This class provides function objects representing quadratic combinations of the elements of their matrix of arguments. More...

#include <QuadraticCombination.hpp>

Inheritance diagram for ipo_function::concrete::QuadraticCombination:

Collaboration diagram for ipo_function::concrete::QuadraticCombination:

Public Member Functions
	QuadraticCombination (size_t const size=0)
	The constructor sets up function as a quadratic combination of size entries. More...

void	resize (size_t const size)
	Resize the matrix of coefficients. More...

void	setCoefficient (size_t const index, double const value)
	Set the value of a coefficient on the diagonal. More...

void	setCoefficient (size_t const row, size_t const col, double const value)
	Set the value of a coefficient. More...

double	getCoefficient (size_t const index) const
	Get the value of a coefficient on the diagonal. More...

double	getCoefficient (size_t const row, size_t const col) const
	Get the value of a coefficient. More...

gsl::matrix const &	getCoefficients () const
	Get the coefficients as a matrix by reference. More...

void	setCoefficients (gsl::matrix const &matrix)
	Set coefficients from a matrix. More...

virtual double	operator() (gsl::vector const &vector)
	The function operator: computes the sum of the vector entries. More...

virtual gsl::vector	gradient (gsl::vector const &vector)
	The function operator: returns the gradient: the coefficients. More...

virtual gsl::matrix	hessian (gsl::vector const &vector)
	The function operator: returns the Hessian: a matrix of 0s. More...

virtual void	setVector (gsl::vector const &vector)
	Set a vector and compute function value, gradient and Hessian efficiently. More...

Public Member Functions inherited from ipo_function::Function
	Function (size_t const size=0)
	Constructor. More...

virtual std::tuple < gsl::vector, gsl::matrix >	derivatives (gsl::vector const &vector)
	Compute or estimate derivative values. More...

Public Member Functions inherited from ipo_function::detail::FunctionBase
	FunctionBase (size_t const size=0)
	Constructor. More...

virtual	~FunctionBase ()=0
	Make the class abstract. More...

size_t	getSize () const
	Get size of vector for function arguments or zero for arbitrary size. More...

Public Member Functions inherited from ipo_function::DerivativesEstimates
	DerivativesEstimates (size_t const size=0)
	Constructor. More...

virtual gsl::matrix	hessian () const

Public Member Functions inherited from ipo_function::GradientEstimate
	GradientEstimate (size_t const size=0)
	Constructor. More...

virtual double	value () const

virtual gsl::vector	gradient () const

Protected Attributes
gsl::matrix	coefficients
	The matrix of coefficients;. More...

Protected Attributes inherited from ipo_function::Function
double	h = std::sqrt( std::numeric_limits<double>::epsilon() )
	Value used for default gradient estimates. More...

double	h2 = std::sqrt( h )
	Value used for default Hessian estimates. More...

Protected Attributes inherited from ipo_function::detail::FunctionBase
size_t const	size
	Size of vector arguments to supply to subclass functions. More...

Protected Attributes inherited from ipo_function::DerivativesEstimates
gsl::matrix	functionHessian
	The Hessian value. More...

Protected Attributes inherited from ipo_function::GradientEstimate
double	functionValue
	The function value. More...

gsl::vector	functionGradient
	The gradient value. More...

Detailed Description

This class provides function objects representing quadratic combinations of the elements of their matrix of arguments.

Each object of this class stores a symmetric $k\times k$ matrix $C$ of coefficients. When the function object is called with a vector argument $\mathbf{v}=(v_1,\ldots,v_k)^\top$ it returns $\mathbf{v}C\mathbf{v}^\top$ . Note that the coefficient of $x_ix_j$ is twice the $(i,j)$ th element of $C$ when $i\ne j$ .

Definition at line 38 of file QuadraticCombination.hpp.

Constructor & Destructor Documentation

QuadraticCombination::QuadraticCombination ( size_t const size = 0 )

The constructor sets up function as a quadratic combination of size entries.

Initially the coefficient of each entry is zero so that a call to function returns zero.

Parameters

size	The size of vectors in the function and derivatives

Definition at line 28 of file QuadraticCombination.cc.

Member Function Documentation

double QuadraticCombination::getCoefficient ( size_t const index ) const

Get the value of a coefficient on the diagonal.

