C++ class supporting the definition and computation of Taylor models for factorable functions. More...

#include <taylor_model.hpp>

Classes
class	Exceptions
	Taylor model exceptions. More...

struct	Options
	Taylor model options. More...

Public Member Functions
unsigned int	nord () const
	Get order of the TaylorModel. More...

unsigned int	nvar () const
	Get number of variables in the TaylorModel. More...

void	reset ()
	Reset the TaylorModel. More...

	TaylorModel (const unsigned int nvar_, const unsigned int nord_)
	Constructor. More...

	~TaylorModel ()
	Destructor. More...

Static Public Member Functions
static void	pause ()
	Pause the program execution and prompt the user. More...

Public Attributes
struct TaylorModel::Options	options

Private Member Functions
void	_cleanup ()
	Clean up the arrays. More...

unsigned int	_get_binom (const unsigned int n, const unsigned int k) const
	Return binomial coefficient $\left(\stackrel{i}{j}\right)$ . More...

unsigned int	_loc_expmon (const unsigned int *iexp)
	Locates position in _posord of monomial term with variable exponents iexp. More...

void	_next_expmon (unsigned int *iexp, const unsigned int iord)
	Generate exponent configuration for subsequent monomial terms. More...

void	_reset ()
	Reset the variable bound arrays. More...

void	_set_binom ()
	Populate array _binom w/ binomial coefficients. More...

void	_set_bndmon ()
	Populate _bndmon w/ bounds on all possible monomial terms. More...

void	_set_bndpow (const unsigned int ix, const T &X, const double scaling)
	Populate _bndpow[ix] w/ bounds on the terms $[X-{\rm mid}(X)]^{ix}$ . More...

void	_set_expmon ()
	Populate array _expmon w/ exponents for monomial terms 1,...,nmon. More...

void	_set_posord ()
	Populate array _posord w/ positions of terms of degrees 1,...,nord. More...

void	_set_prodmon ()
	Populate array _prodmon w/ exponents resulting from the product of two monomial terms 1,...,nmon. More...

void	_size (const unsigned int nvar, const unsigned int nord)
	Set the order (nord) and number of variables (nvar) More...

Static Private Member Functions
template<typename U >
static void	_display (const unsigned int m, const unsigned int n, U *&a, const unsigned int lda, const std::string &stra, std::ostream &os)
	Display the elements of a 2D array. More...

Private Attributes
unsigned int *	_binom
	Binomial coefficients. More...

T *	_bndmon
	Bounds on all the monomial terms 1,...,_nmon for given interval vector . More...

T **	_bndpow
	Bounds on the terms $[X-{\rm mid}(X)]^i$ for given . More...

unsigned int *	_expmon
	Variable exponents for monomial terms 1,...,_nmon. More...

bool	_modvar
	Have any of the model variables been modified? More...

unsigned int	_nmon
	Number of monomial terms. More...

unsigned int	_nord
	Model order of the model. More...

unsigned int	_nvar
	Number of independent variables. More...

unsigned int *	_posord
	Positions of terms of degrees 1,...,_nord. More...

unsigned int **	_prodmon
	Variable exponents resulting from the product of two monomial terms 1,...,_nmon. More...

double *	_refpoint
	Reference point. More...

double *	_scaling
	Variable scaling. More...

TaylorVariable< T > *	_TV
	Taylor variable to speed-up computations and reduce dynamic allocation. More...

Friends
template<typename U >
class	TaylorModel

class	TaylorVariable< T >

Detailed Description

template<typename T>
class TaylorModel< T >

C++ class supporting the definition and computation of Taylor models for factorable functions.

mc::TaylorModel<T> is a C++ base class that supports the definition and computation of Taylor models for factorable functions on a box. The template parameter T corresponds to the type used in computing the remainder error bound.

Definition at line 52 of file taylor_model.hpp.

Constructor & Destructor Documentation

template<typename T>

TaylorModel< T >::TaylorModel	(	const unsigned int	nvar_,
		const unsigned int	nord_
	)

inline

Constructor.

Definition at line 63 of file taylor_model.hpp.

template<typename T>

TaylorModel< T >::~TaylorModel ( )

inline

Destructor.

Definition at line 67 of file taylor_model.hpp.

Member Function Documentation

template<typename T>

void TaylorModel< T >::_cleanup ( )

private

Clean up the arrays.

template<typename T>

template<typename U >

static void TaylorModel< T >::_display	(	const unsigned int	m,
		const unsigned int	n,
		U *&	a,
		const unsigned int	lda,
		const std::string &	stra,
		std::ostream &	os
	)

staticprivate

Display the elements of a 2D array.

template<typename T>

unsigned int TaylorModel< T >::_get_binom	(	const unsigned int	n,
		const unsigned int	k
	)		const

private

Return binomial coefficient $\left(\stackrel{i}{j}\right)$ .

template<typename T>

unsigned int TaylorModel< T >::_loc_expmon ( const unsigned int * iexp )

private

Locates position in _posord of monomial term with variable exponents iexp.

