casa::Gaussian2DParam< T > Class Template Reference

Parameter handling for 2 dimensional Gaussian class. More...

#include <Gaussian2DParam.h>

Inheritance diagram for casa::Gaussian2DParam< T >:

List of all members.

Public Types
enum	{   HEIGHT,   XCENTER,   YCENTER,   YWIDTH,   RATIO,   PANGLE }
Public Member Functions
	Gaussian2DParam ()
	Constructs the two dimensional Gaussians.
	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)
template<class W >
	Gaussian2DParam (const Gaussian2DParam< W > &other)
Gaussian2DParam< T > &	operator= (const Gaussian2DParam< T > &other)
	Copy assignment (deep copy)
virtual	~Gaussian2DParam ()
	Destructor.
virtual uInt	ndim () const
	Variable dimensionality.
virtual const String &	name () const
	Give name of function.
T	height () const
	Get or set the peak height of the Gaussian.
void	setHeight (const T &height)
T	flux () const
	Get or set the analytical integrated area underneath the Gaussian.
void	setFlux (const T &flux)
Vector< T >	center () const
	Get or set the center ordinate of the Gaussian.
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.
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.
void	setPA (const T &pa)
Protected Attributes
T	fwhm2int
T	thePA
	cached vale of the PA
T	theSpa
	cached values of the cos and sine of thePA
T	theCpa
T	theXwidth
	cached vale of the Xwidth = ratio*theYwidth;

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Detailed Description

template<class T>
class casa::Gaussian2DParam< T >

Parameter handling for 2 dimensional Gaussian class.

Intended use:

Internal

Review Status

Reviewed By:

mwieringa

Date Reviewed:

1996/10/d24

Test programs:

tGaussian2D

Prerequisite

• FunctionParam class
• Function class

Etymology

A 2-dimensional Gaussian's parameters.

Synopsis

A Gaussian2D is described by a height, center, and width, and position angle.

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 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 counter-clockwise, 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 FunctionParam class), is used to provide an interface to the Fitting classes.

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

1. The height of the Gaussian. This is identical to the value returned using the height member function.
2. The center of the Gaussian in the x direction. This is identical to the value returned using the xCenter member function.
3. The center of the Gaussian in the y direction. This is identical to the value returned using the yCenter member function.
4. 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.
5. 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 4. 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.
6. The rotation 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 HEIGHT, XCENTER, YCENTER, YWIDTH, RATIO, PANGLE 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.

This class is in general used implicitly by the Gaussian2D class only.

Tip: Other points to bear in mind when fitting this class to measured data are:

• If you need to fit a circular Gaussian to data you MUST set the axial ratio to one, and mask the position angle and axial ratio parameters; This avoids rank deficiency in the fitting routines as the position angle is meaningless when the major and minor axis are equal;
• If fitting an elliptical Gaussian your initial model should not be a circular Gaussian;

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;

Motivation

Gaussian2D objects allow us to represent models of the sky in a more conventional way than the generic interface used in the GaussianND class does.

Template Type Argument Requirements (T)

• T should have standard numerical operators and exp() function. Current implementation only tested for real types (and AutoDiff of them).

Thrown Exceptions

• Assertion in debug mode if attempt is made to set a negative width
• AipsError if incorrect parameter number specified.

To Do

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

Definition at line 195 of file Gaussian2DParam.h.

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Member Enumeration Documentation

template<class T>

anonymous enum

Enumerator:

HEIGHT
XCENTER
YCENTER
YWIDTH
RATIO
PANGLE

Definition at line 199 of file Gaussian2DParam.h.

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Constructor & Destructor Documentation

template<class T>

casa::Gaussian2DParam< T >::Gaussian2DParam

(

)

Constructs the two dimensional Gaussians.

Defaults: height=1, center=0, width(FWHM)=1, pa=0.

template<class T>

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

template<class T>

casa::Gaussian2DParam< T >::Gaussian2DParam	(	const T &	height,
		const T &	xCenter,
		const T &	yCenter,
		const T &	majorAxis,
		const T &	axialRatio,
		const T &	pa
	)

template<class T>

casa::Gaussian2DParam< T >::Gaussian2DParam

(

const Gaussian2DParam< T > &

other

)

Copy constructor (deep copy)

template<class T>

template<class W >

casa::Gaussian2DParam< T >::Gaussian2DParam

(

const Gaussian2DParam< W > &

other

)

[inline]

Definition at line 217 of file Gaussian2DParam.h.

template<class T>

virtual casa::Gaussian2DParam< T >::~Gaussian2DParam

(

)

[virtual]

Destructor.