Parameters

index The index of the coefficient

Returns: The value of the coefficient

Exceptions

IPOException if index out of range

Definition at line 82 of file QuadraticCombination.cc.

References coefficients, and IPOE.

Referenced by getCoefficient().

double QuadraticCombination::getCoefficient	(	size_t const	row,
		size_t const	col
	)		const

Get the value of a coefficient.

It doesn’t matter here if row and col values are interchanged because the coefficient matrix is symmetric.

Parameters

row	The row index of the coefficient
col	The column index of the coefficient

Returns: The value of the coefficient

Exceptions

IPOException if row or col out of range

Definition at line 92 of file QuadraticCombination.cc.

References coefficients, getCoefficient(), and IPOE.

gsl::matrix const & QuadraticCombination::getCoefficients ( ) const

Get the coefficients as a matrix by reference.

Returns: the vector of coefficients

Definition at line 108 of file QuadraticCombination.cc.

References coefficients.

gsl::vector QuadraticCombination::gradient ( gsl::vector const & vector )

virtual

The function operator: returns the gradient: the coefficients.

The return value may change if the coefficients change.

Parameters

vector A vector argument

Returns: The gradient

Reimplemented from ipo_function::Function.

Definition at line 164 of file QuadraticCombination.cc.

References coefficients, ipo_function::GradientEstimate::functionGradient, and IPOE.

gsl::matrix QuadraticCombination::hessian ( gsl::vector const & vector )

virtual

The function operator: returns the Hessian: a matrix of 0s.

The return value may change if the number of coefficients change.

Parameters

vector A vector argument

Returns: The Hessian: a constant symmetric matrix

Reimplemented from ipo_function::Function.

Definition at line 187 of file QuadraticCombination.cc.

References coefficients, ipo_function::DerivativesEstimates::functionHessian, and IPOE.

double QuadraticCombination::operator() ( gsl::vector const & vector )

virtual

The function operator: computes the sum of the vector entries.

Parameters

vector A vector argument

Returns: The quadratic form evaluated at vector

Implements ipo_function::Function.

Definition at line 147 of file QuadraticCombination.cc.

References coefficients, and IPOE.

void QuadraticCombination::resize ( size_t const size )

Resize the matrix of coefficients.

Any new entries are set to zero.

Parameters

size	The new size

Definition at line 32 of file QuadraticCombination.cc.

References coefficients, and ipo_function::detail::FunctionBase::size.

void QuadraticCombination::setCoefficient	(	size_t const	index,
		double const	value
	)

Set the value of a coefficient on the diagonal.

Parameters

index	The index of the coefficient
value	The new value of the coefficient

Exceptions

IPOException if index out of range

Definition at line 52 of file QuadraticCombination.cc.

References coefficients, and IPOE.

Referenced by setCoefficient().

void QuadraticCombination::setCoefficient	(	size_t const	row,
		size_t const	col,
		double const	value
	)

Set the value of a coefficient.

The values of row and col can be interchanged without affecting the result.

Parameters

row	The row index of the coefficient
col	The column index of the coefficient
value	The new value of the coefficient

Exceptions

IPOException if row or col out of range

Definition at line 62 of file QuadraticCombination.cc.

References coefficients, IPOE, and setCoefficient().

void QuadraticCombination::setCoefficients ( gsl::matrix const & matrix )

Set coefficients from a matrix.

This can resize the coefficients.

Parameters

matrix The new coefficients matrix

Exceptions

IPOException if matrix is not symmetric or has wrong size

Definition at line 113 of file QuadraticCombination.cc.

References coefficients, and IPOE.

void QuadraticCombination::setVector ( gsl::vector const & vector )

virtual

Set a vector and compute function value, gradient and Hessian efficiently.

Parameters

vector A vector argument

Implements ipo_function::GradientEstimate.

Definition at line 205 of file QuadraticCombination.cc.

References coefficients, ipo_function::GradientEstimate::functionGradient, ipo_function::DerivativesEstimates::functionHessian, ipo_function::GradientEstimate::functionValue, and IPOE.

Member Data Documentation

gsl::matrix ipo_function::concrete::QuadraticCombination::coefficients

protected

The matrix of coefficients;.

Definition at line 127 of file QuadraticCombination.hpp.

Referenced by getCoefficient(), getCoefficients(), gradient(), hessian(), operator()(), resize(), setCoefficient(), setCoefficients(), and setVector().

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

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation