A two dimensional Gaussian class. More...

#include <Gaussian2D.h>

Inheritance diagram for casacore::Gaussian2D< T >:

Public Member Functions
	Gaussian2D ()
	Constructs the two dimensional Gaussians. More...

	Gaussian2D (const T &height, const Vector< T > &center, const Vector< T > &width, const T &pa)

	Gaussian2D (const T &height, const T &xCenter, const T &yCenter, const T &majorAxis, const T &axialRatio, const T &pa)

	Gaussian2D (const Gaussian2D< T > &other)
	Copy constructor (deep copy) More...

template<class W >
	Gaussian2D (const Gaussian2D< W > &other)

Gaussian2D< T > &	operator= (const Gaussian2D< T > &other)
	Copy assignment (deep copy) More...

virtual	~Gaussian2D ()
	Destructor. More...

virtual T	eval (typename Function< T >::FunctionArg x) const
	Evaluate the Gaussian at `x`. More...

virtual Function< T > *	clone () const
	Return a copy of this object from the heap. More...

virtual Function< typename FunctionTraits< T >::DiffType > *	cloneAD () const

virtual Function< typename FunctionTraits< T >::BaseType > *	cloneNonAD () const

Public Member Functions inherited from casacore::Gaussian2DParam< T >
	Gaussian2DParam ()
	Constructs the two dimensional Gaussians. More...

	Gaussian2DParam (const T &height, const Vector< T > &center, const Vector< T > &width, const T &pa)

	Gaussian2DParam (const T &height, const T &xCenter, const T &yCenter, const T &majorAxis, const T &axialRatio, const T &pa)

	Gaussian2DParam (const Gaussian2DParam< T > &other)
	Copy constructor (deep copy) More...

template<class W >
	Gaussian2DParam (const Gaussian2DParam< W > &other)

Gaussian2DParam< T > &	operator= (const Gaussian2DParam< T > &other)
	Copy assignment (deep copy) More...

virtual	~Gaussian2DParam ()
	Destructor. More...

virtual uInt	ndim () const
	Variable dimensionality. More...

virtual const String &	name () const
	Give name of function. More...

T	height () const
	Get or set the peak height of the Gaussian. More...

void	setHeight (const T &height)

T	flux () const
	Get or set the analytical integrated area underneath the Gaussian. More...

void	setFlux (const T &flux)

Vector< T >	center () const
	Get or set the center ordinate of the Gaussian. More...

void	setCenter (const Vector< T > &center)

T	xCenter () const

void	setXcenter (const T &cnter)

T	yCenter () const

void	setYcenter (const T &cnter)

Vector< T >	width () const
	Set or get the FWHM of the Gaussian. More...

void	setWidth (const Vector< T > &width)

T	majorAxis () const

void	setMajorAxis (const T &width)

T	minorAxis () const

void	setMinorAxis (const T &width)

T	axialRatio () const

void	setAxialRatio (const T &axialRatio)

T	PA () const
	Set/get the rotation angle (orientation) of the Gaussian. More...

void	setPA (const T &pa)

Public Member Functions inherited from casacore::Function< T >
	Function ()
	Constructors. More...

	Function (const uInt n)

	Function (const Vector< T > &in)

	Function (const FunctionParam< T > &other)

	Function (const Function< W, X > &other)

	Function (const Function< T, U > &other)

virtual	~Function ()
	Destructor. More...

uInt	nparameters () const
	Returns the number of parameters. More...

virtual U	eval (FunctionArg x) const =0
	Evaluate the function object. More...

T &	operator[] (const uInt n)
	Manipulate the nth parameter (0-based) with no index check. More...

const T &	operator[] (const uInt n) const

virtual U	operator() () const
	Evaluate this function object at `x`or at `x, y`. More...

virtual U	operator() (const ArgType &x) const

virtual U	operator() (const Vector< ArgType > &x) const

virtual U	operator() (FunctionArg x) const

virtual U	operator() (const ArgType &x, const ArgType &y) const

virtual U	operator() (const ArgType &x, const ArgType &y, const ArgType &z) const

Bool &	mask (const uInt n)
	Manipulate the mask associated with the nth parameter (e.g. More...

const Bool &	mask (const uInt n) const

const FunctionParam< T > &	parameters () const
	Return the parameter interface. More...

FunctionParam< T > &	parameters ()

const Vector< ArgType > &	argp () const
	Get `arg_p` and `parset_p`. More...