---

Member Function Documentation

template<class T>

T casa::Gaussian2DParam< T >::axialRatio

(

)

const

template<class T>

Vector<T> casa::Gaussian2DParam< T >::center

(

)

const

Get or set the center ordinate of the Gaussian.

template<class T>

T casa::Gaussian2DParam< T >::flux

(

)

const

Get or set the analytical integrated area underneath the Gaussian.

Use these functions as an alternative to the height functions.

template<class T>

T casa::Gaussian2DParam< T >::height

(

)

const [inline]

Get or set the peak height of the Gaussian.

Definition at line 240 of file Gaussian2DParam.h.

Referenced by casa::Gaussian2DParam< AutoDiff< T > >::setHeight().

template<class T>

T casa::Gaussian2DParam< T >::majorAxis

(

)

const

Referenced by casa::Gaussian2DParam< AutoDiff< T > >::Gaussian2DParam().

template<class T>

T casa::Gaussian2DParam< T >::minorAxis

(

)

const

template<class T>

virtual const String& casa::Gaussian2DParam< T >::name

(

)

const [inline, virtual]

Give name of function.

Reimplemented from casa::Function< T >.

Definition at line 235 of file Gaussian2DParam.h.

template<class T>

virtual uInt casa::Gaussian2DParam< T >::ndim

(

)

const [inline, virtual]

Variable dimensionality.

Implements casa::Function< T >.

Definition at line 231 of file Gaussian2DParam.h.

template<class T>

Gaussian2DParam<T>& casa::Gaussian2DParam< T >::operator=

(

const Gaussian2DParam< T > &

other

)

Copy assignment (deep copy)

template<class T>

T casa::Gaussian2DParam< T >::PA

(

)

const

Set/get the rotation angle (orientation) of the Gaussian.

PA is given in radians counterclockwise.

Referenced by casa::Gaussian2DParam< AutoDiff< T > >::Gaussian2DParam().

template<class T>

void casa::Gaussian2DParam< T >::setAxialRatio

(

const T &

axialRatio

)

template<class T>

void casa::Gaussian2DParam< T >::setCenter

(

const Vector< T > &

center

)

template<class T>

void casa::Gaussian2DParam< T >::setFlux

(

const T &

flux

)

template<class T>

void casa::Gaussian2DParam< T >::setHeight

(

const T &

height

)

[inline]

Definition at line 241 of file Gaussian2DParam.h.

template<class T>

void casa::Gaussian2DParam< T >::setMajorAxis

(

const T &

width

)

template<class T>

void casa::Gaussian2DParam< T >::setMinorAxis

(

const T &

width

)

template<class T>

void casa::Gaussian2DParam< T >::setPA

(

const T &

pa

)

Referenced by casa::Gaussian2DParam< AutoDiff< T > >::Gaussian2DParam().

template<class T>

void casa::Gaussian2DParam< T >::setWidth

(

const Vector< T > &

width

)

template<class T>

void casa::Gaussian2DParam< T >::setXcenter

(

const T &

cnter

)

[inline]

Definition at line 256 of file Gaussian2DParam.h.

template<class T>

void casa::Gaussian2DParam< T >::setYcenter

(

const T &

cnter

)

[inline]

Definition at line 258 of file Gaussian2DParam.h.

template<class T>

Vector<T> casa::Gaussian2DParam< T >::width

(

)

const

Set or get the FWHM of the Gaussian.

template<class T>

T casa::Gaussian2DParam< T >::xCenter

(

)

const [inline]

Definition at line 255 of file Gaussian2DParam.h.

template<class T>

T casa::Gaussian2DParam< T >::yCenter

(

)

const [inline]

Definition at line 257 of file Gaussian2DParam.h.

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Member Data Documentation

template<class T>

T casa::Gaussian2DParam< T >::fwhm2int [protected]

Constant to scale halfwidth at 1/e to FWHM static const T fwhm2int;

Definition at line 283 of file Gaussian2DParam.h.

template<class T>

T casa::Gaussian2DParam< T >::theCpa [mutable, protected]

Definition at line 289 of file Gaussian2DParam.h.

template<class T>

T casa::Gaussian2DParam< T >::thePA [mutable, protected]

cached vale of the PA

Definition at line 285 of file Gaussian2DParam.h.

template<class T>

T casa::Gaussian2DParam< T >::theSpa [mutable, protected]

cached values of the cos and sine of thePA

Definition at line 288 of file Gaussian2DParam.h.

template<class T>

T casa::Gaussian2DParam< T >::theXwidth [mutable, protected]

cached vale of the Xwidth = ratio*theYwidth;

Definition at line 292 of file Gaussian2DParam.h.

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

• casacore/scimath/Functionals/Gaussian2DParam.h