args &&... args) const

std::string	getDataFileName (const std::string &param) const

std::string	getDataFileNameByName (const std::string &relative_path) const

std::string	getDataFilePath (const std::string &relative_path) const

PerfGraph &	perfGraph ()

const Parallel::Communicator &	comm () const

processor_id_type	n_processors () const

processor_id_type	processor_id () const

Static Public Member Functions
static InputParameters	validParams ()

static Real	pdf (const Real &x, const Real &alpha, const Real &beta)

static Real	cdf (const Real &x, const Real &alpha, const Real &beta)

static Real	quantile (const Real &p, const Real &alpha, const Real &beta)

static Real	betaFunction (const Real &a, const Real &b)
	Beta function: B(a,b) = Gamma(a)Gamma(b)/Gamma(a+b) More...

static Real	incompleteBeta (const Real &a, const Real &b, const Real &x)
	Lower incomplete beta function. More...

static Real	incompleteBetaInv (const Real &a, const Real &b, const Real &p)
	Inverse of lower incomplete beta function. More...

Public Attributes
const ConsoleStream	_console

Protected Member Functions
PerfID	registerTimedSection (const std::string &section_name, const unsigned int level) const

PerfID	registerTimedSection (const std::string &section_name, const unsigned int level, const std::string &live_message, const bool print_dots=true) const

std::string	timedSectionName (const std::string &section_name) const

Protected Attributes
const Real &	_alpha
	Shape parameter 1. More...

const Real &	_beta
	Shape parameter 2. More...

const bool &	_enabled

MooseApp &	_app

const std::string	_type

const std::string	_name

const InputParameters &	_pars

Factory &	_factory

ActionFactory &	_action_factory

MooseApp &	_pg_moose_app

const std::string	_prefix

const Parallel::Communicator &	_communicator

Detailed Description

A class used to generate a Beta distribution.

Definition at line 17 of file Beta.h.

Constructor & Destructor Documentation

◆ Beta()

Beta::Beta ( const InputParameters & parameters )

Definition at line 26 of file Beta.C.

   : Distribution(parameters), _alpha(getParam<Real>("alpha")), _beta(getParam<Real>("beta"))
 {
 }

Member Function Documentation

◆ betaFunction()

Real Beta::betaFunction	(	const Real &	a,
		const Real &	b
	)

static

Beta function: B(a,b) = Gamma(a)Gamma(b)/Gamma(a+b)

Definition at line 76 of file Beta.C.

Referenced by incompleteBeta(), incompleteBetaInv(), StudentT::pdf(), and pdf().

 {
   return std::tgamma(a) * std::tgamma(b) / std::tgamma(a + b);
 }

◆ cdf() [1/2]

Real Beta::cdf ( const Real & x ) const

overridevirtual

Implements Distribution.

Definition at line 64 of file Beta.C.

 {
   return cdf(x, _alpha, _beta);
 }

◆ cdf() [2/2]

Real Beta::cdf	(	const Real &	x,
		const Real &	alpha,
		const Real &	beta
	)

static

Definition at line 41 of file Beta.C.

 {
   if (x <= 0.0)
     return 0.0;
   else if (x >= 1.0)
     return 1.0;
   else
     return incompleteBeta(alpha, beta, x);
 }

◆ incompleteBeta()

Real Beta::incompleteBeta	(	const Real &	a,
		const Real &	b,
		const Real &	x
	)

static

Lower incomplete beta function.

Non-boost implementation from: Section 6.4 of https://www.cec.uchile.cl/cinetica/pcordero/MC_libros/NumericalRecipesinC.pdf

Definition at line 82 of file Beta.C.

Referenced by cdf(), StudentT::cdf(), FDistribution::cdf(), and incompleteBetaInv().

 {
   if (x > ((a + 1.0) / (a + b + 2.0)))
     return 1.0 - incompleteBeta(b, a, 1.0 - x);
 
   const Real tol = 1e-14;
   const unsigned int max_iter = 1e3;
   const Real coef = std::pow(x, a) * std::pow(1.0 - x, b) / a / betaFunction(a, b);
   Real fn = 1.0;
   Real cn = 1.0;
   Real dn = 0.0;
   Real num;
   Real m = 0.0;
   for (unsigned int i = 0; i < max_iter; ++i)
   {
     if (i == 0)
       num = 1.0;
     else if (i % 2 == 0)
     {
       m = i / 2.0;
       num = m * (b - m) * x / (a + 2.0 * m) / (a + 2.0 * m - 1.0);
     }
     else
     {
       m = (i - 1) / 2.0;
       num = -(a + m) * (a + b + m) * x / (a + 2.0 * m) / (a + 2.0 * m + 1.0);
     }
 
     dn = 1.0 / (1.0 + num * dn);
     cn = 1.0 + num / cn;
     const Real cd = cn * dn;
     fn *= cd;
 
     if (std::abs(1.0 - cd) < tol)
       return coef * (fn - 1.0);
   }
 
   mooseAssert(false, "Could not compute incomplete beta function.");
   return coef * (fn - 1.0);
 }

