casa::Lorentzian1D< T > Class Template Reference

A one dimensional Lorentzian class. More...

#include <Lorentzian1D.h>

Inheritance diagram for casa::Lorentzian1D< T >:

List of all members.

Public Member Functions
	Lorentzian1D ()
	Constructs the one dimensional Lorentzians.
	Lorentzian1D (const T &height)
	Lorentzian1D (const T &height, const T &center)
	Lorentzian1D (const T &height, const T &center, const T &width)
	Lorentzian1D (const Lorentzian1D< T > &other)
	Copy constructor (deep copy)
template<class W >
	Lorentzian1D (const Lorentzian1D< W > &other)
Lorentzian1D< T > &	operator= (const Lorentzian1D< T > &other)
	Copy assignment (deep copy)
virtual	~Lorentzian1D ()
	Destructor.
virtual T	eval (typename Function1D< T >::FunctionArg x) const
	Evaluate the Lorentzian at x.
virtual Function< T > *	clone () const
	Return a copy of this object from the heap.
virtual Function< typename FunctionTraits< T >::DiffType > *	cloneAD () const
virtual Function< typename FunctionTraits< T >::BaseType > *	cloneNonAD () const

---

Detailed Description

template<class T>
class casa::Lorentzian1D< T >

A one dimensional Lorentzian class.

Intended use:

Public interface

Review Status

Reviewed By:

tcornwel

Date Reviewed:

1996/02/22

Test programs:

tLorentzian1D

Prerequisite

• Lorentzian1DParam
• Function

Etymology

A Lorentzian1D functional is designed exclusively for calculating a Lorentzian (or Normal) distribution in one dimension. Other classes exist for calculating these functions in two ( Lorentzian2D ) and N ( LorentzianND ) dimensions.

Synopsis

A Lorentzian1D is described by a height, center, and width. Its fundamental operation is evaluating itself at some x. The parameters (height, center and width) may be changed at run time.

The width of the Lorentzian (for the constructors or the setWidth function) is always specified in terms of the full width at half maximum (FWHM). It is always positive and attempts to set a non-positive width will throw an assertion when in debug mode.

The peak height of the Lorentzian can be specified at construction time or by using the setHeight function. Alternatively the setFlux function can be used to implicitly set the peak height by specifying the integrated area under the Lorentzian. The height (or flux) can be positive, negative or zero, as this class makes no assumptions on what quantity the height represents.

Tip: Changing the width of the Lorentzian will not affect its peak height but will change its flux; So you should always set the width before setting the flux;

The parameter interface (see Lorentzian1DParam class), is used to provide an interface to the Fitting classes.

There are 3 parameters that are used to describe the Lorentzian:

1. The height of the Lorentzian. This is identical to the value returned using the height() member function.
2. The center of the Lorentzian in the x direction. This is identical to the value returned using the center() member function.
3. The width (FWHM) of the Lorentzian. To aid convergence of the non-linear fitting routines this parameter is allowed to be negative. This does not affect the shape of the Lorentzian as the square of the width is used when evaluating the function.

An enumeration for the HEIGHT, WIDTH and CENTER parameter index is provided, enabling the setting and reading of parameters with the [] operator. The mask() methods can be used to check and set the parameter masks.

Example

       Lorentzian<Double> gf(5.0, 25.0, 7);
       gf(25);            // = 5.0
       gf[HEIGHT](1.0);
       gf.setWidth(2.0);                
       gf[CENTER](0.0);
       gf(1);             // = 0.5*height = 0.5

Template Type Argument Requirements (T)

• T should have standard numerical operators and exp() function. Current implementation only tested for real types.
• To obtain derivatives, the derivatives should be defined.

Thrown Exceptions

• Assertion in debug mode if attempt is made to set a negative width
• AipsError if incorrect parameter number specified.
• Assertion in debug mode if operator(Vector<>) with empty Vector

To Do

• Lorentzians that know about their DFT's could be required eventually.

Definition at line 135 of file Lorentzian1D.h.

---

Constructor & Destructor Documentation

template<class T>

casa::Lorentzian1D< T >::Lorentzian1D

(

)

[inline]

Constructs the one dimensional Lorentzians.

Defaults: height=1, center=0, width(FWHM)=1.
Warning: Could not use default arguments that worked both with gcc and IRIX

Definition at line 145 of file Lorentzian1D.h.

template<class T>

casa::Lorentzian1D< T >::Lorentzian1D

(

const T &

height

)

[inline, explicit]

Definition at line 146 of file Lorentzian1D.h.

template<class T>

casa::Lorentzian1D< T >::Lorentzian1D	(	const T &	height,
		const T &	center
	)		[inline]

Definition at line 147 of file Lorentzian1D.h.

template<class T>

casa::Lorentzian1D< T >::Lorentzian1D	(	const T &	height,
		const T &	center,
		const T &	width
	)		[inline]

Definition at line 149 of file Lorentzian1D.h.

template<class T>

casa::Lorentzian1D< T >::Lorentzian1D

(

const Lorentzian1D< T > &

other

)

[inline]

Copy constructor (deep copy)

Definition at line 155 of file Lorentzian1D.h.

template<class T>

template<class W >

casa::Lorentzian1D< T >::Lorentzian1D

(

const Lorentzian1D< W > &

other

)

[inline]

Definition at line 157 of file Lorentzian1D.h.

template<class T>

virtual casa::Lorentzian1D< T >::~Lorentzian1D

(

)

[inline, virtual]

Destructor.

Definition at line 165 of file Lorentzian1D.h.

---

Member Function Documentation

template<class T>

virtual Function<T>* casa::Lorentzian1D< T >::clone

(

)

const [inline, virtual]

Return a copy of this object from the heap.

The caller is responsible for deleting this pointer.

Implements casa::Function< T, T >.

Definition at line 177 of file Lorentzian1D.h.

template<class T>

virtual Function<typename FunctionTraits<T>::DiffType>* casa::Lorentzian1D< T >::cloneAD

(

)

const [inline, virtual]

Reimplemented from casa::Function< T, T >.

Definition at line 178 of file Lorentzian1D.h.

template<class T>

virtual Function<typename FunctionTraits<T>::BaseType>* casa::Lorentzian1D< T >::cloneNonAD

(

)

const [inline, virtual]

Reimplemented from casa::Function< T, T >.

Definition at line 180 of file Lorentzian1D.h.

template<class T>

virtual T casa::Lorentzian1D< T >::eval

(

typename Function1D< T >::FunctionArg

x

)

const [virtual]

Evaluate the Lorentzian at x.

template<class T>

Lorentzian1D<T>& casa::Lorentzian1D< T >::operator=

(

const Lorentzian1D< T > &

other

)

[inline]

Copy assignment (deep copy)

Definition at line 161 of file Lorentzian1D.h.

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

• casacore/scimath/Functionals/Lorentzian1D.h