template<typename T>

void TaylorModel< T >::_next_expmon	(	unsigned int *	iexp,
		const unsigned int	iord
	)

private

Generate exponent configuration for subsequent monomial terms.

template<typename T>

void TaylorModel< T >::_reset ( )

private

Reset the variable bound arrays.

template<typename T>

void TaylorModel< T >::_set_binom ( )

private

Populate array _binom w/ binomial coefficients.

template<typename T>

void TaylorModel< T >::_set_bndmon ( )

private

Populate _bndmon w/ bounds on all possible monomial terms.

template<typename T>

void TaylorModel< T >::_set_bndpow	(	const unsigned int	ix,
		const T &	X,
		const double	scaling
	)

private

Populate _bndpow[ix] w/ bounds on the terms $[X-{\rm mid}(X)]^{ix}$ .

template<typename T>

void TaylorModel< T >::_set_expmon ( )

private

Populate array _expmon w/ exponents for monomial terms 1,...,nmon.

template<typename T>

void TaylorModel< T >::_set_posord ( )

private

Populate array _posord w/ positions of terms of degrees 1,...,nord.

template<typename T>

void TaylorModel< T >::_set_prodmon ( )

private

Populate array _prodmon w/ exponents resulting from the product of two monomial terms 1,...,nmon.

template<typename T>

void TaylorModel< T >::_size	(	const unsigned int	nvar,
		const unsigned int	nord
	)

private

Set the order (nord) and number of variables (nvar)

template<typename T>

unsigned int TaylorModel< T >::nord ( ) const

inline

Get order of the TaylorModel.

Definition at line 74 of file taylor_model.hpp.

template<typename T>

unsigned int TaylorModel< T >::nvar ( ) const

inline

Get number of variables in the TaylorModel.

Definition at line 71 of file taylor_model.hpp.

template<typename T>

static void TaylorModel< T >::pause ( )

static

Pause the program execution and prompt the user.

template<typename T>

void TaylorModel< T >::reset ( )

inline

Reset the TaylorModel.

Definition at line 77 of file taylor_model.hpp.

Friends And Related Function Documentation

template<typename T>

template<typename U >

friend class TaylorModel

friend

Definition at line 57 of file taylor_model.hpp.

template<typename T>

friend class TaylorVariable< T >

friend

Definition at line 56 of file taylor_model.hpp.

Member Data Documentation

template<typename T>

unsigned int* TaylorModel< T >::_binom

private

Binomial coefficients.

Definition at line 175 of file taylor_model.hpp.

template<typename T>

T* TaylorModel< T >::_bndmon

private

Bounds on all the monomial terms 1,...,_nmon for given interval vector $X$ .

Definition at line 171 of file taylor_model.hpp.

template<typename T>

T** TaylorModel< T >::_bndpow

private

Bounds on the terms $[X-{\rm mid}(X)]^i$ for given $X$ .

Definition at line 177 of file taylor_model.hpp.

template<typename T>

unsigned int* TaylorModel< T >::_expmon

private

Variable exponents for monomial terms 1,...,_nmon.

Definition at line 167 of file taylor_model.hpp.

template<typename T>

bool TaylorModel< T >::_modvar

private

Have any of the model variables been modified?

Definition at line 173 of file taylor_model.hpp.

template<typename T>

unsigned int TaylorModel< T >::_nmon

private

Number of monomial terms.

Definition at line 163 of file taylor_model.hpp.

template<typename T>

unsigned int TaylorModel< T >::_nord

private

Model order of the model.

Definition at line 159 of file taylor_model.hpp.

template<typename T>

unsigned int TaylorModel< T >::_nvar

private

Number of independent variables.

Definition at line 161 of file taylor_model.hpp.

template<typename T>

unsigned int* TaylorModel< T >::_posord

private

Positions of terms of degrees 1,...,_nord.

Definition at line 165 of file taylor_model.hpp.

template<typename T>

unsigned int** TaylorModel< T >::_prodmon

private

Variable exponents resulting from the product of two monomial terms 1,...,_nmon.

Definition at line 169 of file taylor_model.hpp.

template<typename T>

double* TaylorModel< T >::_refpoint

private

Reference point.

Definition at line 179 of file taylor_model.hpp.

template<typename T>

double* TaylorModel< T >::_scaling

private

Variable scaling.

Definition at line 181 of file taylor_model.hpp.

template<typename T>

TaylorVariable<T>* TaylorModel< T >::_TV

private

Taylor variable to speed-up computations and reduce dynamic allocation.

Definition at line 184 of file taylor_model.hpp.

template<typename T>

struct TaylorModel::Options TaylorModel< T >::options

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

taylor_model.hpp

Classes

Public Member Functions

Static Public Member Functions

Public Attributes

Private Member Functions

Static Private Member Functions

Private Attributes

Friends

Detailed Description

template<typename T> class TaylorModel< T >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename T>
class TaylorModel< T >