Bool	parsetp () const

void	lockParam ()
	Compiler cannot always find the correct 'const' version of parameter access. More...

void	unlockParam ()

virtual void	setMode (const RecordInterface &mode)
	get/set the function mode. More...

virtual void	getMode (RecordInterface &mode) const

virtual Bool	hasMode () const
	return True if the implementing function supports a mode. More...

ostream &	print (ostream &os) const
	Print the function (i.e. More...

Public Member Functions inherited from casacore::Functional< FunctionTraits< T >::ArgType, U >
virtual	~Functional ()
	Destructor. More...

virtual U	operator() (const FunctionTraits< T >::ArgType &x) const =0
	Map a Domain `x` into a Range `y` value. More...

Public Member Functions inherited from casacore::Functional< Vector< FunctionTraits< T >::ArgType >, U >
virtual	~Functional ()
	Destructor. More...

virtual U	operator() (const Vector< FunctionTraits< T >::ArgType > &x) const =0
	Map a Domain `x` into a Range `y` value. More...

Additional Inherited Members
Public Types inherited from casacore::Gaussian2DParam< T >
enum	{ HEIGHT, XCENTER, YCENTER, YWIDTH, RATIO, PANGLE }

Public Types inherited from casacore::Function< T >
typedef FunctionTraits< T > ::ArgType	ArgType

typedef const ArgType *	FunctionArg

Protected Attributes inherited from casacore::Gaussian2DParam< T >
T	fwhm2int
	Constant to scale halfwidth at 1/e to FWHM. More...

T	thePA
	cached vale of the PA More...

T	theSpa
	cached values of the cos and sine of thePA More...

T	theCpa

T	theXwidth
	cached vale of the Xwidth = ratio*theYwidth; More...

Protected Attributes inherited from casacore::Function< T >
FunctionParam< T >	param_p
	The parameters and masks. More...

Vector< ArgType >	arg_p
	Aid for non-contiguous argument storage. More...

Bool	parset_p
	Indicate parameter written. More...

Bool	locked_p
	Indicate that parameters are expected to be locked from changing. More...

Detailed Description

template<class T>
class casacore::Gaussian2D< T >

A two dimensional Gaussian class.

Intended use:

Public interface

Review Status

Reviewed By:: tcornwel
Date Reviewed:: 1996/02/22
Test programs:: tGaussian2D

Prerequisite

Etymology

A Gaussian2D functional is designed exclusively for calculating a Gaussian (or Normal) distribution in two dimensions. Other classes exist for calculating these functions in two (Gaussian1D) and N (GaussianND) dimensions.

Synopsis

A Gaussian2D is described by a height, center, and width, and position angle. Its fundamental operation is evaluating itself at some (x,y) coordinate. Its parameters (height, center and width, position angle) may be changed at run time.

The width of the Gaussian (for the constructors or the setWidth function) is always specified in terms of the full width at half maximum (FWHM). The major axis is parallel with the y axis when the position angle is zero. The major axis will always have a larger width than the minor axis.

It is not possible to set the width of the major axis (using the setMajorAxis function) smaller than the width of the current minor axis. Similarly it is not possible to set the width of the minor axis (using the setMinorAxis function) to be larger than the current major axis. Exceptions are thrown if these rules are violated or if the either the major or minor axis is set to a non-positive width. To set both axis in one hit use the setWidth function. All these restrictions can be overcome when the parameters interface is used (see below).

The position angle is the angle between the y axis and the major axis and is measured counterclockwise, so a position angle of 45 degrees rotates the major axis to the line where y=-x. The position angle is always specified and returned in radians. When using the setPA function its value must be between -2pi and + 2pi, and the returned value from the pa function will always be a value between 0 and pi.

The axial ratio can be used as an alternative to specifying the width of the minor axis. It is the ratio between the minor and major axis widths. The axial ratio is constrained to be between zero and one, and specifying something different (using setAxialRatio) will throw an exception.

The peak height of the Gaussian 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 Gaussian. 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 Gaussian 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 Gaussian2DParam class), is used to provide an interface to the Fitting classes.

