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casacore::Gaussian2DParam< T > Class Template Reference

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

#include <Gaussian2DParam.h>

Inheritance diagram for casacore::Gaussian2DParam< T >:
casacore::Function< T > casacore::Functional< FunctionTraits< T >::ArgType, U > casacore::Functional< Vector< FunctionTraits< T >::ArgType >, U > casacore::Gaussian2D< T >

Public Types

enum  {
  HEIGHT,
  XCENTER,
  YCENTER,
  YWIDTH,
  RATIO,
  PANGLE
}
 
- Public Types inherited from casacore::Function< T >
typedef FunctionTraits< T >
::ArgType 
ArgType
 
typedef const ArgTypeFunctionArg
 

Public Member Functions

 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 Stringname () const
 Give name of function. More...
 
height () const
 Get or set the peak height of the Gaussian. More...
 
void setHeight (const T &height)
 
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)
 
xCenter () const
 
void setXcenter (const T &cnter)
 
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)
 
majorAxis () const
 
void setMajorAxis (const T &width)
 
minorAxis () const
 
void setMinorAxis (const T &width)
 
axialRatio () const
 
void setAxialRatio (const T &axialRatio)
 
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 xor 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
 
Boolmask (const uInt n)
 Manipulate the mask associated with the nth parameter (e.g. More...
 
const Boolmask (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...
 
virtual Function< T, U > * clone () const =0
 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::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...
 

Protected Attributes

fwhm2int
 Constant to scale halfwidth at 1/e to FWHM. More...
 
thePA
 cached vale of the PA More...
 
theSpa
 cached values of the cos and sine of thePA More...
 
theCpa
 
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< ArgTypearg_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::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

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)

Thrown Exceptions

To Do

Definition at line 195 of file Gaussian2DParam.h.

Member Enumeration Documentation

template<class T>
anonymous enum
Enumerator
HEIGHT 
XCENTER 
YCENTER 
YWIDTH 
RATIO 
PANGLE 

Definition at line 199 of file Gaussian2DParam.h.

Constructor & Destructor Documentation

template<class T>
casacore::Gaussian2DParam< T >::Gaussian2DParam ( )

Constructs the two dimensional Gaussians.

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

template<class T>
casacore::Gaussian2DParam< T >::Gaussian2DParam ( const T &  height,
const Vector< T > &  center,
const Vector< T > &  width,
const T &  pa 
)
template<class T>
casacore::Gaussian2DParam< T >::Gaussian2DParam ( const T &  height,
const T &  xCenter,
const T &  yCenter,
const T &  majorAxis,
const T &  axialRatio,
const T &  pa 
)
template<class T>
casacore::Gaussian2DParam< T >::Gaussian2DParam ( const Gaussian2DParam< T > &  other)

Copy constructor (deep copy)

template<class T>
template<class W >
casacore::Gaussian2DParam< T >::Gaussian2DParam ( const Gaussian2DParam< W > &  other)
inline

Definition at line 217 of file Gaussian2DParam.h.

template<class T>
virtual casacore::Gaussian2DParam< T >::~Gaussian2DParam ( )
virtual

Destructor.

Member Function Documentation

template<class T>
T casacore::Gaussian2DParam< T >::axialRatio ( ) const
template<class T>
Vector<T> casacore::Gaussian2DParam< T >::center ( ) const

Get or set the center ordinate of the Gaussian.

template<class T>
T casacore::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 casacore::Gaussian2DParam< T >::height ( ) const
inline

Get or set the peak height of the Gaussian.

Definition at line 240 of file Gaussian2DParam.h.

Referenced by casacore::Gaussian2DParam< casacore::Double >::setHeight().

template<class T>
T casacore::Gaussian2DParam< T >::majorAxis ( ) const
template<class T>
T casacore::Gaussian2DParam< T >::minorAxis ( ) const
template<class T>
virtual const String& casacore::Gaussian2DParam< T >::name ( ) const
inlinevirtual

Give name of function.

Reimplemented from casacore::Function< T >.

Definition at line 235 of file Gaussian2DParam.h.

template<class T>
virtual uInt casacore::Gaussian2DParam< T >::ndim ( ) const
inlinevirtual

Variable dimensionality.

Implements casacore::Function< T >.

Definition at line 231 of file Gaussian2DParam.h.

template<class T>
Gaussian2DParam<T>& casacore::Gaussian2DParam< T >::operator= ( const Gaussian2DParam< T > &  other)

Copy assignment (deep copy)

Referenced by casacore::Gaussian2D< casacore::Double >::operator=().

template<class T>
T casacore::Gaussian2DParam< T >::PA ( ) const

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

PA is given in radians counterclockwise.

Referenced by casacore::Gaussian2DParam< casacore::Double >::Gaussian2DParam().

template<class T>
void casacore::Gaussian2DParam< T >::setAxialRatio ( const T &  axialRatio)
template<class T>
void casacore::Gaussian2DParam< T >::setCenter ( const Vector< T > &  center)
template<class T>
void casacore::Gaussian2DParam< T >::setFlux ( const T &  flux)
template<class T>
void casacore::Gaussian2DParam< T >::setHeight ( const T &  height)
inline

Definition at line 241 of file Gaussian2DParam.h.

template<class T>
void casacore::Gaussian2DParam< T >::setMajorAxis ( const T &  width)
template<class T>
void casacore::Gaussian2DParam< T >::setMinorAxis ( const T &  width)
template<class T>
void casacore::Gaussian2DParam< T >::setPA ( const T &  pa)
template<class T>
void casacore::Gaussian2DParam< T >::setWidth ( const Vector< T > &  width)
template<class T>
void casacore::Gaussian2DParam< T >::setXcenter ( const T &  cnter)
inline

Definition at line 256 of file Gaussian2DParam.h.

template<class T>
void casacore::Gaussian2DParam< T >::setYcenter ( const T &  cnter)
inline

Definition at line 258 of file Gaussian2DParam.h.

template<class T>
Vector<T> casacore::Gaussian2DParam< T >::width ( ) const

Set or get the FWHM of the Gaussian.

template<class T>
T casacore::Gaussian2DParam< T >::xCenter ( ) const
inline

Definition at line 255 of file Gaussian2DParam.h.

template<class T>
T casacore::Gaussian2DParam< T >::yCenter ( ) const
inline

Definition at line 257 of file Gaussian2DParam.h.

Member Data Documentation

template<class T>
T casacore::Gaussian2DParam< T >::fwhm2int
protected

Constant to scale halfwidth at 1/e to FWHM.

Definition at line 282 of file Gaussian2DParam.h.

template<class T>
T casacore::Gaussian2DParam< T >::theCpa
mutableprotected

Definition at line 288 of file Gaussian2DParam.h.

template<class T>
T casacore::Gaussian2DParam< T >::thePA
mutableprotected

cached vale of the PA

Definition at line 284 of file Gaussian2DParam.h.

template<class T>
T casacore::Gaussian2DParam< T >::theSpa
mutableprotected

cached values of the cos and sine of thePA

Definition at line 287 of file Gaussian2DParam.h.

template<class T>
T casacore::Gaussian2DParam< T >::theXwidth
mutableprotected

cached vale of the Xwidth = ratio*theYwidth;

Definition at line 291 of file Gaussian2DParam.h.


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