A three dimensional Gaussian class. More...

#include <Gaussian3D.h>

Inheritance diagram for casacore::Gaussian3D< T >:

Public Member Functions
	Gaussian3D ()
	A functional for a rotated, 3D Gaussian. More...

	Gaussian3D (T height, const Vector< T > &center, const Vector< T > &width, T theta, T phi)

	Gaussian3D (T &height, T &xCenter, T &yCenter, T &zCenter, T &xWidth, T &yWidth, T &zWidth, T &theta, T &phi)

	Gaussian3D (const Gaussian3D< T > &other)
	Copy constructor. More...

template<class W >
	Gaussian3D (const Gaussian3D< W > &other)

virtual	~Gaussian3D ()
	Destructor. More...

Gaussian3D< T > &	operator= (const Gaussian3D< T > &other)
	Assignment operator. 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::Gaussian3DParam< T >
	Gaussian3DParam ()
	Constructs the three dimensional Gaussians. More...

	Gaussian3DParam (Theight, const Vector< T > &center, const Vector< T > &width, Ttheta, Tphi)

	Gaussian3DParam (T &height, T &xCenter, T &yCenter, T &zCenter, T &xWidth, T &yWidth, T &zWidth, T &theta, T &phi)

	Gaussian3DParam (const Gaussian3DParam< T > &other)
	Copy construcor. More...

	Gaussian3DParam (const Gaussian3DParam< W > &other)

Gaussian3DParam< T > &	operator= (const Gaussian3DParam< T > &other)
	Copy assignment. More...

virtual	~Gaussian3DParam ()
	Destructor. More...

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

virtual uInt	ndim () const
	Return dimensionality. 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 total flux of the Gaussian. More...

void	setFlux (const T &flux)

Vector< T >	center () const
	Get or cet the center coordinates of the Gaussian. More...

void	setCenter (const Vector< T > &center)

T	xCenter () const

void	setXcenter (const T &xcenter)

T	yCenter () const

void	setYcenter (const T &ycenter)

T	zCenter () const

void	setZcenter (const T &zcenter)

Vector< T >	width () const
	Get or set the sigma-width of the Gaussian. More...

void	setWidth (const Vector< T > &width)

void	setXwidth (const T &xwidth)

T	xWidth () const

void	setYwidth (const T &ywidth)

T	yWidth () const

void	setZwidth (const T &zwidth)

T	zWidth () const

T	theta () const
	Get or set the rotation angles of the Gaussian. More...

void	settheta (const T &sT)

T	phi () const

void	setphi (const T &sP)

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...

Private Member Functions
T	sq (T v) const
	AutoDiff does not have a square() function, so one is provided here. More...

Additional Inherited Members
Public Types inherited from casacore::Gaussian3DParam< T >
enum
	Parameter handling for the functional for 3D Gaussian Class. More...

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

typedef const ArgType *	FunctionArg

Protected Member Functions inherited from casacore::Gaussian3DParam< T >
void	settrigvals () const

Protected Attributes inherited from casacore::Gaussian3DParam< T >
T	fwhm2int

T	stoT_p

T	stoP_p

T	cosT_p

T	sinT_p

T	cosP_p

T	sinP_p

T	cosTcosP_p

T	cosTsinP_p

T	sinTcosP_p

T	sinTsinP_p

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::Gaussian3D< T >

A three dimensional Gaussian class.

Intended use:

Public interface

Review Status

Test programs:: tGaussian3D

Prerequisite

Etymology

A Gaussian3D functional is designed exclusively for calculating a Gaussian (or Normal) distribution in three dimensions. Other classes exist for calculating these functions in one (Gaussian1D), two (Gaussian2D), and N (GaussianND) dimensions.

Synopsis

A Gaussian3D is described by a height, center, and width, and position angles. Its fundamental operation is evaluating itself at some (x,y,z) coordinate. Its parameters (height, center and width, position angles) may be changed at run time.

The width of the Gaussian is now specified in terms of the full width at half maximum (FWHM), like the 2D and 1D Gaussian functional classes.

The three axis values refer to the x, y, and z axes, and unlike with the 2D Gaussian any of the three axes may be the longest; instead, the position angles are restricted. The first position angle, theta, is the longitudinal angle, referring to the rotation (counterclockwise) around the z-axis. The second, phi, is the latidudinal angle, referring to the rotation around the theta-rotated y axis. The domain of both angles is -pi/4 < A < pi/4, although the angles are not constrained when fitting and can be set outside the domain by setting the parameters directly using Functional operator[]. (Note that the use of theta and phi corresponds to the mathematics convention for these angles, not the physics convention.)

The parameter interface (see Gaussian3DParam class), is used to provide an interface to the Fitting classes.

There are 9 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 center of the Gaussian in the z direction. This is identical to the value returned using the zCenter member function.
The width of the Gaussian along the x-axis.
The width of the Gaussian along the y-axis.
The width of the Gaussian along the z-axis.
The longitudinal position angle, theta (in radians)
The latitudinal position angle, phi (also 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

Gaussian3D<Double> g(9.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0);
Vector<Double> x(3);
x(0) = 1.0; x(1) = 0.5; x(2) = 0.0
cout << "g(" << x(0) << "," << x(1) << "," << x(2) << ")=" << g(x) << endl;

Motivation

The GaussianND class does not contain explicit derivatives and was insufficient for fitting 3D Gaussians to data.

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

Optimize derivative calculations for faster fitting?

Definition at line 145 of file Gaussian3D.h.

Constructor & Destructor Documentation

template<class T>

casacore::Gaussian3D< T >::Gaussian3D ( )

A functional for a rotated, 3D Gaussian.

Similar to Gaussian2D, but the xWidth, yWidth, and zWidth parameters are not adjusted for FWHM; they are identical to the parameters used in the function.

Constructs the three-dimensional Gaussians. Defaults: height = 1, center = {0,0,0}, width = {1,1,1}, theta = phi = 0. The center and width vectors must have three elements.

template<class T>

casacore::Gaussian3D< T >::Gaussian3D	(	T	height,
		const Vector< T > &	center,
		const Vector< T > &	width,
		T	theta,
		T	phi
	)

template<class T>

casacore::Gaussian3D< T >::Gaussian3D	(	T &	height,
		T &	xCenter,
		T &	yCenter,
		T &	zCenter,
		T &	xWidth,
		T &	yWidth,
		T &	zWidth,
		T &	theta,
		T &	phi
	)

template<class T>

casacore::Gaussian3D< T >::Gaussian3D ( const Gaussian3D< T > & other )

Copy constructor.

template<class T>

template<class W >

casacore::Gaussian3D< T >::Gaussian3D ( const Gaussian3D< W > & other )

inline

Definition at line 167 of file Gaussian3D.h.

template<class T>

virtual casacore::Gaussian3D< T >::~Gaussian3D ( )

virtual

Destructor.

Member Function Documentation

template<class T>

virtual Function<T>* casacore::Gaussian3D< T >::clone ( ) const

virtual

Return a copy of this object from the heap.

The caller is responsible for deleting this pointer.

Implements casacore::Function< T >.

template<class T>

virtual Function<typename FunctionTraits<T>::DiffType>* casacore::Gaussian3D< T >::cloneAD ( ) const

inlinevirtual

Reimplemented from casacore::Function< T >.

Definition at line 183 of file Gaussian3D.h.

template<class T>

virtual Function<typename FunctionTraits<T>::BaseType>* casacore::Gaussian3D< T >::cloneNonAD ( ) const

inlinevirtual

Reimplemented from casacore::Function< T >.

Definition at line 185 of file Gaussian3D.h.

template<class T>

virtual T casacore::Gaussian3D< T >::eval ( typename Function< T >::FunctionArg x ) const

virtual

Evaluate the Gaussian at x.

template<class T>

Gaussian3D<T>& casacore::Gaussian3D< T >::operator= ( const Gaussian3D< T > & other )

Assignment operator.

template<class T>

T casacore::Gaussian3D< T >::sq ( T v ) const

private

AutoDiff does not have a square() function, so one is provided here.

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

casa/casacore/scimath/Functionals/Gaussian3D.h

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

template<class T> class casacore::Gaussian3D< T >

Intended use:

Review Status

Prerequisite

Etymology

Synopsis

Example

Motivation

Template Type Argument Requirements (T)

Thrown Exceptions

To Do

Constructor & Destructor Documentation

Member Function Documentation

template<class T>
class casacore::Gaussian3D< T >