A class for handling Gamma joint PDFs. More...

#include <GammaJointPdf.h>

Inheritance diagram for QUESO::GammaJointPdf< V, M >:

Public Member Functions
Constructor/Destructor methods
	GammaJointPdf (const char *prefix, const VectorSet< V, M > &domainSet, const V &a, const V &b)

	~GammaJointPdf ()
	Destructor. More...

Math methods
double	actualValue (const V &domainVector, const V domainDirection, V gradVector, M hessianMatrix, V hessianEffect) const
	Actual value of the Gamma PDF. More...

double	lnValue (const V &domainVector, const V domainDirection, V gradVector, M hessianMatrix, V hessianEffect) const
	Logarithm of the value of the Gamma PDF. More...

virtual void	distributionMean (V &meanVector) const
	Mean value of the underlying random variable. More...

virtual void	distributionVariance (M &covMatrix) const
	Covariance matrix of the underlying random variable. More...

double	computeLogOfNormalizationFactor (unsigned int numSamples, bool updateFactorInternally) const
	Computes the logarithm of the normalization factor. More...

Public Member Functions inherited from QUESO::BaseJointPdf< V, M >
	BaseJointPdf (const char *prefix, const VectorSet< V, M > &domainSet)
	Default constructor. More...

virtual	~BaseJointPdf ()
	Destructor. More...

virtual void	setNormalizationStyle (unsigned int value) const

void	setLogOfNormalizationFactor (double value) const
	Sets a logarithmic value to be used in the normalization factor (stored in the protected attribute m_normalizationStyle.) More...

virtual void	print (std::ostream &os) const
	Print method. Non-pure for backwards compatibility. More...

Public Member Functions inherited from QUESO::BaseScalarFunction< V, M >
void	setFiniteDifferenceStepSize (double fdStepSize)
	Sets the step size for finite differencing gradients. More...

void	setFiniteDifferenceStepSize (unsigned int i, double fdStepSize)

	BaseScalarFunction (const char *prefix, const VectorSet< V, M > &domainSet)
	Default constructor. More...

virtual	~BaseScalarFunction ()
	Destructor. More...

const VectorSet< V, M > &	domainSet () const
	Access to the protected attribute `m_domainSet:` domain set of the scalar function. More...

virtual double	lnValue (const V &domainVector) const
	Returns the logarithm of the function at `domainVector`. More...

virtual double	lnValue (const V &domainVector, V &gradVector) const
	Returns the logarithm of the function and its gradient at `domainVector`. More...

virtual double	lnValue (const V &domainVector, V &gradVector, const V &domainDirection, V &hessianEffect) const

Protected Attributes
V	m_a

V	m_b

Protected Attributes inherited from QUESO::BaseJointPdf< V, M >
unsigned int	m_normalizationStyle

double	m_logOfNormalizationFactor

Protected Attributes inherited from QUESO::BaseScalarFunction< V, M >
const BaseEnvironment &	m_env

std::string	m_prefix

const VectorSet< V, M > &	m_domainSet
	Domain set of the scalar function. More...

Additional Inherited Members
Protected Member Functions inherited from QUESO::BaseJointPdf< V, M >
double	commonComputeLogOfNormalizationFactor (unsigned int numSamples, bool updateFactorInternally) const
	Common method (to the derived classes) to compute the logarithm of the normalization factor. More...

Detailed Description

template<class V = GslVector, class M = GslMatrix>
class QUESO::GammaJointPdf< V, M >

A class for handling Gamma joint PDFs.

This class allows the mathematical definition of a Gamma Joint PDF.

Definition at line 47 of file GammaJointPdf.h.

Constructor & Destructor Documentation

template<class V , class M >

QUESO::GammaJointPdf< V, M >::GammaJointPdf	(	const char *	prefix,
		const VectorSet< V, M > &	domainSet,
		const V &	a,
		const V &	b
	)

Constructor for a shape-scale parameterisation of a Gamma(a,b) pdf defined on domainSet.

Constructs a new object of the class, given a prefix, the domain set, and the parameters a and b of the Gamma PDF.

The parameters a and b are the shape and scale parameters, respectively. That is, the pdf is

\[ f(x) = C x^{a-1} \exp \left( x / b \right), \]

where C is a normalising constant.

Indeed, a and b are vectors and in multiple dimensions the pdf is just the product of Gamma(a_i, b_i) pdfs distributions in each dimension. That is, they are independent.

Note: the parameters a and b correspond to the shape and scale parameters k and \(\theta\) in the Wikipedia entry for the Gamma distribution.

Definition at line 34 of file GammaJointPdf.C.

References QUESO::BaseEnvironment::displayVerbosity(), QUESO::BaseScalarFunction< V, M >::m_env, QUESO::BaseScalarFunction< V, M >::m_prefix, and QUESO::BaseEnvironment::subDisplayFile().

   :
   BaseJointPdf<V,M>(((std::string)(prefix)+"uni").c_str(),domainSet),
   m_a(a),
   m_b(b)
 {
   if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 54)) {
     *m_env.subDisplayFile() << "Entering GammaJointPdf<V,M>::constructor()"
                             << ": prefix = " << m_prefix
                             << std::endl;
   }
 
   if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 54)) {
     *m_env.subDisplayFile() << "Leaving GammaJointPdf<V,M>::constructor()"
                             << ": prefix = " << m_prefix
                             << std::endl;
   }
 }

template<class V , class M >

QUESO::GammaJointPdf< V, M >::~GammaJointPdf ( )

Destructor.

Definition at line 58 of file GammaJointPdf.C.

59 {

60 }

Member Function Documentation

template<class V , class M >

double QUESO::GammaJointPdf< V, M >::actualValue	(	const V &	domainVector,
		const V *	domainDirection,
		V *	gradVector,
		M *	hessianMatrix,
		V *	hessianEffect
	)		const

virtual

Actual value of the Gamma PDF.

This routine calls method lnValue() and returns the exponent of the returning value of such method.

Implements QUESO::BaseJointPdf< V, M >.

Definition at line 64 of file GammaJointPdf.C.

References QUESO::queso_require_equal_to_msg.

 {
   queso_require_equal_to_msg(domainVector.sizeLocal(), this->m_domainSet.vectorSpace().dimLocal(), "invalid input");
 
   queso_require_msg(!(domainDirection || gradVector || hessianMatrix || hessianEffect), "incomplete code for gradVector, hessianMatrix and hessianEffect calculations");
 
   // No need to multiply by exp(m_logOfNormalizationFactor) because 'lnValue()' is called [PDF-06]
   return exp(this->lnValue(domainVector,domainDirection,gradVector,hessianMatrix,hessianEffect));
 }

template<class V , class M >

double QUESO::GammaJointPdf< V, M >::computeLogOfNormalizationFactor	(	unsigned int	numSamples,
		bool	updateFactorInternally
	)		const

virtual

Computes the logarithm of the normalization factor.

This routine calls BaseJointPdf::commonComputeLogOfNormalizationFactor().

Implements QUESO::BaseJointPdf< V, M >.

Definition at line 145 of file GammaJointPdf.C.

References QUESO::BaseJointPdf< V, M >::commonComputeLogOfNormalizationFactor().

 {
   double value = 0.;
 
   if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 2)) {
     *m_env.subDisplayFile() << "Entering GammaJointPdf<V,M>::computeLogOfNormalizationFactor()"
                             << std::endl;
   }
   value = BaseJointPdf<V,M>::commonComputeLogOfNormalizationFactor(numSamples, updateFactorInternally);
   if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 2)) {
     *m_env.subDisplayFile() << "Leaving GammaJointPdf<V,M>::computeLogOfNormalizationFactor()"
                             << ", m_logOfNormalizationFactor = " << m_logOfNormalizationFactor
                             << std::endl;
   }
 
   return value;
 }

template<class V , class M >

void QUESO::GammaJointPdf< V, M >::distributionMean ( V & meanVector ) const

virtual

Mean value of the underlying random variable.

Reimplemented from QUESO::BaseJointPdf< V, M >.

Definition at line 117 of file GammaJointPdf.C.

 {
   queso_assert_equal_to(m_a.sizeLocal(), m_b.sizeLocal());
   queso_assert_equal_to(m_a.sizeLocal(), meanVector.sizeLocal());
 
   for (unsigned int i = 0; i < m_a.sizeLocal(); ++i) {
     meanVector[i] = m_a[i] * m_b[i];
   }
 }

template<class V , class M >

void QUESO::GammaJointPdf< V, M >::distributionVariance ( M & covMatrix ) const

virtual

Covariance matrix of the underlying random variable.

Reimplemented from QUESO::BaseJointPdf< V, M >.

Definition at line 129 of file GammaJointPdf.C.

 {
   queso_assert_equal_to(m_a.sizeLocal(), m_b.sizeLocal());
   queso_assert_equal_to(m_a.sizeLocal(), covMatrix.numRowsGlobal());
   queso_assert_equal_to(covMatrix.numCols(), covMatrix.numRowsGlobal());
 
   covMatrix.zeroLower();
   covMatrix.zeroUpper();
 
   for (unsigned int i = 0; i < m_a.sizeLocal(); ++i) {
     covMatrix(i,i) = m_a[i] * m_b[i] * m_b[i];
   }
 }

template<class V , class M >

double QUESO::GammaJointPdf< V, M >::lnValue	(	const V &	domainVector,
		const V *	domainDirection,
		V *	gradVector,
		M *	hessianMatrix,
		V *	hessianEffect
	)		const

virtual

Logarithm of the value of the Gamma PDF.

If the normalization style (m_normalizationStyle) is zero, then this routine calls a environment method which handles basic PDFs, e.g. basicPdfs()->gammaPdfActualValue() and adds the log of the normalization factor (m_logOfNormalizationFactor) to it; otherwise the method uses the formula: \( lnValue = \sum[ (a_i-1)*log(domainVector_i) -domainVector_i/b_i + m_logOfNormalizationFactor \), where a and b are the parameters of the Gamma PDF.

Reimplemented from QUESO::BaseScalarFunction< V, M >.

Definition at line 81 of file GammaJointPdf.C.

 {
   queso_require_msg(!(domainDirection || gradVector || hessianMatrix || hessianEffect), "incomplete code for gradVector, hessianMatrix and hessianEffect calculations");
 
   double aux = 0.;
   double result = 0.;
   for (unsigned int i = 0; i < domainVector.sizeLocal(); ++i) {
     if (m_normalizationStyle == 0) {
       aux = log(m_env.basicPdfs()->gammaPdfActualValue(domainVector[i],m_a[i],m_b[i]));
     }
     else {
       aux = (m_a[i]-1.)*log(domainVector[i]) - domainVector[i]/m_b[i];
     }
     if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 99)) {
       *m_env.subDisplayFile() << "In GammaJointPdf<V,M>::lnValue()"
                               << ", m_normalizationStyle = "      << m_normalizationStyle
                               << ": domainVector[" << i << "] = " << domainVector[i]
                               << ", m_a[" << i << "] = "          << m_a[i]
                               << ", m_b[" << i << "] = "          << m_b[i]
                               << ", log(pdf)= "                   << aux
                               << std::endl;
     }
     result += aux;
   }
   result += m_logOfNormalizationFactor; // [PDF-06]
 
   return result;
 }