TaylorVariable< T > Class Template Reference

C++ template class for definition of and operation on variables in a Taylor model. More...

#include <taylor_model.hpp>

Public Member Functions
T	B () const
	Return range bounder. More...
T	bound () const
	Return range bounder. More...
const T &	boundT () const
	Return reference to range bounder in T arithmetic. More...
TaylorVariable< T > &	C ()
	Recenter remainder term. More...
TaylorVariable< T > &	center ()
	Return reference to current remainder. More...
double	constant () const
	Return coefficient value in constant term. More...
TaylorModel< T > *	env () const
	Return pointer to TaylorModel environment. More...
BooleanType	isCompact () const
double *	linear () const
	Return pointer to array of size nvar comprising coefficients in linear term. More...
TaylorVariable< T > &	operator*= (const TaylorVariable< T > &)
TaylorVariable< T > &	operator*= (const double)
TaylorVariable< T > &	operator*= (const T &)
template<typename U >
TaylorVariable< T > &	operator+= (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< T > &	operator+= (const U &)
TaylorVariable< T > &	operator+= (const double)
template<typename U >
TaylorVariable< T > &	operator-= (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< T > &	operator-= (const U &)
TaylorVariable< T > &	operator-= (const double)
TaylorVariable< T > &	operator/= (const TaylorVariable< T > &)
TaylorVariable< T > &	operator/= (const double)
TaylorVariable< T > &	operator= (const double)
	More overloaded operators. More...
TaylorVariable< T > &	operator= (const TaylorVariable< T > &)
TaylorVariable< T > &	operator= (const T &)
TaylorVariable< T >	P () const
	Cancel remainder error term and return polynomial part. More...
double	P (const double *x) const
	Evaluate polynomial part at point x More...
TaylorVariable< T >	polynomial () const
	Cancel remainder term and return polynomial part. More...
double	polynomial (const double *x) const
	Evaluate polynomial part at point x More...
double *	quadratic (const int opt=0) const
	Return pointer to array of size nvar comprising coefficients in quadratic term (diagonal coefs if opt=0; upper triangular part otherwise) More...
T	R () const
	Return const reference to current remainder. More...
double *	reference () const
	Return pointer to array of size nvar comprising reference point. More...
T	remainder () const
	Return const reference to current remainder. More...
TaylorVariable< T > &	set (TaylorModel< T > *TM, const unsigned int ix, const T &X)
	Set the index and range for the variable ivar, that belongs to the interval X. More...
	TaylorVariable (const double d=0.)
	Constructor for a real scalar. More...
	TaylorVariable (const T &B)
	Constructor for a T variable. More...
	TaylorVariable (TaylorModel< T > *TM, const unsigned int ix, const T &X)
	Constructor for the variable ix, that belongs to the interval X More...
	TaylorVariable (const TaylorVariable< T > &TV)
	Copy constructor for identical range bounder. More...
template<typename U >
	TaylorVariable (TaylorModel< T > *&TM, const TaylorVariable< U > &TV)
	Copy constructor for different range bounder with implicit type conversion. More...
template<typename U >
	TaylorVariable (TaylorModel< T > *&TM, const TaylorVariable< U > &TV, const T &(U::*method)() const )
	Copy constructor for different range bounder with explicit type conversion class member function. More...
template<typename U >
	TaylorVariable (TaylorModel< T > *&TM, const TaylorVariable< U > &TV, T(*method)(const U &))
	Copy constructor for different range bounder with explicit type conversion non-class function. More...
	TaylorVariable (TaylorModel< T > *TM, const double d=0.)
	Private constructor for a real scalar in a specific TaylorModel. More...
	~TaylorVariable ()
	Class destructor. More...

