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casacore::Gaussian2D< T > Class Template Reference
scimath package (libcasa_scimath) » Functionals_module

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`#include <Gaussian2D.h>`

## Public Member Functions

| Gaussian2D ()
| Constructs the two dimensional Gaussians.
| 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).
template<class W>
| Gaussian2D (const Gaussian2D< W > &other)
Gaussian2D< T > & | operator= (const Gaussian2D< T > &other)
| Copy assignment (deep copy).
virtual | ~Gaussian2D ()
| Destructor.
virtual T | eval (typename Function< T >::FunctionArg x) const
| Evaluate the Gaussian 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
Public Member Functions inherited from casacore::Gaussian2DParam< T >
| 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)
Public Member Functions inherited from casacore::Function< T, U >
| Function ()
| Constructors.
| Function (const uInt n)
| Function (const Vector< T > &in)
| Function (const FunctionParam< T > &other)
template<class W, class X>
| Function (const Function< W, X > &other)
virtual | ~Function ()
| Destructor.
uInt | nparameters () const
| Returns the number of parameters.
virtual U | eval (FunctionArg x) const =0
| Evaluate the function object.
T & | operator[] (const uInt n)
| Manipulate the nth parameter (0-based) with no index check.
const T & | operator[] (const uInt n) const
virtual U | operator() () const
| Evaluate this function object at xor at x, y.
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.
const Bool & | mask (const uInt n) const
const FunctionParam< T > & | parameters () const
| Return the parameter interface.
FunctionParam< T > & | parameters ()
const Vector< ArgType > & | argp () const
| Get arg_p and parset_p.
Bool | parsetp () const
void | lockParam ()
| Compiler cannot always find the correct 'const' version of parameter access.
void | unlockParam ()
virtual void | setMode (const RecordInterface &mode)
| get/set the function mode.
virtual void | getMode (RecordInterface &mode) const
virtual Bool | hasMode () const
| return True if the implementing function supports a mode.
ostream & | print (ostream &os) const
| Print the function (i.e.
Public Member Functions inherited from casacore::Functional< FunctionTraits< T >::ArgType, T >
virtual | ~Functional ()
| Destructor.
virtual T | operator() (const FunctionTraits< T >::ArgType &x) const=0
| Map a Domain x into a Range y value.
Public Member Functions inherited from casacore::Functional< Vector< FunctionTraits< T >::ArgType >, T >
virtual | ~Functional ()
| Destructor.
virtual T | operator() (const Vector< FunctionTraits< T >::ArgType > &x) const=0
| Map a Domain x into a Range y value.

## Additional Inherited Members

Public Types inherited from casacore::Gaussian2DParam< T >
enum | { HEIGHT , XCENTER , YCENTER , YWIDTH , RATIO , PANGLE }
Public Types inherited from casacore::Function< T, U >
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.
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;
Protected Attributes inherited from casacore::Function< T, U >
FunctionParam< T > | param_p
| The parameters and masks.
Vector< ArgType > | arg_p
| Aid for non-contiguous argument storage.
Bool | parset_p
| Indicate parameter written.
Bool | locked_p
| Indicate that parameters are expected to be locked from changing.

## 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

- Gaussian2DParam
- Function

### 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:

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 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.
6. 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;
casacore::Gaussian2D::Gaussian2D
Gaussian2D()
Constructs the two dimensional Gaussians.
Definition Gaussian2D.h:187
casacore::Vector
Definition Vector.h:82

### 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 175 of file Gaussian2D.h.

## Constructor & Destructor Documentation

## Gaussian2D() [1/5]

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 187 of file Gaussian2D.h.

References casacore::Gaussian2DParam< T >::Gaussian2DParam().

Referenced by clone(), cloneAD(), cloneNonAD(), Gaussian2D(), Gaussian2D(), and operator=().

## Gaussian2D() [2/5]

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 188 of file Gaussian2D.h.

References casacore::Gaussian2DParam< T >::center(), casacore::Gaussian2DParam< T >::Gaussian2DParam(), casacore::Gaussian2DParam< T >::height(), casacore::pa(), and casacore::Gaussian2DParam< T >::width().

## Gaussian2D() [3/5]

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 191 of file Gaussian2D.h.

References casacore::Gaussian2DParam< T >::axialRatio(), casacore::Gaussian2DParam< T >::Gaussian2DParam(), casacore::Gaussian2DParam< T >::height(), casacore::Gaussian2DParam< T >::majorAxis(), casacore::pa(), casacore::Gaussian2DParam< T >::xCenter(), and casacore::Gaussian2DParam< T >::yCenter().

## Gaussian2D() [4/5]

template<class T>

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

inline

Copy constructor (deep copy).

Definition at line 199 of file Gaussian2D.h.

References Gaussian2D(), and casacore::Gaussian2DParam< T >::Gaussian2DParam().

## Gaussian2D() [5/5]

template<class T>
template<class W>

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

inline

Definition at line 201 of file Gaussian2D.h.

References Gaussian2D(), and casacore::Gaussian2DParam< T >::Gaussian2DParam().

## ~Gaussian2D()

template<class T>

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

inline virtual

Destructor.

Definition at line 209 of file Gaussian2D.h.

## Member Function Documentation

## clone()

template<class T>

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

inline virtual

Return a copy of this object from the heap.

The caller is responsible for deleting this pointer.

Implements casacore::Function< T, U >.

Definition at line 221 of file Gaussian2D.h.

References Gaussian2D().

## cloneAD()

template<class T>

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

inline virtual

Reimplemented from casacore::Function< T, U >.

Definition at line 222 of file Gaussian2D.h.

References Gaussian2D().

## cloneNonAD()

template<class T>

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

inline virtual

Reimplemented from casacore::Function< T, U >.

Definition at line 224 of file Gaussian2D.h.

References Gaussian2D().

## eval()

template<class T>

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

virtual

Evaluate the Gaussian at x.

## operator=()

template<class T>

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

inline

Copy assignment (deep copy).

Definition at line 205 of file Gaussian2D.h.

References Gaussian2D(), and casacore::Gaussian2DParam< T >::operator=().

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

- scimath/Functionals/Gaussian2D.h