sgpp::base::ScalarFunctionHessian Class Reference

Abstract base class for scalar-valued functions \(f\colon [0, 1]^d \to \mathbb{R}\) together with their gradients \(\nabla f\colon [0, 1]^d \to \mathbb{R}^d\) and Hessians \(H_f\colon [0, 1]^d \to \mathbb{R}^{d \times d}\) (e.g., Hessians of objective functions in optimization). More...

#include <ScalarFunctionHessian.hpp>

Inheritance diagram for sgpp::base::ScalarFunctionHessian:

Public Member Functions
virtual void	clone (std::unique_ptr< ScalarFunctionHessian > &clone) const =0
	Pure virtual method for cloning the Hessian.
void	eval (const DataMatrix &x, DataVector &value, DataMatrix &gradient, std::vector< DataMatrix > &hessian)
	Convenience method for calculating \(f(\vec{x})\) together with \(\nabla f(\vec{x})\) and \(H_f(\vec{x}) \in \mathbb{R}^{d \times d}\) for multiple \(\vec{x}\).
virtual double	eval (const DataVector &x, DataVector &gradient, DataMatrix &hessian)=0
	Pure virtual method for calculating \(f(\vec{x})\) together with \(\nabla f(\vec{x})\) and \(H_f(\vec{x}) \in \mathbb{R}^{d \times d}\).
size_t	getNumberOfParameters () const
	ScalarFunctionHessian (size_t d)
	Constructor.
virtual	~ScalarFunctionHessian ()
	Destructor.

Protected Attributes
size_t	d
	dimension of the domain

Detailed Description

Abstract base class for scalar-valued functions \(f\colon [0, 1]^d \to \mathbb{R}\) together with their gradients \(\nabla f\colon [0, 1]^d \to \mathbb{R}^d\) and Hessians \(H_f\colon [0, 1]^d \to \mathbb{R}^{d \times d}\) (e.g., Hessians of objective functions in optimization).

Constructor & Destructor Documentation

ScalarFunctionHessian()

sgpp::base::ScalarFunctionHessian::ScalarFunctionHessian ( size_t  d )

inlineexplicit

Constructor.

Parameters

d	dimension of the domain

~ScalarFunctionHessian()

virtual sgpp::base::ScalarFunctionHessian::~ScalarFunctionHessian ( )

inlinevirtual

Destructor.

Member Function Documentation

clone()

virtual void sgpp::base::ScalarFunctionHessian::clone ( std::unique_ptr< ScalarFunctionHessian > &  clone ) const

pure virtual

Pure virtual method for cloning the Hessian.

It should generate a pointer to the cloned object and it's used for parallel computations (the eval() method might not be thread-safe).

Parameters

[out]

clone

pointer to cloned object

Implemented in sgpp::base::ComponentScalarFunctionHessian, sgpp::base::InterpolantScalarFunctionHessian, sgpp::base::ScaledScalarFunctionHessian, and sgpp::base::WrapperScalarFunctionHessian.

eval() [1/2]

void sgpp::base::ScalarFunctionHessian::eval ( const DataMatrix &  x, DataVector &  value, DataMatrix &  gradient, std::vector< DataMatrix > &  hessian  )

inline

Convenience method for calculating \(f(\vec{x})\) together with \(\nabla f(\vec{x})\) and \(H_f(\vec{x}) \in \mathbb{R}^{d \times d}\) for multiple \(\vec{x}\).

Parameters

	x	matrix \(\vec{x} \in [0, 1]^{N \times d}\) of evaluation points (row-wise)
[out]	value	vector of size \(N\), where the \(k\)-th entry is \(f(\vec{x}_k)\) (where \(\vec{x}_k\) is the \(k\)-th row of \(x\))
[out]	gradient	matrix of size \(N \times d\) where the \(k\)-th row is \(\nabla f(\vec{x}_k)\)
[out]	hessian	\(N\)-vector of Hessians \(\nabla^2 f(\vec{x}_k) \in \mathbb{R}^{d \times d}\)

References d, eval(), sgpp::base::DataMatrix::getNrows(), sgpp::base::DataMatrix::getRow(), sgpp::base::DataMatrix::resize(), and sgpp::base::DataMatrix::setRow().

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity().

eval() [2/2]

virtual double sgpp::base::ScalarFunctionHessian::eval ( const DataVector &  x, DataVector &  gradient, DataMatrix &  hessian  )

pure virtual

Pure virtual method for calculating \(f(\vec{x})\) together with \(\nabla f(\vec{x})\) and \(H_f(\vec{x}) \in \mathbb{R}^{d \times d}\).

Parameters

	x	evaluation point \(\vec{x} \in [0, 1]^d\)
[out]	gradient	gradient \(\nabla f(\vec{x}) \in \mathbb{R}^d\)
[out]	hessian	Hessian matrix \(H_f(\vec{x}) \in \mathbb{R}^{d \times d}\)

Returns

\(f(\vec{x})\)

Implemented in sgpp::base::ComponentScalarFunctionHessian, sgpp::base::InterpolantScalarFunctionHessian, sgpp::base::ScaledScalarFunctionHessian, and sgpp::base::WrapperScalarFunctionHessian.

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), eval(), and sgpp::base::ComponentScalarFunctionHessian::eval().

getNumberOfParameters()

size_t sgpp::base::ScalarFunctionHessian::getNumberOfParameters ( ) const

inline

Returns

dimension \(d\) of the domain

References d.

Member Data Documentation

d

size_t sgpp::base::ScalarFunctionHessian::d

protected

dimension of the domain

Referenced by sgpp::base::WrapperScalarFunctionHessian::clone(), eval(), sgpp::base::InterpolantScalarFunctionHessian::eval(), sgpp::base::ScaledScalarFunctionHessian::eval(), and getNumberOfParameters().

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

• base/src/sgpp/base/function/scalar/ScalarFunctionHessian.hpp