This class defines the unimodal map "2 |x|^gamma - a" on [-1,1] with the usage of interval arithmetic. More...

#include </cur/unifexp/mapunimi.h>

Inheritance diagram for unifexp::mapUnimodalIntv< numType >:

Public Member Functions
	mapUnimodalIntv (const numType &_gamma1, const numType &_gamma2=1)
	The constructor.
std::string	name () const
	Returns the name of the object.
int	countCritical () const
	Returns the number of critical points.
numType	criticalPoint (int n) const
	Returns the subsequent critical points.
numType	leftBound () const
	Returns the left bound of the domain of the map.
numType	rightBound () const
	Returns the right bound of the domain of the map.
void	image (const numType &x1, const numType &x2, numType &y1, numType &y2) const
	Computes an enclosure of the image of the given interval.
numType	minLogDerivative (const numType &x1, const numType &x2, const numType &y1, const numType &y2) const
	Computes the minimal log of the derivative over those points in the interval [x1,x2] whose images may fall into [y1,y2].
Private Member Functions
numType	gammaRoot (numType x, bool upperBound) const
	An auxiliary function for the computation of the root of degree gamma of the absolute value of a number.
Private Attributes
IntervalType	gamma
	The exponent of the map.
IntervalType	log2gamma
	The cached value of log (2 gamma).

Detailed Description

template<class numType>
class unifexp::mapUnimodalIntv< numType >

This class defines the unimodal map "2 |x|^gamma - a" on [-1,1] with the usage of interval arithmetic.

It is suitable for rigorous computations. Recommended values of gamma are between 1 and 3. Valid values of the parameter are between 0.5+ and 1 (optimal value: 1).

Definition at line 57 of file mapunimi.h.

Constructor & Destructor Documentation

template<class numType >

unifexp::mapUnimodalIntv< numType >::mapUnimodalIntv	(	const numType &	_gamma1,
		const numType &	_gamma2 = `1`
	)		`[inline]`

The constructor.

Provide the numerator and the denominator for the exponent gamma to make sure its value is computed in a rigorous way as an interval.

Definition at line 106 of file mapunimi.h.

Member Function Documentation

template<class numType >

int unifexp::mapUnimodalIntv< numType >::countCritical ( ) const [inline, virtual]

Returns the number of critical points.

Implements unifexp::mapType< numType >.

Definition at line 124 of file mapunimi.h.

template<class numType >

numType unifexp::mapUnimodalIntv< numType >::criticalPoint ( int n ) const [inline, virtual]

Returns the subsequent critical points.

Implements unifexp::mapType< numType >.

Definition at line 130 of file mapunimi.h.

template<class numType >

numType unifexp::mapUnimodalIntv< numType >::gammaRoot	(	numType	x,
		bool	upperBound
	)		const `[inline, private]`

An auxiliary function for the computation of the root of degree gamma of the absolute value of a number.

Returns the upper or lower bound for the result.

Definition at line 148 of file mapunimi.h.

template<class numType >

void unifexp::mapUnimodalIntv< numType >::image	(	const numType &	x1,
		const numType &	x2,
		numType &	y1,
		numType &	y2
	)		const `[inline, virtual]`

Computes an enclosure of the image of the given interval.

Implements unifexp::mapType< numType >.

Definition at line 175 of file mapunimi.h.

References unifexp::resetRounding().

template<class numType >

numType unifexp::mapUnimodalIntv< numType >::leftBound ( ) const [inline, virtual]

Returns the left bound of the domain of the map.

Implements unifexp::mapType< numType >.

Definition at line 136 of file mapunimi.h.

template<class numType >

numType unifexp::mapUnimodalIntv< numType >::minLogDerivative	(	const numType &	x1,
		const numType &	x2,
		const numType &	y1,
		const numType &	y2
	)		const `[inline, virtual]`