Private Member Functions
const T &	_bndmon (const unsigned int i) const
	Get bounds on all monomial terms in TaylorModel. More...
T &	_bound (T &bndmod) const
	Range bounder. More...
T &	_bound_eigen (T &bndmod) const
	Range bounder - eignevalue decomposition-based approach. More...
T &	_bound_LSB (T &bndmod) const
	Range bounder - Lin & Stadtherr approach. More...
T &	_bound_naive (T &bndmod) const
	Range bounder - naive approach. More...
void	_center_TM ()
	Center remainder error term _bndrem. More...
void	_clean ()
	Clean private members. More...
unsigned int	_expmon (const unsigned int i) const
	Get monomial term exponents in TaylorModel. More...
void	_init ()
	Initialize private members. More...
TaylorVariable< T >	_intpow (const TaylorVariable< T > &TM, const int n)
	Recursive calculation of nonnegative integer powers. More...
unsigned int	_nmon () const
	Get number of monomial terms in TaylorModel. More...
unsigned int	_nord () const
	Get model order in TaylorModel. More...
unsigned int	_nvar () const
	Get number of variables in TaylorModel. More...
unsigned int	_posord (const unsigned int i) const
	Get term positions in TaylorModel. More...
unsigned int	_prodmon (const unsigned int i, const unsigned int j) const
	Get exponents of monomial term products in TaylorModel. More...
double	_refpoint (const unsigned int i) const
	Get reference point in TaylorModel. More...
void	_reinit ()
	Reinitialize private members. More...
double	_scaling (const unsigned int i) const
	Get scaling in TaylorModel. More...
TaylorVariable< T > *	_TV () const
	Get pointer to internal TaylorVariable in TaylorModel. More...
void	_update_bndord ()
	Update _bndord w/ (naive) bounds for individual terms of degrees 0,...,_nord() More...
	TaylorVariable (TaylorModel< T > *TM, const T &B)
	Private constructor for a range in a specific TaylorModel. More...

Static Private Member Functions
static double *	_eigen (const unsigned int n, double *a)
	Wrapper to LAPACK function _dsyev doing eigenvalue decomposition of a symmetric matrix. More...

Private Attributes
T *	_bndord
	Bounds for individual terms of degrees 0,...,_nord+1. More...
T *	_bndrem
	Pointer to the remainder error bound. More...
T	_bndT
	Interval bound evaluated in T arithmetic. More...
double *	_coefmon
	Coefficients for monomial terms 1,...,nmon. More...
TaylorModel< T > *	_TM
	Pointer to underlying TaylorModel object. More...

Friends
template<typename U >
TaylorVariable< U >	acos (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	asin (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	atan (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	cos (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	exp (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	hull (const TaylorVariable< U > &, const TaylorVariable< U > &)
template<typename U >
bool	inter (TaylorVariable< U > &, const TaylorVariable< U > &, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	inv (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	log (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator* (const TaylorVariable< U > &, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator* (const double, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator* (const TaylorVariable< U > &, const double)
template<typename U >
TaylorVariable< U >	operator* (const U &, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator* (const TaylorVariable< U > &, const U &)
template<typename U >
TaylorVariable< U >	operator+ (const TaylorVariable< U > &)
template<typename U , typename V >
TaylorVariable< U >	operator+ (const TaylorVariable< U > &, const TaylorVariable< V > &)
template<typename U , typename V >
TaylorVariable< U >	operator+ (const TaylorVariable< U > &, const V &)
template<typename U , typename V >
TaylorVariable< U >	operator+ (const V &, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator+ (const double, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator+ (const TaylorVariable< U > &, const double)
template<typename U >
TaylorVariable< U >	operator- (const TaylorVariable< U > &)
template<typename U , typename V >
TaylorVariable< U >	operator- (const TaylorVariable< U > &, const TaylorVariable< V > &)
template<typename U , typename V >
TaylorVariable< U >	operator- (const TaylorVariable< U > &, const V &)
template<typename U , typename V >
TaylorVariable< U >	operator- (const V &, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator- (const double, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator- (const TaylorVariable< U > &, const double)
template<typename U >
TaylorVariable< U >	operator/ (const TaylorVariable< U > &, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator/ (const double, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	operator/ (const TaylorVariable< U > &, const double)
template<typename U >
std::ostream &	operator<< (std::ostream &, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	pow (const TaylorVariable< U > &, const int)
template<typename U >
TaylorVariable< U >	pow (const TaylorVariable< U > &, const double)
template<typename U >
TaylorVariable< U >	pow (const double, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	pow (const TaylorVariable< U > &, const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	sin (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	sqr (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	sqrt (const TaylorVariable< U > &)
template<typename U >
TaylorVariable< U >	tan (const TaylorVariable< U > &)
template<typename U >
void	TaylorModel (const unsigned int nvar, const unsigned int nord)
template<typename U >
class	TaylorVariable
template<typename U >
TaylorVariable< U >	xlog (const TaylorVariable< U > &)

Detailed Description

template<typename T>
class TaylorVariable< T >

C++ template class for definition of and operation on variables in a Taylor model.

mc::TaylorVariable<T> is a C++ template class for definition of and operation on the variables participating in a Taylor model of a factorable function. The template parameter T corresponds to the type used in computing the remainder error bound in the Taylor model.

