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

#include <Gamma.h>

Inheritance diagram for Gamma:

Public Types
typedef DataFileName	DataFileParameterType

Public Member Functions
	Gamma (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	incompleteGamma (const Real &a, const Real &x)
	Lower incomplete gamma function. More...

static Real	incompleteGammaInv (const Real &a, const Real &p)
	Inverse of lower incomplete gamma 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. More...

const Real &	_theta
	Scaling. 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 Gamma distribution.

Definition at line 17 of file Gamma.h.

Constructor & Destructor Documentation

◆ Gamma()

Gamma::Gamma ( const InputParameters & parameters )

Definition at line 27 of file Gamma.C.

   : Distribution(parameters), _alpha(getParam<Real>("shape")), _theta(getParam<Real>("scale"))
 {
 }

Member Function Documentation

◆ cdf() [1/2]

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

overridevirtual

Implements Distribution.

Definition at line 64 of file Gamma.C.

 {
   return cdf(x, _alpha, 1.0 / _theta);
 }

◆ cdf() [2/2]

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

static

Definition at line 43 of file Gamma.C.

 {
   if (x <= 0.0)
     return 0.0;
   else
     return incompleteGamma(alpha, beta * x);
 }

◆ incompleteGamma()

Real Gamma::incompleteGamma	(	const Real &	a,
		const Real &	x
	)

static

Lower incomplete gamma function.

Non-boost implementation from: Temme, N. (1994). A Set of Algorithms for the Incomplete Gamma Functions. Probability in the Engineering and Informational Sciences, 8(2), 291-307.

Definition at line 76 of file Gamma.C.

Referenced by cdf(), and incompleteGammaInv().

 {
   const Real tol = 1e-14;
   const unsigned int max_iter = 1e6;
   const Real coef = std::pow(x, a) * std::exp(-x) / std::tgamma(a + 1.0);
   Real cn = 1.0;
   Real an = a;
   Real val = 1.0;
   for (unsigned int i = 0; i < max_iter; ++i)
   {
     an += 1.0;
     cn *= x / an;
     val += cn;
     if (std::abs(cn / val) < tol)
       return coef * val;
   }
 
   mooseAssert(false, "Could not compute incomplete gamma function.");
   return coef * val;
 }

◆ incompleteGammaInv()

Real Gamma::incompleteGammaInv	(	const Real &	a,
		const Real &	p
	)

static

Inverse of lower incomplete gamma function.

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

Definition at line 98 of file Gamma.C.

Referenced by quantile().

 {
   Real x = a > 1.0 ? a : std::pow(p * std::tgamma(a + 1.0), 1.0 / a);
   const Real scale = std::tgamma(a);
   const Real tol = 1e-14;
   const unsigned int max_iter = 1e6;
   Real f;
   Real df;
   for (unsigned int i = 0; i < max_iter; ++i)
   {
     f = incompleteGamma(a, x) - p;
     if (std::abs(f) < tol)
       return x;
     df = std::pow(x, a - 1.0) * std::exp(-x) / scale;
     x -= f / df;
   }
 
   mooseAssert(false, "Could not find inverse of incomplete gamma function.");
   return x;
 }

◆ pdf() [1/2]

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

overridevirtual

Implements Distribution.

Definition at line 58 of file Gamma.C.

 {
   return pdf(x, _alpha, 1.0 / _theta);
 }

◆ pdf() [2/2]

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

static

Definition at line 33 of file Gamma.C.

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

◆ quantile() [1/2]

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

overridevirtual

Implements Distribution.

Definition at line 70 of file Gamma.C.

 {
   return quantile(p, _alpha, 1.0 / _theta);
 }

◆ quantile() [2/2]

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

static

Definition at line 52 of file Gamma.C.

 {
   return incompleteGammaInv(alpha, p) / beta;
 }

◆ validParams()

InputParameters Gamma::validParams ( )

static

Definition at line 17 of file Gamma.C.

 {
   InputParameters params = Distribution::validParams();
   params.addClassDescription("Gamma distribution");
   params.addRequiredRangeCheckedParam<Real>("shape", "shape > 0", "Shape parameter (k or alpha).");
   params.addRangeCheckedParam<Real>(
       "scale", 1.0, "scale > 0", "Scale parameter (theta or 1/beta).");
   return params;
 }

Member Data Documentation

◆ _alpha

const Real& Gamma::_alpha

protected

Shape.

Definition at line 47 of file Gamma.h.

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

◆ _theta

const Real& Gamma::_theta

protected

Scaling.

Definition at line 49 of file Gamma.h.

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

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

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

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Gamma()

Member Function Documentation

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ incompleteGamma()

◆ incompleteGammaInv()

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ quantile() [1/2]

◆ quantile() [2/2]

◆ validParams()

Member Data Documentation

◆ _alpha

◆ _theta