There are 6 parameters that are used to describe the Gaussian:

The height of the Gaussian. This is identical to the value returned using the height member function.
The center of the Gaussian in the x direction. This is identical to the value returned using the xCenter member function.
The center of the Gaussian in the y direction. This is identical to the value returned using the yCenter member function.
The width (FWHM) of the Gaussian on one axis. Initially this will be the major axis, but if the parameters are adjusted by a Fitting class, it may become the axis with the smaller width. To aid convergence of the non-linear fitting routines this parameter is allowed to be negative. This does not affect the shape of the Gaussian as the squares of the widths are used when evaluating the function.
A modified axial ratio. This parameter is the ratio of the width on the 'other' axis (which initially is the minor axis) and axis given by parameter YWIDTH. Because these internal widths are allowed to be negative and because there is no constraints on which axis is the larger one the modified axial ratio is not constrained to be between zero and one.
The position angle. This represents the angle (in radians) between the axis used by parameter 4, and the y axis, measured counterclockwise. If parameter 4 represents the major axis width then this parameter will be identical to the position angle, otherwise it will be different by 90 degrees. The tight constraints on the value of the rotation angle enforced by the setPA() function are relaxed so that any value between -6000 and 6000 is allowed. It is still interpreted in radians.

An enumeration for the 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

Gaussian2D<Double> g(10.0, 0.0, 0.0, 2.0, 1.0, 0.0);
Vector<Double> x(2);
x(0) = 1.0; x(1) = 0.5;
cout << "g(" << x(0) << "," << x(1) << ") = " << g(x) << endl;

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

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

Definition at line 179 of file Gaussian2D.h.

Constructor & Destructor Documentation

template<class T>

casacore::Gaussian2D< T >::Gaussian2D ( )

inline

Constructs the two dimensional Gaussians.

Defaults: height=1, center=0, width(FWHM)=1, PA=0. The center and width vectors must have two elements
Warning: Could not use default arguments that worked both with gcc and IRIX

Definition at line 191 of file Gaussian2D.h.

template<class T>

casacore::Gaussian2D< T >::Gaussian2D	(	const T &	height,
		const Vector< T > &	center,
		const Vector< T > &	width,
		const T &	pa
	)

inline

Definition at line 192 of file Gaussian2D.h.

template<class T>

casacore::Gaussian2D< T >::Gaussian2D	(	const T &	height,
		const T &	xCenter,
		const T &	yCenter,
		const T &	majorAxis,
		const T &	axialRatio,
		const T &	pa
	)

inline

Definition at line 195 of file Gaussian2D.h.

template<class T>

casacore::Gaussian2D< T >::Gaussian2D ( const Gaussian2D< T > & other )

inline

Copy constructor (deep copy)

Definition at line 203 of file Gaussian2D.h.

template<class T>

template<class W >

casacore::Gaussian2D< T >::Gaussian2D ( const Gaussian2D< W > & other )

inline

Definition at line 205 of file Gaussian2D.h.

template<class T>

virtual casacore::Gaussian2D< T >::~Gaussian2D ( )

inlinevirtual

Destructor.

Definition at line 213 of file Gaussian2D.h.

Member Function Documentation

template<class T>

virtual Function<T>* casacore::Gaussian2D< T >::clone ( ) const

inlinevirtual

Return a copy of this object from the heap.

The caller is responsible for deleting this pointer.

Implements casacore::Function< T >.

Definition at line 225 of file Gaussian2D.h.

template<class T>

virtual Function<typename FunctionTraits<T>::DiffType>* casacore::Gaussian2D< T >::cloneAD ( ) const

inlinevirtual

Reimplemented from casacore::Function< T >.

Definition at line 226 of file Gaussian2D.h.

template<class T>

virtual Function<typename FunctionTraits<T>::BaseType>* casacore::Gaussian2D< T >::cloneNonAD ( ) const

inlinevirtual

Reimplemented from casacore::Function< T >.

Definition at line 228 of file Gaussian2D.h.

template<class T>

virtual T casacore::Gaussian2D< T >::eval ( typename Function< T >::FunctionArg x ) const

virtual

Evaluate the Gaussian at x.

template<class T>

Gaussian2D<T>& casacore::Gaussian2D< T >::operator= ( const Gaussian2D< T > & other )

inline

Copy assignment (deep copy)

Definition at line 209 of file Gaussian2D.h.

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

casa/casacore/scimath/Functionals/Gaussian2D.h

Public Member Functions

Additional Inherited Members

Detailed Description

template<class T> class casacore::Gaussian2D< T >

Intended use:

Review Status

Prerequisite

Etymology

Synopsis

Example

Template Type Argument Requirements (T)

Thrown Exceptions

To Do

Constructor & Destructor Documentation

Member Function Documentation

template<class T>
class casacore::Gaussian2D< T >