Definition at line 42 of file taylor_model.hpp.

Constructor & Destructor Documentation

template<typename T>

TaylorVariable< T >::TaylorVariable	(	TaylorModel< T > *	TM,
		const double	d = 0.
	)

Private constructor for a real scalar in a specific TaylorModel.

template<typename T>

TaylorVariable< T >::TaylorVariable ( TaylorModel< T > *  TM, const T &  B  )

private

Private constructor for a range in a specific TaylorModel.

Member Function Documentation

template<typename T>

const T& TaylorVariable< T >::_bndmon ( const unsigned int  i ) const

inlineprivate

Get bounds on all monomial terms in TaylorModel.

Definition at line 168 of file taylor_variable.hpp.

template<typename T>

T& TaylorVariable< T >::_bound ( T &  bndmod ) const

private

Range bounder.

template<typename T>

T& TaylorVariable< T >::_bound_eigen ( T &  bndmod ) const

private

Range bounder - eignevalue decomposition-based approach.

template<typename T>

T& TaylorVariable< T >::_bound_LSB ( T &  bndmod ) const

private

Range bounder - Lin & Stadtherr approach.

template<typename T>

T& TaylorVariable< T >::_bound_naive ( T &  bndmod ) const

private

Range bounder - naive approach.

template<typename T>

void TaylorVariable< T >::_center_TM ( )

private

Center remainder error term _bndrem.

template<typename T>

void TaylorVariable< T >::_clean ( )

private

Clean private members.

template<typename T>

static double* TaylorVariable< T >::_eigen ( const unsigned int  n, double *  a  )

staticprivate

Wrapper to LAPACK function _dsyev doing eigenvalue decomposition of a symmetric matrix.

template<typename T>

unsigned int TaylorVariable< T >::_expmon ( const unsigned int  i ) const

inlineprivate

Get monomial term exponents in TaylorModel.

Definition at line 160 of file taylor_variable.hpp.

template<typename T>

void TaylorVariable< T >::_init ( )

private

Initialize private members.

template<typename T>

TaylorVariable<T> TaylorVariable< T >::_intpow ( const TaylorVariable< T > &  TM, const int  n  )

private

Recursive calculation of nonnegative integer powers.

template<typename T>

unsigned int TaylorVariable< T >::_nmon ( ) const

inlineprivate

Get number of monomial terms in TaylorModel.

Definition at line 152 of file taylor_variable.hpp.

template<typename T>

unsigned int TaylorVariable< T >::_nord ( ) const

inlineprivate

Get model order in TaylorModel.

Definition at line 146 of file taylor_variable.hpp.

template<typename T>

unsigned int TaylorVariable< T >::_nvar ( ) const

inlineprivate

Get number of variables in TaylorModel.

Definition at line 149 of file taylor_variable.hpp.

template<typename T>

unsigned int TaylorVariable< T >::_posord ( const unsigned int  i ) const

inlineprivate

Get term positions in TaylorModel.

Definition at line 156 of file taylor_variable.hpp.

template<typename T>

unsigned int TaylorVariable< T >::_prodmon ( const unsigned int  i, const unsigned int  j  ) const

inlineprivate

Get exponents of monomial term products in TaylorModel.

Definition at line 164 of file taylor_variable.hpp.

template<typename T>

double TaylorVariable< T >::_refpoint ( const unsigned int  i ) const

inlineprivate

Get reference point in TaylorModel.

Definition at line 172 of file taylor_variable.hpp.

template<typename T>

void TaylorVariable< T >::_reinit ( )

private

Reinitialize private members.

template<typename T>

double TaylorVariable< T >::_scaling ( const unsigned int  i ) const

inlineprivate

Get scaling in TaylorModel.

Definition at line 176 of file taylor_variable.hpp.

template<typename T>

TaylorVariable<T>* TaylorVariable< T >::_TV ( ) const

inlineprivate

Get pointer to internal TaylorVariable in TaylorModel.

Definition at line 143 of file taylor_variable.hpp.

template<typename T>

void TaylorVariable< T >::_update_bndord ( )

private

Update _bndord w/ (naive) bounds for individual terms of degrees 0,...,_nord()

template<typename T>

BooleanType TaylorVariable< T >::isCompact

(

)

const

Routine which returns BT_FALSE if there are components equal to "nan" or "INFTY".
Otherwise, BT_TRUE is returned.