◆ incompleteBetaInv()

Real Beta::incompleteBetaInv	(	const Real &	a,
		const Real &	b,
		const Real &	p
	)

static

Inverse of lower incomplete beta function.

Non-boost implementation uses Newton-Raphson to find root of incompleteBeta(a, b, x) - p

Definition at line 124 of file Beta.C.

Referenced by quantile(), StudentT::quantile(), and FDistribution::quantile().

 {
   if (a < b)
     return 1.0 - incompleteBetaInv(b, a, 1.0 - p);
 
   // Try with Newton method
   Real x = 0.5;
   const Real tol = 1e-14;
   const unsigned int max_iter = 1e3;
   const Real scale = betaFunction(a, b);
   Real f;
   Real df;
   for (unsigned int i = 0; i < max_iter; ++i)
   {
     f = incompleteBeta(a, b, x) - p;
     if (std::abs(f) < tol)
       return x;
     df = std::pow(x, a - 1.0) * std::pow(1.0 - x, b - 1.0) / scale;
     x -= f / df;
     // There's a divergence so try out bisection
     if (x < 0 || x > 1.0)
       break;
   }
 
   // Try with bisection method
   Real x1 = 0; // f(0) = -p
   Real x2 = 1; // f(1) = 1 - p
   for (unsigned int i = 0; i < max_iter; ++i)
   {
     x = (x2 + x1) / 2.0;
     f = incompleteBeta(a, b, x) - p;
     if (std::abs(f) < tol)
       return x;
     else if (f < 0)
       x1 = x;
     else
       x2 = x;
   }
 
   mooseAssert(false, "Could not find inverse of incomplete gamma function.");
   return x;
 }

◆ pdf() [1/2]

Real Beta::pdf ( const Real & x ) const

overridevirtual

Implements Distribution.

Definition at line 58 of file Beta.C.

Referenced by FDistribution::pdf().

 {
   return pdf(x, _alpha, _beta);
 }

◆ pdf() [2/2]

Real Beta::pdf	(	const Real &	x,
		const Real &	alpha,
		const Real &	beta
	)

static

Definition at line 32 of file Beta.C.

 {
   if (x <= 0.0 || x > 1.0)
     return 0.0;
   else
     return std::pow(x, alpha - 1.0) * std::pow(1.0 - x, beta - 1.0) / betaFunction(alpha, beta);
 }

◆ quantile() [1/2]

Real Beta::quantile ( const Real & p ) const

overridevirtual

Implements Distribution.

Definition at line 70 of file Beta.C.

 {
   return quantile(p, _alpha, _beta);
 }

◆ quantile() [2/2]

Real Beta::quantile	(	const Real &	p,
		const Real &	alpha,
		const Real &	beta
	)

static

Definition at line 52 of file Beta.C.

 {
   return incompleteBetaInv(alpha, beta, p);
 }

◆ validParams()

InputParameters Beta::validParams ( )

static

Definition at line 17 of file Beta.C.

 {
   InputParameters params = Distribution::validParams();
   params.addClassDescription("Beta distribution");
   params.addRequiredRangeCheckedParam<Real>("alpha", "alpha > 0", "Shape parameter 1.");
   params.addRequiredRangeCheckedParam<Real>("beta", "beta > 0", "Shape parameter 2.");
   return params;
 }

Member Data Documentation

◆ _alpha

const Real& Beta::_alpha

protected

Shape parameter 1.

Definition at line 48 of file Beta.h.

Referenced by cdf(), pdf(), and quantile().

◆ _beta

const Real& Beta::_beta

protected

Shape parameter 2.

Definition at line 50 of file Beta.h.

Referenced by cdf(), pdf(), and quantile().

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

stochastic_tools/include/distributions/Beta.h
stochastic_tools/src/distributions/Beta.C

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Beta()

Member Function Documentation

◆ betaFunction()

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ incompleteBeta()

◆ incompleteBetaInv()

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ quantile() [1/2]

◆ quantile() [2/2]

◆ validParams()

Member Data Documentation

◆ _alpha

◆ _beta