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator*=

(

const TaylorVariable< T > &

)

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator*=

(

const double

)

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator*=

(

const T &

)

template<typename T>

template<typename U >

TaylorVariable<T>& TaylorVariable< T >::operator+=

(

const TaylorVariable< U > &

)

template<typename T>

template<typename U >

TaylorVariable<T>& TaylorVariable< T >::operator+=

(

const U &

)

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator+=

(

const double

)

template<typename T>

template<typename U >

TaylorVariable<T>& TaylorVariable< T >::operator-=

(

const TaylorVariable< U > &

)

template<typename T>

template<typename U >

TaylorVariable<T>& TaylorVariable< T >::operator-=

(

const U &

)

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator-=

(

const double

)

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator/=

(

const TaylorVariable< T > &

)

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator/=

(

const double

)

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator=

(

const double

)

More overloaded operators.

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator=

(

const TaylorVariable< T > &

)

template<typename T>

TaylorVariable<T>& TaylorVariable< T >::operator=

(

const T &

)

Friends And Related Function Documentation

template<typename T>

template<typename U >

TaylorVariable<U> acos ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> asin ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> atan ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> cos ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> exp ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> hull ( const TaylorVariable< U > &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

bool inter ( TaylorVariable< U > &  , const TaylorVariable< U > &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> inv ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> log ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator* ( const TaylorVariable< U > &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator* ( const double  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator* ( const TaylorVariable< U > &  , const double    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator* ( const U &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator* ( const TaylorVariable< U > &  , const U &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator+ ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U , typename V >

TaylorVariable<U> operator+ ( const TaylorVariable< U > &  , const TaylorVariable< V > &    )

friend

template<typename T>

template<typename U , typename V >

TaylorVariable<U> operator+ ( const TaylorVariable< U > &  , const V &    )

friend

template<typename T>

template<typename U , typename V >

TaylorVariable<U> operator+ ( const V &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator+ ( const double  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator+ ( const TaylorVariable< U > &  , const double    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator- ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U , typename V >

TaylorVariable<U> operator- ( const TaylorVariable< U > &  , const TaylorVariable< V > &    )

friend

template<typename T>

template<typename U , typename V >

TaylorVariable<U> operator- ( const TaylorVariable< U > &  , const V &    )

friend

template<typename T>

template<typename U , typename V >

TaylorVariable<U> operator- ( const V &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator- ( const double  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator- ( const TaylorVariable< U > &  , const double    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator/ ( const TaylorVariable< U > &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator/ ( const double  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> operator/ ( const TaylorVariable< U > &  , const double    )

friend

template<typename T>

template<typename U >

std::ostream& operator<< ( std::ostream &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> pow ( const TaylorVariable< U > &  , const int    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> pow ( const TaylorVariable< U > &  , const double    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> pow ( const double  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> pow ( const TaylorVariable< U > &  , const TaylorVariable< U > &    )

friend

template<typename T>

template<typename U >

TaylorVariable<U> sin ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> sqr ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> sqrt ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

TaylorVariable<U> tan ( const TaylorVariable< U > &  )

friend

template<typename T>

template<typename U >

void TaylorModel ( const unsigned int  nvar, const unsigned int  nord  )

friend

template<typename T>

template<typename U >

friend class TaylorVariable

friend

Definition at line 57 of file taylor_variable.hpp.

template<typename T>

template<typename U >

TaylorVariable<U> xlog ( const TaylorVariable< U > &  )

friend

Member Data Documentation

template<typename T>

T* TaylorVariable< T >::_bndord

private

Bounds for individual terms of degrees 0,...,_nord+1.

Definition at line 333 of file taylor_variable.hpp.

template<typename T>

T* TaylorVariable< T >::_bndrem

private

Pointer to the remainder error bound.

Definition at line 335 of file taylor_variable.hpp.

template<typename T>

T TaylorVariable< T >::_bndT

private

Interval bound evaluated in T arithmetic.

Definition at line 337 of file taylor_variable.hpp.

template<typename T>

double* TaylorVariable< T >::_coefmon

private

Coefficients for monomial terms 1,...,nmon.

Definition at line 331 of file taylor_variable.hpp.

template<typename T>

TaylorModel<T>* TaylorVariable< T >::_TM

private

Pointer to underlying TaylorModel object.

Definition at line 141 of file taylor_variable.hpp.

---

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

• taylor_model.hpp
• taylor_variable.hpp